Abstract

An ideal semiconductor device would permit unimpeded flow of electrons from its source to its drain in a fashion that can be switched on and off by its gate at high frequency. Electron flow through real semiconductor devices is impeded by interactions with the crystalline structure of the material. Electrons which interact with the crystal may generate phonons which manifest as thermal energy generation and degrade real device performance from its ideal limit. Accurate simulation of electron-phonon interactions cannot rely on the traditional continuum assumption because of the reduced length and time scales of modern semiconductor devices. Allowable electron-phonon interactions are constrained by the conservation of energy and momentum. Direct enforcement of the conservation laws is achieved through computation of an interaction table that contains thousands of rows each of which representing a conservative interaction. The rows represent both phonon and electron creation and annihilation. The electron and phonon wavevector space is discretized into 65,856 elements and the table is computed by searching the discretized wavevector space for electron and phonon states that first satisfy the conservation of momentum. Subsequently, these states are compared against the conservation of energy using the phonon and electron dispersion relations. Anisotropic phonon dispersion relations were calculated using a second nearest neighbor lattice dynamics approach with interatomic force constants from Density Functional Theory. Electron dispersion relations were computed using an empirical pseudopotential approach. This method was demonstrated for computation of electron-phonon interactions in silicon, resulting in an initial interaction table containing approximately 58,000 interactions. Computation of the electron energies associated with the first conduction band in an anisotropic manner illustrate reasonable agreement with published work. The interaction densities show similar functionality relative to the electron-phonon interaction rate predictions and phonon generation rates from published literature. The interaction table directly enforces the conservation laws on all electron-phonon interactions and the interaction table approach can be used for high fidelity electron-phonon simulations to quantify the mechanism, rate, and location of thermal losses arising at the nanoscale.

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