Where is the voltage drop? A numerical study using a quantum kinetic equation

Michael James McLennan, Purdue University

Abstract

In this thesis, we present a numerical method for evaluating the full Wigner function $-$iG$\sp<$(r; k; E) throughout a device by solving a steady-state quantum kinetic equation in two dimensions, in the linear response regime. This method has two advantages over conventional treatments of mesoscopic devices. First, dissipative processes can be included within the device. Second, we can compute any quantity of interest, such as electron density or current density, throughout the entire device. We will first show that under low bias conditions, the diagonal elements of the Wigner function can be used to define a local electrochemical potential ($\mu$) that lends insight into the internal transport physics. We examine the difficulties associated with measuring $\mu$, with numerical examples. By computing $\mu$ throughout a four-terminal junction, we clearly show that the "quenching" of the Hall resistance observed in narrow wires at low magnetic fields is not an intrinsic effect, but rather an artifact of the measurement probes. We also use the local electrochemical potential profile to clarify the nature of the spreading resistance associated with the narrowing of a current lead, and to illustrate the formation of residual resistivity dipoles around impurities. Finally, we present example computations of the electrostatic potential ($\phi$) and show that it can be viewed as a convolution of $\mu$ with a screening function.

Degree

Ph.D.

Advisors

Datta, Purdue University.

Subject Area

Electrical engineering

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