Anion vacancies as a source of persistent photoconductivity in II-VI and chalcopyrite semiconductors

Stephan Lany and Alex Zunger

Phys. Rev. B 72, 035215 – Published 18 July 2005

Abstract

Using first-principles electronic structure calculations we identify the anion vacancies in II-VI and chalcopyrite $Cu − III − {VI}_{2}$ semiconductors as a class of intrinsic defects that can exhibit metastable behavior. Specifically, we predict persistent electron photoconductivity ( $n$ -type PPC) caused by the oxygen vacancy $V_{O}$ in $n$ -ZnO, originating from a metastable shallow donor state of $V_{O}$ . In contrast, we predict persistent hole photoconductivity ( $p$ -type PPC) caused by the Se vacancy $V_{Se}$ in $p − {CuInSe}_{2}$ and $p − {CuGaSe}_{2}$ . We find that $V_{Se}$ in the chalcopyrite materials is amphoteric having two “negative- $U$ ”-like transitions, i.e., a double-donor transition $ε (2 + ∕ 0)$ close to the valence band and a double-acceptor transition $ε (0 ∕ 2 -)$ closer to the conduction band. We introduce a classification scheme that distinguishes two types of defects: type $α$ , which have a defect-localized-state (DLS) in the band gap, and type $β$ , which have a resonant DLS within the host bands (e.g., the conduction band for donors). In the latter case, the introduced carriers (e.g., electrons) relax to the band edge where they can occupy a perturbed-host state. Type $α$ is nonconducting, whereas type $β$ is conducting. We identify the neutral anion vacancy as type $α$ and the doubly positively charged vacancy as type $β$ . We suggest that illumination changes the charge state of the anion vacancy and leads to a crossover between $α$ - and $β$ -type behavior, resulting in metastability and PPC. In ${CuInSe}_{2}$ , the metastable behavior of $V_{Se}$ is carried over to the $(V_{Se} − V_{Cu})$ complex, which we identify as the physical origin of PPC observed experimentally. We explain previous puzzling experimental results in ZnO and ${CuInSe}_{2}$ in the light of this model.

Received 13 January 2005

DOI:https://doi.org/10.1103/PhysRevB.72.035215

Authors & Affiliations

Stephan Lany and Alex Zunger

National Renewable Energy Laboratory, Golden, Colorado 80401, USA

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Issue

Vol. 72, Iss. 3 — 15 July 2005

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Images

Figure 1
(Color online) Schematic energy-level diagram of a substitutional impurity in a semiconductor. Bonding and antibonding levels (red solid lines) are formed due to the interaction between the energy level $ε_{vac}^{λ, γ}$ of the pure vacancy and the atomic energy level $ε_{I}^{λ, γ}$ of the impurity atom (black dotted lines), as a function of the perturbation strength $Δ V = ε_{I}^{λ, γ} - ε_{H}^{λ, γ}$ , where $ε_{H}^{λ, γ}$ is the atomic orbital energy of the replaced host atom ( $λ$ denotes the sublattice and $γ$ the symmetry representation). $α$ - and $β$ -type behavior is distinguished by the relative position of the antibonding state and the host CBM (blue solid line): The defect is $α$ -type when the DLS is below the CBM; it is $β$ -type when the DLS is above the CBM, and forms a PHS (blue dashed line) just below the CBM.Reuse & Permissions
Figure 2
Calculated density of states of the host crystals and the angular momentum decomposed local DOS at the neutral $(V_{X}^{0})$ and charged $(V_{X}^{2 +})$ vacancy site for (a) ZnO and (b) ${CuInSe}_{2}$ . The occupied DLS, i.e., the $a_{1}^{2} (V_{O}^{0})$ and the $a^{2} (V_{Se}^{0})$ level, and the unoccupied DLS resonance in the conduction band, i.e., the $a_{1}^{0} (V_{O}^{2 +})$ and the $a^{0} (V_{Se}^{2 +})$ level, are indicated. In ${CuInSe}_{2}$ , the unoccupied $b$ symmetry level of $V_{Se}^{0}$ is also shown.Reuse & Permissions
Figure 3
(Color online) (a) Schematic energy diagram for $V_{O}$ in ZnO, causing $n$ -type PPC. Electrons that occupy the DLS or the PHS are depicted as solid circles. (b) Configuration coordinate diagram, where the calculated defect formation energies $Δ H$ (squares) refer to oxygen-rich conditions $(Δ μ_{O} = 0)$ . Note that the calculated formation energies $Δ H [V_{O}^{0}]$ and $Δ H [V_{O}^{+}]$ are underestimated when $d_{Zn − Zn}$ exceeds 3.2 Å (dotted lines, cf. Ref. 53). In these cases, the solid lines show a qualitative continuation of the $Δ H$ . In the $β$ -type metastable state, two electrons are released to the shallow perturbed host state, leading to $n$ -type PPC.Reuse & Permissions
Figure 4
Formation energies $Δ H$ of the different charge states of $V_{anion}$ in (a) ZnO and (b) ${CuInSe}_{2}$ in the limit of anion-poor conditions $(Δ μ_{O} = - 3.53 eV, Δ μ_{Se} = - 0.83 eV)$ , as a function of the Fermi level $Δ E_{F}$ within the band gap. Solid lines and closed circles show the formation and transition energies of the equilibrium stable states, respectively.[56] Note that the line for $Δ H (V_{Se}^{2 +})$ is vertically displaced by $- 0.2 eV$ for enhanced graphical clarity. Dashed lines and open circles show the formation and transition energies in the light-induced metastable configuration. $α$ - and $β$ -type behavior of the respective states is indicated.Reuse & Permissions
Figure 5
(Color online) Single-particle energies of the $a_{1}$ symmetric vacancy defect levels (red) and the thermal $ε (2 + ∕ 0)$ transition energy (blue) for the anion vacancy in II-VI and chalcopyrite semiconductors, relative to the host band edges. The valence-band offsets are taken from Refs. 71, 72; the data shown take into account the correction $Δ E_{V}$ (cf. Sec. 3) for the position of the VBM. (The zero of the energy axis is chosen arbitrarily.)Reuse & Permissions
Figure 6
(Color online) (a) Schematic energy diagram for $V_{Se}$ in ${CuInSe}_{2}$ , causing $p$ -type PPC. (b) Configuration coordinate diagram, where the calculated defect formation energies $Δ H$ (squares) refer to Se-rich conditions $(Δ μ_{Se} = 0)$ and to $Δ E_{F} = 0$ (the relative energies of the branches do not depend on $Δ E_{F}$ ). Note that the LDA calculated formation energies for $V_{Se}^{0}$ and $V_{Se}^{+}$ are underestimated when $d_{In − In}$ exceeds 3.9 Å (dotted lines, cf. Ref. 53). In these cases, the solid lines show a qualitative continuation of the $Δ H$ . In the metastable $α$ -type state, two free holes are released to the valence band, leading to $p$ -type PPC.Reuse & Permissions

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