Identification of Ge vacancies as electronic defects in methyl- and hydrogen-terminated germanane

Two-dimensional (2D) materials are of high interest for fundamental studies as well as practical electronic applications since several of them exhibit high free carrier mobility and their structures can be designed to produce novel electrical and optical properties. For example, germanane, a covalently terminated germanium graphane analogue, has generated considerable interest as a unique electronic 2D material due to its potential to tune the electronic structure via altering the identity of the covalently terminated ligand.¹ While early studies initially predicted pristine GeH to have excellent transport behavior, specifically, room temperature electron mobilities in the range of 18 000 cm² V⁻¹ s⁻¹, initial conductivity measurements showed that these materials are extremely resistive, likely due to the large amount of defects and disorder in GeH.^2,3 Recently, Madhushankar et al. have reported GeH field effect transistors with both electron and hole mobilities in the range of 70–150 cm²/V s, indicating the feasibility of germanane as a viable electronic 2D material.⁴ 

For all 2D materials, defects within the lattice or associated ligands can introduce localized states that limit mobility, carrier injection, and optical properties. Indeed, their separated layer structure renders them particularly sensitive to the local chemical environment, local dielectric constant, and substrate morphology.^5–7 Numerous studies have reported evidence of defects in single- or multi-layer 2D materials in terms of chemical bonding, Fermi level movements, and degraded carrier transport features.^8–11 As with other electronic materials, deep level defects with energy levels within the germanane bandgap are likely to introduce charge trapping and scattering which reduces the otherwise high mobility predicted theoretically. These concerns have motivated efforts to reduce apparent defect densities in graphene, WS₂, and other 2D materials through chemical processes.^12–14 Nevertheless, the ability to measure defects in 2D materials is challenging since atomic layer thicknesses limit optical absorption and excitation. Furthermore, the high 2D surface-to-volume ratio enables air adsorption or chemisorption to strongly affect electronic features. Until now, researchers have imaged defects with transmission electron and scanning tunneling microscopies^15–19 and calculated energy levels of general defect types in 2D materials.^20–22 In previous theoretical work, it was assumed that the relevant defects are restricted to the ligand level, such as H-ligand vacancies or Ge adatoms.^23,24 However, in the present letter, we will show by combining theory with experiment that the vacancies in the backbone network which were previously ignored are actually the crucial defects when it comes to electronic properties.

We have identified the deep-level defects using a combination of depth-resolved cathodoluminescence spectroscopy (DRCLS),²⁵ surface photovoltage spectroscopy (SPS),²⁶ and density functional theory (DFT).²⁷ Here, we show that DRCLS can detect electronic features at a near-nanometer scale and can distinguish between intrinsic versus extrinsic surface and bulk features in van der Waals (VDW) multilayers with near-nanometer scale depth resolution. DRCLS detects numerous deep level defects that occur at the same energies for GeH and GeCH₃, implying that ligand termination is not responsible for these defects. These defect levels closely match the values predicted by DFT for germanium vacancies and double vacancies having different amounts of hydrogen passivation, as well as impurity atoms from the deintercalation process which change interlayer spacing and shift defect energies.

Figure 1(a) shows DRCL spectra with incident beam energy E_B = 4.5 keV in the near infrared (IR) and extended visible ranges, respectively, for GeCH₃ bulk powder platelets. The deconvolved features in Fig. 1(a) include a high energy peak at 1.56 eV which corresponds to the GeCH₃ bandgap. This energy is in good agreement with diffuse reflectance absorption (DRA) measurements reported earlier for GeCH₃ flakes.² Figure 1(a) shows discrete emission peaks at energies below the bandgap which correspond to defect states with optical transitions of 0.81 eV, 0.96 eV, 1.02 eV, and 1.37 eV relative to the GeCH₃ valence and conduction bands. We used depth-dependent CL spectra to identify and avoid ambient oxidation features due to, e.g., GeO₂²⁸ (see supplementary material).

