Discrete State Simulation of Electrical Conductivity and the Peltier Effect for Arbitrary Band Structures
- PDF / 107,617 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 77 Downloads / 182 Views
Discrete State Simulation of Electrical Conductivity and the Peltier Effect for Arbitrary Band Structures Peter P. F. Radkowski III and Timothy D. Sands Applied Science and Technology Graduate Group and Materials Science and Engineering University of California Berkeley, California 94720 Abstract An object-oriented, discrete state method for simulating coupled systems was defined. A proof-of-principle simulation of the effect of acoustic phonon scattering on electrical current was performed. Steady-state and relaxation processes were numerically simulated. A relaxation time constant was measured. The numerical simulation of Peltier cooling and heating was defined as a special case of the scattering and transport physics of the proof-of-principle simulation. The scattering terms were designed to account for local interface conditions. Introduction In thermoelectric refrigeration devices, an electric potential pumps heat up a temperature gradient. As shown in Figure 1, an electric current flows counter-clockwise through a circuit of n-type and p-type semiconductor legs connected in series. Both holes and electrons carry heat from cold to hot. However, heat transport by charge carriers is offset by the thermal conductivity of the host crystal lattice. Lattice heat conductivity is directed down the temperature gradient by the net diffusion of phonons from the high phonon concentrations of the hot end.
Q
+ Q
Currents are coupled by electron-phonon scattering Figure 1. Coupled Currents in a Thermoelectric Device. Electron-phonon (hole-phonon) coupling regulates charge transport, Peltier heating and cooling, and Joule heating.
G8.5.1
The coupling of the electron/hole and phonon currents is fundamental to the operation of thermoelectric refrigerators. For example, as the electron current crosses the cold junction, heat is absorbed from the lattice by virtue of the Peltier cooling effect. This involves a net absorption of phonons while maintaining the conservation of total energy and total momentum. In the homogeneous material of the n-type leg, the electrons undergo collisions with the lattice and emit phonons. Finally, at the hot end, thermal energy is dumped into the heat sink as electrons lose energy by emitting phonons. Scientists and engineers are investigating the thermoelectric performance of new structural and material configurations. [1-2] A design goal is to enhance the thermal transport capacity of charge carriers relative to the thermal transport capacity of lattice vibrations. Quantum confinement design schools try to improve thermoelectric performance by judiciously engineering variations in electron and phonon dispersion relations. Other design schools manipulate defect and interface scattering of phonons. To compare and coordinate these design efforts, it is desirable to develop a simulation tool that efficiently incorporates a quantum mechanical model of electron and phonon scattering within a classical transport scheme that is computationally tractable. The reported model uses quantum mechanical scat
Data Loading...
