A New Look at Calcium Digermanide CaGe₂: A High-Performing Semimetal Transparent Conducting Material for Ge Optoelectronics

We started our examinations from the attempts to grow CaGe₂ films on Al₂O₃ (sapphire) substrate. In doing so, a solid phase epitaxy (SPE) method was chosen suggesting some similarities between CaGe₂ thin films and CaSi₂ transparent conducting layers obtained previously Shevlyagin et al. (2022a). Schematic illustration of the CaGe₂ SPE, which is a two-stage process, is pictured in Figure 1a. A set of the samples was obtained with varied Ca-Ge thickness (10-120) nm and annealing temperature (600-850)^oC. All grown films can be divided into two groups based on their stability, which is directly associated with phase composition driven by the growth conditions. Stable after air exposure and storage for 1 year samples demonstrate simultaneous partial optical transparency at least in the red spectral region (Figure 1d), sufficient electrical conductivity to supply the LED by passing a DC current through it (Figure 1e) and relatively smooth surface with RMS roughness not exceeding 3 nm in accordance with atomic force microscopy (AFM) data (Figure 1b). The latter is of great importance for developing TCMs with high FOM values, since pronounced surface relief could deteriorate both transparency and electrical conductivity, to say nothing of difficulties with materials processing towards real electrode engineering (lithography, patterning etc.). Scanning electron microscopy (SEM) investigations show that stable Ca-Ge layers consist of large grains and form continuous films (Figure 1c), while energy dispersive X-ray spectroscopy (EDX) confirms stoichiometry of CaGe₂ (Figure S1 in Supporting information). For unstable CaGe₂ films, in most cases their degradation took place within a few hours depending on its thickness except for the thinnest ones exhibiting some changes in their appearance obvious by a naked eye just after growth ending. The readers are further addressed to Supporting information for optical microscopy data and planar SEM images (Figure S2), which are helpful to express and preliminary examine the CaGe₂ films stability, while rigorous phase identification for the grown Ca-Ge layers probed with XRD and Raman method will be given below.

It is known that CaGe₂ can exist in several polymorph modifications, with hexagonal (space group #186), two trigonal (space groups #166 and #164) and monoclinic (space group #12) crystal lattices being the most frequently observed Yaokawa et al. (2018, 2021); Tobash and Bobev (2007). The former two phases referred to as hR6 (or 6R) and h2 (or 2H) were experimentally observed including thin epitaxial films, while the latter two are metastable. In addition, it was reported that fluorine diffusion and crystal lattice stress release can promote stabilization of the other hexagonal (h4 or 4H) and trigonal (hR3 or 3R) CaGe₂ polymorphs. In this view, the Ca-Ge phase diagram is quite similar to the Ca-Si one in terms of the variety of phases and compounds. However, while both h3R and h6R trigonal CaSi₂ polymorphs are (i) stable, (ii) semimetal in nature and (iii) tolerant to degradation under ambient conditions, it is not the case for CaGe₂. Additional challenges arise, since h2- and hR6-CaGe₂ can be hardly separated by means of Raman spectroscopy and XRD examination Vogg et al. (2000b); Hara et al. (2021); Arguilla et al. (2017). For example, Figure 1h represents a typical XRD pattern of the decomposed film obtained. The observed peaks can be attributed as diffraction from CaGe₂ and CaO crystal planes. However, it was further specified that GeH (germanane) and CaO formation took place rather than both hR6-CaGe₂ decomposition and h2-CaGe₂ preservation. The trick is that GeH and h2-CaGe₂ diffraction peaks are hardly distinguishable Itoh et al. (2022); Pinchuk et al. (2014), which can be clearly seen by comparing the two XRD patterns corresponding to stable and decomposed Ge-Ca layers (Figure 1h). The only difference is in the observed CaO related peak in the latter case. The presence of the GeH in the decomposed film instead of the h2 phase is supported by Raman measurements presented in Figure 1g. The broad phonon bands centered at 275 cm^-1 (Ge-Ge bonds) and 225 cm^-1 (Ge-H bonds) can be categorically assigned to GeH (the pink graph) Bianco et al. (2013). This spectrum is in a marked contrast with that of measured from the stable CaGe₂ film (the green graph). At least four relatively narrow peaks were resolved, assigned as E_g and A_1g phonon modes of h2-CaGe₂. Thus, XRD measurements allowed detecting CaO presence, while Raman spectroscopy did the same for GeH. As a result, hR6-CaGe₂+H₂O$\rightarrow$CaO+2GeH can be tentatively suggested as an origin of the observed decomposition of thin CaGe₂ layers after air exposure. Concerning growth conditions, which lead to CaGe₂ decomposition, it can be stated that (i) thin ($<$15 nm) films show this tendency regardless annealing temperature, (ii) increase in total Ge-Ca thickness results in the presence of both h2 and hR6 phases and (iii) further increase in thickness opens a stability window for CaGe₂ in h2 modification with no hR6 traces, which suggest single-phase film growth. Too low annealing temperature results in CaGe formation (insulating phase), while too high temperature treatment does in re-evaporation of the deposited layers.

