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}^{eff} = ⟨ E_{i} ⟩ / k_{B}

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

(4.2.9)

⟨ E_{i} ⟩ = \frac{\sum_{k} p_{i} (k) E_{∥, i} (k)}{\sum_{k} p_{i} (k)}

where $p_{i} (k)$ is the occupation probability of the $i$ -th subband, $E_{∥, i} (k)$ is the in-plane energy for the in-plane state $k$ , and $k_{B}$ 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_{eff} = \sum_{i} T_{i}^{eff} \sum_{k} p_{i} (k) = \frac{1}{k_{B}} \sum_{i} \sum_{k} p_{i} (k) E_{∥, i} (k)

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