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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 Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b02189 • Publication Date (Web): 16 Oct 2017 Downloaded from http://pubs.acs.org on October 18, 2017
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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
KEYWORDS
GaAs
nanowires,
wurtzite,
exciton,
magneto-photoluminescence
spectroscopy, effective mass, gyromagnetic factor, band-structure.
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 1 ACS Paragon Plus Environment
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WZ formation is both a complication to be dealt with and a potential feature to be exploited, e.g., 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, ∆Ed, and the Zeeman splitting of the band gap free exciton in WZ GaAs formed in core-shell InGaAs-GaAs NWs. The quantitative analysis of ∆Ed at different temperatures
r (T=4.2 and 77 K) and for different directions of B allows determining 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
r r and ~0 for B // cˆ and B ⊥ cˆ , respectively. This latter result provides fundamental insight into the band structure of wurtzite GaAs.
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The high surface-to-volume ratio of semiconductor nanowires (NWs) leads to the formation of crystal phases not attainable in the same semiconductors at ambient conditions1. 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)1,2,3,4. 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 structure2,5,7,8,9,10,11,12,13,14 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)5,15,16,17. Furthermore, the splitting between the Γ9V and Γ7V valence bands (VBs) is commonly found equal to about 110 meV5,12,15, and the separation between the Γ7C and Γ8C conduction bands (CBs), is ∼70 meV, as suggested in Ref. 5 and confirmed by later reports13,15. 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. Since the Γ8C CB arises from the zone folding of a L-CB, the electron mass associated to Γ8C is expected to be larger (at least two times) than the one associated to 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 discussion section. Few experimental studies addressed the carrier effective mass in WZ GaAs NWs, even though this fundamental parameter provides precious indications on the 3 ACS Paragon Plus Environment
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band structure and rules the carrier response to external forces and the extent of quantum confinement18,19. 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 nanodots15. 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 GaAs5,24. Magnetic fields up to 28 T were applied along and perpendicular to the WZ ĉ axis, in order to disclose possible electronic anisotropies related to the lattice hexagonal symmetry. The exciton line exhibits diamagnetic shift (∆Ed), Zeeman
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splitting (∆EZ), and circular dichroism (CD) that all depend on the field intensity and/or direction. The ∆Ed 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 ∆EZ that, at 28 T, varies from 7 meV 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 (as expected for WZ crystals).
r Furthermore, for B ⊥ cˆ the axial symmetry of the WZ electronic states is strongly perturbed, leading to a mixing between Γ5 (bright) and Γ6 (dark) exciton states29,30,31.
r r A completely different behavior is observed in the Faraday configuration ( B // k // cˆ ), as shown in Figure 3. Panel (a) 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 corresponding multiplication factors are shown in the figure for each field), as it can be better appreciated in Figure 3 (b) showing the PL spectra recorded at B=28 T under opposite circular polarizations. 8 ACS Paragon Plus Environment
(a)
σ σ
− +
r r B // k // cˆ
T = 77 K -/+
-
(b)
Γ5
Γ5
B=28 T
T = 77 K B = 28 T
+
Γ5
σ+
26 T
σ-
24 T 22 T 20 T 18 T
(c)
16 T
0.3
14 T
24 T
12 T
10 T
10 T 8T
0.2
20 T 28 T
6T
0.1
ρCD
PL Intensity (arb. units)
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PL Intensity (arb. units)
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6T
B =4 T
4T
0.0
2T 0T
1.50
-0.1
FE
1.52 1.54 Energy (eV)
1.51 1.52 1.53 1.54 Energy (eV)
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, Γ5 and Γ5 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.
