A Study of Some Contemporary Issues in Electron Devices: Electrical contact, heating, and amplifier stability

Abstract

This thesis presents a theoretical study of three fundamental topics of contemporary interest to electron devices: electrical contact resistance under AC condition, a nonlinear, steady state theory of thermal and electrical conduction on a one-dimensional conductor, and the absolute instability in a traveling wave tube.

Poor electrical contact is known to be a major cause of failures in all electrical/electronic systems, ranging from small scale consumer electronic devices to large scale military and aerospace systems. The quality of contact is often measured by the contact resistance, which has been treated mostly under steady state (DC) condition. This thesis considers the vastly more complex problem of AC contact resistance. By analyzing an AC current flowing through two Cartesian current channels, with different dimensions and different electrical resistivity, in contact with each other at an interface, the AC contact resistance as a function of frequency is calculated. Scaling laws are obtained and interpreted in terms of the degree of current crowding exhibited at the junction as a result of resistive skin effects in the respective current channels. Our AC results always reduce to the corresponding DC results under the low frequency limit where the resistive skin depths are much larger than the channel sizes. In some geometry and at some frequency, the AC contact resistance may become negative, meaning that the total AC resistance in the two current channels is less than the AC bulk resistances from the individual channels. The contact resistance on a slightly uneven joint is also evaluated as unique scalings of contact resistance was found with frequency. The mathematically divergent field at the sharp corner at the joint is given some attention, under AC condition.

The second problem concerns the degree of ohmic heating in a current-carrying conductor. We present a nonlinear, steady state, theory of thermal and electrical conduction on a 1-dimensional conductor using several models to specify the temperature dependence in the thermal and electrical conductivities. The temperature distribution is presented for each model, together with the parameter space for the existence of the steady state solutions. Nonexistence of a steady state solution may suggest the possibility of thermal runaway. The temperature distribution calculated according to the theory has been favorably compared with experiments on a field emitter made of a carbon nanotube fiber.

The last problem concerns the stability of a traveling wave tube (TWT) which is a central component in virtually all communications satellites. High mission demands require high power, at which stable operation of TWT may become an issue. This thesis examines an absolute instability in a TWT that could occur at the upper and lower edges of the amplification band. We use the Briggs-Bers criterion to confirm the previous findings on the existence of absolute instability at the upper band edge when the electron beam current that powers the TWT is sufficiently high. We correct the erroneous previous conclusion on the non-existence of absolute instability at the lower band edge. The temporal-spatial evolution of the Green’s function was calculated. It corroborated the above-mentioned results, and it shows, for the first time, transient exponential growth as a fractional power of time initially, followed by simple exponential growth in time or decay in time, depending on whether the current threshold for absolute instability is exceeded.