PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 2/05 p:/C|RC!DaIeDue.indd-p.1 ELECTRONIC CHARACTERIZATION AND FABRICATION OF CVD DIAMOND PIEZORESISTIVE PRESSURE SENSORS By Sondes Sahli I \ A DISSERTATION Subnfinedto Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Electrical Engineering 1997 I32 4M "(HS ABSTRACT ELECRONIC CHARACTERIZATION AND FABRICATION OF CVD DIAMOND PIEZORESISTIVE PRESSURE SENSORS By Sondes Sahli Diamond piezoresistive sensors outperform their Si or SiC counterparts in sensitivity, especially in harsh environments and at high temperatures. In this work, the resistivity and gauge factor (GF) of in-situ B-doped polycrystalline chemical vapor deposited (CVD) diamond grown on insulating substrates, were studied. A hot filament CV D reactor was built, optimized for 4” wafers and used for film deposition. The effect of substrate, post deposition annealing and electric field on the resistiv- ity of CVD diamond were studied using three types of films: small grain (1 - 2 pm), large grain (up to 170 um) and homoepitaxial. In-situ B-doped and undoped films deposited on oxidized, n-type and p-type silicon were used. Resistivity, temperature and electric field ranges of 0.27 - 535 0cm, 300 - 633 K and 10 - 650 V/cm, respectively, were explored. The role of grain boundaries (03s) in current flow was studied by performing four-point probe I-V across many grains, potential profile across five grains and two- point-probe I-V within a single grain and across an individual GB. The potential profiles revealed non-uniform current flow and the I-V data across individual GBs suggested the existence of potential barriers at CBS The pressure response of small grain films was measured in the pressure, resistiv- ity and field ranges of 10 - 740 Torr, 0.29 - 116 Gem and 10 - 255 V/cm, respectively. The results showed that higher doping minimized GF fluctuations with electric field. Cantile- ver beam measurements in the temperature range of 22 - 80 °C revealed that GF is con- stant with temperature at low resistivity, but increases at intermediate resistivity and decreases at high resistivity. Intra- and inter-grain GF measurements achieved an intra- grain GF of 4062 and provided direct evidence that the presence of GBs lowers GF. Copyright by SONDES SAHLI 1997 To my parents, my sister and my brothers and to all those whose path crossed mine ACKNOWLEDGMENTS I would like to thank Allah (soobhanahowa taalah) for providing me with the ability to complete this work. I owe my greatest thanks to my parents who worked hard and sacrificed much so I can reach my goals. A very special thank you goes to my sister, my brothers and my friends for their encouragements. I would like to thank my advisor, Dr. Dean Aslarn, for his guidance and the members of my oral committee, Dr. Jes Asmussen, Dr. David Grummon and Dr. Karen Klomparens for their comments. Many thanks also go to all faculty, staff and students at Michigan State University who made my school years enjoyable with their help and smile. vi TABLE OF CONTENTS LIST OF TABLES ix LIST OF FIGURES x 1 Research Motivation and Goals 1 1.1 Introduction ......................................................................................................... 1 1.2 Objective of this Work ......................................................................................... 2 1.3 Dissertation Organization .................................................................................... 5 2 Background 6 2.1 Introduction ......................................................................................................... 6 2.2 Diamond Sensors ................................................................................................. 6 2.2.1 Diamond Piezoresistive Sensors .............................................................. 8 2.2.2 Other Diamond Sensors ......................................................................... 11 2.3 Theory of Piezoresistance Property ................................................................... 12 2.3.1 Definition of Gauge Factor .................................................................... 12 2.3.2 Piezoresistance in Single Crystal Semiconductors ................................ 15 2.3.3 Piezoresistance Models in Polycrystalline Semiconductors .................. 24 2.4 Current Understanding of Diamond Piezoresistance ......................................... 29 2.4.1 Single Crystal Diamond ........................................................................ 29 2.4.2 Polycrystalline Diamond ....................................................................... 30 2.5 Diamond Film Technology ................................................................................ 33 2.5.1 Chemical Vapor Deposition of Diamond ............................................... 33 2.5.2 Doping ................................................................................................... 38 2.5.3 Patterning .............................................................................................. 39 2.5.4 Metallization ......................................................................................... 41 2.6 Summary ........................................................................................................... 43 vii 3 Diamond Film Technology 44 3.1 Introduction ....................................................................................................... 44 3.2 Hot Filament Chemical Vapor Deposition Reactor ........................................... 44 3.2.1 System Testing and Optimization .......................................................... 46 3.2.2 System Operation .................................................................................. 57 3.3 Sample fabrication ............................................................................................. 59 3.3.1 Small Grain Film ................................................................................... 59 3.3.2 Large Grain Fihn ................................................................................... 62 3.3.3 Homoepitaxial Film ............................................................................... 69 3.4 Summary ........................................................................................................... 71 4 Resistivity Characterization 72 4.1 Introduction ....................................................................................................... 72 4.2 Effect of Substrate Conduction .......................................................................... 73 4.3 Effect of Anneal on Resistivity .......................................................................... 73 4.3.1 Experimental Details ............................................................................. 74 4.3.2 Results ................................................................................................... 74 4.3.3 Discussion ............................................................................................. 76 4.4 Effect of Electric Field on Resistivity ................................................................ 78 4.4.1 Experimental Details ............................................................................. 79 4.4.2 Electric Field Effect as a function of Doping ........................................ 79 4.4.3 Electric Field Effect as a function of Temperature ................................ 81 4.4.4 Electric Field Effect as a function of Morphology ................................ 81 4.4.5 Discussion ............................................................................................. 84 4.5 Current Flow Study ........................................................................................... 85 4.5.1 Experimental ......................................................................................... 87 4.5.2 Four Point Probe Measurements ........................................................... 87 4.5.3 Potential Profile Measurements ............................................................. 89 4.5.4 Intra- and Inter-grain I-V ....................................................................... 89 4.5.5 N on-uniform Current Flow .................................................................... 93 4.6 Summary ........................................................................................................... 95 viii 5 Sensor characterization 96 5. 1 Introduction ....................................................................................................... 96 5.2 Gauge Factor Measurement Setup ..................................................................... 97 5.2.1 Pressure Sensor Setup ........................................................................... 97 5.2.2 Cantilever Beam Setup ........................................................................ 101 5.3 Effect of Electric Field on Piezoresistance ...................................................... 101 5.4 Effect of Temperature on Piezoresistance ....................................................... 109 5.5 Summary ......................................................................................................... l 1 1 6 Intra-grain Gauge Factor 115 6.1 Introduction ..................................................................................................... 1 15 6.2 Measurement Setup ......................................................................................... 115 6.3 Gauge Factor for Different Path Morphologies ............................................... 117 6.4 Summary ......................................................................................................... 123 7 Summary and Future Research 124 7. 1 Introduction ..................................................................................................... 124 7.2 Summary of Contributions .............................................................................. 124 7.2.1 Results Reported for the First Time ..................................................... 124 7.2.2 Other Significant Results ..................................................................... 126 7.3 Future Research ............................................................................................... 126 BIBLIOGRAPHY 128 ix 2.1 2.2 2.3 2.4 3.1 4.1 4.2 LIST OF TABLES Comparison of diamond properties and some commonly used semiconductors 7 Summary of reported GF data for polycrystalline diamond ................................ 9 Reported temperature dependence of GP of polycrystalline diamond for different resistivities .......................................................................................... 10 Longitudinal GP for films dominated by [100], [110], [111] and random grain orientation [51] ......................................................................................... 29 Typical deposition parameters ........................................................................... 59 Sample specifications ........................................................................................ 79 Summary of linear I-V data ............................................................................... 94 1.1 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 LIST OF FIGURES Steps needed to put CVD diamond piezoresistors on the market ..................... 4 Simple geometry to define GF ....................................................................... 13 Energy band structure of Si ............................................................................ 16 Constant energy ellipsoids in k-space near the conduction band minima of Si ................................................................................................................ 17 (a) Conduction band under zero strain and an electric field in the [100] direction, electrons moving parallel to the field, kx, have larger eflective mass than those moving perpendicular to the field, ky, k2. (b) As a result of tension in the [100] direction, the kx band minima are lowered ................ 19 The factor P(N,T) with which the piezoresistive coefficient at RT must be multiplied to obtain GF at temperature T and donor concentration N in Si 21 Simplified and roughly drawn valence band diagram of Si under (a) zero stress and (b) uniaxial tension ........................................................................ 23 (a) Schematic of a grain and surrounding CBS in polysilicon. (b) Corresponding energy band diagram assuming p-type doping and neglecting the physical width of GB. Traps with density Qt having energy in the bandgap capture holes creating a barrier potential qVB and a space charge region, Lw. (c) Scattering in GB is modeled by a potential barrier with height qx and width Lgb’ The different components of carrier transport across the barrier are indicated ........................................................ 25 Longitudinal gauge factor as a function of doping concentration for Boron (_) and Phosphorus (----) doped polysilicon. The calculation are based on a grain size of 60 nm and a texture dominated by [110] orientation. Curves b show the same calculation with GB assumed to be insensitive to strain [51] ................................................................................. 28 a) Resistivity, (b) Hall mobility and (c) hole concentration measurements of simultaneously deposited polycrystalline (PD), homoepitaxial (HMD) and highly oriented (HOD) films. Films deposited in the same run have the xi 2.10 2.11 2.12 2.13 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 same number .................................................................................................. 32 Atomic C-H-O diamond deposition phase diagram indicating the diamond growth domain [66] ....................................................................................... 35 Growth rate for different CVD methods correlate with the temperature of the as mixture needed for growth [66] ............................................................ 37 Irvin curve for single crystal (O) and polycrystalline (A) B-doped diamond. The open symbols refer to effective doping concentration, NA-ND, and the closed symbols to the free hole concentration, p .................. 40 Interface band diagram of Ti on diamond: (a) as deposited Ti, (b) high concentration of electrically active defects created via carbide formation and/or ion bombardment, (c) the defects created in (b) decrease the effective Ti/diarnond barrier height ................................................................ 42 Schematic of the hot filament reactor ............................................................. 45 (a) Filament assembly and (b) substrate holder .............................................. 47 Effect of filament to substrate separation ....................................................... 49 Effect of methane ........................................................................................... 50 Temperature gradient over the 4 inch substrate .............................................. 51 Effect of (a) pressure and (b) gas flow rate at D(F,S) = 2.5 cm ....................... 52 Effect of initial high temperature cure on filament ......................................... 54 Effect of repeated use on filament .................................................................. 55 Effect of multiple runs on the room temperature filament resistance ............. 56 Types of CVD diamond films used in this work ............................................. 