p-Type Doping of GaN Nanowires Characterized by

Letter pubs.acs.org/NanoLett

p‑Type Doping of GaN Nanowires Characterized by Photoelectrochemical Measurements Jumpei Kamimura,*,† Peter Bogdanoff,‡ Manfred Ramsteiner,† Pierre Corfdir,† Felix Feix,† Lutz Geelhaar,† and Henning Riechert† †

Paul-Drude-Institut für Festkörperelektronik, Hausvogteiplatz 5-7, 10117 Berlin, Germany Helmholtz-Zentrum Berlin für Materialien und Energie GmbH, Institute for Solar Fuels, Hahn-Meitner-Platz 1, 14109 Berlin, Germany

‡

S Supporting Information *

ABSTRACT: GaN nanowires (NWs) doped with Mg as a ptype impurity were grown on Si(111) substrates by plasmaassisted molecular beam epitaxy. In a systematic series of experiments, the amount of Mg supplied during NW growth was varied. The incorporation of Mg into the NWs was confirmed by the observation of donor−acceptor pairs and acceptor-bound excitons in low-temperature photoluminescence spectroscopy. Quantitative information about the Mg concentrations was deduced from Raman scattering by local vibrational modes related to Mg. In order to study the type and density of charge carriers present in the NWs, we employed two photoelectrochemical techniques, open-circuit potential and Mott−Schottky measurements. Both methods showed the expected transition from n-type to p-type conductivity with increasing Mg doping level, and the latter characterization technique allowed us to quantify the charge carrier concentration. Beyond the quantitative information obtained for Mg doping of GaN NWs, our systematic and comprehensive investigation demonstrates the benefit of photoelectrochemical methods for the analysis of doping in semiconductor NWs in general. KEYWORDS: GaN, nanowires, Mg doping, MBE, photoelectrochemical, Raman spectroscopy measuring large numbers of NWs. In particular, the first Hall measurements of NWs were published only recently,32,33 although such measurements are the standard method to characterize doping in thin films. A less demanding contact geometry is required for photoconductivity as well as fieldeffect transistor measurements, and the electrical properties of Si-doped GaN NWs were characterized this way. 34−36 However, such single NW measurements require the growth of long NWs, which is hindered by the fact that in molecular beam epitaxy (MBE), the synthesis technique for the majority of past studies, Mg incorporation induces lateral growth and coalescence.18−26 A much easier approach for the contacting of NWs is pursued in photoelectrochemical (PEC) measurements,37 for which the as-grown NW ensembles are simply immersed into a liquid electrolyte to form a NW−electrolyte contact. Such measurements are possible for any sample morphology, and the experimental procedure is basically the same for measurements on NWs and thin films. Complicated processing steps involving expensive facilities such as electron beam lithography are not required. Furthermore, PEC measurements directly provide an

G

aN-based nanowires (NWs) have received increasing attention over the past decade for light-emitting devices1−5 and solar energy harvesting.6−12 By alloying with In, the bandgap of this material class can be tuned from the ultraviolet to the near-infrared region, thus covering the entire solar spectrum. In the NW geometry, a wider spectral range for efficient light emission and absorption can be achieved than in the corresponding planar films, because strain induced by lattice mismatch in heterostructures can elastically relax at the free NW sidewalls.13,14 In addition, the pinning of the Fermi level at the NW sidewalls gives rise to a radial Stark effect that is advantageous for solar energy applications. 15 For the implementation of these benefits in semiconductor devices, extrinsic doping and the evaluation of electrical properties are key prerequisites. GaN is known as n-type material, and the realization of p-type GaN by doping with Mg16,17 triggered a rapid increase of applied research around 1990 that was eventually recognized by the Nobel prize in physics 2014. The doping of GaN NWs by Mg has been investigated in a number of publications,18−30 but the electrical properties of such NWs have been reported to our knowledge in only a single publication.28 Characterizing the electrical properties of NWs is generally difficult for any material system, because to this end individual dispersed NWs are contacted for electrical measurements, which requires challenging processing procedures.31 Furthermore, this approach is not practical for © 2017 American Chemical Society

Received: November 1, 2016 Revised: January 20, 2017 Published: February 6, 2017 1529

DOI: 10.1021/acs.nanolett.6b04560 Nano Lett. 2017, 17, 1529−1537

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Figure 1. SEM top-view (left) and cross-sectional (right) images of GaN NWs; (a) undoped, (b) TMg = 430 °C, (c) TMg = 470 °C, (d) TMg = 510 °C, (e) TMg = 550 °C, and (f) TMg = 590 °C.

