Silicon carbide (SiC) as the third generation semiconductor has many outstanding properties, such as wide bandgap, high critical electric field strength, large carrier saturation velocity, high thermal conductivity, and good radiation resistance, which make it suitable for radiation detectors working in high temperature and high radiation conditions.^[1,2] SiC based radiation detectors are presently being developed for applications in the energetic particle detection, such as α, β, x-ray, and neutron, which would deteriorate the performance of devices.^[3–5]

To quantitatively characterize the degradation of a detector, minority carrier lifetime, defect concentration, and effective doping concentration (N_eff) are commonly extracted before and after irradiation. But either trap induction rate or doping compensation rate varies with the type and energy of the incident particle, and the defect affecting the minority carrier lifetime, namely Z1/2 defect, is not a single energy level defect,^[6–8] leaves it a challenge to predict the degradation of carrier lifetime, thus the degradation of a detector. Quinn et al. investigated detector degradation by using defect models in MEDICI simulations. A relative simple Z1/2 model including single energy defect level with one cross-section was investigated without providing the comparison between simulation and experimental results.

In this paper, detector performance is simulated by ISE-TCAD, comparing with the degradation results reported in Ref.[9]. A different approach inducing Z1/2 defect as two individual defect energy levels, instead of modifying carrier lifetime of SiC, is adopted in our simulation. Acceptable agreement is achieved by comparing the simulated charge collection efficiency (CCE) with the reported one. It shows that the presented model to deal with Z1/2 defect is applicable for degradation analysis. Based on the approach mentioned above, this work focuses on building a scheme to further predict the degradation of detector performance during its operation.

In Ref. [9], the doping compensation and carrier lifetime reduction were considered as the main factors that lead to the degradation. N_eff was calculated through C–V measurement and carrier lifetime was extracted from the variation of CCE with bias voltage. Theoretical CCE versus bias voltage is typically obtained by drift-diffusion analytical expression^[10,11]

As L_p is a function of hole lifetime (τ_p), CCE is a function of τ_p if the working condition of the device and the incident particle are given. A constant value of τ_p is given by the Shockley–Read–Hall (SRH) theorem^[12]

Figure 1 shows the simulation result of a 2 MeV α particle perpendicular incidence into a SiC schottky detector at a bias voltage of −10 V. The integrated charge of such a current pulse reaches 90% of its maximum at time 3.22 ns after the bombardment. The profiles of electron density and hole density at different moments after the bombardment are plotted in Fig. 1(b). Obviously, the condition of N_d ≫ δp is not satisfied even if 4 ns has passed.

Fig. 1.

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	Fig. 1. Incidence of a 2 MeV α particle into a –10 V biased SiC Schottky detector at 1 ns: (a) pulse current and integrated output charge, (b) electron and hole density along the trajectory at different moments.

In addition, for the condition δn ≈ δp ≫ N_d, namely the high injection condition, the recombination rate R could be written as

Thus, it is improper to use the extracted τ_p from Eq. (1) in TCAD simulation, and τ_n also has an effect on the CCE calculation, which will be discussed later.

Considering the fact that a decreasing τ_p results from an increasing N_t, which is the concentration of Z1/2 defect in this case, it is preferred to induce defect levels when calculating current pulses. It should be noted that, N_t can be obtained neither from Eq. (2) nor from Eq. (3) using a τ_p extracted from Eq. (1).

A schematic cross-section of detectors reported in Ref. [9] is shown in Fig. 2. Values of N_eff, Schottky barrier height φ_b, and ideal factor n before and after radiation are listed in Table 1.

Fig. 2.

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	Fig. 2. Schematic cross-section of detectors reported in Ref. [9].

Table 1.

Table 1.

Table 1. Detector parameters before and after irradiation reported in Ref. [9]. . Irradiation Dose Neff/cm−3 φb/eV n 24 GeV proton unirradiated 2.18 × 1015 1.70 1.19 24 GeV proton 9.37 × 1013 cm−2 1.43 × 1015 1.72 1.18 8.2 MeV electron unirradiated 2.49 × 1015 1.03 1.034 8.2 MeV electron 20 Mrad 1.67 × 1015 1.13 1.036 8.2 MeV electron 40 Mrad 6.89 × 1014 1.54 1.032 60Co γ 2.49 × 1015 1.03 1.034 60Co γ 20 Mrad 2.28 × 1015 1.03 1.033 60Co γ 40 Mrad 2.21 × 1015 1.03 1.034

Table 1. Detector parameters before and after irradiation reported in Ref. [9]. .

