Solid State Communications 160 (2013) 26–31

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Solid State Communications

0038-10

http://d

n Corrnn Cor

E-m

l.sorba@

journal homepage: www.elsevier.com/locate/ssc

Internal field induced enhancement and effect of resonancein Raman scattering of InAs nanowires

Jaya Kumar Panda a, Anushree Roy a,n, Achintya Singha b, Mauro Gemmi c, Daniele Ercolani d,Vittorio Pellegrini d, Lucia Sorba d,nn

a Department of Physics, Indian Institute of Technology Kharagpur, Pin 721302, Indiab Department of Physics, Bose Institute, 93/1, Acharya Prafulla Chandra Road, Kolkata-700 009, Indiac Center for Nanotechnology Innovation @ NEST, Istituto Italiano di Tecnologia, Piazza S. Silvestro 12, I-56127 Pisa, Italyd NEST-Istituto Nanoscienze-CNR and Scuola Normale Superiore, Piazza S. Silvestro 12, I-56127 Pisa, Italy

a r t i c l e i n f o

Article history:

Received 28 September 2012

Received in revised form

4 February 2013

Accepted 6 February 2013

by R. Merlinthe first higher lying direct band gap energy (E1) and the refractive index of the InAs nanowires in the

Available online 13 February 2013

Keywords:

A. InAs nanowires

E. Resonance Raman

98/$ - see front matter & 2013 Elsevier Ltd. A

x.doi.org/10.1016/j.ssc.2013.02.003

esponding author. Tel.: þ91 3222 283856; fa

responding author. Tel.: þ39 050509 118; fa

ail addresses: anushree@phy.iitkgp.ernet.in (A

sns.it (L. Sorba).

a b s t r a c t

An internal field induced resonant intensity enhancement of Raman scattering of phonon excitations in

InAs nanowires is reported. The experimental observation is in good agreement with the simulated

results for the scattering of light under varying incident wavelengths, originating from the enhanced

internal electric field in an infinite dielectric cylinder. Our analysis demonstrates the combined effect of

internal field induced Raman scattering. Furthermore, the difference in the relative contribution of

electro-optic effect and deformation potential in Raman scattering of nanowires and bulk InAs over a

range of excitation energies is discussed by comparing the intensity ratio of their LO and TO

phonon modes.

& 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Nanoparticles couple uniquely with electromagnetic (EM)radiation. Local field enhancement of visible EM radiation bynanometer-sized metal particles is well studied in the literature[1–3]. There are quite a few reports on the strong coupling of thelocal field of metal particles (under EM radiation) with thedielectric system in metal–dielectric conjugated nanostructuresand also with dielectric nanostructures in metallic matrix [4–6].Though, not very commonly found in the literature, the opticalresonance in dielectric nanostructures, alone, by EM radiation hasalso been discussed in the literature [7,8]. The incident mono-chromatic electromagnetic radiation creates a distribution ofelectric fields within the dielectric nanostructures. The resonanceoccurs for a certain combination of the size of particles, wave-length of incident radiation and relative refractive index of themedium. The resultant effect is manifested in large enhancementsin Raman scattering intensity from the dielectric particles, whenthe excitation wavelength is close to its EM eigenmode.

EM energy inside an irradiated cylinder was first calculatedanalytically by Ruppin [9]. A strong enhancement of local/internalfield in dielectric nanostructures, like silicon nanowires (NWs)and nanocones of varying diameters was experimentally observed

ll rights reserved.

x: þ91 3222 255303.

x: þ39 050509 417.

. Roy),

[10]. To the best of our knowledge no such report is available forIII–V semiconductors. Moller et al. [11] showed that the variationof the integral intensity of the phonon modes with laser excita-tion energy, which revealed a redshifted E1 gap of the NWs ofwurtzite (WZ) phase compared to bulk InAs of zinc blende (ZB)phase. The comparison of band-gap resonance of the phononmodes for InAs bulk and NWs clearly demonstrated relativelyhigher enhancement in Raman intensity in the case of the latter.However, this point was not been addressed in their article. In amore recent report [12], variation in efficiency of coupling of lightwith InAs NWs for different polarization configurations, wasdiscussed. It was shown that the observed increase in Ramanintensity in NWs cannot be explained by the well known antennaeffect [13], a polar characteristics of inelastic scattering cross-section, observed in case of semiconductor NWs. The true originfor larger enhancement scattering intensity in InAs NWs of WZphase is still unknown. Probing strong coupling of radiation withsemiconductor nanostructures is technologically relevant, sincethe development of ultrahigh-Q and ultralow-threshold lasersoften exploits this unique characteristic of semiconductors [14].

