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

Abstract

Abstract.A non-linear numerical finite element method (FEM) model of a thermo-electric focal plane array (FPA) 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 in function of spatial coordinates and lock-in frequency. Experimental data are provided at an optical power level of 1W. 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 are 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 are discussed as well.Keywords: Thermo-electric detector, FEM model, non-linear thermal modeling IntroductionLock-in thermography greatly improves the sensitivity and the image resolution as compared to steady-state thermography [1]. The latter one suffers from high lateral heat spreading which results in a poor resolution. In our study, a similar lock-in technique is applied on Seebeck focal plane array's (FPA's) to improve the resolution (pixel density) and/or thermal cross-talk performance. In contrast to lock-in thermography, the thermal profile is probed by the Seebeck effect, by means of electrodes, instead of a contactless IR camera measurement. Lock-in thermo-electric FPA detectors can be used for laser beam profilometry [2]. Partial absorption of high power laser beams can result in a temperature distribution with local surface temperature maxima which exceeds 100 K above room temperature. In this temperature range, some non-linear thermal parameters (e.g. the thermal conductivity of GaAs) will change significantly with respect to its constant property-value. Hence, most relevant non-linear thermal parameters should be taken into account for accurate modeling. This paper is concerned with thermal cross-talk reduction in function of spatial coordinates and lock-in frequency. The impact of the temperature dependence of the absorption coefficient, the thermal conductivity, the heat transfer coefficient and the Seebeck coefficient, further referenced as non-linear thermal parameters, on the thermal cross-talk level in function of the applied lock-in frequency are investigated.