Theoretical Thermal Conductivity of Porous Silicon: Nonlinear Behavior
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J. E. Lugo+ J. A. de Rio and J. Tagiiefia-Martinez. Centro de Investigaci6n en Energia, Universidad Nacional Aut6noma de M6xico, A.P. 34, Temixco, Morelos, M6xico. +Facultad de Ciencias, Universidad Aut6noma del Estado de Morelos, Av. Universidad 1001, 62210, Cuernavaca, Morelos, Mexico. ABSTRACT The use of porous silicon (PS) in fabricating optoelectronic devices is in progress. However, the performance of such applications still needs to be improved. In particular, in solar cells heat must be dissipated to avoid a decay in their efficiency and one of the properties of PS that must be evaluated is the effective thermal conductivity. It is well known that the thermal conductivity of silicon is temperature dependent. Thus we cannot use a standard effective medium approach to obtain its effective thermal response. In this work, we extend the averaging volume and surface methods [1] to consider nonlinear effects in the effective transport coefficients. We model PS as composed of c-Si cylindrical columns covered by different overlayers (i.e. a-Si or Si0 2 ) immersed in another medium. In our model the effective thermal conductivity has an explicit dependence on the temperature gradient. We present a parametric analysis of the model, compare it with the c-Si behavior and evaluate the importance of the nonlinear contribution. INTRODUCTION. Real systems are heterogeneous, polycrystalline, amorphous, multicomponent or porous and the prediction of their properties presents an interesting basic challenge. Nevertheless, these derivations from homogeneity might be useful to produce devices. In particular, a nanocomposite material that has received special attention lately for its potential optoelectronic applications and cheap production process is porous silicon (PS) [2]. However, PS is a very fragile material and there is a search to introduce other material inside the pores to improve its mechanical properties, while maintaining its optical properties [2]. Its thermal properties, in particular the effective thermal conductivity, are also relevant to study heat dissipation. Our previous works [1], [3] seem to indicate that, due to the relation between the characteristic length of the PS structure and the observation length, an effective medium theory is capable of describing the transport phenomena. Thus, in principle, we can obtain the effective thermal conductivity using one of these smoothing theories. However, the non-linear character of the thermal conductivity of c-Si is well known, i.e. its thermal conductivity is temperature dependent. On the other hand, the materials used to give strength to PS are polymers, which also lead to a non-linear thermal conductivity. Clearly, it seems necessary to study the role of the non-linearity of the transport coefficients of the PS main components on the effective thermal conductivity. One of the first assumptions of the effective medium theories is that the transport coefficients are constant. Few attempts exist in the literature to extend this type of calculation. 81 Mat. Res. So
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