A New PSPICE Subcircuit for the Power MOSFET Featuring Global Temperature Options TM October 1999 Abstract accepted by users, and the ease of parameter extraction should be demonstrated. An empirical sub-circuit was implemented in PSPICE® and is presented. It accurately portrays the vertical DMOS power MOSFET electrical and for the first time, thermal responses. Excellent agreement is demonstrated between measured and modeled responses including first and third quadrant MOSFET and gate charge behavior, body diode effects, breakdown voltage at high and low currents, gate equivalent series resistance, and package inductances for temperatures between -55oC and 175oC. Parameter extraction is relatively straight forward as described. Method A sub-circuit approach is employed which is empirical. It is developed to provide black box conformity to the power MOSFET throughout the operating regime normally traversed by the dictates of most power circuit applications including junction temperature. Although device thermal behavior is the driving force, respect is maintained toward the physics and the SPICE algorithms. The developed sub-circuit schematic is shown in Figure 1. Introduction There are many forms of SPICE, each with its own strengths and weaknesses. PSPICE was chosen for the following reasons. 1. An evaluation copy capable of considerable circuit analysis for power circuits is available. Circuit simulation commonly uses one of the SPICE [1] programs. However, power circuits require proper models for unique devices which are not included in the supplied libraries. Efforts have been published to model the power MOSFET [2-10] with varying degrees of success. The more successful papers have used sub-circuit representation. To date, a thermal model has not been offered. 2. The PROBE feature provides excellent displays. 3. Programmed time slice defaults and DC convergence routines make it very friendly. Objective 4. The switch algorithm of PSPICE provides a very smooth transition from off to on. It is the goal of this effort to provide for the first time a thermal sub-circuit model capable of providing accurate simulation throughout all of the power MOSFET regimes. In addition the sub-circuit should be readily understood and 10 ESG 6/8 - LGATE + 20 9 18/8 VTO DBREAK 16 + 21 MOS1 6 RIN DBODY MOS2 11 + EBREAK 17/18 CIN 8 RSOURCE - LSOURCE 7 S1A 12 S2A 13/8 14/13 13 CA S1B + S2B 2 LDRAIN RDRAIN EVTO RGATE DRAIN DPLCAP + GATE Other forms of SPICE were not investigated, but they should be amenable to the development of a similar sub-circuit by paralleling the teachings of this work. 5 - 1 AN9210.1 17 15 3 SOURCE RBREAK 18 RVTO EGS 6/8 - CB EDS + 14 5/8 IT 19 VBAT + - FIGURE 1. PSPICE MODEL SUBCIRCUIT 1 1-888-INTERSIL or 321-724-7143 PSPICE™ is a registered trademark of MicroSim Corporation | Intersil (and design) is a trademark of Intersil Americas Inc. Copyright © Intersil Americas Inc. 2001. All Rights Reserved Application Note 9210 Driving constraints for this work were: 5. The SPICE device equations should not be modified. 6. Global temperature should be included. 7. All modes and levels of power MOSFET operation should be modeled. 8. The sub-circuit should be empirically developed to complement the device physics and the source code algorithms. 9. The sub-circuit should be acceptable to a circuit design user. 10. Parameter extraction should require little or no iteration. Temperature Modeling Use is made of voltage controlled voltage sources and model statements in order to form master/slave circuit relationships. In this manner, resistors can often be used to establish a first and second order temperature correction where direct PSpice algorithms will not permit thermal modeling. An Overview (Figure 1) The primary device for gate controlled positive or negative current flow is provided by Mos1 which is defined by the level 1 model MOSMOD. The second order effect of threshold voltage is set by Mos2 combined with the voltage VTO. Model MOSMOD also defines Mos2 but with a 1 percent scaling. It is necessary that RSOURCE and RDRAIN be provided as separate resistors, rather than being included with the MOSFETs. In this manner, 1st and 2nd order temperature effects may be added as described by model RDSMOD. The thermal variation of KP as provided by the source code is a satisfactory representation. However, the threshold voltage of Mos1 must be modified by the voltage dependent voltage source EVTO. EVTO provides an additive or subtractive voltage in series with the gate as a function of temperature. It is equal to the sum of VBAT and the product of It and RVTO. Temperature variation is provided by model RVTOMOD. Avalanche breakdown of the MOSFET is provided by the clamp circuit of DBREAK in series with EBREAK. The value of EBREAK is provided by the multiplier of EBREAK and the product of It times RBREAK. Temperature variation is provided by model RBKMOD. High current voltage drops are provided by RS of the model DBKMOD including thermal sensitivity. The power MOSFET being modelled contains a third quadrant diode as a fabrication consequence, and it is represented by DBODY. Model DBDMOD provides the leakage current IS, the transit time for stored charge effects TT, the body diode series resistance RS, temperature dependence of this resistor TRS1 and TRS2, and the MOSFET output capacitance CJO. The inductances associated with the device terminals are represented by LSOURCE, LGATE, and LDRAIN. 