def g1(nsigma, c):
"""
EGDM g1
nsigma=sigma/kT: must be nsigma>=1.
c must be 0<=c<=1, recommended c<0.1
"""
delta = 2.0 * (ad.log(nsigma**2 - nsigma) -
ad.log(ad.log(4))) / (nsigma**2)
return ad.exp(0.5 * (nsigma**2 - nsigma) * (2 * c)**delta)
def Ef(self, ctx, eq):
c = ctx.varsOf(eq)['c']
c_raw = c
c = where(c > self.c_eps, c, self.c_eps) # avoid NaN
if self.logger.isEnabledFor(logging.INFO):
if np.any(nvalue(c_raw) != nvalue(c)):
self.logger.info(
'Ef(%r): clipping c<%r, min(c)=%r' %
(eq.prefix, self.c_eps, np.amin(
nvalue(c_raw))))
N0 = self.N0(ctx, eq)
return ctx.varsOf(eq.thermal)['Vt'] * log(c / N0)
def mobility(self, parent, ctx, eq):
mu0 = ctx.param(eq, 'mu0')
gamma = ctx.param(eq, 'gamma')
v = gamma * sqrt(ctx.varsOf(eq.poisson)['Ecellm'] + 1e-10)
v_max = log(1e10)
v_min = -v_max
v = where(v < v_max, v, v_max)
v = where(v > v_min, v, v_min)
mu = mu0 * exp(v)
mu_face = eq.mesh.faceaverage(mu)
ctx.varsOf(eq)['mu_face'] = mu_face
ctx.varsOf(eq)['mu_cell'] = mu
def solve_analytical(self, ctx, eq, fixed):
hole, = eq.hole
electron, = eq.electron
C = fixed
Nc = electron.dos.N0(ctx, electron)
Nv = hole.dos.N0(ctx, hole)
Vt = ctx.varsOf(eq.thermal)['Vt']
Ec = ctx.varsOf(electron)['Ebandv']
Ev = ctx.varsOf(hole)['Ebandv']
uc = exp(Ec/Vt)
uv = exp(Ev/Vt)
# TODO: rewrite to avoid overflow, reference to middle of bandgap
Ef = Vt*log((C*uc + sqrt((C*C*uc + 4*Nc*Nv*uv)*uc))/(2*Nc))
n = Nc*exp((Ef-Ec)/Vt)
p = Nv*exp((Ev-Ef)/Vt)
return Ef, dict({id(hole): p, id(electron): n})
def b(self, a, i, b0=None):
return self._b(a, ad.log(i), b0=b0)
def Ef_correction(self, ctx, eq):
info = self._load(ctx, eq)
return (-info['b'] - log(info['c'])) * info['Vt']