To outline some intermediate results on experiments of growth stable CaGe₂ films, we illustrated it by a schematic phase diagram shown in Figure 1f, which reflects chemical composition of the obtained samples addressed by Raman and XRD measurements in relation to growth conditions. In brief, it appears to be that a stable and single-phase h2-CaGe₂ film could not be grown thinner than 20 nm and below annealing temperature of 750^oC (region I). Outside the optimal ranges, the following processes make sense: phase coexistence (II), monogermanide formation (region III), total decomposition (region IV) and film re-evaporation (region V).

After resolving the stability issue, optical and electrical properties of the h2-CaGe₂ films can be discussed from the view of both modeling and some practical aspects toward the TCMs performance. This screening was performed by first principles calculations, while extracted information is of high value in supporting optical and electrical measurements. We started for the band structure calculations of the fully relaxed h2-CaGe₂ primitive cell and the resulting electron band diagram is shown in Figure 2a. There are multiple crossings at the Fermi level for both valence and electron bands. One can see at least one electron and one hole pockets above Fermi level (holes energy is counted inversely to that of for electrons) tinged with red and green, respectively. In addition, some peculiarities of the h2-CaGe₂ band structure are of great importance. First, CaGe₂ in h2 modification is a trivial indirect-type semimetal Markov et al. (2019), which means that electron and valence band extreme points located at the different k-points ($\Gamma$ and M, respectively) with the so-called negative band gap of about 0.6 eV (the sum of the electrons and holes pockets maximal energy offset with respect to Fermi level). Secondly, one can observe that with the exception of mentioned carriers pockets, there is a wide energy gap diving below and above Fermi level to about 0.6 and 0.3 eV, respectively. It resulted in a very low electron density of states (DOS) near Fermi levels compared to pure metals, but significantly larger than for semiconductors even under degeneracy doping. On the one hand, this electronic bands configuration allows demonstrating very low resistivity in the order of 10^-5-10^-4 $\Omega\cdot$cm for h2-CaGe₂ thin films (see Supporting information S3 for Hall measurements performed on the films of different thickness) compared with bulk single-crystals Evers and Weiss (1974). From the other hand, low electronic DOS should results in the low optical DOS as well. Calculated complex dielectric function of the h2-CaGe₂ phase is plotted in Figure 2b and explains well the low optical losses in the IR spectral range up to 0.8 eV.

To provide an experimental verification of the ab initio calculations, optical transparency and sheet resistance were measured for 100-nm thick CaGe₂ film on Al₂O₃ substrate obtained under the growth conditions, which correspond to formation of a stable Ca-Ge phase (region I; Figure 1a). A typical experimental transmittance spectrum of the CaGe₂/Al₂O₃ sample is presented in Figure 2c together with the optical modeling results based on calculated complex dielectric function of the h2-CaGe₂ and the data available for Al₂O₃. In doing this, obtained dielectric constants within Fresnel law were used to calculate optical response of the CaGe₂/Al₂O₃ system assuming a smooth and sharp interface between materials and zero scattering. One can see a close agreement between theoretical and experimental evaluations. In addition, relatively thick (100 nm) CaGe₂ is semitransparent from the near-infrared (NIR) to middle-infrared (MIR) spectral ranges, while optical transparency of the CaGe₂/Al₂O₃ system reaches 60% at 2500 nm.

Next, rigorous investigations were performed to define CaGe₂ growth conditions (thickness and annealing temperature), which lead to the highest FOM value in accordance with the following expression: FOM = -1/[R${}_{sheet}\cdot$ln(T)], where R_sheet and T are sheet resistance and optical transmittance (at the selected wavelength or averaged over the specific range), respectively Gordon (2000). The results of this screening is shown as 3D mapping in Figure 2d. It was found that the transparency window of the h2-CaGe₂ itself is located in the near-IR (1-3 $\mu$m) spectral range. The measured sheet resistance varied from 8 to 30 $\Omega$/sq. depending on both film thickness and annealing conditions. After all, 60 nm thick CaGe₂ film annealed at 750^oC demonstrated the highest relative optical transparency of 78% at 2.25 $\mu$m and moderate sheet resistance of 16 $\Omega$/sq. These parameters give the FOM values of the 0.33 and 0.13 $\Omega^{-1}$ at the wavelength of maximal transmittance (2250 nm) and for an transparency averaged over (400-7000) nm range, respectively. Obtained FOM value for the h2-CaGe₂ is competitive with other state-of-the-art TCMs currently applied for NIR-MIR applications Gao et al. (2021); Khamh et al. (2018); Tong et al. (2016); Wang et al. (2019); Fukumoto et al. (2022).

