🔬 materials science

Extrinsic Bulk Photovoltaic Effect from Asymmetric Defect Scattering

This paper presents an *ab initio* Boltzmann framework demonstrating that asymmetric electron-defect scattering in monolayer GeS generates a tunable extrinsic bulk photovoltaic effect, which can exceed intrinsic shift currents by over an order of magnitude and peaks at specific defect fractions that shift with temperature.

Original authors: Zixun Wang, Andrew M. Rappe

Published 2026-10-20

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Zixun Wang, Andrew M. Rappe

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of solid materials, light does more than just illuminate; it can push electricity. In certain crystals that lack a center of symmetry, shining a beam of light can generate a direct electric current without the need for a battery or a junction between two different materials. This phenomenon, known as the bulk photovoltaic effect, has long been understood as a property of the material itself. Scientists have spent decades mapping out how the internal structure of a crystal, specifically the way its electrons shift when hit by a photon, creates this current. These intrinsic mechanisms are like the engine of a car: they are built into the design and work as long as the engine is running. However, real-world materials are never perfect. They contain imperfections, or defects, where atoms are missing or swapped for others. For a long time, these defects were viewed merely as obstacles that slowed down the flow of electricity, acting like potholes on a highway. The prevailing assumption was that while defects might change the details of how current flows, they were not the primary source of the current itself.

A team of researchers at the University of Pennsylvania has now challenged this view, revealing that these very imperfections can make an important contribution to the total photocurrent through a process called asymmetric scattering. Imagine a crowd of people walking through a hallway; if the walls are perfectly smooth, they walk straight. But if the walls have irregular bumps, the people might bounce off them in a way that pushes the whole crowd in one specific direction. In this material, when light excites electrons, they collide with defects. Because the material lacks a center of symmetry, these collisions are not random; they favor one direction over the other. This "skew scattering" creates a net flow of charge that, under specific conditions, can be far stronger than the current generated by the perfect crystal structure alone.

The researchers found that the relationship between defects and electricity is not a simple story of "more is better" or "less is better." Instead, there is a delicate balance. If a material has too few defects, there are not enough collisions to push the electrons in a specific direction. If it has too many, the electrons get scattered so frequently that they lose their momentum and the current dies down. The study showed that there is a specific, optimal amount of defects where the current peaks. For the material they studied, this sweet spot occurs when roughly one in every thousand sulfur atoms is missing or replaced. At this precise concentration, the defects act as a highly efficient pump for electricity.

What makes this discovery particularly striking is the role of temperature. The researchers simulated what happens when the material is cooled down to absolute zero. In this frozen state, the thermal vibrations of the atoms, which usually interfere with electron movement, disappear. The model predicted that under these conditions, at a fixed defect fraction in the dilute regime, the photocurrent generated by the defects could become more than a million times stronger than it is at room temperature. At selected low-temperature defect fractions, the current produced by these imperfections can exceed the current from the perfect crystal structure by more than an order of magnitude. This suggests that the amount of defects in a material is not just a flaw to be minimized, but a tunable parameter that can be adjusted to maximize energy harvesting.

The team tested two different types of defects: a missing sulfur atom and a sulfur atom replaced by a selenium atom. Both types produced this dramatic effect, but they behaved differently. The missing atom created a strong peak in current at a very low defect concentration, while the swapped atom required a higher concentration to reach its peak. Interestingly, for the swapped atoms, the direction of the current actually flipped depending on the concentration, a nuance that only a detailed simulation could reveal. This flipping behavior indicates that the microscopic details of how electrons bounce off different types of defects are complex and unique to each imperfection.

This work does not just explain a theoretical curiosity; it offers a new way to think about designing solar cells and light sensors. Traditionally, engineers strive to make materials as pure as possible to avoid defects. This research suggests that for certain applications, introducing a controlled, specific amount of defects could be the key to unlocking much higher efficiency. The study confirms that by carefully managing the density of imperfections and the temperature of the environment, it is possible to harness the bulk photovoltaic effect to levels that were previously thought impossible. The findings provide a clear roadmap for future experiments, showing that the path to better energy conversion might lie not in perfection, but in the strategic use of imperfection.

Technical Summary: Extrinsic Bulk Photovoltaic Effect from Asymmetric Defect Scattering

Problem Statement
In noncentrosymmetric, single-phase materials, the bulk photovoltaic effect (BPVE) generates direct photocurrents without junctions. While first-principles calculations have extensively characterized intrinsic mechanisms—such as shift currents, injection currents, and ballistic currents—extrinsic mechanisms have remained largely unquantified in real materials. Specifically, asymmetric defect scattering (skew scattering), identified in early kinetic theories and suggested by experiments to reshape carrier distributions, has not been evaluated quantitatively from first principles. Consequently, the magnitude and controllability of extrinsic photocurrents generated by defect asymmetry are unknown.