Figure 2. Photoluminescence spectra acquired at 10 K of the (a) near-band edge and (b) total emission of GaN NWs grown with various Mg cell temperatures indicated in the diagrams. The spectra in (b) have been vertically shifted for clarity. (c) Intensity ratio INBE/IMg as a function of the Mg cell temperature. The intensity INBE is related to near-band edge transitions, that is the total integrated intensity of the (D0,XA), XA, and XB lines. The Mg-related emission intensity IMg is the total intensity of the transitions DAP, (A0,XA), and of the one at 3.45 eV.

GaN NWs were grown in the self-induced approach on ptype Si(111) substrates by plasma-assisted MBE. Prior to the growth, the native oxide of the p-Si substrates was removed by an ex situ HF (5%) treatment followed by an in situ thermal cleaning until the 7 × 7 reconstructed surface of Si(111) was observed by reflection high-energy electron diffraction (RHEED). Then, the Si substrates were exposed to nitrogen plasma for 5 min by opening the shutter of the N plasma cell before NW growth was initiated by the opening of the Ga shutter. After the observation of the first RHEED signal indicating the nucleation of GaN, NWs were grown for 1.5 h with a Ga flux of 5 nm/min and an active nitrogen flux of 10 nm/min (fluxes are indicated in equivalent growth rates as deduced from reference experiments with planar layers).46 The substrate temperature (Tsub) was 800 °C and was measured by a pyrometer. Note that usually lower substrate temperatures are chosen for such samples to facilitate the incorporation of Mg. However, we wanted to obtain a high crystalline quality as warranted by high substrate temperatures.47 To compensate Mg re-evaporation, we used rather high Mg fluxes. For Mg

average value for the entire NW ensemble. More specifically, measurements of the open-circuit potential (OCP) in the dark and under illumination allow the identification of the conductivity type, and an analysis of capacitance−voltage curves obtained by Mott−Schottky measurements provides in addition the density of net ionized dopants as well as information about the flat-band potential.37 Such experiments have been carried out with NWs made from various materials but without any systematic investigation of how the measurements vary with dopant concentration.38−45 Here, we employ both types of PEC measurements to study the electrical properties of a systematic series of GaN NW samples grown by MBE with different supplies of Mg. Photoluminescence (PL) and Raman spectroscopy confirm that the Mg concentration in the samples varies in a systematic way, and the highest value is estimated as 5 × 1019 cm−3. By the PEC methods, we observe the expected transition from n- to ptype conductivity with increasing Mg concentration and quantify the charge carrier concentration. 1530


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Figure 3. Raman spectra from undoped as well as Mg-doped GaN NWs with different TMg as indicated in the figure. The Raman spectrum of p-type Si(111) is shown for comparison. For clarity, different spectral regions are displayed with different resolution, and the intensities in the different diagrams were scaled differently. The inset shows an estimation of the Mg acceptor concentration (blue circles) based on the ratio ILVM/IE2 (red squares) as a function of TMg. ILVM and IE2 are the intensities of the most prominent LVM peak at 656 cm−1 and the E2(high) phonon line, respectively.

