LIFETIME ESTIMATION OF POWER MOSFETS By Petros G. Taskas                A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of   Electrical Engineering  Master of Science  2016 ABSTRACT LIFETIME ESTIMATION OF POWER MOSFETS By Petros G. Taskas In this document a theory is proposed that all power MOSFETs will go through three regions of operation during their lifetime with respect to the threshold voltage. Equations are presented for this proposed theory and analytical assumptions are made. The first region that will be examined is when the MOSFET is healthy and all parameters of the MOSFET are kept constant. The second region of operation is when the gate oxide begins to degrade and the threshold voltage begins to dip. The third region of operation is when Fowler-Nordheim tunneling begins to dominate the threshold voltage of the device and the threshold voltage begins to continuously rise.  An accelerated aging experiment was conducted to try and prove the proposed theory. Adverse effects were seen in the devices tested and the regions of operation were modified in order to account for the large shift in the threshold voltage. Here the proposed equations were reformulated to account for the different trapped charges in the device throughout its lifetime. The equations formulated differ from the proposed theory and are presented as new findings for the different regions of operation for power MOSFETs. Data was also collected to calculate the turn on resistance and these findings will be published at a later date. A final conclusion is given based on the data collected and the different effects seen that account for the threshold voltage change in power MOSFETs. This new theory may also be applied to insulated-gate bipolar transistors (IGBTs) and various other power MOSFETs. iii ACKNOWLEDGEMENTS  I would like to thank my advisor Dr. Peng for his continuous guidance and support during my time at Michigan State University. innovative knowledge in the field has been a great help to me throughout my research assistantship from my undergraduate years to the completion of my Masters program.  guidance, support, and  I would like to thank my committee members Dr. Sepúlveda and Dr. Wang for their help and guidance during my thesis research. I would like to thank Dr. Albrecht for his support and willingness to sit down with me to talk about the numerous effects and concepts in MOSFETs. This helped me a great deal with my conclusion. I would like to thank my parents Georgios and Fani, my brother Athanasios, and my sister Stefani for their continuous love and support throughout my six and half years of university. Thank you for pushing me to do my best. I would like to thank my grandmothers Aspasia Taskas and Stavroula Maggos for their continuous love and support. I would like to thank Jaclyn Konopka for her support and help editing my thesis. I would also like to thank the Hattar family, parents Fares and Khalida, brothers Zaid, Murad, Odai, and Machail, for being with me throughout the years. Thank you for becoming a part of my family. You are all invaluable to me. iv I would like to thank my lab mates for their help throughout my time in the research lab and I would like to thank Ujjwal for the proposed theory in chapter 3. I would like to also thank Ameer Janabi for discussing numerous concepts with me. Lastly I would like to thank my friends Annie Elshoff, Aaron Brakoniecki, Terry Pharaon, Po-yuan Han, Sierra Santia, and Junseo Jung for their support and guidance through the numerous obstacles I encountered during my time at Michigan State University. Your help was greatly appreciated. v TABLE OF CONTENTS  LIST OF TABLES ........................................................................................................... vii LIST OF FIGURES ........................................................................................................ viii Chapter 1  Introduction to Power MOSFETs ............................................................... 1 Chapter 2  Power MOSFET Background ..................................................................... 3 2.1     Power MOSFET ............................................................................................... 3 2.1.1 V-MOSFET Structure ................................................................................. 3 2.1.2 VD-MOSFET Structure .............................................................................. 4 2.1.3 U-MOSFET Structure................................................................................. 6 2.2     Failures Due to Thermo-Mechanical Stress...................................................... 7 2.2.1 Bond-wire Cracking and Liftoff ................................................................... 8 2.2.2 Die-attach Degradation and Failure ......................................................... 10 2.3     Electrical Failures of Power MOSFETs .......................................................... 11 2.3.1 Gate Oxide Breakdown ............................................................................ 11 2.3.2 Maximum Drain to Source Voltage Breakdown ....................................... 12 Chapter 3  Proposed Lifetime Theory ........................................................................ 14 3.1     Introduction ..................................................................................................... 14 3.2 General Theory for Identification of Key Operating Regions in Power MOSFETs ....................................................................................................... 16 3.3     Variation of Failure Precursors Based on Proposed Theory ........................... 18 3.4     Variation of Threshold Voltage ....................................................................... 19 3.5     Analytical Interpretation .................................................................................. 21 3.6     Conclusion ...................................................................................................... 23 Chapter 4  Accelerated Aging Process ..................................................................... 24 4.1     Test Setup ...................................................................................................... 24 4.1.1 Power MOSFET Test Circuit .................................................................... 25 4.1.2 Test Circuit Equipment............................................................................. 25 4.1.3 Data Acquisition Equipment ..................................................................... 26 4.2     Test Procedure ............................................................................................... 28 4.2.1 Normal Operation of the Power MOSFET ................................................ 28 4.2.2 Aging the Power MOSFET ....................................................................... 28 4.2.3 Data Acquisition ....................................................................................... 29 4.3     Thermomechanical Stress Isolation from Electrical Stresses ......................... 31 4.4     C-V Measurement .......................................................................................... 32 4.5     Annealing........................................................................................................ 32 vi  Chapter 5  Evaluation of Test Data............................................................................ 34 5.1     Test Data ........................................................................................................ 34 5.2     Critical Evaluation ........................................................................................... 38 5.2.1 Introduction .............................................................................................. 38 5.2.2 Evaluation with Respect to the Proposed Theory .................................... 39 5.2.3 Evaluation with Respect to the more Probable Solution .......................... 41 5.3     Future Work .................................................................................................... 48 5.4     Conclusion ...................................................................................................... 