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Electrical transport properties of Ge-doped GaN nanowires
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Nanotechnology Nanotechnology 26 (2015) 135704 (8pp)
doi:10.1088/0957-4484/26/13/135704
Electrical transport properties of Ge-doped GaN nanowires M Schäfer1, M Günther1, C Länger2, J Müßener1, M Feneberg3, P Uredat1, M T Elm1, P Hille1, J Schörmann1, J Teubert1, T Henning1, P J Klar1 and M Eickhoff1 1
I. Physikalisches Institut, Justus-Liebig-Universität Gießen, Heinrich-Buff-Ring 16, D-35392 Gießen, Germany 2 Institut für Angewandte Physik, Justus-Liebig-Universität Gießen, Heinrich-Buff-Ring 16, D-35392 Gießen, Germany 3 Institut für Experimentelle Physik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, D39106 Magdeburg, Germany E-mail: [email protected] Received 1 December 2014, revised 11 February 2015 Accepted for publication 14 February 2015 Published 11 March 2015 Abstract
The conductivity and charge carrier concentration of single GaN nanowires (NWs) doped with different concentrations of Ge were determined by four-point resistivity and temperaturedependent Seebeck coefficient measurements. We observed high carrier concentrations ranging from 9.1 × 1018 to 5.5 × 1019 cm−3, well above the Mott density of 1.6 × 1018 cm−3, and conductivities up to 625 S cm−1 almost independent of the NW diameter. The weak temperature dependence of the conductivity between 2 and 10 K could be assigned to the formation of an impurity band. For the sample with the highest conductivity metallic behaviour was found, indicated by a positive temperature coefficient of the resistivity. The near band edge emission analyzed by micro-photoluminescence spectroscopy showed only a small increase of the peak width up to 70 meV and no spectral shift for carrier concentrations up to 5.5 × 1019 cm−3. The latter was attributed to the simultaneous influence of band filling, band gap renormalization, and strain. Keywords: GaN nanowires, electrical transport properties, Seebeck coefficient, micro photoluminescence, charge carrier concentration, gallium nitride, molecular beam epitaxy (Some figures may appear in colour only in the online journal) 1. Introduction
different techniques [7–9]. Quantitative analysis of the resistance in four-point probing geometry or determination of carrier concentration by thermoelectric characterization is only reported for typically longer and thicker Si-doped microwires grown by MOCVD revealing a conductivity and carrier concentration up to 2700 S cm−1 and 2.6 × 1020 cm−3, respectively [10]. Germanium (Ge) as a shallow donor in GaN has a similar activation energy of approximately 20 meV as Si [11] and has been proven to be an alternative dopant for GaN NWs and AlN/GaN NW heterostructures grown by PAMBE on Si(111) substrates [12, 13]. Since the ionic radius of the Ge atom is similar to that of Ga the bond length to nitrogen changes only by 1.4% compared to 5.5% for Si [14], resulting in substantially smaller lattice deformations and the absence of
GaN nanowires (NWs) currently attract intense research interest. Due to lateral strain relaxation they exhibit a low density of extended structural defects and hence are regarded as an ideal platform for the realization of nanoscale electronic and optoelectronic devices with improved performance and stability [1–3]. Additionally, their high surface to volume ratio makes them suitable for applications in photo detectors or different types of chemical sensors [4–6]. For such applications understanding and control of doping processes is a basic requirement. Commonly, silicon is used as a donor for n-type GaN NWs grown by plasma-assisted molecular beam epitaxy (PAMBE) and the influence of Si-incorporation on the optical and electrical properties has been studied by 0957-4484/15/135704+08$33.00
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structural degradation in thin GaN:Ge films even for very high carrier concentrations of 4 × 1020 cm−3, as reported in [15]. The determination of the free carrier concentration of single NWs by Hall measurements has recently been demonstrated but requires high processing effort [16–18] and bears difficulties in interpretation due to the nanosized geometry [19]. Common top- [9, 20] and back-gate [1, 9] fieldeffect transistor measurements are often questioned because of uncertainties determining the gate capacitance and hysteresis effects caused by interface charging [21]. Extraction of the charge carrier density from the temperature-dependent Seebeck coefficient for degenerate NWs was reported in [10, 22] and is also pursued in the present work. We present a systematic study of the influence of Gedoping on the electrical properties of single GaN NWs. The electrical conductivity is determined by four-point resistivity measurements and the free carrier concentration is analyzed by temperature-dependent Seebeck coefficient measurements. The relation of carrier concentration and photoluminescence properties of single NWs is also discussed.
was measured in a range between 1.6 and 280 K using a bath cryostat cooled with liquid helium. For temperature-dependent analysis of the Seebeck coefficient, samples with a layout shown in figure 1(b) were fabricated. A meandered micro-heater (Ti/Au) placed in the vicinity of the NW was used to apply a thermal gradient along the NW. To measure the thermoelectric voltage the NW is contacted by two branched metal leads which also serve as four-point resistive thermometers5, each calibrated at different temperatures stabilized in the cryostat and used to determine the temperature difference ΔT. Thermoelectric measurements were performed in an Oxford MicroStatHiResII flow cryostat and a temperature range from 80 K (5 K) to 280 K using liquid nitrogen (helium). Single NW micro photoluminescence spectroscopy (μPL) was performed in the same cryostat at T = 4 K. The 325 nm excitation light from a HeCd laser was focused by a 20-fold UV objective (NA 0.4) onto the NW, and the emitted PL was collected with the same objective, dispersed using a 3600 lines mm−1 grating in a 250 mm spectrometer, and detected with a cooled charge-coupled device camera.
