  This paper presents a classical thermodynamic calculation of a Greens
function that describes the declining rate of entropy growth as protons move
under an applied electric field, through an amorphous SiO$_2$ layer in a MOS
field-effect device gate oxide. The analysis builds on work by McLean and
Ausman (1977) and Brown and Saks (1991). Polynomial models of fitting
parameters dB/d$\alpha$, y$_0$, and A/y$_0$ based on interpolation TABLE I of
McLean and Ausman are presented. Infinite boundary conditions are introduced
for the parameter dB/d$\alpha$. Polynomial representations are shown of
dB/d$\alpha$, y$_0$, A/y$_0$ and the Greens function as a function of the
dispersion parameter $\alpha$. The paper shows that parameters y$_0$ and
A/y$_0$ are nearly conic sections with small residuals of a few percent. This
work is intended as a first step toward a near-equilibrium thermodynamic
continuous-time random walk (CTRW) model (anomalous diffusion) of damage
introduced into thick-oxide silicon-based powerMOS parts by space radiation
effects such as those found in the Jovian radiation belts. Charge transport in
amorphous silica electrical insulators is by thermally activated tunneling, not
Brownian motion.
