Thermodynamic Theory of Hot-Electron Transport in Silicon

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Abstract
Hot electron transport in a semiconductor is analyzed through a thermodynamic treatment. Analytic solution of the Boltzmann transport equation is obtained assuming extremely high electron-electron scattering condition. Particle and energy balance equations are solved using rigorous particle and thermal energy flow expressions derived from the transport equation. Obtained velocity-field relationship for electrons in silicon with electrode distance longer than 10 µm is in good agreement with the experimental data. It is found that saturation velocity increases for shorter samples due to electron cooling through electrodes. Moreover, for samples with length between 0.1 µm to 1 µm, particle and thermal energy currents strongly couple. Because of this coupling, anomalous phenomena such as excess voltage and higher electron temperature will appear.

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