Direct visualization of polaron formation in the thermoelectric SnSe

SnSe is a layered material that currently holds the record for bulk thermoelectric efficiency. The primary determinant of this high efficiency is thought to be the anomalously low thermal conductivity resulting from strong anharmonic coupling within the phonon system. Here we show that the nature of the carrier system in SnSe is also determined by strong coupling to phonons by directly visualizing polaron formation in the material. We employ ultrafast electron diffraction and diffuse scattering to track the response of phonons in both momentum and time to the photodoping of free carriers across the bandgap, observing the bimodal and anisotropic lattice distortions that drive carrier localization. Relatively large (18.7 Å), quasi-one-dimensional (1D) polarons are formed on the 300-fs timescale with smaller (4.2 Å) 3D polarons taking an order of magnitude longer (4 ps) to form. This difference appears to be a consequence of the profoundly anisotropic electron–phonon coupling in SnSe, with strong Fröhlich coupling only to zone-center polar optical phonons. These results demonstrate a high density of polarons in SnSe at optimal doping levels. Strong electron-phonon coupling is critical to the thermoelectric performance of this benchmark material and, potentially, high performance thermoelectrics more generally.

Thermoelectric materials convert a difference in temperature into an electrical potential (i.e., the thermoelectric effect) and promise to become increasingly important components of energy-harvesting devices and technologies (1–3). This could make a significant contribution to sustainability efforts by enabling electrical power generation from otherwise wasted heat. Unfortunately, the combination of thermal and electrical properties that leads to high thermoelectric performance is not found in naturally occurring materials (4); efficient thermoelectrics must be engineered. The figure of merit for thermoelectric efficiency is ZT=(S2σ/κ)T, where T is the absolute temperature, S is the Seebeck coefficient (induced voltage per temperature gradient), σ is the electrical conductivity, and κ is the thermal conductivity. Historically, increasing ZT has consisted in starting with compounds with a high Seebeck coefficient (e.g., selenides), and then selecting for good electrical conductivity and low thermal conductivity. In this sense, the ideal thermoelectric has been referred to as a “phonon glass–electron crystal” (5)—a concept that, interestingly, also seems to apply to lead halide perovskite light-harvesting materials (6). Nanostructuring has also been explored as a way to further reduce the thermal conductivity of thermoelectrics without significantly impacting electrical conductivity (7), but concerns regarding manufacturing and longevity favor the use of bulk materials (8). In practice, attempts to optimize the performance of bulk thermoelectric materials by favorably influencing a single parameter have not been a successful strategy, because the key properties are all interdependent (7). Thus, developing a more sophisticated understanding of the fundamental interdependencies between key material parameters (S, σ, and κ) is widely recognized as critical to the development of high-performance thermoelectrics.Recently, tin selenide (SnSe) has been shown to exhibit remarkable thermoelectric efficiency, while also being non–lead based and composed of earth-abundant elements (9–11). Its high performance owes to three factors: 1) an anomalously low lattice thermal conductivity ¡1 W·m−1 ·K⁻¹ (9) at room temperature that decreases even further at higher temperature, 2) an electrical conductivity that increases notably above 600 K, and 3) a high Seebeck coefficient. These factors combine to yield a profound enhancement in thermoelectric performance in SnSe above 600 K, from ZT≈0.1 to a maximum ZT > 2 at 800 K (9, 10). In the case of undoped SnSe, this enhancement is associated with a second-order Pnma→Cmcm phase transition (Fig. 1 A and B) of a displacive character (15) but, at a microscopic level, is related to changes in the character of the electron–phonon (16) and phonon–phonon (17) interactions that control electrical and thermal transport in the material.Open in a separate windowFig. 1.(A) SnSe has a layered orthorhombic structure in the Pnma phase at room temperature. (B) The Pnma structure is derived from 3D distortion of the higher-symmetry (distorted rock salt) Cmcm phase, which is stable above 750 K. Crystallographic directions are all given with respect to the low-temperature Pnma phase, and structures were rendered using Visualization for Electronic and Structural Analysis (VESTA) (12). (C) Diagram of the electronic structure of Pnma SnSe in the b⋆–c⋆ plane at 300 K. Three distinct valleys are present in both the valence and conduction bands: at Γ, 2/3 Y, and 3/4 Z (13). Photoexcitation at 800 nm (1.55 eV) photodopes electrons and holes into all three valleys. (D) Schematic (single valley) band structure diagram immediately following photoexcitation, which generates delocalized conduction band electrons (equivalent picture for holes not shown). (E) Schematic band structure diagram after carrier localization indicating a polaron peak below the Fermi energy E_F. (F) Configuration coordinate showing the free energy of the system as carriers self-localize via phonon dressing; that is, the generation of a local lattice distortion (14). The phonon wavevector dependence of this dressing process is probed directly through the UEDS experiments reported here.Unlike most previous studies, which have attempted to understand the enhancement of thermoelectric properties in SnSe in terms of lattice anharmonicity and the Pnma→Cmcm phase transition (17–20), in this work, we focus on the momentum dependence of electron–phonon coupling in the Pnma phase specifically (21). We seek to develop a full understanding of the carrier–lattice interactions that may also contribute to thermoelectric performance. To this end, we use ultrafast electron diffraction (UED) and ultrafast electron diffuse scattering (UEDS) (22–26) to directly probe electron–phonon interactions in momentum and time following the photodoping of carriers (Fig. 1C). A feature of these ultrafast measurements is that they freeze out changes in electronic and phonon band structure that result from in-plane thermal expansion (temperature-dependent lattice constants), uncoupling those effects from those due exclusively to the photodoped carriers that are the subject of our investigations. The results presented here clearly reveal profoundly momentum-dependent electron–phonon coupling in SnSe, as is expected from Fröhlich coupling in a polar lattice (16). However, the ultrafast diffuse scattering signals also show clear signatures of the “phonon dressing” (lattice distortion) that drives photocarrier localization and polaron formation (Fig. 1 D–F), even at high levels of photocarrier doping [equivalent to the doping levels previously used to optimize the power factor in SnSe (10)].