Addressing the Fundamental Electronic Properties of Wurtzite GaAs

Letter Cite This: Nano Lett. 2017, 17, 6540-6547

pubs.acs.org/NanoLett

Addressing the Fundamental Electronic Properties of Wurtzite GaAs Nanowires by High-Field Magneto-Photoluminescence Spectroscopy Marta De Luca,†,‡ Silvia Rubini,§ Marco Felici,† Alan Meaney,∥ Peter C. M. Christianen,∥ Faustino Martelli,⊥ and Antonio Polimeni*,† †

Dipartimento di Fisica, Sapienza Università di Roma, 00185 Roma, Italy Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland § Istituto Officina dei Materiali CNR, Basovizza 34149 Trieste, Italy ∥ High Field Magnet Laboratory (HFML − EMFL), Radboud University, NL-6525 ED Nijmegen, The Netherlands ⊥ Istituto per la Microelettronica e i Microsistemi CNR, 00133 Roma, Italy

Nano Lett. 2017.17:6540-6547. Downloaded from pubs.acs.org by STEPHEN F AUSTIN STATE UNIV on 07/31/18. For personal use only.

‡

S Supporting Information *

ABSTRACT: At ambient conditions, GaAs forms in the zincblende (ZB) phase with the notable exception of nanowires (NWs) where the wurtzite (WZ) lattice is also found. The WZ formation is both a complication to be dealt with and a potential feature to be exploited, for example, in NW homostructures wherein ZB and WZ phases alternate controllably and thus band gap engineering is achieved. Despite intense studies, some of the fundamental electronic properties of WZ GaAs NWs are not fully assessed yet. In this work, by using photoluminescence (PL) under high magnetic fields (B = 0−28 T), we measure the diamagnetic shift, ΔEd, and the Zeeman splitting of the band gap free exciton in WZ GaAs formed in core−shell InGaAs−GaAs NWs. The quantitative analysis of ΔEd at different temperatures (T = 4.2 and 77 K) and for different directions of B⃗ allows the determination of the exciton reduced mass, μexc, in planes perpendicular (μexc = 0.052 m0, where m0 is the electron mass in vacuum) and parallel (μexc = 0.057 m0) to the ĉ axis of the WZ lattice. The value and anisotropy of the exciton reduced mass are compatible with the electron lowest-energy state having Γ7C instead of Γ8C symmetry. This finding answers a long discussed issue about the correct ordering of the conduction band states in WZ GaAs. As for the Zeeman splitting, it varies considerably with the field direction, resulting in an exciton gyromagnetic factor equal to 5.4 and ∼0 for B⃗ //ĉ and B⃗ ⊥ĉ, respectively. This latter result provides fundamental insight into the band structure of wurtzite GaAs. KEYWORDS: GaAs nanowires, wurtzite, exciton, magneto-photoluminescence spectroscopy, effective mass, gyromagnetic factor, band-structure and the separation between the Γ7C and Γ8C conduction bands (CBs) is ∼70 meV, as suggested in ref 5 and confirmed by later reports.15 The closeness between the two conduction bands might be the reason for the uncertainty on their relative order reported in the literature. Theoretical investigations1,2,11 on this topic have also obtained quite different results. Because the Γ8C CB arises from the zone folding of a L-CB, the electron mass associated with Γ8C is expected to be larger (at least two times) than the one associated with a Γ7C level. As a consequence, the experimental determination of the value of the reduced mass of the band gap exciton would be instrumental to assess whether the CB minimum has a Γ7C or a Γ8C symmetry, as detailed in the following. Few experimental studies addressed the carrier effective mass in WZ GaAs NWs, even though this fundamental

