1. Theory

Definition: Power device compact models describe high-voltage MOSFETs (LDMOS and vertical DMOS) and IGBTs, whose behaviour is dominated by a lightly doped drift region: its bias-dependent resistance, its depletion capacitances and, in the IGBT, the stored minority-carrier charge that modulates its conductivity (HiSIM HV 2.4.2; MathWorks; Lauritzen et al.).
High-voltage MOSFETs: HiSIM_HV extends the surface-potential HiSIM model with an explicit drift-region resistance and overlap charges; lumped-charge models split the LDMOS into body and drain substructures (HiSIM HV 2.4.2; Subramanian et al.).
IGBTs: The Hefner model combines an internal MOSFET with a wide-base bipolar transistor described by ambipolar transport, base charge, avalanche and nonlinear capacitances; the Lauritzen lumped-charge model offers a simpler, easily extracted alternative (MathWorks; Lauritzen et al.).
Why bipolar at high voltage: The specific on-resistance of a silicon unipolar drift region rises as about $B V^{2.5}$ , so above several hundred volts conductivity modulation in the IGBT gives lower conduction loss (background knowledge; computed).

2. Working Principle

Drift resistance: Current through the drift region sees a resistance set by its doping, length and cross-section, reduced by accumulation under the gate overlap and increased by depletion from the substrate (HiSIM HV 2.4.2).
Conductivity modulation: In the IGBT the MOSFET’s electron current is the base current of a pnp whose holes flood the drift region, so the excess charge $Q_{e b}$ lowers the base resistance far below its ohmic value (MathWorks).
Charge storage and tail: At turn-off the excess charge must recombine, giving a tail current that decays with the ambipolar lifetime (MathWorks; Lauritzen et al.; background knowledge for the decay form).
Miller capacitance: The gate-drain capacitance is large while the drift region under the gate is accumulated and drops sharply once it depletes, which shapes the Miller plateau in switching (MathWorks; Lauritzen et al.).

3. Applications

Power conversion: Switching-loss and EMI simulation of converters and inverters with IGBTs and power MOSFETs (Lauritzen et al.; MathWorks).
Smart power ICs: LDMOS in BCD processes for drivers and regulators, using HiSIM_HV or lumped-charge models (HiSIM HV 2.4.2; Subramanian et al.).
Data-sheet models: Parameter extraction from data-sheet curves and capacitances for discrete devices (Lauritzen et al.).
Thermal design: Self-heating in HiSIM_HV and temperature-dependent models from 233 to 423 $K$ (HiSIM HV 2.4.2; Subramanian et al.).