result of this lateral growth, coalescence between adjacent NWs is observed for high TMg, and the overall morphology is strongly affected. The NW length is about 0.6 μm for all samples. Figure 2a shows the near-band edge LT-PL spectra taken at 10 K for GaN NW samples grown with different Mg fluxes. The PL spectrum for the NWs grown with low Mg flux (TMg = 470 °C) is dominated by the recombination of A excitons bound to donors (D0,XA) at 3.471 eV, indicating that little Mg was incorporated into these NWs. The energy position of the (D0,XA) line agrees well with that found for bulk GaN crystals,47,48 which means that the NWs are essentially free of homogeneous strain. The full width at half-maximum (fwhm) for this line is 1.6 meV, which is in agreement with what was reported for nominally undoped GaN NWs grown at the same temperature.47 The lines centered at 3.478 and 3.484 eV are related to free A and B excitons, respectively, that at 3.466 eV corresponds to the recombination of excitons bound to Mg acceptors (A0,XA), and the lines between 3.4 and 3.425 eV correspond to the recombination of excitons bound to I1 basal plane stacking faults (I1,X).49 With increasing TMg, the line width of the (D0,XA) transition increases significantly (fwhm of 13 meV for TMg = 550 °C). We ascribe this increase to the increase in the coalescence degree with TMg (see Figure 1), which results in larger inhomogeneous strain.50 The evolution of the (A0,XA) line with TMg is of particular interest for the assessment of the Mg incorporation into our NWs. The (A0,XA) line not only gets stronger with increasing TMg but also redshifts and broadens. This change could be related to the development with increasing TMg of an additional line related to Mg and centered at 3.45 eV that actually dominates the PL spectrum for TMg = 590 °C (a similar behavior was reported in ref 51 for a p-doped GaN film). However, as a note of caution we point out that self-induced unintentionally doped GaN NWs often show an emission band around 3.45 eV, which arises from exciton recombination at inversion domain boundaries.52,53 Another indication of Mg incorporation is the observation of PL from donor−acceptor pairs (DAP). Figure 2b depicts the same spectra as seen in Figure 2a in a wider energy range. All spectra exhibit a broad emission band peaking at 3.28 eV and

doping, effusion cell temperatures (TMg) between 430 and 590 °C were used, corresponding to beam equivalent pressures of 1.3 × 10−8 to 7.8 × 10−7 mbar. In the following, the GaN NW sample grown without intentional incorporation of Mg is referred to as undoped. The NW morphology was analyzed with a scanning electron microscope (SEM). Low-temperature PL (LT-PL) spectroscopy was carried out by exciting the GaN NW ensembles with the 325 nm line of a continuous-wave HeCd laser. The laser light was focused down to a spot with a 2 μm diameter using a near-UV objective with a numerical aperture of 0.65. The PL signal was collected with the same objective, sent to a 80 cm focal length monochromator for spectral dispersion (600 g/mm grating), and detected using a liquid-N2-cooled charge-coupled device (CCD). For micro-Raman , the samples were optically excited at 3.06 eV (405 nm). The Raman signal was dispersed with a 1800 g/mm grating in an 80 cm spectrograph and detected by a liquid-N2-cooled CCD. These measurements were performed at room temperature in backscattering geometry, along the caxis of the NWs. For the PEC measurements, the samples (1 × 1 cm2 size) were mounted onto a sample holder using epoxy resin. The sample holder had a hole at its center in order to contact the sample from the backside without any contact to the electrolyte. As a backside contact, an In−Ga eutectic alloy was used. OCP measurements were carried out using a potentiostat in a three-electrode PEC cell with a platinum wire as the counter electrode, a Ag/AgCl electrode as the reference electrode (Eref = +200 mV versus normal hydrogen electrode), H2SO4 (0.5 M) as an electrolyte, and a Xe lamp as a light source (light intensity ≈ 100 mW/cm2). Mott−Schottky measurements were performed in the same PEC cell in the dark using a potentiostat/frequency analyzer. The signal was modulated with 10 mV amplitude with frequencies ranging from 1 to 10 000 Hz. SEM images revealing the morphologies of all the GaN NW samples grown with different Mg fluxes are displayed in Figure 1. In agreement with previous reports,18−26 increasing the Mg flux leads to an increase in NW diameter, which in our case is from 52 ± 30 (undoped) to 130 ± 80 nm (TMg = 590 °C). As a 1531


