The temperature affects many of the parameters in the equations above, and the following equations show how. One of the most significant parameters that varies with the temperature for a semiconductor is the band-gap energy:

[\begin{array}{ll} {EG_{nom} = 1.16 - 7.02e^{- 4}\frac{{\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ N\ mathalpha\rbrack\lbrack char\ O\ mathalpha\rbrack\lbrack char\ M\ mathalpha\rbrack\rbrack}^{2}}{{\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ N\ mathalpha\rbrack\lbrack char\ O\ mathalpha\rbrack\lbrack char\ M\ mathalpha\rbrack\rbrack} + 1108.0}} & \ \end{array}]

[\begin{array}{ll} {EG\left( T \right) = 1.16 - 7.02e^{- 4}\frac{T^{2}}{{\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ N\ mathalpha\rbrack\lbrack char\ O\ mathalpha\rbrack\lbrack char\ M\ mathalpha\rbrack\rbrack} + 1108.0}} & \ \end{array}]

The leakage current temperature's dependence is:

[\begin{array}{ll} {IS\left( T \right) = {\lbrack font\ rm\ \lbrack char\ I\ mathalpha\rbrack\lbrack char\ S\ mathalpha\rbrack\rbrack} e^{\frac{logfactor}{\lbrack font\ rm\ \lbrack char\ N\ mathalpha\rbrack\rbrack}}} & \ \end{array}]

[\begin{array}{ll} {JSW\left( T \right) = {\lbrack font\ rm\ \lbrack char\ J\ mathalpha\rbrack\lbrack char\ S\ mathalpha\rbrack\lbrack char\ W\ mathalpha\rbrack\rbrack} e^{\frac{logfactor}{\lbrack font\ rm\ \lbrack char\ N\ mathalpha\rbrack\rbrack}}} & \ \end{array}]

where `logfactor' is defined as

[\begin{array}{ll} {logfactor = \frac{\lbrack font\ rm\ \lbrack char\ E\ mathalpha\rbrack\lbrack char\ G\ mathalpha\rbrack\rbrack}{V_{t}\left( {\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ N\ mathalpha\rbrack\lbrack char\ O\ mathalpha\rbrack\lbrack char\ M\ mathalpha\rbrack\rbrack} \right)} - \frac{\lbrack font\ rm\ \lbrack char\ E\ mathalpha\rbrack\lbrack char\ G\ mathalpha\rbrack\rbrack}{V_{t}\left( T \right)} + {\lbrack font\ rm\ \lbrack char\ X\ mathalpha\rbrack\lbrack char\ T\ mathalpha\rbrack\lbrack char\ I\ mathalpha\rbrack\rbrack}\ln\left( \frac{T}{\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ N\ mathalpha\rbrack\lbrack char\ O\ mathalpha\rbrack\lbrack char\ M\ mathalpha\rbrack\rbrack} \right)} & \ \end{array}]

The contact potentials (bottom-wall an sidewall) temperature dependence is:

[\begin{array}{ll} {VJ\left( T \right) = {\lbrack font\ rm\ \lbrack char\ V\ mathalpha\rbrack\lbrack char\ J\ mathalpha\rbrack\rbrack}\left( \frac{T}{\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ N\ mathalpha\rbrack\lbrack char\ O\ mathalpha\rbrack\lbrack char\ M\ mathalpha\rbrack\rbrack} \right) - V_{t}\left( T \right)\left\lbrack {3 \cdot \ln\left( \frac{T}{\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ N\ mathalpha\rbrack\lbrack char\ O\ mathalpha\rbrack\lbrack char\ M\ mathalpha\rbrack\rbrack} \right) + \frac{\lbrack font\ rm\ \lbrack char\ E\ mathalpha\rbrack\lbrack sub\ \lbrack char\ G\ mathalpha\rbrack\ \lbrack char\ n\ mathalpha\rbrack\lbrack char\ o\ mathalpha\rbrack\lbrack char\ m\ mathalpha\rbrack\rbrack\rbrack}{V_{t}\left( {\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ N\ mathalpha\rbrack\lbrack char\ O\ mathalpha\rbrack\lbrack char\ M\ mathalpha\rbrack\rbrack} \right)} - \frac{\lbrack font\ rm\ \lbrack char\ E\ mathalpha\rbrack\lbrack char\ G\ mathalpha\rbrack\lbrack char\ (\ mathalpha\rbrack\lbrack char\ T\ mathalpha\rbrack\lbrack char\ )\ mathalpha\rbrack\rbrack}{V_{t}\left( T \right)}} \right\rbrack} & \ \end{array}]

[\begin{array}{ll} {PHP\left( T \right) = {\lbrack font\ rm\ \lbrack char\ P\ mathalpha\rbrack\lbrack char\ H\ mathalpha\rbrack\lbrack char\ P\ mathalpha\rbrack\rbrack}\left( \frac{T}{\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ N\ mathalpha\rbrack\lbrack char\ O\ mathalpha\rbrack\lbrack char\ M\ mathalpha\rbrack\rbrack} \right) - V_{t}\left( T \right)\left\lbrack {3 \cdot \ln\left( \frac{T}{\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ N\ mathalpha\rbrack\lbrack char\ O\ mathalpha\rbrack\lbrack char\ M\ mathalpha\rbrack\rbrack} \right) + \frac{\lbrack font\ rm\ \lbrack char\ E\ mathalpha\rbrack\lbrack sub\ \lbrack char\ G\ mathalpha\rbrack\ \lbrack char\ n\ mathalpha\rbrack\lbrack char\ o\ mathalpha\rbrack\lbrack char\ m\ mathalpha\rbrack\rbrack\rbrack}{V_{t}\left( {\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ N\ mathalpha\rbrack\lbrack char\ O\ mathalpha\rbrack\lbrack char\ M\ mathalpha\rbrack\rbrack} \right)} - \frac{\lbrack font\ rm\ \lbrack char\ E\ mathalpha\rbrack\lbrack char\ G\ mathalpha\rbrack\lbrack char\ (\ mathalpha\rbrack\lbrack char\ T\ mathalpha\rbrack\lbrack char\ )\ mathalpha\rbrack\rbrack}{V_{t}\left( T \right)}} \right\rbrack} & \ \end{array}]

