ASDA M 2000. Tlw Tliird Iiiimiuiioaul GimCorr/rrc.rice uif Advanced Seniicondircror Doviccs 29 uiid hficro.r~.r/rsts. Sifioleiticc~ Cusile. Slovukiu. 16- 18 Ocioher 2000, Supporied by fbe Eiiinlwaii Corfsnissiorr, DGXII. H u r r i u r i fiiiwiinl P r o ~ r u ~ i i ~ i i r HiSIr-Lei~el Scieiifqic Curfereiices, Coiifrucf Nu. HPCF-CT-2000-0(10 I7

Comprehensive Analysis of S i c Power Devices Using a Fully Coupled Physical Transport Model

G. Wachutka, M. Lades, W. Kaindl

Institute for Physics of Electrotechnology, Munich University of Technology, Arcisstr. 21 , D-80290 Munich, Germany.

Phone: +49 89 2892 3 122, FAX: +49 89 2892 3 164

We formulated an extended electrothermal drifr-diffusion model including the dynamic action of incompletely ionized impurities and validated the model by deriving a consistent set of material parameters for 4H- and 6H-SiC power devices. On this basis we performed detailed numerical studies of the coupled eflects between transient impurity kinetics and impact ionization, which may alter the reverse blocking characteristics ofpower devices under short switching conditions.

1. Introduction Silicon carbide (Sic) power devices receive strong attention because of their promising

properties for challenging industrial applications in the fields of high-voltage engineering and power transmission. Most notable are the wide band gap, being larger by a factor of 2.5 - 3 compared to silicon, the excellent thermal conductivity, and a breakdown field strength which exceeds that of silicon by a factor of nearly 10. In the past decade, enormous progress has been made in Sic process and device technology to exploit the attractive features of S ic as electronic material [l]. The state of the art is documented by various well-performing prototypes of high power devices which show robust bipolar operation under high temperature conditions with a maximum temperature nearly three times above that of silicon, very high blocking capability of reverse-biased pn- and Schottky-junctions due to the high breakdown field, and significant reduction of switching losses as a result of the much smaller amount of stored charge in the on-state compared to conventional silicon devices. So, in many respects, S ic devices turn out to be clearly superior to conventional silicon-based devices.

The development of S ic power devices is considerably facilitated and accelerated by “virtual experiments” using computer simulations. This involves the numerical analysis of the device operation on the basis of accurate physical device models. Virtual experiments allow visualizing the “internal life” of a device and thereby, on the one hand, to identify deficiencies and failure mechanisms which are not yet understood satisfactorily so far, and, on the other hand, to optimize the device performance in the various regimes of the operating area by an improved design. To this end, we formulated a comprehensive self-consistently coupled electrothermal transport model which accurately decribes, on the continuous-field level, various physical effects particularly relevant to Sic devices. They include, among others, several field-dependent generation-recombination mechanisms specific of wide-gap materials and their impact on the blocking capability, the consequences of anisotropic material properties such as the carrier mobilities and electric permittivity, the effect of incomplete dopant ionization, and the action of trap dynamics and impurity kinetics on fast switching transients (e.g., dynamic punch-through).

While the implications of tliese effects with respect to the static on-state behavior and the blocking characteristics have been demonstrated in previous work [2, 3, 41, we focus in this paper on the investigation of the coupled effect of impurity kinetics and impact ionization, which has been suspected to be the cause of the experimentally observed reduced breakdown voltage in 4H- and 6H-Sic pn-diodes under transient conditions [5 , 61. As theoretical basis, we also briefly review the underlying transport model [7, 21 and discuss the extraction of the kinetic coefficients entering the impurity dynamics. By means of own experiments, these

0-7803-5939-9/00/$10.00 02000 IEEE

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material parameters were validated with reference to several real devices investigated for this purpose.

2. Modcl equations Virtual experiments of state-of-the-art silicon power devices are usually based on the so-

called electrothermal drift-diffusion model. It is a natural approach to adapt this widely tried model to S ic devices by supplementing it with extensions for those physical mechanisms which are particularly relevant in wide bandgap semiconductors [2]. In this way we arrive at a set of 4+Ctp coupled differential equations for the vector of independent state variables (4 p , vy T , NT):

c--a(ZaT)= aT a ( ( z I T + + , , ) j , , +(F,,T ++,,)j,,) at

an 1 - - a N,: - - -VJ,i = (G - R)+ C- + C ( e r N r - c:!'n(Nlp - Nr )) at 4 D at a p I - - d N - - + -VJ, = (G - R)+ C A A at + C(e: (NI,, - Nr )- c : p N r ) at 4

(3)

a N r - = -(e: + e: + c::n + c : p ) ~ r + (e: + c ~ p n ) ~ ~ , , (4)

( 5 )

Non-uniform temperature distributions T(7,t) are governed by a heat flow equation, Eqn. (l), where c denotes the specific heat capacity and Z the thermal conductivity tensor. The distributions of the electron and hole densities, n and p , are obtained by the carrier balance equations, Eqns. (2) and (3). The electron and hole currents are driven by the gradients of the respective quasi-Fermi potentials, I+" and I+p, and the temperature, T, according to the constitutive current relations

at

v(zav)= q ( n - p + C N , - E N ; - E ( 2 ~ ( N l P IIJ - N F ) + 21yNr))

j, = -qvfiv(a4v + E V T ) (v = n , p ) , (6)

where ,E, denotes the mobility tensor and pv the tensor of thermoelectric power of electrons and holes, respectively, while q is the elementary charge.