High-Voltage MOSFETs

Name	Formula	Related Formulae	Variables/Constants
HiSIM_HV drift-region resistance	$R_{d r i f t} = \frac{V _{dd p}}{I _{dd p}} T_{d r i f t} + R S H \cdot N R D, I_{dd p} = \frac{W _{e f f, L D} N F X _{o v} q N _{d r i f t} μ _{d r i f t} V _{dd p}}{L _{d r i f t} + R D R D L 1}$	$W_{d e p, s u b} = \frac{2 ϵ _{S i} ( V B I S U B - R D V D S U B V _{d s} - R D V S U B V _{s u b, s} )}{q} \frac{N S U B S U B}{N O V E R ( N S U B S U B + N O V E R )}, T_{d r i f t} = \frac{L _{d r i f t}}{D D R I F T - W _{d e p, s u b}}$	$R_{d r i f t} : d r ain - s i d e d r i f t r es i s t an ce$ $V_{dd p} : p o t e n t ia l d r o p b e tw ee n t h e in t er na l d r i f t n o d e an d t h e d r ain$ $I_{dd p} : d r i f t - r e g i o n c u r r e n t$ $T_{d r i f t} : d e pl e t i o n cor r ec t i o n (1 w i t h o u t an a c t i v e s u b s t r a t e t er mina l), R S H$ $N R D : d i f f u s i o n s h ee t r es i s t an ce an d n u mb er o f s q u a r es$ $W_{e f f, L D} : e f f ec t i v e w i d t h$ $N F : n u mb er o f f in g er s$ $X_{o v} : d r i f t - r e g i o n t hi c k n ess$ $N_{d r i f t} : d r i f t d o p in g$ $μ_{d r i f t} : d r i f t m o bi l i t y, L_{d r i f t} = L D R I F T 1 + L D R I F T 2 : d r i f t l e n g t h, R D R D L 1 : l e n g t h cor r ec t i o n$ $W_{d e p, s u b} : s u b s t r a t e d e pl e t i o n w i d t h$ $V B I S U B : b u i l t - in p o t e n t ia l t o t h e s u b s t r a t e, N S U B S U B$ $N O V E R : s u b s t r a t e an d d r i f t d o p in g$ $D D R I F T : d r i f t d e pt h; H i S I M H V 2.4.2 : t h ese e q u a t i o n s f or C O R D R I F T = 1 (d e f a u l t), t h e d r i f t p o t e n t ia l so l v e d i t er a t i v e l y b y t h e s im u l a t or, t h e l e g a cy H V 1 f or m R_{d r i f t} = (R_{d} + V_{d s} R D V D) (1 + R D V G 11 - R D V G 11/ (R D V G 12 V_{g s})) (1 - V_{b s} R D V B) T_{d r i f t} f or C O R D R I F T = 0, C O S Y M 0 f or a sy mm e t r i c L D M O S an d 1 f or sy mm e t r i c H V M O S, an d T = T_{0} + δ T f or se l f - h e a t in g$ $(co m p u t e d : an a ss u m e d 1 mm w i d e, 2 μ m l o n g, 0.5 μ m t hi c k d r i f t r e g i o n d o p e d 2 \times 1 0^{16} c m^{- 3} w i t h 1000 c m^{2} / (V s) g i v es 12.5 Ω, or 12.5 Ω mm)$
