Impact of Charge Transitions at Atomic Defect Sites on Electronic Device Performance

Chapter C Weibull distribution

The Weibull distribution is used in this work to capture asymmetric Gaussian-shaped property distributions such as Si–N bond lengths in amorphous silicon nitride. The Weibull distribution parametrization used for this work is given by

$$\begin{array}{}\text{(C.1)}& f(E)=\frac{b}{a}{\left(\text{±}\frac{E-c}{a}\right)}^{b-1}{\mathrm{e}}^{-{\left(\text{±}\frac{E-c}{a}\right)}^b},\end{array}$$

with the scale parameter $a$, the shape parameter $b$ and the location parameter $c$. The plus sign before the $(E-c)$ term corresponds to the Weibull minimum distribution as employed for the CTLs of OVs and HBs in Sections 4.1.7 and 4.1.7 and the Si–N bond lengths in Section 5.2.2. The minus sign corresponds to the Weibull maximum distribution used for $E_{\mathrm{form}}$ of HBs in Section 4.1.5 .