Optimization of thin-film thermoelectric radiation sensor with separate disposition of absorbing layer and comb thermoelectric transducer

Abstract

An analytical optimization of the structure of the thin-film thermoelectric radiation sensor with the separate disposition of the absorbing layer and the comb thermoelectric transducer is presented. A problem of the optimization of this sensor is solved by the method of Lagrange multipliers. The specific total volt–watt sensitivity has been chosen as a goal function and expression of the thermal time constant has been used as a constraint. The length of the absorbing layer of the radiation sensor and the distance between the boundary of this layer and the line of the disposition of cold thermojunctions of the thermoelectric transducer have been chosen as independent variables. The obtained system of equations for components of the gradient of Lagrange function in extremum point is solved by numerical method. Dependencies of optimum values of the specific total volt–watt sensitivity and corresponding values of independent variables on the thermal time constant, the thickness of the substrate layer, the thermal conductivity of the material of the substrate layer and the convection coefficient of the structure have been determined. The present analytical model of the optimization of the thermoelectric radiation sensor can be used in order to obtain the maximum value of the specific total volt–watt sensitivity under the given value of the thermal time constant.