Si Donor Incorporation in GaN Nanowires - Nano Letters (ACS

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Si donor incorporation in GaN nanowires Zhihua Fang, Eric Robin, Elena Rozas-Jiménez, Ana Cros, Fabrice Donatini, Nicolas Mollard, Julien Pernot, and Bruno Daudin Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.5b02634 • Publication Date (Web): 01 Oct 2015 Downloaded from http://pubs.acs.org on October 1, 2015

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Si donor incorporation in GaN nanowires Zhihua Fang*,1, 2, 3, Eric Robin4, Elena Rozas-Jiménez5, Ana Cros5, Fabrice Donatini1, 3, Nicolas Mollard4, Julien Pernot1, 3, 6 and Bruno Daudin1, 2 1

2

Univ. Grenoble Alpes, F-38000 Grenoble, France

CEA, INAC-SP2M, "Nanophysique et semiconducteurs" group, F-38000 Grenoble, France 3

4

5

CNRS, Inst. NEEL, F-38042 Grenoble, France

CEA, INAC, MINATEC Campus, 17 rue des Martyrs, F-38054 Grenoble Cedex 9, France

Materials Science Institute, University of Valencia, P.O. Box 22085, ES-46071, Valencia, Spain 6

Institut Universitaire de France, 103 boulevard Saint-Michel, F-75005 Paris, France

KEYWORDS: GaN, nanowires, Si doping, EDX, four probe resistivity, field effect transistor, electron mobility

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ACS Paragon Plus Environment

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ABSTRACT

With increasing interest in GaN based devices, the control and evaluation of doping are becoming more and more important. We have studied the structural and electrical properties of a series of Si-doped GaN nanowires (NWs) grown by molecular beam epitaxy (MBE) with a typical dimension of 2-3 µm in length, and 20-200 nm in radius. In particular, high resolution energy dispersive X-ray spectroscopy (EDX) has illustrated a higher Si incorporation in NWs than that in two-dimensional (2D) layers and Si segregation at the edge of the NW with the highest doping. Moreover, direct transport measurements on single NWs have shown a controlled doping with resistivity from 102 to 10-3 Ω.cm, and a carrier concentration from 1017 to 1020 cm-3. Field effect transistor (FET) measurements combined with finite element simulation by NextNano3 software have put in evidence the high mobility of carriers in the non-intentionally doped (NID) NWs.

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Semiconductor NWs have drawn great attention in both fundamental physics and nanoelectronic applications due to their unique dimensions and peculiar properties. Particularly, III-nitride NWs such as GaN NWs are extremely interesting due to the absence/reduced density of extended defects compared to their 2D layers counterpart, which could open new pathways for the design of optoelectronic nanodevices.1-3 MBE grown GaN NWs are a perfect candidate for this task considering their high crystallinity and excellent optical properties.4-6 The doping of MBE grown GaN nanowires is crucial for the realization of these optoelectronic nanodevices.7 Si is normally used as an effective shallow donor for achieving ntype doping.8 It has been reported that Si doping is associated with defects formation and increasing strains in 2D GaN.9-11 Concerning GaN NWs, both Calarco et al.12 and Furtmayr et al.13 have found visible morphology and density changes of MBE grown GaN NWs on Si substrate upon doping. More nucleation sites at the nanowires side walls and the existence of an additional SiN layer at the NW / Si substrate interface have been proposed for possible explanations.12,13 However, the mechanism behind these variations, such as hypothetical inhomogeneities of Si dopant distribution along the growth direction and the wire radius and their impact on the growth kinetics of GaN NWs, is far from being understood. Moreover, the electrical transport properties of MBE grown GaN NWs are even less explored. Due to the nanoscale dimension and the one dimensional geometry, conventional transport measurements, such as Hall-effect measurement and capacitance-voltage measurement, are very challenging in the case of NWs. In the literature, both Calarco et al.12,14,15 and Sanford et al. 16-19 have performed extended studies to extract the carrier concentration and mobility of GaN NWs via various photoconductivity measurements. However, direct transport measurements on single MBE grown GaN NW have been rarely reported. 3


