Large‐Scale Formation of Uniform Porous Ge Nanostructures with Tunable Physical Properties

Porous germanium (PGe) nanostructures attract a lot of attention for various emerging applications due to their unique properties. Consequently, there is an increasing need for the development of low‐cost synthesis routes that are compatible with large‐scale production. Bipolar electrochemical etching (BEE) is a widely used solution for producing porous Ge layers. However, the lack of controllable production of large‐scale uniform PGe layers is the limiting factor for mainstream applications. Large‐scale homogeneous PGe layers formation is demonstrated by improving the BEE process. The PGe structures demonstrate excellent homogeneity in thickness and porosity, with a relative variation of below 2% across the 100 mm wafer. Furthermore, this process enables accurate tuning of the PGe's physical properties through variation of the etching parameters. PGe structures with porosity ranging from 40% to 80% and an adjustable thickness, while preserving low surface roughness are demonstrated, giving access to a large variety of PGe nanostructures for a wide range of applications. Ellipsometry and X‐ray reflectivity are employed to measure the porosity and thickness of PGe layers, providing fast and non‐destructive methods of characterization. These findings lay the groundwork for the large‐scale production of high‐quality PGe layers with on‐demand characteristics.


Introduction
Porous semiconductor materials have received an increasing interest for both fundamental research and advanced applications owing to their unique mechanical and physicochemical properties compared to their bulk material counterparts. [1][2][3][4] Porous germanium (PGe) in particular shows and low-cost technique providing PGe layers with high material purity and densely packed nanocrystals. However, its widespread adoption remains strongly dependent on the controllable production of homo geneous PGe layer on large surfaces.
In the last two decades, the electrochemical porosification of germanium (Ge) experienced major advancements. The bipolar electrochemical etching (BEE) was introduced [36,37] to overcome the observed lateral dissolution of the PGe [34] when applying a silicon-like unipolar anodic etching [38,39] on Ge substrate. Accordingly, adding a cathodization step allows to passivate the porous layer formed during the previous anodization step. BEE produced PGe with various structures and morphologies has been reported by tuning BEE etching and passivation para meters. [16,35,40] Recently, the Fast BEE was introduced, [33] allowing higher etching rates for thicker PGe layers production. Since then, this technique has been used to produce tubular and columnar morphologies, [41] broadening the implementation of PGe as anode material for Li-ion batteries. [42] Despite the progress made in the fundamental understanding of the electrochemical etching of Ge [36,37,43] and the demonstrated suitability for various emerging applications, the formation of homogeneous PGe layers on large surfaces and the control of its structural properties remain difficult to achieve because of the number of interfering factors during BEE. Indeed, para meters such as substrate characteristics, ratio etching/passivation pulse duration, and current density or electrolyte composition have strong impact on the final PGe properties (porosity, thickness, and morphology). [35,40] Furthermore, PGe morphological characteristics (thickness and porosity) are often extracted using local and destructive techniques such as scanning electron microscopy (SEM), which are not suitable for large scale assessment of the PGe homogeneity.
In this work, we demonstrate large-scale formation of homogeneous PGe layers by a modified BEE. The proposed method allows fine tuning and control of the porous layer thickness and porosity. Accordingly, widely tunable highly uniform PGe layer across 100 mm wafer has been demonstrated. Additionally, we show that ellipsometry mapping and X-ray reflectivity (XRR) are very accurate and nondestructive characterization techniques, to measure the PGe layer thickness and porosity.