60 Nucleation and patterning .............................................................................. 61 Temperature and gas profiles during RTP anneal ........................................... 61 (a) processed 4" wafer, (b) CVD diamond resistor (c) SEM and ((1) Raman ....................................................................................................... 63 Raman Spectra of the B-doped film ............................................................... 64 (a) Light microscope photo of doped CVD film and (b) corresponding grain size distribution .................................................................................... 65 AFM of different types of GBs ....................................................................... 66 AFM of typical well defined GB .................................................................... 67 xii 3.18 3.19 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 Typical intra-grain AFM ................................................................................. 68 Raman Spectrum of B-doped homoepitaxial diamond ................................... 70 Resistivity after anneal vs. resistivity before anneal. Inset: ratio of resistivity after anneal to that before anneal ................................................... 75 Raman spectra and SEM of samples used in the anneal study ....................... 77 Effect of electric field on resistivity for different doping levels ..................... 80 Normalized resistivity vs. field of small grain sample as a function of temperature. (a) p40 and (b) (p40 - p600) / p40 as a function of T .................... 82 Ratio of room temperature resistivity to low-field resistivity for B-doped homoepitaxial, highly oriented, large grain and small grain films ................. 83 Four-probe resistivity measurements as a function of temperature ................ 86 Potential profile measurements and corresponding probe positions .............. 88 I-V data and corresponding probe positions ................................................... 90 Current flow in polycrystalline diamond with non-uniform grain size modeled in terms of paths made of small grains and paths made of large grains .............................................................................................................. 92 (a) Differential pressure measurement setup and (b) plate model ................. 98 Pressure response of wire strain gauge ......................................................... 100 Schematic diagram of a cantilever beam setup ............................................. 100 Room temperature pressure response measured using different electric fields. Insets: (i) SEM, (ii) Raman and (iii) zero strain IV ............................ 102 Room temperature pressure response measured using different electric fields. Insets: (i) SEM, (ii) Rarnan and (iii) zero strain IV ............................ 103 Room temperature pressure response measured using different electric fields. Insets: (i) SEM, (ii) Rarnan and (iii) zero strain IV ............................ 104 Calculated GF as a function of strain for SS4S6. Inset: (I) GF at 20 microstrains and (0) zero strain resistivity ................................................... 106 Calculated GF as a function of strain for SS7082. Inset: (I) GF at 20 microstrains and (0) zero strain resistivity ................................................... 107 Calculated GF as a function of strain for SS7OS4. Inset: (I) GF at 20 microstrains and (0) zero strain resistivity ................................................... 108 xiii 5.10 5.11 5.12 6.1 6.2 6.3 Summary of room temperature GF vs. resistivity data reported in literature ....................................................................................................... 110 Effect of temperature on GF ......................................................................... 112 Summary of data reported in literature on the effect of temperature on GF ................................................................................................................. 113 Small grain I-V at different strains and corresponding probe location. Insets: Cantilever beam setup, relative resistance change vs. strain and extracted GF ................................................................................................. 116 Large grain I-V at different strains and corresponding probe location. Inset: Relative resistance change vs. strain and extracted GF ...................... 118 Intra-grain I-V at different strains and corresponding probe location. Inset: Relative resistance change vs. strain and extracted GF ...................... 120 xiv CHAPTER 1 Research Motivation and Goals 1.1 Introduction As automation and control find their way into more products, the need for sensors to measure and monitor the performance of these products increases. The sensor market revenues are projected to reach $5.9 billions in 1999 split up into 40% pressure, 30% tem- perature, 13% acceleration, 13% vibration and 4% others [1]. Today, most pressure sen- sors are based on silicon device technology: 90% piezoresistive (lower cost and easier signal conditioning) and 10% capacitive [1]. Since pressure sensors cannot be hermeti- cally sealed, the sensor material without passivation will be exposed to its environment during operation. The operation of silicon pressure sensors under chemically harsh, high radiation and high temperature environments is limited by leakage current (~ 150°C), plas- tic deformation (~600°C) [2] and corrosion. Thus, there is a need for new sensor materials suitable for such environments. The high chemical resistance, radiation hardness, thermal conductivity, wide energy gap, high dielectric strength and moderately good carrier mobilities of diamond, make it an excellent material for use in high temperature and chemically harsh environ- ments. However, single crystal natural and synthetic diamonds are too expensive and 2 scarce to be considered for the sensor market. Lately, a less expensive, low pressure dia- mond synthesis technique which uses chemical vapor deposition (CVD) has been devel- oped. Although the properties of homoepitaxial CVD diamond rival those of natural diamond, the need for a diamond substrate makes them too costly. The properties of CVD polycrystalline diamond films (PDF), deposited on non-diamond substrates, are being constantly improved [5]. As the cost of CVD diamond is projected to reach $1.06-1.68/ cm2 [6], PDF pressure sensors will be able to compete with the silicon ones, especially in applications where increased performance and reliability have a higher priority than cost and where the operating conditions cannot be withstood by Si sensors. 1.2 Objective of this Work The discovery [7][8] of a large piezoresistive gauge factor (GP) in p—type CVD dia- mond films has generated continued interest for diamond piezoresistive sensors [9][10][l 1]. GFs as high as 1000 and 700 at room temperature and 200°C [1 1], respectively, have been measured using cantilever beam, three-point bending fixture and differential pressure setup. The technology of a multisensor test chip for pressure and temperature sen- sors was developed using process techniques compatible with Si technology [8]. Earlier works characterizing the performance of CVD diamond piezoresistors were limited to proving the feasibility of these sensors by measuring the film response to applied strain and looking for samples that had larger sensitivity. Although a general trend of increasing GF with resistivity was established and some data on the effect of temperature on GF has been published, current understanding of GP in CVD diamond is not sufficient to understand the observed scattering in reported GF values. 3 The goal of this work is to provide a better understanding of the piezoresistive property in B—doped polycrystalline diamond and eventually contribute to their commercialization. Figure 1.1 gives an overview of what needs to be done in order to put CVD diamond piezoresistive sensors on the market. Sensor characterization aims at understanding the effect of film properties on GF and identify the best film for piezoresistive application. Since GF is defined as the fractional change of resistance to strain, understanding of piezoresistivity is not possible without understanding of the electrical and mechanical properties of CVD diamond. For this reason the study scheme shown in Figure 1.1 covers film characterization as well as sensor characterization. Besides characterizing sensor performance, a high yield, low cost diamond sensor fabrication technology needs to be developed and fully tested. This work will be limited to those tasks with solid frames. The task to accomplish was dictated by one or more of the following: (i) feasibility of the task given our lab facilities, (ii) necessity of the task to understanding and improving GF and (iii) complete unavailability of similar measurements in the literature. Specifically, the following issues will be addressed: (1) study the effect of substrate conduction, anneal, electric field on the resistivity of CVD diamond to determine the appropriate processing and operating conditions for stable resistivity. (2) perform intra- and inter-grain I-V to understand current flow in CVD diamond. (3) characterize the effect of electric fields and temperature on GF and relate the results to the observed scattering in reported GF. 8939a aim we Schm— mac: -650 $5825 mo 80am £1 2383th Al 20E 6502m— AL >-_ nuance:— cca A55 T 22". 0585 as a 32:2 .m> a 3:26.80 8335 TT T * - mega. 580m ==m . 585 ”58580 eager—nan e5 any .on :23 Ba mezzo: RBoSfiuH :oumotpam .302 ooggptunm 833/ Saab owsmo Samar—883:0 coma—om QBom EoEoSmaoE ' I I I I I I I I l — 39090.5 Homgnooz 39805 BEBE 880m 0535 2955 96 Figure 1.1 Steps needed to put CV D diamond piezoresistors on the market 5 (4) measure intra- and inter-grain GF. 1.3 Dissertation Organization This dissertation has six major chapters: background, diamond film technology, re- sistivity characterization, sensor characterization and intra-grain gauge factor. In chapter two a summary of previous work on diamond sensor with emphasis on piezoresistors is pre- sented. An overview of current status of the electrical and mechanical properties of B- doped CVD diamond is presented. Chapter three gives details of the development of a 4” wafer hot filament reactor used for diamond deposition. The different types of samples used in this study are described. In chapter four, the effect of conducting substrate, anneal and electric field on the resistivity of B-doped CVD diamond are studied. Intra- and inter-grain conduction are investigated. Chapter five focuses on measuring the effect of electric field and temperature on the piezoresistive gauge factor of B-doped CVD diamond using a mem- brane and a cantilever beam setup. Chapter six deals with intra- and inter- grain gauge factor measurements including the analysis of the effect of grain-boundary on the gauge factor of polycrystalline diamond. The last chapter summarizes the work of this dissertation and pre- sents suggestions for future related research. CHAPTER 2 Background 2.1 Introduction This chapter presents an overview of the recent progress in diamond sensors with an emphasis on piezoresistive sensors. The concept of piezoresistance is introduced and the piezoresistive gauge factor (GF) is defined. Piezoresistive models for both single crys- tal and polycrystalline semiconductors are presented through the examples of silicon and polysilicon, respectively. Since both stress and resistance are needed to interpret piezore- sistance data, a review of the major findings on the mechanical and electrical properties of CVD diamond is provided. Diamond film processes used in sensor fabrication such as deposition, doping, patterning and metallization are described. 2.2 Diamond Sensors Recent progress in the chemical vapor deposition (CVD) of diamond has led to inexpensive polycrystalline diamond films which make diamond electronic devices and sensors economically feasible. Numerous efforts continuously improve the properties of CVD diamond films aiming to reach those of single crystal, as indicated by Table 2.1. In the case of active electronic devices, such as diodes and field effect transistors, CVD 7 diarnond’s potential is challenged by the absence of well established n-type doping, stable native oxide and monocrystalline heteroepitaxial growth. In contrast, the use of diamond as a sensor material does not require n-type doping or monocrystalline diamond. Piezoresistive sensors, Negative temperature coefficient thermistors, flow sensors and chemical sensors have been fabricated using techniques similar or compatible with Si batch processing technology. Table 2.1 Comparison of diamond properties and some commonly used semiconductors. Properties Si GaAs SiC (11:32:33 P013521: :33“ Band gap, Eg (eV) 1.12 1.42 3.0 5.45 Electron mobility, [in (cmst) 1450 8500 600 1800'200 23 [3] Hole mobility, 111; (cmst) 1500 400 1600 09-165 [4] Break down field, BB 3 60 40 100 1-10 [12] (Vlcm)x105 Electron saturation velocity, vs 1 1 2.5 2.7 (cm/sec)x107 Dielectric constant, a, 11.7 10.9 9.7 5.5 6.7 [13] Thermal conductivity, 1 1.5 0.5 20 4 - 21.8 [14] (W/cm.K) Thermal expansion coef., K 2.6 5.9 4.7 1.1 2.6 [15] (11°C) x 10*5 Lattice constant, a (A) 5.43 5.65 4.36 3.57 Melting point (0C) 1412 1240 2540 4000 Density (glcm3) 2.328 5.317 3.216 3.52 Hardness (GPa) 9 7 24.8 100 Young’s modulus, Y (GPa) 130-180 85 700 1050-1200 800-1180 [16] Poisson ratio, v .22-.24 .31-.32 .1-.21 .071-.148 [16] Johnson figure of Merit (W Qsec'2)x1023 9 3651 10142 73938 Keyes figure of Merit 444 90.3 6.3 13.8 2.2.1 Diamond piezoresistive sensors Interest for diamond piezoresistive sensors grew with the first quantitative study of the piezoresistive gauge factor in homoepitaxial and polycrystalline diamond films [7]. Several groups have since confirmed the observed large piezoresistive gauge factor for dif- ferent diamond films. For synthetic diamond, the gauge factor, extracted from the work of Latsa et. al, was found to be higher than 103 [8]. The gauge factor for homoepitaxial diamond, measured using a boron doped type 2a film epoxied on a stainless cantilever beam, was reported to be at least 550, four times higher than the highest value for Si [8]. There is not enough information on the characteristics of the homoepitaxial and the synthetic sample to understand the difference in their GF, although differences in doping and defects were cited as potential reasons. Relatively few data are available for monocrystalline diamond probably due to high cost. The piezoresistive property of polycrystalline diamond was studied for different structures, doping levels and temperatures using cantilever beam, three-point bending fixture and differential pressure setups. Table 2.2 lists most data published on room temperature GP for CVD diamond along with the corresponding sample specifications. A room temperature GF as high as 1000 has been attained [11]. GF is not always used to characterize the sensitivity of diamond piezoresistors. 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Snag <2 8-8 82:: 28~:.§~.m o; 2-2 3: 23868 332823 6 882-2 82 .8 832 _ 2 a a as, 8.320% 6 28685 82 com 238: 33205 6 8862 an m S: .5388 aoaa 6 86: .N .. .3 8d E 25528 88205 6 832 T o .. <2 .3. some 232882 a 8368.5 26.6me EEG 389 a 663662 68866 6m 66:86 Quagmbobom 6 m0 6 856596 2380922 63.63% m.