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In this letter, we have done a comprehensive study of the structural and electrical properties of Si-doped GaN NWs in a wide range of Si content. In particular, we have demonstrated that the Si content in GaN NWs is higher than in the 2D case, as a clue that NW geometry and the concomitant easy strain relaxation through free surface is actually enhancing the Si solubility limit. Transport measurements (four-probe resistivity and its temperature dependence) have shown a controlled doping level, and FET measurements combined with finite element simulation have enabled us to determine the carrier concentration and furthermore the mobility of NID NWs. The growth method of GaN NWs by plasma-assisted MBE has been described previously in details.20,21 Low-resistivity (less than 5 mΩ·cm) n-type Si (111) was used as growth substrate. The substrates were etched in a diluted HF solution for 30 seconds before loading into the chamber and were annealed at an elevated temperature (870 °C) for 10 minutes till the observation of a clear 7 x 7 reconstruction in reflection high energy electron diffraction (RHEED) pattern. In order to minimize the possible temperature offset between surface and thermocouple reading, the surface temperature measurement has been calibrated using the melting point of Aluminum (662 °C) as assessed by RHEED observation. The substrate temperature was then calibrated using a Ga desorption method.20,21 A 3 nm AlN buffer layer was deposited to ensure a homogeneous nucleation and decrease the mosaicity of the NWs.22 The metal fluxes were calibrated using RHEED oscillations when growing 2D GaN layers. The nitrogen flow rate was 0.6 standard cubic centimeter per minute (sccm), with a plasma power of 300 W, while the Ga flux rate was 0.08 ML/s for this series of samples. The n-type doping was achieved using a Si effusion cell, by exposing GaN NWs to the Si flux, starting 20 minutes after completion of their nucleation till the end of the growth. This experimental procedure, namely 4


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providing the Si flux after the completion of the NW nucleation has been chosen to exclude parasitic, Si-flux dependent effects during the nucleation stage. Different samples were grown in the same conditions except the doping level by varying the Si cell temperature from 850 °C to 950 °C. The growth time was 20 hours unless otherwise mentioned. The top view and side view morphology variations were followed by field-emission scanning electron microscope (FESEM) (ZEISS Ultra 55 microscope). Micro-Raman measurements were performed by means of a HORIBA Jobin Yvon iHR320 spectrometer with Peltier-cooled charge coupled device detector and a 532 nm doubled YAG laser. Spectra were obtained in backscattering geometry at room temperature from as grown NWs. A 50x microscope objective was used to focus the excitation laser on the sample and collect the scattered light to the spectrometer. High resolution-EDX spectra were acquired using a ZEISS Ultra 55 SEM equipped with FlatQuad annular detector from Bruker at 4 kV while X-ray maps were collected using a FEI Osiris TEM equipped with super X detectors at 200 kV. Si concentrations were computed using the zeta-factor method23 for STEM EDX data and φρz standard method24 for the SEM EDX data, and the experimental errors are computed from the counting statistic. Electrical contacts have been fabricated using electron beam lithography (FESEM FEI Inspect F50 fitted with Raith Elphy Quantum lithography system), for samples 1-5 (Table 1). Firstly, the Si wafer with 500 nm thick thermal oxide and various markers has been prepared to disperse the as-grown NWs; secondly, the NWs have been mechanically dispersed and precisely located in the electron beam lithography tool with respect to the markers; thirdly, a 300 nm or 500 nm (according to the radius of the NW) thick PMMA resist has been spin-coated on the substrate; fourthly, the exposure is done according to the previous localizations and the designed patterns with proper electron beam dose. Finally, evaporation of Ti / Al (30 / 50 or 90 nm) and 5