2. Sample preparation and experimental details 3. Results and discussion
Non-intentionally doped (n.i.d.) and Ge-doped (0001̄)oriented GaN NWs were grown in a self-assembled catalystfree process by PAMBE on Si(111) substrates using nitrogenrich growth conditions according to the growth process described in [12]. The length of the investigated NWs varied between 1.5 and 2 μm, their diameter between 40 and 120 nm. Germanium was evaporated from an effusion cell operated between 900 and 950 °C, corresponding to beam equivalent pressures BEPGe between 5.0 × 10−10 and 1.3 × 10−9 mbar. The average Ge-concentrations [Ge] of the NW ensembles were determined to 1.0 × 1020, 1.4 × 1020, 1.6 × 1020, and 3.3 × 1020 cm−3 by a combination of time-of-flight secondary ion mass spectrometry and energy dispersive x-ray spectroscopy in a transmission electron microscope [12]. The NWs were detached from the substrate in an ultrasonic bath and dispersed on a thermally wet oxidized Si(100) substrate with an oxide thickness of 775 nm. Electrical contacts were processed by combined photo- and electron beam lithography4. A Ti/Au (25 nm/200 nm) metallization was thermally evaporated without additional cleaning steps and patterned by a lift-off process. One of the resulting four-point structures for conductivity measurements of a 2 μm long NW is exemplarily shown in figure 1(a). After annealing for 60 s at 550 °C in vacuum the contacts show Ohmic behavior. The conductivity of the NW middle segment was calculated based on the room temperature resistance obtained from dc I–V curves, taking the NW diameter determined by SEM images into account. The temperature-dependence of the resistance
3.1. Conductivity
The room temperature two-point resistance of n.i.d. NWs shows strong variations, even for NWs from the same ensemble. As shown in figure 1(c), highly resistive NWs (type 1) with a resistance above 1 MΩ (crosses) as well as conductive NWs (type 2) with a resistance in the range of 40 – 200 kΩ (open squares) are found, both comparable to reported values for n.i.d. NWs [8, 23]. Since the diameter of both types of NWs varies in the same range between 45 and 80 nm, the different conductivities are most likely caused by the presence of structural defects or unintentionally incorporated impurities whose origin will be discussed below. To analyze the contact resistance current voltage (I–V) measurements in two-point and four-point geometry at room temperature were compared for n.i.d. and Ge-doped NWs. Figure 1(d) shows the deduced resistances of the middle segment of 36 conductive6 single NWs in both geometries (two-point: R2P, open symbols; four-point: R4P, filled symbols). For clarity the x-axis is divided into five sectors representing the respective Ge-concentrations [Ge] of the NW ensemble between 0 (for n.i.d. NWs) and 3.3 × 1020 cm−3. 5
Usually thermocouples are used to connect macroscopic samples to determine the Seebeck coefficient in order to completely exclude the contribution of the cables to the thermoelectric voltage. Due to the nanosized geometry of NWs this cannot be done and hence a thermoelectric voltage drop across the gold leads connecting the hot and cold part of the NW to thermal equilibrium cannot be excluded. Since the Seebeck coefficient of gold is in the order of 1.8 μV K−1 at room temperature (0.8 μV K−1 at 80 K) the influence on the measurements should be small compared to the Seebeck coefficient of the NWs (20 to 120 μV K−1). 6 Highly resistive NWs are not included, since their resistance measured in four-point geometry is almost the same as in two-point geometry.
4
For processing a SUSS MA 56 mask aligner, a Jeol JSM 7001F thermal field emission scanning electron microscope (SEM) equipped with a XeDraw2 writing system from XENOS Semiconductor Technologies GmbH and single resist (PMMA) layer technology were used. 2
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Figure 1. (a) SEM image of a 2 μm long NW contacted in four-point geometry. (b) SEM image of a 2 μm long NW with two resistive
thermometers and micro heater. (c) Two-point resistance of highly resistive (crosses) and conductive (squares) n.i.d. NWs as a function of their diameter. (d) Resistance of middle segments in individual NWs measured in two-point (R2P: open symbols) and four-point (R4P: filled symbols) geometry for 36 conductive NWs with different Ge-concentrations. The measurement error is smaller than the size of the symbols. Vertically aligned R2P and R4P values of equal color correspond to the same NW. Dashed (solid) lines show the average value of R2P (R4P). Inset in (d): conductivity of the NWs as a function of the average Ge-concentration. The conductivity was obtained from the four-point resistance considering the individual NW geometry, as reported in [12]. The error bars are dominantly caused by the uncertainties in the NW geometry determined from SEM images. The line is a guide to the eye.
The values for R2P show strong wire-to-wire variations and an overall decrease by more than two orders of magnitude with increasing [Ge]. However, the average values (dashed lines) do not exhibit a clear trend. In contrast, the results for R4P show significantly smaller variations and the mean values (solid lines) systematically decrease over two decades from 40 kΩ to 550 Ω. Hence, the strong fluctuations of R2P are caused by variations in the contact resistance which turns out to be in the same order of magnitude as the four-point resistance of the NW middle segment. This demonstrates that four-point measurements are inevitable for reliable electric characterization of single NWs. To obtain the electrical conductivity σ the NWs have been approximated to be of cylindrical shape with the individual diameter and length of the middle segment in the NW due to individual NW processing determined by SEM analysis. The results in the inset of figure 1(d) show a continuous increase of the conductivity from 35 S cm−1 to above 400 S cm−1 for an increasing [Ge] up to 1.6 × 1020 cm−3. For higher doping concentrations up to [Ge] = 3.3 × 1020 cm−3 the conductivity saturates at around 450 S cm−1, most likely due to decreasing carrier mobility caused by a high density of ionized donors, self-compensation, or electrically inactive incorporation of Ge. A maximum conductivity of 625 S cm−1 is observed. The wire-to-wire fluctuation can be caused by variations in the concentration of active Ge donors [12] or by mobility variations due to different densities of structural defects. Since the geometric diameter of the NWs was used to
calculate the conductivity and an influence of a possible depletion region was neglected, the values represent a lower limit (see discussion below). Nevertheless, the obtained values are in good agreement with reports on Ge-doped thin films with conductivities in the range from 30 to 1500 S cm−1 for carrier concentrations of 2 × 1018 – 2 × 1020 cm−3, respectively [15, 24]. The dependence of the conductivity on the NW diameter for different doping concentrations is shown in figure 2. For n.i.d. NWs of type 2 a systematic increase of the conductivity with increasing diameter is observed, in agreement with the results reported in [23, 25]. In contrast, the conductivity of Ge-doped NWs does not show a systematic dependence on their diameter. Generally, the electrical properties of GaN NWs are strongly affected by surface band bending [23, 25]. An increase of the donor concentration above a critical value leads to a decreasing depletion width and the formation of a conductive channel inside the NWs [8, 25]. Hence, a strong dependence of the conductance on the NW diameter is expected for undoped or moderately doped NWs while for high doping concentrations only a weak dependence is anticipated. Accordingly, for all Ge-doped NWs investigated here the influence of the depletion region on the conductivity can be neglected. Furthermore a residual carrier concentration above 2.8 × 1018 cm−3 can be estimated for type 2 n.i.d. NWs according to the model proposed in [23], as these NWs show a measurable conductivity already for a diameter of 50 nm. 3
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Figure 2. Conductivity for NWs with different Ge-concentration as a function of the NW diameter. The gray shaded area depicts the region spanned by n.i.d. NWs.
