M.Sc Thesis

M.Sc StudentRubin Tal
SubjectA Simple Constitutive Model for Dielectric Charging Based
on Frenkel-Poole Mechanism and a Derivation of
Maxwell Stresses
DepartmentDepartment of Mechanical Engineering
Supervisor PROF. David Elata
Full Thesis textFull thesis text - English Version


The operation of MEMS relies on integration of electrical and mechanical components. The electrical components are composed of conductors, semi-conductors and insulators. Sometimes the dielectric properties of a material are also significant.

Current flow through insulators and semi-conductors is largely understood, especially when dealing with materials of crystalline structure. However, conduction through amorphous dielectric insulators is only partially modeled. In this work, we try to step out of the steady state conduction model which was developed for electronics, and set foot into the transient conduction-charging mechanism which was observed in MEMS applications.

Conduction through amorphous dielectrics occurs under sufficient electric loads. In electronics which is a practice older than MEMS, this conduction has been encountered and analyzed in order to compensate for its occurrence. The model developed for electronic circuits predicts the proportion of the steady state current density, for metal-insulator-metal (MIM) structures. This model is insufficient for some MEMS applications.

Dielectric materials and insulators in general have a small amount of free charge carriers. Therefore, for current to flow through an insulator, charge carriers should be injected into the insulator. This phenomenon is not vital for electronics, but in some MEMS applications, particularly capacitive devices, the amount of charge stored in the dielectric layer can greatly affect the reliability and performance of the device.

This work uses both classic electrodynamics and quantum solid-state theory in order to explain phenomena that are, on one hand, quantum mechanical in nature, and on the other hand, outside the range of traditional solid-state treatment.

A second phenomenon occurring in dielectrics is expansion due to stresses caused by an interaction between their internal structure and an external electric field. It is well known that a dielectric material subjected to an electric field will expand and move into a region of high field intensity in order to lower the potential energy of the system.

We present a concise approach to integration of electrodynamics into continuum mechanics.