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subsequent lift-off have been carried out. All the transport measurements have been performed in the FEI Inspect F50 FESEM-setup equipped with a nano-probing SmarAct system, and a Gatan liquid helium stage has been used in the case of the temperature dependence measurements. The influence of Si doping on GaN NW morphology is shown in Figure 1. The length and the radius of the NWs are found to be almost constant up to a Si cell temperature of about 925 °C. Upon higher Si doping (two samples with Si cell temperature of 938 °C and 950 °C), the radius of the NWs is gradually increased while their length is decreased. From the side view SEM images in Figure 1(a)-(c), a widening of the NW is observed at higher Si doping, which is more pronounced with the highest Si content. Interestingly, the top facets of the NW switched from 6-fold symmetry to 12-fold symmetry with the highest doping as shown in Figure 1(d), suggesting a different growth regime. A closer observation of the most doped NWs (Figure 1(e) and (g)) reveals a continuous increase of the NW radius from the base, until reaching a certain equilibrium value. It has been recently demonstrated that the diameter of GaN NWs grown by MBE is indeed self-regulated so that the effective Ga/N flux ratio is close to the stoichiometric value in steady-state growth conditions.25 Consistently, the present results suggest that heavy Si doping is associated with an increased diffusion length of Ga adatoms along the NW side walls, which leads to an increased Ga effective flux on top and to the concomitant, self-controlled diameter widening until reaching the equilibrium. The influence of Si doping on strain state of the NWs was investigated by Raman spectroscopy. Raman spectra of as-grown NWs with different Si doping levels are shown in Figure 2(a), while the spectrum of the silicon substrate is included at the bottom as a reference. The peak corresponding to the E2h mode is observed in all samples. For NID GaN NWs, its center is at 565.6 cm-1, somehow lower than the value expected for relaxed bulk GaN (567 cm6


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) . A small but progressive decrease of the phonon frequency is observed as the silicon content

in the samples increases (Figure 2(b)). This trend is broken in the most doped sample (with Si cell temperature of 950 °C), where the mode shifts back sharply to higher frequencies. This behavior points to an increase of the tensile strain with increasing silicon content up to a value around 0.15 %, beyond which the relaxation of the lattice takes place. Meanwhile, as the amount of incorporated silicon increases the E2h peak becomes somewhat wider, changing from 7 to 10 cm-1. This is a consequence of the lattice disorder induced by the impurities. Starting for sample with Si cell temperature of 900°C a broad band centered at 658 cm-1 begins to arise. The intensity of this band increases strongly in samples with higher silicon content. This peak is ascribed to a disorder activated mode and has been reported for Mg, Ge and Si doped samples.28,29 At the same time, four new modes arise at 319, 390, 414 and 763 cm-1, and they are clearly visible in the most doped samples. To our knowledge, these modes have not been reported before, and do not match with the broad bands characteristic of SiNx.30 However the mode at 414 cm-1 is close to a zone boundary phonon that could be activated due to the disorder induced by the incorporation of Si to the GaN lattice. With the purpose of elucidating this feature and mapping the Si content at the nanoscale, two NWs grown with the highest Si cell temperature (950 °C) have been analyzed by EDX in a TEM (Figure 3(a)) and SEM (Figure 3(b)), respectively. The top view facet is hexagonal since it is a polished plan-view sample, which means the analyzed NW was cut at a certain height at radius of 100~130 nm, below the symmetry change of top facet. The measured Si concentrations from the two NWs with two techniques are similar, which excludes a potential contamination of the samples. From the TEM-EDX data profile Figure 3(c), the NW has a core with an average Si concentration of 2.5 x 1020 at/cm3 and an outer part of around 17 nm with a much higher Si 7


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concentration of around 6.5 x 1020 at/cm3. The SEM-EDX data (white points in (c)) from the other NW fall in the same range. More observations show that all NWs grown with the highest Si cell temperature have very similar Si concentrations ranging from 2-4 x 1020 at/cm3 in the core with a mean value around 2.8 ± 0.4 x 1020 at/cm3 (calculated from 10 NWs, not shown). The outer part of the NWs is strongly enriched in Si compared to the core containing from 6 x 1020 up to 1021 at/cm3. The overall thickness of this Si-rich shell ranges between 10 nm up to 40 nm. Additional TEM-EDX and SEM-EDX measurements have been performed on the sample corresponding to the Si cell temperature of 938 °C. TEM-EDX shows a relatively constant Si concentration throughout the NW with an average value of 1020 at/cm3, and it is consistent with concentrations measured by SEM-EDX with the FlatQuad annular detector (0.5~1.5 x 1020 at/cm3) (see Supporting Information). The Si concentration plateau of 2.8 ± 0.4 x 1020 at/cm3 measured by EDX in the most heavily doped sample is assigned to a Si solubility limit, which is significantly higher than the theoretically predicted value (around 5 x 1019 at/cm3)31. The basic mechanism responsible for this solubility increase is not clear at this stage and may be tentatively assigned either to the eased strain relaxation in NWs, which tends to push back the transition to extended defects formation, or to a decrease in Si dopant formation energy in NWs, as recently reported in the case of Si-doped AlN NWs32,33. Interestingly, in the case of 2D layers, Sánchez-Páramo et al.10 have reported a lattice relaxation of Si-doped 2D GaN layers above a concentration of 5x1018 cm3

