Optimization of doping concentration for three-dimensional bulk silicon microrefrigerators

We designed and fabricated a three-dimensional (3D) silicon microrefrigerator, which demonstrates a cooling power density over 200W/cm with only ~1degC cooling. The high cooling power density is mainly due to the high thermal conductivity and heat spreading effects. These devices have potential application in hot-spots management to reduce the chip peak temperature and realize on chip thermal management. A finite element model is developed to study and optimize these 3D devices. The simulation results showed that the optimized doping concentration to achieve the maximum cooling for these 3D silicon microrefrigerators (5e18 cm^-3) is different from the conventional ID device, where S²sigma achieves the maximum at the doping of 5e19 cm^-3. At its optimized doping concentration, these silicon microrefrigerators could reach a maximum cooling of 3degC. Further studies prove that this deviation is due to the nonidea factors inherent within the device, e.g. semiconductor-metal contact resistance, Joule-heating from probe contact resistance etc. Thus to optimize the real device, it is necessary to chose a full model considering all the nonideal factors