~ £an 3-3 OWE onév «Ta a: ma 6 25% HE mm 026m EH 3 028m ma 3 08am HS 8 05mm em 0 www-ma one momfig ooToa oaToE ooén E: K: mu 05mm ma 3 026m ma 3 08am H3 3 08am 5 WTNA 2-x .6”— coumficflfi 626663 958 60885302 mafia 62695 28235 9233 a m0 11 Based on samples with listed resistivity, GF seems to increase with resistivity. The fact that samples with the same resistivity have different GFs suggests that grain size, structure, substrate and processing maybe affecting piezoresistivity. No systematic study of these factors is available. The piezoresistive effect of CVD diamond was studied above room temperature, up to 300°C. The reported results are summarized in Table 2.3. The samples being tested have different resistivity and possibly other characteristics such as substrate, doping method, post processing steps and contact metals. A general trend in the data could be distinguished when considering the temperature effect on piezoresistivity in relation to resistivity. The piezoresistive sensitivity seems to change from being constant with temperature at low resistivity, to increasing at intermediate resistivity and decreasing at high resistivity. The existence of films were the piezoresistive effect is preserved at high temperature strongly suggest the use of diamond piezoresistors in high temperature environments. The results listed in Tables 2.2 and 2.3 demonstrate the feasibility and confirm the high sensitivity of B-doped CVD diamond piezoresistors. The current challenge for diamond piezoresistors is to deliver stable, reliable and reproducible performance especially under high temperature and harsh environment. 2.2.2 Other diamond sensors The negative temperature coefficient (NTC) of the resistivity of B-doped CVD diamond has been used for the fabrication of NTC thermistors by several groups [21][22][23][24]. Some of the advantages of diamond thermistors are: (i) high B factors in 12 the range of ~1000 to 5500 K [24][25], as compared to 2000 to 4000 K for conventional metal-oxide thermistors [26], (ii) operating temperature range up to 600°C in oxygen ambient (iii) chemical inertness and (iv) typical response time of 25 us as compared to 115 ms for Pt resistive temperature detectors [21]. A hydrogen gas sensor was fabricated using a layered Pd/insulating-diamond/p- type -diamond configuration on tungsten substrate [27]. Current-voltage (l-V) and capacitance -voltage-frequency (C-V-F) measurements showed good hydrogen sensitivity for temperature and frequency as high as 85°C and lOOKHz, respectively. Thanks to its high thermal conductivity, the addition of a diamond interlayer in an Ni/Diamondlquartz (Ni/D/Q) structure was found to increase the frequency response of the Ni/Q flow sensor from 120kHz to above 220kHz [28]. This high frequency flow sensor will be useful for measuring high speed flow transitions. Diamond radiation detectors are based on photoconduction and take advantage of diamond’s large bandgap and high radiation hardness. Metal/diamond/metal structures are reported to detect the ultraviolet, X-rays, y-rays, neutrons, high energy electrons and charged particle [29][30][32][31][33]. Diamond diodes [34] and p-channel MIS capacitors [35] showed good performance as UV radiation detectors. 2.3 Theory of piezoresistance effect 2.3.1 Definition of Gauge Factor The gauge factor of a material is defined as the fractional change of resistance, R, of a material per unit strain, 8. The longitudinal gauge factor, GP], for the simple geometry 13 N '1144 ‘4' >Y Figure 2.1 Simple geometry to define GF. l4 depicted in Figure 2.1 can be derived as follows: _ 9: R“fl (u) Differentiating: dR = 5d]; + E-dx + Eff—fly) + pit—‘12) (2.2) W yz Z y y Z .dR_dp dx dy dz D1v1d1ng by R. T — F+Tt——-y__-z— (2.3) ldR ldp GF,:EI-E-=1+Uy+UZ+EIF (2.4) _ dx _ (dy/y) _ (dz/z) . where 8, — 7 , ‘Dy — _(d—x/—x_) and v2 — _(—c_17r/_x) .For sermconductors, ldp GF z —— 2.5 ’ e, p ( ) The change of resistivity due to uniaxial longitudinal stress, 0'], can also be written in terms of piezoresistive coefficient, El [36]: Using this equation in conjunction with Hook’s law, 6’ = E8, (2.7) yields the following formula for the gauge factor: GF, = 1 + u), + uz + 1t,E , (2.8) where E is Young’s modulus. For uniaxial stress in the longitudinal direction, the Young’s modulus and Poisson ratios are given by [36]: E-1 - S’ d - Sf 29 —§l,vy——‘S"l'an Vz—-§1, (') 15 where Sy, S2 and S] are the compliance coefficients. This leads to a GF in the form: Sy Sz 1t, GF,: 1_-S—l_§l+§-l (2.10) 2.3.2 Piezoresistance in single crystal semiconductors As seen from the definition of GF, two terms contribute to the piezoresistive response, one based on geometrical changes and the other due to a change of resistivity with strain. Since the geometrical factor is relatively low, the large GF reported for semi- conductors can only be due to the strain dependency of the resistivity. Without loss of gen- erality, silicon, the most widely used semiconductor, is chosen as an example to explain the principle of piezoresistance in semiconductors. Since resistivity is dependent on the energy band diagram and the conduction and valence band structures are different, the explanation for the piezoresistivity is different for n- and p-type silicon. O N-type Silicon The study of the energy band diagram for silicon as a function of wavenumber shows that the conduction band has six energy minima, along the [100], [T 00], [010], [0T0], [001] and [OOT]. Figure 2.2 shows how the energy E around a minimum varies with k. In order to obtain a good insight into the three dimensional band structure, it is usual to plot the surfaces of equal energy in k-space. Figure 2.3, shows a plot of the energy valleys near the conduction band minima of Si. Applying an electric field in [100] results in elec- trons moving parallel to the field having an effective mass m* u and those perpendicular having m*l , where m*, is defined by: 16 1t 21: allll] k[000] -a-[100] Figure 2.2 Energy band structure of Si [37]. 17 1001} [T00] [0T0] - - [010] [100] [GOT] Figure 2.3 Constant energy ellipsoids near the conduction band minima of Si [37]. 18 _ (2.11) and m* II > m*i as illustrated in Figure 2.4a. The one dimensional equation of motion in each valley is written as: dvx 1 (a)... = .72qu ‘2'”) where or = 1, 2, .., 6, m2, and nu are the effective mass and number of electrons in the val- ley, respectively. The total equation of motion is obtained by superposition: 6 dvx dvx a = 2 (ti—t)a' (2'13) a=1 Under equilibrium and no strain, all valleys are equally populated. Thus, (2.14) where n is the electron concentration. Since the effective mass of electrons in the [100] and [I00] minima is m* II and those in [010], [010], [001] and [DOT] is m*J_ , the equation of motion becomes: CM 1 n 1 n 1 1 2 The total effective mass is given by: 1 1 2 1 —_ = — — +——- , 2.16 "1* 3(M*i 01*”) ( ) When tension is applied in the [100] direction, assuming no change in volume, lat- tice spacing increases in [100] and [100] directions, but decreases in the particular direc- l9 A V Ev- V kl ‘ > k" [010], [CID], [001] and [DOT] [100] and [100] (a) E \/ ‘ E:- -P— V 15’"- kl ¢ > 1‘11 [010], [CID], [001] and [001] [100] and [T00] (13) Figure 2.4 (a) Conduction band under zero strain and an electric field in the [100] direction, electrons moving parallel to the field, [100] and [T00], have larger effective mass than those moving perpendicular to the field, [010], [0T0], [001] and [001']. (b) As a result of tension in the [100] direction, the [100] and [001] minima are lowered. 20 tions, [010], [CID], [001] and [OOT]. Since increase of the lattice constant in silicon was found to decrease the bandgap [38], the energy band minima in the direction of tension become lower than the other four directions, as shown in Figure 2.4b. Consequently, the proportion of electrons in the [100] and [100] valleys, which see the larger effective mass m* ", increases. Since resistivity is defined by: "1* p = (2.17) nqz‘c where 1: accounts for inter- and intra-valley scattering, the increase of the total effective mass with tension results in an increase of resistivity. It is worth mentioning that the effect of strain on resistivity is not limited to chang- ing the equilibrium population of the conduction valleys. A detailed discussion of the ways in which strain can affect resistivity showed that strain-induced changes in effective mass within a valley and intra-valley scattering are small and that the effect of strain on inter-valley scattering is only important at high temperatures when inter-valley scattering is appreciable [39]. It has been observed experimentally that the piezoresistive GF depends on doping and temperature. Figure 2.5 shows these effects in terms of the factor P(N,T), defined by: GF(T) “RT P(N, T) = (2.18) where N, is the donor concentration and nm is the piezoresistance coefficient at room temperature [40]. Assuming that the strain induced shift in band minima is independent of doping, the proportion of conduction electrons displaced due to strain is smaller for higher doping. Consequently, the relative change of resistivity, and hence GF, is smaller for 21 15 - . I T = - 50°C P(N,T) T=0°C 1.0 . 0.5 - T = 25 °C -_l . T: 50°C r: 100°C _ T=1 0°C o.o - . . 10M 10" 10"I 10'9 1010 cm -3 N—> Figure 2.5 The factor P(N,T) with which the piezoresistive coefficient at room temperature must be multiplied to obtain GF at temperature T and donor concentration N in Si [40]. 22 higher doping. The decrease of GP at high temperature is due to increased intervalley lat- tice scattering [41]. Since lattice scattering is more prominent at lower doping, the effect of temperature on GF is more prominent at lower doping. O P-type Silicon Experimentally, it has been found GF of p-type Si is larger than that of n-Si and thus most applications use p-Si [40]. In order to understand this difference, the effect of strain on the valence band structure must be investigated. As seen in Figure 2.2, there are two valence sub-bands, heavy- and light-hole bands, degenerate at k=0, and a split-off band 40 meV below these bands. Since the difference in the sub-bands effective masses and mobilities is not the same for all crystal directions, constant energy surface cannot be described as ellipsoids or spheres. Constant energy surfaces are warped/coupled in such a way that they have cubic symmetry individually [42]. When stress is applied, the valence bands split and redistribution of holes takes place [42]. Due to the large energy separation between the split-off band and the other two, the effect of stress on this band is usually neglected. Based on the experimental result that tension leads to an increase of the resis- tivity of p-Si [43], it was inferred that tension causes the sub-band with the high effective mass to move up relative to the sub-band with low effective mass [40], as illustrated in Figure 2.6. This results in an increase in the proportion of electrons having higher effec- tive mass and consequently lower mobility and higher resistivity. The fact that the differ- ence in the sub-band energies is larger in the [111] direction explains the higher piezoresistive effect measured in that direction [40]. Similar to n-Si, GF decreases with doping and temperature. 23 E(k) A heavy hole band/ light hole band / split-off band E(k) heavy hole band//‘ \\ light hole band / \ split-off band (b) Figure 2.6 Simplified and roughly drawn valence band diagram of Si under (a) zero stress and (b) uniaxial tension. 24 2.3.3 Piezoresistance Models in polycrystalline semiconductors In general, polycrystalline materials consist of crystalline grains interconnected by grain boundaries. This deviation from a single crystal lattice affects conduction and hence requires a change in piezoresistive theory. Since polysilicon is the most studied polycrys- talline semiconductor and both polysilicon and polycrystalline diamond have the same columnar structure, this section is devoted to reviewing the piezoresistive models of poly- silicon. In order to talk about piezoresistive models for polysilicon, conduction models in polysilicon must first be covered. O Conduction in polysilicon A schematic diagram of a grain and surrounding GBs in polysilicon is shown in Figure 2.7a. Grains are considered as small single crystals with the same lattice structure and hence the same energy band diagram as single crystal Si. The grain boundaries (GBs) are composed of disordered atoms and contains a large number of defects and dangling bonds which act as trapping states and/or segregation sites [44] [45]. Figure 2.7b shows the corresponding band structure assuming p-type doping and neglecting the physical dimen- sion of GB. Trapping of holes creates a potential barrier at the boundary and a depletion region into the grains [44][45]. In the early works, the junction between neighboring grains was modeled by an abrupt Schottky barrier [44] [45] (Figure 2.7b). Later, Lu et al. [46] and Mandurah et al. [47] proposed to model energy band discontinuity and scattering in GB by an additional potential barrier, as shown in Figure 2.7c. Based on the disordered nature of GBs and the presence of the GB potential barri- ers, it was inferred that GB resistivity is very high and that carrier transport is dominated 25 Grain boundary / \ Grain Figure 2.7 (a) Schematic of a grain and surrounding GBs in polysilicon. (b) Corresponding energy band diagram assuming p-type doping and neglecting the physical width of GB. Traps with density Qt having energy in the bandgap capture holes creating a barrier potential qVB and a space charge region, Lw [44] [45]. (c) Additional barrier, qx, introduced to account for scattering in GB. The different components of carrier transport across the barrier are indicated [47]. 26 by motion from one grain to the other across 6B3 [44]. Transport in the grain obeys the same principles as in single crystal Si. Transport across GB was modeled by two different approaches. The first approach considers different emission processes across GB namely thermionic emission (TE) over the GB barrier and thermionic field emission (TFE) or tun- neling [45][48]. TFE was sometimes divided in two components: thermionic field emis- sion through the space charge barrier, referred to as TFE, and thermionic field emission through the scattering potential, referred to as TFES [46][47]. In the second approach GB was regarded as an amorphous semiconductor where carriers move via hopping and diffu- sive scattering [49] [50]. Irrespective of the approach being used to model transport across GB, the effective resistivity of a grain-GB pair can be written as: L L Lgb W t3 = pg—f + pw‘i‘ + pgb-f- (2.19) where pg, pgb and pW are the resistivities and Lg, Lgb and LW are the widths of the unde- pleted grain, the GB and the depletion region, respectively, and L = Lg+ Lgb-I-Lw. Usually pgb and pW are lumped in one term that refers to conduction in both GB and the depletion region. The exact forms for pgb and pW depend on the assumptions for each approach and on the doping concentration, grain size and orientation and density and energy distribution of traps. O Piezoresistance in polysilicon Assuming that the small signal effective resistivity of a grain-GB pair can be written in terms of the resistivity of the undepleted grain, pg, and that of the depletion region plus 27 GB, oh, and that the grain and GB are uniformly strained, the longitudinal GF can be written as [51]: S'.. l P 7‘ pbrt GF =1—2fi(1_5ij)+_ [ 813 + lb 11 SH pg + prb/Lg pb + Png/Lb where Sij is the Kronecker delta, S’ii and S’ij are the compliance coefficients of crystalline ] (2.20) Si for the axis system aligned with the crystal lattice and the axis system aligned with the longitudinal direction, respectively, and Lg and Lb, and Mg and tr“, are the thicknesses and longitudinal piezoresistive coefficients, of the undepleted grain and the depletion region plus GB, respectively. As for polysilicon GF >> 1, the geometrical piezoresistive effects can be neglected and GF can be approximated by: GF=2—- , (2.21) L with or = fl, - —b . In order to get GF of a polysilicon film, the equation for GF of a single 8L8 grain-GB pair should be averaged over all grain orientations taking into consideration their distribution in the film. The lower GF reported for polysilicon compared to single Si is consistent with the above equation as long as 1c“, is lower than nlg. Moreover, it is clear that GF changes with at and hence with the relative contribution of grain and GB to resistivity. Early works on GF of polysilicon [52] assumed that GB resistance does not change with strain but found poor agreement for lower doping concentration. Assuming that (i) transport over the GB barrier is due to both thermionic emission and diffusion, (ii) the height of GB barrier is not affected by strain and (iii) the effect of strain on the grain band structure follows the band- shift and band warpage models for n- and p-type polysilicon, respectively, French et al. [51] calculated “lb- GF values calculated using this model for polysilicon films dominated by [100], [110], [111] and random grain orientation are shown in Table 2.4. The variation of 28 30 — - -3o Gauge Factor (p-type) N o I Gauge Factor (n-type) 10- l l 1024 1025 1026 -3 N(m ) Figure 2.8 Longitudinal gauge factor as a function of doping concentration for Boron (_) and Phosphorus (---) doped polysilicon. The calculation are based on a grain size of 60 nm and a texture dominated by [110] orientation. Curves b show the same calculation with GB assumed to be insensitive to strain [51]. 