To test h2-CaGe₂ TCM under the real photovoltaic device operations, we grew a corresponding thin film on the Ge(111) substrate instead of Al₂O₃ transparent one using the same optimized conditions found previously (60 nm thick CaGe₂ layer annealed at 750^oC). The deposition and annealing of the Ge-Ca bilayer was done through a tantalum mask for in situ formation of the two CaGe₂ pads. Thus, we obtained a MSM photodetector acting as two back-to-back Schottky junctions with a schematic design pictured in Figure 3a. Raman measurements suggest a good crystallinity of the grown semimetal layers with observed phonon bands corresponding only to CaGe₂ and Ge with no traces of film decomposition and other Ca-Ge alloys. Figure 3b demonstrates dark I-V characteristic of the planar MSM structure with clear Schottky behavior. Under the assumption of the thermionic-field emission regime Katz et al. (2001), a Schottky barrier height was calculated to be 0.5 eV, while reverse saturation current is equal to 50 nA. Under laser illumination at 1550 nm, CaGe₂/Ge/CaGe₂ MSM diode demonstrates no photocurrent generation under zero-bias condition. However, even a small bias voltage results in pronounced photocurrent, wherein current flow is enhanced by two orders of magnitude at the applied 2V under illumination compared to dark conditions. Thus, a typical operation of the MSM PD with symmetrical Schottky contacts was confirmed. Next, a room temperature photoresponse at the bias voltage of 2V was measured for the CaGe₂/Ge/CaGe₂ MSM PD. Results obtained are plotted in Figure 3c together with characteristics of the commercial Ge PD. It is obvious that application of the CaGe₂ transparent electrodes resulted in the spectral range expanded into the shortwave IR region below the band gap of Ge (0.67 eV). We estimated a photoelectric threshold energy to be 0.54 eV (2300 nm), which well correlates with Schottky barrier height obtained from the I-V curve. Moreover, there is the photoresponse enhancement in the (1200-1900) nm range owing to a high transparency of the CaGe₂ electrodes, which result in higher photogeneration occurring in Ge. Thus, a simple but effective approach of advancing Ge-based photodiode performance in terms of maximal sensitivity and red shifting of the cut-off wavelength is demonstrated.

Despite a high NIR-MIR TCM performance, the grown CaGe₂ films have low optical transparency in the visible spectral range. Fortunately, it can be tuned by making a perforated mesh electrode by direct fs-laser patterning. For this purpose, 60 nm thick CaGe₂ film was processed using a flat-top square-shape laser beam as schematically illustrated in Figure 4a. The laser fluence was kept slightly above the single-pulse ablation threshold of the corresponding CaGe₂ film (see detailed description of the ablation threshold measurements in Supporting information - Figure S4). Typical morphology of the 60-nm thick CaGe₂ film grown on Al₂O₃ substrate after laser processing is demonstrated by top-view SEM image in Figure 4b, with the photograph of the resulted Al₂O₃/CaGe₂ sample after laser perforation clearly demonstrating the enhanced optical transparency compared to non-perforated areas (Figure 4c). The sidewalls of the CaGe₂ mesh are smooth and no traces of the ejected submicron-sized particles can be found, which suggest high suitability of the CaGe₂ material for laser patterning. It is important to note, that a maximal rim height of the square-shape openings was about 90 nm (Figure S5), which is only 1.7 higher than initial CaGe₂ film thickness indicating that under chosen laser patterning conditions the outward radial mass transfer of the molten Ca-Ge is not much intense.

