## Date of Award

9-2008

## Document Type

Thesis

## Degree Name

Master of Science (MS)

## Legacy Department

Electrical Engineering

## Committee Chair/Advisor

Harrell, William R

## Committee Member

Bridgwood , Michael A

## Committee Member

Sosolik , Chad E

## Abstract

The current flow due to Space-Charge-Limited (SCL) emission is well known and the associated current-voltage power law relationship can be observed in many materials, particularly in insulators and semiconductors. Under an applied field, the space-charge effect occurs due to the carrier injection, and the resulting current due to the presence of the space-charge effect is referred to as SCL current. In the SCL current theory, the presence of localized traps in a material has a significant effect on the transport of injected carriers; however, in the first order SCL model, the trap barrier height is assumed to be constant for any applied field. According to the theory of the Poole-Frenkel (PF) effect, the barrier height is lowered in the presence of an electric field. The PF effect, which is also a well known conduction mechanism, is the thermal emission of charge carriers from Coulombic traps in the bulk of a material enhanced by an applied field. When an electric field is applied, the potential barrier on one side of the traps is reduced, and due to this barrier lowering, the thermal emission rate of electrons from the traps is increased. Since the presence of traps has a significant effect on the SCL current, the barrier lowering due to the PF effect needs to be incorporated into the SCL model.

The incorporation of the PF effect into the SCL model has been accomplished already; however, the classical PF model was used. The classical PF model is based on the Boltzmann approximation for defining the trapped carrier concentration, which fails to predict the saturation of carrier emission once the trap barrier height has been reduced to the ground state. Therefore, the classical PF model leads to erroneous results at high fields, which is where it typically becomes significant. A more physically accurate model, which is referred to as the modern PF model, has been introduced by using the Fermi-Dirac distribution function to define the trapped carrier concentration. The modern PF model can predict PF saturation, and therefore, this model yields more accurate predictions at high fields. In this research, an SCL current model incorporating a modern PF model was derived and analyzed. The SCL model incorporating the classical PF model predicts a current enhancement due to the PF effect; however, it predicts a continuous, gradual increase in the current with voltage for all applied fields, which is unphysical. According to the first order SCL current theory, the SCL current-voltage characteristics shift from the shallow-trap field region to the trap-free-square law region at a transition field. At this transition field, the current increases very sharply for a small change in voltage, which is referred to as the Trap-Filled-Limit (TFL) law. By incorporating the modern PF model, not only does the model predict a higher current level, but the model also predicts a vertical asymptote in the current-voltage characteristics, and this asymptote occurs at the TFL law. A more advanced SCL model was also derived by incorporating the modern PF model and using the exact Poisson equation. The two models discussed above, the SCL models incorporating the classical and modern models of the PF effect, used an approximation in the Poisson equation. By using the exact Poisson equation, instead of the model asymptotically approaching infinity at the TFL law, it predicts a proper transition from the shallow-trap SCL region to the trap-free-square law region. Also, when the PF saturation field is lower than the TFL law, this transition occurs at the PF saturation field instead at the TFL law.

## Recommended Citation

Takeshita, Satoshi, "MODELING OF SPACE-CHARGE-LIMITED CURRENT INJECTION INCORPORATING AN ADVANCED MODEL OF THE POOLE-FRENKEL EFFECT" (2008). *All Theses*. 473.

https://open.clemson.edu/all_theses/473