Direct Synthesis of Hyperdoped Germanium Nanowires

A low-temperature chemical vapor growth of Ge nanowires using Ga as seed material is demonstrated. The structural and chemical analysis reveals the homogeneous incorporation of ∼3.5 at. % Ga in the Ge nanowires. The Ga-containing Ge nanowires behave like metallic conductors with a resistivity of about ∼300 μΩcm due to Ga hyperdoping with electronic contributions of one-third of the incorporated Ga atoms. This is the highest conduction value observed by in situ doping of group IV nanowires reported to date. This work demonstrates that Ga is both an efficient seed material at low temperatures for Ge nanowire growth and an effective dopant changing the semiconductor into a metal-like conductor.

A nisotropic Ge nanostructures have been used as active components for different applications including field effect transistors, 1 lithium ion batteries, 2 solar cells, 3 and humidity sensors. 4 Ge nanowires (NWs) have been successfully prepared by different methods in bottom-up and top-down approaches. 5 The most popular synthesis approach is the use of metal growth promoters in bottom-up processes including vapor−liquid−solid (VLS), 6 supercritical-fluid− liquid−solid (SCFLS), 7 and solution−liquid−solid (SLS) 8 mechanisms as well as the growth by solid metal seeds. 9 Many metallic growth seeds have been described in the literature to result in highly crystalline Ge NWs. 9−11 For some of the above-mentioned applications doping of the NWs is a prerequisite, which can be achieved either by external sources during crystal growth 12−14 or by the incorporation of atoms from metal seeds 15−18 used for the realization of anisotropic crystal constitution. The incorporation of dopants in the Ge matrix has recently been the focus of several studies, and rather effective doping with heavy group III atoms has been observed in low-temperature growth of Ge NWs using In as seeding material 19 and also for Bi in Ge nanoparticles. 20 The electrical properties of the In-containing Ge NWs have not been investigated, which might be related to pronounced twinning of the NWs derived by that approach. Therefore, the actual activity and effect of the nature of the incorporated In atoms on the electronic properties are unknown. In contrast, Bicontaining Ge nanoparticles exhibit an increased charge carrier density when compared to undoped Ge crystals prepared by the same method. 20 Even though Ga is known to be an excellent p-dopant for Ge, to the best of our knowledge, Ga has not been used for vaporbased growth strategies of Ge nanostructures in the past. The electrodeposition using Ga as nucleation sites for the growth of Ge microwires, the so-called electrochemical liquid−liquid growth mode, is the only exception where Ga was identified as an effective growth promoter. 21,22 This type of growth using Ga as an electrode and seed leads to protuberances along the microwires. The Ga-seeded microwires typically showed highly pronounced tapering and incorporation of 8−10 at. % Ga in the Ge matrix. This is accompanied by p-type behavior in the electronic properties. 21 However, the dopant activation was poor and the carrier concentration was several orders of magnitude lower than the actual Ga concentration. 22 First indications for suitable conditions of Ga-mediated Ge NW growth can be deduced from the binary Ge−Ga phase diagram. The Ga/Ge eutectic is very close to the melting point of Ga (29.8°C) with only 0.006 at. % Ge (<1 at. % at 200°C) in the Ga melt ( Figure S1 in the Supporting Information; SI). 23 According to the classification of metal particles acting as catalysts for NW formation, Ga can be considered to be a "type B" catalyst with a eutectic containing less than 1 at. % of the semiconductor material and the absence of germanide phases in the binary phase diagram. 24 Our study illustrates that Ga can be an efficient metal growth seed for single-crystalline Ge NWs at temperatures slightly above 200°C in vapor phase syntheses. During the synthesis ∼3.51 ± 0.29 at. % Ga is incorporated in the growing Ge matrix, leading to the formation of a material with dramatically altered electronic properties. Such hyperdoped Ge NWs with ∼5 × 10 20 cm −3 active p-dopant atoms will exhibit quasimetallic conductivity.