2 The effective series resistance associated with the gate is modelled by the resistor RGATE. A gate to source input capacitance is represented by CIN. MOSFET output capacitance is provided by model DBDMOD as described above. Feedback capacitance is provided by DPLCAP as defined by model DPLCAPMOD. A diode was used for this function to provide a square root dependency with drain to source voltage. The voltage dependent voltage generator ESG is added to assure that the drain to source voltage is imposed across the feedback capacitor while forcing the feedback current flow into the gate node. It is further necessary that the ideality factor N of model DPLCAPMOD be made large to exclude forward diode conduction during third quadrant operation of the MOSFET. A capacitor CA is switched in parallel with CIN when the gate to source voltage becomes sufficiently negative. This switching is implemented by the switch S1A. Model S1AMOD defines the switch closed resistance, open resistance, and the gate to source voltages through which the fully on to fully off transition occurs. During this transition, switch S1B also transitions from fully off to fully on. Switch S1B is defined by model S1BMOD. Voltage controlled voltage generator EGS provides the proper charge state for CA when switch S1A is open. In a similar manner, the capacitor CB is switched in parallel with CIN when the drain to gate voltage becomes negative. Switch S2A is defined by model S2AMOD for the on resistance, off resistance, and drain to gate voltage transition range. During this transition switch S2B also transitions as defined by model S2BMOD. Voltage controlled voltage generators EDS and EGS provide the proper charge state for CB when switch S2A is open. In order to facilitate DC convergence, PSPICE provides a minimum conductance between all nodes as defined by the PSPICE analysis options. In order to assure that a floating gate initial condition will not exist should a modeler drive from a current source, a very large gate to source resistor RIN is added. Inclusion of RIN is recommended but not required. All sub-circuit elements are treated as being independent of temperature if they are not otherwise defined. Gate propagation effects [15], radiation effects, and inherent VDMOS design deficiencies are not modelled. This is discussed later. All discussions apply equally to P channel although N channel is discussed exclusively. Applications The sub-circuit combined with external circuitry may be analyzed for many responses. Three circuits are modelled to demonstrate the capability of the PSPICE sub-circuit model. A synchronous rectifier producing 100 watts at 5 volts DC from a 100KHz square wave demonstrates the ability to handle the first and third quadrant regimes of two MOSFETs, including conversion efficiency versus temperature. Calculated waveforms are presented, but they are unsupported by Application Note 9210 measured data. The diode recovery waveform is modelled and compared to the measured response. Switching waveforms of the power MOSFET are also modelled and compared to the measured results. The schematic of a synchronous rectifier circuit is shown in Figure 2. The rectifier power MOSFETs are a pair of cross coupled RFH75N05 megafet devices. Conduction is offered by a forward gate bias with negative drain current (third quadrant mosfet operation) and voltage blocking is assured by a slightly negative gate bias for first quadrant MOSFET operation. L2 40nh 10 9 V1 + L1 20µh 2 - + 4 R3 2mΩ OUTPUT VOLTAGE (V) SYNCHRONOUS RECTIFIER 5 3 POWER OUT = 100W FREQUENCY = 100kHz T = +25oC 1 100 5 200 + FIGURE 3. RECTIFIER OUTPUT VOLTAGE VM3 - VM4 6 11 + VM1 - R2 5Ω R1 5Ω 3 1 VM2 - 7 8 XM1 RFH75N05 EFF = (1/(1 + AVG(AVG(I(VM4) * V(8) + I(VM3) * V(7) + I(R3) * V(4.5) ))/AVG(AVG(I(R4) * V(5)))) C1 100µF R4 0.25Ω XM2 RFH75N05 8 FIGURE 2. SYNCHRONOUS RECTIFIER CIRCUIT VM1 to VM4 are voltage sources of zero potential and are used to permit a recording of branch currents. The transformer secondary normally used in a supply of this sort is represented by voltage source V1 and leakage inductance L2. Filter inductor L1 and capacitor C1 provide energy storage and smoothing for the 100KHz square wave of V1. Rise and fall times of the square wave are not