29 GF with film texture is due to the anisotropic nature of the piezoresistive effect in Si. The model was also used to calculate the effect of doping on GP for a [110] textured film with average grain size of 60 nm. The shape of the graph shown in Figure 2.8 was explained by the effect of doping on the relative contribution of grain and GB to resistivity. At high doping the film is dominated by grain effects and the decrease of GP is due to the same high doping effects in single crystal Si. At low doping, GB effects are more prominent and the decrease of GP is due to the lower piezoresistive sensitivity of the GB barrier. Table 2.4 Longitudinal GP for films dominated by [100], [110], [111] and random grain orientation [5 1] ' Texture [100] [110] [111] Random 5: == GF(n-type) -97.2 451.4 -53.4 -82.1 GF(p-type) 61.5 111.7 122.9 87.5 2.4 Current Understanding of Diamond piezoresistance 2.4.1 Single crystal diamond Since the valance band structure of p—type silicon and diamond are similar to a cer- tain degree, Taher et al. extended the interpretation of the piezoresistive property of the former to the latter [8]. Observing that the split-off band in diamond is separated from the heavy- and light-hole hands by only 6 meV, as compared to 40 meV for Si, the authors suggested that the effect of stress on the split-off band may be the reason for the higher GF in monocrystalline diamond, as compared to Si. 30 2.4.2 Polycrystalline CVD diamond Although, p-type diamond has been used to fabricate sensors [22], heaters [25] and field emitters [53], the role of grains and GBs in electronic and mechanical prOperties is not well understood. Such understanding is necessary in order to establish a piezoresistive model. 0 Electrical Properties The effect of GBs on the electrical properties of polycrystalline diamond has been addressed by measuring and interpreting the effective electrical properties of CVD diamond. For the so called not-intentionally doped CVD diamond films, p-type conduction has been identified and space-charge-limited-current (SCLC) [54][55], variable range hopping [56] and GB-barrier [57] conduction mechanisms have been suggested. Poole-Frenkel conduction [12][56] was observed at high fields. Trap levels of 0.62, 1.38 and 0.95 eV [58] were evaluated from frequency and temperature conductance measurements. The existence of these traps was attributed to the polycrystalline nature of the film. Recently, contact current mode scanning force microscopy (CCM-SFM) revealed that grains have lower conductance than GBs for undoped films [59]. It is worth mentioning that the origin of conduction in the undoped films is not clear. For B-doped CVD diamond films, frequency conduction measurements for different doping levels showed activation energies in the range of 0.18 to 1.07 eV and identified three conduction mechanisms namely band conduction, hopping conduction and frequency-dependent thermal emission of carriers from trap levels [58]. Werner and co-authors reported that variable range hopping conduction dominates at room 3l temperature, and that metallic conduction appears at doping concentrations about 8x1020 cm’3 [60] [61]. Examples of all and resistivity measurements of simultaneously deposited polycrystalline and homoepitaxial films with different doping levels are shown in Figure 2.9 [62]. Comparison of the homoepitaxial and polycrystalline properties in [62] showed that: (i) two conduction mechanisms are present for polycrystalline and homoepitaxial films: valence band conduction at high T, and nearest-neighbor hopping conduction at low T, with a higher transition T for polycrystalline films. Additionally, impurity band conduction appears at high doping. (ii) the mobility of polycrystalline films is 2 orders of magnitude lower than that of homoepitaxial films. (iii) the temperature behavior of polycrystalline mobility could not be correlated to any of the following individual scattering models: GB-barrier, dislocations, stacking faults, impurities. (iv) the 3 - 5 times higher compensation ratio for polycrystalline films suggests trapping and/or segregation at GB. (v) highly oriented polycrystalline films showed improved electrical properties. (vi) parallel conduction in GB is possible. As seen from this review, although various conduction mechanisms have been suggested to explain the measured effective electrical properties of CVD diamond, a band diagram of a grain-GB pair is not available and the question of whether conduction is higher in GB or in grains has not been answered. 32 Temperature (°C) 0 -l00 450 In I l l [U o . 7 . 10‘ - '3 0 - ‘ ( II-f- I A _ .9- .I'" _ $ l06 , I , + . C'- +'+'+'*"'+ a , E) V - b 104 _ a - :E F E 3 102 - _ M 0 “114132003 p) o PD2(l03 p) 10° ' I mam ' ‘ + H003 C1 903 -2 lo I' I I I I I I I I I o 4 6 s 10 12 (a) 1000/MK") Temperature (°C) Temperature (°C) 390 p .190 300 9 .190 l000 : 102° - n: o. o HMD2(IO'3p) I'- m ~ \ 0 913200:3 p) p ‘0 I HM03 M++++ IE . + H003 1,7 100 — :- 3 lo a PD3 I ' IO _ Z 8 N ' .... .- E CIO+ ’ iii 0 3 3 ' g 10" - 000 + >\ _ 0 ++ 3: l0 . D Q L- Q . + E I = S 12 o D U '0 ' 2 + .2 . —- o '3 :1: lo .. :I: 1 .1 0 1mm 0 __ '0 E o PD2 = I HMD3 10‘ — + HOD3 D P03 °~' r r 1 1 r I ‘06 r I l l I r r 012345768 0l234576 (1,) room (K") (c) 1000/r (K") Figure 2.9 (a) Resistivity, (b) Hall mobility and (c) hole concentration measurements of simultaneously deposited polycrystalline (PD), homoepitaxial (HMD) and highly oriented (HOD) films. Films deposited in the same run have the same number [62]. 33 0 Mechanical Properties When modeling piezoresistivity in polycrystalline material, it is important to consider the stress/strain distribution. Evidence of internal stress in CVD diamond has been reported based on Raman spectroscopy [63]. Inhomogeneous and highly localized stress distribution has been observed by several groups [63]. Larger internal stresses are observed at the growth surface as compared to the nucleation surface. Although the average internal bulk stress appears to be small, large stress concentrations near GB and twin boundaries are revealed by finite element modeling and micro-Raman [63]. Internal stresses/strains in CVD diamond are believed to be the result of lattice and thermal mismatch between diamond film and the non-diamond substrate, interaction between GBs, twin boundaries, defects associated the presence of impurities such as hydrogen, and limited growth space in continuous films. The presence of internal stress/strain gradients in CV D diamond results in non-uniform stress distributions even when a uniform external stress is applied. 2.5 Diamond film technology For the exploitation of diamond’s potential as a semiconductor, successful deposi- tion, doping, patterning and metallization processes must be achieved. 2.5.1 Chemical vapor deposition of diamond The growth of diamond by high pressure techniques is well established since the 19508 when GE researchers succeeded in transforming graphite to monocrystalline syn- thetic diamond [64]. The high pressure high temperature conditions required to reach the 34 thermodynamically stable region for diamond make such process costly and only suitable for small area coverage. Interest in diamond was renewed by successful chemical vapor deposition from hydrocarbon mixture in a lower pressure temperature domain where dia- mond is thermodynamically metastable [65]. Deposition rates in the range of 10 nm/hr and co-deposition of graphite jeopardized the future of CVD techniques, until the discov- ery that addition of atomic hydrogen allowed for preferential etching of graphite. Since then several methods and reactor configurations have been developed for decomposing carbon carrier gases and producing atomic hydrogen. Three types of growth techniques can be distinguished: (1) Hot filament chemical vapor deposition (HFCVD): An electrically heated filament thermally cracks H2 into atomic hydrogen, activates and dissociates the hydrocarbon gases and enhances surface processes such as diffusion, chemical reactions via thermal excita- tion and electron bombardment [65]. (ii) Plasma enhanced chemical vapor deposition (PECVD): Activation of the hydro- carbon gas mixture is achieved by D.C., R.F., microwave plasmas or their modifications. (iii) Combustion growth: The hydrocarbon gas mixture is burned at atmospheric pres- sure using a simple welding torch.The simplicity and high growth rate of this technique are offset by non-uniform deposition [65]. For HFCVD and MPCVD, a less than 5% methane to hydrogen mixture is usually used. Sometimes other carbon carrier gases are used instead of methane. Oxygen has been frequently added either directly, 02, CO or C02, or as part of the carbon carrier gas. Bach- mann and co-authors compiled numerous published CVD recipes and constructed the C/ H/O phase diagram plotted in Figure 2.10 [66]. The diagram shows that all successful dia- 35 I ’ non C2H2 9 "a L03 C2H6 , "\ ~eLhan l CH 9 ~55) methqfiol'm ’ 0.9 ,.-" enlarged ." ..v' section '\\\ (3‘ /’ tam. , H 0.1 x01): = 0/(0+H) " 0.9 iliamond carbon growth region , ® diamond 1‘ no growth 0 non-diamond carbon 0 position of undiluted compound I ' orientation line “a limit of diamond domain / set of connected experimental data ‘ Figure 2.10 Atomic C-H-O diamond deposition phase diagram indicating the diamond grth domain [66]. 36 mond growth experiments appear within a well defined “diamond domain.” One of the general trends revealed by Bachmann’s review is the improvement in diamond film quality at the expense of growth rate with the decrease of carbon content and increase in oxygen content. He correlated the temperature of the CVD gas phase with the growth rate and deposition method, as shown in Figure 2.11. The increase in deposition rate with gas tem- perature is generally attributed to a more efficient supply of the diamond growth species. Investigations of diamond growth mechanisms show that methyl and acetylene are the main growth species [67]. Besides gas composition and temperature, gas pressure and sub- strate temperature control the diamond deposition process. Successful diamond deposition was reported for substrate temperature in the range of 400 - 1350 °C where poor quality sets the low temperature limit and absence of growth the high one. Bachmann observed that the “diamond domain” narrows as substrate temperature increases. Deposition pres- sures in the range of 1 - 200 Torr were used depending on the substrate temperature, gas temperature and gas composition. CVD diamond Films have been deposited on different substrate materials. Monoc- rystalline diamond substrates lead to homoepitaxial films whereas non-diamond and poly- crystalline diamond substrates result in the deposition of polycrystalline diamond. For non-diamond substrates a nucleation procedure is necessary to produce the diamond pre- cursors. The most widely used pre-deposition techniques are diamond powder or other types of abrasive polishing and ultrasonic agitation in a diamond powder suspension. An in-situ nucleation procedure consisting of a pre-deposition phase with 5% methane and negatively biased substrate was shown to produce a nucleation density as high as 1010 cm'2 on Si [68]. The first polycrystalline diamond films consisted of randomly oriented 37 hot RF and 1000 J» DC lasma, arc ischarges, plasma jets. A 100 " oxy-acetylene g flames 8 ... e 10 {-3 3 2 low pressure 90 1 4' rmcrowave plasma :3 hot filament E .-l 0.1 - low pressure DC or RF glow discharges thermal decomposition 0-01 I l I I I l 1000 2000 3000 4000 5000 6000 7000 Temperature of the CVD gas phase (K) Figure 2.11 Growth rate for different CV D methods correlate with the temperature of the gas mixture needed for grth [66]. 38 grains interconnected by grain boundaries. The search for polycrystalline diamond films with improved electronic properties lead to the development of deposition techniques for highly oriented films. As CVD diamond technology matures designers of deposition reactors are pres- sured to deliver cheaper and better diamond quality. Some of the challenges they face involve achieving low temperature deposition, large area uniform films, 3D coatings, ori- ented and homoepitaxial films and high growth rates. 2.5.2 Doping Because the 2000 K temperature necessary for effective diffusion in diamond is too high [69], diamond doping is performed either during growth, or by subsequent ion- irnplantation. Boron, aluminum, phosphorus, lithium and nitrogen have been tested as dopants for diamond [70]. Currently boron is the only dopant successfully used to fabri- cate diamond devices and sensors. P-type conduction in B-doped films was established by Seebeck and Hall effect measurements. Diborane (B2H6) [71], boron trioxide (B203) [72] and boron powder [21] have been used as source for in-situ doping. IR measurements have confirmed that boron atoms occupy substitutional sites [72]. Boron incorporation was observed to be higher for [111] orientation and to increase with twinning and grain bound- ary (GB) angle [73]. Diamond quality, grain size, growth rate, hydrogen and oxygen con- tents, and twinning, dislocation and planar defect densities are affected by boron doping; but the effect varies with doping level [73][74][75][76]. The boron activation energy in polycrystalline diamond was found to decrease with doping starting at about 0.37 eV [21]. This decrease has been attributed to the appearance of an impurity band that increases in 39 width until the onset of metallic conduction at B concentrations greater than 1021 cm'3 [60]. Hall, resistivity and secondary ion mass spectroscopy (SIMS) measurements showed a high compensation ratio, that decreases with doping level, in B-doped polycrystalline diamond [62]. A diamond Irvin curve relating hole concentration and resistivity was com- piled and is shown in Figure 2.12 [60]. Although B-doped diamond films have been exten- sively characterized, dopant segregation and/or trapping at GBs are neither confirmed nor refuted [62]. 