RESULTS AND DISCUSSION
Scanning electron microscopy (SEM) imaging reveals a high density of Ge NWs achieved using a Ga-mediated lowtemperature chemical vapor deposition (CVD) synthesis approach as shown in Figure 1a. A very slight tapering is discernible in these NWs, and the diameters average about 100 nm, while typical lengths are several micrometers. A scanning transmission electron microscopy energy dispersive X-ray spectroscopy (STEM-EDX) map for Ga and Ge near the NW tip is shown in the inset of Figure 1a, nicely visualizing the Ga particle at the tip of the Ge NWs. Transmission electron microscopy (TEM) was used to study microstructural proper-ties of the Ge NWs. For that purpose Ge NWs were deposited onto lacey carbon grids by direct transfer using shear force. The single-crystalline nature of the Ga-seeded Ge NWs is revealed by high-resolution TEM as illustrated in Figure 1b. The fast Fourier transformation (FFT) pattern shown in the inset depicts the growth direction of the Ge NWs to be along the ⟨111⟩ axis, which is the typical orientation for group IV NWs of this diameter. 25 Slight tapering can also be noticed in the TEM image of the inset along a NW of several micrometers and is discussed vide inf ra.
The local composition of the NWs has been determined by STEM-EDX. The Ga particle terminating the NW contains ≤1 at. % Ge according to EDX data, which is slightly higher than the expected value at room temperature. According to the phase diagram, Ge is essentially immiscible in Ga at room temperature (0.006 at. %), but the liquid phase at the growth temperature of 210°C contains up to 1 at. % Ge. 23 Conversely, according to the phase diagram at the growth temperatures applied here a maximum of ∼0.07 at. % Ga should be expected in the Ge NWs. 23 However, STEM-EDX mapping of a NW section reveals a much higher homogeneously distributed concentration of Ga in the Ge matrix ( Figure 2a). The average Ga content determined by EDX in these NWs is 3.51 ± 0.29 at. % (1σ standard deviation). For an overview of NWs in the diameter range 65−150 nm see Figure S2 of the Supporting Information. The accuracy of all EDX values should be