associated with crack formation in the 2D layer. The present results suggest that the large

amount of free surfaces, which are specific to NWs, are favorable for the relaxation of tensile strain induced by the presence of Si, making its incorporation easier, while leading to an elastic strain relaxation without the formation of cracks. Surface segregation of Si in the periphery of 8


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the GaN NWs when above the solubility limit is consistent with the increasing intensity of the broad Raman band around 658 cm-1 for increasing Si content and is assigned to an increase of Sirelated defects in the periphery of the NWs for the Si cell temperature above 900 °C. This feature is consistent with the theoretical prediction of Si segregation to the surface under N-rich and Sirich growth conditions31,34. In fact, a similar phenomenon has been recently reported on highly doped GaN NWs grown on diamond where the presence of a shell with Si content above the solubility limit has been observed.35 Such a segregation of Si dopant in the periphery has also been observed in the case of InN NWs.32 As shown in Figure 1(d), in the case of the highest Si content related with the formation of Si enriched GaN outer shell, the symmetry of the top facets of the NWs is changed from 6 to 12. It has been demonstrated for long that MBE-grown NID GaN NWs exhibit a 6-fold symmetry top facet, with vertical walls made of m-planes.21,36 Such a morphology is consistent with theoretical calculations which have shown that m-plane surface energy (118 meV/Å2) is indeed smaller than a-plane surface energy (123 meV/Å2)37. The symmetry change of the most heavily doped sample is a clue that a Si enriched shell exists and the associated defects have a tendency to equalize the surface energy of m-planes and a-planes in this case. Moreover, the trend of symmetry change is already observable for some NWs for the sample with Si cell temperature of 938 °C (Figure 1(b)), and the appearance of a broad Raman band around 658 cm-1 further confirms the association of the symmetry change and the progressively increased defect concentration in the shell of the NWs. Furthermore, this lattice deformation and change in surface energy is expected to discourage nucleation on the NW sidewalls and promote either Ga adatom desorption or diffusion along them, consistent with the previous hypothesis that the increase of Ga adatom diffusion length along the sidewalls might be responsible for the progressive NW widening. 9


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Moreover, we have studied the intrinsic electrical properties of GaN NWs via direct transport measurements. Room temperature four-probe resistivity measurements have been performed on 20 single NWs from sample 1 to 5 (see Table 1), except for the most heavily doped sample. The specific geometry (the conical shape and the length of around 1.5 µm) and inhomogeneous dopant distribution (the Si enriched shell witnessed by EDX measurements) of the most doped sample have prevented reliable electrical characterization of these NWs to be performed. An example of one contacted NW with a lower doping level is shown in the inset of Figure 4. In the four-probe measurements, a current I is established through the two outer contacts while the voltage drop V between the two inner contacts is measured. Using four-probe measurements, the resistivity of the NW can be inferred without the influence of the contact resistance. Current density is limited to 900 A/cm2 to avoid heating issues during the measurement, and reverse polarity measurements have been done to exclude the effect of the potential offset. Assuming a homogeneous conduction of through the whole section of the NW, the resistivity of the NW between the two inner contacts can be calculated using the following equation:

= ×

√

/

(1)

L is the length of the NW between the two inner contacts and r is the radius of the circumscribed circle of the hexagonal cross section of the NW, which are measured from high resolution SEM images of each contacted NW. Figure 4 shows the four probe resistivity value versus NW radius of samples 1 to 5. The resistivity value varies from 102 to 10-3 Ω.cm, corresponding to the range from NID NWs to the second most doped ones. For sample 1 (NID NWs), the resistivity spreads from 102 to 3 x 10-2 Ω.cm for 6 NWs, implying an inhomogeneous residual doping among these NWs38 or the influence of different surface states. For samples 2 to 5 (doped NWs), the resistivity of NWs 10


