Surface State and Interface Effects on the Capacitance-Voltage Relationship in Schottky Barriers

Abstract

In the presence of an interfacial layer and semiconductor surface states, a Schottky barrier height φ_b decreases with increasing electric field E at the surface of the semiconductor. If the semiconductor doping concentration N_d is uniform throughout the depletion region and if $${\mathrm{[\; (qN}}_d{\mathrm{/\epsilon )\; (d\phi }}_b{\mathrm{/dE)-E]\; [\; (d}}^2{\phi }_b{\mathrm{/dE}}^2\text{) (dE/dV) ]≪1,}$$ where V is the applied voltage and ε is the semiconductor permittivity, the slope of the (capacitance)⁻² vs voltage relationship is constant and can be interpreted to give N_d. The voltage intercept of the relationship yields an apparent barrier height φ_a related to the true barrier φ_b by φ_a=φ_b−E (dφ_b/dE) + (qN_d/2ε) (dφ_b/dE)², where q is the electron charge. From the measured variation of φ_a with N_d and one absolute measure of φ_b at one value of N_d, φ_b(E), and dφ_b(E)/dE may be deduced. From dφ_b(E)/dE the surface state density as a function of energy in the bandgap and the minimum value of interface thickness divided by relative interface permittivity can be obtained. Using the data of Archer and Atalla for vacuum cleaved Au‐Si diodes to illustrate our method, the surface state density is found to peak at a value of ∼2×10¹⁴ cm⁻²·eV⁻¹ at about 0.83 below the conduction band and the minimum value of interface thickness divided by relative dielectric constant is found to be of the order of 5 Å. Criteria are given which show how Schottky diode capacitance‐voltage data may be further used, in conjunction with photoelectric barrier measurements, to detect the presence of deep lying impurities or the penetration of surface state charge into the body of the semiconductor.