J. Shewchun

Minority carrier MIS tunnel diodes and their application to electron- and photo-voltaic energy conversion—I. Theory☆

Abstract If the insulating layer in a metal-insulator-semiconductor (MIS) diode is very thin ( A for AlSiO2Si), measureable tunnel current can flow between the metal and the semiconductor. If the insulating layer is even thinner ( A ), tunnel currents are so large that they can significantly disturb the semiconductor from thermal equilibrium. Under such conditions, MIS diodes exhibit properties determined by which of the following tunneling processes is dominant; tunneling between the metal and the majority carrier energy band in the semiconductor, between the metal and the minority carrier energy band, or between the metal abd surface state levels. In the present paper, minority carrier MIS tunnel diodes are analysed using a very general formulation of the tunneling processes through the insulator, transport properties in the semiconductor, and surface state effects. Starting from solutions for diodes with relatively thick insulating layers where the semiconductor is essentially in thermal equilibrium, solutions are obtained for progressively thinner insulating layers until non-equilibrium effects in the semiconductor are observed. It is shown that such minority carrier MIS tunnel diodes with very thin insulating layers possess properties similar to p-n junction diodes including exponential current-voltage characteristics which approach the “ideal diode” law of p-n junction theory. The theory adequately describes the observed properties of experimental devices reported in a companion paper. The diodes have application as injecting contacts, as photodiodes or elements of photodiode arrays, and as energy conversion devices employing the electron- or photo-voltaic effects.

Absorption coefficient of silicon for solar cell calculations

Abstract The optical absorption coefficient is an important parameter in calculating the performance characteristics of solar cells. For silicon solar cells it is desirable to know the absorption coefficient over the range of 1.1–4.0 eV and over a wide range of temperature, particularly when evaluating the concentration type systems. An analytical (empirical) expression has been developed for this purpose. We have interpreted the available experimental data in terms of three bands of silicon. With our fit, the experimental data can be explained to within an accuracy of 20% and its validity extends from 1.1 to 4.0 eV and over the temperature range of 20–500°K.

Theory of metal‐insulator‐semiconductor solar cells

Recent reports in the literature indicate that the introduction of an interfacial oxide layer in a Schottky barrier can greatly increase the photovoltaic conversion efficiency of such devices. We propose an explanation for the operation of such solar cells based on the concept that they are minority‐carrier nonequilibrium MIS tunnel diodes. Calculations of efficiency as a function of insulator thickness, substrate carrier concentration, surfaces states, and oxide charge are presented. These indicate that a maximum theoretical efficiency of 21% is possible under AM2 illumination for high substrate doping and low interface defect density.

Current multiplication in metal-insulator-semiconductor (MIS) tunnel diodes☆

In contrast to thick insulator structures, metal-insulator-semiconductor (MIS) diodes with very thin insulating layers (< 30 A for the silicon-silicon dioxide system) allow appreciable tunnel current flow between the metal and the semiconductor causing the semiconductor to depart significantly from thermal equilibrium conditions when the diode is biased. Under such conditions, recent experiments have demonstrated that multiplication of minority carrier current can occur in the contact region. This multiplication process is described in detail by deriving analytical expressions characterizing this process and its dependence upon the metal, insulator, and semiconductor parameters for one specific class of diode. Numerical methods are used to investigate the multiplication properties under more general conditions. Solutions obtained by this method indicate that values of the small signal multiplication factor, M, in the range of 102–103 can be obtained with appropriately designed diodes. The applications of the multiplication process to a transistor structure and to a photodiode with internal multiplication properties are described briefly.

Minority carrier effects upon the small signal and steady-state properties of Schottky diodes

Abstract Schottky diode theory is re-evaluated by applying the combined thermionic emission-diffusion theory to both the majority and minority carrier flows across the metal-semiconductor contact. Under both steady-state d.c. and small signal a.c. conditions, numerical solutions to the semiconductor transport equations subject to boundary conditions determined from the combined theory are used to investigate the effects of minority carriers upon the properties of uniformly doped Schottky diodes. High injection effects and contact limitations are shown to influence the minority carrier injection ratio and the total stored minority carrier charge. It is further shown that the small signal impedance of a large class of Schottky diodes becomes inductive under moderate forward bias.

Non-equilibrium effects on metal-oxide-semiconductor tunnel currents☆

Abstract A d.c. tunnel current saturation under negative bias is observed for N -type MOS devices when average oxide thicknesses of d 0 A and non-degenerate (10Ω cm) semiconductors are employed. A model is proposed that allows the voltage distribution across devices in such a non-equilibrium situation to be calculated. Theoretical tunnel current expressions are derived and a comparison with experimental results made. The dependence of the existence of this saturation on semiconductor doping concentration, oxide thickness, and minority carrier injection is investigated. Consideration of band tunnel currents, and the effects of surface state charge, oxide charge, and work function differences on these currents, is shown to be sufficient to explain much of the observed current-voltage characteristic.

Nitrogen−implanted silicon. II. Electrical properties

This paper presents measurements of capacitance−voltage, Hall−effect, and diode characteristics on nitrogen−implanted silicon as a function of anneal temperature. The results of these three types of electrical measurements are consistent and show that less than 1% of the implanted nitrogen exhibits donor effects following anneals in the temperature range ∼700−900 °C. Hall−effect measurements performed as a function of temperature indicate that nitrogen in silicon has an ionization energy of 0.017±0.002 eV. Room−temperature Hall−effect measurements combined with stripping techniques have shown that the distribution of electrically active nitrogen is constant as a function of implantation depth. These results are believed to be due to a donor (substitutional) position involving <1% of the implanted nitrogen ions; this interpretation is consistent with the lattice location and damage results presented in Paper I.

Nitrogen-implanted silicon. I. Damage annealing and lattice location

The radiation damage and implanted atom location properties of nitrogen−implanted silicon have been studied. Helium−ion backscattering has been used to measure the damage for samples implanted at various doses and annealed to temperatures as high as 900 °C. The location of the implanted nitrogen in the silicon lattice has been investigated by using the 15N(p,α)12C nuclear reaction together with channeling techniques. The results indicate that ≳90% of the implanted atoms are located in nonsubstitutional positions in the silicon lattice, and that the implanted nitrogen has not outdiffused for anneals to 1185 °C. The results presented here will be used in Paper II to help explain many of the observed electrical porperties of nitrogen−implanted silicon.

Application of the small-signal transmission line equivalent circuit model to the a.c., d.c. and transient analysis of semiconductor devices

Abstract It is shown that the use of the small signal transmission line equivalent circuit model is not restricted solely to the small signal a.c. analysis of semiconductor devices. Simple algorithms are described which allow it to be used to compute the d.c. and the large signal transient properties of semiconductor devices to any desired precision. The approach is demonstrated by computing the a.c., d.c. and transient properties of an N + P junction diode.

Ellipsometric Technique for Obtaining Substrate Optical Constants

A method for determining substrate optical constants, surface film thickness, and surface film optical constants has been devised by measuring the ellipsometer angles Δ and ψ at several angles of incidence. This method, previously reported as impossible, solves in a simple fashion the ellipsometry equations for one consistent values of surface film thickness in association with compatible values of substrate optical constants. The technique is advantageous in that vacuum ellipsometry is eliminated and previously unmeasured materials such as alloy structures may be studied readily. Data on aluminum, molybdenum, and silicon are presented illustrating the technique.