HiSIM_HV overlap charges	$Q_{o v er} = W_{e f f} N F L_{o v er L D, m o d} C_{o x} (V_{g s} - V F B O V E R - ϕ_{s, o v er}) (inversion)$	$Q_{o v er, d} = Q_{o v er} + W_{e f f} N F QO V A D D L_{o v er L D, m o d} (V_{d p} - V_{c h}), L_{o v er L D, m o d} = L O V E R L D - W_{j u n c, o v}$	$Q_{o v er} : g a t e - o v er l a p c ha r g e o v er t h e d r i f t r e g i o n$ $L_{o v er L D, m o d} : bia s - d e p e n d e n t o v er l a p l e n g t h$ $C_{o x} : o x i d e c a p a c i t an ce p er a r e a$ $V F B O V E R : o v er l a p f l a t - ban d v o l t a g e$ $ϕ_{s, o v er} : o v er l a p s u r f a ce p o t e n t ia l$ $QO V A D D : coe f f i c i e n t o f t h e a dd e d d r i f t - p o t e n t ia l c ha r g e$ $V_{d p}, V_{c h} : d r i f t an d c hann e l p o t e n t ia l s$ $L O V E R L D : o v er l a p l e n g t h$ $W_{j u n c, o v} : j u n c t i o n e n cr o a c hm e n t; H i S I M H V 2.4.2 : t h ese e q u a t i o n s, a d e pl e t i o n an d a cc u m u l a t i o n f or m, a s u r f a ce - p o t e n t ia l o v er l a p m o d e l se l ec t e d b y n o n - z er o N O V E R an d a s im pl i f i e d V_{g s} - d e p e n d e n t m o d e l f or N O V E R = 0; H i S I M cor e o n t h e S u r f a ce - P o t e n t ia l M o d e l s p a g e$ $(n o co m p u t e d v a l u e)$
Lumped-charge LDMOS and the silicon limit	$q_{i B}, q_{a d B}, q_{i D}, q_{a d D} (body and drain lumped charges)$	$R_{o n, s p} \approx 5.93 \times 1 0^{- 9} B V^{2.5} Ω c m^{2} (ideal silicon drift region)$	$q_{i B}, q_{a d B} : b o d y in v er s i o n an d d e pl e t i o n or a cc u m u l a t i o n c ha r g es$ $q_{i D}, q_{a d D} : d r ain - s i d e e q u i v a l e n t s$ $R_{o n, s p} : s p ec i f i c o n - r es i s t an ce$ $B V : b r e ak d o w n v o l t a g e in v o l t s (s i l i co n l imi t, ba c k g r o u n d k n o w l e d g e); S u b r amanian e t a l . : a l u m p e d - c ha r g e L D M O S m o d e l s pl i tt in g t h e d e v i ce in t o b o d y an d d r ain s u b s t r u c t u r es, c ha r g es f r o m P o i sso n^{'} s e q u a t i o n a l o n g a v er t i c a l l in e, p a r am e t er s W, L B, L D, T O X, N B, N D, μ_{0}, T E M P E X P, V F B B, L A M B D A, T H E T A, V M A X an d f o u r f i tt in g p a r am e t er s (o n e in a l a t er v er s i o n), v a l i d a t e d a t 233, 300 an d 423 K, an d s t a t e d t o m ee t p o w er - M O S F E T m o d e l r e q u i r e m e n t s b e tt er t han s h or t - c hann e l ma cr o m o d e l s$ $(co m p u t e d : t h e s i l i co n l imi t g i v es 52 mΩ c m^{2} a t 600 V an d 296 mΩ c m^{2} a t 1200 V, w hi c h i s w h y bi p o l a r co n d u c t i v i t y m o d u l a t i o n, a s in t h e I GB T, i s u se d a t hi g h v o l t a g e)$

