Value and Anisotropy of the Electron and Hole Mass in Pure Wurtzite

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Value and Anisotropy of the Electron and Hole Mass in Pure Wurtzite InP Nanowires Davide Tedeschi, Marta De Luca, Andres Granados del Aguila, Qian Gao, Gina Ambrosio, Mario Capizzi, Hark Hoe Tan, Peter C. M. Christianen, Chennupati Jagadish, and Antonio Polimeni Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b02469 • Publication Date (Web): 22 Sep 2016 Downloaded from http://pubs.acs.org on September 27, 2016

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Value and Anisotropy of the Electron and Hole Mass in Pure Wurtzite InP Nanowires D. Tedeschi,‡ M. De Luca,‡, + A. Granados del Águila,†,  Q. Gao, G. Ambrosio,‡ M. Capizzi,‡ H. H. Tan, P. C. M. Christianen,† C. Jagadish, and A. Polimeni‡,* ‡

Dipartimento di Fisica, Sapienza Università di Roma, Piazzale A. Moro 2, 00185 Roma, Italy †

High Field Magnet Laboratory (HFML – EMFL), Radboud University, Toernooiveld 7,

NL-6525 ED Nijmegen, The Netherlands 

Department of Electronic Materials Engineering, Research School of Physics and Engineering, The Australian National University, Canberra, ACT 2601, Australia

ABSTRACT. The effective mass of electrons and holes in semiconductors is pivotal in determining the dynamics of carriers and their confinement energy in nanostructured materials. Surprisingly, this quantity is still unknown in wurtzite (WZ) nanowires (NWs) made of III-V compounds (e.g., GaAs, InAs, GaP, InP), where the WZ phase has no bulk counterpart. Here, we investigate the magneto-optical properties of InP WZ NWs grown by selective-area epitaxy that provides perfectly ordered NWs featuring high crystalline quality. The combined analysis of the energy of free exciton states and impurity levels under magnetic field (B up to 29 T) allows us to disentangle the dynamics of oppositely charged carriers from the Coulomb interaction, and, thus,

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to determine the values of the electron and hole effective mass. By application of B along different crystallographic directions, we also assess the dependence of the transport properties with respect to the NW growth axis (namely, the WZ ĉ axis). The effective mass of electrons along ĉ is me//  (0.078  0.002) m0 (m0 is the electron mass in vacuum) and perpendicular to ĉ is

me  (0.093  0.001) m0 , resulting in a 20% mass anisotropy. Holes exhibit a much larger (320%) and opposite mass anisotropy, with their effective mass along and perpendicular to ĉ equal to mh//  (0.81  0.18) m0 and mh  (0.250  0.016) m0 , respectively. While no full consensus is found with current theoretical results on WZ InP, our findings show trends remarkably similar to the experimental data available in WZ bulk materials, such as InN, GaN, and ZnO.

KEYWORDS Wurtzite InP nanowires, impurity states, excitons, magneto-photoluminescence, carrier effective mass


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Introduction. In low-dimensional semiconductors, it is common practice to employ the band structure parameters of the bulk materials (e.g., band gap energy, carrier effective mass, energy of impurity levels, gyromagnetic factor) for estimating the electronic and optical properties of quantum heterostructures and nanostructures1,2. However, this approach breaks down in many types of NWs, the most striking case being that of non-nitride III-V NWs, which grow very often in the wurtzite (WZ) phase3, a crystal phase not existing in the bulk form, where zincblende (ZB) is ubiquitous. As a consequence, even some basic band structure properties are not very well known in WZ NWs. As a notable example, the value of the fundamental band gap energy, Eg, of GaAs4,5, InAs6,7, and GaP8 WZ NWs is object of current debate, while only in InP WZ NWs a definite band gap energy (~70 meV larger than in ZB) is reported9. Crystal phase represents also a degree of freedom that enables the realization of novel 1D homostructures, in which the lattice structure varies along the NW growth axis while keeping the NW composition uniform10,11. However, the energy diagram of these interesting homostructures requires the knowledge not only of Eg but also of the electron and hole effective mass12. Finally, knowing the effective mass is especially important for predicting and understanding device properties for which carrier mobility plays a crucial role. In semiconductors, the carrier effective mass, m, can be determined by optical and transport experiments under an applied magnetic field, B. Recently, WZ InGaAs13 and InP14 NWs were investigated by magneto-photoluminescence (magneto-PL). However, in optical experiments, the Coulomb interaction strongly modifies single-particle states and only information about the reduced mass, gyro-magnetic factor, and circular dichroism of excitons could be attained13,14. In this work, free exciton, donor-acceptor, and free-electron to neutral-acceptor recombinations in WZ InP NWs were studied by PL under high magnetic fields (up to B=29 T). The diamagnetic


