6.5 Pn-Junctions as Thermoelectric Devices

Figure 6.24: Principle configuration of a large area pn-junction thermoelectric generator.

As an alternative to classical thermoelectric devices, a structure incorporating a large area pn-junction [299] is investigated in this section. The principle design of a large area pn-junction thermoelectric generator is shown in Fig. 6.24. Both electrical contacts are at the cooled end of the structure and a temperature gradient is applied along the pn-junction. In contrast to conventional thermoelectric devices, the thermal generation of electron-hole pairs is explicitly used within large area pn-junction generators.

The underlying physical functionality is based on the temperature influence on the device's electrostatics. A temperature gradient within the structure leads to the generation of an electrical current, which is caused by the effect of the temperature on the electrostatic potential of a pn-junction. Basically, the higher temperature $T_1$ leads to a smaller energy step $\Delta E_1$ from the potential of the n- to the p-layer compared to the step $\Delta E_0$ at the lower temperature $T_0$ . By having a temperature gradient in a large area pn-junction, both conditions occur neighboring to each other with the result that carriers at different potentials come into contact and thus experience a driving force to the colder region. The relations are illustrated in Fig. 6.25.

Because both types of carriers, electrons and holes, are moving in the same direction (ambipolar drift and diffusion), away from the pn-junction at the higher temperature $T_1$ , this region becomes depleted and the local thermal equilibrium is disturbed. The generation-recombination balance is shifted to higher generation to compensate the off-drifting carriers.

At the part of the structure with the lower temperature $T_0$ , the opposite effect takes place. The incoming carriers enhance the recombination, which results in a circular electrical current within the large area pn-junction from the hot region with enhanced generation to the cold side with increased recombination. Using selective contacts to both the n- and p-type layers, this circular current can be diverted to an external load and a power source is established, a thermoelectric element.

Figure 6.25: Energy relations in large area pn-junction thermoelectric generators.

The internal functionality of the device can best be illustrated for significant limiting cases. A structure with a length of $20\,\ensuremath{\mathrm{mm}}$ and a total thickness of $2.4\,\ensuremath{\mathrm{mm}}$ is investigated as an example. The p- and n-layer are symmetrically doped with a maximum concentration of $10^{20}\,\ensuremath{\mathrm{cm}}^{-3}$ and separated by a $0.4\,\ensuremath{\mathrm{mm}}$ thick intrinsic layer. Electric contacts are applied at the cooled end of the structure.

For an open circuit, no current can flow to the outside. This situation is illustrated in Figures 6.26 and 6.27. Carrier generation takes place at the heated end of the device with peaks at the borders of the intrinsic layers, where carriers are extracted to the conducting layers.

Figure 6.26: Local generation rate at open circuit conditions.

Figure 6.27: Electron current density at open circuit conditions.

Figure 6.28: Local generation rate at short circuit conditions.

Figure 6.29: Electron current density at short circuit conditions.

Figure 6.30: Local generation rate at matched load conditions.

Figure 6.31: Electron current density at matched load conditions.

The generated carriers are accelerated and accumulate to a current starting from the hot thermal contact to the competition region of the device, where the temperature starts to be too low for further carrier generation. Contrary to the heated end, recombination takes place and the current density is reduced again until zero. The total generation of carriers is exactly compensated by recombination throughout the entire structure. The other extreme is represented by a short circuit of the electric contacts as demonstrated in Figures 6.28 and 6.29. Beyond the generation zone, almost the entire current density reaches the electric contacts while recombination is reduced to a minimum. This yields even higher generation rates and the device state adjusts to an accordingly high electric current density.

At matched load conditions, which is shown in Figures 6.30 and 6.31, generation and current density adjust to an equilibrium between the two cases presented above. The existence of recombination indicates that the device is not fully optimized at this stage.

Subsections

• 6.5.1 Temperature Control by Graded Material Alloys
• 6.5.2 Generation Enhancement by Additional Traps
• 6.5.3 Optimization of Device Characteristics

M. Wagner: Simulation of Thermoelectric Devices