The Richardson constant for thermionic emission in Schottky barrier diodes
Abstract
The Richardson equation appropriate to thermionic emission in Schottky barrier diodes is derived. For a semiconductor having an energy band with ellipsoidal constantenergy surfaces in momentum space, the Richardson constant A _{1}∗ associated with a single energy minimum is A ^{∗}_{1}=4φ {qk ^{2}}/{h ^{3}}(l ^{2}m _{y}m _{z}+m ^{2}m _{z}m _{x}+n ^{2}m _{x}m _{y}) {1}/{2} where l, m and n are the direction cosines of the normal to the emitting plane relative to the principal axes of the ellipsoid and m_{x}, m_{y} and m_{z} are the components of the effective mass tensor. In the Ge conduction band, summation of emission from all the energy minima gives maximum and minimum ratios of A∗ to the free electron value A (= 120 A/cm ^{2}/°K ^{2}) of 1·19 and 1·07 for the <100> and <111> directions respectively. In the silicon conduction band, maximum and minimum ratios of 2·15 and 2·05 occur for the <111> and <100> directions respectively. The theoretical predictions are in good agreement with experimental results from WSi and AuGaAs diodes.
 Publication:

Solid State Electronics
 Pub Date:
 April 1965
 DOI:
 10.1016/00381101(65)901164
 Bibcode:
 1965SSEle...8..395C