A new physics-based circuit model for 4H-SiC power diodes implemented in SABER

A New Physics-Based Circuit Model for 4H-Sic Power Diodes Implemented in SABER

R. Kolessar and H.-P. Nee

Royal Institute of Technology Department of Electrical Engineering

Electrical Machines and Power Electronics S-100 44 Stockholm, Sweden

remy.kolessar @ekc. kth .se

Abstruct- A circuit-oriented model for 4H-Sic power diodes is presented. The modeling technique used in this work was previously ap- plied to a silicon (Si) power diode model for both turn-on and turn-off transients, and presents a good trade-off between accuracy and speed. The model is physics-based, but includes judicious approximations for fast calculation, and includes up-to-date physical models for silicon carbide, with temperature dependence. The proposed model is practically implemented in the circuit simulator SABER, using the MAST modeling language. Model performances are compared to measurements on 2.5 kV 400 A Si IGBT/SiC diode modules from ABB at various input cur-

NOMENCLATURE

j-order polynomial coefficient in subregion i ( ~ m - ~ + j ) . electric field (V/cm). valance band energy level (ev). donor effective ionization energy (eV). Fermi energy level (eV). bandgap energy (eV). anode (cathode) h-parameter (cm2/s). displacement current density (A/cm2). hole current density (A/cm2). anode (cathode) recombination current density (A/cm2). time-dependent variable for the moving boundaries (cmW3). electron (hole) density-of-state effective mass (kg). electron concentration ( ~ m - ~ ) . intrinsic carrier concentration ( ~ m - ~ ) . donor (acceptor) concentration ( ~ m - ~ ) . density-of-states in the conduction (valance) band ( ~ m - ~ ) . hole concentration ( ~ m - ~ ) . carrier concentration at the left (right) boundary of the excess charge ( ~ m - ~ ) . elementary charge (As). charge in subregion i (As). diode reverse recovery charge (As). junction temperature (K). anode (cathode) voltage drop (V). depletion region voltage (V). diode n-base width (cm).

X / , r k P electron (hole) mobility (cm2/V.s). 7 high-level lifetime (s). rn ,p

left (right) boundary of the excess charge (cm).

low-level electron (hole) lifetime (s).

I. INTRODUCTION

Silicon carbide (Sic) is a possible candidate to replace silicon commercially for power devices in a near future, thanks to its remarkable electronical and physical properties compared to conventional silicon (Si) technology, e.g. higher critical electric field (x4-20), higher thermal conductivity (x3-13) and temperature capability (x2-3) [l]. It is therefore interesting to be able to already investigate its impact and benefits on the design of modern power electronic systems.

For that purpose, accurate physics-based models for circuit simulation are required for S i c devices, with good predictive capabilities. To achieve such model performances at circuit level, a good trade-off between accuracy and efficiency has to be obtained. Fast and relatively simple models often give a too much simplified representation of the complex physics in- volved during transients of the device, and thus provide limited ability to implement advanced physical models [2]. On the other hand, more accurate models, with better physical representation, most often use complex algorithms or geometric approximations that are not always suitable for simulation at circuit level [3,4].

The physics-based modeling technique used in this work presents an interesting trade-off between simplicity and accuracy, and was previously used for Si power diode models with good results [S, 61. Indeed, due to its original formal- ism, the model presents a good ability to support a wide range of physical models with a very flexible implementation procedure. Therefore, this modeling technique appears to be partic- ularly appropriate for implementation of silicon carbide physical models.

A set of relevant 4H-Sic physical models, which are today available are presented. These models have been included in the circuit power diode model, and implemented in the circuit simulator SABER [7].

The proposed circuit model for silicon carbide diodes is validated by comparison with measurements on 2.5 kV 400 A Si-IGBT / Sic diode modules from ABB [8]. Good agreement

0-7803-6618-2/01/$10.00 0 2001 IEEE 989

is obtained between simulation and measurements.

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11. THE MODELING TECHNIQUE

The modeling technique used in this work is described more extensively in [5,6], and only basic principles are presented here. The main idea for describing high injection level effects is to divide the n- region of the diode into a number of subre- gions (typically five to ten), and apply a Charge Control Equa- tion (CCE) for each subregion with the charge Qi, see Fig. l . Moving boundaries for the total excess charge are also taken into account, which results in the following system of differ- ential equations

+ = -+ + jp(x1) - jp(x1) +q . K,a ( t ) % - q * Kf( t ) @&c

where the first term on the right hand accounts for carrier recombination with a carrier lifetime T . The second and third terms are the net charge supply. The last two terms account for the moving boundaries 21 and x,.