T

he high surface-to-volume ratio of semiconductor nanowires (NWs) leads to the formation of crystal phases not attainable in the same semiconductors at ambient conditions.1 A renowned case is represented by GaAs NWs, in which the wurtzite (WZ) lattice can be often found at variance with bulk and thin film crystals, where only the zincblende (ZB) phase is observed. This has prompted the necessity of a full understanding of the basic electronic properties of the WZ lattice of non-nitride III−V compounds (e.g., InP, InAs, and GaAs).1−4 ZB GaAs, along with Si, is the most investigated semiconductor. However, in the case of WZ GaAs NWs, even the band gap energy value5,6 and the conduction band structure2,5,7−14 are still debated. Nevertheless, recent works on NWs, whose crystal purity was carefully assessed, point to an energy of the band gap exciton of WZ GaAs close to 1.520 eV at low temperature (the corresponding quantity in ZB is equal to 1.515 eV).5,15−17 Furthermore, the splitting between the Γ9 V and Γ7 VU valence bands (VBs) is commonly found equal to about 110 meV,5,12,15 © 2017 American Chemical Society

Received: May 24, 2017 Revised: October 3, 2017 Published: October 16, 2017 6540

DOI: 10.1021/acs.nanolett.7b02189 Nano Lett. 2017, 17, 6540−6547

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Nano Letters parameter provides precious indications on the band structure and rules the carrier response to external forces and the extent of quantum confinement.18,19 Previous works inferred the effective mass of electrons and/or holes through the carrier quantization energy associated with the formation of subbands in WZ quantum wires20 or with the carrier confinement energy in polytype nanodots.15 Values of the electron and hole effective mass were reported also by theoretical investigations1,2,11 showing a carrier mass increase and anisotropy stemming from the lowered symmetry of the WZ with respect to the ZB lattice. Instead, no previous theoretical determination of the carrier gyromagnetic factor, or g-factor, is available. The g-factor is especially important for it regulates spin properties and turns out to be a stringent validation quantity for model calculations of semiconductors. For this quantity too, very few experimental studies exist. The electron g-factor, ge, of WZ GaAs was determined (ge = 0.28) by spin-dynamics measurements under magnetic field (maximum field 0.4 T orthogonal to the NW axis) in core/shell GaAs/AlGaAs WZ NWs21 and the exciton g-factor, gexc, was derived by the Zeeman splitting (maximum field 10 T) observed in WZ/ZB quantum disks formed in GaAs NWs (gexc varying between 1.3 and 1.8 for field varying from perpendicular to parallel to the NW axis).22 Finally, high-field magneto-photoluminescence measurements were performed to assess the character of excitons in ZB GaAs NWs.23 In this work, we report on magneto-photoluminescence (PL) measurements at T = 4.2 and 77 K in WZ GaAs formed in core−shell (c-s) InGaAs−GaAs NWs. The PL spectra show an extremely narrow (∼1 meV) emission line at 1.522 eV, originating from the band gap exciton recombination in WZ GaAs.5,24 Magnetic fields up to 28 T were applied along and perpendicular to the WZ ĉ axis, in order to disclose possible band structure anisotropies related to the lattice hexagonal symmetry. The exciton line exhibits diamagnetic shift (ΔEd), Zeeman splitting (ΔEZ), and circular dichroism (CD) that all depend on the field intensity and/or direction. The ΔEd data are quantitatively reproduced and show that excitons moving in a plane containing ĉ are 9% heavier than in a plane perpendicular to ĉ. A markedly more pronounced anisotropy is exhibited by ΔEZ that at 28 T varies from 7 to 0 T. (b) Comparison between normalized PL spectra at B = 0 and 28 T, highlighting the absence of a sizable Zeeman splitting and the presence of a line narrowing induced by the magnetic field. The 28 T spectrum has been red-shifted for ease of comparison with the 0 T spectrum. Relative multiplication factors are provided. (c) Comparison between PL spectra at B = 27 T recorded under opposite circular light polarizations, showing the absence of circular dichroism in the Voigt configuration.