critical, but were set at 40ns. Gate coupling resistors R1 and R2 are somewhat critical, in that too high a value will restrict the conduction transition time of the MOSFET. Alternatively, a value too low will permit a high voltage drain spike to appear on the gate of the MOSFET. The calculated output voltage turn on transient is shown in Figure 3. Of course this represents a feed forward circuit response only. In practice, the modelled drive circuit with pulse width modulation and feedback would provide a much faster response which would be slew rate limited. The ripple voltage is 5mV RMS. The efficiency for this portion of the synchronous rectifier circuit is plotted in Figure 4 as a function of temperature from -25oC to 150oC. As a convenience, the equation used by PROBE (PSPICE's waveform plotter routine) is included. This equation yields a solution rapidly. RECTIFIER EFFICIENCY (%) + 98 96 94 92 POWER OUT = 100W FREQUENCY = 100kHz 0 50 100 AMBIENT TEMPERATURE (oC) FIGURE 4. RECTIFIER EFFICIENCY Transition voltage waveforms of the input voltage, one drain voltage, and one gate voltage are plotted in Figure 5. The value of drain voltage during third quadrant conduction is approximately -0.2 volts. Other waveforms are readily available by use of the PSPICE system. TC = +25oC DRAIN V(7) 20 VOLTAGE (V) - 300 TIME (µs) V(3) 10 V(7) 0 GATE V(3) INPUT V(9.2) V(9.2) -10 100 300 5100 5300 TIME (ns) FIGURE 5. 3 TRANSITION VOLTAGE WAVEFORMS Application Note 9210 RECOVERY WAVEFORMS DRAIN CURRENT (A) -30 * * * * * * * ** * ** 10 * 0 * * MODEL * * * 8 4 * * * * * * DATA * * * * * * * * * * * * * * * ** * -20 * * * 20 TC = +25oC GATE VGS (V) TJ = +25oC DRAIN VDS (V) Figure 6 shows the MOSFET current of the parasitic 3rd quadrant diode vs time as modelled with the sub-circuit and as measured using the Berman SM30 equipment. Measurements show very little temperature sensitivity. Therefore it is not modelled. * * * 0 * 0.5 * -10 Measured vs Modelled Characteristics * * MODEL DATA ** 200 TIME (ns) 3.5 FIGURE 8. SWITCHING TIME WAVEFORMS 0 100 2.5 TIME (µs) * * 1.5 300 The device characteristics have been measured (data points) and modelled (solid line) as plotted in Figures 9 to 19. Thermal responses were omitted from some figures to improve the clarity of presentation. 400 FIGURE 6. DIODE RECOVERY WAVEFORMS SWITCHING WAVEFORMS Discussion Of Results Switching time measurements of the power MOSFET are usually taken in a circuit similar to that of Figure 7. Although parasitic wiring inductance is not normally shown, it exists and is modelled as shown. The waveforms of gate and drain voltages are presented as measured and modelled in Figure 8. Switching times of Figure 8 are listed in Table 1. Excellent correlation generally exists between measured and modelled information over the current range from zero to three times the device rated current. As the drain voltage is increased from zero volts with a constant gate voltage, the MOSFET transitions from the linear mode to the saturated mode. Conformance of modelled to actual data is very good in the constant current regime (saturated mode). A forcing of conformance exists for the very high gate voltages in the linear mode, with departure existing for the linear mode with lesser values of constant gate voltages. TABLE 1. SWITCHING TIME DATA PARAMETER DATA MODEL UNITS Turn on Delay Time 72 67 ns Rise time 238 208 ns Turn Off Delay Time 440 460 ns Fall Time 259 240 ns LD 5nh LS 8nh I1 RDD 11Ω 160 LDD 10nh 0 FIGURE 7. SWITCHING TIME CIRCUIT 120 VDD 25V ID (A) CDD 260µF 10 * * 7V * * * * ** * * ** 10V 5 XM1 RFHH75N05 11 RG 25Ω 4 12 LG 5nh 1 2 RL 1Ω The actual drain voltage in the linear mode is seen to be as much as 20 percent below the modelled value in worst cases. This represents a conservative error for circuit calculations in that the conduction loss is somewhat less than modelled. In addition, the gate drive is usually high under MOSFET conduction, thereby avoiding operation in the regions of discussion. * ** * * * ** * 40 * * ** * * * * ** 1.5 80 * * * TA = +25oC 5V * * * MODEL * DATA VGS = 4V * * 3.0 4.5 VDS (V) FIGURE 9. OUTPUT CURVES 4 6V * 6.0 * Application Note 9210 The discrepancy results because the PSPICE algorithm for a mosfet assumes the channel surface concentration to be constant. In the power MOSFET, the surface concentration is gaussian along the channel length. Hence, the observed behavior is as would be expected. Omission of Mos2 would not impact circuit performance, however a reverence of attached importance to the MOSFET threshold voltage mandates modelled to measured agreement. The modelled response can be improved by changing the PSPICE algorithm, however changes of this type were ruled out for this work. * * ** * 160 -175oC * * ID (A) 120 80 40 * * * * * * * * * ** -25oC * * * * * * ** * * * 3 4 * ** * * 65 BVDSS (V) -55oC VDS >> VGS IDS = 1mA VGS = 0 60 * 55 * * MODEL * DATA -50 0 50 TJ (oC) 100 150 FIGURE 12. BREAKDOWN VOLTAGE, LOW CURRENT BVDSS MODEL DATA * 5 Excellent agreement exists. 