Hefner IGBT Model

Name	Formula	Related Formulae	Variables/Constants
Hefner IGBT: MOSFET channel current	$I_{m os} = \frac{K P ( V _{g s} - V T ) ^{2}}{2 [ 1 + T H E T A ( V _{g s} - V T ) ]} (V_{d s} > (V_{g s} - V T) / K F)$	$I_{m os} = \frac{K F \cdot K P [ ( V _{g s} - V T ) V _{d s} - K F V _{d s}^{2} /2 ]}{1 + T H E T A ( V _{g s} - V T )} (triode)$	$I_{m os} : e l ec t r o n c u r r e n t o f t h e in t er na l M O S F E T$ $K P : t r an sco n d u c t an ce (d e f a u l t 0.38 A/ V^{2})$ $V T : t h r es h o l d (d e f a u l t 4.7 V)$ $T H E T A : t r an s v er se - f i e l d f a c t or (d e f a u l t 0.02 V^{- 1})$ $K F : t r i o d e f a c t or (d e f a u l t 1)$ $V_{g s}, V_{d s} : in t er na l M O S F E T v o l t a g es; M a t hW or k s : t h ese e q u a t i o n s w i t h GM I N an d S C A L E t er m s, a f t er H e f n er$ $(co m p u t e d : a t V_{g s} = 15 V, t h e d e f a u l t s g i v e I_{m os} = 16.7 A in s a t u r a t i o n)$
Hefner IGBT: bipolar currents and base width	$I_{css} = \frac{I _{T}}{1 + b} + \frac{b}{1 + b} \frac{4 D _{p}}{W ^{2}} Q_{e b}, I_{b ss} = \frac{Q _{e b}}{T A U} + (\frac{Q _{e b}}{Q _{B}})^{2} \frac{4 N _{B}^{2}}{n _{i}^{2}} J S N E \cdot A R E A$	$W = W B - W_{b c j}, W_{b c j} = \frac{2 ϵ _{S i} ( V _{b c} + V _{bi} )}{q N _{B}}, Q_{B} = q W N_{B} A R E A, b = \frac{M U N}{M U P}$	$I_{css} : s t e a d y - s t a t e co l l ec t or c u r r e n t$ $I_{T} : an o d e c u r r e n t$ $b : ambi p o l a r m o bi l i t y r a t i o$ $D_{p} : h o l e d i f f u s i v i t y$ $W : u n d e pl e t e d ba se w i d t h$ $Q_{e b} : e x cess ba se c ha r g e$ $I_{b ss} : ba se c u r r e n t$ $T A U : ambi p o l a r l i f e t im e (d e f a u l t 7.1 μ s)$ $Q_{B} : ba c k g r o u n d ba se c ha r g e$ $N_{B} : ba se d o p in g (d e f a u l t 2 \times 1 0^{14} c m^{- 3})$ $n_{i} : in t r in s i c d e n s i t y (1.45 \times 1 0^{10} c m^{- 3})$ $J S N E : e mi tt er s a t u r a t i o n c u r r e n t d e n s i t y (d e f a u l t 6.5 \times 1 0^{- 13} A / c m^{2})$ $A R E A : d e v i ce a r e a (d e f a u l t 1 \times 1 0^{- 5} m^{2})$ $W B : m e t a l l u r g i c a l ba se w i d t h (d e f a u l t 90 μ m)$ $W_{b c j} : ba se - co l l ec t or d e pl e t i o n w i d t h$ $V_{bi} : 0.6 V, M U N$ $M U P : 1500 an d 450 c m^{2} / (V s); M a t hW or k s : t h ese e q u a t i o n s, I_{T} = V_{a e} / R_{b} w i t h a co n d u c t i v i t y - m o d u l a t e d ba se r es i s t an ce, an d an e mi tt er - ba se v o l t a g e s w i t c hin g b e tw ee n d e pl e t i o n an d d i f f u s i o n f or m s$ $(co m p u t e d : b = 3.33, so 1/ (1 + b) = 0.23; W_{b c j} = 8.3, 25.5 an d 62.3 μ m a t 10, 100 an d 600 V; Q_{B} = 28.8 nC f or t h e f u l l 90 μ m ba se an d d e f a u l t a r e a)$
Hefner IGBT: avalanche and capacitances	$M = \frac{1}{1 - ( V _{b c} / B V _{c b o} ) ^{B V N}}, B V_{c b o} = B V F \cdot 5.34 \times 1 0^{13} N_{B}^{- 0.75}$	$Q_{d g} = C_{g d o} V_{d g} (V_{d g} + V T D \leq 0), C_{g d o} = C O X D \cdot A G D, C_{cer} = \frac{Q _{e b} C _{b c j}}{3 Q _{B}}$	$M : a v a l an c h e m u l t i pl i c a t i o n$ $B V_{c b o} : o p e n - ba se b r e ak d o w n$ $B V N : e x p o n e n t (d e f a u l t 4)$ $B V F : u ni f or mi t y f a c t or (d e f a u l t 1)$ $Q_{d g} : g a t e - d r ain c ha r g e$ $C_{g d o} : g a t e - d r ain o x i d e c a p a c i t an ce$ $C O X D : i t s v a l u e p er a r e a (3.5 \times 1 0^{- 8} F / c m^{2})$ $A G D : g a t e - d r ain o v er l a p a r e a (d e f a u l t 5 \times 1 0^{- 6} m^{2})$ $V T D : d e pl e t i o n t h r es h o l d (1 \times 1 0^{- 3} V)$ $C_{cer} : co l l ec t or - e mi tt er r e d i s t r ib u t i o n c a p a c i t an ce$ $C_{b c j} : ba se - co l l ec t or d e pl e t i o n c a p a c i t an ce; M a t hW or k s : t h ese e q u a t i o n s, I_{m u l t} = (M - 1) (I_{m os} + I_{css} + I_{ccer}) + M I_{g e n}, a g e n er a t i o n c u r r e n t f r o m T A U an d t h e d e pl e t i o n w i d t h, a l o g a r i t hmi c d e pl e t i o n t er m f or Q_{d g} ab o v e - V T D, an d C GS = 1.24 \times 1 0^{- 8} F / c m^{2}$ $(co m p u t e d : B V_{c b o} = 1004 V f or t h e d e f a u l t d o p in g; M = 1.69 a t 80 p er ce n t o f B V_{c b o}; C_{g d o} = 1.75 nF, f a l l in g t o a d e pl e t i o n c a p a c i t an ce o f 0.020 nF o v er A G D a t 100 V)$

