Current transport in metal-semiconductor barriers

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A theory for calculating the magnitude of majority carrier current flow in metal-semiconductor barriers is developed which incorporates Schottky's diffusion (D) theory and Bethe's thermionic emission (T) theory into a single T-D emission theory, and which includes the effects of the image force. A low electric field limit for application of this theory is estimated from consideration of phonon-induced backscattering near the potential energy maximum. A high electric field limit associated with the transition to T-F emission is estimated from calculations of the quantum-mechanical transmission of a Maxwellian distribution of electrons incident on the barrier. The theory predicts a wide range of electric field ≈ 2 × 10 2 to 4 × 10 5 V/cm over which the T-D theory may be applied to metal- n-type Si barriers at 300°K. The corresponding range for metal- n-type GaAs barriers is 9 × 10 3 to 8 × 10 4V/ at 300°K. The decreased upper limit is due mainly to the smaller electron effective mass in GaAs, the increased lower limit to a small optical-phonon energy and a shorter electron-optical-phonon mean-free path. The theory predicts Richardson constants of 96 and 4.4 A/cm 2/°K 2 for metal- n-type Si and metal- n-type GaAs barriers respectively. Experimental measurements on both metal-Si and metal-GaAs barriers are in general agreement with the theory. Values of the barrier n[( q/ kT)(d V/d ln J)] appreciably greater than unity are predicted for the field-dependent barrier height which occurs when an interface layer of the order of atomic thickness exists between the metal and the semi-conductor. A field dependence of the barrier height is shown to have no first order effect on the derivative of the 1/ C 2 vs. V relationship for the barrier. The intercept of a 1/ C 2 vs. V plot is shown to yield the barrier height extrapolated linearly to zero field in the semiconductor. Experimental evidence for the existence of interface layers in near-ideal Schottky barriers is also presented.