SPS features determined the energy level positions of defects within the GeCH₃ bandgap. SPS electric potential differences between a Kelvin probe tip and the sample surface were measured continuously while illuminated by monochromatic light scanned over a 0.5–4.5 eV energy range. Here, slope changes with increasing photon energy measure the onsets of the photostimulated population and depopulation transitions between defect levels and the valence or conduction bands. An upward (downward) change in the slope corresponds to a majority carrier population (depopulation) of near-surface states. Excitation at the bandgap energy produces a relatively high density of electrons and holes, lowering net charge at the surface and decreasing band bending. In Fig. 1(b), the large change in contact potential difference (Δcpd) beginning at 1.6 eV identifies the bandgap energy, while the sign of Δcpd changes, and hence, the Fermi level E_F movement relative to the vacuum level E_VAC signifies the n- or p-type nature of the band bending. Here, the downward Δcpd slope with increasing photon energy signifies a reduction in p-type band bending. The onset of valence-to-conduction band absorption at 1.60 eV is in good agreement with the 1.56 eV DRCLS bandgap emission in Fig. 1(b), considering the 0.05 eV and 0.04 eV spectral resolutions, respectively, of the two measurements. In addition, Fig. 1(b) shows Δcpd slope changes at 0.85, 1.05, and 1.40 eV, corresponding to CL energies again in close correspondence with sub-bandgap peak features in Fig. 1(a). Based on these Δcpd slope changes relative to the sign of band flattening at the bandgap energy, Table I identifies energy level positions for each of the GeCH₃ defects.

The 0.85, 1.02, and 1.38 eV DRCLS features are in excellent agreement with SPS transition energies. The absence of a pronounced SPS feature at 0.95 eV may be due to finite energy widths of defect density of states which exceeds the SPS spectral resolution. Transient SPS performed at 1.2 eV, sufficient to excite the 1.05 eV transition, yielded preliminary surface state densities of 1.5 × 10¹⁰–4.8 × 10¹¹ cm⁻² for assumed bulk carrier densities of 10¹⁵–10¹⁸ cm⁻³, respectively.^29,30

In order to determine the physical nature of these defect states, we monitored the energies and intensities of their optical features as a function of ligand, chemical synthesis, and electron beam damage. Comparison of Figs. 2(a) and 2(b) shows the effect of varying ligand termination in relation to the observed mid-gap states. Both GeH and Ge(CH₃)_0.6H_0.4 show mid-gap states similar to those observed in GeCH₃ in Fig. 1, indicating that the observed states are not affected by ligand termination but are related to defects in the germanium scaffold. Electron diffraction in transmission electron microscopy (TEM) was used to establish the crystallinity of both GeH and GeCH₃ (see supplementary material). High resolution imaging in the TEM of these materials proved to be challenging, due in part to the low knock-on damage threshold of hydrogen and the low thermal stability of GeH and GeCH₃, which amorphize at 75 and 200 °C, respectively. Utilizing low-dose techniques and low accelerating voltages enabled nanocrystallinity in GeCH₃ to be observed (see supplementary material).

XPS showed the presence of residual Ca and I with Ca being common to both GeH and GeCH₃. DFT calculations of defect energy are sensitive primarily to an additional atom near the defect site that spreads the layers further apart. Figure 2(c) shows the effect of extending the duration of the CaGe₂ deintercalation of GeCH₃ from one week to three weeks. The extended de-intercalation procedure resulted in the removal of the 1.02 eV peak, indicating that this mid-gap feature is due to the incomplete removal of CaGe₂ from between the GeCH₃ layers. The presence of Ca between GeCH₃ layers is expected to alter the interlayer spacing and introduce defect emission. For example, DFT calculations indicate the existence of a mid-gap state when a Ca atom is placed at a divacancy with no passivating hydrogen atoms (see supplementary material). Hence, Figs. 2(a) and 2(b) appear to provide a first example of an impurity situated between 2D layers producing a highly localized state with an energy level deep within the bandgap.

Electron beam irradiation provided us with a method to introduce displacement or thermal damage and identify features associated with the resultant defects. We measured DRCL spectra of GeCH₃ irradiated with increasing incident beam voltages E_B up to 25 kV. Between E_B = 5 and 15 kV, no noticeable changes occurred over the visible range. For E_B = 20 kV, only slight changes were evident, whereas an ∼13% increase in the I(1.37 eV)/I(1.60) peak ratio occurred for E_B = 25 kV (see supplementary material). For E_B = 20 keV and 10 nA beam current, the area ratio A(1.37 eV)/A(1.57 eV) increased steadily with exposure time, i.e., fluence, by >75% (see supplementary material). Both results showed that electron beam irradiation can increase defect emission, but only above E_B = 15 keV. The relative increase in the 1.37 eV defect peak coupled with the similarity of the GeCH₃ and GeH spectra indicates that this defect is introduced by damage to the Ge scaffold. Such damage is likely introduced thermally since a kinematic calculation of displacement damage suggests that much higher threshold voltages are required to displace Ge atoms within a solid matrix.³¹ 