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Article considered to potentially deviate by ±0.5 at. % due to the limited sensitivity of the method. Complementary bulk quantification of hyperdoped Ge NW samples using laserassisted inductively coupled plasma mass spectrometry (LA-ICP-MS) reveals high concentrations of Ga in the Ge NWs. The most accurate comparison of the data obtained by EDX and LA-ICP-MS is based on Ge nanorod samples after removal of all access Ga on the surface, suggesting an overestimation of ∼0.5 at. % by EDX analysis. These investigations will be published in detail elsewhere. An EDX line scan across a typical NW shows the replication of the Ge signal in the Ga channel, and no hints toward a potential core−shell formation have been observed (Figure 2b). This is a representative result for different positions along a NW. The diminishing NW diameter along its axis can be attributed to the incorporation of the Ga growth promoter in the Ge NW body and not caused by an additional vapor−solid growth of Ge on the NW sidewalls. 15 EDX line scans along the Ge NW growth axis reveal a quite homogeneous distribution of Ga with only a minor fluctuation around 3.91 ± 0.27 at. % (1σ) as illustrated in Figure 2c. A radial scan as illustrated in the inset of Figure 2c shows a similar distribution (3.86 ± 0.24 at. %; 1σ). In general, EDX profiles display fluctuations around a mean value in the 3−4 at. % range and thus indicate a random incorporation of Ga in the Ge NW matrix, as can be expected from a self-doping process involving the catalyst particle. In contrast, doping profiles will differ along the NW axis when impurities are preferentially incorporated via vapor−solid growth on the sidewalls, leading to tapering of the NWs. 12 The remarkably high Ga concentration might be a consequence of solute trapping at step edges during the Ge NW growth. This model has been discussed for the incorporation of Al in Si NWs, where unusually high Al concentrations in the Si NW body have been observed. 17,26 According to the literature, the group IV NW growth can proceed with successive addition of bilayers through a step flow process, 27 and during this process catalyst atoms can be trapped in the bilayer due to the high growth rate. However, the NW growth presented here is quite slow when considering the growth time of hours. Nevertheless, a step flow process to form the bilayer could be assumed as being fast even though the overall growth rate is slow. The actual bilayer growth via step flow requires an initial nucleation event with a distinct energy barrier that has to be overcome. A reason for the small overall growth rate can be the slow decomposition of the Ge precursor and thus an extended time span for the buildup of sufficient supersaturation in the Ga growth seed to overcome the nucleation barrier. Once the new layer is growing, the supersaturation drops dramatically and enrichment of the growing materials has to take place before a new layer forms. The actual efficiency of incorporation during this crystal growth process is most likely due to the similar atomic radii of Ga and Ge and therefore an absence of strain by the incorporation of Ga in the Ge lattice. 28 Therefore, we propose the same model of solute trapping as applied to Al incorporation in Si NWs. 17 Within this scenario the observed high Ga content in the Ge matrix becomes plausible. A direct experimental proof of the trapping of the Ga growth promoter in the Ge matrix during the Ge NW growth could most probably be achieved using a combined strategy of presented methods for Al-seeded Si NWs, but would ideally require in situ TEM imaging facilities. 27,29 However, the high Ga concentration trapped in the Ge matrix represents a metastable material composition. At temperatures close to the growth temperature no changes in the composition could be recorded for heating cycles of 10 h at 250°C due to limited and very slow diffusion processes at these temperatures. Typical for metastable compositions, increased annealing temperatures lead to diffusion processes and thus Ga segregation. This effect can be illustrated best monitoring twin structures, which are a minor fraction in the nanowire samples. Figure S3 shows a twin along the axis of a Ge 0.97 Ga 0.03 NW grown at 230°C without a sign of Ga enrichment at the interface even after 10 h at 250°C, while a similar twin heated for 6 h at 400°C shows not only strain effects in the TEM but also Ga enrichment/segregation at the interface of both crystals in the STEM-EDX. The twin structures are ideal to illustrate this effect because the mobility of the segregated Ga at interfaces is limited when compared to a surface diffusion. Similar phase separation of a component in a metastable Gebased alloy can be found in the well-known GeSn system when the crystalline phase is heated above a threshold temperature, which depends on the initial composition. 30 The electronic properties of the hereafter called Ge 0.97 Ga 0.03 NWs have been determined after treatment in 2% hydrofluoric acid to remove any Ga from the NWs surface. The NWs have been deposited on Si substrates with a 100 nm thick, thermally grown SiO 2 layer by dry transfer and contacted by aluminum pads fabricated by electron-beam lithography, sputter deposition, and lift-off techniques. Two-terminal I−V measurements of Ge 0.97 Ga 0.03 NWs with different diameters as well as an intrinsic Ge NW grown by Au-mediated CVD are shown in Figure 2a.
The Ge 0.97 Ga 0.03 NW devices integrated in two-point measurement modules show ohmic behavior as expected for a highly doped semiconductor in conjunction with very high current levels. The thereof calculated resistance of the hyperdoped Ge 0.97 Ga 0.03 NWs is about 3 orders of magnitude lower than for the intrinsic Ge NW and thus amply illustrates the strong impact of the incorporation of the Ga seed material in the Ge crystal (lower inset of Figure 3a). Due to the high conductivity values of the Ge 0.97 Ga 0.03 NWs, we neither expected nor could measure any noticeable field effect response in the back-gated NW field effect transistor. Also, in lowtemperature resistance measurements in transverse magnetic fields we found a negligibly small magnetoresistance effect. Spread in the two-probe I−V characteristics of different NWs (see Figure S4 of the Supporting Information) could be traced back to variations in the individual contact resistances by complementary four-probe measurements. From four-point measurements exemplarily shown in Figure 3b, we determined resistivity values quite typically to be as large as 300 μΩcm for Ge 0.97 Ga 0.03 NWs, while intrinsic Ge NWs grown by using Au as growth promoter reveal resistivity values of about 11 Ωcm 30 as described in the literature.
From the resistivity values measured in this study we deduce an electronically active impurity concentration of ∼5 × 10 20 cm −3 for p-dopants, such as Ga, in bulk Ge samples using literature data. 31 This is far above the solubility limit of Ga in Ge at thermodynamic equilibrium, which would lead to a maximum Ga concentration of 3.1 × 10 19 cm −3 (∼0.07 at. %) according to the phase diagram. 23 Therefore, the value determined here suggests that approximately one-third of the ∼3.5 at. % Ga atoms (1.5 × 10 21 cm −3 ) are electronically active and are expected to be at substitutional sites in the Ge lattice. In addition, Ge 0.97 Ga 0.03 NWs can withstand remarkably high