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having different radii and coming from the same sample is quite constant, a signature of negligible surface conduction or reduced conduction due to near-surface depletion at room temperature, and hence validating the assumption of a homogeneous conduction through the whole section of the NW. However, caution must be taken for sample 2 since the two wires radii are close (27 nm and 31 nm). The resistivity of NWs from the different samples gradually decreases from 2 x 10-2 Ω.cm to 10-3 Ω.cm, while increasing the doping level. These two features have revealed the ability to achieve homogeneous doping level from one wire to another and furthermore to control the doping level through variation of the Si cell temperature in the MBE system. However, room temperature measurements do not provide much information about the conduction regime in the NWs. Therefore, temperature dependent four-probe resistivity measurements down to 5 K have been performed on four representative NWs with different doping levels. Figure 5 shows the results of four probe resistivity versus 1/T for these four NWs. It discloses a temperature dependent conduction for the NID and lightly doped GaN NWs (samples 1 and 2, respectively), and a metallic behavior for more doped NWs (samples 3-5). For the sample 1 and sample 2, free electron in the conduction band dominates with a typical donor ionization regime for T > 50 K, while a temperature independent conduction controls the resistivity for T < 50 K. This is a signature of doping level below the metal-insulator transition (MIT) dominating the conduction at high temperature. The critical MIT concentration nMIT has been established at 1.6 x 1018 cm-3 according to the experimental work on Si doped GaN epilayers39. The resistivity temperature dependence of samples 1 and 2 for T > 50 K demonstrates the same behavior as observed for Si-doped GaN epilayers containing a carrier concentration of 0.1 to 0.6 x 1018 cm-3 as shown in Fig. 5. However, the resistivity temperature 11


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dependence of these two NWs differs from that of epilayers at low temperature (T < 50 K). Whereas nearest neighbor hopping happened in epilayers, a metallic conduction is found to control the resistivity in NWs. This degenerate conduction could have different origins induced by the high surface to volume ratio of the NWs: i) near surface carrier depletion due to upward band bending induced by surface states or adsorbed species40, leading to metallic conduction in a core at low temperature, surrounded by a semiconducting shell, which dominates the conduction at 300 K; ii) inhomogeneous radial doping with a NW shell doping above the nMIT. Actually, as an example for sample 5, EDX has revealed a homogenous Si doping, making the effect the more likely in the present case. For more doped NWs, the resistivity does not vary with respect to temperature, until down to 5K, showing a metallic behavior. This finding is consistent with EDX observation (an average Si concentration of 1020 at/cm3) for sample 5. Moreover, this outcome is also compatible with the high doping level achieved on microwires previously reported41 (the gray dashed line in Figure 5). To further evaluate the doping level and the mobility quantitatively, back gate (BG) and lateral gate (LG) FET measurements combined with 2D finite element simulation using NextNano3 42 have been carried out. In NWFETs, the source, the drain and the lateral gate are defined by electron beam lithography mentioned before, and either the BG (the metalized back side of Si substrate) or the LG is biased to modify the current in the NW channel. A SEM image of one real device is shown in Figure 6(a) while schematics of BG and LG FET measurements are illustrated in Figure 6(b) and (c), respectively. Two sets of typical NW channel current (Isd) versus source-drain voltage (Vsd) data measured from a single NID GaN NW-FET at different BG and LG voltages are 12


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demonstrated in Figure 6(d) and (e). The linear Isd-Vsd relationship at zero gate voltage reveals the ohmic characteristics of the source and drain contacts; the conductance decreases when the negative BG or LG voltage increases, inferring that the intrinsic doping for NID NW is n-type. For doped NWs, however, the conductance does not vary while changing the gate voltage, showing that the doping level in these NWs is much higher than that in NID ones. The BG FET is commonly used to estimate the doping concentration and the mobility in the NW, with the BG-NW capacitance C modeled using the following analytical equation2,43.

