Abstract
The law of mass action refers to the product of concentration of reactants, which for a particular material is a function only of temperature. For non-degenerate semiconductors the law of mass action is represented by the product NP=NCNV exp- EG/KBT. Through solutions to the quantum Liouville equation, it is determined that the law of mass action is generally invalid.
Highlights
For a specific material, non-degenerate statistics and equilibrium, the electron density, N NC exp-[(Ec EF)/kBT], and hole density, P Nv exp[(Er Ev)/kBT], yield, a temperature dependent classical law of mass action 1,:z: NP NC Nv exp-EG/k,T.Quantum mechanically, it is known, Wigner3, that modifications to the classical density-potential energy relation arise from gradients in charge density, which represent quantum mechanical attractive and repulsive forces
Exp-[(Ec EF)/kBT], and hole density, P Nv exp[(Er Ev)/kBT], yield, a temperature dependent classical law of mass action 1,:z: NP NC Nv exp-EG/k,T. It is known, Wigner3, that modifications to the classical density-potential energy relation arise from gradients in charge density, which represent quantum mechanical attractive and repulsive forces
Which with some manipulation can be placed in the form of density curvatures, as in equation (1)
Summary
R. GOVINDANb aScientific Research Associates, Inc., Glastonbury, Connecticut Applied Research Laboratory, State College, Pennsylvania. The law of mass action refers to the product of concentration of reactants, which for a particular material is a function only of temperature. For non-degenerate semiconductors the law of mass action is represented by the product NP N Nv exp- EG/kBT. Through solutions to the quantum Liouville equation, it is determined that the law of mass action is generally invalid
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