Antibonding coupling for defect-tolerant GeSe

GeSe crystallizes in an orthorhombic layered structure with the Pnma 62 space group (Fig. 1a). Both Ge and Se atoms are three fold coordinated with each other. There is only one type of Ge and Se: GeSe is a binary chalcogenide both chemically and structurally. There are therefore only six possible point defects in GeSe: cation vacancy (V_Ge), anion vacancy (V_Se), cation interstitial (Ge_i), anion interstitial (Se_i), cation-replace-anion antisite (Ge_Se), and anion-replace-cation antisite (Se_Ge). This is simpler than in multicomponent semiconductors such as Cu(In,Ga)Se₂ (CIGS) and Cu₂ZnSn(S,Se)₄ (CZTSSe)^32,33.

We first used density functional theory (DFT) to calculate the bandstructure, density of states (DOS), and partial DOS of GeSe, since the electronic properties of point defects depend sensitively on the structure. The conduction band minimum (CBM) of GeSe is dominated by the Ge 4p orbital, with significant coupling with the Se 4p orbital; and negligible coupling with the Se 4s orbital (Fig. 1b). This indicates the strong covalent character of GeSe, agreeing well with the above electronegativity analysis, and differing from perovskites with their high ionicity. As for the VBM, it is predominantly made up of the Se 4p orbital and the Ge 4p orbital due to p–p coupling, with a substantial contribution from the Ge 4s orbital. This is seen in the bandstructure of GeSe and the partial DOS of the Ge 4s orbital (Fig. 1b).

The reason that the inner-shell Ge 4s orbital is present in the VBM is illustrated through an atomic orbital picture (Fig. 1c): the Ge 4s and 4p orbitals are too far apart in energy to hybridize directly^4,34; and the Se 4p orbital is close to the Ge 4s orbital in energy, allowing these to the couple and giving rise to a filled antibonding orbital at the VBM^3,4. The CBM also has an antibonding character originating from the Ge 4p–Se 4p coupling. In the lone pair model, the asymmetrically layered-crystal structure of GeSe arising from the stereochemically active lone pairs accounts for the contribution of the Ge 4s orbital to the VBM⁴. This differs from other IV–VI materials such as PbS and SnTe, which have symmetric structures^4,7. The partial oxidation of Ge to its Ge²⁺ oxidation state contributes an antibonding 4s character to the VBM, as in lead–halide perovskites.

We then calculated the formation energies and transition energy levels of the six possible point defects in GeSe mentioned above; we used the generalized gradient approximation (GGA) in these studies. The most striking observation is the high formation energies for all the defects, higher than 1.2 eV in their neutral charge states (Fig. 1e, f). This is in contrast with CH₃NH₃PbI₃, in which defects have low formation energies (close to zero)^14,15. This is attributed to the stronger covalent Ge–Se bonds compared with the soft Pb–I bonds in perovskites. The second notable feature is that V_Ge, with the lowest formation energy, has a shallow level with (-/0) and (2-/-) transition energy levels only 0.05 and 0.15 eV above the VBM, whereas defects with deep levels such as Ge_Se, Ge_i, V_Se, and Se_Ge have high formation energies (Supplementary Fig. 1). These are reconfirmed by Heyd-Scuseria-Ernzerhof (HSE) calculations (Supplementary Fig. 2).

The low formation energy of V_Ge is attributed to energetically unfavorable Ge 4s–Se 4p antibonding coupling, where the fully occupied antibonding state has no electronic energy¹⁴. The shallow nature of V_Ge originates from the antibonding state at the VBM, a defect-tolerant electronic structure known to lead to shallow defects (Supplementary Fig. 3). This state pushes the VBM to a higher level such that the acceptor defect is shallower near the VBM than that without strong s–p coupling. The strongly covalent GeSe with an antibonding VBM, therefore, exhibits mostly shallow defects.

We used deep-level transient spectroscopy (DLTS) to investigate the defect energy levels, concentrations, and types in semiconductor devices. The DLTS spectrum of GeSe photovoltaic devices fabricated using the previously-reported rapid thermal sublimation approach²⁴ is shown in Supplementary Fig. 4. Two positive peaks denoted as H1 and H2 are observed at 285 K and 310 K, indicating two types of hole trap defects in the GeSe film. The activation energy (E_a) and capture cross-section (σ) values determined from the Arrhenius plots are 0.35 eV and 4.3 × 10⁻²³ cm² in H1, and 0.51 eV and 7.6 × 10⁻²¹ cm² in H2, respectively (Fig. 1d). The concentration of defects (N_T) calculated from the equation of N_T = 2ΔC*N_A/C₀ (N_A is the net acceptor concentration in GeSe film) are 1.3 × 10¹² cm⁻³ for H1 and 3.0 × 10¹² cm⁻³ for H2, lower than state-of-art chalcogenides such as CIGS (~4.2 × 10¹³ cm⁻³) and CZTS (~3.7 × 10¹⁴ cm⁻³)^35,36.