The lower and higher energy components are prevalently σ − and σ + polarized and are denoted, respectively, as Γ5− and Γ5+ , based on the notation known for WZ bulk crystals in magnetic field29,30,31. The intensity difference between these components is due to a thermally favored occupation of the lowest energy state, Γ5− . Figure 3 (c) shows the spectral dependence of the CD degree ρ CD = [I (σ − ) − I (σ + ) ] [I (σ − ) + I (σ + ) ] for different B’s, where I (σ ± ) is the PL intensity corresponding to the specific circular polarization. A steady increase of the modulus of ρCD with B is observed up to 20 T, followed by saturation at
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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 to note that the imperfect (i.e., ρCD15 T. A detailed discussion of the presented results is now in order.
6
∆EZ (meV)
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4
g e − g h // = 5.4
g e − g h // = 2.9
(B < 16 T )
(B ≥ 16 T )
2 T=4.2 K T=77 K
0 0
5
10
15 B (T)
20
25
Figure 5. Field dependence of the Zeeman splitting recorded under Faraday configuration at two different temperatures. The exciton g-factor is indicated for two seemingly linear regimes below and above 15 T. The lines are fits to the data by ∆EZ = µ B g e − g h // B . The data uncertainty is shown for one point, only.
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
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WZ NWs is 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 δ µ = µ exc − µ exc
] [(µ
// , ⊥ exc
]
⊥ + µ exc ) 2 = +9.2% . δµ, though small, could be
obtained in all the investigated samples in different experimental conditions (e. g., magnetoPL 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 δ µ = +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 is formed by holes and electrons belonging to Γ9V and Γ7C, respectively5,10,11,12,25. However, this latter attribution has been challenged by several works that, instead, find Γ8C as the minimum energy level for electrons in the CB2,7,8,9, despite 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 crystal1. Since the (Γ9V-Γ7C) and (Γ9V-Γ8C) transitions share the same optical selection rule (i.e., emitted/absorbed photons can be polarized only ⊥ cˆ )42, a linearpolarization analysis of the FE emission cannot help in the attribution of the lowest-energy
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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 Γ7C1,2,11. Along with our experimental data, Table I reports the values of me and mh (see first 6 rows) for carriers moving along and perpendicular to the WZ ĉ axis, as calculated by different authors1,2,11.
Table I. Ref. [1]
Ref. [2]
Ref. [11]
// e
0.060
0.090
0.08
// e
1.060
1.050
0.17
// h
0.75
1.026
0.96
⊥ e
0.075
0.082
0.11
⊥ e
0.107
0.125
0.09
⊥ h
0.12
0.134
0.16
m ( Γ7 C ) m ( Γ8 C ) m (Γ9 V ) m (Γ7 C ) m ( Γ8 C ) m (Γ9 V )
µ
⊥ exc
(Γ7 C − Γ9 V )
0.046
0.051
0.065
µ
⊥ exc
(Γ8 C − Γ9 V )
0.057
0.065
0.058
µ
// , ⊥ exc
0.055
0.070
0.076
µ
// , ⊥ exc
0.159
0.183
0.094
δ µ (Γ7 C − Γ9 V )
18%
31%
16%
δ µ (Γ8 C − Γ9 V )
94%
95%
47%
This work
0.052
(Γ7 C − Γ9 V )
0.057
(Γ8 C − Γ9 V )
9.2%
Table I. Effective mass values of electrons, me, and holes, mh, according to Refs. 1,2, and 11. 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.
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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 I 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 m i// , ⊥ = m i// ⋅ m i⊥ (with i=e,h)43 to estimate the exciton reduced mass in the Voigt configuration as // , ⊥ µ exc = (me// , ⊥ ⋅ mh// , ⊥ ) (me// , ⊥ + mh// , ⊥ ) . The theoretical exciton mass anisotropy δ µ is
reported for both the 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
δ µ 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
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excitation measurements, whose quantitative analysis led to me⊥ = 0.15 m0 and mh⊥ = 0.5 m0 . ⊥ = 0.12 m0 , differs largely from the value (0.054 m0) The resulting exciton reduced mass, µ exc
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), g exc = g e// − g h// is not constant over the entire field interval considered and is equal to 5.4 for B
