The three-dimensional numerical analysis has been carried out to figure out the effect of the thermoelectric element thickness on the thermal performance of the thermo-electric micro-cooler. The small-size and column-type thermoelectric cooler is considered. It is known that tellurium compounds currently have the highest cooling performance around the room temperature. Thus, in the present study, $Bi_{2}Te_{3}$ and $Sb_{2}Te_{3}$ are selected as the n- and p-type thermoelectric materials, respectively. The thermoelectric leg considered is less than $20{mu}m$ thick. The thickness of the leg may affect the thermal and electrical transport through the interfaces between the leg and metal conductors. The effect of the thermoelectric element thickness on the thermal performance of the cooler has been investigated with parameters such as the temperature difference, the current, and the cooling power.