50 BIBLIOGRAPHY ........................................................................................................... 52  vii LIST OF TABLES  Table 5.2.1: MOSFET Switching Table ........................................................................ 43 viii LIST OF FIGURES  Figure 1.1: Single Phase Inverter using MOSFETs ......................................................... 1 Figure 2.1.1: V-MOSFET Structure ................................................................................. 4 Figure 2.1.2: VD-MOSFET Structure ............................................................................... 5 Figure 2.1.3: U-MOSFET Structure ................................................................................. 7 Figure 2.2.1: von-Mises Distribution ................................................................................ 9 Figure 2.2.2: Bond-wire Liftoff ......................................................................................... 9 Figure 2.2.3: Die-attach to Copper ................................................................................ 10 Figure 2.3.1: High Resolution Transmission Electron Micrograph ................................. 12 Figure 2.3.2: Snapback Breakdown .............................................................................. 13 Figure 3.2: Effects of Gate Oxide Degradation (a) Formation of Localized Conduction Path. (b) Enhanced Electron Trapping .......................................................................... 18 Figure 3.5: Variation of Threshold Voltage with Aging................................................... 22 Figure 4.1.1: Test Circuit Configuration ......................................................................... 25 Figure 4.1.2: Test Circuit ............................................................................................... 26 Figure 4.1.3: Test Setup with DAQ ................................................................................ 27 Figure 4.2.3: Stressing and Data Acquisition Process................................................... 30 Figure 5.1.1: MOSFET Threshold Voltage Due to Aging ............................................... 36 Figure 5.1.2: MOSFET Gate Capacitance Due to Aging ............................................... 37 Figure 5.2.3: Hole Trapping, Annealing, and Reversible Compensation ....................... 44   1 Chapter 1 Introduction to Power MOSFETs A power metal-oxide-semiconductor field-effect-transistor (MOSFET) is a type of electric switch that can be programmed through a digital signal processor to turn on and off. Power MOSFETs also have different voltage and current ratings, which can be used for many applications. Power MOSFETs are used in a wide variety of applications from home Do It Yourself projects to commercial projects. Some of the major uses for power MOSFETs are inverters, buck and boost converts as well as AC/AC and DC/DC converters. Figure 1.1 shows a single phase inverter using MOSFETs. Here Vd is the drain to source voltage and Vo is the output voltage.   Figure 1.1 Single Phase Inverter using MOSFETs 2 The different topologies mentioned above can be applied to and are not limited to hybrid and fully electric vehicles, solar panel systems, induction heating, electroshock weapons, and household appliances such as refrigerators or electric ovens. Today these devices are becoming more and more prominent in many different applications as can be seen with vehicles transitioning more towards hybrid, electric, and autonomous vehicles. A major issue raised by power MOSFETs increase in use is their reliability and which trends and parameters should be taken into consideration in estimating remaining lifetime. These trends in the different parameters that can be measured may correlate to the reliability of the device. For example, temperature monitoring of the device is important to make sure that it does not exceed the rating of the device specified by the data sheet. In the industry, the reliability of these devices is very important because of the important applications they are used in. For instance, when purchasing a hybrid or electric vehicle, the consumer will not want to go back to the dealership every thousand or five thousand miles driven to get the inverter replaced because the power MOSFETs have failed again. It is therefore vital to study MOSFET reliability, trends, and parameters so that they can be safely and efficiently used in important daily appliances. Not only can the failure or malfunction of power MOSFETs cause the inverter to get damaged but it can cause other electric components such as the electric motor to fail without the correct protection and will ultimately cause distrust between the consumer and the product. Monitoring key parameters such as threshold voltage, is a must to make inverters and other topologies more reliable and efficient. 3 Chapter 2 Power MOSFET Background The following is a general description of the main properties and models of power MOSFETs. The MOSFETs are examined are the V-MOSFET, VD-MOSFET, and the U-MOSFET all from [8]. Different failure profiles of the devices are also explained.  2.1  Power MOSFET 2.1.1 V-MOSFET Structure The V-MOSFET structure was developed in the 1970s. This structure has the  source separated from the drain by a P-base region. As seen in figure 2.1.1 [8], the gate is a V-groove and goes through the P-base region into the N-drift region. The oxide is on the surface of the V-groove. Without any bias applied to the gate,    becomes reverse biased if the drain electrode has a positive bias applied to it. Next we have  , which is overlapping the source electrode over the junction. It is noted that   is short circuited due to this overlap. When a positive gate bias is applied to the gate, it attracts electrons under the gate oxide to the semiconductor surface which provides a path for current flow from the source and drain of the MOSFET. Here the internal resistance of the MOSFET restricts the maximum allowable current the MOSFET can carry. The V-MOSFET structure is no longer used due to various manufacturing difficulties. 4  2.1.2 VD-MOSFET Structure In our experiment the VD-MOSFET is the MOSFET type that is used. The VD abbreviation stands for vertical-diffused. In this MOSFET the  substrate is heavily doped and the P-base is fairly weak. Figure 2.1.2 shows the VD_MOSFET structure. If no bias is applied to the gate, a high positive DC link voltage can be applied across the drain and source to form  . When this junction is formed between the P-base region and the N-drift region, it becomes reverse biased. Here the N-drift region is lightly doped. When a positive bias is applied to the gate, the current starts to flow across the drain and source only after a positive drain voltage is applied. When these voltages are applied an inversion layer can be formed, which will provide a path to transport Figure 2.1.1 V-MOSFET Structure 5 electrons. This inversion layer is created in the P-base region. As the electrons move through the source region into the channel they then enter the N-drift region. Then the electrons are transported through the JFET (Junction Field-Effect Transistor) region. When current flows in the JFET region, the internal resistance begins to increase. So the gate width has to be optimized in order to try and minimize the internal resistance as current flows. The doping concentration of this region can also be doped more heavily to try and reduce this resistance as the current flows through. As the current flow continues on its path, the electrons will again enter the N-drift region, only this time below . The current in this region is nonuniform which creates a much larger resistance in the in the drift region. To reduce the effect of the JFET region, trench-gate power MOSFETs started to be developed.  