2.5.3 Patterning Because of diamond’s resistance to chemical attack, standard wet etch patterning techniques are not possible. Two patterning techniques can be applied to diamond: selec- tive deposition and selective dry etching. Selective deposition is achieved by selective nucleation or by masking the areas where growth is not desirable. 8102 was successfully used as a masking layer by Masood et al. [77], Roppel et al. [78] and Davidson et al. [79]. Hirabayashi et al. first nucleated the Si substrate by ultrasonic treatment, then used a photoresist mask for etching Si to 60- 70nm using an Ar+ ion beam [80]. A simple selective nucleation technique, which consist spinning a layer of photoresist pre-mixed with diamond powder and lithographically pat- terning it, was developed by researchers at Michigan State University [77]. A variation of this technique achieved a very high nucleation density of 10” cm'2 [81]. Selective etching of CVD diamond with SiOz or Si3N4 as mask, was performed at atmospheric pressure, in oxygen environment at 700°C, in a rapid thermal processor [77]. 2 102.0 A e ‘0‘ 102I -> O . O Q o O 8. \ OO 1020 0 % o ‘ . o o t , _ o . NA ND 10" . A c 65., o ('6‘ i 5 i0) 0 a 8 '013 : A o 2 A . A o 10” o O z ' . o 4; o 1o'° _ Z p O o 10" . A . 0 1o“ . o o 00 1013 10“ 102 1 102 10‘ Resistivity (9cm) Figure 2.12 Irvin curve for single crystal (0) and polycrystalline (x) B-doped diamond. The open symbols refer to effective doping concentration, N AND, and the closed symbols to the free hole concentration, p [60]. 41 2.5.4 Metallization Metal contacts to diamond have been extensively studied due to their importance in the electrical characterization of diamond films. Two general categories of metals have been used, namely carbide and non-carbide fornring metals. Carbide forming metals such as Ti, Mo and Ta [82][83][84] were shown to give ohmic contacts upon anneal. Recently, the work of Tachibana et al. [85] on Ti contacts revealed that a TiC layer creates a surface layer rich in electrically active defects resulting in the observed ohmic behavior. Reported values of metal barrier heights on single crystal diamond were in the range of 1.5-2 eV independent of the metal [85]. Since the Fermi level was found to be pinned at the dia- mond surface [86], surface modification was suggested as a means to achieve ohmic con- tacts. Laser radiation [87], argon sputtering [88], hydrogenation [84] are found to results in ohmic contacts to various metals. However, it has been shown that, for non-carbide forming metals, the ohmic behavior changes to rectifying after annealing because the absence of there is no carbide layer to prevent the altered diamond surface from diffusing into the metal [88]. The metal-diamond band diagram shown in Figure 2.13 was proposed [88] to illustrate the effect of sputtering and carbide formation on the depletion width and consequently tunneling current. Ohmic contacts were observed after heavy boron doping either in-situ or implanted, regardless of the metal being used [89][90][91]. Heavy doping is believed to narrow the width of the depletion region at the metal-diamond interface which increases tunneling current. Al and Mg contacts change from ohmic to rectifying as the resistivity of B-doped diamond increases while Au contacts are ohmic even at 140 Qcm [90]. AW, NW and Ni/Ti/W ohmic contacts to B-diamond were stable even after annealing at 650°C for 78hrs [92]. Since the adhesion and stability of Ti/Au contacts dete- 42 metal diamond (a) ear-deposited metal /— Ec on diamond E; ------ EF ¢oI / Ev (b) i 09-— Ec high cone. otdetects I I at diamond surface Er: _____ E; -> narrower depletion region —¢.;':,|2—'—,— E -> more tunneling tunneling V I l carbide C) detect layer (0) i u—' EC high cone. of defects ' l at diamond surface ' I ' I Er _§fi_ 1- _____ E -> lower effective bamer -I— h—J F height «be e ) ¢o all} I I Ev fl Figure 2.13 Interface band diagram of Ti on diamond: (a) as deposited Ti, (b) high concentration of electrically active defects created via carbide formation and/or ion bombardment, (c) the defects created in (b) decrease the effective Ti/diamond barrier height [85]. 43 riorates after cycling at 400°C due to interdiffusion of the two metals, a Tifl‘i-Si—N/Au combination was tested and did not show any interdiffusion even after 100 hr heat treat- ment [93]. 2.6 Summary This overview of the current status of diamond sensors shows major achievements in sensor fabrication and characterization. Although piezoresistive diamond sensors have been successfully fabricated and a GP as high as 1000 has been measured, the observed scattering in sensor response and the role of grains and GBs in electrical conduction are still not understood. CHAPTER 3 Diamond Film Technology 3.1 Introduction For the exploitation of diamond’s potential as a semiconductor, successful deposi- tion, patterning, doping, post-deposition anneal and metallization processes must be achieved. Details of the 4-inch wafer deposition system and of the initial tests performed to optimize its operation are given in the first section. Sample fabrication processes are described in the second section. 3.2 Hot Filament chemical vapor deposition reactor The doped diamond films used in this work were deposited in HFCVD reactor designed and built with the help of A. Masood and BS. Hong. This reactor extends the deposition area of a 2 inch reactor previously built at Ford Motor Co. by J. Potter and M. Tamor, to 4 inches. A schematic of the system is shown in Figure 3.1. The reaction cham- ber consist of an 18 inch diameter stainless steel vacuum chamber with a 10-inch door to insert the samples. Ultra-pure (99.995%) methane (CH4) and hydrogen (Hz) are used as the reactant gases and their flow rates are independently controlled by MKS type 1159 mass flow controllers. The operating pressure is controlled by a MKS type 250 pressure 1mm DIA. HOLES FILLED _L 0.0,. / l T BORON POWDER HOLDER FILAMENT ms... I" ..l PYROMETER TEMPERATURE " CONTROL VENT N2 SAMPLE THERMOCOU PLE PRESSURE VACUUM PUMP . I _ CONTROL Figure 3.1 Schematic of the hot filament reactor. 46 controller and a type 248 upstream valve. The base pressure is measured by a MDC ther- mocouple vacuum gauge. The filament assembly consists of ten 5 inch long and 0.02 inch diameter cross section Tantalum filaments mounted as shown in Figure 3.2a. The frame is made of two Molybdenum bars which serve as electrodes, and two Boron Nitride (BN) electrically insulating bars which make it possible to connect the filaments in series. Molybdenum hooks support the filaments and provide tension to diminish sagging. The filament temper- ature is measured optically by a dual wavelength series 8125G-CT Williamson pyrometer. Either a 4 inch Si wafer or a graphite plate is used as a substrate holder. The substrate holder is attached to a moving stage using Mo nuts and Ta rods, as depicted in Figure 3.2b. The stage is designed with the capability to adjust the filament to substrate distance, D(F,S), in the range of 0 - 3 cm. The Ta rods are used to protect the moving mechanism from. the high temperature environment near the filament and to minimize heat loss from the substrate to the body of the chamber. 3.2.1 System testing and optimization The 4.5 x 5 inch2 filament array generates enough heat to reach very high substrate temperature without any external heating. Due to the limitation of the K-type thermocouple used for measuring the temperature, the maximum recorded substrate temperature is 1000°C. Several measurements are performed to characterize the temperature profile on the substrate as a function of operating conditions and filament aging. 47 Mo electrode Boron Nitride Ta filament (a) (b) Figure 3.2 (a) Filament assembly and (b) substrate holder. 48 . Effect of deposition conditions The effect of filament temperature, Tf, filament to substrate separation, D(F,S), operating pressure, P, gas flow rate and gas composition on the substrate temperature are investigated. Major results are summarized as follows: (i) The substrate temperature increases nearly linearly with filament temperature, as shown in Figure 3.3. (ii) As D(F,S) increases the substrate temperature that corresponds to a given fila- ment temperature, decreases as illustrated by Figure 3.3. (iii) Figure 3.4 shows that for the same total gas flow of 200 sccm, the presence of CH4 in the gas results in slightly higher substrate temperatures. (iv) Using three K-type thermocouples connected as indicated in Figure 3.5, reveals that the substrate is not uniformly heated. The hottest spot in the substrate is the center point Tcl and the temperature decreases symmetrically towards the edges. The maximum temperature gradient, Tc 1-Tc3, increases with filament temperature. (v) Figure 3.6a reveals that, for the same filament temperature, the substrate tem- perature increases with P up to 50 Torr. Above 50 Torr, substrate temperature starts to decrease probably due to heat loss to the surroundings caused by increased and uncon- strained gas species. The maximum temperature gradient is also affected by pressure and seems to reach its lowest value around 50 Torr. (vi) The effect of gas flow rate on substrate temperature was measured for filament temperatures, Tf, of 2142 and 2205 °C. The results plotted in Figure 3.6b reveal that the substrate temperature does not change with flow at 2142 °C. However, at 2205 °C the effect of flow is slightly noticeable. At low flow rate, the sensitivity of substrate tempera- Tcl (°C) 1000 950 850 800 750 700 650 600 550 49 P = 50 Torr, H2 / CH4 = 199/ l (sccm/sccm) I I I I I x X 11‘ at 55 at 0o “3 at 3’ X at a I/ a? 0 69 * I\ 0 $0. X * N. 5 o x 4’ ° 9 x x Q 0 $6?” Q x °O Filament x c T 1 D(F,S) v C 4” Siwafer 5m 1 l l l l l l l l 1400 1500 1600 1700 1800 1900 2000 2100 2200 2300 2400 Filament Temperature (°C) Figure 3.3 Effect of filament to substrate separation. Tcl (°C) 50 P = 50 Torr, D(F,S)=2.5cm 950 750 r Filament 1 Tel V 4” Si wafer 1 700 2000 2050 2100 2150 2200 2250 2300 Filament Temperature (°C) Figure 3.4 Effect of methane. 2350 2400 Tcl, Tc2, Tc3 (°C) 51 P = 50 Torr, H2 = 200 sccm, D(F,S) = 1.5 cm. 900 _ l l I l T I I .1 850 “ g m Tel - Tc3 - i W 800- g .. . h Tc2 . Tc3 750 ' _ Ml ' The In In» In «no no me an no filament Temperature (°C) TC3 700 - ‘ 650 - a 600 - 4 550 . Filament - Tc2 vTc2 vTcl Tc3 ' 500 _ 4” Si wafer . 1500 1600 1700 1800 1900 2000 2100 2200 2300 Filament Temperature (°C) Figure 3.5 Temperature gradient over the 4 inch substrate. Tcl, Tc2, Tc3 (°C) Tc 1, Tc2, Tc3 (°C) 52 H2 = 100 sccm, Tf = 2207°C 950 l’ I I I T I I T 900 4” wafer _ 850 a , 2 800 a 750 .., 1 , " s Tc3 700 - '1 650 1 TC] 600 - J Tc2 550 L l l l l l l J O 50 100 1 50 200 250 300 350 400 450 Pressure ('Torr) (a) —Tf = 2205°C, -- Tf = 2142°C, P = 50 Torr 900 ~ / TC3 CH4+H2 850 — 4 *4_*-—-i’,,x—--X ------ x / |\ °°° " r T cl [ substrate I 750- o-o—e-- -—o--—@--;_-__:_:_9_____.———————--"""* i YI/I’i TC2 700 - . to pump *+¥---:’,,§-——fl ------ fl 65° 6 260 460 600 360 1000 Flow Rate (sccm) (b) Figure 3.6 Effect of (a) pressure and (b) gas flow rate at D(F,S) = 2.5 cm. 53 ture is slightly higher and the temperature gradient slightly lower. 0 Effect of filament aging Before using the filament as a source of heat for the substrate, it is important to study its long term behavior. When current is increased through a new filament for the first time, its temperature first increases then it slowly decreases reaching a steady state value. These instabilities result in unstable substrate temperature as shown in Figure 3.7. How- ever, after the first high temperature cycle, the filament temperature stabilizes. To avoid these instabilities, each new filament is subjected to a high temperature curing cycle prior to actual deposition runs. The curing cycle is carried out in H2 environment and lasts for almost 2 hours. The filament temperature is increased by 10°C at a time and allowed to reach a steady state. Besides stability, long term repeatability of the filament behavior is important. Several runs revealed that the filament temperature needed to reach a given substrate tem- perature increases with filament use. For example, Figure 3.8 shows that a filament tem- perature of 2100°C heats the substrate to 875 and 575°C after 9 and 24 hours of operation, respectively. Interestingly, the room temperature resistance of the filament also changes with use: first it increases then it stabilizes, as shown in Figure 3.9. Quick examination of cross sections of used filaments reveals they get covered by an outer shell believed to be Tantalum carbide. This change in filament material maybe the reason for the observed increase in filament resistance and change in heat radiation. Tcl (°C) 54 P = 50 Torr, H2 = 200 sccm, D(F,S) = 2.5 cm. 0 Tc1 * Tc2 X T04 - new filament -- filament after 3 hrs. 1100 800r 700 - l T I Filament ¢ D(F,S) * Tc1 4” Si wafer l I l 1600 1800 Filament Temperature (°C) 2000 2200 Figure 3.7 Effect of initial high temperature cure on filament. Tcl (°C) 55 P = 50 Torr, H2 = 200 sccm, D(F,S) = 2.5cm 1000 I 700 I 600 I I I I I I I fi Filament Tcl I 4” Si wafer 1500 1600 1700 1800 1900 2000 2100 2200 2300 Filament Temperature (°C) Figure 3.8 Effect of repeated use on filament. 56 P = 50 Torr, H2 = 500 sccm, CH4 = 2.5 sccm, D(F,S) = 1.5cm 5 Resistance (52) 0 10 20 30 40 Time (hours) Figure 3.9 Effect of multiple runs on the room temperature filament resistance. 57 0 New temperature control scheme Based on the observed changes in filament with time, it appears that if constant fil- ament temperature control is used, the substrate temperature will vary between runs by as much as 250°C. Whereas, if a constant substrate temperature profile is to be maintained for all runs, filament temperature may need to be varied by as much as 200 °C. A system- atic study of the effect of filament temperature in the range of 2200 - 2500°C showed a variation in deposition rate but not diamond quality [94]. Consequently, it seems more rea- sonable to adopt a constant substrate temperature control scheme. This is achieved by using the substrate temperature signal as an input to a temperature controller, setting the set-point equal to the desired substrate temperature and connecting the generated control signal to the filament power supply. 3.2.2 System operation Typical deposition conditions used through out this work are listed in Table 3.1. The system start up and shut down procedures are kept the same for all runs as described next: Curing procedure for new filaments: (1) Pump down the deposition chamber to a base pressure of 10 mTorr. (2) Introduce H2 and wait for the pressure to reach 50 Torr. (3) Manually increase the filament temperature until the low temperature limit of the pyrometer is reached (~900 °C). (4) Manually increase the filament temperature by 25°C and wait for it to reach a 58 steady state value (~3 min). (5) Repeat (4) until desired operating filament temperature is reached. Start up procedure: (1) Load the samples and doping source and adjust D(F,S). (2) Pump down the deposition chamber to a base pressure of 10 mTorr. (3) Introduce H2 and wait for the pressure to reach 50 Torr. (4) Manually increase the filament temperature to reach the desired substrate tem- perature, then switch the temperature control to automatic and wait for the substrate tem- perature to stabilize. (5) Introduce CH4 and record the time of the start of deposition. Shut down procedure: ( 1) Turn off CH4 to terminate deposition. (2) Keep H2 on for another 5-10 min. This treatment removes a surface carbon- aceous layer believed to be the reason for the observed conduction in undoped CVD dia- mond fihns [21]. (3) Manually decrease the filament current to zero (~20 min) and shut off its power supply. (4) Evacuate the chamber and wait for the system to cool down. (5) Back fill the chamber with nitrogen and remove the samples. 