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shift of those transitions was quantitatively reproduced, thereby permitting the determination of the effective mass of electrons (me) and holes (mh) via independent measurements. In order to  highlight anisotropies related to the WZ hexagonal lattice structure, B was applied along and

perpendicular to the NW axis and the emitted light was resolved with respect to circular polarization. me is found to be 20% smaller along the NW growth axis, namely the WZ ĉ axis, than perpendicular to it. An opposite behavior is found for holes, whose mass is more than three times heavier for motion parallel to ĉ than perpendicular to ĉ. These trends interestingly resemble those observed experimentally in other WZ materials that exist in the bulk form, such as GaN15,16,17, InN18, and ZnO19,20. Current theoretical calculations for WZ InP show, instead, a rather scattered picture regarding carrier effective mass values and anisotropies12,21,22,23,24,25. Our first experimental assessment of these quantities will be able to guide further refinement in the theoretical investigation of the electronic properties of this interesting material. Samples. Arrays of InP WZ NWs were grown by selective-area metal-organic vapor-phase epitaxy (SAE) on a (111)A InP substrate. Before NW growth, a 30 nm-thick SiO2 layer was deposited on the InP substrate and patterned by electron beam lithography to create an hexagonal array of circles. This was followed by chemical etching of the SiO2 layer to open up an array of holes down to the InP substrate. We designed patterns with different hole diameters, d=120, 310, and 650 nm and with pitch equal to 200, 600, and 1000 nm, respectively. The NWs were grown on the patterned substrate at 730 °C for 20 minutes with trimethylindium and phosphine as precursors at a flow rate of 6.1×10-6 and 4.9×10-4 mol/min (V/III ratio=80), respectively. The NW section is hexagonal. Details about the NW structural properties are reported in section S1 in the Supporting Information (SI) and in Refs. 26 and 27, where it was shown that the NWs are taper-free with a pure WZ phase (i.e. with a negligible density of stacking faults and ZB inserts)


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and have smooth surfaces. Scanning electron microscopy (SEM) images of the NW arrays with d=650, 310, and 120 nm are shown in the insets of Figure 1. The 650 and 310 nm diameter arrays exhibit an extremely homogeneous distribution of wire diameters and lengths, whereas NWs with d=120 nm exhibit some degree of non-uniformity. (D,A) /(e,A)

T=10 K d =650 nm

FE L U

PL Intensity (arb. units)

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(D,A) /(e,A)

d =310 nm

FE L U

(D,A) /(e,A)

d =120 nm

FE L d2

1.45

1.46 1.47 1.48 Energy (eV)

U

d1

1.49

Figure 1. PL spectra recorded at T=10 K from arrays of InP WZ NWs with diameter, d=650, 310, and 120 nm from top to bottom. (D,A) and (e,A) indicate donor-acceptor and free-electron to neutral-acceptor recombination, respectively. These two bands are nearly superimposed and cannot be spectrally resolved. FE indicates the free exciton peak. U and L are two FE components as discussed in the main text. d1 and d2 in the d=120 nm NWs are defect-related recombinations. The insets display SEM images of the NWs in which the PL spectra were recorded. Scale bars are 4 m.