6 VGS = 0 VGS (V) FIGURE 10. TRANSFER CURVES -55oC 150 Excellent agreement exists. -25oC -175oC ID (A) ID = 1mA VDS = VGS 5 100 * * * VGTH (V) 50 * 3 MODEL * * DATA 10 30 * 50 BVDSS (V) 70 FIGURE 13. BREAKDOWN VOLTAGE, HIGH CURRENT BVDSS 1 MODEL Excellent agreement exists. * DATA -50 0 50 TJ (oC) 100 150 ID = 75A VGS = 10V * * Excellent agreement exists. This would not be so without the inclusion of Mos2 to represent the sharp corners of the many hexagonal cells of the structure. The flat part of the hex cells results in a two dimensional diffusion during processing and the establishment of a source to body junction cross-over concentration at the surface, resulting in Mos1 as modelled. However, the corners of the hex cells introduce a three dimensional diffusion resulting in a lower source to body junction cross-over concentration at the surface. The unpublished work of Klodzinski, et al [11] processed test and control devices upon a common wafer where the corners of the hex source implant were excluded versus included, revealing threshold voltages approximately 0.4 volts higher for the test. 5 RDS(ON) (mΩ) FIGURE 11. THRESHOLD VOLTS 10 * 5 * MODEL * DATA -50 0 50 100 150 TJ (oC) FIGURE 14. ON RESISTANCE vs TEMPERATURE Excellent agreement exists. Application Note 9210 -55oC * * * * * * -200 * MODEL * DATA MODEL DATA * -1.0 * 25 ID (A) FIGURE 18. BODY DIODE CURVES All three measured data curves were noted to cross at a drain current of 180amps. Excellent agreement exists. Excellent agreement exists. TJ = +25oC VDS ** RL = 0.667Ω VDD = 50V IG = 3.44mA TC= +25oC * * * * * * * * * * * 0 6 * * 0 * * * -80 * 40 60 * * * * * * * MODEL 8000 * CISS * * * C0SS * * * * * * 2000 * * * CRSS 5 * * * 10 15 20 VDS (V) FIGURE 17. CAPACITANCE CURVES Excellent agreement exists. 6 -0.4 -0.2 Good agreement exists. The departure seen between modelled and measured exists for the same reason as the departure of the output curves in the linear regime. This would also be improved by changing the PSpice algorithm as suggested relative to Figure 9. Parameter Extraction * DATA * -0.6 FIGURE 19. 3RD QUADRANT MOSFET CURVES TC = +25oC * MODEL VDS (V) Excellent agreement exists. The non linear behavior of gate charge for negative gate bias is seldom shown. A significant increase in turn on delay results by operating from a negative gate voltage. * ** * DATA TIME (µs) CAPACITANCE (pF) * * MODEL DATA FIGURE 16. GATE CHARGE CURVES * * +5V -60 -0.8 4000 * * +10V 20 * +7V -6 * 6000 * * VGS * * +4V -40 * -30 * * VGS = 0V -20 * * * * * * * * ID (A) * VGS (V) VDS (V) * -0.5 VDS (V) 50 FIGURE 15. TRANSCONDUCTANCE CURVES 30 -175oC * -150 ** * -25oC * * * * * 25 -100 -175oC * 50 * * ID (A) GFS (S) * * * * -50 * 75 ** -55oC -25oC * * * VGS = 0 * VDS >> VGS The sub-circuit is chosen to minimize interdependencies between parameters. A listing of the sub-circuit is presented in Table 2 as a template which routes the Modeler through extraction with guiding comments. Although the template is a complete and workable PSPICE sub-circuit listing, all parameter values except KP and VTO are chosen to be transparent to the results of the analysis. As the transparent values are replaced with extracted values, the model is developed. The listing in Table 2 is structured so that parameters being extracted have very little dependency upon those values which are not yet determined. If desired after completing the extraction, an iteration may be made for the comfort of the Modeler. Application Note 9210 EXTRACTION OF MODEL PARAMETERS FROM PHYSICAL MEASUREMENTS TABLE 3. FINAL MODEL TABEL 2. TEMPLATE .SUBCKT RFH75N05 2 1 3 ; rev 3/20/91 *Nom Temp=25 deg C .SUBCKT TEMPLATE 2 1 3 ; rev 12/17/90 *Nom Temp=25 deg C Mos1 16 6 8 8 MOSMOD M=0.99 ; .MODEL MOSMOD NMOS (VTO=3 KP=10 +IS=1e-30 N=10 TOX=1 L=1u W=1u) Step 1 Mos1 16 6 8 8 MOSMOD M=0.99 .MODEL MOSMOD NMOS (VTO=3.48 KP=78.5 +IS=1e-30 N=10 TOX=1 L=1u W=1u) Mos2 16 21 8 8 MOSMOD M=0.01 ; Vto 21 6 0 Step 2 Mos2 16 21 8 8 MOSMOD M=0.01 Vto 21 6 0.6 Rsource 8 7 RDSMOD 1e-12 ; Step 3 Rsource 8 7 RDSMOD 2e-3 Rdrain 5 16 RDSMOD 1e-12 ; Step 4 Rdrain 5 16 RDSMOD 3.07e-3 .MODEL RDSMOD RES (TC1=0 TC2=0) Step 5 .MODEL RDSMOD RES (TC1=5.2e-3 TC2=1.37e-5) Evto 20 6 18 8 1 ; Rvto 18 19 RVTOMOD 1 It 8 17 1 Vbat 8 19 DC 1 .MODEL RVTOMOD RES (TC1=0 TC2=0) Step 6 Evto 20 6 18 8 1 Rvto 18 19 RVTOMOD 1 It 8 17 1 Vbat 8 19 DC 1 .MODEL RVTOMOD RES (TC1=-3.78e-3 TC2=-7.51e-7) Ebreak 11 7 17 18 1000 ; Dbreak 5 11 DBKMOD Rbreak 17 18 RBKMOD 1 Step 7 Ebreak 11 7 17 18 58.4 Dbreak 5 11 DBKMOD Rbreak 17 18 RBKMOD 1 .MODEL RBKMOD RES (TC1=0 TC2=0) ; Step 8 .MODEL RBKMOD RES (TC1=9.5e-4 TC2=-1.17e-6) .MODEL DBKMOD D (RS=0 TRS1=0 TRS2=0) ; Step 9 .MODEL DBKMOD D (RS=8e-2 TRS1=2.5e-3 