Quantum mechanical electron transmission coefficient at interfaces and ballistic electron emission microscopy

We derive the quantum mechanical transmission coefficient for the electron transport across a plane interface of a metal/semiconductor or semiconductor/semiconductor heterostructure. An effective mass model is used for the conduction band in each layer of the system. Non-diagonal mass tensors and indirect band minima are covered by the model. The quantum effects for the electron transmission are investigated for the system Au(111)/Si(111) as a test case. We find sizeable corrections originating from quantum effects.