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Electric current flowing through a normal metal-insulator-superconductor (NIS) junction accompanied by the heat transfer from normal metal to superconductor is able to cool electrons in the normal metal electrode below the lattice temperature under certain conditions. The tunneling electric current dependence on biasing voltage at different normal metal electrode electron temperatures is calculated. Refrigerators with one and with two NIS junctions are investigated. Further, the cooling power of SNIS and SINIS refrigerators, its dependence on biasing voltage and on the temperature of normal metal electrode electrons are investigated. With reduced insulator layer thickness the resistivity of a NIS junction decreases. Thus, the cooling power of a refrigerator increases. But simultaneously the probability for Andreev reflections which diminish the efficiency of the refrigerator increases. Therefore, the optimal thickness of the insulator layer needs to be found. A method for calculating an optimal insulator layer thickness based on the introduction of a new function that needs to be minimized is described. Geometrical limits on the influence of Andreev reflection are determined.