Higher mobility in bulk semiconductors by separating the dopants from the charge-conducting band – a case study of thermoelectric PbSe

Abstract

In the rigid band approximation dopants in semiconductors only change the Fermi level and carrier concentration such that different dopants are thought equivalent when fully ionized. In this work we examine the small but significant difference in mobility due to the type of dopant in heavily doped PbSe by studying n-type samples doped with Br, In and Bi. We propose that cation and anion dopants lead to a difference in mobility at high concentrations. This can be understood considering the predominance of cation states to the conduction band and anion states to the valence band. For higher mobility and better performance for most applications of heavily doped semiconductors, dopants should be on the site that is of less influence on the chargeconducting band. This concept can be viewed as an analog of modulation doping on the atomic level. Its physical origin is the random potential due to disorder that perturbs carriers, which is also the origin of Anderson localization at low temperature, a well-studied topic in theoretical physics. In thermoelectric PbSe, the selection of dopant can lead to 10% difference in mobility and in zT.

Compromise and Synergy in High‐Efficiency Thermoelectric Materials

“…Therefore, unequivocal experimental evidence for the benefits of modulation doping in high‐temperature TE materials is still in the process of being researched. For a single‐phase material, Snyder et al proposed that the choice of dopant would make a difference in the carrier mobility of heavily doped semiconductors. In order to gain a high mobility, the acceptor dopants, which produce holes in the valence band, would best be placed on the cation site and primarily disrupt the conduction band rather than the valence band.…”

“…In order to gain a high mobility, the acceptor dopants, which produce holes in the valence band, would best be placed on the cation site and primarily disrupt the conduction band rather than the valence band. Similarly, donor dopants are best placed on the anion site, as the conduction bands are less disturbed and the resultant n‐type material is likely to have higher mobility …”

High Thermoelectric Performance in PbSe–NaSbSe2 Alloys from Valence Band Convergence and Low Thermal Conductivity

“…To do this, we must assume that the position of the Σ-band does not change appreciably with NaSbSe 2 alloying. [40,52] The energy differences between L-and Σ-valence bands estimated from the work functions of each compound are presented in Figure 7c and show that the ΔE L−Σ decreases with NaSbSe 2 fraction down to ≈0.16 eV for 9% NaSbSe 2 . [40,52] The energy differences between L-and Σ-valence bands estimated from the work functions of each compound are presented in Figure 7c and show that the ΔE L−Σ decreases with NaSbSe 2 fraction down to ≈0.16 eV for 9% NaSbSe 2 .…”

Calculation of dopant solubilities and phase diagrams of X–Pb–Se (X = Br, Na) limited to defects with localized charge

“…However, it is well-known that Na is a p-type dopant in PbQ systems 5,6,8,9,14,30,31 with Na substitution on the Pb +2 sublattice producing one conducting hole for each substitution. Thus, the Na…”

“…PbSe is chosen because the lead chalcogenides (PbQ, Q = Te, Se, S) with the rock-salt structure are excellent thermoelectric materials [5][6][7][8][9][10][11][12][13] for applications between 600 K and 900 K, 14 where its zT exceeds 1 13 for both p-type 6 and n-type 8 materials. Br is chosen due to its comparable size and electronic structure to Se, and reported zT = 1.1 AE 0.1 at 850 K. 8 Similarly, Na provides fine control over hole carrier concentration 5,15 that leads to zT close to 1 at 850 K in PbSe.…”