Figure 3. (a) Photoluminescence spectra of WZ GaAs NWs in Faraday configuration at T = 77 K for different magnetic fields and opposite circular light polarizations. For B > 0 T, Γ−5 and Γ+5 are the Zeeman split components of the FE, highlighted by σ− and σ+ circular polarization filtering. The differently polarized spectra are normalized at their maximum, while the relative intensity between the opposite circularly polarized spectra is maintained. (b) Comparison between PL spectra at B = 28 T recorded under opposite circular light polarization showing clear line Zeeman splitting and circular dichroism. (c) Energy dependence of the circular dichroism degree of PL signal for different field values.

narrowing is a consequence of the field-induced modification of the density of states from 3D- to 1D-like that is especially apparent at higher temperature, when thermal broadening is more important. The absence of Zeeman splitting points to a zero or negligibly small gexc for this field direction, as we will detail later. Notably, this result contrasts previous findings in

InGaAs26 and InP27,28 WZ NWs, where a line separation could ⃗ . In addition, panel (c) shows that the be revealed for B⃗ ⊥k//ĉ PL spectra are identical upon circular polarization filtering. In fact, when B⃗ ⊥k⃗ no circular dichroism is expected, thus confirming the correct relative alignment between the field and the NW orientation in the setup. 6542


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Nano Letters Furthermore, for B⃗ ⊥ĉ the axial symmetry of the WZ electronic states is strongly perturbed, leading to a mixing between Γ5 (bright) and Γ6 (dark) exciton states, therefore indicated as Γ5/6 for B > 0 T.29−31 A completely different behavior is observed in the Faraday ⃗ ), as shown in Figure 3. Panel (a) configuration (B⃗ //k//ĉ displays the PL spectra for different field intensities and opposite circular polarization. The exciton line clearly splits and blueshifts. It is found that under σ+ polarization PL is less intense than under σ− (the relative intensity between the opposite circularly polarized spectra is maintained in the figure), as it can be better appreciated in Figure 3b showing the PL spectra recorded at B = 28 T under opposite circular polarizations. The lower and higher energy components are prevalently σ− and σ+ polarized and are denoted, respectively, as Γ−5 and Γ+5 , based on the notation known for WZ bulk crystals in magnetic field.29−31 The intensity difference between these components is due to a thermally favored occupation of the lowest energy state, Γ−5 . Figure 3c shows the spectral dependence of the CD degree ρCD = [I(σ−) − I(σ+)]/[I(σ−) + I(σ+)] for different Bs, where I(σ±) is the PL intensity corresponding to the specific circular polarization. A steady increase in the modulus of ρCD with B is observed up to 20 T, followed by saturation at higher fields. The sign reversal of ρCD through the spectrum reveals the opposite circular polarization of the FE split components. Magneto-PL measurements performed at T = 4.2 K in the Voigt and Faraday configurations are shown in Figure S2 in the Supporting Information. The results obtained at 77 K are confirmed both for the diamagnetic shift and for the Zeeman splitting, as it will be shown in Figures 4 and 5. It is interesting

Figure 5. Field dependence of the Zeeman splitting recorded under Faraday configuration at two different temperatures. The exciton gfactor is indicated for two seemingly linear regimes below and above 15 T. The lines are fits to the data by ΔEZ = μB|ge − gh//|B. The data uncertainty is shown for one point only.

to note that the imperfect (i.e., ρCD < 1) circular dichroism observed at 77 K becomes significantly higher at 4.2 K, where ρCD = 0.6 at the Γ−5 transition (see Supporting Information S2). A similar decrease in the degree of circular polarization with increasing temperature was also observed in wurtzite nanocrystals,32 and it can be ascribed to a relaxation of the optical selection rules associated with thermally activated broadening/ dephasing processes. We also point out that no Zeeman splitting is observed at 4.2 K in the Voigt geometry, as in the 77 K measurements. The reduced thermal broadening (combined with the system spectral resolution) will permit to set an upper ⃗ , limit to ΔEZ at the highest field and, hence, to gexc for B⃗ ⊥k//ĉ as it will be discussed in the following. Theoretical Analysis. The exciton energy Eexc under magnetic field is determined by the diamagnetic shift, ΔEd, and by the Zeeman splitting, ΔEZ, according to Eexc(B) = Eexc(0) + ΔEd(B) ±

1 ΔEZ(B) 2

(1)

The explicit expression and extent of the different terms in eq 1 depend on the field orientation and on the exciton properties. In particular, the functional dependence of ΔEd on the magnetic field differs according to the relative strength of the exciton binding energy and of the magnetic energy, usually gauged by ℏωc = (ℏeB)/(μ). When these quantities are comparable over the magnetic field range probed, as in the present case, simplified approaches cannot be used, and the diamagnetic shift can be modeled by employing a variational method resulting in (see also paragraph S3 in the Supporting Information)33−35 9