Results and Discussions
Ge electrochemical porosification requires the use of BEE, where the anodic pulses enable effective etching, and the cathodic pulses protect the porous structure from dissolution during the etching step. [36,37] This additional complexity, compared to Si porosification, makes the formation of homogenous porous Ge layers by BEE very challenging. When applying standard symmetrical BBE process on large surface, the resulting layers exhibit inhomogeneous surface colors as demonstrated by Figure S1, Supporting Information. Typical cross-sectional SEM image of porous Ge structures obtained by standard BEE process (Figure 1a) shows the lateral etching induced damages that locally alters the PGe layer's quality. The origin of these inhomogeneities can be attributed to an excessive formation of hydrogen gas during the BEE. The mechanism of Ge passivation step has already been described in previous works, [33,40] showing that the formation of hydrogen terminations on the surface of the PGe structure, protects it against dissolution during the subsequent etching step. As a biproduct of this reaction, hydrogen gas is also formed inside the structure. The growth and evolution of H 2 bubbles generate a pressure on the pore walls inducing physical damages to the small and fragile PGe crystallites. Moreover, the large H 2 bubbles stuck inside of the pores can isolate parts of the structure from the system, locally causing etching in lateral direction, which is detrimental for the porous layer homogeneity over the large surface. Figure 1b schematically illustrates the accumulation of the H 2 bubbles inside the porous structure and the consequent potential damage that may locally occur during the porous layer formation.
To overcome these undesirable passivation effects, we introduced some modifications to commonly used BEE conditions. Indeed, to reduce the quantity of produced H 2 gas, we employed a low passivation current density of 1 mA cm −2 . Additionally, a rest time has been introduced at the end of each etching/passivation cycle. The extra time after each cycle let the system reach the equilibrium potential as well as it enables the H 2 gas to escape from the porous structure as shown in Figure 1b. Moreover, the proportion of ethanol in the electrolyte is increased by 20% to reduce the surface tension of the solution. [44] This helps releasing the residual H 2 bubbles, and facilitating the electrolyte penetration inside the nanoscale sized porous structure enabling an efficient diffusion of the ions toward the bottom of the pores. As a result, the introduced modifications increase the overall stability of the process, inhibiting the damage of the PGe layers during the etching while enabling homo geneous PGe structures formation over large surfaces. Using this improved BEE recipe, well-defined PGe structure with good lateral and in-depth uniformity has been obtained as revealed by SEM micrograph (Figure 1c).
To date conventional porosification cells for electrochemical etching of semiconductors employ a clamping mechanism to maintain the wafer inside the cell and to seal the reservoir for the electrolyte. [34,45,46] Figure 2a shows typical homogenous PGe layer produced in conventional 100 mm wafer porosification cell. Since the edge of the wafer is isolated from the electrolyte, it cannot be porosified leading to the formation of bulk material rim surrounding the porous structure. Moreover, the clamping mechanism causes additional defects/inhomogeneities in the porous structure (as indicated by red arrows in Figure 2a) near the edges of the PGe layer. These combined effects reduce the effective usable surface of the wafer by over 25%, which is significant especially in case of rare and expensive material such as Ge. Additionally, the interface between the bulk material and the porous structure can cause formation of defect, accumulation of materials and other problems for applications aiming the use of full wafers such as epitaxial growth of heterostructures. To avoid these problems additional steps such as laser cutting or mechanical grinding to remove the rim [47] need to be undertaken, increasing the fabrication process's cost and complexity. Most industrial fabrication processes are developed to work with the whole wafers to ensure the highest possible efficiency. Consequently, any unusable parts of the substrate or additional steps will have a negative impact on process throughput. To overcome this issue, we have developed custom www.advmatinterfaces.de design [48] of porosification cell enabling the porosification of the entire wafer's surface (edge included). Schematic illustration of this design is shown in Figure 3b along with the produced uniform edge-to-edge PGe layer on full 100 mm wafer ( Figure 3c).
To study the impact of the etching parameters on the PGe layer's uniformity, the etching current density was varied between 0.5 and 5.0 mA cm −2 . Indeed, as shown in Figure 3, the improved stability of the proposed BEE recipe enables the etching current density variation while preserving the PGe layer's uniformity. Indeed, Figure 3a shows a linear increase of etching rate with etching current density. Compared to previously reported data, [33] homogeneous PGe layers can be produced even above 2.5 mA cm −2 effectively avoiding the lateral dissolution at high etching current densities. This allows to achieve high etching rates of above 40 nm min −1 , being previously reported only by Fast BEE. [33] Moreover, for a given current density, the PGe layer thickness is found to increase linearly over time (Figure 3b). This testifies that the etching rate remains constant during the BEE process. This characteristic enables time-based thickness modulation of PGe layers from few nm up to 4 µm. Furthermore, the porosity can be successfully tuned from 40% to 80% by varying the etching current  www.advmatinterfaces.de density within the selected range, providing the formation of adjustable medium to high porosity layers (Figure 3c). Two main porosification regimes can be distinguished: I) From 0.5 to 2.0 mA cm −2 , porosity exhibits high porosity layers to the etching current density, enabling wide range of porosity variation between 40% and 70%. II) Meanwhile, for an etching current density ranging from 2.0 to 5.0 mA cm −2 , the porosity is found to vary only between 70% and 80% allowing very fine porosity modulation in this regime.
For all porosities the PGe structure is formed by interconnected mesopores, separated by Ge skeleton. Although the pores are disordered at a short range, a certain degree of ordering can be detected at a long range, particularly in the case of high porosities (Figure 3d-i). This shows that the PGe layers maintain its sponge-like morphology, regardless of the etching current density. This is possible thanks to the high degree of passivation. Other morphologies such as "pine-tree" and "fish-bone," have been reported in the literature for lower degrees of passivation. [40] While the porosity of the PGe layer vary as a function of the etching current density, the pore size seems to remain the same as shown by the cross-sectional SEM images of PGe structures with porosities between 40% and 80% in Figure 3d-i. The image processing reveals an average pore diameter, around 5 ± 1 nm across all the porosities. This value is consistent with the observations by transmission electron microscopy (TEM) presented in Figure 5a as well as with the values indicated in literature. [33,40] The obtained average pore size classifies at the lower end of the mesoporous size domain. The provided flexibility in tuning of PGe structure's physical properties enables the possibility of on-demand porous layers formation, depending on the desired characteristics. Many applications can take advantage of this kind of versatility such as energy storage systems, [7] thermoelectric devices, [11] or nanoengineered compliant substrates for epitaxial growth. [21,23] The demonstration of wafer-scale production and use of porous Ge substrates for various applications, comes with a crucial need to develop fast and nondestructive characterization methods easily applicable for post-production PGe wafer's quality assessment. To date, PGe layers are mainly characterized by SEM. Accordingly, we have employed this method on various locations along the PGe wafer's diameter as reference data to assess the accuracy of the nondestructive characterization techniques. Figure 1c shows a well-defined interface between the PGe layer with sponge-like morphology and bulk Ge material. The Figure 4a shows that the PGe layer thickness remains constant along the wafer's diameter with a mean value of 206 ± 4 nm (Figure 4b). The SEM can also be used to evaluate the porosity, using image treatment software. In the present case the porosity value is estimated to be 67 ± 12%. To assess this estimation using nondestructive technique, we first employed XRR measurement to precisely determine the porosity. Indeed, it allows to measure the critical angle of porous layer, which is directly linked to the material's density