Figure 2.1.2 VD-MOSFET Structure 6 2.1.3 U-MOSFET Structure Etching trenches in silicon began in the 1980s. This technique was used to create the U-MOSFET which is also known as a trench-gate MOSFET. Figure 2.1.3 [8], shows the structure of the U-MOSFET. It can be seen that the trench that surrounds the gate, spans from the source which is doped with  through the P-base region into the N-drift region. The oxide is formed in the trench area, throughout the gate region. As with the VD-MOSFET, if there is no bias applied to the gate, this structure can also support a high positive drain voltage. In figure 2.1.3 the junction,  , is formed between the N-drift region and the P-base region which becomes reverse biased. Although the N-drift region is fairly thick, is lightly doped. In order for drain current to begin to flow, a positive bias must be applied to the gate with a positive drain voltage. Once these conditions are met the current will begin to flow. The current first flows through the P-base region because of the inversion layer that is formed in the channel. Once the electrons move through the P-base region they will enter the N-drift region. In the U-MOSFET structure there is no JFET region so that when the current spreads throughout the N-drift region, the internal resistance becomes greatly reduced compared to the VD-MOSFET. The widths of the N-drift regions will be taken equal to each other in order to show that when comparing the VD-MOSFET to the U-MOSFET, the U-MOSFET has the lower internal resistance. This resistance was created to be smaller because in the VD-MOSFETs structure, the internal resistance was greater than the turn-on resistance of the device.   7  2.2  Failures Due to Thermomechanical Stresses As the temperature begins to rise in these devices, it starts to alter many physical properties which can change the physics of the devices themselves. The mechanical parameters that can change the electrical parameters of the device are bond-wire cracking, bond-wire liftoff, die-attach degradation, and die-attach failure. These parameters can change the turn on resistance which can affect the electrical parameters of the device. Power cycling which leads to thermo-cycling is the main cause of these failures.  Figure 2.1.3 U-MOSFET Structure 8 2.2.1 Bond-wire Cracking and Liftoff Bond-wire cracking and liftoff are the most prominent areas of failure for power devices [19]. Bond-wires degrade over time before these failures start occurring and over time will cause a failure in the device. This is due to the applications they are used in and the environments they are placed working in. For example, in hybrid vehicles, when left out in the sun on a hot day, the whole inverter system gets even hotter than the ambient outdoor temperature is because the heat is trapped. So if one was to turn the car on and have the cooling system kick on full power to cool off the devices, that temperature fluctuation could start to cause this cracking or liftoff of the bond-wires. The main cause of the bond-wire liftoff is how the junction temperature fluctuates. If the junction its self is fluctuating from 20° C to 150° C or higher and it keeps repeating, then this type of failure is more likely. Also when systems are power cycled or thermo-cycled the junction temperature is most likely to fluctuate. In order to try and keep this failure from happening a cooling system must be integrated and used to control the junction temperature of the device. The device case temperature should also be monitored when cooling the device off. If cooling happens to fast causing the temperature of the device to go lower than it needs to go, the device then has to heat up causing the cooling system to shut off. This can lead to a temperature fluctuation process in which the device heats up too much and then gets cooled off too fast to a temperature lower than needed which would cause the bond-wires to crack or liftoff. Figure 2.2.1 from [20] shows the von-Mises distribution which leads to the bond-wire cracking.  9  A cooling system must have a control in which it moderately cools off a device and tries to keep the temperature within a small area of fluctuation in order to keep bond-wire cracking or liftoff to a minimum. Liftoff more prominently occurs when the temperature of the device is exceeded for long periods of time which can cause the solder on the bond-wire to melt then causing the wire to liftoff. In a test done in [20] bond-wire liftoff due to bond-wire cracking can be seen in figure 2.2.2.  Figure 2.2.1 von-Mises Distribution Figure 2.2.2 Bond-wire Liftoff 10 2.2.2 Die-attach Degradation and Failure Die-attach degradation and failure also occur due to thermomechanical stresses of the device. As the device is heated slowly and the temperature keeps rising, this form of failure is likely to happen [21]. This failure is not as likely to happen as bond-wire liftoff. Die-attach degradation causes the overheating of the gate oxide. The gate oxide can subsequently burn and lead to an immediate failure in the device. As can be seen in figure 2.2.3 [22], as the die-attach solder begins to heat up it does not dissipate heat the same way copper does. So as it heats up the properties of the materials will heat up differently causing stress and the die-attach to start degrading and failing. The stress directions on the materials can also be seen in figure 2.2.3. There are shear stresses on the die-attach material and peeling stresses on the copper. This helps demonstrate how exactly the die-attach will begin to fail due to the stresses.   Figure 2.2.3 Die-attach to Copper 11 2.3  Electrical Failures of Power MOSFETs The three types of electrical failures that will be briefly discussed are the gate oxide breakdown, maximum drain to source voltage breakdown, and maximum drain current breakdown.  2.3.1 Gate Oxide Breakdown Gate oxide breakdown can be caused immediately or overtime. For the gate oxide to break down immediately, a very high voltage applied across the gate and source would be needed. This voltage would have to exceed the maximum rating of the device by up to three or four times. The immediate breakdown due to overvoltage is unlikely to happen in a real system due to protection circuitry from the gate drive. On the other hand, over time the gate oxide will degrade due to potential over stresses on the device. This can happen in a normally operating device. Every time the MOSFET is switched on and off the voltage applied is an electrical stress to the gate. This means over time the oxide will degrade. When the oxide is degrading this means that the thickness of the dielectric material of the gate is decreasing throughout its life. As the oxide diminishes, this can cause an immediate failure of the oxide once it becomes too thin. After the oxide has degraded completely or it has broken after getting thin, the MOSFET will immediately fail. Once the MOSFET fails due to the gate oxide degradation, the gate of the MOSFET will be shorted to the drain and source causing the gate drive to start supplying more current and no voltage. At this point control of the gate is lost and the MOSFET is considered dead. Some MOSFETs have thicker gate oxide than others 12 causing that gate to be stronger. This should allow the MOSFET to live longer since there is more gate oxide to degrade before it fails. Figure 2.3.1 [23] shows a high resolution transmission electron micrograph of a MOSFET before the oxide has degraded. Once this oxide has been fully degraded it will cause a short in the MOSFET.   2.3.2 Maximum Drain to Source Voltage Breakdown All power MOSFETs have a maximum drain to source voltage. This is considered the breakdown voltage of the device. If this voltage is exceeded, then it will cause the MOSFET to enter the breakdown region. The drain to source terminal would then break because the channel cannot sustain the voltage. All MOSFETS have different breakdown voltages. There are curves such as the one shown in figure 2.3.2 [24], that Figure 2.3.1 High Resolution Transmission Electron Micrograph 13 allow you to see the drain to source breakdown voltage with respect to the drain current and the gate to source voltage. This figure displays a snapback breakdown effect.    