The right-hand sides of Eqs. (2) and (3) represent a net carrier generation rate which includes contributions from band-to-band transitions (e.g. Auger recombination, impact ionization) and external excitation, summarized in the term (G-R), and contributions arising from transitions through deep and shallow impurities in the bandgap. The latter are modelled by an additional balance equation [SI, Eqn. (4), for each relevant impurity state. Here, N r denotes the density of occupied energy states of the impurity species rp (rp E traps). The emission and capture coefficients, e r and tip, model the electronic properties of the respective impurity species. The charged energy states in the bandgap contribute to the total electrical charge density on the right-hand side of Poisson's equation, Eqn. (S ) , where z y

and zr denote the charge number of an empty and an occupied state, respectively.

3. Dynamic ionization effects Impurities can be classified in generation-recombination centers, deep traps which are

predominantly coupled to only one of the bands, and dopants. In 4H- and 6H-SiC, the latter have to be considered also as "deep" energy states due to rather large ionization energies [2].

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For a "slow" external excitation, the corresponding change of the density of occupied impurities follows quasi-instantaneously and, therefore, the balance equation (4) can be replaced by a Gibbs distribution [9], thus eliminating N T as independent variable:

L J

If the external excitation is faster than the characteristic time constant needed for impurity charging or discharging

1 e: +er +c:n+crp

the corresponding occupation of the impurity cannot follow instantaneously and dynamic ionization occurs. The resulting basic effect is a dynamically extended depletion region as shown in Fig. 1 with a corresponding redistribution of the electric field. When a reverse bias pulse with a ramping time shorter than qp is applied to a pn-junction in electrothermal equilibium, first only a certain portion of the static background charge is available, since the free carriers trapped in a deep center cannot be emitted fast enough or, likewise, a not hlly ionized dopant state cannot ionize fast enough. Hence, a dynamically enlarged depletion region is formed in order to provide the charge required for sustaining the bias voltage. The maximum width of the dynamically extended depletion region may easily reach twice the static extension and occurs when the final reverse bias is reached.

(8) z =

"E $. -0.5

-g -1.0

U F 0 .- -1.5

U

& -2.0 I

-2.5

-3.0 0 1 2 3 4 0 50 loo 150 200 25030035o.ux)

distance [pm] teinperature [K] Figure 1: Transient response of the depletion region of a B-doped n'p-diode during a 100V/20 ns reverse bias ramp at 300 K.

Figure 2: Measured ionization time constants of boron, aluminum, and the cubic site of nitrogen in 4H- and GH-Sic.

Being the "key" property for estimating thc dynamic role of dopants in SIC, the ionization time constants of the cubic site of nitrogen (N,), aluminum (Al), and boron (B) have been measured by thermal admittance spectroscopy (TAS) and deep level transient spectroscopy (DLTS) [lo] as shown in Fig. 2. It tums out that the dynamic properties of N, and AI are not really relevant for practical applications, because they cannot influence the device operation not even in view of the shortest switching times encountered in today's power device applications. Dynamic ionization of By on the other hand, may influence the device characteristics even at temperatures above 400 K. One major and quite serious implication of this effect is the possibility of dynamic punch-through which possibly destroys a device exhibiting a back-to-back junction configuration [2, 1 I]. Hence, this effect has to be carefully taken into account for the proper design of fast-switching B-doped power devices.

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Another interesting phenomenon is the coupling of dynamic ionization with impact ionization. For the sake of brevity, we will restrict the discussion to the case of a pn-diode with non-punch-through (NPT) design that we have investigated among a number of other configurations [12]. Dynamic ionization leads to the emission of free carriers within the dynamically extended depletion region. This mechanism will result in an additional drift current due to the large electric field within the depletion region. Hence, the question arises, whether the breakdown characteristics of a junction will be altered by such an additional contribution to the avalanche generation rate. The pn-diode investigated shows a static avalanche breakdown at 680 V. In Fig. 3 and 4, the transient I-V characteristics and the internal electric field distributions during a reverse bias pulse with 10 ns are shown. Assuming an Al-doped layer which has negligible ionization time constants, the same breakdown voltage is obtained. In case of a B-doped layer, however, the diode is initially able to sustain a voltage ramp of 1000 V far beyond the static breakdown. After the end of the pulse, a remaining transient current proves that dopant ionization still continues within the depletion region, which finally leads to a breakdown more than 90 ns after the end of the pulse. The corresponding reduced maximum electric field at the junction subsequently relaxes towards its equilibrium and exceeds the critical field after 110 ns. As a result, dynamic ionization leads to more robust transient reverse breakdown characteristics. The breakdown voltage is mainly determined by the maximum electric field which is significantly reduced by the effect of dynamic ionization.

0 40 80 120 " 0 5 10 15 time [ns] dis tn i~e [pi]

Figure 3: Transient current of a B-doped n"p-junction during a 1000 V reverse bias pulse with a rise time of 10 ns at 300 K.

Figure 4: Distribution of the electric field in a n'p-diode with NPT design during a 1000 V reverse bias pulse with a rise time of 10 ns at 300 K.

4. Conclusions Our simulations demonstrate that a dynamic reduction of the breakdown voltage of SIC

pn-junctions due to transient ionization of dopants and traps cannot occur for two-dimensional homogeneous structures. The dynamical redistribution of the electric field generally leads to a more robust reverse blocking behavior. However, the dynamically enlarged depletion region can lead to dynamic punch-through for improper designs.

As basis for our analysis, we formulated a fully coupled electrothermal transport model covering the physical effects particularly relevant to Sic devices. The systematic calibration of the material parameters provides the prerequisite for the predictive quantitative simulation of realistic device structures.

References

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[12] M. Lades, Ph.D. thesis, Institute for Physics of Electrotechnology, 1999.