ΔEd(γ ) =

∑ Ai γ i i=1

(2)

where Ai are coefficients derived by a numerical solution to the problem, γ = 4.26 × 10−6[εr/(μexc/m0)]2B is a sort of effective magnetic field acting on the exciton, and εr is the material ⃗ , we can determine μ//,⊥ dielectric constant. For B⃗ ⊥k//ĉ exc , which corresponds to a FE moving in a plane containing the ĉ axis (e.g., the m- or a-plane in the WZ lattice). Instead, when B⃗ // ⃗ , the pertinent exciton mass is μ⊥exc, relative to carrier k//ĉ motion crossing the ĉ axis, namely the WZ c-plane.36

Figure 4. (a) Field dependence of the diamagnetic shift (symbols) in Voigt configuration at the indicated temperatures. The solid lines are a fit to the data via eq 2 using the exciton reduced mass as a fit parameter, whose value is given in the figure. The Zeeman splitting is negligible in this field configuration. (b) The same as (a) in Faraday configuration. In this case the data have been spin-averaged to get rid of the Zeeman splitting (see Figures 3 and 5). 6543


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is formed by holes and electrons belonging to Γ9V and Γ7C, respectively.5,10−12,25 However, this latter attribution has been challenged by several works that instead find Γ8C as the minimum energy level for electrons in the CB,2,7−9 although the Γ9V−Γ8C optical transition should have small oscillator strength and it should barely appear in optical experiments. However, it can be argued that the nanowire surface and the electromagnetic-field distribution within the wire geometry may induce a relaxation in the selection rues. Hence, a reasonable oscillator strength could be obtained also for an optical interband transition with a very weak oscillator strength at Γ = 0 in the corresponding bulk crystal.1 Because the (Γ9V−Γ7C) and (Γ9V−Γ8C) transitions share the same optical selection rule (i.e., emitted/absorbed photons can be polarized only⊥ĉ),42 a linear-polarization analysis of the FE emission cannot help in the attribution of the lowest-energy CB state. However, the nature of this state could be finally settled by determining the effective mass of electrons and holes (me and mh, respectively) involved in the FE recombination. Indeed, me is expected to be sizably greater for Γ8C than for Γ7C.1,2,11 Along with our experimental data, Table 1 reports the values of me and mh (see first six rows) for carriers moving along and perpendicular to the WZ ĉ axis, as calculated by different authors.1,2,11

For ΔEZ, instead, quite different expressions hold depending on the field configuration. For bulk WZ materials, in the Voigt ⃗ ), the Zeeman splitting is given by26,27,29,30,37 geometry (B⃗ ⊥k//ĉ ΔEZ(B) =

2 Δ56 + ge2⊥μB2 B2

(3)

where Δ56 is the analytic part of the exchange interaction that separates the Γ5 bright exciton (with energy E5) from the Γ6 dark exciton (with energy E6 = E5 − Δ56) in WZ crystals.29 ge⊥ is the electron gyromagnetic factor for B⃗ ⊥ĉ, while μB is the ⃗ ),26,27,29,30,37 Bohr magneton. In the Faraday geometry (B⃗ //k//ĉ ΔEZ(B) = |ge// − gh//|μB B

(4)

where ge// and gh// are the electron and hole g-factors, respectively. Notice that in WZ bulk crystals gh = gh// cos ϑ, where ϑ is the angle between B⃗ and the ĉ axis.29−31,38 The T = 4.2 K data are up-shifted in both panels for clarity reasons. Uncertainties are within the symbol size. Figure 4a shows the field dependence of [Eexc(B) − Eexc(0)] ⃗ . The data recorded at T = 4.2 and 77 K are for B⃗ ⊥k//ĉ displayed as different symbols. No sizable variation in the diamagnetic shift and thus in the exciton reduced mass is observed with varying T. Within a k·p approach, this finding is consistent with the small variation of the band gap energy in the temperature interval considered.39 The experimental results are nicely reproduced by eq 2 with μ//,⊥ exc = 0.057 m0 as best fit

