Thermoelectric generators (TEG) are cost effective solid-state devices with low thermal efficiencies. The limitations, due to the operational temperature of the thermoelectric materials, suppress the Carnot efficiency increase of the device. Although thermoelectric generators have considerable advantages over the other renewable energy devices, low convergence efficiency of the device retains thermoelectric devices behind its competitors. In order to keep up with the competition, improvement of device efficiency becomes crucial for the practical applications. The design configuration of the device pin legs, lowering the overall thermal conductance, can improve the device efficiency. Therefore, in the present study, the influence of pin leg geometry on thermal performance of the device is formulated thermodynamically. In this case, the exponential area variation of pin legs is considered and dimensionless geometric parameter 'a' is introduced in analysis. The influence of dimensionless geometric parameter on efficiency and power output is demonstrated for different temperature ratios and external load resistance ratios. It is found that increasing dimensionless geometric parameter improves the thermal efficiency of the device; however, the point of maximum efficiency does not coincide with the point of the maximum device output power. (C) 2013 Elsevier Ltd. All rights reserved.