4H-SiC Auger recombination coefficient under the high injection condition

Power semiconductor devices based on silicon carbide (SiC) have recently received significant attention for high-voltage operations. Commercialized SiC devices include metal oxide semiconductor field effect transistors (MOSFETs) and Schottky barrier diodes (SBDs), both of which have lower on-resistance and higher breakdown voltage than their Si counterparts. SiC SBDs and MOSFETs are unipolar devices because they conduct electricity using only electrons. By contrast, bipolar devices, which use electrons and holes for electrical conduction, exhibit conductivity modulation effects, resulting in lower on-resistance than that of unipolar devices. SiC bipolar devices are expected to operate at voltages higher than 10 kV with relatively low on-resistance. Because conductivity modulation can be realized using crystals with long carrier lifetimes, devices based on epitaxial layers with low recombination center concentrations are preferable. ^1,2)

In general, carrier lifetime is determined by Shockley–Read–Hall (SRH), surface, radiative, and Auger recombination processes. ^3–7) The SRH recombination process depends on the crystal's perfection because this process is based on electronic transitions and holes through the recombination center. ^8–11) In 4H-SiC, the most common recombination centers are Z_1/2 centers, and reductions in the concentration of the Z_1/2 center have been reported, which are widely called lifetime enhancement processes. ^1,2,12,13) Meanwhile, the surface recombination process depends on the surface structure and damage near the surface. ^14–19) In the case of 4H-SiC, chemical-mechanical polishing (CMP) is effective in achieving low surface recombination velocities. ^16,17)

When the recombination center concentrations are sufficiently low, radiation and Auger recombination take precedence over carrier recombination. Although the radiative recombination coefficient B and Auger recombination coefficient C have been reported experimentally, ^3–7) the constant C has been shown in each report.

On the one hand, owing to the Coulomb enhancement of the Auger process, C is dependent on the donor concentration under conditions of low injection, as reported in Si. ²⁰⁾ On the other hand, C decreased with the increase in N, which is the excited carrier concentration, in the high injection condition. This is because of the screening of the Coulomb enhancement effect. ²⁰⁾ Therefore, we need to clarify the dependence of C on N to discuss the theoretical limit of on-resistance of the SiC bipolar devices. In addition, it has been reported that C is dependent on the trap concentration owing to the effects of trap-assisted Auger recombination (TAAR). ²¹⁾ Thus, it is important to observe trap concentration dependence of C. In this study, we estimated C in the high injection condition using the low-doped SiC epilayer, including dependence on N and the trap concentration.

The samples are n-type epitaxy layers with a donor concentration of 10¹⁴ cm⁻³ and film thicknesses of 150 μm (T-150) and 250 μm (T-250). These samples were treated with carbon ion implantation, annealing at 1650 °C, and CMP of the sample surface to extend the carrier lifetime. ^1,2,22) We also evaluated a p-type sample (P-100) with an acceptor concentration of 6 × 10¹⁴ cm⁻³ and a thickness of 100 μm. ^18,23) To evaluate the effect of TAAR, two self-standing epilayer samples with a donor concentration of 1 × 10¹⁵ cm⁻³ were used, and one of the self-standing epilayers was implanted with 1 × 10¹⁵ cm⁻² of protons (H⁺) with an acceleration energy of 0.95 MeV to induce traps.

For carrier lifetime measurements, a third harmonic yttrium aluminum garnet laser with a wavelength of 355 nm and a pulse width of 1 ns was used as the excitation light source. A continuous-wave laser with a wavelength of 637 nm was used as the probe light, and micro-time-resolved free carrier absorption (FCA), ^24–27) which constitutes an objective lens, was used.

Figure 1 shows the time-resolved FCA decay curves observed from T-250 for various excited carrier concentrations N. To estimate N, the injected photon concentration and photon penetration depth were used. The injected photon concentrations were calculated using the power of the excited laser (approximately 0.001–1 mW), an oscillation frequency of 100 Hz, and the spot area of the laser (1.7 × 10⁻⁴ cm²), and the resulting injected photon concentrations were approximately 10¹⁴–10¹⁷ cm⁻². The penetration depth was set to 42 μm at 355 nm, ²⁸⁾ and the distribution of excited carriers after excitation was calculated. Subsequently, the distribution of excited carriers from the surface to the penetration depth was averaged, and this average value was taken as N (resulting in N of approximately 10¹⁶–10¹⁹ cm⁻³). As shown in Fig. 1, with increasing excited carrier concentration N, the decay became faster.