The carrier distribution in each subregion is approximated by second degree polynomials with time-varying coefficients

In order to ensure a non-quasi static model, the excess charge Qi is linked at every moment to the spatial distribution of the carrier concentration since we have

The resulting system (1) has to be solved with the following simplified moving boundary conditions depending on the state of the diode, i.e. turn-on, on-state or turn-off,

(4) if p~ > 0 then 21 = 0 else pl = 0 if p , > 0 then x, = else p , = 0,

where pr and p , are respectively the carrier concentrations at the boundaries x1 and xT, which is illustrated in Fig. 1.

Note that the model parameters are all of physical nature, i.e. device active area, diode base width and doping level, h- parameters for emitter recombination and high-level carrier lifetime.

111. IMPLEMENTATlON OF PHYSICAL MODELS FOR 4H-SlC DIODES

At circuit simulation level, it is very important to include only the most relevant physical models in order to fulfill the requirement of fast computation time. These models are very

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Concentration

Pi N -

PI

+-

Voltage, Current t

Fig. 1. a) Simplified principle of the PIN diode model discretization and carrier distribution during the diode reverse recovery showing the different boundary conditions. b) 'Qpical voltage (plain) and current (dashed) waveforms for a typical diode tum-off.

well described for silicon devices, and their impact on the calculation accuracy is well known [9].

The problem is however more complex for silicon carbide devices, since the physical models themselves are, in most cases, not completely well described or understood. In order to derive and implement a pertinent set of physical models, a study to identify relevant physical models for S i c diodes was performed using MEDIC1 with a special simulation package for 4H-Sic [ 101, including advanced models like bandgap narrowing, Auger recombination and impact ionization. In partic- ular, the impact of different physical models for 4H-Sic from [ 111 on the switching behavior of a silicon carbide diode was studied. The physical models that proved to have noticeable influence for S i c diodes are presented hereafter. Temperature behavior is included in each case, even if not always validated.

A. Lifetime

Due to the lack of specific information for Sic, low-level lifetime is usually approximated .assuming Shockley-Read-

Hall recombination mechanisms. For the model purpose, only the high injection lifetime 7, which is defined as

7- = 7, + TP, (5)

has to be included, and its value is typically in the range 0.1- 2 ps. The temperature behavior is based on an empirical derivation from Lindefelt [I21 for the range 300 K 5 T 5 450 K ,

T w ~ ( 3 0 0 K ) . 2.1724. - - 1.1724). (6) ( 300K

B. Mobility Model

The equations for the low field mobilities for holes and electrons from [ 111 can be directly implemented in the diode model. These equations are based on measurements from [ 131 for 4H-SiC, and are defined for the electron and hole mobilities

, respectively as

108.9 : pp(T) = 15.9+ 1 + (+&3$)0.34

Moreover, the anisotropic properties of 4H-Sic is expressed by

Pn,L = Pn 7 Pn,(l = 1*2Pn (9) PPJ = PP 1 P p , ( ( = PP. (10)

C. Incomplete Ionization of Doping Atoms in the Base

In a S ic diode at room temperature and depending on the doping concentration, not all doping atoms are completely ionized, as it is the case for Si structures. This is due to the wide- bandgap of Sic compared to Si. The impact of incomplete ionization is discussed here for the lowly doped base only. In- deed, the effect of incomplete ionization in the highly doped emitters can be considered with the concept of h-parameters. This is treated in a following section.

In the case where the dynamic effects of incomplete ionization is not considered, the following equation can be used [ 1%

(1 1) N d Nd+ =

1 + 2 . e z p (w) ’

E d is a single effective ionization energy level given by E, - E d = 65 meV for doping with N [ 1 11.

However, the donor doping concentrations for the base layer of high power S ic diodes are in the low 1015 ~ m - ~ . With the value of E d at these impurity levels, the doping atoms are found to be almost completely ionized, even at a temperature of 400 K. Therefore, for a range of temperature of 300-400 K and donor doping levels below 1 x 10l6 cmb3, we can use the following approximation

Nd+ N Nd. (12)

Temperature (K) Fig. 2. Intrinsic carrier concentration in 4H-Sic with temperature using (17).