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and therefore its corresponding porosity. As the porosity of the layer increases the value of critical angle decreases. This enables the distinction between the critical angle of PGe layer (θ PGe ) and of the bulk Ge (θ Ge ) as shown in Figure 4b. The porosity can therefore be calculated using Equation (1). Variation of PGe critical angle with porosity is shown in Figure S2, Supporting Information. XRR enables non-destructive determination of porosity without relying on indirect image processing algorithms. Figure 4c shows radial profile of porosity of full wafer with an average value of 72 ± 2%. This result agrees with the estimation made by SEM images treatment. These methods give us good indication about the uniformity of the PGe layers, but they are still, not suitable for the fast feedback loop necessary for large-scale production.
Regardless of the precision and the accuracy of the provided information (layer's porosity, thickness, and homogeneity), SEM remains local and destructive method, which is nonrepresentative of the whole PGe wafer's surface and unsuitable for quality control in production line. On the other hand, XRR is nondestructive and production-line compatible, but it does not offer reliable measurement of the PGe thickness. For this reason, we employed more complete fast and non-destructive ellipsometry measurements to access both thickness and porosity at the same time. Mapping with over 100 measurement points was performed to evaluate uniformity of the PGe over the entire 100 mm wafer as shown in Figure 4d,e. The mean thickness of the PGe layer is evaluated to be 207 ± 3 nm (Figure 4d). In terms of porosity, the mean value is 72 ± 1% as shown in Figure 4e. These results demonstrate excellent uniformity of the PGe layer over the wafer's surface with a standard deviation below 2% for both thickness and porosity obtained by customdesigned porosification cell and optimized BEE recipe (similar results are obtained for medium porosity layers as shown in Figure S3, Supporting Information). Moreover, the obtained data are consistent with both SEM and XRR measurements, making the ellipsometry mapping a fast, accurate, and nondestructive technique suitable for fast feedback characterization of PGe layers.
For applications such as epitaxial growth, the crystalline quality, and surface morphology are crucial characteristics of the substrate. To further quality investigation of fabricated PGe layers high resolution transmission electron microscopy (HRTEM), X-ray diffraction (XRD), and atomic force microscopy (AFM) are used. The HRTEM image of a typical PGe structure made by BEE (Figure 5a) shows Ge atoms oriented in crystalline structure without any observable presence of amorphous phase or oxides on the surface of the crystallites. To investigate if there is any bending of the crystallites in the

