# Thermally induced band gap increase and high thermoelectric figure of merit of n-type PbTe

## TL;DR

This study demonstrates that the increasing band gap of n-type PbTe with temperature significantly enhances its thermoelectric performance, with calculations aligning well with experimental data and identifying optimal band gaps for high efficiency.

## Contribution

The paper provides first-principles calculations of temperature-dependent thermoelectric properties of PbTe, revealing the beneficial effect of band gap increase on thermoelectric figure of merit.

## Key findings

- Band gap of PbTe increases with temperature.
- Calculated thermoelectric properties match experimental data.
- Optimal band gap values maximize thermoelectric efficiency.

## Abstract

Unlike in many other semiconductors, the band gap of PbTe increases considerably with temperature. We compute the thermoelectric transport properties of n-type PbTe from first principles including the temperature variation of the electronic band structure. The calculated temperature dependence of the thermoelectric quantities of PbTe is in good agreement with previous experiments when the temperature changes of the band structure are accounted for. We also calculate the optimum band gap values which would maximize the thermoelectric figure of merit of n-type PbTe at various temperatures. We show that the actual gap values in PbTe closely follow the optimum ones between 300 K and 900 K, resulting in the high figure of merit. Our results indicate that an appreciable increase of the band gap with temperature in direct narrow-gap semiconductors is very beneficial for achieving high thermoelectric performance.