Circles are from the exact calculation combining (14), (15) and (16) in (13).

D. Intrinsic Carrier Concentration

The intrinsic carrier concentration ni is expressed as [ 141

The densities-of-states Nc and Nv are given by

312 Nc(T) = 2.50945 10” * ( 7 % ~ ~ ) ~ ’ ~ . (A) (14)

Nv(T) = 2.50945 * lo1’ ( m d ~ ) ~ ’ ~ . ( &)3’;J5)

if we assume parabolic bands [ 111. No model is today available for the temperature dependence

of the intrinsic bandgap Eg for 4H-Sic. However, an approximation based on 6H-Sic data is given by [ 111, and yields

Eg(T) = 3.19 - 3.3. 10-3(T - 300K) eV. (16)

Combining (14), (15) and (16) with (13) allows to calculate ni as a function of T. A more convenient expression for ni as a function of temperature can be obtained by using () and fitting the coefficient to the exact calculation.

(17)

The intrinsic carrier concentration in 4H-Sic based on (17) is plotted as a function of temperature in Fig. 2.

E. Emitters and h-Parameters

The concept of h-parameters is widely used for analytical calculation of emitter recombination and efficiency at high injection level [ 15,161. This permits with a simple formulation to account for more complex physical phenomena like bandgap narrowing or Auger recombination.

Calculations based on MEDIC1 simulations confirm that the equations are still valid for silicon carbide, with the recombination current being proportional to the square of the carrier

ni(T) = A ~ T ~ / ~ exp ( - A ~ / T ) .

99 1

concentrations at the respective emitter edge

j l = q h p : (18) j r = qhr$. (19)

Generally, for highly doped and deep emitter profiles in silicon structure, the h-parameters are constant with weak temperature dependence. But for thin emitters, as usually obtained in S i c structures (emitter depth <5 pm) [ 171, the h-parameter is not constant with temperature [ 161. This can be partly at- tributed to the increase in ionized doping atoms with increasing temperature, but also to more complex physical phenomena like bandgap narrowing and Auger recombination.

Practically and for a given emitter design (basically emitter depth and doping), calculation of h-parameters are performed by MEDIC1 simulations and an empirical law of the following form is used

The coefficients ah,,, are determined by fitting with results from MEDICI, Fig. 3.

E Diode voltage

The diode voltage is computed by adding the emitter voltage drops Va (anode) and V k (cathode) to V, (base). This results in

(2 1) I ) Diode blocking voltage: At turn-off conditions, most of

the diode voltage is sustained by the depletion region. Abrupt junction approximations are sufficient for description of silicon carbide structures (even though the model can include different profiles), since emitters in S i c diodes are usually thin and highly doped, as discussed previously.

Using this approximation, the following expressions can be derived from Poisson's equation for calculation of the diode voltage at reverse blocking conditions. The electric field distribution is given by

v d = v a + vm + v k

(22) E W s a t

and the blocked voltage by a further integration of (22) over the depletion region

Note that the eventual transport of holes in the depletion region is accounted for.

2) Emitter voltage drops: The same Boltzmann equations used for Si PIN diodes are used for SIC. These equations for the calculation of voltage drops at the anode and cathode respectively read

Z x " - ~ ' " ' ' I ' ' ' I " ' I " ' J

280 320 360 400 440

Temperature (K)

I . . . I . . . I . . . I . . . l Temperature (K)

280 320 360 Qw 440

(b)

Fig. 3. h-parameters with temperature at the anode a) and cathode b) for emitter depths of 2 p m and 5 p m respectively, and doping at 1 x I O l 9 cmP3. The circles and squares are MEDICI simulations.

and kT

Vk = -1In 4 ($). Fig.4 shows calculations using (24) and (25) for a donor

concentration of N d =1 x loi5 ~ m - ~ . The difference is more relevant at the anode where the value are >2.5 V for 4H-SiC, whereas it is typically < 1 V for Si pn junctions. This is due the larger bandgap and thus contact potential of 4H-Sic structures compared to their Si counterparts.

V, on the other hand is smaller in Sic than for Si devices. This is because of the usually higher doping concentration in the base ( IO1' cm-3 range for S ic compared to cm-3 for Si), since we have a low-high junction barrier in that case.

G. Displacement Current

The displacement current j d during turn-off of Si diodes is, in most cases negligible, since most of the reverse current is due to the charge sweep out.