59 Table 3.1: Typical deposition parameters. Filament temperature (°C) 2100-2300 Substrate temperature (°C) 350-900 Gas composition (CH4/I-12 sccm) 400/4 Filament to substrate separation (cm) 1-1.2 Base pressure (mTorr) 10 Deposition pressure (Torr) 50 3.3 Sample fabrication As shown in Figure 3.10, three types of CVD films are used in this study: small grain films deposited on oxidized silicon, large grain films deposited on commercially available free standing polycrystalline diamond and homoepitaxial films deposited on single crystal substrate. 3.3.1 Small grain film The oxidized silicon substrate is selectively nucleated using a selective nucleation technique, developed at Michigan State University in collaboration with Ford Motor company. As shown in Figure 3.11, the wafer is spin coated with a mixture of diamond powder and photoresist (DPPR) then lithographically patterned. This procedure is compatible with IC process technology and ensures that no mechanical damage is imposed on the substrate. The wafer with the DPPR pattern is introduced into the deposition chamber, the photoresist burns off as soon as the filament heats up leaving the diamond seeds behind. The diamond seeds grow in all directions until a continuous l-Zum thick 60 dOped diamond small grain film undoped diamond oxidized Si , doped diamond large grain film _ . Large grain undoped dramond . . doped diamond homoeprtaxral film F , _ g smgle crystal type 2a dramond Figure 3.10 Types of CVD diamond films used in this work. 61 DPPR Sio2 Figure 3.11 Nucleation and patterning. T, N2 A T (600 °C) .' """"" I I \ I \ | \ ‘ \ : N2 (5 1/min) ‘ t \ ————————— I . .----\ , 0 10 20 30 Time (min) Figure 3.12 Temperature and gas profiles during RTP anneal. 62 undoped diamond layer is deposited. A l-l.5 pm thick B-doped layer is deposited in a subsequent run. The undoped layer isolates the doped diamond from the substrate resulting in better electronic properties [95]. Boron doping is achieved in-situ using two types of doping sources: (i) boron powder [8], for low resistivity samples and (ii) boron wafer [96], for high resistivity samples. The doping level was varied by (i) filling less holes of the boron powder holder depicted in Figure 3.1, (ii) using a fresh vs. partially depleted boron wafer or (iii) changing the distance between the doping source and the wafer. The films are annealed in a rapid thermal processor (RTP) in N2 environment fol- lowing the cycle depicted in Figure 3.12. Evaporated Al, annealed in RTP at 450°C in N2, is used to achieve ohmic contacts to the B-doped diamond. Figure 3.13a shows a fully processed 4" wafer which yields 6 different samples. Details of a diamond resistor are shown in Figure 3.13b. The diamond film is characterized using scanning electron microscopy (SEM) and Raman spectroscopy (514 nm, 300 mW and spectral resolution of 4.9 cm‘l). Representative SEM and Raman are shown in Figure 3.13c and 3.13d. 3.3.2 Large grain film Commercially available undoped (170 pm thick) optically smooth free standing polycrystalline diamond obtained from Diamonex is used as a substrate. A 1-2 pm Boron-doped film is grown in the HFCVD using Boron powder as a source. The deposition conditions are the same as those listed in Table 3.1, with substrate and filament temperatures of 900°C and 2300°C, respectively. The Raman spectrum of the 63 V (d) Intensity (a.u.) I 1200 1400 1600 Raman Shift (cm'1) Figure 3.13 (a) processed 4" wafer, (b) CVD diamond resistor (c) SEM and (d) Raman. Intensity (A.u.) — _ MW 1 1 I 1 I 1 1 1 200 1300 1400 1500 1600 Raman Shift (cm") Figure 3.14 Raman Spectra of the B-doped large grain film. 65 100 11111 NurrberofGrains 2 810141822263034 GrainArea(1O°umZ) Figure 3.15 (a) Light microscope photo of doped CVD film and (b) corresponding grain size distribution. Figure 3.16 AFM of different types of GBs. 67 Figure 3.17 AFM of typical well defined grooves. 160.000 me 68 Figure 3.18 Typical intra-grain AFM. 69 doped film, shown in Figure 3.14, displays excellent diamond quality. Using the method of line intercepts [97] the grain size distribution of the doped film was determined from the representative light microscope photo shown in Figure 3.15a. The histogram shown in Figure 3.15b, generated by Mario Gatto, an undergraduate student at the Electrical Engineering Department at Michigan State University, indicates that the majority of grain sizes are in the range of 50 - 80 um. The volume fraction of the inter-grain area is around 12%. Finer details of the film surface structure are obtained using atomic force microscopy (AFM). Figure 3.16 shows that typical GBs consist of either well defined grooves or irregularly shaped voids 0.2 - 0.5 pm deep, as obtained from cross-sectional analysis at 10 different locations in the sample. The grooves range in width between 0.5 - 1 pm and are not steep as seen in Figure 3.17. The irregular voids ranging in width between 1.6 - 7 pm sometimes contain smaller grains or twins. The grooves and voids suggest that polishing did not completely smooth the film surface. Typical intra-grain morphology is shown in Figure 3.18. The average surface roughness is less than 5 nm. The observed microstuctures are consistent with those observed on film deposited on [111] synthetic diamond and attributed to multi-nucleation homoepitaxy [98]. 3.3.3 Homoepitaxial film A 1-2 pm thick B-doped layer is deposited in a HFCVD on a 3mm x 3mm type 2a [100] oriented diamond wafer purchased from Bubbledee Ham's. The doped diamond layer shows excellent Raman spectra, as seen in Figure 3.19. Metal contacts are established by sputtering a double layer of Ti and Pt. 70 1 ' 1 0.8 ' .1 =2 “1 0.6 - 1 E 2 9. 5 0.4 *- 1 0.2 - - O l l l l l l l l l 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 Shift Wavenumber in 1/cm Figure 3.19 Raman Spectrum of B-doped homoepitaxial diamond. 71 3.4 Summary In this chapter, the newly designed 4 inch HFCVD system used to deposit diamond films for this work is characterized. A special temperature control scheme is implemented to use the heat generated by the 4.5 x 5 inch filament array for substrate heating without degrading diamond quality. Sample fabrication processes namely nucleation, patterning, doping, anneal and metallization are described. Distinction is made between the three types of samples used in this work: small grain, large grain and homoepitaxial. The films were characterized by light microscopy, scanning electron microscopy, atomic force microscopy and Raman spectroscopy. CHAPTER 4 Resistivity Characterization 4.1 Introduction As resistivity is the sensing parameter for piezoresistive sensors, characterization of the resistivity of B-doped CVD diamond films is needed in order to understand the operation and improve the design of diamond piezoresistors. Although the resistivity of doped and undoped CVD diamond films has been characterized, (i) most studies are performed on films grown on conducting Si and (ii) there is a scatter in the reported resistivity behavior. Since the aim of this research is to develop stable piezoresistive sensors, it is important to (i) study the effect of substrate on conduction and (ii) understand the scattering in resistivity data. In this chapter the effect of substrate on resistivity is studied for films grown on n- Si, p-Si and oxidized Si. The effects of annealing and electric fields on resistivity are investigated. Four point probe resistivity, potential profile, intra- and inter-grain I-V measurements are performed. A simple model that distinguishes between large grain and small grain current paths is proposed to interpret the data. 72 73 4.2 Effect of substrate conduction Some CVD diamond films generally referred to as not intentionally doped, were observed to be electrically conducting even though they were grown without a doping source [55]. Neither the origin of conduction nor the effect of the non insulating substrate are well understood. Since in this research Si is used as substrate, it is important to investi- gate the effect of substrate conduction on film conduction. Undoped diamond is deposited on three substrates: n-Si, p-Si and oxidized Si, in the same run. The as grown resistivity is characterized using a four-point probe station. The results show that the films grown on p-Si and n-Si are observed to be conducting. The origin of conduction in these so called not intentionally doped films has been attributed to surface conduction as well as substrate shunting [99]. The films grown on insulating oxi- dized Si are not conducting which makes oxidized Si a good choice to grow diamond sam- ples for sensor applications. 4.3 Effect of Annealing on Resistivity Annealing has been observed to improve the reliability and high temperature stabil- ity of diamond resistors [21]. For CVD diamond on Si, it has been observed that resistivity increases with annealing in neutral environments at temperatures in the range of 350 - 800°C for undoped films [100][101][102], but stays constant for B-doped (10 Dem) [103]. The undoped films were observed to be electrically conducting even though they were grown without a doping source. As there is no study of the effect of annealing on the resistivity of p-type diamond as a function of doping for films deposited on insulating substrates, the efl‘ect of annealing 74 on resistivity is studied as a function of doping level and quality, as determined by Raman, for in-situ B-doped polycrystalline diamond films deposited on oxidized Si. 4.3.1 Experimental details The diamond films used in this study are of the small grain type described in section 3.3.1. In order to span a resistivity range of 0.27-535 Qcm three series of films, OP, A and D, are doped in three different runs. The doping level and diamond quality of each sample are controlled by varying their distance from the doping source and the doping method, and their position under the filament, respectively. Samples in series OP are doped using boron powder [8]. A fresh boron wafer is used for A, whereas a boron wafer that has been partially depleted through previous runs is used for D. A four-point probe setup is used for resistivity measurement thus eliminating the problem of the effect of contact resistance [104]. The resistivity is computed using the four-point probe data and the thickness of the doped layer. 4.3.2 Results The effect of annealing on the resistivity of series OP, A and D is illustrated in Figure 4.1. For as-grown resistivity above 1 Gem, the resistivity after anneal, pan, is higher than that before annealing, Pba- The ratio of the resistivity after anneal to that before, plotted in the inset of Figure 4.1, suggests that the effect of anneal increases with the as-grown resistivity. Samples from series A and D exhibit higher sensitivity to anneal than those from series OP. In order to understand this difference, Raman and SEM of annealed samples are carefully studied as shown in Figure 4.2. All samples show small peak around 1520 cm'1 75 1o4 : I 89' sOP — o 5.22“ A05 T A SeriesD 103 5 . . . ' : pba = resustrvnty before anneal I paa = resistivity after anneal 102 = " E 5 Al O D2 0 — A / Cl _ D4 x "g “ 0P12 '9 3 0' D3/Dlé'" 101 5 0P6 ,I 6 - E A3 0 " 6.8 _ A2 C2," 0- 1 0 _ 0134‘" 2 ' 0 E 093 Z ’I 0 1 1 1 I g 10'1 10° 101 102 103' _ . P2 pba(£2cm) 10-1 ' I llllllll l I lllllll l llllllll l llJJllll 1 1111111 10'1 10° 101 102 103 104 Figure 4. l Resistivity after anneal vs. resistivity before anneal. Inset: ratio of resistivity after anneal to that before anneal. 76 characteristic of clusters of sp2 carbon [105]. This peak tends to be very noisy and weak, indicating that the films contain relatively little sp2 (to which the Raman probe is 50 times more sensitive than to sp3). The spectra show that, as doping increases, the graphitic peak decreases for all samples; whereas the diamond peak becomes sharper for series D but deteriorates for series OP and A. A similar trend has been reported [106] with the difference that high doping has been observed to result in needle-like structures. Based on the representative SEMs shown in Figure 4.2, the grain size and surface morphology are different even among samples from the same series. The Raman spectra of Figure 4.2 along with the resistivity data in Figure 4.1 suggest that there is a correlation between the Raman spectra and the effect of anneal. Samples with comparable as- grown resistivity but different diamond quality, as determined by Raman spectra, such as OP91/A3, OP12/Al and D4/A1 reveal that the effect of anneal on resistivity increases with diamond quality. For samples with comparable diamond quality, such as A1-A3, the resistivity increase due to anneal is highest for the lowest doping level. 4.3.3 Discussion The previous results suggest that resistivity increase with anneal is more prominent for low doping level and high quality diamond. The effect of anneal on the lightly doped samples is consistent with the observed increase of the resistivity of undoped films deposited directly on Si [100]. The anneal effect was attributed to an increase in trap density due to hydrogen outdiffusion [100]. A decrease of the OH bond absorption peaks in the IR spectra of B—doped films after anneal was reported [107]. While the role of surface conduction as compared to bulk conduction is not clear, it may be assumed that in the case 1200 77 Intensity (arbitrary units) .1400. Raman Shift (cm‘1) Figure 4.2 Raman spectra and SEM of samples used in the anneal study. 78 of doped films, the traps vacated by hydrogen outdiffusion are to be filled by holes. Assuming that the average density of traps generated by hydrogen is the same for all doping levels and that these traps may capture holes, one can expect trapping to result in wider depletion region at the grain boundary of lightly doped films [108]. This will increase the resistivity through anneal more for low doping than for high doping. The fact that variation of resistivity with anneal is affected by diamond quality suggests that the GB content and/or traps may vary with quality. The characterization of H-content and trap density in B-doped CVD diamond as a function of film quality is necessary to understand the correlation between annealing and diamond quality. 4.4 Effect of Electric Field on Resistivity In the course of investigating the effect of anneal on resistivity, the resistance value is observed to vary with the current and/or voltage applied to measure it. Given that GF is computed from resistance data, it is important to investigate the effect of electric bias on the measured resistance. Studies of the high field behavior of the resistivity of homoepi- taxial and undoped polycrystalline films have reported nonlinear characteristics. This effect has been attributed to extra carrier generation via impact ionization [109] and Poole- Frenkel conduction [12][110]. There is no similar study done for p-type polycrystalline diamond grown on insulating substrate. In this section the effect of electric field on the resistivity of p—type CVD grown on oxidized Si is investigated for different doping levels and grain size and orientation. 