Lock-in thermo-electric detector arrays: thermal cross-talk prediction by non-linear model

A non-linear numerical finite element method model of a thermo-electric focal plane array detector is presented here. Laser induced thermo-voltage profiles tend to spread out for small lock-in frequencies as the thermal diffusion length is inversely proportional to the square-root of the lock-in frequency. This leads to a frequency and spatial dependent thermal cross-talk level. In this paper we investigate the thermal cross-talk level quantitatively as a function of spatial coordinates and lock-in frequency. Experimental data are provided at an optical power level of 1 W. The impact of non-linear thermal parameters as the temperature dependence of the absorption coefficient, the thermal conductivity, the heat transfer coefficient and the Seebeck coefficient on the thermal profile and cross-talk level generated inside the detector material is studied in detail. Heat losses that are included in the model are conduction and laminar free convection. The relative importance of the above-mentioned non-linear thermal parameters in terms of thermal cross-talk for steady-state solutions is discussed as well.