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PGe structure, a PGe layer with ≈70% porosity and ≈1 µm thickness is characterized by XRD, since the high porosity and thickness make this type of structure most keen to crystal bending and misorientation. Figure 5b shows 2θ scan with only (400) and (200) [49] peaks of Ge, without signs of any other orientations. Combined, the HRTEM and XRD studies demonstrate the crystalline nature of the porous structure, maintaining the substrate orientation without formation of any amorphous phase or crystal bending. Furthermore, Figure 5c shows a typical AFM scan of the PGe layer's surface topology of the sponge-like structure showing a smooth surface and low RMS (root mean square) roughness below 3 nm. AFM scans for various PGe structures can be found in Figure S4, Supporting Information. These surface characteristics were found to be the same for all the produced porous structures independently of their porosity as can be seen in Figure 5d. The high single oriented crystallinity combined with low surface roughness and good lateral uniformity make these PGe layers an excellent candidate as virtual substrate for wafer-scale epitaxy. Recently, it has been demonstrated that, as porosified PGe substrates allow epitaxial growth of monocrystalline Ge membranes. [50] It has been also showed that native oxides, that may be formed on PGe surface following a long storage time and/or longer period of exposure to ambient atmosphere, can be easily removed by diluted acidic solutions such as HBr.
Oxide-free PGe surface can be obtained, allowing monocrystalline Ge growth on top of it. [51]

Conclusion
We demonstrated the fabrication of edge-to-edge, 100 mm wafer-scale, homogenous, and reproducible PGe layers. This is possible, thanks to a finely optimized BEE process with an additional rest time step to enable efficient evolution of H 2 produced during the passivation step. The edge-to-edge layers enabled by custom designed porosification cell increasing the high-quality PGe surface by over 25% per 100 mm wafer compared to conventional porosification cells. Moreover, we show that the PGe structural properties such as thickness and porosity can be accurately tuned by varying the etching parameters to create PGe layers with on-demand characteristics depending on the desired application. The produced PGe layers' properties are easily assessable by production line compatible, fast, and nondestructive techniques enabling the characterization of entire surface. The resulting PGe layers present excellent homogeneity with less than 2% variation for both thickness and porosity. The HRTEM and XRD analysis shows that the PGe structure maintains the substrate crystalline nature, without any misorientation of the crystallites. More- www.advmatinterfaces.de over, the porous substrates show a good surface topology with RMS roughness below 3 nm over the entire range of accessible porosities. This provides an opportunity for wafer-scale epitaxial growth of detachable III-V heterostructures for optoelectronics and photovoltaics applications. These results demonstrate the viability of BEE for large-scale production of high purity, crystalline PGe layers with on demand characteristics and lay the groundwork for various applications of PGe structures.

Experimental Section
Bipolar Electrochemical Etching: Electrochemical etching of Ge was performed in custom-designed 100 mm electrochemical cell, composed of Teflon body, solid copper working electrode, and Platinum wire counter electrode. Gallium doped, p-type, (100) oriented Ge wafers with 6° miscut toward (111) direction, and resistivity of 8-30 mΩ cm were used as substrate. Prior to a galvanostatic BEE, Ge wafers were deoxidized in the HF (49%) solution for 5 min, rinsed with EtOH (99%, Anhydrous), and dried under N 2 flow. The BEE was carried out in HF (49%):EtOH (99%, Anhydrous) (4:1, V:V) electrolyte using asymmetric anodic (etching), cathodic (passivation) pulses, and 1 s rest time at the end of each cycle. The passivation pulses were fixed at 1 mA cm −2 current density and 1 s pulse duration. The etching current density varied between 0.5 and 5.0 mA cm −2 with pulse duration fixed at 1 s. Prior to BEE, a direct current was applied to initiate the formation of pores and to obtain their even distribution on the sample surface. [33] The total duration of BEE varied between 2 min and 1 h.
Materials Characterization: Cross-sectional profile of samples was observed by SEM using Zeiss LEO 1540 XB at 4.3 mm of working distance and 20 keV of acceleration voltage, to measure thickness of the layer. The roughness measurements were performed, using the AFM Veeco Dimension 3100 in tapping mode with SSS-NCHR silicon probe and with a scan size of 5 × 5 and 1 × 1 µm 2 . The XRD and XRR measurements were performed using Rigaku Smartlab HRXRD system with Cu Kα X-ray source, Ge (220)×2 monochromator and HYPIX-3000 hybrid pixel array 2D detector. The Powder XRD configuration was used to investigate the crystalline nature of the PGe layer. The XRR was used to measure the critical angle of PGe layer. The porosity (P) was then calculated using Equation (1) where θ PGe and θ Ge correspond to the critical angle of the PGe layer and of the bulk Ge, respectively. [52,53] (1 ) 100 Fast feedback characterization of 100 mm wafers of PGe was performed by ellipsometry using a J.A. Woollam Co. VASE instrument, including mapping of the wafers. Spectral ranged from 500 to 900 nm and a model based on an effective material approximation (EMA) using the Bruggerman analysis mode. This model used a mix of Ge and air to represent the PGe layers on a Ge substrate, [54] allowing thickness and porosity estimation. Ge material uses a Cody-Lorentz built-in function to model the dielectric model of Ge as a wavelength-dependent oscillator, [55,56] we used E 0 and E g as 6 and 1 eV respectively.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.