Nanowire emission properties at zero magnetic field. The PL spectra at low temperature (T=10 K) of the different NW arrays are shown in Figure 1. They were collected in backscattering geometry, with laser and PL wavevector directions parallel to the NW long symmetry axis. Different recombination bands contribute to the PL spectrum. An intense


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emission can be observed at 1.452 eV. As detailed in section S2 in SI, this relatively broad band comprises two different transitions: i) a neutral-donor to neutral-acceptor transition, (D,A), on the low-energy side of the band and ii) a free-electron to neutral-acceptor transition, (e,A), on the high-energy side of the band. Contrary to previous reports9,26, our measurements highlight the presence of two almost degenerate impurity-related transitions in WZ InP NWs. These spectral features are common to all the three arrays independent of the NW diameter. In the d=120 nm array though, two additional defect-related emissions at 1.486 eV (d1) and 1.473 eV (d2) are observed, and their origin is under investigation. The double peak at about 1.493 eV is due to the free exciton (FE) recombination, as confirmed by the studies reported in section S2 in SI and by polarization-resolved PL measurements in Ref. 9. The FE line shape resembles preceding findings in high-purity ZB bulk InP28 and GaAs29. The energy separation between the lower- and upper-energy components (indicated as L and U in Figure 1, respectively) is about 1.8 meV. The origin of this doublet was previously explained in GaAs29,30 in terms of elastic scattering between neutral donors and polaritons (that are exciton-photon mixed quasi-particles carrying the optical excitation through the crystal). At specific energy, the elastic-scattering cross-section of neutral donors has a maximum. In turn, this leads to a modification of the polariton population distribution in the renowned upper and lower energy branches29,30. Very similar observations were also reported in InP and interpreted using a model in which polaritons undergo scattering with different elements28,31. In both cases, a dip is observed in the PL spectra as shown in Figure 1. From now on, the upper (U) and lower (L) energy branches will be treated on an equal footing as two distributions of distinct states. For simplicity reasons, we will refer to these states as U and L exciton components. A similar behavior was reported also in bulk WZ GaN32.


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Nanowire emission properties under magnetic field. Model. In a semiconductor, the extent and functional dependence of the variation of the electron-hole recombination energy vs B depend on the relative strength between the carrier magnetic energy c  eB m and the Coulomb attraction energy, R, to which each carrier pair is subjected to33. In the range of B values investigated in this work (0-29 T), different limits hold depending on the specific transition considered34. In the (e,A) case, if one averages over spinsplit levels, the recombination energy E ( e,A ) of the pair changes with B as35,36

E( e,A ) B   ECB B  0  E A B  0 

e B  E A B , 2m e

(1)

where energies are referred to the top of the valence band, ECB is the conduction band (CB) bottom energy, and E A is the hole-occupied acceptor-level energy. Since free electrons in the CB interact with the neutral acceptor impurities through a negligibly small Coulomb force (namely R0 and c R  1 ), the electron energy variation is given by eB 2me  , namely by that of the first Landau level in the conduction band37. In addition, the variation of EA with B, E A B  , can be neglected due to the deep character of the acceptor levels (i.e., large binding

energy 40 meV). In fact, E A ( B  19 )  0.075 meV for carbon acceptors in GaAs38. Therefore, Eq. (1) provides the effective mass of free electrons directly. What about the hole effective mass mh? In principle, mh could be inferred from the field dependence of the (D,A) transition energy given by (after averaging over spin-split levels) e2 E( D,A ) B   E D B  0  E A B  0  E D B   E A B   4


 1   ,  rD,A B 

(2)

