Electron temperature¶

In NEGF simulations, electrons are in general not in thermal equilibrium. Their population does not necessarily follow the Fermi-Dirac distribution at the lattice temperature specified by Temperature. However, one can define characteristic temperature to discuss pseudo-equilibrium occupation of the subbands.

Subband temperature¶

(4.2.8)¶\[T_i^\mathrm{eff} = \langle E_i \rangle / k_\mathrm{B}\]

The averaged kinetic energy for \(i\)-th subband is an expectation value of the in-plane kinetic energy:

(4.2.9)¶\[\langle E_i \rangle = \frac{\sum_k p_i(k) E_{\parallel,i} (k)}{\sum_k p_i(k)}\]

where \(p_i(k)\) is the occupation probability of the \(i\)-th subband, \(E_{\parallel,i} (k)\) is the in-plane energy for the in-plane state \(k\), and \(k_\mathrm{B}\) the Boltzmann constant. (4.2.8) is given in the output file EnergyEigenstatesSubbandTemperature.txt.

Effective electron temperature¶

The effective electron temperature is the statistical average over all subbands:

(4.2.10)¶\[T_\mathrm{eff} = \sum_i T_i^\mathrm{eff} \sum_k p_i(k) = \frac{1}{k_\mathrm{B}} \sum_i \sum_k p_i(k) E_{\parallel,i} (k)\]

(4.2.10) is given in the output file Effective_Temperature.dat for each bias.