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260, 358, 365, and 656 cm−1 are clearly detected in good agreement with the theoretically predicted frequencies of 267, 359, 366, and 660 cm−1.59 Experimental evidence for the LVMs at 358 and 365 cm−1 is reported here for the first time, although it should be noted that a mode around 358 cm−1 can also be seen in the Raman spectrum of a heavily Mg doped GaN film in ref 60 but was not assigned to an LVM. According to theory, the LVMs at 359 and 366 cm−1 are of A1 and E symmetry, respectively.59 As discussed already above for the LO phonon mode of GaN, the observation of the LVM with E symmetry can be explained by the fact that light coupling into and out of the NWs occurs predominantly through their sidewalls.55,56 In addition to the vibrations of substitutional Mg atoms on a Ga site, LVMs of Mg−H complexes are detected at 2130, 2149, 2166, 2186, and 2219 cm−1. These hydrogen-related Raman lines have been reported previously for Mg concentrations above 6 × 1018 cm−360 and are presumably the origin of the acceptor related PL line at 3.45 eV. The superimposed broad Raman band in the range from 2220 to 2270 cm−1 is also observed in accordance with previous reports on heavily Mgdoped GaN films.61 In contrast, we did not detect a Raman peak around 3100 cm−1, previously assigned to a MgNH complex that is assumed to be responsible for electrical compensation of the p-type doping.62 The peak at 2330 cm−1 originates from Raman scattering by N2 molecules in the ambient air. Last, it is noteworthy that very weak Mg-related LVMs can be seen also for TMg = 470 °C. The intensities of LVMs in Raman spectra can be utilized to estimate the respective impurity concentration.63 As a reference signal from the GaN host material, we use the intensity of the E2(high) phonon line which is expected to be essentially unaffected by the Mg doping. Consequently, we determine the concentration of Mg atoms on Ga sites from the relationship [Mg] = S·ILVM/IE2, where ILVM and IE2 are the intensities of the most prominent LVM peak at 656 cm−1 and the E2(high) phonon line, respectively. For the determination of the scaling factor S, we extracted the intensity ratio ILVM/IE2 from Raman spectra shown in refs 59 and 60 for GaN/Mg layers grown on sapphire (0001) substrates by MBE with Mg concentrations of 1.2 × 1019 and 8 × 1019 cm−3 (488 nm excitation). Because the morphology of the Mg-doped NW ensembles approaches that of a compact layer for the highest doping levels [see Figure 1f], it is reasonable to use the spectrum obtained for backscattering from a C-plane surface for reference purposes. In addition, we verified that the ratio ILVM/IE2 does not change significantly when changing the excitation wavelength from 405 to 473 nm. Using the obtained scaling factor of S = 7.8 × 1020 cm−3, we estimated the concentration [Mg] ≈ 5 × 1019 cm−3 for the most heavily doped sample (TMg = 590 °C). As shown in the inset of Figure 3, the ratio ILVM/IE2 indicates an increasing Mg doping level in the samples with TMg = 510, 550, and 590 °C, respectively. However, because the morphology and hence the scattering geometry differs for these samples, the estimation of the Mg concentration can be considered reasonably accurate only for the highest TMg. The maximum Mg concentration we deduced is in the range of the highest Mg concentrations measured by secondary ion mass spectrometry for both planar layers60,62,64 and NWs.19,20 Now that we have ascertained that the Mg concentration in our GaN NW samples varies systematically as intended, we turn to the investigation of the free charge carriers by PEC methods. First, we consider OCP measurements performed in the dark and under illumination. Two representative examples of the

associated with DAP transitions and their LO phonon replica. To analyze more quantitatively the effect of Mg on the PL spectra, we define the intensity INBE related to near-band edge excitons as the total integrated intensity of the (D0,XA), XA, and XB lines, and the Mg-related emission intensity IMg as the total intensity of the transitions DAP, (A0,XA), and of the one at 3.45 eV. The ratio INBE/IMg, plotted in Figure 2c as a function of Mg cell temperature, exhibits a strong and monotonic decrease with increasing TMg, indicating a clear evidence of increasing Mg incorporation into our GaN NWs. In order to estimate the actual Mg concentration in our NWs, we performed Raman spectroscopy. Figure 3 shows Raman spectra of all the GaN NW samples together with a reference spectrum taken on a bare p-Si(111) substrate. For clarity, different spectral regions are displayed with different resolution. In our experimental geometry, the dominating Raman signatures of the GaN host lattice are the E2(high) and LO phonon modes that we observe at about 567 and 734 cm−1, respectively.54 We attribute the small downshift of the E2(high) phonon line (from 567 to 566 cm−1) with increasing doping concentration to the tensile strain induced by coalescence between adjacent NWs.18 However, the large decrease in the energy of the LO phonon from 741 to 734 cm−1 cannot be explained in a consistent manner by tensile strain alone.55 Hence, we ascribe the additional shift of the LO phonon frequency to the change in the NW morphology induced by the Mg flux already discussed in relation with Figure 1. For relatively thin NWs, the coupling of light into and out of the NWs occurs in our geometry dominantly through their M-plane sidewalls, and this coupling geometry gives rise to the E1(LO) phonon mode at approximately 741 cm−1.55,56 The importance of the regular NW morphology is corroborated by the fact that surface-related phonon modes (S1 and S2) at frequencies below the E1(LO) phonon line57 are seen only for undoped NWs and the lowest TMg = 430 °C. In contrast, the limit of a fully coalesced NW ensemble (TMg = 590 °C) resembles more the case of a compact GaN layer. In this case, light is backscattered from a C-plane surface, and in this geometry the A1(LO) phonon line at 734 cm−1 is observed.56 Consequently, we explain the Mg-induced shift of the LO phonon partially by the observation of quasi-LO (QLO) phonon modes with a continuous change from the E1 toward the A1 character. It should be mentioned that a similar doping-induced shift of the LO phonon frequency in Mg-doped GaN NWs was interpreted by Wang et al. in terms of LO phonon-plasmon coupling and decoupling.25 However, in our case we know from the OCP and Mott−Schottky measurements discussed below that increasing Mg flux leads to a transition from the n-type conductivity of the nominally undoped NWs to electrical compensation and finally p-type conductivity, and this transition is inconsistent with a monotonic downshift of a LO phonon-plasmon coupled mode. Also, note that phonon confinement would lead to a frequency downshift with decreasing diameter and thus cannot explain the observed behavior, either.58 Another effect of the change in morphology with increasing Mg flux is the occurrence of broad Raman bands at 320 cm−1 for the heavily doped samples with TMg ≥ 470 °C, because these bands are attributed to disorder-activated (DA) phonon scattering.59 In addition, the spectra contain modes originating from the Si substrate as indicated in the figure. As a fingerprint of Mg atoms incorporated substitutionally on Ga sites, for TMg > 470 °C the local vibration modes (LVMs) at 1532


