II. Metastability of anion vacancies in II-VI and chalcopyrite semiconductors
III. Doping of chalcopyrite photovoltaic semiconductors
Established in 1978, the Solid State Theory for PV group has continuously accompanied a wide range of experimental PV research efforts at NREL by providing scientific underpinning modeling and predictions pertaining to PV materials and phenomena. The use of state-of-the-art computational quantum theory has come of age in the late seventies and early eighties when a combination of advanced mathematical algorithms with powerful computers transformed the previous, highly-simplified text book quantum models into quantitative and predictive tools of material science, now able to tackle problems of real complexity. We are leaders in this historic endeavor. The special feature of Solid-State-Theory-for-PV is that whereas experiment is the ultimate test of truth, it is also complex; Theory is able to separate the effects of the many, otherwise convoluted variables that control the ultimate solar cell performance, thus enabling better control as well as design of systematic improvements. The SST-PV group at NREL is unique in that: (i) it has consistently provided (through 130 journal publications and continued appearances at important PV meetings) research on SST both to NREL researchers and to contractors and collaborators, nationally and internationally; (ii) it continues to enjoy a special relationship with the Office of Science (SC), whereby SC provided, in the past 16 years funding and computer access for our Method-Development efforts. These methods have been applied by us to numerous PV problems; (iii) being co-located within a PV Lab, we formed unique synergism with the technical PV community; (iv) we have been the only group to train PV specialists in theory, as can be judged from the List of PV Publications. Some of the names include H.K. Yoshida; D. Wood; S. Froyen; J. Bernard; S.H. Wei; S.B. Zhang; J. Jaffe and twelve others.
Over the years, our effort involved theoretical modeling of the following categories: Click here to get the titles of our PV publications, sorted into categories (a) Silicon: 3d impurities [5-15]; converting Si to direct gap materials [16-23]; main-group defects in Si [24-26]. (b) III-V's: impurity effects [27-29], surface states [30-31], band offsets [32-35], Schottky barriers [36-39], alloy bowing [40-44], phase-diagrams [45-51], alloys with Si, Ge [52-53], PV-funded Spontaneous ordering [54-70], epitaxial effects [71-78]; (c) II-VI's and thin-film chalcopyrites (CH): Band structures and alloy bowing [79-87], XPS [88-93], CH alloys with II-VI [94], CH band offsets [95-97], CH alloy bowing [98], defects in CH [99-107], the effects of Ga-addition and Na [108-109], Doping CH [110-117], grain-boundaries in CH [118-121], TCO's [122]; (d) Predicting new PV materials [124-131].
II. Metastability of anion vacancies in II-VI and chalcopyrite semiconductors
Solar cells based on Cu(In,Ga)Se2 (CIGS) frequently show metastability effects, i.e. a persistent change in the junction capacitance and in solar cell performance parameters like the open-circuit voltage. Such metastability occurs either upon illumination with photon energies equal or higher than the absorber band-gap, or, in a similar but distinct way, after application of a voltage bias. Experimentally, this phenomenon is well characterized, but its origin remains unclear. It was speculated that the light-induced effect arises from defects that change the charge state in a metastable manner, but that bias-induced metastability involves migration of Cu vacancy defects. Under certain conditions, the open-circuit voltage and the solar cell efficiency can even improve upon light-soaking procedures, but, it is not generally clear whether the defects responsible for metastability cause harm or good to the solar cell performance.
Using first-principles electronic structure calculations, we investigated metastability caused by anion vacancies in II-VI and chalcopyrite semiconductors [1,2,7]. Anion vacancies in these materials show intriguing properties such as unexpected symmetry breaking in zincblende II-VIs [7], persistent electron photoconductivity in ZnO, and persistent hole photoconductivity in chalcopyrites [2]. In a more detailed study [1] for the photovolatic chalcopyrites CuInSe2 (CIS) and CuGaSe2 (CGS), we found that the formation of (VSe-VCu) vacancy complexes is thermodynamically favorable at room temperature, and that this complex can exists in two charge states q = +1 and q = -1, resulting in a donor and an acceptor configuration, respectively. The change between both configurations is associated with the formation (q = -1) and breakup (q = +1) of a metal-metal bond between the group III atoms next to the Se vacancy [7]. The dynamics of the charge state change is desribed by the calculated configuration coordinate diagram shown in Fig. I.1 below for CIS where the In-In distance serves as the reaction coordinate. Metastability arises from the presence of energy barriers separating the two configurations with small and large interatomic In-In distance.
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| Fig. I.1: Calculated configuration coordinate diagram for the (VSe-VCu) vacancy complex in CIS. The q = +1 donor configuration is equilibrium stable in p-type CIS (large dIn-In, state 1). Photoexciation (transition 1 → 2) produces free electrons that can be captured by the complex with an activation barrier DE1=0.1eV into a localized state. Atomic relaxation (transition 2 → 3) leads then to the configuration with small dIn-In. In this configuration, the complex acts as an acceptor with binding energy Ea=0.27eV. Ionization of the acceptor corresponds to the transition (3 → 4). Activated with DE2=0.35eV, the complex returns into the initial state by hole capture (transition 3 → 1). |
Both the presence of light-induced carriers, and the change of Quasi-Fermi levels that occurs when a voltage bias is applied, can trigger a switching between the two charge states explaining the experimental observation of persistent changes in the capacitance of the solar cell junction and in the charged defect distribution [1]. Further support for the correct identification of the proposed vacancy complex as the source of metastability is provided by the calculated acceptor level at 0.27eV above the valence band edge which also observed experimentally. Thus, the (VSe-VCu) vacancy complex is identified as the source of both light- and bias-induced metastability, and there is no need to invoke migration of defects to explain the bias-induced effect.
