Charging capacitors from thermal fluctuations using diodes at different temperatures

We consider the thermal energy harvesting capability of two circuits. The first consists of a diode and capacitor in series. We solve the time-dependent Fokker-Planck equation (FPE) and show the capacitor initially charges but then discharges to zero. The transient peak charge is found to increase with temperature, capacitance, and diode quality. The second circuit has one small capacitor, two storage capacitors, and two diodes wired in opposition. With the diodes at different temperatures a non-zero permanent charge is stored on the capacitors. In addition, we find a current circulates to significantly boost the total stored charge. The maximum charge can be 100 times larger than the single diode system. However, when resistors are used in place of diodes we show that the transient and permanent charge is always zero. Separate solutions to the time-independent FPE quantitatively confirm the enhanced magnitude of the steady state charge.