Effect of a Magnetic Field on Steady-State Charge Carrier Distribution

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Abstract
The carrier distribution, space charge, and related quantities in a nondegenerate semiconductor are examined theoretically in rectangular Hall geometry with an applied magnetic field, and in cylindrical geometry with the self‐magnetic field only. Solutions in rectangular geometry are found for the special cases of zero and infinite recombination coefficient and for space‐charge conditions giving rise to constant and quadratic electric field configurations (symmetric recombination conditions). Solutions in cylindrical geometry are of zero order in the radius, i.e., n and p are constant, but not the equilibrium values; the recombination coefficient is variable. The pinch gain, np/ni2, is determined essentially by the product of the transport numbers, the sum of the carrier mobilities, the magnetic permeability, the square of the axial current density, and the reciprocal of the recombination coefficient.

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