Methodology
The authors develop a first-principles framework combining the Boltzmann transport equation (BTE) with ab initio inputs to compute extrinsic BPVE currents. The methodology integrates:

Optical Excitation: Ab initio optical generation rates ( $G_{nk}$ ) derived from interband momentum matrix elements.
Scattering Mechanisms: A linear collision operator ( $L$ ) comprising inelastic electron-phonon scattering ( $L_{ph}$ ), elastic symmetric defect scattering ( $L_{sym}$ ), and elastic skew (asymmetric) defect scattering ( $L_{skew}$ ).
Defect Modeling: The skew scattering rate is derived from the antisymmetric component of the electron-defect transition matrix. The single-defect transition matrix is expanded through second order in the defect perturbation potential ( $V_d$ ) via the T-matrix expansion. This expansion yields a skew scattering rate that is cubic in the defect potential and linear in the defect fraction ( $n_{imp}$ ).
Numerical Implementation: The framework is applied to monolayer GeS (a noncentrosymmetric material) using Density Functional Theory (DFT) and Density Functional Perturbation Theory (DFPT). Calculations utilize the Quantum ESPRESSO package and the Perturbo software for electron-defect interactions. The steady-state distribution is solved via fixed-point iteration on a $100 \times 100 \times 1$ k-mesh, separating the growing carrier population from the steady-state current-carrying component.
Analytical Modeling: A minimal angular-harmonic model is derived to interpret the competition between skew conversion and defect-induced relaxation, predicting scaling laws for photocurrent versus defect fraction.

Key Contributions

Quantitative Framework: The paper presents the first ab initio evaluation of extrinsic BPVE currents driven by asymmetric defect scattering in a real material system, moving beyond the relaxation-time approximation.
Analytical Insight: The authors derive a minimal model revealing that the extrinsic photocurrent exhibits a non-monotonic dependence on defect fraction. The current arises from the conversion of current-free optical alignment (even harmonics) into current-carrying components (odd harmonics) via skew scattering. However, defects also act as relaxation centers that suppress these components.
Optimal Defect Fraction: The competition between skew conversion (which scales with $n_{imp}$ ) and defect-induced relaxation (which scales with $n_{imp}$ ) leads to a unique optimal defect fraction ( $n_{opt}$ ) where the photocurrent peaks.
Temperature Dependence: The framework explicitly models temperature effects, showing that cooling shifts the optimal defect fraction to lower values and significantly enhances the current magnitude in the phonon-dominated regime.

Results
Applied to monolayer GeS with sulfur vacancies ( $V_S$ ) and isovalent selenium substitutions ( $Se_S$ ), the study finds:

Scaling Behavior: At $T=300$ K, the extrinsic conductivity initially scales linearly with defect fraction ( $J \propto n_{imp}$ ) in the dilute, phonon-dominated regime. As defect scattering dominates, the current scales inversely ( $J \propto n_{imp}^{-1}$ ), creating a self-limiting response with a distinct peak.
Peak Positions: For $V_S$ , the peak occurs at $n_{imp} \sim 10^{-3}$ for electrons and $n_{imp} \sim 10^{-4}$ for holes. For the weaker scatterer $Se_S$ , the peak shifts to higher defect fractions, remaining largely linear within the computed range.
Cooling Enhancement: Cooling to 0 K suppresses phonon scattering rates ( $\Gamma_m$ ), shifting the crossover to lower defect fractions. At fixed low defect fractions, the enhancement factor $|J(0\text{ K})|/|J(300\text{ K})|$ exceeds six orders of magnitude.
Magnitude Relative to Intrinsic Current: In the cold, dilute regime, the total extrinsic current can exceed the intrinsic shift current by more than an order of magnitude (factors of 7–77 depending on the defect type and fraction).
Defect Specificity: Different defect types exhibit distinct behaviors, including sign reversals in the hole channel for $Se_S$ , suggesting that photocurrent measurements could serve as a diagnostic tool for identifying defect types.

Significance
The paper establishes that extrinsic mechanisms driven by asymmetric defect scattering are not merely perturbative corrections but can dominate the total photocurrent in noncentrosymmetric materials under specific conditions. The findings demonstrate that the defect fraction itself acts as a tunable parameter for optimizing BPVE performance. By identifying a finite optimal defect fraction and showing that cooling can enhance extrinsic currents by orders of magnitude, the work provides a theoretical basis for engineering defect populations to maximize photocurrent generation, potentially surpassing intrinsic limits in materials like monolayer GeS. The study highlights the necessity of including skew scattering in first-principles transport calculations to accurately predict and interpret bulk photovoltaic responses.

More like this