Linear Stability of Electron-Flow Hydrodynamics in Ungated Semiconductors

Semiconductors play an important role in modern electronic technology. They are present in most sensing and transduction applications, satisfying requirements such as compactness, tunability and portability. It is known that any fluctuation in electron density inside a semiconductor produces acceleration or deceleration of the electrons that generates electromagnetic radiation. For this reason, in recent years this has been proposed as a source of radiation for what is called the 'THz gap' in the electromagnetic spectrum. Radiation sources at this frequency range can provide an improvement over current techniques in bioimaging and sensing due to advantages such as non-ionizability and easy absorption by water. An understanding of how electron-flow instabilities occur and the parameters that affect them is needed to determine if semiconductors can be used as THz radiation sources.

The main motivation of this work is to analyze from a hydrodynamic perspective the conditions under which instabilities occur in electron flow in ungated semiconductors. A continuum description of the electron flow is presented. The governing equations include Gauss' law, the mass, momentum and energy conservation equations for electrons and a constitutive equation for energy flux in the lattice. Linear stability analysis was used to study the instabilities of the steady-state solution of this system of equations.

Three configurations were analyzed. The first is one-dimensional, with a mathematical model that is thermally uncoupled in that it does not consider electron-lattice interactions, and it is assumed that the lattice and electron temperatures are not affected by the electron flow. The second configuration is two-dimensional, but still thermally uncoupled. The third is a thermally-coupled one-dimensional analysis in which electron-lattice interactions exist, and the lattice and electron temperatures are dependent variables. The driving force in all cases is due to an imposed external electric field.

Stability analysis in the thermally-uncoupled configurations showed that the instability spectrum becomes denser when the configuration goes from one to two dimensions. The uncoupled system becomes more unstable when the applied voltage increases. Changes in the material parameters such as doping density and length of the semiconductor can also affect stability. In general, the thermally-coupled configuration does not become unstable with higher applied voltages. However, it does if electronic heat conduction and energy loss from electrons to the lattice through scattering are neglected. Therefore, control of these phenomena is crucial for the generation of instabilities in semiconductors. Applied voltage and room temperature can determine suitable operating conditions for THz electromagnetic sources based on semiconductors.