79 4.4.1 Experimental details Table 4.1 lists the specifications for the CVD diamond films used in this section. With the exception of the highly oriented sample, described in [111], all films are doped in situ in HFCVD using boron powder [77]. Diamond quality and continuity are characterized by SEM and Raman. The electric field and the resistivity are computed based on I-V data and sample dimensions. The highest applied field is limited by the voltage limit of the current source used in the experiment. All measurements are carried at room temperature under atmospheric pressure. Table 4.1 Sample Specifications Grain p Sample Source (11m) Undoped Anneal Contact (0cm) Homoepitaxial Dubbelldee NA Type 2a 600 °C, 10-7 Torr Ti-Pt 1.13 Harris Corp. Highly Kobe Steel 10-100 Plasma CVD 600°C, 10-7 Torr Ti-Pt 136 oriented USA. on high p p-Si Large grain Diamonex 40-170 Plasma CVD 600°C. N2 Al 1.26 Company on Si02 Small grain Michigan 12 HFCVD 600°C. N2 Al 21.13 State Univ. on Si02 4.4.2 Electric field effect as a function of doping Figure 4.3 shows the room temperature resistivity of four small grain diamond resistors as a function of electric field. All resistors have the same dimensions and are cut out of a single wafer processed in the same run to minimize structural differences. The variation in doping level is probably due to the samples not being at the same distance from Pflwm) 80 25 1 1 11m, 1 . trntq r 1 1.1.11, 1 . 111111, 1 1 tmn G- ------ 0 ------- 0-2‘ 20 r “‘0 — \ \ \ \ \ X- ------ -X ------- X— ______ X\ N 15 '- \\ " X‘xxt. G ------ e ------ «y-e-—amm-e\ x ‘09033 m _ - 5 ~ . e ------ e ------- o ------ e ------ Figure 4.9 Current flow in polycrystalline diamond with non-uniform grain size modeled in terms of paths made of small grains and paths made of large grains. 93 probably reflect intra-grain conduction. 4.5.5 Non-uniform current flow Table 4.2 shows a summary of the linear I-V data obtained from the four-point probe, the potential profile and the two-point probe measurements. Interestingly, A—IV decreases with increasing probe separation. As there is a wide spread of grains sizes, it may be assumed that current paths with small and large grains have conductivities 0'88 and 0'18, respectively, as indicated in Figure 4.9. The average conductivity in the film, Oavgr is written in terms of contribution of all paths: 6 = :03 avg + 261g 8 Other studies have shown that for the same doping conditions the measured resistivity of large grain films is higher than that of small grain films [81]. Consequently, the resistivity for small-grain paths is expected to be lower than that of large grain paths. As the probe separation increases the probability of occurrence of small grain paths increases. Thus the resistivity of the dominant path(s) decreases leading to lower resistance for longer path(s). It is not clear at this point if the resistivity variation with grain size is due to variation in doping incorporation with grain orientation and GB angle [120] or GB vs. grain contribution to conduction. Depending on the conduction mechanism, current flow could be affected by the observed variation of GB potential barrier heights and widths as in the case of polysilicon [108]. Non-uniform current flow results in non-uniform potential profiles and could give the impression of a spread of activation energies [121] if different conduction 94 mechanisms exist for different doping levels. Interestingly, non-uniform current flow could be one of the reasons why electrical properties of CVD diamond do not show good quantitative fit to simple models that use average parameters and assume spatial uniformity, such as the boundary barrier model [120]. Figure 4.7 shows that the potential drop along the characterized path increases linearly with distance for 104A, but not for 10‘°A and 10'5A. Since as the applied current increases, the potential drop and hence electric field increases, the observed difference in potential profiles maybe related to the effect of electric field on resistivity presented in 4.4. In this context, the data in Figure 4.7 can be interpreted as follows: as the applied electric field increases, the resistance of the shortest path decreases until it becomes the least resistance path. This suggests that as electric field increases current flow becomes more uniform. Table 4.2 Summary of linear I-V data Measurement Shortest path I (A) .ATY Four point probes 1587 um 10‘3 0.7 K9. Potential profile 190 pm: 3 large grains 10'4 10 K9. 2 probes on rough diamond 6-14 pm: within a single grain 10’6 6.7-5.5 MD. 95 4.6 Summary In this chapter, the effect of substrate, post deposition anneal and electric field on the resistivity of B-doped polycrystalline CVD diamond deposited on insulating substrate, were studied. The anneal study reveals for the first time that the resistivity decrease with anneal is lower at high doping and varies with diamond quality. The electric field study shows for the first time that resistivity decreases with increasing electric field for fields up to 103V/cm. This field effect seems to be related to the presence of GBs and is found to be less pronounced at high dOping, high temperature and for highly oriented films. Four-point probe I-V across many grains, potential profile across five grains and two-point-probe I-V within a single grain and across an individual GB reveal non-uniform current flow in B- doped polycrystalline diamond. Inter-grain I-V across individual GBs with different widths suggests the existence of potential barriers at GBs. CHAPTER 5 Sensor characterization 5.1 Introduction The purpose of sensor characterization is to understand and eventually improve the performance of CVD diamond piezoresistive sensors. Early work on CVD diamond piezoresistors suggests that performance may be affected by operating conditions and film properties. As piezoresistance characterization is based on resistance measurements and the resistance of CVD diamond is affected by electric field, it is important to determine if the electric field affects piezoresistivity. Since the greatest potential for diamond pressure sen- sors would be at high temperature where the performance of their Si counterparts deteriorates, it is important to characterize them at high temperature. In this chapter, the effects of electric field and temperature on GF of B-doped CVD diamond are measured as a function of doping level. The results, when correlated with data published in the literature, show that both field and temperature effects seem to be less prominent with increased doping. 96 97 5.2 Gauge factor measurement setup Early GF measurements used a cantilever beam and three point bending structure [7] [9]. In this work, a cantilever beam and a membrane based setup are used. The strain equations for the cantilever beam setup developed in [36] will be summarized. As strain calculation for the membrane based setup is highly dependent on the assumptions made to convert pressure to strain, it is important to fully describe it. 5.2.1 Pressure sensor setup A schematic of a membrane based setup consistent with commercially available differential pressure sensors is depicted in Figure 5.1. A hole with 8.35 mm diameter is ' drilled in the center of a standard 2-3/ ” stainless steel blank flange. The sample is rigidly glued on the flange, with the diamond piezoresistor radially aligned at the center of the hole facing outward in order to facilitate making electric connections. The flange is then used to seal one of the ports of a vacuum chamber. The chamber is pumped down thus subjecting the sample to a differential pressure equal to the difference between atmospheric pressure and the pressure inside the chamber. As the sensitivity of piezoresistors is generally characterized in terms of gauge factor, CF = [Iii—R - é , where R0 and e are the stress-free resistance and the applied strain, 0 pressure values must be transformed to strain values. Plate theory for uniform pressure load is used for this purpose. The appropriate plate model and boundary conditions for this setup are checked using a commercially available wire strain gauge. The gauge is mounted on an oxidized Si substrate similar to those used in the actual samples. The pressure response of i 98 Vacuum Chamber Diamond piezoresistor Constrained Palm edge Differential pressure P = Patm - Pin (a) Uniform pressure load (P = Pam, - Pin) Clamped edges Sample under pressure (b) Figure 5 .1 (a) Differential pressure measurement setup and (b) plate model. 99 the wire strain gauge is plotted in Figure 5.2. Pressure is transformed to strain using the circular plate model for small deflection, clamped edges and uniform load [122]: 3P(1-v2)(r§—3r2) 3P(1—v2)(r(2,- r2) 8, = 2 and e, = 8Eh2 , (5.1) where e] and at are the radial and circumferential strains, E and v are Young’s modulus and Poisson ratio for Si, P is the differential pressure, h is the Si thickness and r0 is the radius of the area under pressure. The longitudinal gauge factor obtained using the computed strain values is 2.667 which is close to the manufacturer specified value of 2.105i0.5%. The discrepancy maybe due to the large dimension of the strain gauge as compared to the hole diameter. Based on this strain gauge test, the small deflection, uniform load and clamped edge model seems appropriate for this measurement setup. Since the diamond films show good physical adhesion to the oxidized Si substrate when subjected to scratch testing, it is reasonable to assume that strain is transmitted ideally across the diamond-substrate interface. The presence of the 3pm diamond layer changes the strain on the 400 um uncoated oxidized silicon substrate by a correction factor computed using the theory of bi-fringed coatings [123]: hd Ed 1+1)” , 52 where E and v and h are Young’s modulus, Poisson ratio and thickness of silicon (Si subscript) and Diamond (d subscript), respectively. Microstrain 0 10 20 30 (RO'R) /R0 (x 10-5) 0 —- N W # UI OI \l on 0 100 200 300 400 500600700 800 P1111 - P11 (Torr) Figure 5 .2 Pressure response of wire strain gauge. piezoresistor force Figure 5.3 Schematic diagram of a cantilever beam setup. 101 5.2.2 Cantilever beam setup A schematic of a cantilever beam setup is shown in Figure 5.3. Assuming that at the fixed ena’e beam can neither rotate nor translate and neglecting shear deformation, the strain due to a small deflection as a result of a concentrated bending force F, can be written as [36]: 3h 1 8 — $(l-§(a+b)) - 5 (5.3) where h, l, a, b and 8 are as indicated in Figure 5.3. Two of the advantages of the cantilever beam technique are its ease and the possibility to apply both compressive and tensile strains. 5.3 Effect of electric field on piezoresistance The effect of electric field on piezoresistivity is studied by measuring the pressure response of diamond piezoresistors of the small grain type with resistivities of 0.29, 10 and 116 0cm, in the pressure and field ranges of 10 - 740 Torr and 10 - 250 V/cm, respec- tively. The resistance of the diamond piezoresistor is measured by maintaining a constant DC voltage bias and measuring the current as a function of pressure. Assuming uniform current flow in the diamond piezoresistor, the resulting I-V data is used along with sample dimensions to compute the resistance change and the electric field. The measured change of resistance with pressure for the 0.29, 10 and 116 Qcm samples are plotted in AR 9 R0 9 Figures 5.4 - 5.6, respectively. The insets show representative (i) SEM and (ii) Raman. Based on SEM the average grain size is approximately equal to 2 pm for all samples. The (Ft-R0)/R0 (x10'4) 102 Microstrain 0 10 20 30 2 I l l I I I -2 _ o 10V/cm o 61V/cm _ v103V/cm I 144V/cm A 251V/cm -6 _ -10 _ _ £2 (11) A131 (111) -14 — 8 :5,- 8' o — 4 0 '1 1 1 1 1 _ 1200 1400 1600 0 20 40 Raman Shift (cm'l) WV) '18 l 1 l l l I l l -100 0 100 200 300 400 500 600 700 800 Differential Pressure(torr) Figure 5.4 Room temperature pressure response measured using different electric fields. Insets: (i) SEM, (ii) Raman and (iii) zero strain IV. 103 Microstrain O 10 20 30 2 l I I " Nib. \\ A ‘ A A A A A A '2 _ .0 o ‘ ‘ A VA ‘5‘ - 15V/cm ' , _ o 20V/cm ' v 29V/cm ' . p I 59V/cm b _6 _ A 236V/Cm o . 3 . . o (1) ° . E —- . ’3 o a: '- 22,» -1o — . '" 0.4 ' (iii) ..‘2 A . ‘3 <2 :3 0.2 - -14 — 8 $13 . ‘ A A 0-0 ' 1 J 1 1 1 _ 1200 1400 1600 0 20 4o Raman Shift (cm'1) WV) 1 1 1 L 1 1 1 1 O 100 200 300 400 500 600 700 800 Differential Pressure(torr) Figure 5.5 Room temperature pressure response measured using different electric fields. Insets: (i) SEM, (ii) Raman and (iii) zero strain IV. Microstrain 0 10 20 30 2 f I r I r I -2 — _ o 23V/cm 0 55V/cm w? v 109V/cm 2 '6 " I 204V/cm 5 A 254V/cm O E ’3 0F 95 — 0.09- 9 (ii) 0.07 (1“) c: A 0.05' -14 — 3 3 0.03 O A — 0.01 : ._ 120014001600 -o.01 0 20 4o Raman Shift (cm'1) WV) -18 1 1 1 1 1 1 1 1 -100 0 100 200 300 400 500 600 700 800 Differential Pressure(torr) Figure 5.6 Room temperature pressure response measured using different electric fields. Insets: (i) SEM, (ii) Raman and (iii) zero strain IV. 105 lowest resistivity sample shows twinned grains. The Raman spectra show low graphitic content for all samples although the intensity of the diamond peak varies among samples. The pressure response of the lowest resistivity sample is nearly linear and changes little with electric field bias. For the high resistivity samples, linearity deteriorates and the sensitivity of the piezoresistor changes with applied electric field. Large fluctuations are observed especially for the 116 (2cm sample. Inset (iii) of Figures 5.4 - 5.6 show linear IV. In order to minimize the effect of the fluctuations on GF calculation, the data is first smoothed using a least square approximation and then used to compute GF. Figures 5.7 - 5.9 show the calculated GF for the three samples. Higher GF at lower strains is observed for the low resistivity sample. The zero strain resistivity, p0, and GF at 20 micro- strains, GF(20u£), are plotted as a function of applied field in the insets. Although GF of all samples seems to depend on electric field, the field effect differs from one sample to the other. GF of the lowest resistivity sample decreases with increasing electric field. As shown in the inset of Figure 5.7, in the field range of 10 - 251 V/cm, GF(20|.L£) and p0 decrease by 25% and 1.03%, respectively. The 10 and 1 l6 (2cm samples exhibit a different trend of GP dependence with electric field: first an increase with field then a decrease. Their GF(20u£) reaches maximum values of 37 and 35 at 29 V/cm and 109 V/cm, respectively. Their p0 decreases by 1.41% and 49.5% in the field ranges of 15-236V/cm and 23-255V/cm, respectively. A further consideration is the effect of electric field on linearity and offset. Although it is not possible to measure these parameters accurately using this simple membrane setup, the data in Figure 5.4 - 5.6 show that the highly doped sample has better linearity and offset. Unfortunately, as in the case of silicon [124] and polysilicon [51], GF 106 42 _ A 27 - 0.290 m _ ‘ 3 25 — 0.289 E 38 — 1% 23 - o (D - 0.288 9}, ‘ 21 — o? 34 — - 0.287 19 _ 100 200 300 30 _ E(V/cm) 26 - o 1OV/cm o 61V/cm _ v 103V/cm 22 - I 144V/cm A 251V/cm 18 r J l l 0 10 2O 30 40 Microstrain Figure 5 .7 Calculated GF as a function of strain for 88486. Inset: (I) GF at 20 microstrains and (O)zero strain resistivity. GF 107 100 - 10.79 - 9i - : 10.67 0? 6° ' . 0 I ' ' 10.61 0 100 200 300 ’ E(V/cm) 40 - o 15V/cm 20 I 0 20 V/cm ; v 29V/cm " I 59V/cm A 236V/cm O .. 0 10 20 30 40 Microstrain Figure 5.8 Calculated GF as a function of strain for 887082. Inset: (I) GF at 20 microstrains and (O)zero strain resistivity. GF 108 100 40 — A 1 110 80 - 8’ 20 _. - 90 g 1.1. ‘ Cl ' CD - - 70 ‘0’? 