There are only two deep acceptor defects, Se_Ge and Ge_Se. We associate the H1 and H2 defects observed in the DLTS fitting results at 0.35 eV and 0.51 eV with Se_Ge and Ge_Se, respectively. No V_Ge is observed in the DLTS measurement since V_Ge is too shallow to produce a response in the DLTS signal. Note that the densities of deep defects in GeSe including Se_Ge and Ge_Se are at a magnitude of 10¹² cm⁻³, well below the bulk density of GeSe (~10¹⁵) cm⁻³ dominated by V_Ge^24,30. Admittance spectroscopy (AS) measurements further confirmed the low densities of deep-level defects in GeSe. The E_a values deduced from the Arrhenius plots are 0.29 eV and 0.45 eV, while the integrated defect densities of these two defects are 1.6 × 10¹³ cm⁻³ and 3.5 × 10¹² cm⁻³ (Supplementary Fig. 5), respectively. In sum, defects with low formation energies generate only shallow levels, whereas deep-level defects have high formation energies and their density is low.

Photovoltaic device performance

When we fabricated devices using an architecture of ITO/CdS/GeSe/Au, we obtained a low PCE of 1.4%, with a V_oc of 0.23 V, a J_sc of 15.7 mA cm⁻², and a FF of 40% (Fig. 2a). We reasoned that this inferior performance could arise from surface states. We then characterized the density of interfacial defects at the CdS/GeSe heterojunction through a combination of capacitance-voltage (C-V) profiling and drive-level capacitance profiling (DLCP) measurements. C-V measurements are sensitive to free carriers as well as bulk and interfacial defects, while DLCP measurements are responsive to free carriers and bulk defects^37,38. Thus, the density of interfacial defects at the heterojunction is estimated by subtracting N_DLCP (defect density calculated from DLCP) from N_C-V (defect density calculated from C-V). We calculated an interfacial defect density of 2 × 10¹² cm⁻² at the GeSe/CdS interface (Fig. 2b), which can lead to severe recombination losses.

We focused therefore on surface passivation of GeSe films. We posited that Sb₂Se₃ would act as a bridge between CdS and GeSe. Recently, a buried CdS/Sb₂Se₃ homojunction has been reported to arise due to the interfacial diffusion of cadmium, forming a good interface between CdS and Sb₂Se₃ layers³⁹. We applied DFT to investigate the interface formation energy between GeSe and Sb₂Se₃ with a preferred orientation of [111] for GeSe and [221] for Sb₂Se₃. The formation energy is −0.12 eV, indicating that the growth of GeSe on Sb₂Se₃ is feasible. X-ray diffraction (XRD) was then used to characterize the orientation of both GeSe and Sb₂Se₃ layers. When we deposited a GeSe film onto a [211]-oriented Sb₂Se₃ layer (Supplementary Fig. 6), we found that the modified GeSe has a preferred [111] orientation, whereas the peaks of (200) and (400) with the lowest surface energies for GeSe disappear completely (Supplementary Fig. 7). This confirms the strong interaction between [211]-oriented Sb₂Se₃ and [111]-oriented GeSe, in agreement with theoretical calculations.

Photovoltaic devices that use the modified GeSe films are improved with a V_oc of 0.36 V, a J_sc of 26.9 mA cm⁻², a FF of 54%, and a PCE of 5.2% (Fig. 2a). This efficiency is 3.7× higher than that of control devices. DFT calculations were used to study further the role of Sb₂Se₃: dangling bonds on the surface of [111]-oriented GeSe film lead to localized states inside the bandgap, causing recombination losses (Fig. 2c), whereas the electron distribution becomes delocalized following modification with Sb₂Se₃ (Fig. 2d). C-V profiling and DLCP measurements reveal an order of magnitude lower interfacial defect density (2 × 10¹¹ cm⁻²) than in the control devices (2 × 10¹² cm⁻²) (Fig. 2b). Achieving high-performance GeSe solar cells will require further work on the passivation of surface defects rather than bulk defects.

