# Nonlinear Thermoelectrics

**Nonlinear Thermoelectrics**

Thermoelectric coefficients such as the Seebeck coefficient, determine how good a material is for the solid state refrigeration and power generation. In the linear transport theory the Peltier coefficient is equal to the Seebeck coefficient multiply by the temperature and both of these parameters are independent of the applied field and the applied temperature gradient. However, if the fields are high enough these relations do not hold.

Using the Monte Carlo technique, we simulated the thermoelectric transport in InGaAs under applied biases and temperature gradients. Results show that the Peltier coefficient becomes nonlinear at experimentally achievable currents on the order of 105Acm-2. The nonlinear Seebeck, however, is only important when high temperature gradients on the order of degrees over nanometer length are applied.

At low temperatures the Peltier coefficient of degenerate semiconductors and metals goes to zero. However, the nonlinear Peltier is not a strong function of temperature. Since the nonlinear heat current depends on the third power of current, there are regimes in which the non-linear Peltier can overcome the joule heating. We showed that at T=77K the cooling power of a single barrier InGaAs microcooler can be enhanced by a factor of seven compared to that predicted by the linear thermoelectric transport.

Figure-Calculation of cooling versus applied current for InGaAs at T=300K and T=77K based on linear and nonlinear thermoelectric effects. For each temperature the results are reported for the corresponding optimum dopings of the linear transport theory, which are 1018cm-3 and 5«1015cm-3 for T=300K and T=77K respectively.