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around 2.4 V versus Ag/AgCl obtained by the Mott−Schottky measurements discussed below. This discrepancy indicates that the OCP value under illumination did not reach the flat-band potential due to the high carrier recombination rate. This effect is also the most likely explanation for the reduction in ΔOCP observed for TMg > 510 °C, because these samples suffer most from coalescence, which is known to introduce crystal defects.65,66 In any case, OCP measurements are a simple way to determine the conductivity type of semiconductor NWs. In order to obtain quantitative information about the charge carrier concentration, we performed Mott−Schottky measurements in the dark. The inverse square of the measured capacitance is plotted as a function of the applied potential to facilitate the analysis according to the Mott−Schottky equation that describes the relationship between the charge layer capacitance C and the applied potential E37 1 2 = 2 (E − Efb) 2 (1) C εA eN

OCP response are depicted in Figure 4a. For the undoped sample, upon illumination the OCP decreases rapidly and

Figure 4. Results of OCP experiments with GaN NWs in a threeelectrode PEC cell. All voltages are indicated with respect to the reference electrode. (a) OCP response of undoped and Mg-doped (TMg = 510 °C) GaN NWs. Initially, the light was off, and it was switched on at time zero. When the OCP saturated, the light was switched off again. The arrows indicate the difference between the saturation values of the OCP under illumination and in the dark, that is, ΔOCP. (b) ΔOCP as a function of Mg cell temperature.

Here, ε = εrε0, εr = 10 is the relative dielectric constant of GaN, ε0 is the permittivity in vacuum, A is the surface area, e is the electron charge, and N is the net ionized donor or acceptor density. The latter value is positive for net ionized donors and negative for net ionized acceptors. Efb is the flat-band potential, and the small influence of temperature is neglected. The term E − Efb = ESC is the potential difference across the space-charge region. The conductivity type is thus directly obtained from the sign of the slope, which is positive and negative for n- and ptype conductivity, respectively. Furthermore, the net ionized donor/acceptor densities can be extracted from the value of the slope in Mott−Schottky plots. Equation 1 is well-known but of limited use in our case because it is derived from the geometry of planar semiconductors. In the nanowire geometry, that equation is not appropriate anymore, and the depletion layer may easily exceed the nanowire radius for sufficiently low carrier density. Therefore, we employ a cylindrical model in order to obtain the net ionized dopant densities for our samples.44,45 In this geometry, the potential difference across the space-charge region can be expressed as

