Thermoelectric properties:Thermoelectric devices are used for cooling hot spots in electronic chips and thermal to electrical energy conversion. Their efficiency is an increasing function of the Figure of Merit: ZT=s S2 T/ k We need therefore materials where charge carriers abound and travel fast (high s), where each carrier carries a lot of heat (high S), and such that the transferred heat does not flow back easily if one side becomes warmer than the other (low k).
Recently ZT values as high as 2.4 have been observed in p-type Bi2Te3/Sb2Te3 superlattices. In other materials such as AgPbmSbTe2+m a ZT of 2.2 has also been observed. In all such materials, the structure plays a very important role in producing a high thermopower. In one case, there was a layered structure, and in the other a granular one. In both materials nanostructures play two roles: energy filtering for electrons in order to increase the thermopower, and mainly phonon scattering in order to reduce k. We have investigated the thermoelectric properties of nanocontacts made with carbon nanotubes, and observed theoretically a large value for the Seebeck coefficient, S. The next step is to compute their thermal conductance in order to predict a reliable ZT value. Thermionic transport in InGaAs/InGaAsP/InGaAs heterostructures:Transport in doped semiconductor heterostructures was modeled by the Boltzmann equation. We developed a Monte Carlo code to solve the latter. It includes scatterings such as electron- optical/acoustic phonons as well as charged and neutral impurities. Coulomb interactions with other electrons were included in the electrostatic potential which is solved using the Poisson equation[1]. The effect of Pauli exclusion principle, which becomes important in high doping or degenerate semiconductors was included using a simple efficient but accurate scheme[2]. Using a Monte Carlo code which we developed, thermionic transport across a single barrier was simulated (see animation here).
The range of non-equilibrium regions where Peltier cooling and heating occurs are identified as shown in the following picture.
Non-linear Peltier effect in single barrier heterostructures:Also, the effect of large applied electric fields, leading to electron heating was calculated analytically using a shifted Fermi-Dirac distribution function with appropriate electronic temperature. In low doped regions (non-degenerate limit), due to small electronic heat capacity, electron heating occurs for relatively small fields, and the electronic temperature is given by the following formula:
Heating will also occur if the electron-phonon coupling is weak. In this case the width of the non-equilibrium regions (also shown in the above figure at the contact-barrier interface) will become larger. Due to this heating, the Peltier coefficient as the ratio of the heat to particle current will become non-linear in the current[3].
M. Zebarjadi, A. Shakouri, K. Esfarjani; Phys. Rev. B, 74, 195331 (2006).
[2] “An improved Monte Carlo algorithm for treating non uniform and degenerate semiconductors” M. Zebarjadi, C. Bulutay, K. Esfarjani and A. Shakouri; Appl. Phys. Lett. 90, 092111 (2007).
[3] “Nonlinear Peltier and Seebeck coefficients in doped semiconductors” |
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A thermoelectric cooler (on the left) works under an applied current which flows in an n-doped semiconductor put in series with a p-doped one as shown in the figure on the left. Under such current flow, both electrons and holes flow from top to bottom thus carrying heat from the top side tand making it cooler than the bottom side |
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A power generator follows the same geometry: two semiconductor legs, one n-doped and the other p-doped, as shown in the figure on the right. Due to the large temperature gradient between the top and bottom heat exchangers, both charge carriers diffuse (flow) from the hot side to the cold one, thereby generating a potential difference between the top of the two legs. If the circuit is closed, the created voltage will dissipate in the load. |