Hydrodynamic equations for semiconductors with nonparabolic band structure

A system of generalized hydrodynamic equations is derived from Boltzmann´s transport equation for semiconductors without the assumption of a parabolic band structure. After some simplifications these equations can be arranged in such a way that their structure is similar to that of the well-known conventional ones. For this purpose the quantity carrier temperature is redefined and five relaxation times have to be introduced instead of the two in use so far, in order to take nonparabolicity into account. For all quantities of interest results from Monte Carlo simulation are presented for silicon with an impurity concentration of up to 10¹⁸ cm^-3 and an electric field of up to 200 kV/cm. They show that two of the five relaxation times are not distinguishable; hence, for silicon at room temperature the number of relaxation times can be reduced to four. Considerable deviations from results derived under the assumption of a parabolic band structure demonstrate the necessity of this generalized hydrodynamic model. The new hydrodynamic model is applied to a n-channel LDD MOSFET with a 0.5-μm channel length. The results agree well with the results of Monte Carlo device simulation