We fabricated over 100 GeSe solar cells (device architecture in Fig. 3a). Figure 3b shows a cross-sectional scanning electron microscope (SEM) image of a device; mapping with false coloring delineates the layers. The thickness of the GeSe layer is 500 nm, and the thickness of the passivation layer is 10 nm (Supplementary Fig. 8). The average grain size of the GeSe film is 250 nm (Supplementary Fig. 9). There is a narrow distribution of PCE values (Fig. 3c), with an average efficiency of 5.2% and a standard deviation of 0.14%. The best-performing device reaches a laboratory PCE of 5.5% (V_oc = 0.36 V, J_sc = 26.6 mA cm⁻², and FF = 57%) (Supplementary Fig. 10). No hysteresis is observed between forward and reverse scans.

We shipped an unencapsulated device to an accredited independent photovoltaic testing laboratory (Newport Corporation PV Lab, USA). This device displays a certified PCE of 5.2% (Fig. 3d), with a corresponding V_oc of 0.38 V, J_sc of 24.6 mA cm⁻², and FF of 56% (accreditation certificate in Supplementary Fig. 11). This is the highest PCE reported so far for GeSe solar cells. Integration of the external quantum efficiency (EQE) collected under the standard AM 1.5 G solar spectrum yields a current density of 23.8 mA cm⁻² (Fig. 3e), in good agreement with the J_sc value measured from J-V characterization (within 5% deviation) and also consistent with the absorption edge of GeSe (Supplementary Fig. 12). When we measured device performance at low-light intensities (Fig. 3f), we found that devices exhibit PCE values of 5.3%, 6.3%, and 8.6% (Supplementary Table 1) as we progress down to 0.01 sun. The corresponding light intensity-dependent J_sc and V_oc are shown in Supplementary Fig. 13 and Fig. 3g. The power value α (0.85) obtained from fitting to J_sc measurement is close to unity (first-order); the slope obtained by linear fitting from V_oc measurement is 1.36(k_BT/q), larger than k_BT/q for trap-free solar cells, indicating that trap-assisted recombination is still present in these GeSe devices.

Device and materials stability

Stability of the GeSe devices was monitored by storing unencapsulated devices in an ambient atmosphere at room temperature and a relative humidity of 50–85%. Devices retain 100% of their initial PCE after storage for 12 months (Fig. 4a). They also show negligible efficiency loss after continuous operation close to the maximum power point (MPP) under 1-sun illumination for 1100 h (Fig. 4b). We then investigated the ultraviolet photostability of unencapsulated devices under ultraviolet irradiation (200–400 nm). They retain their efficiency after exposure to an ultraviolet irradiation dosage of 15.5 kWh m⁻² (Fig. 4c). The thermal stability was investigated by cycling the temperature from −40 to 85 °C for a total of 60 cycles. They show no loss of efficiency after 60 thermal cycles (Fig. 4d).

Temperature-dependent XRD under an ambient atmosphere was applied to explore the origin of air and thermal stability. The film keeps its orthorhombic GeSe (JCPDS 48-1226) phase with no impurity peaks observed (such as GeO₂) even up to 400 °C for 30 min (Fig. 4e). Since XRD is unable to detect amorphous components, we performed X-ray photoelectron spectroscopy (XPS) and energy-dispersive X-ray spectroscopy (EDS) on the same GeSe film after temperature-dependent XRD measurements. Oxygen and carbon are not detected in GeSe films (see magnified XPS spectrum at 520–550 eV and 281–295 eV) (Fig. 4f), consistent with the EDS results (Supplementary Fig. 14). The Ge 3d_5/2 and Ge 3d_3/2 peaks in the Ge 3d spectrum are observed at 29.85 eV and 30.43 eV (Fig. 4g), corresponding to Ge in the +2 oxidation state²⁴. Gaussian-Lorentzian fitting confirms that no peak corresponding to +4 or 0 state of Ge is observed within the detection limit of the XPS instrument. The Se 3d spectrum also reveals that Se is in the expected oxidation state of Se²⁻, corresponding to GeSe (Fig. 4f)³⁰. The above results, therefore, demonstrate the high air and thermal stability of GeSe. In addition, GeSe also exhibits excellent humidity and light stability (Supplementary Fig. 15). The 4s² electrons on the Ge cation in ionic perovskites are exposed, making them vulnerable to oxidation; while the lone-pair electrons on the Ge atoms in covalent GeSe participate in Ge 4s–Se 4p coupling, leading to chemical inactivity.