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Study of Balance Equations for Hot‐Electron Transport in an Arbitrary Energy Band
Author(s) -
Wu HangSheng,
Wu M. W.
Publication year - 1995
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221920116
Subject(s) - hamiltonian (control theory) , physics , balance equation , energy balance , electron , detailed balance , energy–momentum relation , balance (ability) , momentum (technical analysis) , classical mechanics , quantum mechanics , mathematics , thermodynamics , markov model , markov chain , mathematical optimization , statistics , medicine , finance , economics , physical medicine and rehabilitation
In view of the recent disputes of Huang and Wu and Lei about Lei's balance equation theory for an arbitrary energy band, the balance equations for hot‐eléctron transport in an arbitrary energy band are reformulated. In the new formulation the adoption of the effective Hamiltonian method is avoided and all calculations are carried out in laboratory coordinates. In the mean time the crystal momentum k is carefully distinguished from the physical momentum. By introducing a correct equilibrium density matrix of the drifting electron gas in place of that used by Lei, the balance equations together with the distribution function can be derived directly with no need to distinguish the degree of freedom of the center of mass from the relative degree of freedom of the electrons, which is in our opinion neither possible nor necessary at least for a nonparabolic energy band. Some problems associated with the foundation of the balance equation theory are also examined. The result shows that the comment to Lei's theory given by Huang and Wu is correct and to the point. Nevertheless, contrary to their assertion that this theory is inapplicable to the nonparabolic band transport, Lei's balance equations, after a few, however, important corrections, are still applicable to transport for nonparabolic energy bands.