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Because the Auger recombination component is presented only at the beginning of the decay curves, the slopes at initial decay τ_ini were extracted from the decay curve up to 10 ns. The extracted τ_ini for all the samples are shown in Fig. 2, along with τ_ini from the report by Scajev et al. at a higher N than that in our experiments (they employed a slope up to 12 ns). ⁵⁾ However, because τ_ini includes the radiative recombination component, we extracted Auger lifetimes τ_auger by using the following equation with the reported B of 1 × 10⁻¹² cm³ s^−120,29)

$$\begin{eqnarray}&&\displaystyle \frac{1}{{\tau }_{{\rm{auger}}}}=\displaystyle \frac{1}{{\tau }_{{\rm{ini}}}}-B\left({N}_{0}+N\right),\end{eqnarray} \tag{ 1 }$$

where ${N}_{0}$ is the donor or acceptor concentration in the sample. (Kerr and Cuevas ²⁰⁾ and Yablonovitch et al. ²⁹⁾ used bulk carrier lifetime τ_bulk extracted from the observed carrier lifetime of samples with different thicknesses to exclude surface recombination. However, we employed τ_ini, which includes surface recombination contributions, because it was difficult to prepare the samples with different thicknesses). The extracted τ_auger are shown in Fig. 3. τ_auger clearly depended on N for T-250 and those from Ščajev et al. ⁵⁾ Based on the slope of τ_auger against N, ²⁰⁾ we estimated the N dependent C to be 7.4 × 10⁻¹⁹ N^−0.68 cm⁶ s⁻¹. Although τ_auger for T-150 and P-100 did not show a clear dependence on N, and this independence would be due to faster SRH and surface recombination than those for T-250, as expected from the decay curves in our previous report. ²⁵⁾ τ_auger at N > 5 × 10¹⁸ cm⁻³ for T-150 and P-100 show similar values to those in T-250. Therefore, C was 7.4 × 10⁻¹⁹ N^−0.68 cm⁶ s⁻¹ at N > 5 × 10¹⁸ cm⁻³, as shown by the line in Fig. 3.

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Figure 4 shows τ_auger for the samples with and without proton implantation. The sample implanted with protons shows almost the same τ_auger as the sample without proton (H⁺) implantation, even though τ_auger did not show N dependence and is shorter than those for other samples. Therefore, we were not able to confirm the effects of TAAR even in the samples with a high concentration of traps (10¹⁵ cm⁻² proton implantation would induce vacancies with 10¹⁸ cm⁻³ up to 10 μm from the surface). Considering τ_auger of 34 ns at the highest N = 9.4 × 10¹⁸ cm⁻³, C was less than 3.3 × 10⁻³¹ cm⁶ s⁻¹ even with the effects of TAAR induced by proton implantation.

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To confirm the validity of the estimated C, we reproduced the FCA decay curves by calculations. Generally, carrier recombination can be expressed using a partial differential equation that describes the temporal and spatial variations as follows: ¹⁹⁾

$$\begin{eqnarray}\begin{array}{lll}\displaystyle \frac{\partial N(x,t)}{\partial t} & = & {D}_{a}\displaystyle \frac{{\partial }^{2}N(x,t)}{\partial {x}^{2}}-\displaystyle \frac{N\left(x,\,t\right)}{{\tau }_{{\rm{bulk}}}}\\ & & -\,B{N}^{2}-C{N}^{3}+G,\end{array}\end{eqnarray} \tag{ 2 }$$

where t is the time, x is the depth of the semiconductor layer, D_a is the ambipolar diffusion coefficient, and G is the generation rate of excess carriers. We set G = 0 because of the absence of excitation sources, except for the initial laser pulse.

D_a was evaluated using the following equation:

$$\begin{eqnarray}&&{D}_{a}=\displaystyle \frac{p+n}{p/{D}_{{\rm{n}}}+n/{D}_{{\rm{p}}}},\end{eqnarray} \tag{ 3 }$$

where n is the free electron concentration, p is the free hole concentration, and D_n and D_p are the diffusion constants of holes and electrons, respectively, estimated from the mobilities of electrons μ_e and holes μ_h. ³⁰⁾ As N increases, μ_e and μ_h change owing to the influence of electron–hole scattering. ³¹⁾ Thus, D_n and D_p depend on N, and from Eq. (3), D_a also depends on D_n and D_p. The boundary conditions for Eq. (2) between the excited surface and other surfaces are expressed as:

$$\begin{eqnarray}&&\begin{array}{c}{D}_{a}\frac{\partial N(0,\,t)}{\partial x}={S}_{0}N\left(0,\,t\right)\,\mathrm{and}\\ {D}_{a}\frac{\partial N(W,\,t)}{\partial x}=-{S}_{W}N\left(W,\,t\right),\end{array}\end{eqnarray} \tag{ 4 }$$

where S₀ and S_W are the surface recombination velocities on the excited and back surfaces, respectively, and W is the layer thickness of 250 μm at which the value of S_W has negligible effects on the calculated results.