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where E A B  is the same as in Eq. (1) and E D B  is the variation of the donor level energy with B that can be evaluated by numerical methods39,40. Contrary to E A B  , the shallow character of the donor states (i.e., small binding energy 5 meV) leads to E D B  values sizably larger than zero39. The last term in Eq. (2) accounts for the B-induced variation in the average distance of the donor-acceptor pairs, rD,A . In particular, rD,A B depends on the hole effective mass and decreases with increasing B because concomitantly the orbit of the donor-localized electron shrinks thus favoring less distant pairs41. However, to estimate quantitatively this effect, and thus derive mh, the donor density as well as how rD,A B varies with B should be known exactly41. These stringent requirements impede a reliable determination of the hole effective mass via Eq. (2). To this purpose, we resort to the free exciton diamagnetic shift that depends on the exciton reduced mass exc14,42,43. Indeed,  exc  1 me  1 mh 

1

would provide a rather straightforward

determination of the hole mass once the electron and exciton masses are known. However, in the case of the FE recombination in WZ InP (where the exciton binding energy is R~6.4 meV44 and the exciton reduced mass is exc=0.071 m0, as shown later), neither the Landau level approximation (valid for c  R ) nor the B2 dependence (valid for c  R ) can be used to reproduce the exciton diamagnetic shift over the whole range of magnetic field employed and hence obtain exc simply33. In fact, c R  (0  18) for B=(0-29) T. Therefore, in this intermediate field regime, numerical methods are usually employed to model the FE energy shift with B using exc as a fitting parameter14,42,43,45: p

2 9    r 3   exc m0   6     Ap 4.26  10    B  , E FE B   E FE 0  13.6  10   r2   exc m0      p 1 


(3)

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where the coefficients Ap are determined by numerical solution of the Schroedinger equation,

 r =11.7614,46, and m0 is the electron mass in vacuum. Section S4 in SI provides further details on the models we employed to determine the effective mass of electrons [Equation (1)] and the exciton reduced mass [Equation (3)] with specific reference to excitons in WZ crystals. Experimental results. The optical properties of arrays and single NWs (as determined by micro-PL) are very similar (as shown in Section S5 in SI), so magneto-PL was performed on arrays of NWs due to the higher signal and larger statistical relevance. The number of NWs probed in each magneto-PL spectrum is about 100 as resulting from the NW array density and the laser spot size. Measurements were carried out at two temperatures, T=4.2 and 77 K, in order to highlight the dependence of different spectral components on B. The field was directed parallel or perpendicular to the NW ĉ axis, whose direction is perfectly defined in these SAE NW arrays. In both configurations, the PL collection and laser directions were antiparallel to each other and both directed along the NW growth axis (i.e. ĉ). We indicate the emitted photon      wavevector as k and designate B // k // cˆ as Faraday configuration and B  k // cˆ as Voigt

configuration. PL was resolved with respect to circular polarization. We present the results obtained on d=650 nm NWs. Very similar findings were found regardless of the NW diameter (see section S3 in SI), excitation power density, and region of the NW arrays. Figure 2 (a) shows the PL spectra recorded from InP WZ NWs with d=650 nm at B=0 and 29 T in the (D,A)/(e,A) energy region. Measurements were performed at T=4.2 K. B was parallel to   the emitted light wavevector and to ĉ (Faraday geometry, B // k // cˆ ), and only + polarization is

shown for clarity reasons. We point out that circular polarization luminescence filtering indicates a clear band splitting. However, here, we will not discuss the Zeeman splitting data and we focus, instead, on the diamagnetic shift results. We stress that Zeeman splitting was properly


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taken into account in the data analysis and interpretation. At B=0 T, the (D,A) intensity overwhelms the (e,A) intensity and the two bands are not distinguishable. Nevertheless, with increasing B, the (e,A) recombination can be better discerned thanks to the larger B-induced shift of its energy compared to that of the (D,A) recombination, as shown in the 29 T spectrum. B (T) 15

Energy (eV) 1.45

1.46

1.47

(D,A)

(D,A)

5

10

Max

  B // k // cˆ

0



20

T=4.2 K 1.470



(e,A)

(e,A)

m e  0.091 m0

min



1.465 1.460

29 T

0T

25

(D,A)

+

1.455

(a)