TRS2=0) Dbody 7 5 DBDMOD ; .MODEL DBDMOD D (IS=1e-30 RS=0 TRS1=0 +TRS2=0 CJO=0 TT=0) Step 10 Dbody 7 5 DBDMOD .MODEL DBDMOD D (IS=2.23e-12 RS=2.28e-3 TRS1=2.98e-3 +TRS2=2.22E-12 CJO=7.55e-9 TT=4e-8) Lgate 1 9 1e-12 ; Ldrain 2 5 1e-12 Lsource 3 7 1e-12 Rgate 9 20 1 Step 11 Lgate 1 9 5e-9 Ldrain 2 5 1e-9 Lsource 3 7 3e-9 Rgate 9 20 1.2 Cin 6 8 1e-15 ; Step 12 Cin 6 8 4.48e-9 Dplcap 10 5 DPLCAPMOD ; .MODEL DPLCAPMOD D (CJO=0 IS=1e-30 N=10) Esg 6 10 6 8 1 Step 13 Dplcap 10 5 DPLCAPMOD .MODEL DPLCAPMOD D (CJO=2.14e-9 IS=1e-30 N=10) Esg 6 10 6 8 1 Ca 12 8 1e-15 ; S1a 6 12 13 8 S1AMOD S1b 13 12 13 8 S1BMOD .MODEL S1AMOD VSWITCH (RON=1e-5 ROFF=0.1 +VON=-3 VOFF=-1) .MODEL S1BMOD VSWITCH (RON=1e-5 ROFF=0.1 +VON=-1 VOFF=-3) Egs 13 8 6 8 1 Step 14 Ca 12 8 8.98e-9 S1a 6 12 13 8 S1AMOD S1b 13 12 13 8 S1BMOD .MODEL S1AMOD VSWITCH (RON=1e-5 ROFF=0.1 +VON=-2.48 VOFF=-0.48) .MODEL S1BMOD VSWITCH (RON=1e-5 ROFF=0.1 +VON=-0.48 VOFF=-2.48) Egs 13 8 6 8 1 Cb 15 14 1e-15 ; S2a 6 15 14 13 S2AMOD S2b 13 15 14 13 S2BMOD .MODEL S2AMOD VSWITCH (RON=1e-5 ROFF=0.1 +VON=-2.5 VOFF=2.5) .MODEL S2BMOD VSWITCH (RON=1e-5 ROFF=0.1 +VON=2.5 VOFF=-2.5) Eds 14 8 5 8 1 Step 15 Cb 15 14 8.81e-9 S2a 6 15 14 13 S2AMOD S2b 13 15 14 13 S2BMOD .MODEL S2AMOD VSWITCH (RON=1e-5 ROFF=0.1 +VON=-2.25 VOFF=2.75) .MODEL S2BMOD VSWITCH (RON=1e-5 ROFF=0.1 +VON=2.75 VOFF=-2.25) Eds 14 8 5 8 1 Rin 6 8 1e9 ; Step 16 Rin 6 8 1e9 .ENDS .ENDS 7 Application Note 9210 OBTAINING EXPERIMENTAL DATA STEP 3 - RSOURCE When the authors experienced difficulty in parameter extraction the problems were traceable to erroneous data in all cases. The following caveats are offered: The straight line curve of Figure 20 is modified by a chosen value of RSOURCE in order to better fit the measured data for medium to high currents at 25oC. This is shown in Figure 21, where 2E-3 provided the best fit. 11. Obtain all data from a single device. 12. Read gate voltage data to the nearest 0.01 volt. 13. Employ Kelvin sensing to the package leads. VDS >> VGS TJ = +25oC 15. Inconsistencies lurk in data sheet curves and specifications. FINAL MODEL The final model for the RFH75N05 is shown in Table 3 and serves as an aid to understanding as it is developed from the template. SQRT (ID) (A1/2) 14. Avoid self heating (a difficult assignment) 10 5 STEP 1 - MODEL MOSMOD (VTO AND KP) The square root of drain current is plotted versus the gate to source voltage for the MOSFET in the saturated regime; a straight line results. The zero current intercept defines VTO and the slope defines the square root of (KP/2). Vary VTO and KP to obtain the best fit to data for the low to medium current experimental data at 25oC. VTO is not the threshold voltage as measured. In order to use the algorithm of the PSPICE Level 1 model, W (the channel width) and L (the channel length) are defined as one micron. Therefore KP times W divided by L reduces to the model value called KP. Likewise IS, N, and TOX are set to values chosen to avoid other algorithm problems. Figure 20 shows the PSPICE generated curve after the correct values of KP and VTO of model MOSMOD are chosen. 5 VGS (V) 6 FIGURE 21. SQUARE ROOT OF ID STEP 4 - RDRAIN RDRAIN is chosen to fix the PSPICE calculated RDS(ON) value to the measured value at 25oC when the template is biased to the gate voltage and drain current of the specifications. Do not use the specified maximum of RDS(ON). The value developed was 3.07E-3. STEP 5 - MODEL RDSMOD (TC1 AND TC2) RSOURCE and RDRAIN are assumed to have the same temperature coefficients. Although this is not accurate, it is convenient and is deemed to be sufficient for this purpose. If RDS(ON) is measured as a function of temperature, best fit can be obtained by appropriately choosing TC1 and TC2 values of 5.2E-3 and 1.37E-5. RDS(ON) is shown in Figure 22. ID = 75A VGS = 10V 3 RDS(ON) (mΩ) SQRT (ID) (A1/2) 5 VDS >> VGS TJ = +25oC 4 3 1 3 4 10 5 VGS (V) FIGURE 20. SQUARE ROOT OF ID STEP 2 - VTO The threshold voltage is set by fixing the value of VTO. Threshold voltage of a power MOSFET is usually measured in the saturated regime at a low current, typically 1mA. If the PSPICE model is run at 25oC with the gate and drain voltage equal, a voltage will be found to yield 1mA drain current. VTO is this voltage reduced by the measured threshold voltage. The value identified was 0.6 volts. 