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Article currents of more than 1 mA, corresponding to about 12 MA/ cm, 2 before device failure occurs ( Figure S4 inset).
In contrast, electrodeposition of Ge micro/nanowires using Ga as electrode material also leads to the incorporation of Ga in the Ge matrix but results in strongly tapered nano/microwires as well as p-type semiconductor behavior. 21,22 Even though these anisotropic Ge structures contain twice or three times as much Ga (8−10 at. %) when compared to the material described herein, the effect on the electronic properties is very low. The actual number of electronically active Ga atoms is determined to be about 2.3 × 10 15 cm −3 , correlating to ∼10 −7 at. % of electronically active Ga dopants. The differences could be related to temperature effects during growth (40°C for electrodeposition vs 210°C in this study), the actual growth rate, crystal quality, and Ga being incorporated at actual substitutional sites. The extraordinarily large effect on the electronic properties can be also manifested comparing the impact of ∼5 at. % Al incorporation in Si NWs, where only a density of ∼1 × 10 19 cm −3 electronically active impurities has been observed. These values are more than ∼50 times lower than we have observed in the hyperdoped Ge 0.97 Ga 0.03 NWs.
Temperature-dependent resistance measurements have been recorded for Ge 0.97 Ga 0.03 NW devices in four-terminal configurations and compared to Au-seeded Ge NWs. The Au-seeded and thus nominally intrinsic Ge NW shows an increase in resistivity of 6 orders of magnitude under cooling from 300 to 4 K, while the Ge 0.97 Ga 0.03 NWs exhibit a weakly metallic-like temperature-dependent resistivity decrease with a residual resistance ratio of about 1.2 ( Figure 4). A similar behavior is reported for other dopants, such as group VI elements in Si, showing the same temperature dependence when unusually high concentrations of dopants are incorporated in the semiconductor crystal. 32 In these studies the notion "hyperdoping" was coined and represents concentrations of the dopants exceeding their thermodynamic solubility limit. 33,34 These high-impurity concentrations can form a new impurity band that leads to a transition of the semiconductor to a metallic-like conductor (semiconductor−metal transition) instead of an impurity state within the band gap of the semiconductor for small and intermediate doping levels. Hence, following this reasoning the Ge 0.97 Ga 0.03 NWs are hyperdoped with Ga due to their described electronic behavior and the high Ga level representing ∼50 times the solubility limit at the growth temperature and exceeding even 3−4 times the maximum solubility observed at high temperatures. 23 Upon further cooling, a small drop in resistance of ∼30 Ω at 1.6 K is observed (Figure 4 inset and Figure S5), which is suppressed at the lowest temperature of 0.269 K by applying a weak overcritical magnetic field of less than 250 mT ( Figure  S6). This resistance drop is associated with the Al electrodes used in the two-probe measurement that have been fabricated by sputtering and are expected to contain a small amount of oxygen impurities, causing the critical temperature increase of Al (1.1 K in the clean limit) to 1.6 K. 35 The Ge 0.97 Ga 0.03 NW measured down to 0.269 K did not show a superconducting transition, but a possible onset of superconductivity below this temperature cannot be ruled out by this study

CONCLUSION
We demonstrate the successful Ga-assisted growth of Ge NWs at low temperatures of 210°C. This process leads to hyperdoping of the Ge NWs with Ga concentrations of ∼3.5 ± 0.29 at. %, which is ∼50 times higher than the solubility limit

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Article at this temperature. The high Ga incorporation efficiency is probably due to solute trapping during the growth of Ge bilayers. Hyperdoping of Ga in Ge leads to metal-like behavior conductivity of the NWs, and the importance of contact resistances in devices prepared using Al as contact material was identified.