To find out N_t in the electron irradiated device, energy deposition in a 390 μm thick SiC layer by 8.2 MeV electron is carried out by CASINO 2.4. As shown in Fig. 3, the distribution of energy deposition is uniform, and nearly 99% of the transmitted electrons remain at an energy of 7.95 MeV. Thus, a dose of 40 Mrad is equivalent to a fluence of 1.33 ×10¹⁵ cm⁻². As the Z1/2 defect introduction rate of 8.2 MeV electron is 0.44–0.57 cm⁻¹ reported in Ref. [13], N_t is obtained as 5.89 – 7.63 ×10¹⁴ cm⁻³.

Fig. 3.

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	Fig. 3. Simulation result from CASINO 2.4. Vertical incidence of 8.2 MeV electrons into a 390 μm SiC layer. (a) Energy of the transmitted electrons. (b) Profile of energy deposition in SiC.

A defect introduction rate of 24 GeV protons has never been reported. Considering that both a 24 GeV proton and 8.2 MeV electron will pass through a 390 μm thick SiC layer easily, and τ_p extracted for the proton irradiated (9.37 ×10¹³ cm⁻²) device is 3.3 ns and is almost the same as that of the 40 Mrad electron irradiated device. Thus, it may be assumed that N_t of the proton irradiated device is approximate to that of the electron irradiated device, and both N_t are evenly distributed.

The Z1/2 defect can trap two electrons and thus has three charge states, i.e., empty (Z⁺), singly occupied (Z⁰), and doubly occupied (Z⁻) states. Figure 4 shows the schematic of free carrier capture and emission at Z1/2 defect. Transitions between Z⁻ and Z⁰ and between Z⁰ and Z⁺ are measured as an acceptor state at E_c – 0.65 eV and a donor state at E_c – 0.4 eV, respectively; σ_n1(σ_n2) and σ_p1(σ_p2) stand for the electron and hole capture cross sections of the acceptor (donor) state. Parameters of Z1/2 are listed in Table 2, including the defect energy levels, charge states, and carrier capture cross-sections.

Fig. 4.

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	Fig. 4. Schematic of carrier capture and emission at the Z1/2 defect.

Table 2.

Table 2.

Table 2. Parameters of Z1/2 defect at 300 K from Ref. [8]. . Energy level Type Electron capture cross-section/cm2 Hole capture cross-section/cm2 Ec − 0.40/eV donor 5.494 × 10−15 1.986 × 10−14 Ec − 0.65/eV acceptor 0.945 × 10−16 1.1 × 10−13

Table 2. Parameters of Z1/2 defect at 300 K from Ref. [8]. .

Although the donor level and the acceptor level interact with each other, they can be treated as two independent levels and both two-interacted-levels model and two-independent-levels model will lead to the same carrier lifetime if the following conditions are satisfied:^[14]

In addition, CCE is considered as 1 when unirradiated SiC Schottky detectors are biased −1000 V. In this case, the thickness of the depletion layer reaches 22 μm. As the penetration depth is about 18 μm for a 5.486 MeV α particle in SiC, the excited e–h pairs by the injected high energy particles are completely laid in the space charge region.

CCE versus applied voltage was calculated based on several basic parameter models, such as (i) SRH and Auger recombination models, (ii) high field saturation and carrier–carrier scattering mobility models, and (iii) trap models.^[15] CCE_sim and CCE_exp hereafter stand for the calculated CCE and the reported experimental CCE in Ref. [9], respectively.

In addition, except for the case which would add no trap and modify the carrier lifetime directly, τ_n and τ_p are set as 0.6 μs and 0.3 μs respectively to ensure the agreement between CCE_sim and CCE_exp for diodes before irradiation (see Fig. 9, N_t = 0).

4.1. CCE calculated with specific τ_n and τ_p

Figure 5 shows the effect of τ_n on CCE when τ_p remains a same value of 3 ns as Ref. [9]; CCE decreases with decreasing τ_n for a fixed applied voltage. As can be seen from this figure, CCE_sim well agrees with CCE_exp only if τ_n is equal to or smaller than 1 ns.

Fig. 5.

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	Fig. 5. Comparison between CCEexp and CCEsim obtained with different τn. (a) CCEsim for 2.0 MeV α particle, (b) CCEsim for 4.14 MeV α particle, (c) CCEsim for 5.48 MeV α particle, (d) CCEsim when τn = 1 ns and τp = 3 ns.