Figure 2.3.2 Snapback Breakdown 14 Chapter 3 Proposed Lifetime Theory 3.1  Introduction This chapter will explain why and how gate oxide degradation plays a prominent role in power MOSFET failure. A general theory has been proposed that power MOSFETs go through three operating regions as gate oxide degradation occurs. In region I, the gate oxide is not aged and considered to be fresh and healthy. In region II, the gate oxide has started aging and the degradation of the oxide initiates. In region III, Fowler-Nordheim tunneling of electrons begins to occur in the gate oxide. The physics behind gate oxide degradation will be explained and shown with analytical equations that show voltage throughout the three with the gate oxide degrading as it ages helps to determine the health of power MOSFETs. This also provides an advanced warning for power MOSFET failures. Lastly, this pinpoints the instant of failure initiation due to oxide degradation and point of critical failure in power MOSFETs. Power MOSFETs are a crucial component of power converters used in high voltage and high power applications. Since the reliability of power MOSFETs is critical to the operation of these power converters, effective forecasting of power MOSFET failures is essential. Prognosis can be defined as a forecast of a likely failure with the help of a 15 failure precursor- an indicator of impending failure [1]. The key failure precursors of power MOSFETs with aging identified in the literature are: Threshold voltage, VTH [2]-[5], shift in threshold voltage [5], and switching time variations [6]. Aging and gate oxide degradation are very closely related and plays a prominent role in power MOSFET failure. However, the variation of the threshold voltage with aging due to oxide degradation is not consistent across all literature. The threshold voltage (VTH) of a power MOSFET is reported to increase with aging [3]-[4], whereas other studies have found -[6]. To explain this difference in failure precursor variation with gate oxide degradation, the general theory is proposed that power MOSFETs go through three distinct operating regions as gate oxide degradation occurs over time. The identification of three operating regions MOSFETs.  1) Region I (Normal operation region):  This region corresponds to the operation of power MOSFETs before the initiation of gate oxide degradation. The failure precursors remain constant in this region and do not affect the MOSFET which will be re  2) Region II (Operation after initiation of gate oxide degradation): The gate oxide, like any other dielectric, degrades over time. This region corresponds to the operation of power MOSFETs after the initiation of gate oxide degradation. In this case, the MOSFET aging process has begun and started to take an 16 effect and the failure precursors have begun   3) Region III (Operation after initiation of Fowler-Nordheim tunneling of electrons into the oxide): With gradual gate oxide degradation, the oxide field increases to a point where Fowler-Nordheim tunneling [9] of electrons occurs in gate oxide and the failure precursors start to show accelerated aging characteristics. The power MOSFET   3.2  General Theory for Identification of Key Operating Regions in Power MOSFETs Gate oxides, like any other dielectric, when stressed under an electric field degrades over time and eventually breaks down. The failure precursors of Power MOSFETs vary with gate oxide degradation. The identification of key operating regions of power MOSFETs due to gate oxide degradation can be explained with the existing physics of gate oxide degradation.  I. Region I (Normal operation region) A fresh oxide has a finite dielectric thickness. The gate oxide is assumed to maintain its thickness over a long period of time after which it slowly begins to degrade. The failure precursors remain constant in this operating region as the gate oxide degradation and aging have not initiated yet. 17 II. Region II (Operation after initiation of gate oxide degradation) Even with a very low field stress, the degradation of the gate oxide begins to occur over time. The thermo-mechanical or (E) model explains the breakdown of SiO2 oxide in terms of field enhanced bond breakage under low field stress [10]-[11]. The Si-Si bond breakage leads to formation of traps which create localized conduction paths in the oxide. The increase in localized conduction paths in the oxide can be considered equivalent to thinning of the gate oxide, as indicated by t, a reduction of gate oxide thickness in figure 3.2ainto account the reduction of gate oxide thickness due to localized conduction paths as a result of charge trapping. The effective gate oxide thickness does not necessarily indicate the uniform reduction of overall gate oxide thickness; rather it indicates the localized reduction of gate oxide thickness due to formation of localized conducting links in the gate oxide.  III. Region III (Operation after Initiation of Fowler-Nordheim tunneling of electrons into oxide) With continuous reduction of gate oxide thickness, the oxide field begins to increase. When the oxide field is in the range of 5-7 MV/cm [12]-[14], Fowler-Nordheim (FN) tunneling of electrons dominates in the oxide [11]-[13], [15]-[16] which contributes to hole generation and trapping. As a result, enhanced electron trapping occurs in the oxide as shown in figure 3.2b and the nature of the trapped charges is negative [4], [15]-[18].  18     3.3  Variation of Failure Precursors Based on Proposed Theory The key failure parameter indicators identified in the literature are: threshold voltage, shift in threshold voltage, and switching time variations. Only threshold voltage will be examined in great detail. The three operating regions henceforth are referred to as Region I, Region II and Region III. To review the structure of a Power VD-MOSFET, refer to Figure 3 [8].   Figure 3.2 Effect of Gate Oxide Degradation. (a) Formation of Localized Conduction Path.  (b) Enhanced Electron Trapping 19 3.4  Variation of Threshold Voltage The threshold voltage of a MOSFET is the voltage at which the inversion of the channel occurs in the MOSFET. The threshold voltage of a power VD MOSFET, neglecting the trapped positive charge, is given by [8],   (3.4.1)  where k ), T is the absolute temperature,  is the doping concentration of P-base region,  is the intrinsic carrier concentration for silicon, q is the charge of an electron (),  is the dielectric constant of semiconductor, and   is the specific oxide capacitance. The intrinsic carrier concentration  in silicon is a function of temperature given by   (3.4.2) and the specific gate oxide capacitance  is given by,   (3.4.3) where is the dielectric constant for silicon dioxide gate material () and is the gate oxide thickness. For threshold voltage measurements at a particular 20 temperature, the threshold voltage is a function of gate oxide capacitance alone, or alternatively the gate oxide thickness, as intrinsic carrier concentration in (3.4.2) becomes constant.  1) Region I In operating region I, the gate oxide is assumed to be fresh without any degradation. Since the gate oxide thickness remains the same, the threshold voltage given by (1) is constant in this operating region.  2) Region II In operating region II, the initiation of oxide degradation leads to thinning of gate oxide or alternatively, an increase in gate capacitance. The oxide thickness is represented by equivalent gate oxide thickness  to take into account the reduction of gate oxide thickness in equation (3.4.1)   (3.4.4)  The second term of the threshold voltage in equation (3.4.4) can be ignored as it is small compared to its first term [8]. The threshold voltage decreases with reduction of gate oxide thickness.   21 3) Region III In operating region III, the oxide field reaches the FN threshold allowing a path for FN electrons to flow. It leads to enhanced electron trapping in the oxide, which can be taken into account by introducing negative trapped charge   in (3.4.1) as   (3.4.5)  The threshold voltage in equation (3.4.5) begins to increase because of trapped charges. The gate oxide continues to degrade but the threshold voltage increases as trapped charges become dominant in equation (3.4.5).  3.5  Analytical Interpretation Figure 3.5 shows the variation of threshold voltage in power VD-MOSFET in three operating regions based on analytical expressions (1)-(5).Initially, the gate oxide is fresh and the power MOSFET is said to be operating in Region I. The threshold voltage is constant in this region as the gate oxide thickness is assumed to remain constant in equation (3.4.1). After the initiation of gate oxide degradation, the power MOSFET is said to be operating in region II where the threshold voltage decreases/dips due to thinning of gate oxide as given by equation (3.4.4). The decrease in threshold voltage continues until the gate oxide degrades to a thickness permitting an oxide field of 7 MV/cm at which the FN tunneling starts to occur.  