Lumped-Charge IGBT Model

Name	Formula	Related Formulae	Variables/Constants
Lumped-charge basic IGBT model	$\frac{1}{τ _{e f f}} = \frac{1}{τ _{E}} + \frac{1}{τ _{B}}$	$C_{ce 0} = C_{oes} - C_{r es} (V_{ce} = 0), I_{t ai l} (t) \approx I_{t ai l} (0) e^{- t / τ_{e f f}}$	$τ_{e f f} : e f f ec t i v e l i f e t im e$ $τ_{E}, τ_{B} : e mi tt er an d ba se r eco mbina t i o n l i f e t im es$ $C_{ce 0} : z er o - bia s co l l ec t or - e mi tt er c a p a c i t an ce$ $C_{oes}, C_{r es} : d a t a - s h ee t o u tp u t an d r e v er se - t r an s f er c a p a c i t an ces$ $I_{t ai l} : t u r n - o f f t ai l c u r r e n t (e x p o n e n t ia l d ec a y, ba c k g r o u n d k n o w l e d g e); L a u r i t z e n e t a l . : a b u f f er - l a y er, p u n c h - t h r o ug h I GB T m o d e l u s in g l u m p e d c ha r g es a t t h e e d g es o f t h e in t er na l ba se, a p h y s i c a l in t er na l B J T an d an e m p i r i c a l t anh - ba se d M O S F E T w i t h p a r am e t er b, γ f r o m t h e c ha r g e in t h e M i l l er pl a t e a u, C_{ce 0} f r o m d a t a - s h ee t c a p a c i t an ces, a ba se t r an s i t t im e T_{0} f r o m τ_{e f f} an d t h e r a t i o o f ini t ia l t o t ai l c u r r e n t, a s m oo t hin g o f ba se - w i d t h v a r ia t i o n n e a r p u n c h - t h r o ug h, an d v a l i d a t i o n o n an I n t er s i l 12 N 60 B 3 D (9 A a t 18 V, 40 A a t 100 an d 400 V) an d a M i t s u bi s hi C M 1200 H A - 34 H (1200 A a t 42 an d 800 V)$ $(co m p u t e d : a ss u m e d τ_{E} = 2 μ s an d τ_{B} = 5 μ s g i v e τ_{e f f} = 1.43 μ s; t h e H e f n er d e f a u l t T A U o f 7.1 μ s l e a v es 87 p er ce n t o f t h e t ai l a f t er 1 μ s)$

Important Questions

Ques: How does the Hefner model combine the MOSFET and the bipolar transistor in an IGBT?

The internal MOSFET supplies the electron current that drives a wide-base pnp. MathWorks gives the channel current $K P (V_{g s} - V T)^{2} / {2 [1 + T H E T A (V_{g s} - V T)]}$ in saturation, 16.7 $A$ at 15 $V$ for the defaults (computed). The collector current is $I_{T} / (1 + b) + [b / (1 + b)] (4 D_{p} / W^{2}) Q_{e b}$ , where $b$ is the electron-to-hole mobility ratio, 3.33 for the defaults (computed), and $Q_{e b}$ the excess charge in the undepleted base of width $W$ . The base current combines recombination $Q_{e b} / T A U$ with emitter injection that grows as $Q_{e b}^{2}$ . The anode current flows through a base resistance that falls as the charge modulates the conductivity. The structure makes the IGBT a MOSFET-driven bipolar device, with the voltage-controlled input of the MOSFET and the low on-voltage of the bipolar transistor. Reference: MathWorks, ‘SPICE NIGBT’, Simscape Electrical block reference page, after A. R. Hefner (1992, 1994) (fetch-tool summary).

Ques: What sets the undepleted base width and breakdown in the Hefner model?

The base doping. The undepleted width is $W = W B - W_{b c j}$ with $W_{b c j} = 2 ϵ_{S i} (V_{b c} + V_{bi}) / (q N_{B})$ (MathWorks). For the default $2 \times 1 0^{14}$ $c m^{- 3}$ base, the depletion width is 8.3 $μ m$ at 10 $V$ , 25.5 $μ m$ at 100 $V$ and 62.3 $μ m$ at 600 $V$ (computed), so the 90 $μ m$ base never punches through below about 1000 $V$ . Breakdown follows $B V_{c b o} = B V F \cdot 5.34 \times 1 0^{13} N_{B}^{- 0.75}$ , 1004 $V$ for the defaults (computed), and multiplication $M = 1/ [1 - (V_{b c} / B V_{c b o})^{B V N}]$ reaches 1.69 at 80 per cent of it with BVN = 4 (computed). Because W shrinks with voltage, the bipolar gain and the stored charge depend on collector voltage, which the model captures through $4 D_{p} / W^{2}$ and $Q_{B} = q W N_{B} A R E A$ . A thinner base doped more heavily would lower the on-voltage but also the breakdown voltage (background knowledge). Reference: MathWorks, ‘SPICE NIGBT’, Simscape Electrical block reference page, after A. R. Hefner (1992, 1994) (fetch-tool summary).

Ques: What causes the IGBT tail current and how do the models describe it?