This value is already above the reported Mott density of 1.6 × 1018 cm-3 for bulk GaN [26]. We attribute the fairly high conductivity of n.i.d. NWs to the presence of oxygen and silicon as residual impurities. Furtmayr et al demonstrated the diffusion of Si from the substrate into GaN NWs by electron energy loss spectroscopy (EELS) [27]. Due to the limited resolution of EELS the presence of Si could only be detected in close vicinity of the interface. In order to investigate the occurrence of Si diffusion by conductivity measurements n.i.d. NWs with a length of 2 μm contacted by six individual terminals, allowing spatially resolved conductivity measurements in three different segments, were prepared (inset of figure 3). The results for nine different NWs in figure 3 show that the conductivity decreases by almost one decade from 80 to 10 S cm−1 when the distance to the NW base is increased from 600 to 1300 nm. As the diameter is almost constant along the NW these changes are attributed to diffusion of Si from the Si(111) substrate into the NW, contributing to the residual conductivity of n.i.d. NWs with a diameter down to 50 nm. Since at all positions the conductivity of n.i.d. NWs is significantly smaller than that of the lowest Ge-doped NWs, the effect of co-doping can be neglected for the extraction of the corresponding electrical parameters for doped NWs. The temperature-dependence of the resistivity was analyzed between 1.6 and 280 K for selected NWs with different conductivities and doping concentrations (NWs of the n.i.d., [Ge] = 1.4 × 1020 cm−3, and [Ge] = 1.6 × 1020 cm−3 ensemble). For all investigated NWs only a weak influence of the temperature on the resistivity and an almost constant value at temperatures below 10 K was found, as presented in figure 4. The extracted activation energy between 70 and 280 K for the NW with a conductivity of 34 S cm−1 (310 S cm−1) is (5 ± 1) meV ((2 ± 1) meV) which is significantly lower than the ionization energy of Ge in the case of low doping concentrations (around 20 meV for n = 3 × 1017 cm−3 [11]) and indicates the formation of an impurity band due to high
Figure 3. Spatially resolved conductivity for nine different single n.i. d. NWs. Each NW is represented by one type of symbol. The three individual segments are marked by A, B, and C in accordance with the sample structure shown in the inset.
Figure 4. Arrhenius plot of normalized resistance (R(T)/R0(280 K)) for three NWs with different conductivities.
concentrations of incorporated Ge atoms [28, 29]. For the investigated NW with the highest conductivity, we have observed a positive temperature coefficient of the resistivity, i.e. metallic behavior, further confirming the high donor concentration in Ge-doped GaN NWs. 3.2. Charge carrier concentration
To determine the charge carrier concentration of individual Ge-doped GaN NWs we followed an approach based on temperature-dependent measurements of the Seebeck coefficient as reported for degenerate GaN NWs in [22] and Sidoped GaN microwires in [10]. Using the structures shown in 4
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Figure 6. Seebeck coefficient as a function of temperature for one n.i.d. and four Ge-doped GaN NWs. The error is in the order of the size of the symbols.
Figure 5. Thermoelectric voltage as a function of heater power and
resulting temperature difference ΔT. Inset: transient thermoelectric voltage for different heating powers.
a lower limit7 adapting equation (1) derived from semi-classical Mott relation [22].
figure 1(b) the transient thermoelectric voltage of individual NWs was measured. The voltage instantaneously increases with the heating power steps as exemplarily shown for a temperature of 282 K and a NW with [Ge] = 1.0 × 1020 cm−3 in the inset of figure 5. The thermoelectric voltage as a function of heating power and the resulting temperature difference along the NW linearly increases from −40 to 250 μV for heater powers up to 5 mW and a corresponding temperature difference ΔT up to 3.5 K as depicted in figure 5. The offset at ΔT = 0 is caused by thermoelectric voltages in the cables. Evaluation of the slope yields a Seebeck coefficient of Q = −82.3 μV K−1 at the average temperature of 282 K. This Seebeck coefficient is comparable to results reported for ntype GaN wires [10, 22] and GaN thin films [30] with carrier concentrations above 1 × 1019 cm−3. Following this method, the Seebeck coefficients for one type 2 n.i.d. NW and two individual Ge-doped NWs from each of the ensembles with [Ge] = 1.0 × 1020 cm−3 and [Ge] = 1.6 × 1020 cm−3 were determined at different temperatures between 80 and 280 K, as presented in figure 6. The error is in the order of the size of the symbol. A linear decrease of the Seebeck coefficients with increasing temperature is observed for all investigated samples. The absolute value of the extracted slope decreases with increasing [Ge]. The linearity is maintained for temperatures down to 5 K, as exemplarily shown for the n.i.d. NW. This further confirms the degenerate doping level of the n.i.d. and Ge-doped NWs due to doping concentrations above the Mott density. Hence, assuming parabolic bands as well as a constant effective mass, which is valid for carrier concentrations up to 1020 cm−3 [31, 32] and an energy independent scattering time the carrier concentration n can be estimated as
n=
⎛ ⎞3 T⎟ ⎜ π 2k B2 m* ⋅ ⎟ ⎜⎜ Q⎟ 2 2/3 2 π ⋅ ℏ q 3 ⎝ ⎠
( )
(1)
Here, kB is the Boltzmann constant, q the elementary charge, ℏ reduced Planck’s constant, m* = 0.231 × me the electron (density of states) effective mass [31, 32], T the temperature, and Q the Seebeck coefficient. In contrast to [10] we have evaluated the slope of the linear dependence shown in figure 6 instead of just one Seebeck coefficient at a certain temperature to exclude uncertainties in the determination of the absolute temperature. The error in the determination of the slope is small and can be neglected in comparison to the uncertainty in the effective mass, which has a more significant influence on the results. Using equation (1) we obtain carrier concentrations between 9.1 × 1018 and 5.5 × 1019 cm−3 for the five individual NWs as summarized in table 1. The extracted values for n systematically increase with increasing Ge-concentration. They also reflect the wire-towire variations observed in conductivity. The ratio of n and [Ge] varies in the range of 20% to 35% for the investigated single NW in relation to the respective ensemble values, which can be explained–beside the difference of measurements on NW ensembles and on single NW level–by electrically inactive Ge or self-compensation effects at high doping concentrations. The extracted carrier concentrations and the conductivities obtained for single NW of the same 7 The corrections suggested in [10] to address the energy-dependent relaxation time would lead to slightly higher carrier concentrations.