For Sic diodes however, the displacement current is often a non-negligible part of the total recovery current, since

992

3 , I I

05

---- -- rrrd

-

- - _______- ---------

much less excess charge is injected in the n- base than in Si- based structures. This has therefore to be included in the diode model. The displacement current is given by

dE j d = E - - , at

if we assume that j d is uniform and independent of the position in the depletion region, which is justified if the transit time of the charge is negligible compared to the time constant of the currents. Combining (26) with (22), we have

Note that carriers (holes) in transit in the depletion region are also taken into account in (27).

IV. IMPLEMENTATION IN SABER

The basic set of analytical physical models described previously is easily implemented in the circuit level model. The practical implementation is done using a so-called High De- scription Language (HDL) called MAST, which is part of the SABER circuit simulator, and is described in [18]. Note that no external C-routines have to be used for this implementation.

V. MODEL VALIDATION

The performances of the proposed model are tested by comparison with transient measurements on 2.5 kV Si IGBTlSiC PIN diode from ABB. These modules are manufactured by par- alleling four units of large area (40 mm2) 2.5 kV 4H-Sic PiN diodes with four 2.5 kV Si-IGBT chips with an area of 1 cm2 each using a standard high power press-pack technology [8].

A. Experimental

The test-circuit being used is a single pulse circuit as shown in Fig.5. The turn-off transient of diode D1 can be investi- gated when the when the initial forward current from the induc- tive current from L, is commutated from diode D1 to IGBT2

,

993

Fig. 5. Single pulse test-circuit used for both measurements and simulations.

TABLE I MODEL PARAMETERS FOR THE 4H-SiC DIODE.

1 Model Parameter I Value

T (high level lifetime)

tun (base width)

when this one is turned-on. The freewheeling diode D1 is then reverse-biased and reverse recovery occurs.

Measurements of dynamic switching of the Si IGBT/SiC diode modules are performed at a temperature of T = 125°C for forward currents of 50 A and 150 A with a blocking voltage of 800 V, as well as for a forward current of 400 A with a reverse voltage of 1250 V.

B. Simulations

Simulations were performed by implementing the single pulse circuit of Fig. 5 in SABER. The switching behavior of the IGBT. is modeled using a standard MOSFET model with adjusted parameters. The model parameters are extracted for one case and are kept constant for the remaining simulations. The six model parameters are shown in Table I. The temperature is also fixed at T = 125°C.

C. Results and Discussion

SABER simulations using the proposed model and measurements made on the S ic diode modules are presented in Fig. 6 and 7 at various forward currents. Very good agreement between experimental and simulation data is observed for the various conditions. The slight deviations, specially in the diode voltage of Fig. 6 are probably due to limitations in the modeling of the IGBT. Notice the small changes of the recovery current with increasing forward current, which is well predicted by the model. Once again, the same parameters have been used in all cases. The simulations are computed in few seconds on a PC PI11 600 MHz computer.

200

I50

h 100

E 50 4 E a 0

- -50

-100 4- -200 0 1 2 3 4 5

Time (ps)

Fig. 6. Comparison between a) measurements and b) simulations of the Sic diode with forward currents of 50 A and 150 A with a DC link at 800 V.

VI. CONCLUSIONS

In conclusion, a predictive physics-based model for 4H-Sic power diodes suitable for circuit simulation is presented and implemented in the SABER simulator. The set of physical models for 4H-SiC, which was implemented in the model have been discussed in detail. Most of these models include temperature dependence. Analytical equations in some cases are presented for these models in order to simplify the implementation procedure. The proposed model is also validated with measurement results. Model performances are compared favor- ably to an experimental test-circuit built with 2.5 kV 400 A Si- IGBT/4H-SiC diode modules at various forward current conditions.

ACKNOWLEDGMENTS

The authors would like to thank H. Lendenmann from ABB Corporate Research, Sweden for measurement data and fruitful discussions. M. Bakowski and U. Lindefelt are also acknowl- edged for valuable discussions about the Sic models. This

1200 loo0 g 800 g

400 5 6Ml E 200 0

-m 0 2 4 6 8 1 0

Time (ps)

Fig. 7. Comparison between measurements (plain) and simulation (dashed) of the SIC diode with forward currents of 400 A with a DC link at 1250 V.

project is financially supported by ELFORSK and the Swedish Foundation for Strategic Research within the SiCEP program.

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A new physics-based circuit model for 4H-SiC power diodes implemented in SABER

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