Anharmonic Phonon Renormalization and Defect Tolerance of the Thermoelectric Power Factor in Monolayer SnSe
Monolayer tin selenide (SnSe) exhibits phase-dependent anharmonic lattice dynamics, yet their consequences for the thermoelectric power factor (PF) and point-defect tolerance remain unresolved. We combine density functional theory, the stochastic self-consistent harmonic approximation (SSCHA), and Boltzmann transport calculations including electron-phonon and electron-defect scattering to investigate monolayer $α$-SnSe (Pnma) and $β$-SnSe (Cmcm). In dynamically stable $α$-SnSe, SSCHA renormalizes the finite-temperature phonons without changing the qualitative n-type transport picture. In $β$-SnSe, SSCHA removes the harmonic soft-mode instability of the Cmcm phase at 800-1000 K, and thereby enables high-temperature transport calculations; LO/TO-2 is the principal electron-scattering channel. In the lower-density window near $10^{12}$ cm$^{-2}$, the n-type PF reaches 15-19 $μ\mathrm{W}/(\mathrm{K}^{2}\cdot\mathrm{cm})$ at 800-900 K and exceeds the p-type PF primarily because of the higher electrical conductivity. Se vacancies ($V_{\mathrm{Se}}$) produce weaker electron-defect scattering than Sn vacancies ($V_{\mathrm{Sn}}$), and p-type transport is less defect tolerant than n-type transport in both phases. We define an operational critical defect concentration, $C_{\mathrm{crit}}$, at which the PF decreases by 15% relative to the corresponding defect-free value. The lowest $C_{\mathrm{crit}}$ is $8.841\times10^{-5}$ (approximately 88 ppm) for p-type $α$-SnSe with $V_{\mathrm{Sn}}$; for n-type $β$-SnSe with $V_{\mathrm{Se}}$, the 15% threshold is not reached up to $5\times10^{-3}$ (5000 ppm). These results distinguish finite-temperature phonon renormalization in stable $α$-SnSe from anharmonic stabilization in $β$-SnSe and provide defect-concentration limits for preserving the PF.