8 -50 0 50 TJ (oC) 100 150 FIGURE 22. RDS(ON) vs TEMPERATURE Application Note 9210 STEP 6 - MODEL RVTOMOD (TC1 AND TC2) STEP 9 - MODEL DBKMOD (RS, TRS1 AND TRS2) The plot of Figure 21 must be modified to add curves at low and high temperature. A temperature sensitive additive or subtractive voltage is placed in series with the gates of Mos1 and Mos2 by use of EVTO. A 1 volt drop equal to It times RVTO is canceled by a 1 volt supply, VBAT and applied to EVTO. By choosing the values of TC1 and TC2 for model RVTOMOD, the voltage of EVTO is made temperature sensitive. The result is shown in Figure 23, where TC1 and TC2 were chosen for best fit at -3.78E-3 and -7.51E-7. Although reliable data is difficult to obtain for the breakdown voltage at many tens of amperes, it can be done with a small inductive flyback circuit of very low duty cycle. RS of the diode DBREAK may be determined at 25oC. TRS1 and TRS2 may be determined with similar measurements at several temperatures. The curves of Figure 25 present the modelled behavior for RS, TRS1 and TRS2 equal to 8E-2, 2.5E-3, and 0. VGS = 0V -55oC -55oC VDS >> VGS 150 -25oC ID (A) SQRT (ID) (A1/2) -175oC 10 100 50 5 -175oC -25oC 10 -50 3 4 5 6 VGS (V) 50 BVDSS (V) 70 FIGURE 25. BREAKDOWN VOLTAGE vs TEMPERATURE STEP 10(a) - MODEL DBDMOD (IS, RS, TRS1 and TRS2) FIGURE 23. TRANSFER CHARACTERISTICS vs TEMPERATURE STEP 7 - EBREAK EBREAK derives a thermally variant voltage from the product of IT and RBREAK equal to 1.00 volt at 25oC. When the drain voltage rises sufficiently, diode DBREAK provides a voltage clamp to EBREAK. The value of the EBREAK multiplier is equal to the low current value of BVDSS less the forward drop of DBREAK. The multiplier was set at 58.4 for the final model. When operating DBODY in the forward mode, one may develop IS and RS at 25oC assuming a diode ideality value of 1.0, the default value. Measurements at elevated current levels and several temperatures will define TRS1 and TRS2. Measurements are taken with VGS equal to zero. Figure 26 presents the body diode forward characteristics for several temperatures where IS, RS, TRS1, and TRS2 are found to equal 2.23E-12, 2.28E-3, 2.98-E3, and 2.22E-12. STEP 8 - MODEL RBKMOD (TC1 AND TC2) -55oC ID = 75A VGS = 10V VGS = 0 -25oC -50 -175oC -100 ID (A) The low current breakdown voltage of the MOSFET may be measured at several temperatures, such that TC1 and TC2 may be determined for model RBKMOD. Figure 24 plots the low current breakdown voltage as a function of temperature as modeled with TC1 and TC2 equal to 9.5E-4 and -1.17E-6. -150 65 BVDSS (V) 30 -200 60 -1.0 -0.5 VDS (V) FIGURE 26. BODY DIODE CURVES 55 -50 0 50 TJ (oC) 100 150 FIGURE 24. BREAKDOWN VOLTAGE vs TEMPERATURE 9 Application Note 9210 STEP 10(b) - MODEL DBDMOD (CJO, TT) may be determined at 25 volts and 25oC. COSS minus CRSS Then CJO is this value when adjusted to zero drain volts by the factor of the square root of (25+0.7) or 5.07. For the example this equals 7.55E-9. In order to determine TT, equipment similar to the Bermar SM30 may be used. This equipment forces a forward body diode current (If) for a sufficiently long period of time, after which a linear amplifier with high current capability ramps the diode current off at a constant rate, di/dt. (Feedback control is used.) The diode current equals zero at time TF, after the ramp off is initiated. The current continues to ramp, extracting charge from the diode, for an added time TA. At this time, the constant ramp (di/dt) can no longer be maintained and the reverse current has attained a maximum. TT may be solved [12] and entered using: TT = TA/(1-exp(-(TA+TF)/TT)) The value of TT was determined to equal 4E-8. STEP 11 - LGATE, LDRAIN, LSOURCE, RGATE LGATE, LDRAIN, LSOURCE, and RGATE may be measured, estimated or calculated and entered. An approximation for the inductances in nH may be calculated using: L = (5)(length)(loge(4(length/diam))) nH where wire length and diameter are in inches [13]. Values of Lgate, Ldrain, Lsource, and Rgate were approximated at 5E-9, 1E-9, 3E-9, and 1.2 for the final model. CAPACITANCES The capacitances are derived from the measured gate charge curve of Figure 27. They will require some iteration and some judgement calls as will be explained. VDS STEP 15 STEP 13 VGS VDS (V) 30 STEP 12 0 -30 STEP 13 - MODEL DPLCAPMOD (CJO) A feedback capacitor is modelled by using the junction capacitance of a reverse biased diode, DPLCAP, as defined by model DPLCAPMOD. IS and N of model DPLCAPMOD were chosen to avoid undesired diode effects. CJO is chosen as 2.14E-9 to best fit the solid line portion of the VDS curve of Figure 27. STEP 14 - CA, MODELS S1AMOD and S1BMOD (VON and VOFF) The value of CA is chosen to be 8.98E-9 to best parallel the dotted line portion of the VGS curve of Figure 27 labelled step 14. In order to match the dotted line portion it may be necessary to increment VON and VOFF of both model S1AMOD and model S1BMOD. Note that all four values must be incremented by an identical amount before making a PSPICE run. This incremental change will vertically displace the slope provided by CA. The transition voltages of S1A and S1B must always be negative values. The sharpness of transition between the dashed line of step 14 and the solid line of step 12 may be adjusted if necessary by changing the increment between VON and VOFF equally for both S1A and S1B. STEP 15 - CB, MODELS