≅ 2 /ln ( )

(2)

Where is the relative dielectric constant of the oxide, h is the thickness of the gate oxide, and L, r are the length and the radius of the NW channel between source and drain, respectively. However, this model lacks accuracy due to the assumption that an electrostatically metallic cylinder wire is surrounded entirely by the dielectric oxide44, which is not the same case as in reality. In fact, it has been reported that this analytical equation overestimates the capacitance with a factor of 2 to 3 compared with the value obtained by numerical simulation.45,46 Thus, we have used 2D finite element simulation to model the gate-NW capacitance and further extract the doping level of the NW channel (detailed in Figure 6 and Supporting Information). Numerous NID NW FET devices have been evaluated using this method. The doping level of these NWs ranges from 4 x 1017 at/cm-3 to 6 x 1018 at/cm-3, showing an inhomogeneous residual doping among these NWs, which is consistent with resistivity measurements. The gate-NW capacitance value is around a factor of 2 or 3 lower than that calculated by the analytical equation (2), which agrees with the literature and confirms the necessity of numerical simulation in the NW FET system45,46. In addition, the same NW was evaluated by both BG FET and LG FET, and we have found that the doping level determined by BG is twice larger than that 13


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evaluated by LG. One reason for this discrepancy could be that in the case of LG, only the part of the NW facing the LG was depleted, whereas the whole NW channel was involved in depletion with the BG. Moreover, the method of BG is less accurate due to the difficulties to estimate the interface charges between the NW and the oxide. In this 2D simulation, the length of the NW is excluded from the parameters; however, since the L/r ratio of the MBE-grown NWs varies from 25 to 55, 3D simulation is not really necessary considering that there is not so much difference between 2D and 3D simulation results according to the reference46. The error bar in this model comes from the uncertainty of the determination of the device dimensions from the SEM images, such as the NW length, radius and the distance between the LG and the NW. Since the doping level obtained for NID NW is around the metal-insulator transition, we consider that full ionization is achieved in the NWs and the mobility can be deduced by using the following equation,

=

(6)

Where e is the electron charge; ρ is the NW resistivity; n is the electron carrier concentration, which equals the doping level in this case. For sample 1 and 5, we assumed n = determined by FET and EDX, respectively. Mobility dependence on the carrier concentration of these NID NWs is shown in Figure 7. Most of the NID GaN NWs have a state-of-art mobility and a similar behavior compared to GaN films39,47-52 limited by impurity scattering. The two NWs with low mobility values are affected by surface-scattering due to their extreme small radius around 20 nm.43 Even with doped NWs, such as sample 5, the mobility value is quite similar compared to the state-of-art value on the Si

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doped MOVPE GaN microwires41, it implies that we can achieve high doping level in GaN NWs without declining the mobility. Moreover, the LPP+ mode observed by Raman on another as-grown NID sample (the same growth condition as for sample 1), provides an alternative estimation of doping concentration by a detailed fitting based on the dielectric model developed by Hon and Faust53. The doping level is in the range 2-3 x 1017 cm-3, which is in the same order of magnitude as determined by electrical measurements. Considering the inhomogeneous residual doping among different NID NWs, the results of Raman and FET are quite consistent. Whereas for samples with higher doping levels the LPP+ mode is overdamped and cannot be detected, this above mentioned agreement is a further evidence that for NID or lowly doped GaN NWs, Raman spectroscopy, which is comparatively easier to perform than electrical measurements can be safely used to assess the n-type doping level. To summarize, a series of Si doped MBE grown GaN NWs has been investigated structurally and electrically. In particular, we have found that the Si content in GaN NWs is higher than in the 2D case, up to 2~4 x 1020 at/cm3 accompanied with an Si enriched shell for the most doped sample. Direct transport measurements on single NWs have shown a controlled doping with resistivity from 102 to 10-3 Ω.cm, and a carrier concentration from 1017 to 1020 cm-3. FET measurements combined with 2D finite element simulation have shown a high mobility in these NWs, comparable to the state of the art mobility value of GaN epilayer. ASSOCIATE CONTENT Supporting Information

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Additional information, TEM-EDX and SEM-EDX data on sample 5, the detailed method of doping level determination using FET measurements combined with NextNano3 simulation. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Notes The authors declare no competing financial interest. ACKNOWLEDGEMENTS The authors acknowledge Y. Cure for technical assistance of MBE growth, the Nanofab team at Institut Néel for the use of their facilities and their technical assistance, as well as P. Tchoulfian for fruitful discussions.

