The physical phenomena associated with the frequency response of the surface inversion layer of an MOS capacitor are examined. It is shown that the equivalent circuit presented by Lehovec and Slobodskoy for an MOS capacitor in the depletion-inversion mode of operation may be simplified when the capacitor is biased in the heavy inversion layer mode. Further it is shown that an additional resistance, to account for generation-recombination in the depletion region, must be included. This new resistance dominates the response for silicon units, which is shown to be as low as I–5o cps at room temperature. Experimentally, there are at least two observations which cannot be explained by the first order one dimensional model on which these equivalent circuits are based. The frequency responses of complementary units, fabricated on almost identical p- and n-type silicon differ by orders of magnitude, it is typically in the range 1–100 cps for n-type units, but may be as high as 10 Mc/s for equivalent p-type units. In addition, pronounced hysteresis in the bias dependence of the capacitance of some p-type units has been observed. A second-order two dimensional model is proposed to explain these anomalies. This model includes an “external” inversion layer, surrounding the gate electrode, produced during the formation of the oxide. The gate inversion layer, in this model, is coupled to the bulk through an additional RC network, representing the external inversion layer, which is in parallel with the equivalent network of the first order model. An approximate analysis of this second order model predicts a frequency response which is in agreement with experiment. The possibility of charge migration on the surface of the oxide, which serves to decouple the gate inversion layer from the external inversion layer, can account for the hysteresis in the capacitance vs. bias characteristics observed in these units.

Physical limitations on the frequency response of a semiconductor surface inversion layer

The capacitance of a space charge layer, induced on a semiconductor surface, is analyzed to obtain information on the charge of surface states. Capacitance measurements on silicon-silicon oxide-metal combinations are presented, and these indicate a quasi-continuous spectrum of surface states with a density of approximately 1 × 1012 states/cm2 · eV in the range 0.2 to 0.8 eV above the valence band for both, p- and n-type samples, and a total density of 1.7 × 1012 states/cm2. Advantages and limitations of the capacitance-method are discussed.



Die Kapazitat der Raumladungsschicht, die auf einer Halbleiteroberflache induziert ist, wird zur Bestimmung der Oberflachenzustande des Halbleiters ausgewertet. Es wird uber Messungen an der Kombination Silizium-Siliziumoxyd-Metall berichtet. Fur p- und n-Material wird ein quasikontinuierliches Spektrum der Oberflachenzustande mit einer Dichte von etwa 1 × 1012 Zustanden/cm2 · eV innerhalb des Bereichs von 0,2 bis 0,8 eV uber dem Valenzband gefunden. Die Gesamtdichte ist 1,7 × 1012 Zustande/cm3. Vorteile der „Kapazitatsmethode” und mogliche Schwierigkeiten werden diskutiert.

Field Effect-Capacitance Analysis of Surface States on Silicon

Optical Field Effect in Silicon

The dependence of the real and imaginary photo-EMF components on frequency of the incident light modulation has been calculated for Ge and Si MIS structure in the inversion regime at the interface. It is shown that physical parameters of a semiconductor, such as doping levels in the bulk and near the interface, the rate of surface recombination proceeding at the backside of the sample, diffusion coefficient of minority carriers and light absorption coefficient can be derived from the experimental results.

Frequency dependence of the photo-EMF of strongly inverted Ge and Si MIS structures—I. Theory

The a.c. behavior of a semiconductor-insulator-metal capacitor is analyzed as a function of the frequency of a small a.c. voltage and of a d.c. bias voltage. Our analysis differs from previous work by G arrett , B erz and Y unovich , respectively, which dealt mainly with field effect conductivity, in the following respects: 1. Both (I), the extreme case of negligible recombination rate in the space-charge layer, and (II) the opposite extreme case of infinite recombination rate in the space-charge layer, are treated. 2. Deviations from the Boltzmann distributions of carriers in the space-charge layer at current flow are taken into account. 3. Equivalent circuits are derived from which the frequency dependence and the loss angle can be more readily appreciated than from the involved analytic expressions for the impedance. 4. Graphs are provided for the determination of the impedance as function of bias, frequency and of resistivity of the semiconductor for a semiconductor free of surface states.

C. G. B. Garrett

Papers

High-Frequency Relaxation Processes in the Field-Effect Experiment