# Charge Trapping and Variability in CMOS Technologiesat Cryogenic Temperatures

### A Appendix

#### A.1 WKB Approximation

The WKB approximation was developed in 1926 independently by Gregor Wentzel, Hendrik Kramers and Léon Brillouin [178]. It can be used for solving quantum mechanical eigen-value problems iteratively. Thus, it can
also be used for approximating the time independent Schrödinger equation

which can be rewritten as

with . Solving this equation can be done using the ansatz

Plugging the ansatz (A.3) into the Schrödinger equation (A.2) it can be transfered to an inhomogeneous
non-linear differential equation of second order for which results in

Based on the principle that quantum mechanical relations should correspond to classical relations when the phase can be expanded in

Plugging (A.5) into (A.4) and sorting the result by the order in we get

where is of order zero in because . From the zeroth order term the differential equation

can be extracted and solved:

From the first order term the corresponding differential equation

can be solved

Using these results in the ansatz (A.3) the WKB-wavefunction has the from