METHODS
All synthetic procedures and handling of the chemicals for the nanostructure synthesis have been carried out using Schlenk techniques or an argon-filled glovebox (MBraun). Solvents were dried over sodium and stored in a glovebox. The (pentamethylcyclopentadienyl)gallium(I) precursor (Ga(C 5 Me 5 ); GaCp*) was prepared using sonochemical synthesis of GaI and subsequent salt elimination using KCp* in dry benzene according to the literature. 36 tert-Butylgermane (TBG; (C 4 H 9 )GeH 3 ) was purchased from Gelest.
Nanostructure Synthesis. tert-Butylgermane [76 mg (572 μmol)−152 mg (1144 μmol)] was loaded in a 5 mL cell from HIP using a glovebox. The silicone substrates were infiltrated by GaCp* and introduced in the cell before the vessel was closed. Heating this vessel for 6−12 h at temperatures of 210−230°C results in the growth of dense nanowire meshes on the silicone substrate. Data presented herein are limited to the NWs grown at 210°C.
Post growth annealing was performed in a quartz tube at 250−400°C for 6−10 h under a 10% H 2 /90% N 2 atmosphere to test the stability of the material.
Nanostructure Characterization. The Ge NWs were analyzed using a FEI Inspect F50 scanning electron microscope. The Ge NWs were deposited on lacey carbon copper grids by dry transfer using shear force for TEM characterization (Plano). In this study, a FEI TECNAI F20 operated at 200 kV and equipped with high angle annular dark field (HAADF) STEM and EDX detectors was used. The limited accuracy of the EDX analysis can lead to a potential deviation by ±0.5 at. % of the values stated here. The elemental maps were recorded and quantified using the AMETEK TEAM package. The images were recorded and treated using Digital Micrograph software. LA-ICP-MS measurements were performed using a commercially available laser ablation system (New Wave 213, ESI, Fremont, CA, USA) with a frequency-quintupled 213 nm Nd:YAG laser in combination with a quadrupole ICP-MS instrumentation (Thermo iCAP Qc, ThermoFisher Scientific, Bremen, Germany). For quantification, 69 Ga was compared with the 76 Ge signal while standards of metal ratios between 1:99 and 5:95 Ga/Ge were prepared using the metal halogenides dissolved in aqueous potassium hydroxide.
Electrical Characterization. The vapor-grown Ge NWs were deposited by dry transfer onto a highly p-doped Si substrate with a 100 nm thick, thermally grown SiO 2 layer and predefined macroscopic Ti− Au bonding pads. Individual NWs were contacted with 150 nm thick Al pads by electron beam lithography, Al sputter deposition preceded by a HI dip (5 s using 14 % HI to remove any germanium oxide), and lift-off techniques.
The electrical measurements at room-temperature and ambient conditions were performed using a combination of a semiconductor analyzer (HP 4156B) and a probe station. To minimize the influence of ambient light as well as electromagnetic fields, the probe station was placed in a dark box.
Low-temperature measurements (4−300 K) were performed in vacuum at a pressure of approximately 2.5 × 10 −5 mbar using a 4 He cryostat (Cryo Industries CRC-102) and a semiconductor analyzer (Keysight B1500A). Temperature-dependent resistance measurements in the range 0.269−4 K were performed in a 3 He cryostat employing a sourcemeter (Keithley, 2600) in two-probe configuration at a fixed current of 1 μA. Magnetic field dependent measurements were done using a NbTi superconducting solenoid.

* S Supporting Information
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.7b07248.
Experimental procedures as well as a detailed description of the characterization methods, an overview of determined Ga content in several NWs, a J/V plot of several devices in two-point geometry, a low-temperature resistance plot, and a B/R plot at temperatures between 0.269 and 1.6 K (PDF)