5
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ensembles are in very good agreement with data reported in literature [15, 24, 25]. The high carrier concentration of the n.i.d. NW is attributed to residual oxygen and Si donors due to diffusion, as reported above. All carrier concentrations exceed the Mott density, in accordance with the previous results of the diameter-dependence and weak temperature-dependence of the conductivity. Based on these results the carrier mobility can be estimated to be in the range from 10 to 43 cm2 V−1s−1 for the n.i.d. NWs and 34 to 86 cm2 V−1s−1 for NWs with [Ge] = 1.0 × 1020 cm−3 and [Ge] = 1.6 × 1020 cm−3. These values are reasonable compared to reported values for NWs and thin films [1, 10, 15, 24, 25, 33–35]. The reduced mobility of the n.i.d. NWs can be partially attributed to the underestimated conductivity of n.i.d. NWs due to the neglected depletion region resulting in the diameter dependent conductivity, as discussed above. Further, an increase of the carrier mobility with increasing carrier concentration can be expected as, due to the related increase in surface band bending, the contribution of surface scattering is reduced.
Figure 7. Micro photoluminescence spectra of five single NWs at T = 4 K with different carrier concentrations (determined by temperature-dependent analysis of the Seebeck coefficient). The spectra are normalized and vertically shifted for clarity. Experimental data are plotted in black, the modeled luminescence line shapes in red. The vertical green (dotted) and blue (solid) lines mark the positions of Egap + ΔEBGR and Egap + ΔEBGR + ΔEBMS, respectively.
3.3. Photoluminescence
The five single individual NWs with carrier concentrations from 9.1 × 1018 to 5.5 × 1019 cm−3 that were analyzed by Seebeck coefficient measurements, were additionally analyzed by μPL at T = 4 K (cf figure 7). The spectra of all NWs are dominated by a sharp near band edge emission around 3.485 eV. While the emission broadens only slightly from 35 to 70 meV (FWHM) with increasing carrier concentration, no spectral shift is observable even for the highest doped sample. This behavior can be attributed to a compensation of a blue shift due to band filling effects known as Burstein–Moss shift (BMS) by band gap renormalization (BGR) due to many body effects as recently reported in [32] for GaN:Si and GaN:Ge samples with carrier concentrations up to 1019 cm−3. Fits to the experimental line shapes according to the model used in [32] are plotted in red in figure 7. The position of the Fermi energy represented by Egap + ΔEBGR + ΔEBMS and the renormalized band gap given by Egap + ΔEBGR are marked by blue and green vertical lines, respectively. The carrier concentration obtained from the Seebeck coefficient measurement was used as a fixed input parameter for the fitting procedure. In order to model the experimental line shapes based on the discussion in [32], a rigid shift of the spectra due to strain had to be assumed changing the value of Egap. If the strain in the NWs is assumed to be of biaxial type, it ranges from compressive (εxx = −5.3 × 10−4) for the n.i.d. NW with 9.1 × 1018 cm−3 to tensile (εxx = 2.1 × 10−3) for the highest doped NW. While this increase in tensile strain as a function of increasing germanium incorporation is in agreement with the findings of [36], its microscopic origin is not clear at the moment.
Table 1. Beam equivalent pressure BEPGe and Ge-concentration [Ge] of the respective NW ensemble, slope deduced from graph in figure 6 and calculated carrier concentration n for five different doped GaN NWs.
NW 1 2 3 4 5
BEPGe (10−9 mbar)
[Ge] (1020 cm−3)
Slope Q/T (μV K−2)
n (1019 cm−3)
n.i.d. 0.5 0.5 1.0 1.0
n.i.d. 1.0 1.0 1.6 1.6
−0.53 −0.31 −0.27 −0.20 −0.16
0.91 2.05 2.57 4.11 5.53
4. Conclusion The electronic properties of individual Ge-doped GaN NWs were systematically investigated. The obtained results conclusively demonstrate the excellent donor properties of Ge in GaN NWs grown by PAMBE. By elimination of the contact resistances a continuous increase of the conductivity with increasing Ge-concentration up to an average value above 400 S cm−1 for [Ge] = 1.6 × 1020 cm−3 was found and a maximum conductivity of 625 S cm−1 was observed. The conductivity of the Ge-doped NWs was independent of the NW diameter and showed only weak temperature dependence. Emerging metallic behavior for a NW with a conductivity of 436 S cm−1 further confirms that Ge is an efficient donor in GaN NWs. The charge carrier concentrations in the range of 6
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9.1 × 1018 – 5.5 × 1019 cm−3, deduced from analysis of the temperature-dependent Seebeck coefficient, were above the Mott density and confirmed electronic degeneracy. The near band edge emission at constant energy, independent of the carrier concentration, was assigned to an increase of tensile strain with increasing charge carrier concentration due to the incorporation of germanium as shallow donor.
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Acknowledgments Authors from the Justus-Liebig-Universität acknowledge financial support within the LOEWE program of excellence of the Federal State of Hessen (project initiative STORE-E).
