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Investigating Hot-Carrier Effects using the Backward Monte Carlo Method

2.2 Semiclassical Electron Dynamics

In semiconductor devices, where the built-in potential varies very slowly, quantum-mechanical effects like tunneling and reflection are absent [65]. For such devices, electrons can be described as particles with the charge \( -e \) [60]. Thus, the electron obeys Newton’s law of motion [7, 42, 60]:

(2.22) \{begin}{align} \hbar \,\frac {\mathrm {d} \vec {k}}{\mathrm {d} t} = - \nabla _{\vec {r}}\, E_{C0}(\vec {r}) = \vec {F}_e(\vec {r},t), \label {eq:motion_k} \{end}{align}

where \( \hbar \vec {k} \) represents the momentum and \( \vec {F}_e \) the force applied to the electron. The particle’s kinetic energy can be retrieved from the dispersion relation \( \Epsilon (\vec {k}) \). The particle’s velocity corresponds to the group velocity [60]:

(2.23) \{begin}{align} \vec {v}(\vec {k}) = \frac {1}{\hbar } \, \nabla _{\vec {k}} \, \Epsilon (\vec {k}) \label {eq:motion_r} \{end}{align}

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