DFT calculations of specific defects in GeH provide energy levels that correlate with the states observed in DRCLS and help identify likely structures that produce the states. The DFT calculations were done with the Vienna Ab-Initio Simulation Package (VASP),^32,33 using PAW-PBE potentials and Grimme's D2 van der Waals approach for relaxations.^34–36 For the defect calculations, we used a 4 × 4 × 1 supercell of the 6R structure of GeH (confirmed by synchrotron X-ray data) with lattice parameters a = 4 × 4.034 Å and c = 25.443 Å, respectively, which resulted from a relaxation of the perfect cell. The defects considered were Ge vacancies and divacancies with varying levels of passivation, H vacancies, and Stone-Wales type defects. The ion positions in all defective supercells were relaxed for fixed lattice constants with a 3 × 3 × 1 k-point mesh and a plane-wave cutoff energy of 250 eV. Once these cells were relaxed, we performed a density of states calculation using HSE06 and the tetrahedron method for smearing.³⁷ We calculated defect formation energies for 6R GeH with density-functional theory within the HSE functional.

We found that hydrogen vacancies are not responsible for the creation of midgap states. Our calculations show that full passivation of the Ge vacancies is the most likely configuration; however, due to either the formation of hydrogen vacancies or lacking availability of hydrogen, it is not the most observed state. A single germanium vacancy will leave three coordinatively unsaturated nearest neighbor Ge atoms. These nearest neighbor Ge atoms would formally have seven electrons surrounding each atom when counting their two Ge-Ge and one Ge-H covalent bonds. This contrasts with the normal octet electron configuration for each germanium atom in the non-defective material. However, due to the acidic synthesis conditions, it is likely that some or all of these Ge atoms will be terminated with an additional hydrogen atom. Additionally, there is the possibility that two nearest neighbor germanium atoms are removed, leaving behind a divacancy.

Figure 3 shows calculated energy levels for various germanium monovacancies and divacancies with and without additional bonded hydrogen which are in excellent agreement with the measured optical features and corresponding energies. Based on a 1.6 eV bandgap energy, the 0.81 eV DRCLS and 0.85 eV SPS features correspond to a state 0.85 eV below the conduction band, i.e., at E_C − 0.81 to 0.85 eV. In turn, this matches with the DFT density of states peak located 0.80 eV below E_C due to a Ge vacancy (1H) (purple) and the corresponding structure in Fig. 3(c). Similarly, the 1.38 eV DRCLS and 1.40 eV SPS features correspond to a state 1.38–1.40 eV below E_C, i.e., E_C − 1.38–1.40 eV. In turn, this matches with the DFT density of states peak located 1.39 eV below E_C due to a Ge divacancy (1H) (green) and the corresponding structure in Fig. 3(e). Finally, the 0.96 eV DRCLS and 1.05 eV SPS features correspond to a state 0.96–1.05 eV above E_V, i.e., E_V + 0.96–1.05 eV. This matches with the DFT density of states peak located 0.91 eV due to a Ge divacancy (0H) (blue) and the corresponding structure in Fig. 3(d). The correspondence between the defects observed by two independent spectroscopic techniques along with the excellent agreement with DFT density of states calculations suggests that Ge vacancies with an additional bonded H as well as Ge divacancies with or without an additional bonded H can account for all these defects. There appear to be no measured optical features that match with the calculated E − E_V = 0.38 eV or complementary E_C − E = 1.22 eV transitions. However, there appears to be a shoulder in our CLS spectra which is difficult to confirm due to it being near the limit of our detection range. Excitons have previously been reported to have binding energies of 0.28¹ and 0.6 eV³⁸ relative to the conduction band. However, both states that would arise from excitons with these binding energies could not be responsible for those in our spectra. The state at 1.38 eV has been shown by SPS and DFT to be 1.38 eV from the conduction band and the 1.02 eV state was shown to be removable with extended deintercalation time.

This work shows that optical and electrostatic techniques can observe defects in 2D materials, and through chemical processing and DFT calculations, one can identify the likely chemical structure of these defect states. By extension, these results suggest that the quality of 2D materials can be improved by first identifying the nature of defect states using surface sensitive techniques in order to guide subsequent 2D growth and processing.

See supplementary material for a description of the growth process, DRCLS acquisition setup, TEM of GeCH₃, DRCLS and XPS of surface oxidation in GeCH₃, CLS spectral dependence on beam voltage and electron beam dosage, description of the calculation methods for defects, defect formation energies, and calculations of a mid-gap state due to interlayer Ca.

Primary funding for this research was provided by the Center for Emergent Materials: an NSF MRSEC under Award No. DMR-1420451. W.W. acknowledges partial funding from the Air Force Office of Scientific Research under Project No. FA9550-14-1-0332.

The authors declare no competing financial interests.