Surface States and Barrier Height of Metal-Semiconductor Systems

Abstract

The dependence of the barrier height of metal‐semiconductor systems upon the metal work function is derived based on the following assumptions: (1) the contact between the metal and the semiconductor has an interfacial layer of the order of atomic dimensions; it is further assumed that this layer is transparent to electrons with energy greater than the potential barrier but can withstand potential across it. (2) The surface state density (per unit area per electron volt) at the interface is a property only of the semiconductor surface and is independent of the metal. The barrier height φB_n is defined here as the energy needed by an electron at the Fermi level in the metal to enter the conduction band of the semiconductor. With the above assumptions, the barrier height for n‐type semiconductor‐metal contacts is found to be a linear combination of the metal work function φ_m and a quantity φ₀ which is defined as the energy below which the surface states must be filled for charge neutrality at the semiconductor surface. The energy φ₀ is measured from the edge of the valence band. For constant surface state density the theoretical expression obtained is $${\mathrm{\phi Bn=\gamma (\phi }}_m{\text{−χ)+(1−γ)(E}}_g{\mathrm{-\phi }}_0{\mathrm{)-\Delta \phi }}_n$$ , where χ and E_g are electron affinity and the band gap of the semiconductor, respectively, Δφ_n is the image force barrier lowering, and γ is a weighting factor which depends mainly on the surface state density and the thickness of the interfacial layer. The theoretical expression is compared to the presently available φB_n VS φ_m data for Si, GaP, GaAs, and CdS, by fitting the data to straight lines using the method of least squares. The best straight‐line fit was obtained for the GaP data, with probable error limits on the slope and intercept of ±0.03 and ±0.13 eV, respectively. The parameter γ in the theoretical expression is found to range from 0.07 for GaAs to almost unity for the CdS data reported by Goodman indicating weak and strong dependence of the surface barrier height on the metal work function, respectively. The value of φ₀ is roughly a third of the respective band gap energies for Si, GaP, and GaAs, and the surface state density for these semiconductors is found to be in the range 10¹³−10¹⁴ states/cm²/eV, for the experiments cited. Excessive scatter in the data points for the CdS data of Mead and Spitzer casts doubt on the significance of a straight‐line fit for this case. The data of Goodman for CdS obey the Schottky theory for a metal‐semiconductor barrier, but this agreement requires a value of the electron affinity χ which is different from the vacuum‐photothreshold value measured by other authors.