F.A. Lindholm

Application of the superposition principle to solar-cell analysis

The principle of superposition is used to derive from fundamentals the widely used shifting approximation that the current-voltage characteristic of an illuminated solar cell is the dark current-voltage characteristic shifted by the short-circuit photocurrent. Thus the derivation requires the linearity of the boundary-value problems that underlie the electrical characteristics. This focus on linearity defines the conditions that must hold if the shifting approximation is to apply with good accuracy. In this regard, if considerable photocurrent and considerable dark thermal recombination current both occur within the junction space-charge region, then the shifting approximation is invalid. From a rigorous standpoint, it is invalid also if low-injection concentrations of holes and electrons are not maintained throughout the quasi-neutral regions. The presence of sizable series resistance also invalidates the shifting approximation. Methods of analysis are presented to treat these cases for which shifting is not strictly valid. These methods are based on an understanding of the physics of cell operation. This understanding is supported by laboratory experiments and by exact computer solution of the relevant boundary-value problems. For the case of high injection in the base region, the method of analysis employed accurately yields the dependence of the open-circuit voltage on the short-circuit current (or the illumination level).

Impurity concentration dependent density of states and resulting fermi level for silicon

Abstract Utilizing an approach for describing the density of quantum states in a semiconductor as a function not only of energy but also of impurity concentration, we calculate the density of states and the Fermi level in n -type silicon. The calculated densities of states are shown to agree with pertinent experimental results.

Forward-voltage capacitance and thickness of p-n junction space-charge regions

A comprehensive analytical model for the quasi-static capacitance of the space-charge region of p-n junction devices is presented. It describes the capacitance for all voltages, including voltages large enough to cause the junction barrier to vanish. The model applies for exponential-constant doping profiles, the limiting cases of which are the step and the linear-graded profiles. In addition to the analytical model, an iterative technique is developed to yield numerically the thickness of the space-charge region as a function of voltage. The capacitance model shows good agreement when compared with measured dependencies, With an empirical model for circuit simulation, and with models based on device simulation. The model extends previous replacements of the depletion capacitance, provides a tool for circuit simulation, and is intended to provide understanding of the physics related to storage of mobile holes and electrons in the junction space-charge region.

A methodology for experimentally based determination of gap shrinkage and effective lifetimes in the emitter and base of p-n junction solar cells and other p-n junction devices

An experimentally based methodology is described that determines the effective gap shrinkage and lifetime in the emitter of a p-n junction solar cell. It provides the first experimental means available for assessing the importance of gap shrinkage relative to that of large recombination rates in the highly doped emitter. As an additional result of the procedures employed, the base lifetime is also determined. The methodology pertains to a solar cell after the junction is formed. Hence each material parameter determined includes the effects of the processing used in junction fabrication. The methodology consists of strategy and procedures for designing experiments and interpreting data consistently with the physical mechanisms governing device behavior. This careful linking to the device physics uncovers the material parameters concealed in the data. To illustrate the procedures, they are applied to an n+-p solar cell having substrate resistivity of about 0.1 Ω cm.

A method for determining the emitter and base lifetimes in p-n junction diodes

A method is described that provides an experimental means for the first time to separate and determine the emitter and base lifetimes in a p-n diode after the junction has been fabricated. In the method, several static and transient measurements are analyzed using physical models of the diode characteristics. To illustrate the method, diffused silicon diodes are fabricated having substrate (base) impurity concentrations ranging from 1014to nearly 1017phosphorous atoms per cubic centimeter. The results show an emitter lifetime that is much smaller than the base lifetime in the diode having the highest base doping concentration. In this diode, the recombination current from the emitter is 65 percent of the recombination current from the base, demonstrating the significance of the emitter in governing the static current-voltage dependence. The importance of emitter recombination to the transient characteristics is also demonstrated. The paper emphasizes the techniques by which the base and emitter lifetimes are distinguished. It also demonstrates the need for carefully basing the quantitative analysis of the measurements on the underlying diode physics. The method described here applies not only to p-n diodes but also to junction solar cells and transistors.

Analytical and numerical modeling of amorphous silicon p‐i‐n solar cells

Analytical and equivalent‐circuit models based on numerical solutions for a‐Si:H solar cells are presented. The dependencies among such variables as recombination rate and electrical field on terminal and optical excitation are discussed. Based on our physical interpretation of the numerical solutions, we propose an equivalent‐circuit model which separates the currents into photocollected and back injected components. This model clarifies the concept of the limiting carrier and points out that the limiting carrier is the carrier with the least photocollected current. Analytical expressions for uniformly and strongly absorbed light are derived.

Fundamental electronic mechanisms limiting the performance of solar cells

The efficiency of a solar cell depends on the electronic parameters which characterize the transport, recombination, and generation of electrons and holes in semiconductors. This paper describes the many basic mechanisms that can control these electronic parameters in solar cell materials.

A new charge-control model for single- and double-heterojunction bipolar transistors

A new charge-control relation is derived for heterojunction bipolar transistors. The relation is valid for arbitrary doping density profiles and for all levels of injection in the base. It is applicable to both single- and double-heterojunction transistors. The model is an improvement over another recently proposed charge-control model that was valid only for constant doping density and low injection in the base. Large- and small-signal equivalent circuit models are also presented for heterojunction bipolar transistors. Comparisons with numerical and experimental data show excellent agreement. >

One-dimensional non-quasi-static models for arbitrarily and heavily doped quasi-neutral layers in bipolar transistors

A systematic method is presented for deriving non-quasi-static equivalent-circuit models for arbitrarily doped and heavily doped quasi-neutral layers in bipolar transistors. The large-and small-signal models developed improve various aspects of the one-dimensional Gummel-Poon model for transient and frequency circuit simulation. The improvements are assessed by computer simulation and by experiment. In the simulation of high-speed or high-frequency bipolar integrated circuits, the models show advantages over the conventional Gummel-Poon model. It is shown that non-quasi-static effects are significant in the emitter as well as the base layer. The method is developed for homojunction bipolar transistors but in principle applies also to heterojunction bipolar transistors. >

Normal modes of semiconductor p‐n–junction devices for material‐parameter determination

An expression for the dominant normal model (natural frequency) of a p‐n–junction diode is derived. The expression includes the effects of minority charge in the quasineutral emitter as well as the base region, and is applicable for any concentration profiles of impurity and recombination centers, regardless of high recombination rates or band‐edge distortion in the emitter. Its use enables the experimental determination of material parameters pertaining to the relative roles of the emitter and the base in governing the behavior of various junction devices, including diodes, transistors, and solar cells.