Theory of thermoelectric cooling in semiconductor structures
Yu. G. Gurevich and G.N. Logvinov
Departamento de Física, CINVESTAV del I.P.N., Apartado Postal 14-740, 07000, D.F., México, México. SEPI-ESIME Culhuacán, Instituto Politécnico Nacional, Av. Santa Ana 1000, Col. San Francisco Culhuacán, 04430, D.F., México, México.
Recibido el 22 de noviembre de 2006
Aceptado el 10 de agosto de 2007
Abstract
A new approach is suggested to explain the Peltier effect. This approach is based on the idea of the occurrence of induced thermal diffusion fluxes in any non-uniform medium through which a d.c. electric current flows, in particular in a structure composed of two different uniform semiconductors. These induced thermal diffusion fluxes arise to compensate for the change in thermal fluxes carried out by an electric current (drift thermal fluxes) during their driving through the junction in accordance with the general Le Châtelier-Braun principle. The occurrence of these thermal diffusion fluxes leads to temperature non-uniformity in the structure and, as a result, to the junction's cooling or heating. The general heat balance equations are obtained. It is shown that only two sources of heat exist: the Joule source of heat, and the Thomson source of heat. They have commensurable magnitudes in the problem considered. There is no Peltier's source of heating or cooling present. The new equation for the Thomson heat is obtained and its physical interpretation is made. New boundary conditions for the heat balance equation are derived. The analysis of these boundary conditions shows that the Peltier sources of heat are also absent at the junctions. It is shown that, in the general case, the thermoelectric cooling represents the superposition of two effects, the isothermal Peltier effect and the adiabatic Peltier effect. Both essentially depend on the junction surface thermal conductivity. The isothermal Peltier effect disappears in the limiting case of a very small surface thermal conductivity while the adiabatic Peltier effect disappears in the limiting case of a very large surface thermal conductivity. The dependence of thermoelectric cooling on the geometrical dimensions of the structure is discussed. It is shown that the thermoelectric cooling (heating) is a thermodynamically reversible process in the linear approximation of the electric current applied.
Keywords: Thermoelectricity; thermoelectric cooling; Peltier effect.
Resumen
Un nuevo enfoque es sugerido para explicar el efecto Peltier. Este enfoque está basado en la idea de la aparición de flujos de difusión termicos inducidos en cualquier medio no uniforme a través del cual circula una corriente de d.c., en particular en una estructura compuesta de dos semiconductores uniformemente diferentes. Estos flujos de difusión térmicos inducidos aparecen para compensar el cambio de los flujos termicos llevados por una corriente eléctrica (flujos térmicos de deriva) durante su conducción a través de la unión de acuerdo con el principio general de Le Chatelier-Braun. La aparicion de estos flujos de difusión térmicos resulta en la no uniformidad de temperatura en la estructura y, por consiguiente, el enfriamiento o calentamiento de la unión. La ecuación general de balance de energía es obtenida. Se muestra que solamente existen dos fuentes de calor. Existe la fuente de calor de Joule y la fuente de calor de Thompson. Ambos son proporcionales al valor de sus magnitudes en el problema considerado. Cualquier fuente de calentamiento o enfriamiento de Peltier esta ausente. Es obtenida la nueva ecuacion para el calor de Thompson y es llevada fuera de sus interpretaciones físicas de esta. Las nuevas condiciones de frontera para la ecuación de balance de calor son obtenidas. El análisis de estas condiciones frontera muestra que las fuentes de calor de Peltier están también ausentes en la unión. Es mostrado que, en el caso general, el enfriamiento termoeléctrico representa la superposición de dos efectos, el efecto Peltier isotérmico y el efecto Peltier adiabático. Ambos son esencialmente dependientes de la conductividad térmica superficial de la unión. El efecto Peltier isotérmico desaparece en el limitante caso de una muy pequeña conductividad térmica superficial mientras que el efecto Peltier adiabático desaparece en el limitado caso de una muy grande conductividad térmica superficial. La dependencia del enfriamiento termoeléctrico sobre las dimensiones geométricas de la estructura es discutida. Se muestra que el enfriamiento termoeléctrico (calentamiento) es un proceso termodinámico reversible en aproximación lineal con la corriente eléctrica aplicada.
Descriptores: Termoelectricidad; enfriamiento termoeléctrico; efecto Peltier.
PACS:72.15.Jf; 72.20.Pa
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Acknowledgements
This work is carried out within the frame work of the Projects of Consejo Nacional de Ciencia y Tecnologia (CONACYT, Mexico): 46261-F (Prof. Yu.G. Gurevich) and 49715-F (Prof. G.N. Logvinov).
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