Stored charge that can only recombine. When the MOSFET channel turns off, the electron current stops, but the excess charge in the drift region remains and the pnp continues to conduct until it recombines. In the Hefner model the recombination term $Q_{e b} / T A U$ controls this, with a default ambipolar lifetime of 7.1 $μ s$ (MathWorks); a simple exponential decay with that lifetime would leave 87 per cent of the tail after 1 $μ s$ (computed, background knowledge for the exponential). Lauritzen et al. use an effective lifetime from emitter and base lifetimes, $1/ τ_{e f f} = 1/ τ_{E} + 1/ τ_{B}$ , 1.43 $μ s$ for assumed values of 2 and 5 $μ s$ (computed), and a base transit time from the ratio of initial to tail current. Their model matched turn-off waveforms of a 1200 $A$ module well except for some tail data. Reference: MathWorks, ‘SPICE NIGBT’, Simscape Electrical block reference page, after A. R. Hefner (1992, 1994) (fetch-tool summary); P. O. Lauritzen, G. K. Andersen and M. Helsper, ‘A Basic IGBT Model with Easy Parameter Extraction’, IEEE Power Electronics Specialists Conference, Vancouver (June 2001) (appendix equations garbled in the extract) (fetch-tool summary).

Ques: How many parameters does the Lauritzen basic IGBT model have?

The paper says 17, but its lists do not add up. Lauritzen et al. state 11 conduction parameters and 6 capacitance and parasitic parameters, but their Table 1 names 12 for conduction (kP, kV, VT, b, VJ, VPT, ILH, T0, tauB, tauE, RH and RE) and only 5 for capacitance (LE, Cox, gamma, Cge0 and Cce0). Both lists total 17, so the probable explanation is that one parameter, perhaps RE or LE, was counted in the other group (my reading). The model’s point is that most parameters come from data sheets: $C_{ce 0}$ is the output capacitance minus the reverse transfer capacitance at zero collector voltage, and gamma comes from the charge in the Miller plateau. They validated it on a 12N60B3D at 9 and 40 $A$ and on a CM1200HA-34H at 1200 $A$ , at collector voltages up to 800 $V$ . Reference: P. O. Lauritzen, G. K. Andersen and M. Helsper, ‘A Basic IGBT Model with Easy Parameter Extraction’, IEEE Power Electronics Specialists Conference, Vancouver (June 2001) (appendix equations garbled in the extract) (fetch-tool summary).

Ques: How does HiSIM_HV model the drift-region resistance of an LDMOS?

As a bias-dependent resistor between the channel and the drain. In the default CORDRIFT = 1 model, $R_{d r i f t} = (V_{dd p} / I_{dd p}) T_{d r i f t} + R S H \cdot N R D$ , with $I_{dd p} = W_{e f f, L D} N F X_{o v} q N_{d r i f t} μ_{d r i f t} V_{dd p} / (L_{d r i f t} + R D R D L 1)$ and a depletion factor $T_{d r i f t} = L_{d r i f t} / (D D R I F T - W_{d e p, s u b})$ when the substrate terminal is active (HiSIM HV 2.4.2). The internal drift potential is solved by the simulator, so the resistance responds to drain and substrate bias. For an assumed 1 $mm$ wide, 2 $μ m$ long, 0.5 $μ m$ thick drift region doped $2 \times 1 0^{16}$ $c m^{- 3}$ with 1000 $c m^{2} / (V s)$ , the ohmic value is 12.5 $Ω mm$ (computed). The gate-overlap charge, with a surface-potential model selected by non-zero NOVER, captures accumulation over the drift region. Subramanian et al. take a different route for the same device, splitting it into body and drain substructures with lumped charges. Reference: T. Iizuka, H. Kikuchihara, H. Miyamoto, M. Miyake, H. J. Mattausch and M. Miura-Mattausch, ‘HiSIM HV 2.4.2 User’s Manual’, Hiroshima University (9 April 2019) (defaults table and self-heating section not in the extract) (fetch-tool summary); Y. Subramanian, P. O. Lauritzen and K. R. Green, ‘A Compact Model for an IC Lateral Diffused MOSFET Using the Lumped-Charge Methodology’, Proceedings of MSM99, San Juan (1999) (equations garbled in the extract) (fetch-tool summary); Surface-Potential Models (PSP and HiSIM) page of this vault.