Figure Captions Figure 1. (a, c) side view and (b, d) top view SEM images of GaN NWs grown with Si cell temperature of 938 °C and 950 °C, respectively; (e) side view of one NW grown with Si cell temperature of 950 °C; (f) NW length (left axis, black data points) and NW radius (right axis, red data points) of samples grown upon different Si cell temperatures; the blue data points

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correspond to NW length and radius of NID GaN NWs; (g) NW radius variation with the height of the NW, measured along the dashed line in (e). Figure 2. (a) Raman spectra of as-grown samples with different Si cell temperatures, together with a Si substrate reference; (b) Evolution of the peak frequency of the E2h mode as a function of Si cell temperature. The right scale gives the corresponding in-plane strain calculated within the biaxial and deformation potential approximations27. Figure 3. EDX maps of two NWs grown with Si cell temperature of 950 °C obtained: (a) at 200 kV using a FEI Osiris TEM equipped with super X detectors and (b) at 4 kV using a ZEISS Ultra 55 SEM equipped with FlatQuad annular detector. Two elements are highlighted, with green and red corresponding Si and Ga, respectively. Si concentrations were computed using the zeta-factor method23 for STEM EDX data (blue line profile in (c)) and φρz standard method24 for the SEM EDX data (white circles in (c)). The NW thickness of the STEM observation is shown on the red curve in (c). Figure 4. Room temperature four-probe resistivity versus NW radius of samples 1 to 5 ranging from the NID NWs to the second most doped ones, and a SEM image of one contacted NW is included in the inset. Figure 5. Four-probe resistivity of samples with various doping levels (different colors) versus the inverse of the temperature (1000/T), symbols denote the experimental points, solid lines represent fits according to the exponential law

= ! + ! # $%&/'( , where the first term

represents the metallic conduction, the second term stands for the ionization of the electrons from the Si donor level to the conduction band. The dotted line represents resistivity data 17


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determined by Hall measurements for GaN epilayers with different Si doping levels (carrier concentration is designated close to the corresponding line, with a unit of 1018 cm-3 )39, and the gray dashed line stands for high conducting Si-doped GaN microwire previously reported41. Figure 6. (a) A tilted view SEM image of one FET device with both BG (not shown) and LG. Schematic of BG and LG FET measurements, (b) and (c) respectively. BG (d) and LG (e) dependent Isd-Vsd data measured on one NID NW with the radius of 30 nm. The BG and LG voltages for each Isd-Vsd curve are indicated. Cross-sectional (y-z plane) schematics of the BG (f) and LG (g) models considered in NextNano3

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simulation. Calculated 2D electron density

maps in one GaN NW, with BG (h, j, l) and LG (i, k, m) of 0 V, - 5 V, - 10 V respectively. Figure 7. Mobility as a function of carrier concentration for GaN. For sample 1 and 5, we assumed n = Nd, determined by FET and EDX, respectively. Experimental mobilities have been reported for NID GaN films (gray open squares)47,48 and Si doped GaN films (black open circles)39,48-52. and two Si-doped GaN microwires ( blue open triangles)41. The mobility values of our NWs are shown as solid stars; black and red correspond to sample 1 and sample 5, respectively. For sample 1, the radii of the two NWs with lower mobility (less than 10 cm2 V-1 s1

) are 24 nm and 20 nm, and those of the other ones are in the range of 30 – 40 nm.

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Figure 1.

Figure 2.

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Figure 3.

Figure 4.

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Figure 5.

Figure 6.

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Figure 7.

Table 1 Si cell temperature, NW radius, and NW resistivity (300 K) of sample 1-5 Sample

Si cell temperature (°C)

1

-

2

(NID sample)

NW radius NW resistivity (nm) (Ω.cm) 20~30

0.03~70

875

25~30

0.015~0.016

3

900

40~55

0.0023~0.0028

4

925

33~45

0.0027~0.0033

5

938

40~70

0.0012~0.0018


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