Based on the calculated optical transition energies, we predict that the vacancy complex will produce a recombination center in the light-induced metastable configuration, highlighting its detrimental potential for solar cells. It is concluded that the sometimes observed small beneficial effects of light-soaking relies only on a feeble balance between the detrimental effect of recombination centers and the beneficial effect of increased space charge density which occurs when the complexes change persistently their charge state upon illumination. It is suggested that metastability in a CIGS solar cell indicates a less-than-ideal state, and that efforts should be undertaken to produce solar cells not showing metastability.
The large variation of the III-III, e.g. In-In, interatomic distance with charge state results from the population (In-In bond formation) and depopulation (In-In bond breakup) of the Se-vacancy defect level, shown in Fig. I.2 (left) as wavefunction-square plot. This defect state is formed as a bonding-combination of the VSe dangling bonds and lies more than 2eV below the valence band maximum. The antibonding-combination of the VSe dangling bonds forms an empty gap level (Fig. I.2, right) that is responsible for the above mentioned recombination center.
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| Fig. I.2: The isolated Se vacancy in CuInSe2. Cu (cyan), In (green), Se (yellow), the vacancy site is marked white. The defect states of VSe are shown as isosurface plots of the wavefunction-square. The dangling bonds form a deep bonding state below the VBM (left) and a antibonding state inside the band gap (right). |
III. Doping of chalcopyrite photovoltaic semiconductors
Efficient solar cells require the formation of a well-defined p-n junction, which can only be obtained by the controlled formation of acceptor- and donor-like defects, i.e. by p- and n-type doping. Unlike conventional semiconductors which generally require extrinsic doping, i.e. the incorporation of foreign atoms, photovoltaic chalcopyrite materials like CuInSe2 (CIS), CuGaSe2 (CGS), and their alloys CuIn1-xGaxSe2 (CIGS) attain conductivity by deviation from perfect stoichiometry during crystal growth, i.e. by means of intrinsic defects. Thus, CIS can be grown both p- and n-type, while CGS is always obtained p-type. The ability of these chalcopyrite semiconductors to attain conductivity without extrinsic dopants raises two questions which are experimentally not settled so far: (i) What are the growth conditions that optimize the conductivity of a desired type? (ii) Can extrinsic doping improve over the native electrical properties that are dominated by intrinsic defects? These questions acquire particular significance with regard to the experimental difficulty to obtain n-type CIGS when the Ga content exceeds x = 0.3.
In order to address these questions we calculated recently [3-6] the defect concentrations and Fermi level in equilibrium under different growth conditions. This required knowledge of the defect and compound formation energies of all important defects (intrinsic and extrinsic) and competing compounds, which we obtained from first-principles total-energy calculations [3]. Taking into account all boundary conditions for chemical potentials, we compare for Cl-doping [6] the growth conditions that maximize the incorporation of extrinsic ClSe donors with those that maximize the incorporation of intrinsic InCu double donors.
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| Fig. II.1: Defect formation energies as a function of the Fermi level EF for (a) "ClSe favored growth" and (b) "InCu favored growth" of CIS. The vertical arrow marks the equilibrium EF, calculated self-consistently for T = 800K. |
Figure II.1 shows for both scenarios in CIS the formation energies DH of the relevant defects, as a function of Fermi level. Shown is also the position of the equilibrium Fermi level for a growth temperature T = 800K, obtained by a separate thermodynamic calculation. Notably the InCu favored growth yields a higher equilibrium EF, and, hence, better n-type conditions. ClSe favored growth yields overall p-type conditions, resulting from an equilibrium EF in the lower part of the band gap (Fig. II.1, left) and overcompensation of ClSe by intrinsic VCu acceptors. The equilibrium defect concentrations and the net donor/acceptor concentration Dc are shown in Fig. II.2. Thus, we identified maximally Se-poor and Cu-, In-rich growth ("InCu favored growth") as being the optimal condition for obtaining n-type conductivity by intrinsic, halogen-, and Cd-doping. Our results explain why in recent experiments in CIS the electron concentration after Cl-doping did not exceed levels that are frequently obtained without extrinsic dopants. For Cd-doping in CIS, we found [3,4,5] that somewhat higher donor levels can be obtained, but our study indicates that the use of extrinsic donor dopants is rather limited, as any attempt to raise the electron concentration will be counterweighted by an increased compensation ratio. The problem of n-type doping in the larger-gap CGS was traced back to the exceedingly low formation energy of compensating acceptor-like Cu vacancies VCu which form spontaneously even under Cu-rich growth when the Fermi level raises in the band gap. Thus, a Fermi level near the conduction band minimum, which is required for successful n-type doping, can not be obtained in CGS under equilibrium conditions. Therefore, we suggest that n-type CGS may only be obtained under non-equilibrium conditions where the formation of Cu vacancies is kinetically inhibited.
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| Fig. II.2: Calculated defect concentrations in cm-3 for Tgrowth = 800K under (a) "Halogen favored growth" and (b) "InCu favored growth" of CIS. Dc denotes the net donor/acceptor concentration. |
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