saturates at a negative value. When the light is switched off, the OCP slowly increases again. In contrast, for the doped sample the opposite behavior is observed. These results can be understood as follows: in the dark, n-type (p-type) semiconductors in contact with an electrolyte usually exhibit an upward (downward) surface band bending. Under illumination, free minority charge carriers are generated by the absorbed photons, which leads to an upward (downward) shift of the electron (hole) quasi-Fermi level of the NW surface and to a flattening of the bands. As a result, the OCP shifts to negative (positive) potentials. In other words, the shift of the OCP upon illumination indicates the type of conductivity. The response seen in Figure 4a is as expected for GaN, which is p-doped by Mg but n-type when nominally undoped. The difference between the OCP under illumination and in the dark, ΔOCP, is presented for all samples in Figure 4b. As explained above, positive and negative values indicate p- and ntype conductivity, respectively. The nominally undoped sample is n-type, and this is also the case for the sample with TMg = 430 °C. All other samples are p-type. Apparently, the amount of Mg supplied for TMg = 430 °C is not sufficient to compensate the parasitic incorporation of O and Si shallow donors. This finding agrees qualitatively with the spectroscopic results. For samples with TMg up to 470 °C the LT-PL spectra are dominated by the (D0,XA) line and not by the Mg-related transitions [Figure 2a], and in the Raman spectra, Mg-related LVMs are not observed for TMg < 470 °C (Figure 3). In principle, ΔOCP indicates the potential change within the space charge layer resulting from Fermi level pinning at the surface. The saturation in the OCP response under illumination shown in Figure 4a corresponds to the steady state concentration of light-generated charge carriers, which is determined by the competition between their generation and recombination rates. Efficient radiative and nonradiative recombination processes would keep the charge carrier concentration low and thereby the position of the Fermi level away from the expected flat-band position. In fact, the saturated OCP value of 1.2 V versus Ag/AgCl for TMg = 510 °C under illumination is much lower than the flat-band potential of

ESC = −

⎛ x ⎞⎞ eN ⎛ 1 2 ⎜ (R − x 2) + R2 ln⎜ ⎟⎟ ⎝ R ⎠⎠ ⎝ 2ε 2

(2)

where R is the NW radius and x is the radius of the inner uncharged zone. The capacitance of the nanowire ensemble can be described by the well-known formula for cylindrical capacitors45 C=

2πεLD NW S

( Rx )

ln

(3)

where L is the NW length, DNW is the number density of NWs per substrate surface unit, and S is the total substrate surface. Average values for R, L, and DNW can be determined from SEM images, and then the net ionized dopant density N and flatband potential Efb of the NWs can be extracted by fitting eqs 2 and 3 to the experimental Mott−Schottky curves. We note that these equations are based on the assumption of a homogeneous distribution of dopants inside the NWs. Representative Mott−Schottky curves for n- and p-GaN NWs as well as a p-Si substrate used as reference are displayed in Figure 5a,b. Curves related to NWs are completely different from that of the p-Si reference sample. Therefore, the obtained 1533


