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 constant-energy surfaces in momentum space, the Richardson constant A 1∗ associated with a single energy minimum is A ∗1=4φ {qk 2}/{h 3}(l 2m ym z+m 2m zm x+n 2m xm 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 mx, my and mz 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 W-Si and Au-GaAs diodes.
- Publication:
-
Solid State Electronics
- Pub Date:
- April 1965
- DOI:
- 10.1016/0038-1101(65)90116-4
- Bibcode:
- 1965SSEle...8..395C