Table 1. Effective Mass Values of Electrons, me, and Holes, mh, According to References 1, 2, and 11a

parameter and ε //, ⊥ = ε //·ε⊥ = 12.77 from ref 40. As shown in Figure 2, the Zeeman splitting is negligible at all fields. Figure 4b shows the dependence on magnetic field of ⃗ . The data are spin-averaged in [Eexc(B) − Eexc(0)] for B⃗ //k//ĉ order to eliminate the Zeeman splitting contribution from eq 1, thus making the analysis simpler (ΔEZ results are described in Figure 5). The data recorded at T = 4.2 and 77 K overlap as in the Voigt configuration. The solid line is a fit of eq 2 to the data using ε⊥ = 12.4840 and μ⊥exc = 0.052 m0, which is slightly lighter than the exciton mass determined for B⃗ ⊥ĉ. The Zeeman splitting in the Faraday configuration recorded at two different temperatures is shown in Figure 5. Up to B = 15 T, the data can be reproduced by eq 4 with |ge// − gh//| = 5.4. At higher field, ΔEZ(B) slows down and |ge// − gh//| = 2.9 is found for B > 15 T. A detailed discussion of the presented results is now in order. Addressing the Conduction Band Ordering. We first comment on the exciton reduced mass values. Our data show that μexc [= 0.052 m0 (Faraday) and = 0.057 m0 (Voigt)] in GaAs WZ NWs is on average slightly heavier than in ZB bulk GaAs, where μexc = 0.054 m0, as determined by an analysis similar to that employed in the present work (see Section S3 in the Supporting Information).41 Furthermore, μexc is larger when the exciton is moving in a plane containing ĉ with respect to when it is moving in a plane perpendicular to ĉ. This anisotropy ⊥ //,⊥ ⊥ can be quantified by δμ = [μ//,⊥ exc − μexc]/[(μexc + μexc)/2] = +9.2%. δμ, though small, could be obtained in all the investigated samples in different experimental conditions (e.g., magneto-PL temperature and laser power density) and its value is a reliable quantity. We point out that the degree and sign of the exciton mass anisotropy in WZ GaAs is similar to that reported in WZ InP NWs, where δμ = +5.7%.27,28 Beyond their practical interest for assessing the transport properties of NWs, these data are relevant for a critical discussion about the band structure characteristics of WZ III−V NWs. In WZ GaAs, indeed, many authors agree that the lowest-energy exciton state

m// e (Γ7C) m// e (Γ8C) m// h (Γ9V) m⊥e (Γ7C) m⊥e (Γ8C) m⊥e (Γ9V) μ⊥exc(Γ7C − Γ9V) μ⊥exc(Γ8C − Γ9V) μ//,⊥ exc (Γ7C − Γ9V) μ//,⊥ exc (Γ8C − Γ9V) δμ(Γ7C − Γ9V) δμ(Γ8C − Γ9V)

ref 1

ref 2

ref 11

0.060 1.060 0.75 0.075 0.107 0.12 0.046 0.057 0.055 0.159 18% 94%

0.090 1.050 1.026 0.082 0.125 0.134 0.051 0.065 0.070 0.183 31% 95%

0.08 0.17 0.96 0.11 0.09 0.16 0.065 0.058 0.076 0.094 16% 47%

this work

0.052 0.057 9.2%

a The values refer to different critical points of the I Brillouin zone. The corresponding reduced mass values, μexc, of excitons moving in a plane perpendicular (⊥) to and containing (//,⊥) the ĉ axis are reported with the corresponding anisotropy δμ. The quantities experimentally determined in this work are reported in rightmost column.

