Numerical Simulation and Stability Analysis of Thin Flexible Micro Film for Thermotunneling Application

Combined thermionic emission and tunneling of hot electrons (thermo-tunneling) has emerged as a potential new solidstate cooling technology. Practical implementation of thermo-tunneling, however, requires the formation of a nanometer-sized gap spanning macroscopically significant surfaces. Thermo-tunneling 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, flat 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. This presentation is focused on our effort to investigate the stability of the the thin flexible structure under electrostatic and lorenz forces opposing each other. In this presentation, we report the result of numerical simulation with some mathematical simplifications. The mathematical model used for the numerical simulation is well studied in the literature. Using forth-order partial differential beam equation, we studied the steady state solutions of the thermo-tunneling beam model using Galerkin method. Essential output parameters of the model include a central contact area measured by its length (delta) and the thermo-tunneling current. Both parameters are determined as a function of the externally applied external potential and magnetic field. Numerical solutions of the model show two possible operating modes: (1) symmetric deformation with negligibly small current; and (2) asymmetric mode where the B-field controls the current and contact area. Under practical values for the externally applied magnetic and electric fields, it has been shown that the second mode is only possible for electrode with very low work functions, e.g. below 0.5 eV. Therefore, novel materials such as Diamond-like carbon films are likely to be essential in thermo-tunneling applications.