S2AMOD and S2BMOD (VON and VOFF) The value of CB is chosen to be 8.81E-9 to best parallel the solid line portion of the VGS curve of Figure 27 labelled step 15. In order to match the solid line portion it may be necessary to increment VON and VOFF of both model S2AMOD and model S2BMOD. Note that all four values must be incremented by an identical amount before making a PSpice run. This increment change will horizontally displace the slope provided by CB. The sharpness of transition between the solid line and the low voltage dotted line of the VDS curve may be adjusted if necessary by changing the increment between VON and VOFF equally for both S2A and S2B. It is recommended that this increment be small, of the order of several volts. STEP 16 - RIN TJ = +25oC RL = 0.667Ω IG = 3.44mA VDD = 50V STEP 14 20 40 TIME (µs) 60 FIGURE 27. GATE CHARGE CURVES STEP 12 - CIN The value of CIN should be chosen for best fit to the solid line portion of the VGS curve of Figure 27 labeled step 12. A value of 4.48E-9 was found to provide a good fit. 10 RIN can be set to a very large value such as 1E15. However it is recommended that it be chosen low enough to cause 10nA to flow at a gate bias of moderately high voltage, typically 1E9 ohms. Rin functions to provide an initial gate reference voltage near zero even though the Modeler may choose to drive the MOSFET from a current generator. EPILOGUE The final model is completed as shown in Table 3. One may iterate through the steps if desired, but it should not be necessary. Any changes made in the model outside of the above routine should be minimal, if at all. Application Note 9210 Anomalies Recommendations For Future Work Some commercially available power MOSFETs exhibit anomalous behavior which is not modelled in this work. A supporting program of algorithms should be written to address the parameter extraction effort. THE VERTICAL JFET PROBLEM Accurate testing for characterization of power MOSFETs as a function of temperature is required. Studies should be made to identify and correct methods prone to testing error. Devices of this type are not properly modelled. NON OHMIC CONTACT PROBLEMS Some commercially available devices exhibit a non-ohmic series contact resistance from the metallization to the silicon. This seldom happens with present day devices, but, when present, it is most likely to occur from source metal to source silicon for N channel devices, and from drain metal to drain silicon for P channel devices. The effect is seen as a low current non-linearity in RDS(ON) vs drain current for the former case and an excessive voltage drop for the body diode for the latter case. Devices of this type are not properly modelled. Conclusions PSPICE algorithms should be modified to refine and incorporate many of the findings of this work into a new MOS level. If a new MOS level is formed, a modification should be made to the drain current equation in the linear regime to accommodate the non-uniform channel surface concentration of the power MOSFET as described elsewhere. If done, the MOSFET may be more closely modelled in the linear regime of the output characteristic curves and the third quadrant MOSFET regime. (See Figure 9 and Figure 19.) The authors suggest a user defined model value WH to be used in a multiplier which would be applied to Id in the linear regime such that: Multiplier = (1+WH*(1-VDS/(VGS-VTO))2) If the multiplier were applied to the MOSFET of Table 3, the 1st and 3rd quadrant characteristics would be approximately as shown in Figure 28 for VGS = 5 volts. Here, WH is shown for values of 0, 1, and 2. The drain and source are interchanged for VDS < 0, as is done in PSPICE. 125 =2 =1 WH = 0 75 ID (A) A vertical JFET type of structure exists in the VDMOS device used for the industry standard power MOSFET. Many works describe this portion of the device, including Wheatley, et al [14]. The N- lightly doped drain region reaches to the surface of the silicon die, which is bounded by the P doped body. This region of N- is often called the neck of the MOSFET. As the breakdown voltage of the device is designed for increasing values, the depletion layer extends further within the neck laterally, for relatively low drain voltages. In this manner, the neck or vertical JFET becomes pinched off, causing the RDS(ON) to exhibit excess non-linearity with current. In addition an abrupt limiting of the drain current (at large values of drain voltages) occurs for increasing values of gate voltage. This current limiting has a highly localized thermal assist constrained to the neck with time responses in the microsecond region. This anomaly may be suppressed by increasing the neck width and/or implanting a low dose of N type dopant into the neck, just below the surface. LINEAR REGIME 25 T = +25oC KP = 78.6 VTO = 3.48 W = L = 1E6 RSOURCE = 0 RDRAIN = 0 -25 An