22   The equivalent oxide thickness corresponding to an oxide field of 7 MV/cm for initiation of FN tunneling is nearly 285 Å. After the initiation of FN tunneling, the MOSFET is said to be operating in Region III where the threshold voltage begins to increase/rebound as given by equation (3.4.5). In order to show the effect of trapped charges, a fixed oxide thickness of 285 Aº is used in equation (3.4.5) while sweeping the trapped charges. The s not mean that the power MOSFET is nonoperational; rather it indicates that the power MOSFET has stage warning an imminent failure of a power MOSFET. The device could be non-operational at any instant signifying complete loss of gate control. It should be pointed Figure 3.5 Variation of Threshold Voltage with Aging 23 out that the theory explains both the rebound behavior in [3]-[4], and the dip and rebound behavior in [5]-[6] for threshold voltage in power MOSFETs.  3.6  Conclusion This is a proposed general theory that power MOSFETs go through three operating regions over the course of gate oxide degradation. It has been shown that the variation  and the threshold voltage in these operating regions is helpful to: i) determine the health of power MOSFETs, ii) provide advance warnings for MOSFET failures, and iii) pinpoint the instant of failure initiation and critical failure in power MOSFETs. The theory presented can be extended to IGBT failure as well. 24 Chapter 4 Accelerated Aging Process This chapter will focus on the testing setup and testing process of the Power MOSFET. The testing setup will consist of what MOSFET was used, the components in the testing circuit, and the equipment that was used to measure and monitor the different voltage, current and temperature parameters throughout the entire test. The testing process will go through in detail the stressing circuit and the normal operation circuit and how they are both isolated from each other. The isolation of applied thermomechanical stresses from electrical stresses will also be explained and the reasons behind the importance of this isolation.  4.1  Test Setup The test setup consists of a stressing circuit to age the MOSFET and a circuit that runs the MOSFET under normal operating conditions. These circuits are integrated together with three physical switches that can be opened and closed in order to isolate stressing from normal operation.   25 4.1.1 Power MOSFET Test Circuit As shown in Figure 4.1.1, switch 3 corresponds to when the device is being stressed and switches 1 and 2 correspond to when the device is running under normal conditions.  4.1.2 Test Circuit Equipment The pieces of equipment that were used for the test setup shown in figure 4.1.2. There is one power supply needed to age the MOSFET and run the gate driver. A function generator gives the pulse to the gate drive to drive the MOSFET. Next there is a gate resistance added to more clearly see the threshold voltage during turn on and turn off. Figure 4.1.1 Test Circuit Configuration 26 The MOSFET used in the experiment is the IRF510 silicon VD power MOSFET. Anothload. Lastly there are three switches that are set in place to isolate the stressing of the MOSFET from the normal operation of the MOSFET.          4.1.3 Data Acquisition Equipment A Rigol DS1204B oscilloscope was used to show the wave forms of the threshold voltage, drain current and load voltage. The stressing voltage was also monitored on the oscilloscope. One passive voltage probe was used to measure the threshold voltage, one current probe was used to measure the drain current, and two high voltage Figure 4.1.2 Test Circuit 27 probes were used to measure the load voltage and the stressing voltage. An infrared heat sensor was also used to monitor the ambient air temperature and the MOSFET case temperature to make sure there is not a fluctuation in the device temperature. The infrared temperature sensor was running through the normal and aging operation for the whole period of testing. Lastly a Fluke Digital multimeter was used for two purposes. First it was used to check for any shorts in the circuit and secondly it was used make sure all of the connections were hooked up properly from the MOSFET to the test circuit equipment. Figure 4.1.3 shows the data acquisition system and components.     Figure 4.1.3 Test Setup with DAQ 28 4.2  Test Procedure 4.2.1 Normal Operation of the Power MOSFET The first procedure of the test circuit is run under normal operation. In order to run the circuit under normal operation switch 3 should be opened to disconnect the stressing circuit and switches 1 and 2 should be closed to have the gate drive and load connected. Next, 24 V powered the gate drive and then the function generator will be turned on to drive the gate drive from a high 10 V to a low -5 V at 1.7 kHz. These voltage values were chosen from the MOSFET data sheet recommendations. The load voltage supplied is 30 V and the load resistance is . The maximum load voltage should not exceed 100 V so a lower voltage was chosen in order to concentrate the aging of the MOSFET across the gate oxide. This way the drain to source was not stressed and aged to a degree that it would change the results for the threshold voltage. During this normal operation, the threshold voltage will be measured and recorded. Figure 4.1.1 shows the normal operation of the circuit when switches 1 and 2 are closed, and switch 3 is open. The threshold voltage was measured at the point in time when the drain current started to conduct. The threshold voltage was measured this way throughout the entire aging process for consistency.   4.2.2 Aging the Power MOSFET In order to age the MOSFET a voltage stressing technique was used. For the aging process to begin, the normal operation circuit must first be isolated from the stressing 29 circuit by opening switches 1 and 2, which are connected to the gate drive and the load respectively. Next switch 3, which goes directly to the gate, drain, and source must be closed for the stressing to begin. This circuit was setup for a high voltage to be applied across the gate and source, with the source of the MOSFET shorted to the drain. Once these connections are made sure of, the voltage will be turned up slowly, about 1 to 2 V/s to prevent immediate breakdowns within the gate oxide. In order to choose the stressing voltage multiple MOSFETs were used to find a range of voltages corresponding to how long they last before failure. First, three MOSFETs were tested to see at which voltage level there was an immediate breakdown across the gate oxide. Then, more MOSFETs were tested at various other high voltages to see how long it takes for the device to fail. After these tests were completed, it was found that the MOSFET should be stressed at around 65 V to induce accelerated aging of the gate oxide. After running the test at 65.2 V it was found that this voltage was high enough to age the MOSFET but also low enough to be able to plot the threshold voltage across time. Figure 4.1.1 shows the stressing of the MOSFET by applying a constant 65.2 V across the gate and source of the MOSFET with the drain shorted to the source.   4.2.3 Data Acquisition  In order to get measurements of the threshold voltage over a period of time the test circuit must be switched back and forth from normal operation to the stressing circuit throughout the entire process. Figure 4.2.3 shows how the process will be handled. 30 The first stage of the test is to run the MOSFET under normal operation and take the threshold voltage when the MOSFET is new and healthy. This process was described in the normal operations section. Next the MOSFET will be stressed (aged) for three minutes. The stressing will then be stopped and switched to normal operation. Under normal operation, again, the threshold voltage will be measured. It will be aged in three minute intervals for a total of fifteen minutes. Next the MOSFET will be aged in five minute intervals until the total stress time is thirty minutes. Finally, the MOSFET will be aged in ten minute intervals until the total aging time is at least 120 minutes. Again, in between all of the three, five, and ten minute aging intervals, the threshold voltage should be measured and recorded. Throughout the test the temperature was observed and did not change since the normal operation was limited to a maximum of 30 seconds in order to take the threshold voltage measurement.   