Ab InitioStudy of Hot Carriers in the First Picosecond after Sunlight Absorption in Silicon

Abstract

Hot carrier thermalization is a major source of efficiency loss in solar cells. Because of the subpicosecond time scale and complex physics involved, a microscopic characterization of hot carriers is challenging even for the simplest materials. We develop and apply an ab initio approach based on density functional theory and many-body perturbation theory to investigate hot carriers in semiconductors. Our calculations include electron-electron and electron-phonon interactions, and require no experimental input other than the structure of the material. We apply our approach to study the relaxation time and mean free path of hot carriers in Si, and map the band and k dependence of these quantities. We demonstrate that a hot carrier distribution characteristic of Si under solar illumination thermalizes within 350 fs, in excellent agreement with pump-probe experiments. Our work sheds light on the subpicosecond time scale after sunlight absorption in Si, and constitutes a first step towards ab initio quantification of hot carrier dynamics in materials. DOI: 10.1103/PhysRevLett.112.257402 PACS numbers: 78.56.-a, 71.20.Mq, 78.47.db, 88.40.H-Single-junction solar cells based on crystalline Si are rapidly approaching the Shockley-Queisser efficiency limit [1,2]. While the Carnot efficiency of ∼95% sets the ultimate limit for solar energy conversion at room temperature, practical efficiency limits in ordinary photovoltaic (PV) solar cells are significantly lower; e.g., the ShockleyQueisser limit for Si is close to 30% [2]. The main factors limiting efficiency are carrier thermalization and absorption losses [3,4]. For the case of Si under AM1.5 solar illumination [5], nearly 25% of incident solar energy is lost to heat as the nonequilibrium ("hot") carriers generated by sunlight absorption thermalize to the edges of the band gap. Not only is hot carrier thermalization the main source of loss in most PV materials, it is also difficult to prevent, control, and understand with microscopic detail due to the subpicosecond time scale typical of hot carrier relaxation [6]. This scenario is common to other technologies employing hot carriers, including electronics, optoelectronics, and renewable energy devices beyond PV [7][8][9][10][11].The leading mechanisms involved in hot carrier thermalization consist of inelastic electron-phonon (e-ph) and electron-electron (e-e) scattering processes [12]. Relaxation times for e-ph and e-e interactions in semiconductors have been studied extensively by model Hamiltonians with selected phonon modes, simplified electronic band structures, deformation potentials, and/or empirical pseudopotentials [13][14][15][16][17][18]. Hot carrier dynamics in semiconductors has been investigated experimentally using pump-probe optical measurements [19,20].This work has two main goals. First, we present an ab initio approach based on density functional theory (DFT) and many-body perturbation theory to investigate hot carriers in materials. Second, we apply this framework to study hot carrier thermalization a...

First-principles calculations of thermal, electrical, and thermoelectric transport properties of semiconductors

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