The maximum cooling temperature of a thermoelectric refrigerator made of uniform bulk material is limited by its dimensionless figure-of-merit ZT. Cascaded stages are typically needed in order to obtain a higher cooling temperature. Multiple stage configurations have disadvantages of device complexity, and reduced efficiency due to the non-ideal heat spreading between different stages. In this paper, we prove that the maximum cooling temperature can be increased by using a single stage made of

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... nhomogeneous material. This optimization is different from conventional graded materials where there is a large temperature gradient and local material properties are optimized in order to achieve the highest ZT at the local temperature under operation. The new optimization is attributed to the redistribution of the Joule heating and Peltier cooling profiles along the current and heat flow directions. The cooling efficiency can also be increased by a moderate amount. Numerical simulations are used to optimize the doping profile for a thermoelectric cooler based on single crystal silicon. Maximum Cooling of Thermoelectric Materials It is well known that the maximum cooling temperature of a uniform thermoelectric material is equal to 1/2 ZT 2 , where T is the absolute temperature at the cold side, and Z is the material thermoelectric figure-of-merit. The nondimensional figure-of-merit is defined as Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.