Figure 4.2.3 Stressing and Data Acquisition Process 31 4.3  Thermomechanical Stress Isolation from Electrical Stresses This test is setup so that the main focus is on the electrical stresses to the device rather than both the thermomechanical and electrical stresses due to the aging process. Thermomechanical stresses and electrical stresses were talked about in Chapter 2. In this test as explained previously, the gate oxide breakdown of the MOSFET is the point of focus for stressing the device. A voltage higher than the maximum rating of VGS was applied to the MOSFET over periods of time ranging from three minutes to more than three hours. During this stressing no temperature change was noticed in the device. The temperature remained at room temperature which was 75 degrees Fahrenheit. When the device was run under normal operation, with a load, the did not rise until around 2 minutes of operation. Even then the temperature only rose up to around 78 degrees Fahrenheit. This small temperature fluctuation in the device will not cause any of the mechanical failures such as bond-wire liftoff or bond-wire cracking. When running the test, the operation time in normal operation with the load was limited to around 30 seconds to try and completely eliminate any temperature rise within the device. The reason that in this test the different stresses were isolated from each other was to see how the threshold voltage will change throughout its life without encountering thermomechanical stresses. These thermomechanical stresses may change the measurement of the threshold voltage due to heating up and or the breakage of bond-wires. As the temperature rises, it is known that the threshold voltage decreases. This 32 change in threshold voltage is not what would like to be observed in this test. So in this case isolation between the electrical and thermal stresses was set in place.  4.4  C-V Measurement In this experiment one IRF510 MOSFET was used to measure the capacitance over the aging cycle. This was used to see by how much the oxide had begun to degrade and this tool was useful to see the shift in the threshold voltage. Measurements were taken before any aging and in between each aging interval up to 20 minutes of aging. A graph showing the trends of these findings can be seen in Chapter 5. This is a reliable method to check and see if the threshold voltage measured during normal operation is accurate with respect to the C-V measurement.  4.5  Annealing In this experiment, one IRF510 MOSFET was annealed. This technique was used to see what effects were causing the threshold voltage to shift. The device was annealed at 120 C for about one hour after three minutes of aging. The threshold voltage shifted back up from the drop that was experienced in this test. These results will be talked about in more detail in Chapter 5. To anneal any device, the data sheet of that device should be looked at in order to see what maximum temperature the device can handle. Also when annealing a device, if the threshold voltage does not change this means that 33 a much higher temperature than what the device is rated for should be used because the charges are trapped more than  34 Chapter 5 Evaluation of Test Data This chapter will go into detail about the test results. First the data extracted from the testing will be explained. There will be figures showing the trends of the threshold voltage of the power MOSFETs.   5.1  Test Data The threshold voltage of seven MOSFETs were measured to prove the theory of the . As can be seen in Figure 5.1.1, all of the MOSFETs follow the same pattern dipping in the beginning and then continuously rising as the aging process proceeds. There are very few variations from MOSFET to MOSFET throughout the test. All of these MOSFETs were tested at room temperature with no heating or cooling of the device. An interesting phenomenon can be seen in the curve for the MOSFET threshold voltage. After a short period of stressing, the threshold voltage dropped to a negative value. In this case, the MOSFET that was being used is an n-channel MOSFET. Therefore, throughout the whole operation in the negative region of the threshold voltage means that the MOSFET was operating in the depletion mode. The curve starts in the enhancement mode of the MOSFET, then dips into the depletion 35 mode, and finally rebounds back into the enhancement mode. It should be noted that while in the depletion mode the MOSFET is  and needs to be turned off. In Figure 5.1.1, the trend can be seen of the threshold voltage throughout the aging process. Also in Figure 5.1.2, the C-V plot can be seen of one of the MOSFETs stressed in the experiment.              36       Figure 5.1.1 MOSFET Threshold Voltage Due to Aging 37       Figure 5.1.2 MOSFET Gate Capacitance Due to Aging 38 5.2  Critical Evaluation 5.2.1 Introduction As stated in the theory description, a dip and rebound was seen in the threshold voltage. Region I is shown to be the first measurements of the threshold voltage before any aging has begun on the MOSFET. After the aging process has begun we move into region II, where the dip begins. This dip was expected to happen near the beginning of the aging process as shown from the experimental data gathered across multiple MOSFETs. Although the dip was expected to occur, it was not expected to drop down into the depletion mode. After noticing the dip into the negative voltage, the aging was continued to determine if the threshold voltage would rebound. As expected the threshold voltage did rebound, but from a negative voltage. This voltage then continued to rise all the way above the max recommended range for the threshold voltage. Once a two volt rise above the range was seen the aging was stopped with the MOSFETs still functioning correctly. These MOSFETs were not aged until failure of the device because the theory can be explained at the point where the MOSFETs were stopped in the aging process. Each of the modes will be explained in more detail with respect to the measurements taken during the experimental process. The dip into the depletion mode will be explained with a modification of the theory. A fourth equation will be added between the second and third modes of operation in the theory and the second equation will also be modified.  This entails that the second region of operation has two contributing factors.  39 5.2.2 Evaluation with Respect to the Proposed Theory Region I is a well-known topic. In this experiment the MOSFET was only run for 30 seconds to show a measurement in this region. This was done for such a short period because during the MOSFETs life in region I everything is considered constant and nothing should change in this region of operation. The second and third regions are more important due to recognizing when the failure precursors start to initiate in the power MOSFET. After aging for three minutes at 65.2 V, the threshold voltage was measured and seen to have dropped approximately 1.4 V to 2 V. During this period, the gate oxide has begun to degrade and breakdown. This was referred to as enhanced bond breakage. It can be seen that this breakage in the Si-Si bonds has led to a formation of traps and has created a localized conduction path in the gate oxide. So as the oxide was thinning during the aging process, charge trapping was induced in the material. Here holes are trapped because of the bond breakage. Interestingly, after another three minutes of stressing, the n-channel enhancement mode power VD-MOSFET turned into a depletion type MOSFET. The MOSFET remains as a depletion type MOSFET as long as the threshold voltage value remains negative. Notably the resistance up to this point between the drain and source kept dropping until the drain and source terminals become shorted together. So as the threshold voltage dropped the resistance across the drain and source followed respectively. At this point, the MOSFET is normally on and needs to be turned off. It is highly unlikely that this is all due to only