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[35] Cimpoiasu E, Stern E, Klie R, Munden R A, Cheng G and Reed M A 2006 The effect of Mg doping on GaN nanowires Nanotechnology 17 5735 [36] Xie J, Mita S, Hussey L, Rice A, Tweedie J, LeBeau J, Collazo R and Sitar Z 2011 On the strain in n-type GaN Appl. Phys. Lett. 99 141916
[32] Feneberg M et al 2014 Band gap renormalization and Burstein–Moss effect in silicon- and germanium-doped wurtzite GaN up to 1020 cm−3 Phys. Rev. B 90 075203 [33] Rode D L and Gaskill D K 1995 Electron Hall mobility of NGaN Appl. Phys. Lett. 66 1972–3 [34] Cimpoiasu E, Stern E, Cheng G, Munden R, Sanders A and Reed M A 2006 Electron mobility study of hot-wall CVD GaN and InN nanowires Braz. J. Phys. 36 824–7
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Electrical transport properties of Ge-doped GaN nanowires
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Nanotechnology Nanotechnology 26 (2015) 135704 (8pp)
doi:10.1088/0957-4484/26/13/135704
Electrical transport properties of Ge-doped GaN nanowires M Schäfer1, M Günther1, C Länger2, J Müßener1, M Feneberg3, P Uredat1, M T Elm1, P Hille1, J Schörmann1, J Teubert1, T Henning1, P J Klar1 and M Eickhoff1 1
I. Physikalisches Institut, Justus-Liebig-Universität Gießen, Heinrich-Buff-Ring 16, D-35392 Gießen, Germany 2 Institut für Angewandte Physik, Justus-Liebig-Universität Gießen, Heinrich-Buff-Ring 16, D-35392 Gießen, Germany 3 Institut für Experimentelle Physik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, D39106 Magdeburg, Germany E-mail: [email protected] Received 1 December 2014, revised 11 February 2015 Accepted for publication 14 February 2015 Published 11 March 2015 Abstract
The conductivity and charge carrier concentration of single GaN nanowires (NWs) doped with different concentrations of Ge were determined by four-point resistivity and temperaturedependent Seebeck coefficient measurements. We observed high carrier concentrations ranging from 9.1 × 1018 to 5.5 × 1019 cm−3, well above the Mott density of 1.6 × 1018 cm−3, and conductivities up to 625 S cm−1 almost independent of the NW diameter. The weak temperature dependence of the conductivity between 2 and 10 K could be assigned to the formation of an impurity band. For the sample with the highest conductivity metallic behaviour was found, indicated by a positive temperature coefficient of the resistivity. The near band edge emission analyzed by micro-photoluminescence spectroscopy showed only a small increase of the peak width up to 70 meV and no spectral shift for carrier concentrations up to 5.5 × 1019 cm−3. The latter was attributed to the simultaneous influence of band filling, band gap renormalization, and strain. Keywords: GaN nanowires, electrical transport properties, Seebeck coefficient, micro photoluminescence, charge carrier concentration, gallium nitride, molecular beam epitaxy (Some figures may appear in colour only in the online journal) 1. Introduction
different techniques [7–9]. Quantitative analysis of the resistance in four-point probing geometry or determination of carrier concentration by thermoelectric characterization is only reported for typically longer and thicker Si-doped microwires grown by MOCVD revealing a conductivity and carrier concentration up to 2700 S cm−1 and 2.6 × 1020 cm−3, respectively [10]. Germanium (Ge) as a shallow donor in GaN has a similar activation energy of approximately 20 meV as Si [11] and has been proven to be an alternative dopant for GaN NWs and AlN/GaN NW heterostructures grown by PAMBE on Si(111) substrates [12, 13]. Since the ionic radius of the Ge atom is similar to that of Ga the bond length to nitrogen changes only by 1.4% compared to 5.5% for Si [14], resulting in substantially smaller lattice deformations and the absence of
GaN nanowires (NWs) currently attract intense research interest. Due to lateral strain relaxation they exhibit a low density of extended structural defects and hence are regarded as an ideal platform for the realization of nanoscale electronic and optoelectronic devices with improved performance and stability [1–3]. Additionally, their high surface to volume ratio makes them suitable for applications in photo detectors or different types of chemical sensors [4–6]. For such applications understanding and control of doping processes is a basic requirement. Commonly, silicon is used as a donor for n-type GaN NWs grown by plasma-assisted molecular beam epitaxy (PAMBE) and the influence of Si-incorporation on the optical and electrical properties has been studied by 0957-4484/15/135704+08$33.00
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structural degradation in thin GaN:Ge films even for very high carrier concentrations of 4 × 1020 cm−3, as reported in [15]. The determination of the free carrier concentration of single NWs by Hall measurements has recently been demonstrated but requires high processing effort [16–18] and bears difficulties in interpretation due to the nanosized geometry [19]. Common top- [9, 20] and back-gate [1, 9] fieldeffect transistor measurements are often questioned because of uncertainties determining the gate capacitance and hysteresis effects caused by interface charging [21]. Extraction of the charge carrier density from the temperature-dependent Seebeck coefficient for degenerate NWs was reported in [10, 22] and is also pursued in the present work. We present a systematic study of the influence of Gedoping on the electrical properties of single GaN NWs. The electrical conductivity is determined by four-point resistivity measurements and the free carrier concentration is analyzed by temperature-dependent Seebeck coefficient measurements. The relation of carrier concentration and photoluminescence properties of single NWs is also discussed.
was measured in a range between 1.6 and 280 K using a bath cryostat cooled with liquid helium. For temperature-dependent analysis of the Seebeck coefficient, samples with a layout shown in figure 1(b) were fabricated. A meandered micro-heater (Ti/Au) placed in the vicinity of the NW was used to apply a thermal gradient along the NW. To measure the thermoelectric voltage the NW is contacted by two branched metal leads which also serve as four-point resistive thermometers5, each calibrated at different temperatures stabilized in the cryostat and used to determine the temperature difference ΔT. Thermoelectric measurements were performed in an Oxford MicroStatHiResII flow cryostat and a temperature range from 80 K (5 K) to 280 K using liquid nitrogen (helium). Single NW micro photoluminescence spectroscopy (μPL) was performed in the same cryostat at T = 4 K. The 325 nm excitation light from a HeCd laser was focused by a 20-fold UV objective (NA 0.4) onto the NW, and the emitted PL was collected with the same objective, dispersed using a 3600 lines mm−1 grating in a 250 mm spectrometer, and detected with a cooled charge-coupled device camera.
