Four-moment hydrodynamic modelling of a submicrometre semiconductor device in a non-parabolic band structure

Abstract

Two hydrodynamic models for a non-parabolic band structure are proposed in order to obtain closed sets of the first four moment equations derived from the Boltzmann transport equation. Instead of using the Fourier-law heat flux to determine the energy flux and to close the first three moment equations as applied to the conventional hydrodynamic model, the energy flux is solved directly from the third-order moment equation. The physical quantities introduced in the third-order moment equation are expressed in terms of the lower-order moments and the average parameters associated with the random velocity. To close the third-order moment equation, the average parameters related to the random velocity are assumed to be energy dependent. Transport results for a submicrometre silicon -n- diode obtained from the proposed four-moment hydrodynamic models, compared with those from Monte Carlo simulations and from three-moment hydrodynamic models, are studied in detail.

Physics-based solutions to carrier distribution functions in extreme non-equilibrium situations

“…Significant effort has been made in recent years to improve the existing hydrodynamic models [1][2][3][4][5][6][7][8][9] and to derive efficient and accurate kinetic approaches to the carrier distribution function (DF) [10][11][12][13][14][15][16][17][18] in small semiconductor devices. As the device size continues to shrink, nonequilibrium transport effects become more pronounced, and the challenge of developing sophisticated physical transport models to account for pertinent non-equilibrium phenomena has significantly increased.…”