the gate oxide degradation, which will be discussed in more detail in the next section where what is believed to be the real cause behind this threshold voltage lowering effect. Now, at this point in the aging process, the MOSFETs are operating in a region 40 they should not be. Operating the MOSFETs in the depletion region will have a much higher power loss because the switch is conducting for a longer period of time. Continuing into region II aging, the threshold voltage is continuing to drop for a short period of time. The greatest change in the threshold voltage can be seen in Figure 5.1.1, which is a decrease of 6.9 V in MOSFET #7. After aging, as these MOSFETs pass the six and nine minute marks, the MOSFETs start to come out of region II and head into region III. In region III, Fowler-Nordheim tunneling begins to dominate and the threshold voltage begins to rise. This does not mean that Fowler-Nordheim tunneling did not start to occur previous to the six or nine minute mark of stressing, but rather, it means that the trapped charges prior to this step were the dominating factor preceding the rise of the threshold voltage. Now in region III, it is seen that for all MOSFETs the threshold voltage keeps rising. As the threshold voltage rises it is seen that the MOSFET again changed operating modes from a depletion type MOSFET to an enhancement mode MOSFET again. Notably, the MOSFET operating mode changed in order from enhancement to depletion and then back to enhancement. Aging was stopped for each MOSFET when the threshold voltage reached a value close to 6 V. Aging was stopped at this point because all three regions of operation were seen, and it will be assumed that that the threshold voltage will keep rising till failure of the device. The following is an alternative explanation that is more detailed and is the most probable cause of the lowering of the threshold voltage.   41 5.2.3 Evaluation with Respect to the more Probable Solution  Region I, again, is the same in this explanation as it is with respect to the proposed theory. It is assumed that there are no changes to the device so the threshold voltage will stay the same in this region. The confusion belongs in region two. Here the threshold voltage is dropping in the beginning stages of the aging process. It would have been well off if the whole drop in the threshold voltage could be contributed to the gate oxide degradation. As the gate oxide degrades, positive trapped charges are formed in the oxide when the bonds between the silicon atoms. Holes can also be transported through the oxide through radiation-induced oxide charge [24]. These trapped charges may cause the threshold voltage to decrease depending on how many traps have accumulated in the oxide. Also, the devices under the conditions they were operated at will not experience the radiation induced charges. With that being said, the amount of trapped positive charges in the oxide by themselves should not be able to cause the threshold voltage to decrease into the negative region causing the MOSFET to operate in the depletion mode without radiation-induced oxide charge. Radiation-induced charges were not mentioned in the proposed theory. It is well known that most of the positive trapping is at the interface of the substrate and the gate oxide. The gate oxide usually only traps electrons since there is a positive bias being applied. Therefore the amount of stress being applied to the MOSFETs has to be taken into consideration, since it can cause adverse effects to the operation of the oxide and the substrates inside the MOSFETs. In the IRF510PBF MOSFETs it is recommended to not exceed positive or negative 20 V at the gate. When taking the measurements of the threshold voltage these values were not exceeded. But while stressing the MOSFETs the positive 42 20 V was exceeded by over three times at 65.2 V. This is because an accelerated aging test was used. Applying this high of a voltage stress can affect the way the p-body substrate diffuses by decreasing the mobility in the body. The stress can also cause an interface to form quicker which can cause a high buildup of interface traps in the substrate between the gate oxide and the p-substrate. Another factor that can cause these effects may be the body effect.  Diffusion of electrons and holes happens in the substrate of the MOSFET. When the stress is applied to the gate, there is stress being applied to the substrate as well. Here, is where the properties of the substrate can change and cause the mobility of the electrons and holes to change. Also the dopant its self can move around due to the stress being applied. This means the profile of the dopant in the P-base region was changed or moved. What could also be happening in this VD-MOSFET is that the mobility of the holes is slowing down, which can cause a buildup of holes in the substrate of the material. This could then cause the device to a have a body type effect. The electron mobility in this device is assumed to be higher than the hole mobility.  Since there are more holes, a lesser or more negative voltage is needed to turn the device off. The holes that are being trapped can accumulate till the point where it pushes the MOSFET into the depletion mode. As seen in the results, the MOSFET was pushed into the depletion mode during operation in region II. In non-VD-MOSFETs, the body effect is known to cause the threshold voltage to drop because it gets charged up negatively and pushes the electrons toward the channel. This causes the bulk to have a different potential than the source of the MOSFET, which causes the MOSFET to normally stay on. Consequently, a negative voltage or a voltage lower than the source 43 potential of the MOSFET is needed in order to turn the MOSFET off. In the case of the IRF510PBF, which is a VD-MOSFET, the source is shorted to the bulk of the MOSFET which may mean this MOSFET will have a lesser body effect than described for the non-VD-MOSFET case. The lowering of the threshold voltage can be seen because of the trapped charges in the substrate, but the interface charges are believed to be the cause of why the MOSFET goes into the depletion mode. Table 5.2.1 shows the different switching modes for n-channel and p-channel MOSFETs for a better understanding. Here   is when the n-channel MOSFET can turn on and   is when the p-channel MOSFET can turn on. Table 5.2.1: MOSFET Switching Table  MOSFET Mode   Type of MOSFET     Enhancement   Mode    n-channel   ON   OFF   OFF  Depletion   Mode    n-channel   ON   ON   OFF  Enhancement   Mode    p-channel   OFF   OFF   ON  Depletion   Mode    p-channel   OFF   ON   ON  44 The important contributing factor that can be caused with the diffusion are the interface trapped charges. These trapped charges have a direct and important role in how the MOSFET operates. The induced trapped charges may build up quickly in the interface between the substrate and the oxide. As the charges build up more and more, an inversion layer of holes is formed that needs a more and more negative voltage to turn off the MOSFET. So as the space charge width increases this allows more and more charge to be stored and a more and more negative voltage is needed to turn the MOSFET off. This happens in the P-base region. The electrons will flow through into the N-drift region and move along as the holes get trapped.   This also does not mean that the effects that are being seen will not exist in a real world application. When a system is being run, these trapped charges can accumulate in the Figure 5.2.3 Hole Trapping, Annealing, and Reversible Compensation 45 gate oxide, interface, and the substrate. If the MOSFETs are held at room temperature the user will start to see a drop in the threshold voltage. Now if the user wants to get rid of the trapped charges, they may anneal the MOSFET and see that the charges are now free and have recombined. There are charges that are permanent that may seem to go away with the annealing of the device only to reappear and cause a negative shift in the threshold as found in [25]. Also, the interface state trapped charges can repopulate causing the threshold voltage to shift again. The model for hole trapping, annealing, and reversible compensation is shown in figure 5.2.3 [25].  