equivalent circuit model for power MOSFETs that is suitable for use with PSPICE has been demonstrated. The model requires no modifications to the PSPICE algorithms. The model features global temperature representation from -55oC to 175oC for the first time. It addresses static and dynamic behavior over the normal circuit operating range of the device, including 1st and 3rd quadrant MOSFET operation, high current avalanche breakdown operation, body diode stored charge effects, gate charge non-linearities, gate equivalent series resistance (ESR), and package inductances. Gate propagation delay is not modelled [15]. The sub-circuit is empirical in nature and the parameters may be readily extracted by use of terminal measurements. Experimental verification shows excellent agreement between measured and simulated results over the entire thermal, static, and dynamic regimes. 11 SATURATED REGIME -75 -0.3 0.3 0.9 1.5 VDS (V) FIGURE 28. THE WH ADJUSTMENT A value of zero for WH forces the multiplier to equal unity for all values of VDS, thereby retaining the original linear regime equation. Zero should be the default value. Any value of WH greater than 1 results in a negative output resistance and is unacceptable. Therefore WH is bounded by 0 and 1. If this multiplier option were offered, it would be extracted for the model MOSMOD between steps 3 and 4 of Table 2, probably requiring some iteration between WH and Rdrain. Application Note 9210 Acknowledgements The authors express appreciation to Don Burke, Gene Freeman, Nick Magda, Hal Ronan, and Wally Williams for their support and assistance. REFERENCES [1] L. W. Nagel, “SPICE2: A COMPUTER PROGRAM TO SIMULATE SEMICONDUCTOR CIRCUITS,” ERL Memo UCB/ERL M520, University of California, Berkley, May 1975. [2] H. A. Nienhaus, J. C. Bowers, and P. C. Herren, “A High Power MOSFET Computer Model,” Power Conversion International, Jan 1982, pp. 65-73. [3] J. C. Bowers, and H. A. Nienhaus, “SPICE-2 Computer Models for HEXFETs,” International Rectifier HEXFET Data Book, Application Note 954A, pp A153-A160. [4] G. M. Dolny, H. R. Ronan, Jr., and C. F. Wheatley, Jr., “A SPICE II Subcircuit Representation for Power MOSFETs Using Empirical Methods,” RCA Review”, Vol 46, Sept 1985. [5] C. F. Wheatley, Jr., H. R. Ronan, Jr., and G. M. Dolny, “Spicing-up SPICE II Software For Power MOSFET Modeling,” GE/RCA Solid State, Application Note AN8610. [6] S. Malouyans, “SPICE Computer Models for HEXFET Power MOSFETs,” International Rectifier, Application Note 975. [7] H. P. Yee and P.O. Lauritzen, “SPICE Models for Power Mosfets: An Update,” Proc. APEC'88, Feb 1988, pp. 281-289, (Third Annual IEEE Applied Power Electronics Conference and Exposition, New Orleans), IEEE Cat no: 88CH2504-9. [8] C. E. Cordonnier, “Spice Model for TMOS Power MOSFETs,” Motorola Semiconductor, Application Note AN1043, 1989. [9] D. F. Haslam, M. E. Clarke, and J.A. Houldsworth, “SIM ULATING POWER MOSFETS WITH SPICE” Proc. HFPC, May 1990, p. 296. [10] A. Vladimirescu and M. Walker, “A Power MOSFET Macro-Model for Circuit Simulation,” Proc. POWER CONVERSION, Oct 1990, p. 112. [11] S. Klodzinski, C. F. Wheatley, Jr., and J. M. Neilson, Intersil Power, unpublished. [12] Y. C. Kao and J. R. Davis, “Correlations Between Reverse Recovery Time and Lifetime of p-n Junction Driven by a Current Ramp,” IEEE TRANSACTIONS on ELECTRON DEVICES, VOL. ED-17 No. 9, Sept 1970. [13] F. Langford-Smith, Editor, “Radiotron Designer's Handbook,” Fourth Edition, Wireless Press, 1953, Chapter 36.1, p. 1287 [14] C. F. Wheatley, Jr. and H. R. Ronan, Jr., “Switching Waveforms of the L2FET: A 5-Volt Gate Drive Power MOSFET,” Power Electronics Specialist Conference Record, June 1984, p. 238. [15] G. M. Dolny, C. F. Wheatley, Jr., and H. R. Ronan, Jr., “COMPUTER-AIDED ANALYSIS OF GATE-VOLTAGE PROPAGATION EFFECTS IN POWER MOSFETs” Proc. HFPC, May 1986, p. 146. All Intersil U.S. products are manufactured, assembled and tested utilizing ISO9000 quality systems. Intersil Corporation’s quality certifications can be viewed at www.intersil.com/design/quality Intersil products are sold by description only. Intersil Corporation reserves the right to make changes in circuit design, software and/or specifications at any time without notice. Accordingly, the reader is cautioned to verify that data sheets are current before placing orders. Information furnished by Intersil is believed to be accurate and reliable. However, no responsibility is assumed by Intersil or its subsidiaries for its use; nor for any infringements of patents or other rights of third parties which may result from its use. No license is granted by implication or otherwise under any patent or patent rights of Intersil or its subsidiaries. For information regarding Intersil Corporation and its products, see www.intersil.com 12

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