Representative optical transparency spectra of the 60-nm thick CaGe₂ film before and after laser perforation are presented in Figure 4d. The most pronounced changes are observed in the (400-1500) nm range, which are characterized by 3 times higher transparency of the perforated sample in comparison to untreated one, while transparency in the (1500-7000) nm range are intrinsically high for CaGe₂ material owing to its semimetal nature. Raman measurements confirmed (not shown) that even at high perforation ratio, laser ablation does not strongly affect crystallinity of the remaining sections of the CaGe₂ films. Compared with continuous films, a mesh CaGe₂ electrode with an optimal perforation ratio (determined to be 78%) demonstrates six-fold increases in the FOM value reaching 0.75 $\Omega^{-1}$ (see Figure 4e) due to an optical transparency averaged over (400-7000) nm beating 90% after laser processing. The lower perforation ratio is not enough to reach high optical transparency. On the contrary, extensive perforation rate above 80% decreases FOM value owing to drastically increased sheet resistance up to 32 $\Omega$/sq., which is 3 times higher compared with initial smooth CaGe₂ film, however being still acceptable for TCM applications.

Finally, to confirm and highlight the advantage of fs-laser projection lithography in tuning optical properties of CaGe₂ film, a vertical Ge PD was fabricated on a sapphire substrate with a perforated transparent electrode (face contact) and thin Al film acting as a back electrode. The schematic view of the resulting vertical Ge Schottky PD is shown in Figure 4f assuming light irradiation from the CaGe₂ side. As the most illustrative test, we next directly compared the photoresponse characteristics of the two Ge PDs with a flat and perforated CaGe₂ electrodes (Figure 4g). One can see that the latter device generally follows the trend observed for the optical transmittance measurement. For instance, integrated over (600-2000) nm range photoresponse and peak photoresponse value (at 1600 nm) were enhanced by 85% and 44% (the room-temperature photoresponse exceeds 1 A/W under -2V bias voltage), respectively, while an expanded operation spectral range was observed for the Ge device with perforated top electrode. Of great importance, integrating the Ge PD platform with CaGe₂ electrodes has no negative influence on the light detection, which is linearly dependent from the irradiation intensity regardless of CaGe₂ electrode type (see inset in Figure 4g). In addition, we investigated the response speed of the device with a perforated electrode. The relative balance of the Ge PD device versus a switching frequency of pulsed IR light irradiation (@1550 nm laser) is presented in Figure 4h with a relatively high 3dB frequency of 22 kHz, which claims for Ge PD with transparent conducting electrode made from semimetal film to be capable of detecting fast optical signals. The response speed was further evaluated by analyzing the rising and falling edges of the photoresponse time curve under a cycle conditions, which are normally calculated as the time intervals for the response to rise from 10% to 90% and vice versa (Figure 4i). A fast rise/fall time ($\tau_{r}$/$\tau_{f}$) of 27/47 $\mu$s was obtained. We could attribute this relatively quick response speed to the low density of trap centers at the Ge/CaGe₂ heterointerface, which is additionally confirmed by the photoresponse versus incident light dependence, and a very effective separation of photogenerated carriers by the built-in electric field formed at the CaGe₂/Ge Schottky junction area. To sum up, the critical parameters for the developed vertical Ge PD with Schottky type contact made of perforated film of semimetalic CaGe₂ were compared with other Ge Schottky type PDs Kwon et al. (2022); Jiang et al. (2022); Falcone et al. (2022); Huang et al. (2021, 2018); Cho et al. (2016); An et al. (2022); Dushaq et al. (2017); Ang et al. (2008); Zumuukhorol et al. (2019); Yin et al. (2022); Chang et al. (2019); Zeng et al. (2013); Kim et al. (2021); Yang et al. (2017); Luo et al. (2019); Zhao et al. (2020); Xiong et al. (2022) with an emphasis on MSM structures and listed in Table 1.

As can be clearly seen, such phenomena as transparent conducting electrodes have rarely been addressed concerning the applications in Ge PDs except for some works focusing on graphene, ITO and MXenes integration, nothing to say about much fewer reports on Ge/semimetal or Ge/topological insulator heterojunction PDs. The current work demonstrates that low dark current, high responsivity in wide wavelength range and fast response speed is achievable by introducing semimetal CaGe₂ transparent conducting electrode into Ge optoelectronics. In particular, spectral operation range of the proposed Ge PD is the broadest than that of other photodetectors of the same type (Schottky or MSM). Concerning both photoresponsivity and operation speed, fabricated PD is obviously outperform commercially available Ge PD, while demonstrating competitive characteristics even compared to black Ge based PD. Moreover, a self-powered operation (zero bias driving voltage) is not anyhow restricted by CaGe₂ application and could be potentially achievable by the widely known symmetry breaking approach Wang et al. (2020); Zhou et al. (2018) for Schottky type PDs, which could be a question of future work. Thus, obtained results suggest that laser-perforated CaGe₂ thin films have a great potential as transparent conducting materials for Ge optoelectronic devices and applications.