Here, it can be noted that the permanent trapped charges that reappear to cause the threshold voltage shift are holes permanently trapped in the gate oxide. Also the interface will begin to repopulate with charges during normal operation. This is because the charges were imbedded into the material, which leaves states for the charges to be trapped again after they are thermally excited out of the trapped states. It will be difficult to see the voltage shift due to oxide trapped charges. This is because the interface trapped charges and the charges in the P-body will begin to reappear. These charges will shift the threshold voltage more than the oxide trapped charges will. In the end, real systems can experience the shift from an enhancement type MOSFET to a depletion mode and then back to an enhancement type MOSFET.  When the devices threshold voltage begins to rebound and come back up, Fowler-Nordheim tunneling begins to dominate. Again as in the first explanation, Fowler-Nordheim tunneling may begin to occur previous to the voltage rebound but does not have an overwhelming effect. It is again assumed that the threshold voltage will 46 continue to rise even though the testing and stressing was stopped about two hours into the lifetime of the MOSFET.  Now equations (3.4.4) and (3.4.5) will be revisited. Equation (5.2.1) accounts for the trapped positive charges in the oxide due to bond breakage.   (5.2.1)  Here  is the trapped charges in the oxide of the device. The term  accounts for the shift in the lowering of the threshold voltage. Although Equation (5.2.1) accounts for a voltage shift, this value is fairly small compared to the first term of the equation. Interface charges at the surface account for the larger drop in the threshold voltage because there are no radiation induced charges in the device tested. This is why equation (5.2.2) will also be added to take into account the interface charges at the surface in the device.   (5.2.2)  In equation (5.2.2),  is the term for the interface trapped charges. These interface charges along with the charges stored in the oxide during region II operation 47 will cause the threshold voltage to drop to a negative value which will cause the enhancement device to begin operating as a depletion type device. The interface trapped charges will form previous to any degradation in the gate oxide. When Fowler-Nordheim tunneling begins to dominate and the threshold voltage goes above the healthy state threshold voltage of the device, the term   can be taken out of the equation. However, before this happens Equation (3.4.5) which accounts for the trapped positive charges must be modified into Equation (5.2.3).   (5.2.3)  In Equation 5.2.3, the electron charges begin to cancel out the trapped hole charges in the oxide and interface. So this is where region III operation begins. Once Fowler-Nordheim tunneling starts to dominate and control the threshold voltage, the equation can be formed back into equation (3.4.5). This because now the electrons are dominating the change in threshold voltage which is causing a higher and higher or more positive threshold voltage needed to turn the device on. At the point when the threshold voltage reaches a value greater than the region I threshold the term   can be disregarded. This means that Equations (5.2.1) and (5.2.2) 48 account for when the dip in the threshold voltage starts to the lowest negative threshold value. Equation (5.2.3) describes when the threshold voltage begins to rebound. In this equation, the trapped holes must still be accounted for since the device is still operating as a depletion type MOSFET and or the threshold voltage is still lower than the first threshold value in region I. After the threshold voltage rises above the first threshold value, Equation (3.4.5) should be used. The proposed theory has been disproven now that all three regions have been accounted for and explained properly. The equations were revisited and altered in order to account for the trapping which occurs in the interface and the gate oxide. This cannot be directly proven with the data compiled but it is one explanation which is very probable to happen. Additional testing should be done to try and fully prove the newly proposed equations.  5.3  Future Work Many more tests can be performed in order to fully extract the different causes in the threshold voltage shift. One test that should be performed is a finite element analysis (FEA) simulation. When carrying out this simulation, all the parameters from the doping concentrations to the thicknesses and capacitances of the device need to be known. Using FEA, the user should be able to predict how the device should react to different forces placed on the device. The mechanical forces on the device that should be monitored carefully are the heating and cooling of the materials. The electrical forces on the device that should be monitored are the continuous over gate voltage for stressing 49 and the gate current when switching the device on and off. Using FEA the user should be able to recreate the testing platform in the real-world and compare the results of charge trapping and threshold voltage variation. This may better help and explain the results that are being seen in the IRF510 testing.  Another test that should be performed is stressing the MOSFET in a thermal chamber at various temperatures including room temperature. Stressing the device at a lower voltage throughout the temperature ranges should be performed because the device may react differently and charges may not be stored at concentrations as seen at the 65.2 V and at room temperature.  The user should be able to see a threshold voltage shift that will differ from what is being seen at room temperature. An assessment of how the device reacts at over 110° C should also be performed. The observation may point out new findings of which trapped charges will be permanently stored in the interface and in the gate oxide. The ideal case at the higher temperature would be to see minimal charge trapping in the interface and a higher concentration of permanently trapped charges in the gate oxide. When a device in annealed, it should get rid of trapped charges in the device and can hide permanent trapped charges for a period of time also. These charges should reappear in the device. More research of how long permanent trapped charges take to reappear should also be evaluated. Finally, an assessment of how the threshold voltage reacts at below 0° C should also be performed. This data should be collected at different temperatures so that the threshold voltage of the device can be compared and evaluated. The user should then see how trapped charges affect the device at different temperatures. Combining FEA with the 50 thermal chamber testing would be the best scenario to provide the most accurate understanding about what is going on in the MOSFET.  5.4  Conclusion The power VD-MOSFET goes through three regions of operation. Region I being where no change occurs in the MOSFET and the threshold voltage remains constant. The second region of operation is when two different positive trapping methods occur, oxide trapping and interface trapping. The third region of operation is where Fowler-Nordheim tunneling begins to dominate the change in threshold voltage. In region II Fowler-Nordheim tunneling was present but did not play the dominant role. Equation (3.4.4) was to show the dip in the threshold voltage and (3.4.5) is for region III operation where Fowler-Nordheim tunneling begins to dominate. These equations were altered in order to compensate for the positive trapped charges during the dip in the threshold voltage and when the threshold voltage begins rising in region III. Equations (5.2.1), (5.2.2), and (5.2.3) is the result that can be seen. For the latter part of region III, when Fowler-Nordheim tunneling dominates and the threshold value rises above the first value recorded equation (3.4.5) will kept the same. Further analytical experimental simulations using FEA are noted to be performed for a better understanding of what is going on in the substrates and oxide of the MOSFET. Also, thermal chamber testing and annealing are proposed to gain a stronger backing for the newly proposed equations. 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