**2. Mechanism of Radiation-Induced Degradation of SiC**

The radiation-induced degradation of a semiconductor device is commonly understood as the deterioration of its performance under irradiation with high-energy particles. The higher the irradiation dose required for the degradation of a semiconductor, the more radiation-hard it is believed to be.

First, consider the possible mechanisms of the radiation-induced conductivity compensation [29,30].

Assuming, for example, that the main defects generated by fast electrons are vacancies in a SiC sublattice; if the formation of multivacancy complexes is considered unlikely, we have

$$\frac{\text{dV}}{\text{dt}} = \eta\_{\text{FP}} \cdot \text{G} - \frac{\text{V}}{\text{\tau}} - \beta \cdot \text{V} \cdot \text{N} \tag{1}$$

Here V is the concentration of vacancies, G the flux of charged particles, ηFT the probability of vacancy formation by a single particle, τ the lifetime of a vacancy, determined by drains; β the probability of vacancy capture by a free (having no captured vacancy) atom of nitrogen impurity, and N the concentration of free nitrogen atoms. The initial conditions are t = 0, V = 0, N = N0.

The concentration of complexes of secondary defects N<sup>c</sup> (vacancy and impurity atom) can be calculated by the formula

$$\mathbf{N}\_{\mathbf{c}} = \mathbf{N}\_{0} - \mathbf{N} \tag{2}$$

where N<sup>c</sup> being zero at the initial moment of time. The concentration of carriers, electrons (n), is the difference between the concentrations of impurities (shallow donors) and complexes (in the case of deep acceptors).

$$\mathbf{n} = \mathbf{N} - \mathbf{N\_c} = \mathbf{2N} - \mathbf{N\_0} \tag{3}$$

Assuming that the lifetime of a vacancy, determined both by drains and by the impurity capture, substantially exceeds the irradiation time, then, the term V/τ in Equation (1) can be neglected.

A semiconductor can be compensated by two mechanisms. First, the radiationinduced defects create deep acceptor levels, to which electrons from shallow donor levels pass. In this case, no vacancy donor level complexes are formed.

Then, the concentration of vacancies linearly grows with increasing irradiation dose

$$\mathbf{V} = \mathfrak{η}\_{\text{FP}} \cdot \mathbf{G} \tag{4}$$

and the carrier concentration linearly falls:

$$\mathbf{N} = \mathbf{N}\_0 - \eta\_{\rm FP} \cdot \mathbf{G} \tag{5}$$

Thus, with this mechanism being operative, the carrier concentration will linearly decrease with increasing irradiation dose.

In the framework of the second mechanism, the radiation defect (vacancy) interacts with a shallow-impurity atom to give an electrically neutral (or acceptor) center. This occurs when the lifetime of a vacancy is substantially shorter than the irradiation duration, being determined by drains. In this case, the vacancy concentration can be considered stationary and be determined from Equation (1) as

$$\mathbf{V} = \mathfrak{η}\_{\text{FP}} \mathbf{-G} \cdot \boldsymbol{\mathfrak{T}} \tag{6}$$

In this case, the dependence of the carrier concentration on the irradiation dose is determined by the interaction of a vacancy with an impurity. Thus, the contribution of the secondary radiation defects, vacancy + impurity atom complexes, dominates. In this case, the carrier concentration is equal to the concentration of free impurity atoms (N), n = N.

The kinetics of N with second mechanism is described by the equation

$$-\frac{d\mathbf{N}}{dt} = \eta\_{\rm FP} \cdot \boldsymbol{\beta} \cdot \mathbf{G} \cdot \boldsymbol{\tau} \cdot \mathbf{N} \tag{7}$$

possessing the following analytical solution

$$\mathbf{N} = \mathbf{N}\_0 \exp(-\eta\_{\rm FP} \,\beta \cdot \mathbf{\tau} \cdot \mathbf{G} \cdot \mathbf{t})\tag{8}$$

In this case, the concentration of the electrically active impurity will exponentially decrease with increasing irradiation dose. – = F(ΔD) for SiC and Si, where ΔD is the

Figure 1 shows experimental data for Nd–N<sup>a</sup> = F(∆D) for SiC and Si, where ∆D is the irradiation dose.

(9) at a parameter η −1 a factor (η β τ) in the exponent equal to 1.2 −1 **Figure 1.** Conductivity compensation in (1) n-4H-SiC and (2) n-Si under irradiation with 0.9 MeV electrons. Points represent experimental data. The straight line 1 represents a calculation according to Equation (9) at a parameter ηFP of 0.25 cm−<sup>1</sup> . Curve 2 represents a calculation by Equations (5) and (8) at a factor (ηFP β τ) in the exponent equal to 1.2 × 10 −16 cm<sup>2</sup> .

As can be seen from Figure 1, for silicon carbide, in the similarity to GaAs, the carrier concentration linearly decreases with increasing irradiation dose. This means that the first compensation mechanism is operative in SiC, this mechanism being associated with the formation of deep acceptor levels and transition to these levels of electrons from shallow donors. The linear dependence of the carrier concentration on the irradiation dose has also been observed in studies by other researchers, see, e.g., [31,32].
