Temperature dependence of MOSFET characteristics in weak inversion

A knowledge of the MOSFET operating in weak inversion is important for circuits with low leakage specifications. This paper discusses the effect of temperature on the MOSFET in weak inversion. The reciprocal slope
n
of the log I
DS
versus V
GS
relationship between source-drain current I
DS
and gate bias V
GS
may be given by
\frac{1}{(n - 1 - \gamma)^{2}} = \frac{2C\min{ox}\max{2}}{q\epsilon_{s}N_{B}} [\frac{3}{4} \frac{E_{g^{0}}{q} - (\frac{3}{2}\alpha + \frac{k}{q})T]
with
\alpha \equiv (k/q)(38.2 - \ln N_{B} + (3/2) \ln T)
and γ ≡
C_{ss}/C_{ox}
, where C
ox
is the oxide capacitance per unit area, C
ss
the surface states capacitance per unit area,
q
the electronic charge, ε
s
the permittivity of silicon, N
B
the bulk doping concentration,
k
the Boltzmann's constant,
T
the absolute temperature, and
E_{g0}
the extrapolated value of the energy gap of lightly doped silicon at
T = 0
K. This theoretical formula was in good agreement with experimental results in a temperature range of interest.