2. Sample preparation and experimental details 3. Results and discussion
Non-intentionally doped (n.i.d.) and Ge-doped (0001̄)oriented GaN NWs were grown in a self-assembled catalystfree process by PAMBE on Si(111) substrates using nitrogenrich growth conditions according to the growth process described in [12]. The length of the investigated NWs varied between 1.5 and 2 μm, their diameter between 40 and 120 nm. Germanium was evaporated from an effusion cell operated between 900 and 950 °C, corresponding to beam equivalent pressures BEPGe between 5.0 × 10−10 and 1.3 × 10−9 mbar. The average Ge-concentrations [Ge] of the NW ensembles were determined to 1.0 × 1020, 1.4 × 1020, 1.6 × 1020, and 3.3 × 1020 cm−3 by a combination of time-of-flight secondary ion mass spectrometry and energy dispersive x-ray spectroscopy in a transmission electron microscope [12]. The NWs were detached from the substrate in an ultrasonic bath and dispersed on a thermally wet oxidized Si(100) substrate with an oxide thickness of 775 nm. Electrical contacts were processed by combined photo- and electron beam lithography4. A Ti/Au (25 nm/200 nm) metallization was thermally evaporated without additional cleaning steps and patterned by a lift-off process. One of the resulting four-point structures for conductivity measurements of a 2 μm long NW is exemplarily shown in figure 1(a). After annealing for 60 s at 550 °C in vacuum the contacts show Ohmic behavior. The conductivity of the NW middle segment was calculated based on the room temperature resistance obtained from dc I–V curves, taking the NW diameter determined by SEM images into account. The temperature-dependence of the resistance
3.1. Conductivity
The room temperature two-point resistance of n.i.d. NWs shows strong variations, even for NWs from the same ensemble. As shown in figure 1(c), highly resistive NWs (type 1) with a resistance above 1 MΩ (crosses) as well as conductive NWs (type 2) with a resistance in the range of 40 – 200 kΩ (open squares) are found, both comparable to reported values for n.i.d. NWs [8, 23]. Since the diameter of both types of NWs varies in the same range between 45 and 80 nm, the different conductivities are most likely caused by the presence of structural defects or unintentionally incorporated impurities whose origin will be discussed below. To analyze the contact resistance current voltage (I–V) measurements in two-point and four-point geometry at room temperature were compared for n.i.d. and Ge-doped NWs. Figure 1(d) shows the deduced resistances of the middle segment of 36 conductive6 single NWs in both geometries (two-point: R2P, open symbols; four-point: R4P, filled symbols). For clarity the x-axis is divided into five sectors representing the respective Ge-concentrations [Ge] of the NW ensemble between 0 (for n.i.d. NWs) and 3.3 × 1020 cm−3. 5
Usually thermocouples are used to connect macroscopic samples to determine the Seebeck coefficient in order to completely exclude the contribution of the cables to the thermoelectric voltage. Due to the nanosized geometry of NWs this cannot be done and hence a thermoelectric voltage drop across the gold leads connecting the hot and cold part of the NW to thermal equilibrium cannot be excluded. Since the Seebeck coefficient of gold is in the order of 1.8 μV K−1 at room temperature (0.8 μV K−1 at 80 K) the influence on the measurements should be small compared to the Seebeck coefficient of the NWs (20 to 120 μV K−1). 6 Highly resistive NWs are not included, since their resistance measured in four-point geometry is almost the same as in two-point geometry.
4
For processing a SUSS MA 56 mask aligner, a Jeol JSM 7001F thermal field emission scanning electron microscope (SEM) equipped with a XeDraw2 writing system from XENOS Semiconductor Technologies GmbH and single resist (PMMA) layer technology were used. 2
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Figure 1. (a) SEM image of a 2 μm long NW contacted in four-point geometry. (b) SEM image of a 2 μm long NW with two resistive
thermometers and micro heater. (c) Two-point resistance of highly resistive (crosses) and conductive (squares) n.i.d. NWs as a function of their diameter. (d) Resistance of middle segments in individual NWs measured in two-point (R2P: open symbols) and four-point (R4P: filled symbols) geometry for 36 conductive NWs with different Ge-concentrations. The measurement error is smaller than the size of the symbols. Vertically aligned R2P and R4P values of equal color correspond to the same NW. Dashed (solid) lines show the average value of R2P (R4P). Inset in (d): conductivity of the NWs as a function of the average Ge-concentration. The conductivity was obtained from the four-point resistance considering the individual NW geometry, as reported in [12]. The error bars are dominantly caused by the uncertainties in the NW geometry determined from SEM images. The line is a guide to the eye.
The values for R2P show strong wire-to-wire variations and an overall decrease by more than two orders of magnitude with increasing [Ge]. However, the average values (dashed lines) do not exhibit a clear trend. In contrast, the results for R4P show significantly smaller variations and the mean values (solid lines) systematically decrease over two decades from 40 kΩ to 550 Ω. Hence, the strong fluctuations of R2P are caused by variations in the contact resistance which turns out to be in the same order of magnitude as the four-point resistance of the NW middle segment. This demonstrates that four-point measurements are inevitable for reliable electric characterization of single NWs. To obtain the electrical conductivity σ the NWs have been approximated to be of cylindrical shape with the individual diameter and length of the middle segment in the NW due to individual NW processing determined by SEM analysis. The results in the inset of figure 1(d) show a continuous increase of the conductivity from 35 S cm−1 to above 400 S cm−1 for an increasing [Ge] up to 1.6 × 1020 cm−3. For higher doping concentrations up to [Ge] = 3.3 × 1020 cm−3 the conductivity saturates at around 450 S cm−1, most likely due to decreasing carrier mobility caused by a high density of ionized donors, self-compensation, or electrically inactive incorporation of Ge. A maximum conductivity of 625 S cm−1 is observed. The wire-to-wire fluctuation can be caused by variations in the concentration of active Ge donors [12] or by mobility variations due to different densities of structural defects. Since the geometric diameter of the NWs was used to
calculate the conductivity and an influence of a possible depletion region was neglected, the values represent a lower limit (see discussion below). Nevertheless, the obtained values are in good agreement with reports on Ge-doped thin films with conductivities in the range from 30 to 1500 S cm−1 for carrier concentrations of 2 × 1018 – 2 × 1020 cm−3, respectively [15, 24]. The dependence of the conductivity on the NW diameter for different doping concentrations is shown in figure 2. For n.i.d. NWs of type 2 a systematic increase of the conductivity with increasing diameter is observed, in agreement with the results reported in [23, 25]. In contrast, the conductivity of Ge-doped NWs does not show a systematic dependence on their diameter. Generally, the electrical properties of GaN NWs are strongly affected by surface band bending [23, 25]. An increase of the donor concentration above a critical value leads to a decreasing depletion width and the formation of a conductive channel inside the NWs [8, 25]. Hence, a strong dependence of the conductance on the NW diameter is expected for undoped or moderately doped NWs while for high doping concentrations only a weak dependence is anticipated. Accordingly, for all Ge-doped NWs investigated here the influence of the depletion region on the conductivity can be neglected. Furthermore a residual carrier concentration above 2.8 × 1018 cm−3 can be estimated for type 2 n.i.d. NWs according to the model proposed in [23], as these NWs show a measurable conductivity already for a diameter of 50 nm. 3
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Figure 2. Conductivity for NWs with different Ge-concentration as a function of the NW diameter. The gray shaded area depicts the region spanned by n.i.d. NWs.
