Mathematical Modeling and Stability Analysis of a Vacuum Gap Clamped-Clamped Micro-Beam For Thermo-Tunneling Application

Abstract

Combined thermionic emission and tunneling of hot electrons (thermo-tunneling) has emerged as a potential new solid state cooling technology. Practical implementation of thermotunneling, however, requires the formation of a nanometer-sized gap spanning macroscopically significant surfaces. Thermotunneling is a term used to describe combined emission of hot electrons (thermionic emission) and tunneling of electrons through a narrow potential barrier between two surfaces (field emission). Thermo-tunneling of hot electrons across a few nanometer gap has application to vacuum electronics, at panel displays, and holds great potential in thermo-electric cooling and energy generation. Development of new thermo-tunneling applications requires creation of a stable nanometer gap between two surfaces. Formation of such a small scale gap is very challenging. Due to the various type of the forces that come to the picture in the scale of nanometer gap creates a complex interaction between the engaged surfaces. In this project different setups of a test device is suggested to form a nanometer-sized gap appropriate for tunneling current generation. Having a mathematical model describing the physical characteristics of such a system is inevitable in order to examine the stability of the system's dynamics. The first set of externally applied forces selected to stabilize the system is composed of electrostatic force that attracts two surfaces opposed by an electro-magnetic force. The electro-magnetic force is produced by applying an external magnetic field to in the proximity of the thin flexible electrode which carries electrical current due to the electron tunneling. The orientation of the external magnetic field is set to generate a force in the opposite direction of the electrostatic force. The second setup of the experimental model is composed of electrostatic force opposed by the thermoelastic force. The thermoelastic force is generated due to the thermal expansion/contraction of the flexible beam. The configuration of the designed device determines the direction of which the thermoelastic force is applied. This project is focused on our effort to investigate the stability of the thin flexible micro structure under mentioned opposing forces and feasibility study of the fabrication of such a device.