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in the n- and p-type GaN NWs with respect to the Ag/AgCl reference electrode. Because the Fermi levels for n- and p-type GaN are close to the minimum of the conduction band and to the maximum of the valence band, respectively, the difference between the two values of Efb corresponds as expected approximately to the bandgap of GaN (3.4 eV). The occurrence of two different slopes in Mott−Schottky curves was already observed also in Fe2O3 and Cd1−xZnxS and was attributed to the presence of both shallow and deep donors.67,68 It has also been reported previously for MBEgrown GaN layers containing deep level traps.69,70 Similarly, we explain the Mott−Schottky curves of our n-type GaN NWs by the contribution of both shallow and deep donors, as sketched in Figure 5c and explained in the following. The slope in region (1) is observed close to Efb, that is, for small ESC with moderate band bending. Thus, this slope represents shallow donor states [Figure 5c, (1)]. The slope in region (2) occurs for larger ESC and, thus, corresponds to stronger band bending. Under these conditions, the Fermi level Ef shifts so much that deep donor levels are also ionized [Figure 5c, (2)]. In order to estimate the energy position EDD of the deep donor level, we define the difference between Efb and the inflection point from region (1) to (2) in the Mott−Schottky curves [see Figure 5a] as the critical potential Ecrit. As can be seen from the sketches in Figure 5c, with increasing bias at some point Ef crosses EDD, which leads to the ionization of the deep donors resulting in the change of the slope. Ecrit roughly equals EDD and for our n-type GaN NWs it amounts to about 500 mV. This value agrees fairly well with the activation energy 570 meV that was measured by deep level transient spectroscopy for one of the two deep levels found in the depletion region of (In,Ga)N/GaN NW light-emitting diodes (LEDs).71,72 In those studies, the corresponding deep level was assigned to nitrogen antisite defects. This comparison supports our interpretation of the two slopes in the Mott−Schottky plots as originating from shallow and deep donors. Therefore, we attribute the slope observed in region (2) of the Mott− Schottky curves to deep level activation in n-type GaN. For the interpretation of the Mott−Schottky curves for the p-type GaN NWs we have to take into account that Mg in GaN is not a shallow acceptor. In fact, for all the corresponding curves Ecrit is about 300 mV, which is close to the acceptor binding energy of 245 ± 25 meV reported for isolated Mg atoms in GaN.73 However, the acceptor ionization energy of Mg in GaN depends strongly on the acceptor concentration due to the impurity-band formation induced by the wave function overlap of the Mg acceptor states.73 As a consequence, the apparent acceptor ionization energy decreases with increasing acceptor concentration. In particular, for acceptor concentrations above 5 × 1019 cm−3 apparent ionization energies below 70 meV were found.73 Therefore, at high doping levels Mg acceptors exhibit binding energies between those of deep and shallow donors. Because we know from our PL and Raman analysis that all our samples with p-type conductivity contain a high concentration of Mg, we attribute as a consequence both slopes in regions (1) and (2) in the Mott−Schottky curves of p-type NWs to intermediate (relatively deep) Mg acceptors, as sketched in Figure 5d. Region (1) corresponds to the bias regime in which a small fraction of the Mg acceptors (on the level of a few percent of the total Mg acceptor concentration) are thermally ionized at room temperature. In analogy to the contribution of deep donors in n-type NWs, region (2) is attributed to the additional

Figure 5. Results of Mott−Schottky measurements. Mott−Schottky plots for (a) n-type GaN NW samples and a p-Si substrate used as reference, and (b) p-type GaN NW samples (open circles are experimental data points and solid lines are fits). Schematic band diagram for a system with shallow and deep donors (c) and relatively deep acceptors (d) under (0) flat-band condition, (1) small bias condition, and (2) strong bias condition. Ec and Ev are the edge of conduction band and valence band, respectively. ESC is the applied reverse bias with respect to Efb, Ef is the Fermi level, ESD is the shallow donor level, EDD is the deep donor level and EIA is the intermediate acceptor level. The corresponding regions in the Mott−Schottky plot are indicated in (a) for the NW sample with TMg = 430 °C and (b) for the NW with TMg = 470 °C by the labels (0), (1), and (2). (e) Net ionized dopant density obtained from fitting of the slope in the region (1) by eqs 2 and 3 as a function of Mg cell temperature.

data represent the characteristics of our GaN NWs rather than that of the p-Si substrate. For the planar p-Si sample, we extracted an ionized acceptor density of 9 × 1016 cm−3 from a linear fit according to eq 1, which is in good agreement with the doping level specified by the vendor. For the curves related to GaN NWs, we observe two distinct regions (1) and (2) exhibiting strongly different slopes, a phenomenon that will be discussed in more detail below. However, the sign of the slopes implies that the undoped NWs and those grown with TMg = 430 °C are n-type [Figure 5a], while all other samples are ptype [Figure 5b], which is in agreement with the OCP experiments. From a simple visual extrapolation of the Mott− Schottky curves to zero as well as from our fits we find that the flat-band potentials are equal to about −1 V for n-type [Figure 5a] and about 2.4 V for p-type GaN NWs [Figure 5b]. These values represent in fact the relative positions of the Fermi levels 1534