(b) 1.450 Max

  B // k // cˆ

0



-

5(L)

5(L)

-

5(U)



T=4.2 K

+

5 (U)

1.510

-

5(U)

+

5 (L)

5(U) 0T

-

+

5 (L)

29 T



1.505

min

5(L) 1.500

+ +

5 (U)

  exc (U)  0.066 m0 1.495   exc (L)  0.069 m0

(c) 1.49

Energy (eV)


0

Energy (eV)

1.44


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(d) 1.50

Energy (eV)

1.51

0

5

10

15 B (T)

20

25

Figure 2. (a) PL spectra at T=4.2 K from InP NWs with 650 nm diameter at 0 and 29 T in the Faraday configuration. The energy region of the (D,A) and (e,A) transitions is displayed. Only the PL spectrum filtered by counterclockwise ( +) circular polarization is shown. Notice that (e,A) can be seen as a shoulder on the high-energy side of the PL spectrum for B=29 T. (b) Contour plot of the second derivative of the PL spectra from 0 to 29 T in the same energy region of (a). The color scale represents the magnitude of the second derivative. Symbols indicate the peak energy of the (D,A) band. The solid line is a fit of Eq. (1) to the (e,A) data from which the electron effective mass m c is determined. (c) PL spectra at 0 and 29 T in the FE energy region filtered by counterclockwise ( +) circular polarization. The various exciton components are indicated with the pertinent group symmetry ( 5 ) of magneto-excitons in WZ. “+” and “-“ indicate Zeeman split components. (d) Contour plot of the second derivative of the PL spectra from 0 to 29 T in the FE energy region. The color scale represents the magnitude of the second derivative. Arrows point to different FE components.  The solid lines are fits of Eq. (3) to the data (the exciton reduced mass values  exc derived from the fits are reported).


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The detailed field dependence of the two bands is much clearer from the second derivative of the magneto-PL spectra shown in panel (b). Indeed, as exemplified in section S6 in SI, the differential spectra help to highlight spectral features, such as shoulders, whose exact energy can be hard to individuate from the PL spectra directly47. Figure 2 (b) evidences quite distinct behaviors of the (D,A) and (e,A) transitions. First, the (e,A) energy shifts linearly with magnetic field, while the energy of the (D,A) transition follows a quadratic-like dependence especially for B15 T.


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Let us consider the FE spectral region. Figure 3 (c) compares the FE PL spectra at B=0 and 29 T. At high field, four different lines can be observed clearly. The line indicated by BE is due to a bound exciton (the reader is referred to S7 in SI for more details), while the other three lines are due to different components of the free exciton, whose evolution with magnetic field is shown by the contour plot of the differential spectra in Figure 3 (d). In the Voigt configuration, the U and L exciton components blue-shift and split, but no intensity and lineshape dependence on light circular polarization is observed, consistently with the hexagonal crystal symmetry of WZ  NWs13,14. In fact, when B  cˆ , magnetic field mixes bright and dark excitons with 5 and 6

symmetry, respectively, resulting in 5 / 6 excitons that, with increasing B, split into 5/ 6 components that are not sensitive to light chirality (see S4 in SI)48. In particular, 5/ 6 L  is very weak and it can be glimpsed at smaller fields (5-18 T, see S7 in SI). The different attributions are reported in panel (d). The solid lines are fits to the energy of the 5/ 6 L  and 5/ 6 U  states (which are the only ones observable at all B’s) using Eq. (3) and the theory presented in Refs. 14 and 48 and S4 in SI. Also in this case, the Zeeman splitting was also taken into account. Under // ,  this configuration, we obtain the value of  exc [reported in panel (a)] with electron and hole

masses given by the cyclotron effective mass tensor49

m // ,   m//*  m* ,

(4)

where m//* and m* are related to carrier motion parallel and orthogonal to ĉ, respectively (we assumed an isotropic carrier effective mass in the plane orthogonal to ĉ).


