Photoelectron injection at metal-semiconductor interfaces

A modelling of the photoinjection process is developed which permits fitting of the spectral photoresponse of Schottky barriers including the electric field dependence of barrier height and photoresponse by means of two adjustable parameters: the zero field barrier qφ_BO and λ₀ the zero temperature mean free path for optical phonon scattering of high energy electrons. The model assumes an image force potential barrier with Thomas-Fermi screening in the metal. Effects of optical phonon scattering and quantum mechanical transmission are convoluted on the Fowler photoelectron supply function. The effects of phonon scattering are frequently large because the ranges in energies associated with the transverse momentum and normal momentum are approximately the amount by which the quantum energy hv exceeds the barrier energy qφ_B. At high fields, quantum mechanical tunneling dominates the response when hv < qφ_B. At low fields, phonon assisted transmission is appreciable for the same quantum energy range. The calculation of the collection probability includes effects of multiple scattering even for electrons that do not lie initially within the cone of acceptance at the barrier maximum. An approach that considers the probability of collection the same as that of reaching the potential maximum without scattering is found to be acceptable only at high fields. Experimental results are reported from oxide-passivated epitaxial Pt_xSi-〈111〉 n-type Si Schottky barrier diodes with annular Schottky barrier guard rings measured at temperatures of 90 and 298 K for an electric field range from 5 × 10³ to 9 × 10⁴$\text{V}\text{cm}$. The field, spectral and temperature dependences of the photoresponse data are in excellent agreement with theoretical predictions with λ₀ = 110 Å at both 90 and 298 K. The zero field barrier height obtained from fitting photoresponse curves at a number of electric fields is also in excellent agreement with I-V and C-V measurements.