Ques: Does HiSIM_HV 2.4.2 still contain the old drift-resistance model?

The manual is inconsistent. Its introduction says version 2.4.2 excludes the old resistance model of the HiSIM HV1 series, yet Section 15.2 still documents CORDRIFT = 0 as a legacy option, $R_{d r i f t} = (R_{d} + V_{d s} R D V D) (1 + R D V G 11 - R D V G 11/ (R D V G 12 V_{g s})) (1 - V_{b s} R D V B) T_{d r i f t}$ . The most likely reading is that the HV1 implementation was removed and CORDRIFT = 0 now selects a compatibility form with HV1-style parameters inside the 2.x code, which the introduction does not mention (my reading). The legacy form is empirical: resistance rising with drain voltage through RDVD and falling with gate voltage through RDVG11 and RDVG12. The new CORDRIFT = 1 form is physical, built from drift doping, mobility and geometry. Users porting HV1 model cards should check which form their simulator applies. Reference: T. Iizuka, H. Kikuchihara, H. Miyamoto, M. Miyake, H. J. Mattausch and M. Miura-Mattausch, ‘HiSIM HV 2.4.2 User’s Manual’, Hiroshima University (9 April 2019) (defaults table and self-heating section not in the extract) (fetch-tool summary).

Ques: Why does a power device need a bias-dependent gate-drain capacitance?

Because it changes by orders of magnitude during switching. In the Hefner model, $Q_{d g} = C_{g d o} V_{d g}$ while the drift region under the gate overlap is accumulated, with $C_{g d o} = C O X D \cdot A G D$ , 1.75 $nF$ for the defaults; once $V_{d g}$ exceeds $- V T D$ a depletion layer forms under the overlap and the capacitance falls toward $ϵ_{S i} A G D / W_{b c j}$ , 0.020 $nF$ at 100 $V$ (computed). The resulting Miller plateau sets the switching speed, so a constant capacitance mispredicts both the plateau length and the voltage slew rate. Lauritzen et al. extract the corresponding parameter gamma from the charge in the Miller plateau. In HiSIM_HV the overlap charge uses a surface-potential model over the drift region, which gives the same accumulation-to-depletion transition. Reference: MathWorks, ‘SPICE NIGBT’, Simscape Electrical block reference page, after A. R. Hefner (1992, 1994) (fetch-tool summary); P. O. Lauritzen, G. K. Andersen and M. Helsper, ‘A Basic IGBT Model with Easy Parameter Extraction’, IEEE Power Electronics Specialists Conference, Vancouver (June 2001) (appendix equations garbled in the extract) (fetch-tool summary); T. Iizuka, H. Kikuchihara, H. Miyamoto, M. Miyake, H. J. Mattausch and M. Miura-Mattausch, ‘HiSIM HV 2.4.2 User’s Manual’, Hiroshima University (9 April 2019) (defaults table and self-heating section not in the extract) (fetch-tool summary).

References

MathWorks, “SPICE NIGBT,” Simscape Electrical documentation, block reference page (after A. R. Hefner). Available: https://www.mathworks.com/help/sps/ref/spicenigbt.html
P. O. Lauritzen, G. K. Andersen and M. Helsper, “A Basic IGBT Model with Easy Parameter Extraction,” in Proc. IEEE Power Electronics Specialists Conference, Vancouver, June 2001. Available: https://labs.ece.uw.edu/pemodels/papers/IGBT-PESC01.pdf
T. Iizuka, H. Kikuchihara, H. Miyamoto, M. Miyake, H. J. Mattausch and M. Miura-Mattausch, “HiSIM HV 2.4.2 User’s Manual,” Hiroshima University, Apr. 2019. Available: https://www.simetrix.co.uk/supplementary/Docs/HiSim-HV/HiSIM_HV_2.4.2_Users_Manual.pdf
Y. Subramanian, P. O. Lauritzen and K. R. Green, “A Compact Model for an IC Lateral Diffused MOSFET Using the Lumped-Charge Methodology,” in Proc. Modeling and Simulation of Microsystems (MSM99), San Juan, 1999. Available: https://www2.ee.washington.edu/research/pemodels/papers/msmpaper-msm99.pdf

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Power Device Compact Models