We set τ_bulk at 10 μs and S₀ at 1000 cm s⁻¹, considering previous studies. ^19,23,25) With B of 1 × 10⁻¹² cm³ s⁻¹ and C of 7.4 × 10⁻¹⁹ N^−0.68 cm⁶ s⁻¹, we obtained the decay curves shown by the dotted lines in Fig. 1. The calculated decay curves were well reproduced, particularly at high N, and thus, the estimated C was reasonable.

Scajev et al. also reported the N dependence of C and speculated on the screening of the Coulomb enhancement, as seen in Si. ^5,20) Our results also suggest the presence of the Coulomb enhancement screening. However, Scajev et al. showed slightly smaller dependence of C ∝ N^−0.3 compared with our estimation. ⁵⁾ The reasons for the different N dependences may be due to the different estimation method used by Ščajev et al. at N < 2 × 10¹⁹ cm⁻³. ⁵⁾ They estimated C by fitting the shapes of the N dependent decay curves for several separated N ranges (C = 7 × 10⁻³¹ cm⁶ s⁻¹ at N = 10^18–19 cm⁻³ and C = 1.4 × 10⁻³¹ cm⁶ s⁻¹ at N = 2 × 10¹⁹ cm⁻³). Consequently, even though C was estimated from the N dependent decay curves, they discussed N dependence using the estimated C. This method may include errors in N dependent C. Other possible reasons for the different N dependence are the differences in the samples; their samples have shorter τ_epi and larger S than those for our samples. Their short τ_epi and large S induce an apparently short τ_auger and mitigate N dependence. Another possible reason is N dependence of B, as discussed by Ščajev et al. ⁵⁾ Their study, like ours, employed constant B for the analysis because all the previous reports show the same B of 1 × 10⁻¹² cm³ s⁻¹. To reduce the difference in the experimental and calculated decay curves for the relatively low Nas shown in Fig. 1, B lower than 1 × 10⁻¹² cm³ s⁻¹ at low N is required. Therefore, to estimate the longest limit of carrier lifetime using B and C at relatively low N, we need to observe N dependent B, as reported in the other studies, ³²⁾ and this observation will be the subject of our future study.

The estimated C of 7.4 × 10⁻¹⁹ N^−0.68 cm⁶ s⁻¹ at N > 5 × 10¹⁸ cm⁻³ induces a smaller value compared with the reported values of 5–7 × 10⁻³¹ cm⁶ s⁻¹. ^3–7) Therefore, the limit of carrier lifetime at the high injection condition will be longer than those expected so far, and on-resistance of SiC bipolar devices can be reduced if carriers more than 5 × 10¹⁸ cm⁻³ are injected.

We estimated the excited carrier concentration dependent Auger recombination coefficient as 7.4 × 10⁻¹⁹ N^−0.68 cm⁶ s⁻¹ at N > 5 × 10¹⁸ cm⁻³, and the N dependence is concluded to be caused by screening of the Coulomb enhancement. However, we were unable to observe the effects of traps on the Auger recombination coefficient, and thus, TAAR did not increase C more than 3.3 × 10⁻³¹ cm⁶ s⁻¹ at N of 9.4 × 10¹⁸ cm⁻³. The estimated C of 7.4 × 10⁻¹⁹ N^−0.68 cm⁶ s⁻¹ is smaller than the reported values, and thus, the on-resistance of SiC bipolar devices can be reduced if carriers more than 5 × 10¹⁸ cm⁻³ are injected. We expect this estimated C to be useful in the development of SiC bipolar devices with high concentration carrier injection.

The authors thank Mr. A. Miyasaka of Showa Denko K.K. and Dr. K. Kojima, Dr. Y. Yonezawa, and Dr. T. Kato of the National Institute of Advanced Industrial Science and Technology for their cooperation in sample preparation. This work is partly supported by TEPCO Memorial Foundation.