4.2. Proton irradiated detector

Considering that the defect density in the proton irradiated device is assumed to have the same value as that in the 40 Mrad electron irradiated device, N_t in the proton irradiated detector can be taken as 5.89– 7.63 ×10¹⁴ cm⁻³. Thus, three values of N_t (5.89 × 10¹⁴ cm⁻³, 6.76 ×10¹⁴ cm⁻³, and 7.63 × 10¹⁴ cm⁻³) were adopted to find out the optimum N_t value. To make a comparison, an additional N_t = 4.2 × 10¹⁴ cm⁻³, refered to τ_p = 3 ns as calculated from Eq. (2), was also adopted. The results are plotted in Fig. 6.

Fig. 6.

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	Fig. 6. Comparison between CCEexp and CCEsim obtained with different Nt for proton irradiated detector. (a) CCEsim for 2.0 MeV α particle, (b) CCEsim for 4.14 MeV α particle, (c) CCEsim for 5.48 MeV α particle, (d) CCEsim when Nt = 7.63 × 1014 cm−3.

Among these four N_t values, CCE obtained with N_t = 7.63 × 10¹⁴ cm⁻³ shows the best agreement. In case of 2 MeV α particles, CCE_sim is almost the same as CCE_exp. For the 5.48 MeV α particles irradiation case, CCE_sim is similar to CCE_exp, a small difference of about 0.04 is observed. CCE_sim of 4.14 MeV α shows a relative poor agreement compared with the other two cases, especially for the voltage between 100 V and 150 V. As reported in Ref. [9], their simulation result had a similar trend. It is suggested that the 4.14 MeV α particles might actually have their own uncertainty of energies when they reached the surface of the detector, as such energy was obtained by decelerating the ²⁴¹Am α-radiation in air.

An N_t larger than 7.63 × 10¹⁴ cm⁻³ was also simulated (Fig. 7(a)) to find if there is a better alternative. Root-mean-square deviation (R.M.S) was calculated to compare the similarity between the simulation and experimental results (Fig. 7(b)). According to R.M.S, N_t = 7.63 × 10¹⁴ cm⁻³ could be the best value for our simulation.

Fig. 7.

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	Fig. 7. Quantification of the similarity between simulation and experimental results. (a) CCEsim with larger Nt compared with CCEexp. (b) R.M.S calculated for α particle with various energies.

In addition, CCE_sim was also calculated when only one defect level of Z1/2 was considered. N_t remains 7.63 × 10¹⁴ cm⁻³ for such simulation and the results are plotted in Fig. 8. CCE_sim are obviously larger than CCE_exp.

Fig. 8.

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	Fig. 8. CCEsim calculated with acceptor/donor level only when Nt = 7.63 ×1014 cm−3.

4.4. ⁶⁰Co γ-ray irradiated detector

As 4H-SiC is classified as a highly radiation hard material for γ-ray,^[3] the defect introduction rates of γ-ray to SiC epilayer are also less reported. Here, according to τ_p extracted in Ref. [9] for different cases of irradiation, N_t for 40 Mrad γ-ray was assumed in the range of 3.82 × 10¹³ cm⁻³ to 3.82 × 10¹⁴ cm⁻³, and was finally determined to be 3.82 × 10¹⁴ cm⁻³. CCE_sim against biased voltage is shown in Fig. 10.

Fig. 9.

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	Fig. 9. Comparison between CCEsim and CCEexp for different electron irradiation doses.

Fig. 10.

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	Fig. 10. Comparison between CCEsim and CCEexp for different γ irradiation doses.

For 40 Mrad, CCE_sim under an applied voltage lower than 80 V shows a good agreement with CCE_exp. But when the applied voltage is higher than 80 V, CCE_sim is smaller than CCE_exp. For 20 Mrad, CCE_sim shows a good agreement with CCE_exp when the applied voltage is higher than 80 V, but is a bit larger than CCE_exp in the case of below 80 V.

The Z1/2 defect regarded as two individual defect levels was induced to investigate the degradation of SiC Schottky diode detector. Comparing the calculated CCE with experimental CCE, an acceptable approximation was achieved. It is believed that the Z1/2 defect could be treated as two independent defect levels in TCAD to simplify the simulation. It is feasible to analyze the performance of a detector if N_t and N_eff are given in spite of the incidence particle. The effect of other defects and the degradation of mobility should also be investigated if a more precise simulation is required. Based on such a treatment, our further work will focus on the investigation of numerical relationship between Z1/2 defect and carbon vacancy in SiC.^[16]