60 - 0 1 1 50 _ 100 200 300 40 - 0 23 V/cm 20 " 0 55 V/cm v 109V/cm " I 204V/cm 0 10 20 Microstrain 30 40 Figure 5.9 Calculated GF as a function of strain for 887084. Inset: (I) GF at 20 microstrains and (O)zero strain resistivity. 109 high doping decreases GF. 0 Exploring the field effect on GF The effect of electric field on GF is expected given the observed electric field effect on resistivity (section 4.4) and current flow (section 4.5). The effect of electric field on p0 is consistent with the finding that the resistivity decrease with electric field of films with comparable grain size is more prominent at lower doping level [125]. The mechanism for the observed change of GP with electric field is not clear and may be related to changes in current paths with electric field [126] if different paths have different GFs. Since the field effect on GF of polycrystalline diamond is reported for the first time, it is interesting to explore its possible relationship to the scattering in the GF data reported in the literature [7][9][10][11][17][l8]. As shown in Figure 5.10, there is a general trend of increasing GF with resistivity. However, some samples have comparable resistivity but different GFs. In addition to differences in film characteristics, this GF scattering, even from the same group of researchers [9][17][18], may be an indication that different field biases were applied to measure the resistance and/or piezoresistance. 5.4 Effect of temperature on piezoresistance The effect of temperature on CF is characterized in the temperature range of 22-80 °C for small grain type samples with different doping levels using a cantilever beam setup. Heating is achieved by mounting a heater to the cantilever clamp and allowing the temper- ature of the sample to stabilize. A K-type thermocouple is used to measure the tempera- 110 1 000 +EII>Dl> T (°C) Figure 5.11 Effect of temperature on GF. 70 80 113 300 {2cm [11] NA [7] 5 Gem 2 Qcm [10] '14 3 Gem 0.7 9cm 0.07 Qcm 0.01 9cm [10] 1 000 04OI>Cl+ 1n1111111 100 21 A A GF 1 111111] F DD 1 DC] 10 1111111 <1 I 10 100 T (°C) Figure 5.12 Summary of data reported in literature on the effect of temperature on GF. 114 doping lowers the dependence of GP on both field and temperature. Moreover higher doping improves linearity. Unfortunately, higher doping also decreases GF. Intra- and inter-grain GF measurements may help in understanding the field and temperature effects on GF. CHAPTER 6 Intra-grain Gauge Factor 6.1 Introduction The reported piezoresistive gauge factors of single crystal and poly-crystalline diamond are in the ranges of 500 - 3,500 [8] and 10 - 1000 [9][10][l 1], respectively. As the chemical vapor deposited (CVD) diamond is inexpensive, polycrystalline CVD diamond piezoresistive sensors can become commercially viable if their sensitivity can rival that of a sensor made from crystalline diamond. Low GF values of CVD diamond can be attributed to the presence of grain-boundaries (GBs). In this chapter the effect of GB on GF of B-doped polycrystalline diamond is studied by measuring intra- and inter- grain resistance as a function of strain. The extracted gauge factor values show that: (i) intra-grain gauge factor is comparable to single crystal diamond and (ii) the presence of grain-boundaries decreases the gauge factor and deteriorates linearity. 6.2 Measurement setup Four point probe resistivity measurements as a function of strain are performed on the large grain film described in section 3.3.2 with an average film resistivity of 0.28 Qcm. The sample is mounted on a beam of oxidized silicon using Omega’s C-C cement epoxy. 115 116 (O >. >VT mo '03 _ ago 02 GF=133 _ E -0.4 — 0.0 Q — 0 200 400 600 800 Microstrain | I I l I I I | I I I -1E-3 -6E-4 -2E-4 2E-4 6E-4 1E-3 KAI Figure 6.1 Small grain I-V at different strains and corresponding probe location. Insets: cantilever beam setup, relative resistance change vs. strain and extracted GF. 117 Strain is applied using a cantilever beam configuration, as shown in the inset of Figure 6.1. The cantilever beam setup is placed on top of the chuck of a microprobe station. Four tungsten probes connected to an HP4145B semiconductor parameter analyzer are used to measure I-V as a function of stress. The outer probes are used to apply current and the inner ones to measure voltage, eliminating the effect of contact resistance. A video camera and VCR are used to record the microscopic photo of the actual probe location. The probes are placed so that the shortest current path is in the direction of longitudinal strain. The longitudinal GF is defined by: R‘Ro l R. '27 GF, = where R0 and R are the resistances at stain values of zero and 8,, respectively. The resistance at a given strain is determined as the slope of the least square linear fit to the measured I-V data at that strain. The average longitudinal strain is measured by mounting a commercially available wire strain gauge on top of the diamond film. GF is determined as the slope of the least square linear fit to the a}: vs. strain curve. 0 6.3 Gauge factor for different current path morphologies I-V data measured at different regions of the sample are plotted in Figures 6.1 - 6.3. The probe location is indicated by the white dots on the microscope photos shown in the inset. The extracted 9R5 vs. strain curve and resulting GF are also shown at the inset. Figure 0 6.1 shows the piezoresistive response when the shortest path between the voltage probes 118 0.5 — 0.4 '- 0.3 '- 0.2 — 0.1 — 0.0 - _ o ’ -02 ._ I; 12 . _ mo 8C -0.3 —- 3:3 4: - c'r 0. -0.4— V 4 -_ " 0 200 400 600 '0-5 '" Microstrain I I I | | | I I I L J -1E-3 -6E-4 -2E-4 2E-4 6E-4 1E-3 |(A) Figure 6.2 Large grain I-V at different strains and corresponding probe location. Inset: Relative resistance change vs. strain and extracted GF. 119 . . AR . . . . crosses many small grains. The resulting R— vs. strain curve rs nonlinear and a best line fit 0 gives a GF of 133. The data shown in Figure 6.2 is obtained when the voltage probes are placed within a large grain and separated by a single GB. GF value of 283 is obtained. To investigate the effect of GB on GF, the probes are connected such that their shortest path does not cross any GB, as shown in Figure 6.3 The strain curve is linear and the extracted CF is 4062. Assuming that the dominant current path is the shortest path between the current probes for all strains, the I-V data in Figure 6.3, where the voltage probes are placed within a single grain, describe intra—grain current flow. Consequently, the relatively high GF of 4687 corresponds to GP inside a grain. This is consistent with the high GF range of 500- 3500 reported for single crystal homoepitaxial and synthetic diamond [8]. Although it is not clear whether the boundary crossing the shortest path in Figure 6.2 is a GB or a twin- boundary, its presence seems to result in lower GF and poorer linearity. The GB effect on linearity is worse when the number of GBs that cross the shortest current path increases, as seen in Figure 6.1. The low strain measurements seem to be scattered, especially for Figures 6.1 and 6.2, probably due to inaccurate strain values. The measurements in Figures 6.1 - 6.3 show that intra-grain piezoresistive response has higher sensitivity and linearity than inter-grain. Since the crystal structure of the grain does not change with deposition method and conditions, intra- grain GF is expected to be independent of deposition parameters. Thus intra-grain CV D diamond piezoresistors are expected to be more reproducible and reliable than inter-grain piezoresistors. 0.6 0.5 0.4 0.3 0.2 120 | N A A A A - - A A A A A Microstrain llllllllll -1 E3 ~6E-4 -2E-4 2E—4 6E—4 1E-3 |(A) Figure 6.3 Intra-grain I-V at different strains and corresponding probe location. Inset: Relative resistance change vs. strain and extracted GF. 121 It is worth mentioning that the zero strain resistivities obtained from the four-point- probe measurements for the probe configurations in Figures 6.1-6.3 are 0.103, 0.272 and 0.034 (2cm, respectively, and that the average film resistivity is 0.28 9cm. It was found that the above GF results can lead to important information related to resistance of grain and grain-boundaries. Assuming that conduction in B-doped polycrystalline diamond is mainly through 635, the resistance of the shortest path between the voltage probes can be witten as a series combination of contribution of grains, Rg, and GBs, Rb: R = Rb + Rs (6.1) Using this formula the relative change of path resistance with strain can be written as: R‘R0~( 1 )Rg-Rgo ( 01 )Rb-Rbo (62) R0 ~1+01 R5,0 1+0: Rb0 ' Rbo where a = R— . Similarly, starting from path length: 80 L = Lb + Lg , (6.3) where L8 and Lb are the part of the path through grains and GBs, respectively, the relative change of path length is given by: L - L L - L L — L e=__0=( 1 )8 80+( a ) b w (6.4) L0 1 +3 L30 1 + B Lbo where B = L_bo . For uniform strain distribution, since Lg >>> Lb and B z 0 , equation 80 (6.3) becomes: 122 L —L g 80 8 z = e , (6.5) LgO 8 where 8g is the intra-grain strain. Based on equations (6.2)-(6.5): R ’ R0 1 1 01 8b where 8 = —. 88 As in polysilicon, the disordered structure of GB is expected to result in very low GFb as compared to GFg [51]. In this case, equation (6.6) gives: Plugging in GFg = 4062 and GF = 233. 133 yields: Rho GFg-GF a=—z———— R80 GF = 13, 29 (6.8) for the data in Figure 6.2 and 6.1, respectively. The above result provides evidence that 683 have higher resistance than grains and that GB contribution to path resistance increases as more GBs are crossed. The larger GB resistance as compared to grain resistance is consistent with the assumption that current flow in the film is dominated by carrier transport from one grain to the other through GBs (Equation 6.1). The high GB resistance could be due to GB potential barriers, as suspected from inter-grain I-V [126], and/or to Boron desegregation at GB, as reported in [128]. It is important to emphasize that the derived ratio of GB to grain resistance is subject to the assumption that strain distribution along the current path is uniform. As inhomogeneous internal strain distributions were reported for polycrystalline diamond 123 [63], direct measurement of the strain along the current path shown in Figure 6.1 - 6.3 is needed to fully confirm the results of Equation 6.8. 6.4 Summary In this chapter intra-grain GF is measured for the first time and its value, 4062, is comparable to that of single crystal diamond. Intra-grain piezoresistive response shows better linearity than inter-grain and is expected minimize scattering in reported GF data attributed to differences in film deposition and/or processing conditions. Assuming that (i) strain distribution is uniform in CVD diamond, (ii) GF of GB is zero and (iii) current flow is dominated by paths that cross GBs, a simple model is used to determine the effect of GB on GF. Based on this model, the ratio of GB to grain resistance is computed and shown to increase with the number of GBs in the current path. The high GB resistance as compared to grain resistance provides for the first experimental evidence that the role of GBs in electrical conduction in B—doped polycrystalline diamond is to limit current flow. CHAPTER 7 Summary and Future Research 7.1 Introduction The primary objective of this research is to characterize the piezoresistive gauge factor of B-doped CVD diamond. In order to achieve this goal, resistivity and sensor characterization are performed on films deposited on insulating substrates. Resistivity characterization covers the effect of substrate conduction, anneal and electric field on resistivity. It also included intra- and inter-grain I-V measurements. Sensor characterization addresses the effect of electric field and temperature on GF of B-doped CVD diamond. Intra- and inter-grain GF measurements are performed. 7 .2 Summary of Contributions 7.2.1 Results reported for the first time 0 Intra- and inter-grain measurements Four-point probe I-V across many grains, potential profile across five grains and two-point-probe I-V within a single grain and across an individual GB reveal non-uniform current flow in B-doped polycrystalline diamond. I-V measurements across individual 124 125 grain boundaries with different widths suggest the existence of grain boundary potential barriers. Intra-grain piezoresistive response measurements show excellent linearity and a GF of 4687, which offers sensitivity in the same range as single crystal diamond at a much lower cost. Since intra-grain conduction is not affected by grain boundaries, intra-grain GF is expected to be less sensitive to electric field and film quality than inter-grain GF. A simple gauge factor model is derived as used along with intra-and inter-grain GB data to compute the ratio of grain-boundary to grain resistance. The higher GB resistance as compared to grain resistance provides experimental evidence that current follows inter- grain paths as opposed to parallel grain-boundary paths. 0 Effect of electric field on resistivity and CF The pressure response of B—doped chemical vapor deposited (CVD) polycrystal- line diamond piezoresistors is characterized using an experimental setup consistent with commercially available differential pressure sensors. The change of resistance due to pres- sure is measured over a range of 10-740 Torr for samples with resistivities of 0.29, 10 and 116 Qcm. The results show that pressure response is affected by the electric field applied to measure the resistivity. Higher doping minimizes this field dependence and seems to improves linearity at the cost of lower sensitivity. The study of the electric field on resistivity reveals that resistivity decreases with increasing electric field and that the onset and rate of resistivity decrease varies with dop- ing, temperature and grain size and orientation. The absence of field effect in B-doped homoepitaxial diamond suggests that the field effect is related to the presence of grain- 126 boundaries. 0 Effect of anneal on resistivity The anneal study reveals that the resistivity of B-doped polycrystalline diamond decreases after anneal at 600°C in N2 for 10 min. The anneal effect, is found to decrease with doping and to vary with film quality. 7 .2.2 Other significant results 0 A 4” wafer HFCVD system is built and a special temperature control scheme is implemented to use the heat generated by the 4.5 x 5 inch2 filament array for substrate heating without degrading diamond quality. 0 The finding that undoped films grown on conducting Si are conducting whereas those grown on oxidized Si are insulating restricted the samples used in this study to those grown on oxidized Si. 0 Temperature measurements reveal that GF changes from being constant with temperature at low resistivity, to increasing with temperature at intermediate resistivity and decreasing at high resistivity. 7.3 Future Research Although this study improves current understanding of CVD diamond piezoresis- tance, more advances are need in the following areas in order to help commercialize dia- mond piezoresistors: (i) determine the exact role of GBs in electrical and mechanical properties, 127 (ii) improve consistency of diamond quality and enhance doping uniformity, (iii) fabricate a pressure sensor prototype and use it to measure a complete set of performance specifications for CVD diamond sensors, (iv) extend the temperature range for sensor characterization, (v) evaluate sensor reliability and repeatability, and (vi) evaluate sensor performance in industrial environments. 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