This value is already above the reported Mott density of 1.6 × 1018 cm-3 for bulk GaN [26]. We attribute the fairly high conductivity of n.i.d. NWs to the presence of oxygen and silicon as residual impurities. Furtmayr et al demonstrated the diffusion of Si from the substrate into GaN NWs by electron energy loss spectroscopy (EELS) [27]. Due to the limited resolution of EELS the presence of Si could only be detected in close vicinity of the interface. In order to investigate the occurrence of Si diffusion by conductivity measurements n.i.d. NWs with a length of 2 μm contacted by six individual terminals, allowing spatially resolved conductivity measurements in three different segments, were prepared (inset of figure 3). The results for nine different NWs in figure 3 show that the conductivity decreases by almost one decade from 80 to 10 S cm−1 when the distance to the NW base is increased from 600 to 1300 nm. As the diameter is almost constant along the NW these changes are attributed to diffusion of Si from the Si(111) substrate into the NW, contributing to the residual conductivity of n.i.d. NWs with a diameter down to 50 nm. Since at all positions the conductivity of n.i.d. NWs is significantly smaller than that of the lowest Ge-doped NWs, the effect of co-doping can be neglected for the extraction of the corresponding electrical parameters for doped NWs. The temperature-dependence of the resistivity was analyzed between 1.6 and 280 K for selected NWs with different conductivities and doping concentrations (NWs of the n.i.d., [Ge] = 1.4 × 1020 cm−3, and [Ge] = 1.6 × 1020 cm−3 ensemble). For all investigated NWs only a weak influence of the temperature on the resistivity and an almost constant value at temperatures below 10 K was found, as presented in figure 4. The extracted activation energy between 70 and 280 K for the NW with a conductivity of 34 S cm−1 (310 S cm−1) is (5 ± 1) meV ((2 ± 1) meV) which is significantly lower than the ionization energy of Ge in the case of low doping concentrations (around 20 meV for n = 3 × 1017 cm−3 [11]) and indicates the formation of an impurity band due to high
Figure 3. Spatially resolved conductivity for nine different single n.i. d. NWs. Each NW is represented by one type of symbol. The three individual segments are marked by A, B, and C in accordance with the sample structure shown in the inset.
Figure 4. Arrhenius plot of normalized resistance (R(T)/R0(280 K)) for three NWs with different conductivities.
concentrations of incorporated Ge atoms [28, 29]. For the investigated NW with the highest conductivity, we have observed a positive temperature coefficient of the resistivity, i.e. metallic behavior, further confirming the high donor concentration in Ge-doped GaN NWs. 3.2. Charge carrier concentration
To determine the charge carrier concentration of individual Ge-doped GaN NWs we followed an approach based on temperature-dependent measurements of the Seebeck coefficient as reported for degenerate GaN NWs in [22] and Sidoped GaN microwires in [10]. Using the structures shown in 4
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Figure 6. Seebeck coefficient as a function of temperature for one n.i.d. and four Ge-doped GaN NWs. The error is in the order of the size of the symbols.
Figure 5. Thermoelectric voltage as a function of heater power and
resulting temperature difference ΔT. Inset: transient thermoelectric voltage for different heating powers.
a lower limit7 adapting equation (1) derived from semi-classical Mott relation [22].
figure 1(b) the transient thermoelectric voltage of individual NWs was measured. The voltage instantaneously increases with the heating power steps as exemplarily shown for a temperature of 282 K and a NW with [Ge] = 1.0 × 1020 cm−3 in the inset of figure 5. The thermoelectric voltage as a function of heating power and the resulting temperature difference along the NW linearly increases from −40 to 250 μV for heater powers up to 5 mW and a corresponding temperature difference ΔT up to 3.5 K as depicted in figure 5. The offset at ΔT = 0 is caused by thermoelectric voltages in the cables. Evaluation of the slope yields a Seebeck coefficient of Q = −82.3 μV K−1 at the average temperature of 282 K. This Seebeck coefficient is comparable to results reported for ntype GaN wires [10, 22] and GaN thin films [30] with carrier concentrations above 1 × 1019 cm−3. Following this method, the Seebeck coefficients for one type 2 n.i.d. NW and two individual Ge-doped NWs from each of the ensembles with [Ge] = 1.0 × 1020 cm−3 and [Ge] = 1.6 × 1020 cm−3 were determined at different temperatures between 80 and 280 K, as presented in figure 6. The error is in the order of the size of the symbol. A linear decrease of the Seebeck coefficients with increasing temperature is observed for all investigated samples. The absolute value of the extracted slope decreases with increasing [Ge]. The linearity is maintained for temperatures down to 5 K, as exemplarily shown for the n.i.d. NW. This further confirms the degenerate doping level of the n.i.d. and Ge-doped NWs due to doping concentrations above the Mott density. Hence, assuming parabolic bands as well as a constant effective mass, which is valid for carrier concentrations up to 1020 cm−3 [31, 32] and an energy independent scattering time the carrier concentration n can be estimated as
n=
⎛ ⎞3 T⎟ ⎜ π 2k B2 m* ⋅ ⎟ ⎜⎜ Q⎟ 2 2/3 2 π ⋅ ℏ q 3 ⎝ ⎠
( )
(1)
Here, kB is the Boltzmann constant, q the elementary charge, ℏ reduced Planck’s constant, m* = 0.231 × me the electron (density of states) effective mass [31, 32], T the temperature, and Q the Seebeck coefficient. In contrast to [10] we have evaluated the slope of the linear dependence shown in figure 6 instead of just one Seebeck coefficient at a certain temperature to exclude uncertainties in the determination of the absolute temperature. The error in the determination of the slope is small and can be neglected in comparison to the uncertainty in the effective mass, which has a more significant influence on the results. Using equation (1) we obtain carrier concentrations between 9.1 × 1018 and 5.5 × 1019 cm−3 for the five individual NWs as summarized in table 1. The extracted values for n systematically increase with increasing Ge-concentration. They also reflect the wire-towire variations observed in conductivity. The ratio of n and [Ge] varies in the range of 20% to 35% for the investigated single NW in relation to the respective ensemble values, which can be explained–beside the difference of measurements on NW ensembles and on single NW level–by electrically inactive Ge or self-compensation effects at high doping concentrations. The extracted carrier concentrations and the conductivities obtained for single NW of the same 7 The corrections suggested in [10] to address the energy-dependent relaxation time would lead to slightly higher carrier concentrations.