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Nano Letters acceptor ionization, which sets in when Ef crosses the binding energy [Figure 5d, (2)]. Consequently, the slope in region (2) reflects the total concentration of Mg acceptors. Now we turn to the quantitative analysis of the electrically active dopant concentrations. We determined the net ionized dopant density for thermally ionized donors or acceptors in NWs by fitting the Mott−Schottky curves in region (1) according to eqs 2 and 3 as explained above and in more detail in Supporting Information. The resulting ionized dopant densities N are shown in Figure 5e as a function of the Mg cell temperature. We note that we verified from our fit results that the depletion width at the critical potential was smaller than the average NW radius for all investigated samples, that is, the NWs were not fully depleted at the inflection point. Furthermore, we observed that the obtained values of N for ntype samples varied systematically with modulation frequency by about a factor of 2, and meaningful data were obtained for the p-type samples only for the low-frequency range between 1 and 100 Hz. The frequency dependence is discussed in more detail in Supporting Information, and here we only point out that the frequencies used for the further analysis of our p-type samples fall in the frequency range reported for similar measurements on a p-GaN layer.74 Consequently, we display in Figure 5e the mean N values averaged over the different modulation frequencies, and the error bars indicate the corresponding standard deviations. We observe in Figure 5e for TMg ≤ 430 °C only a partial compensation of the unintentional n-type conductivity, then for TMg > 430 °C a transition to p-type conductivity, and finally, for TMg ≥ 470 °C an increase in net ionized acceptor density with Mg flux. It is interesting to consider the results for the extreme samples in more detail. For the undoped GaN NWs, a net ionized shallow donor concentration of about 1.2 × 1018 cm−3 has been obtained. Because the donor levels of the typical unintentionally incorporated donors Si and O are very shallow, the corresponding extracted concentration is regarded as a free carrier density (assuming the deep donor states being fully occupied by electrons), This value is higher than that previously reported for unintentionally doped nanowires.75 However, we note that similar results have been reported for nominally undoped GaN NWs in refs 34, 36 (2 × 10 17 −6 × 1018 cm−3).34,36 The observation of narrow excitonic transitions for the sample grown with TMg = 470 °C (Figure 2b) is consistent with the fact that the unintentional n-type doping is compensated by the Mg acceptors. For the sample grown with the largest Mg flux, a net concentration of thermally ionized acceptors of 1.2 × 1018 cm−3 has been extracted, which corresponds approximately to the free hole density at room temperature.76 In order to estimate the total acceptor concentration from region (2) of the Mott−Schottky curve, we employ for simplicity in approximation the linear model of eq 1 [cf. solid line in the respective region of Figure 5b], because the formulas for the cylindrical geometry cannot be easily applied to this region of the curve. We expect the associated error to be small since the morphology of the sample resembles already that of a planar layer due to the pronounced coalescence occurring at large Mg fluxes (see Figure 1). The obtained value of 5 × 1019 cm−3 is in good agreement with the concentration of Mg atoms on Ga sites determined by Raman spectroscopy, and the ratio between hole density and Mg concentration is in accordance with what has been reported for planar layers.66,75

In summary, we have comprehensively investigated the Mg doping of GaN NWs. The increasing Mg content in our systematic series of NW samples is reflected in a consistent manner by changes in both the LT-PL and Raman spectra. Especially the LVM of substitutional Mg on Ga site allows for an estimate of the actual Mg concentration, and the highest value we have obtained is about 5 × 1019 cm−3. The most important part of our study is the determination of the electrical properties of the NWs by PEC methods. OCP measurements have revealed the conductivity type of the GaN NWs and as expected it changes from n-type for nominally undoped NWs over compensation for low Mg concentration to p-type for moderate to high Mg concentrations. We have confirmed this trend by an analysis of Mott−Schottky curves. In addition, we have obtained quantative values of net thermally ionized donors (acceptors) in n-type (p-type) NWs, which can be interpreted in terms of free electron (free hole) concentrations. The highest deep acceptor concentration we have extracted agrees well with the Mg concentration determined by Raman spectroscopy, and the highest hole concentration is determined to be 1.2 × 1018 cm−3. Beyond the direct benefit resulting from the information about the electrical properties of Mg-doped GaN NWs, our systematic study demonstrates that these two PEC techniques (OCP and Mott− Schottky measurements) are very useful for analyzing electrical doping in semiconductor NWs in general.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.6b04560. Detailed discussion of the fitting and of the frequency dependence of the Mott−Schottky plots (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Jumpei Kamimura: 0000-0003-3465-9869 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank A.-K. Bluhm for SEM support, H.-P. Schönherr for the maintenance of the MBE system, and U. Jahn, O. Brandt, as well as R. van de Krol for a critical reading of the manuscript. Stimulating discussions with A. Waag are gratefully acknowledged. J.K. is grateful for a JSPS Postdoctoral Fellowship for Research Abroad. P.C. acknowledges funding from the Fonds National Suisse de la Recherche Scientifique through project 161032.

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REFERENCES

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p-Type Doping of GaN Nanowires Characterized by

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