The depletion capacitances temperature dependence is:

[\begin{array}{ll} {CJ\left( T \right) = {\lbrack font\ rm\ \lbrack char\ C\ mathalpha\rbrack\lbrack char\ J\ mathalpha\rbrack\rbrack}\left\lbrack {1 + {\lbrack font\ rm\ \lbrack char\ M\ mathalpha\rbrack\lbrack char\ J\ mathalpha\rbrack\rbrack}\left( {4.0e^{- 4}\left( {T - {\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ N\ mathalpha\rbrack\lbrack char\ O\ mathalpha\rbrack\lbrack char\ M\ mathalpha\rbrack\rbrack}} \right) - \frac{VJ\left( T \right)}{\lbrack font\ rm\ \lbrack char\ V\ mathalpha\rbrack\lbrack char\ J\ mathalpha\rbrack\rbrack} + 1} \right)} \right\rbrack} & \ \end{array}]

[\begin{array}{ll} {CJSW\left( T \right) = {\lbrack font\ rm\ \lbrack char\ C\ mathalpha\rbrack\lbrack char\ J\ mathalpha\rbrack\lbrack char\ S\ mathalpha\rbrack\lbrack char\ W\ mathalpha\rbrack\rbrack}\left\lbrack {1 + {\lbrack font\ rm\ \lbrack char\ M\ mathalpha\rbrack\lbrack char\ J\ mathalpha\rbrack\lbrack char\ S\ mathalpha\rbrack\lbrack char\ W\ mathalpha\rbrack\rbrack}\left( {4.0e^{- 4}\left( {T - {\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ N\ mathalpha\rbrack\lbrack char\ O\ mathalpha\rbrack\lbrack char\ M\ mathalpha\rbrack\rbrack}} \right) - \frac{PHP\left( T \right)}{\lbrack font\ rm\ \lbrack char\ P\ mathalpha\rbrack\lbrack char\ H\ mathalpha\rbrack\lbrack char\ P\ mathalpha\rbrack\rbrack} + 1} \right)} \right\rbrack} & \ \end{array}]

The transit time temperature dependence is:

[\begin{array}{ll} {TT\left( T \right) = {\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ T\ mathalpha\rbrack\rbrack}\left( 1 + {\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ T\ mathalpha\rbrack\lbrack char\ T\ mathalpha\rbrack\lbrack char\ 1\ mathalpha\rbrack\rbrack}\left( {T - {\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ N\ mathalpha\rbrack\lbrack char\ O\ mathalpha\rbrack\lbrack char\ M\ mathalpha\rbrack\rbrack}} \right) + {\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ T\ mathalpha\rbrack\lbrack char\ T\ mathalpha\rbrack\lbrack char\ 2\ mathalpha\rbrack\rbrack}\left( {T - {\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ N\ mathalpha\rbrack\lbrack char\ O\ mathalpha\rbrack\lbrack char\ M\ mathalpha\rbrack\rbrack})^{2}} \right) \right.} & \ \end{array}]

The junction grading coefficient temperature dependence is:

[\begin{array}{ll} {MJ\left( T \right) = {\lbrack font\ rm\ \lbrack char\ M\ mathalpha\rbrack\lbrack char\ J\ mathalpha\rbrack\rbrack}\left( 1 + {\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ M\ mathalpha\rbrack\lbrack char\ 1\ mathalpha\rbrack\rbrack}\left( {T - {\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ N\ mathalpha\rbrack\lbrack char\ O\ mathalpha\rbrack\lbrack char\ M\ mathalpha\rbrack\rbrack}} \right) + {\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ M\ mathalpha\rbrack\lbrack char\ 2\ mathalpha\rbrack\rbrack}\left( {T - {\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ N\ mathalpha\rbrack\lbrack char\ O\ mathalpha\rbrack\lbrack char\ M\ mathalpha\rbrack\rbrack})^{2}} \right) \right.} & \ \end{array}]

The series resistance temperature dependence is:

[\begin{array}{ll} {RS\left( T \right) = {\lbrack font\ rm\ \lbrack char\ R\ mathalpha\rbrack\lbrack char\ S\ mathalpha\rbrack\rbrack}\left( 1 + {\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ R\ mathalpha\rbrack\lbrack char\ S\ mathalpha\rbrack\rbrack}\left( {T - {\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ N\ mathalpha\rbrack\lbrack char\ O\ mathalpha\rbrack\lbrack char\ M\ mathalpha\rbrack\rbrack}} \right) + {\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ R\ mathalpha\rbrack\lbrack char\ S\ mathalpha\rbrack\lbrack char\ 2\ mathalpha\rbrack\rbrack}\left( {T - {\lbrack font\ rm\ \lbrack char\ T\ mathalpha\rbrack\lbrack char\ N\ mathalpha\rbrack\lbrack char\ O\ mathalpha\rbrack\lbrack char\ M\ mathalpha\rbrack\rbrack})^{2}} \right) \right.} & \ \end{array}]