5
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ensembles are in very good agreement with data reported in literature [15, 24, 25]. The high carrier concentration of the n.i.d. NW is attributed to residual oxygen and Si donors due to diffusion, as reported above. All carrier concentrations exceed the Mott density, in accordance with the previous results of the diameter-dependence and weak temperature-dependence of the conductivity. Based on these results the carrier mobility can be estimated to be in the range from 10 to 43 cm2 V−1s−1 for the n.i.d. NWs and 34 to 86 cm2 V−1s−1 for NWs with [Ge] = 1.0 × 1020 cm−3 and [Ge] = 1.6 × 1020 cm−3. These values are reasonable compared to reported values for NWs and thin films [1, 10, 15, 24, 25, 33–35]. The reduced mobility of the n.i.d. NWs can be partially attributed to the underestimated conductivity of n.i.d. NWs due to the neglected depletion region resulting in the diameter dependent conductivity, as discussed above. Further, an increase of the carrier mobility with increasing carrier concentration can be expected as, due to the related increase in surface band bending, the contribution of surface scattering is reduced.
Figure 7. Micro photoluminescence spectra of five single NWs at T = 4 K with different carrier concentrations (determined by temperature-dependent analysis of the Seebeck coefficient). The spectra are normalized and vertically shifted for clarity. Experimental data are plotted in black, the modeled luminescence line shapes in red. The vertical green (dotted) and blue (solid) lines mark the positions of Egap + ΔEBGR and Egap + ΔEBGR + ΔEBMS, respectively.
3.3. Photoluminescence
The five single individual NWs with carrier concentrations from 9.1 × 1018 to 5.5 × 1019 cm−3 that were analyzed by Seebeck coefficient measurements, were additionally analyzed by μPL at T = 4 K (cf figure 7). The spectra of all NWs are dominated by a sharp near band edge emission around 3.485 eV. While the emission broadens only slightly from 35 to 70 meV (FWHM) with increasing carrier concentration, no spectral shift is observable even for the highest doped sample. This behavior can be attributed to a compensation of a blue shift due to band filling effects known as Burstein–Moss shift (BMS) by band gap renormalization (BGR) due to many body effects as recently reported in [32] for GaN:Si and GaN:Ge samples with carrier concentrations up to 1019 cm−3. Fits to the experimental line shapes according to the model used in [32] are plotted in red in figure 7. The position of the Fermi energy represented by Egap + ΔEBGR + ΔEBMS and the renormalized band gap given by Egap + ΔEBGR are marked by blue and green vertical lines, respectively. The carrier concentration obtained from the Seebeck coefficient measurement was used as a fixed input parameter for the fitting procedure. In order to model the experimental line shapes based on the discussion in [32], a rigid shift of the spectra due to strain had to be assumed changing the value of Egap. If the strain in the NWs is assumed to be of biaxial type, it ranges from compressive (εxx = −5.3 × 10−4) for the n.i.d. NW with 9.1 × 1018 cm−3 to tensile (εxx = 2.1 × 10−3) for the highest doped NW. While this increase in tensile strain as a function of increasing germanium incorporation is in agreement with the findings of [36], its microscopic origin is not clear at the moment.
Table 1. Beam equivalent pressure BEPGe and Ge-concentration [Ge] of the respective NW ensemble, slope deduced from graph in figure 6 and calculated carrier concentration n for five different doped GaN NWs.
NW 1 2 3 4 5
BEPGe (10−9 mbar)
[Ge] (1020 cm−3)
Slope Q/T (μV K−2)
n (1019 cm−3)
n.i.d. 0.5 0.5 1.0 1.0
n.i.d. 1.0 1.0 1.6 1.6
−0.53 −0.31 −0.27 −0.20 −0.16
0.91 2.05 2.57 4.11 5.53
4. Conclusion The electronic properties of individual Ge-doped GaN NWs were systematically investigated. The obtained results conclusively demonstrate the excellent donor properties of Ge in GaN NWs grown by PAMBE. By elimination of the contact resistances a continuous increase of the conductivity with increasing Ge-concentration up to an average value above 400 S cm−1 for [Ge] = 1.6 × 1020 cm−3 was found and a maximum conductivity of 625 S cm−1 was observed. The conductivity of the Ge-doped NWs was independent of the NW diameter and showed only weak temperature dependence. Emerging metallic behavior for a NW with a conductivity of 436 S cm−1 further confirms that Ge is an efficient donor in GaN NWs. The charge carrier concentrations in the range of 6
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9.1 × 1018 – 5.5 × 1019 cm−3, deduced from analysis of the temperature-dependent Seebeck coefficient, were above the Mott density and confirmed electronic degeneracy. The near band edge emission at constant energy, independent of the carrier concentration, was assigned to an increase of tensile strain with increasing charge carrier concentration due to the incorporation of germanium as shallow donor.
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Acknowledgments Authors from the Justus-Liebig-Universität acknowledge financial support within the LOEWE program of excellence of the Federal State of Hessen (project initiative STORE-E).
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