In the case of electrons, both the mass values at the Γ7C and the Γ8C point of the first Brillouin zone are shown, while for the holes only the mass at Γ9V is displayed, given that the symmetry of the VB maximum is well assessed. In order to compare the theoretical values with the experimental results, in Table 1 we also report the values of μexc estimated by using the theoretical electron and hole effective masses related to the appropriate carrier motion considered. In particular, the theoretical values of μ//,⊥ exc (corresponding to magneto-PL measurements in the Voigt configuration) were evaluated by considering first the electron and hole effective masses calculated for carrier motion parallel and orthogonal to the WZ ĉ axis and then by using the cyclotron effective mass tensor mi//, ⊥ = mi// ·mi⊥ (with i = e,h)43 to estimate the exciton reduced mass in the Voigt //,⊥ //,⊥ //,⊥ configuration as μ//,⊥ + m//,⊥ exc = (me ·mh )/(me h ). The theoretical exciton mass anisotropy δμ is reported for both the 6544


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CB minimum having Γ7C symmetry and address a very important, still open issue concerning the electronic structure of WZ GaAs NWs. The Zeeman splitting data show a strong anisotropy upon field direction; at maximum field B = 28 T, ΔEZ is close to zero and equal to about 7 meV for B⃗ ⊥ĉ and B⃗ // ĉ, respectively. This finding spots an interesting issue regarding the exchange interaction and spin properties in WZ GaAs, especially at the light of the different behaviors of other III−V WZ materials, such as InGaAs26 and InP.27 Experimental Section. Magneto-PL measurements were performed at T = 4.2 and 77 K by using a bath cryostat and by placing the samples in a water-cooled Bitter magnet. PL was excited by a frequency-doubled Nd:YVO4 laser (λexc = 532 nm) and focused using a long focal length objective. The luminescence was collected by the same objective, dispersed by a 0.30 m monochromator, and detected by a liquid N-cooled Si CCD.

CB minima considered. Clearly, the comparison between experimentally and theoretically determined quantities points to Γ7C as the only possible CB minimum. In fact, while no large differences can be noticed in μ⊥exc against the choice of the CB minimum symmetry, μ//,⊥ exc is largely dependent on whether the electron belongs to Γ7C or to Γ8C. In the latter case, the //,⊥ calculated values of μ exc are sizably larger than the experimental ones observed in the present work. Furthermore, the exciton mass anisotropy δμ deviates from our experimental values much more for Γ8C than for Γ7C electrons. From the experimental side, there are only few, indirect estimations of the electron and hole effective mass in WZ GaAs. In ref 20, the quantum confinement of electrons and holes in thin WZ GaAs NWs (diameter ranging from 10 to 16 nm) was studied by PL and PL excitation measurements, whose quantitative analysis led to m⊥e = 0.15 m0 and m⊥h = 0.5 m0. The resulting exciton reduced mass, μ⊥exc = 0.12 m0, differs largely from the value (0.054 m0) we found by the quantitative analysis of the FE diamagnetic shift and from the theoretical expectations (these latter irrespective of the CB minimum choice). Such a large discrepancy may be attributed to the strong interplay between the carrier mass and the specific choice of the WZ/ZB band gap offset in determining the energy eigenstates of the quantum wires. In ref 22, magneto-PL measurements on quantum disks made of type-II WZ/ZB GaAs homostructures were analyzed in terms of a fixed WZ hole effective mass equal to 0.766 m0 and WZ electron effective mass values varying between 0.1 m0 and 1.0 m0. Also in this case, the resulting range of exciton reduced masses (μexc = 0.088 m0/ 0.434 m0) exceeds largely the values we found from the diamagnetic shift data. However, the mixed-crystal character of the transitions reported in ref 22 does not allow for a straightforward comparison. Exciton Gyromagnetic Factor. Let us now discuss the Zeeman splitting results. In the Faraday configuration (Figure 5), gexc = |ge// − gh//| is not constant over the entire field interval considered and is equal to 5.4 for B < 15 T. This nonlinear behavior of the exciton g-factor with the magnetic field is similar to what previously found in InGaAs and InP WZ NWs26,27 and in other semiconductor nanostructures,44 and it can be ascribed to B-induced mixing effects in the VB states.45 The lack of the observation of a sizable Zeeman splitting in the Voigt configuration is quite puzzling and suggests that |ge⊥| = 0 or a very small value. In fact, if we take into account the spectral resolution of our setup (

Addressing the Fundamental Electronic Properties of Wurtzite GaAs

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