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Table I. Values of the exciton reduced mass (in units of m0) determined under different field configurations and in different types of InP NW samples. SAE data refer to present work, while VLS data refer to previously published results on Au-seeded vapor-liquid-solid WZ NWs14. The mass uncertainty is  // ,  equal to 0.001 m0.  exc and  exc were measured in the Faraday and Voigt configuration, respectively.

SAE VLS

  exc

// ,   exc

0.069 (L) 0.067 (U) 0.06814

0.072 (L) 0.071 (U) 0.07214

Table I reports the exciton reduced mass values derived by an average over various measurements performed on NW arrays with different diameters. The L component of the exciton is heavier than the U component that is likely due to the different k-dispersion of the two energy branches around 28,29,30,31. Table I also shows values of the exciton reduced mass previously determined in InP WZ NWs with average d=140 nm and grown by the Au-seeded vapor-liquid-solid (VLS) mechanism14. In those measurements, the U and L components could not be resolved because magneto-PL was performed at 77 K. The excellent agreement found between the two sets of data supports the general validity of our results and their independence on the NW morphology and/or size. To summarize, we determined the exciton reduced mass of InP WZ NWs in a plane containing // ,   the WZ ĉ axis, i.e.  exc , and in a plane perpendicular to ĉ , i.e.  exc . We also determined the

free electron mass perpendicular to the WZ ĉ axis, me . In order to fully disentangle the electron and hole masses as well as the mass along different directions, we still need to determine me// . Moreover, we want to confirm the value of me determined at 4.2 K, where the large weight of the (D,A) recombination hindered the precise fitting of the field dependence of the (e,A) recombination. This is accomplished by performing magneto-PL experiments at higher temperature.


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0

5

B (T) 10 15

1.468

Peak energy (eV)

20

25

0

5

B (T) 10 15

20

25

  B  k // cˆ

  B // k // cˆ

1.464



1.460



1.456

me  0.092 m0

me// ,   0.085 m0

(c)

1.452 



T = 77 K


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



(d) T = 77 K

B = 28 T

B = 28 T

24 T

24 T

20 T

20 T

16 T

16 T

12 T

12 T

8T

8T

4T

4T

0T 1.44

(e,A) 1.45

(a) 1.46

Energy (eV)

1.47

0T 1.44

(e,A) 1.45

(b) 1.46

1.47

Energy (eV)

Figure 4. (a) T=77 K PL spectra recorded from InP NWs with 650 nm diameter under magnetic field in the Faraday configuration. The spectral region displayed is that relative to the (e,A) recombination. Blue and red lines refer to clockwise ( -) and counterclockwise ( +) circular polarization, respectively. (b) The same as (a) but for the Voigt configuration. Here, the luminescence is insensitive to circular polarization filtering. (c) Energy of the (e,A) recombination as a function of B in the Faraday configuration. Different symbols correspond to different circular polarizations as detailed in the legend. The gray line is a fit to the Zeeman-split averaged data by the first Landau level, see Equation (1). The value of the electron effective mass is indicated. (d) Energy of the (e,A) recombination as a function of B in the Voigt configuration. The gray line is a fit to data by the first Landau level in Equation (1). The value of the electron effective mass is indicated.

In fact, at 77 K the (D,A) band is fully ionized because of the small binding energy of donors (~5 meV) and only the (e,A) recombination can be observed, see S2 in SI. Figures 4 (a) and (b) display the magnetic field evolution of the (e,A) band at 77 K under Faraday and Voigt configurations, respectively. Intense exciton recombination is observed at 1.485 eV (not shown).


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In the Faraday geometry, the (e,A) band blue-shifts and splits with increasing B. In the Voigt configuration, a similar shift is observed but no line splitting is found under   filtering, consistently with the WZ hexagonal symmetry.   Figure 4 (c) shows the diamagnetic shift of the (e,A) band for B // k // cˆ . For B

Value and Anisotropy of the Electron and Hole Mass in Pure Wurtzite

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