We also remark that the study on phonon dynamics revealsother interesting phenomena associated with NWs. The dipole-allowed Raman scattering by TO phonons in a polar semiconductoris a result of deformation-potential (DP) induced electron–phononinteraction, whereas the Raman scattering by LO phonon involvesboth DP-induced and electro-optic (EO) interactions. The latter isthe Frohlich-type interaction, coupling interband electronic energystates by the electric field of the LO phonon [15]. Thus, the

J.K. Panda et al. / Solid State Communications 160 (2013) 26–31 27

comparison of the intensity ratio of these two phonon modeshas the potential to shed light on the above effects in thesesemiconductors.

In this paper we explain the enhancement of coupling of lightwith NWs by simulating the scattering intensity of infinitely longcylinder of InAs of a fixed diameter under different wavelengthsof excitation. We have discussed the internal field enhancedspontaneous Raman scattering from InAs NWs and its depen-dence on the wavelength of excitation laser source. Furthermore,the difference in the intensity ratio of LO and TO phonon modesin InAs bulk and NWs near the resonance excitation energy isaddressed in view of the difference in their electronic structure. InSection 2 of this article, we have briefly discussed the technique ofsample growth, which we have followed. Other experimentaldetails are also available in Section 2. Results on HRTEM andRaman scattering measurements on NWs are discussed in Section3. Section 4 deals with variation of enhanced Raman scatteringfrom InAs NWs for varying excitation wavelengths as well as abrief discussion explaining the observation. In Section 4 wecompare the intensity ratio of the LO and TO phonon modes forNWs and bulk InAs by resonance Raman spectroscopy. Section 5summarizes our results with a few concluding remarks.

2. Experimental details

Aligned InAs NWs were grown on InAs substrate (111)B usingchemical beam epitaxy technique at 42575 1C, with metallor-ganic line pressures of 0.3 and 1.0 Torr for TMIn and TBAs,respectively [16]. The structure of the NWs was studied usingZeiss Ultraplus field emission gun scanning electron microscope(SEM) and Zeiss LIBRA 120 transmission electron microscope(TEM). For TEM and Raman measurements, samples were pre-pared by mechanically removing NWs from the substrate with arazor blade and then transferred onto 300 mesh copper TEM gridscoated with 50 nm carbon films. Samples were placed on a Sisubstrate for Raman measurements. Raman measurements werecarried out using a micro-Raman setup equipped with Arþ–Krþ

laser (Model 2018-RM, make Newport, USA) as the excitationlight source, a spectrometer (model T64000, make JY, France) anda CCD detector. For resonance Raman measurements, spectra ofboth bulk and InAs NWs were recorded at ten different wave-lengths of excitation between 457 nm and 647 nm.

3. TEM and Raman scattering measurements

In Fig. 1(a) and (b) we show a characteristic SEM image and adark field TEM image of the NW, respectively. More details ofthe structural analysis of this sample have been discussed elsewhere[17]. The average diameter and length of the NWs are estimatedafter measuring 15 different NWs to be 4472 nm and 2.070.2 mm,respectively. In order to measure the length fraction of WZ and ZB inthe NW, we collected dark field TEM images of the NWs oriented in[2-1-10]. In this orientation the pattern of the WZ and ZB structuresare distinguishable and the diffraction pattern of WZ and ZB do notsuperimpose. Therefore a dark field image shows different contrastfor the two crystal structures. Then, the fraction of WZ to the totallength of the NW is estimated in the sample to be 0.95.

Raman spectra of InAs bulk and NWs, recorded at 78 K using514.532 nm as excitation wavelength, are shown in Fig. 2. Theexperimental data points are shown by þsymbols. By deconvolutingthe spectra (dashed lines in Fig. 2) with Lorentzian functions wehave estimated the allowed phonon wavenumbers. For bulk InAs[111] in back scattering geometry, TO and LO phonons appear at217.2 cm-1 and 239.0 cm�1 (as obtained by deconvoluting the

spectrum by two Lorentzian functions for these two modes). In arecent article, [12] the optical phonon modes in InAs NWs of WZphase has been discussed in detail by studying azimuthal-dependence Raman scattering intensity. For NWs, in addition tothe LO mode at 239.0 cm�1 and the A1/E1 mode at 217.2 cm�1

(TOh), a new EH2 mode, a folded phonon mode of WZ phase, appear at

212.1 cm�1 (TOl) [11,12]. Here we would like to mention that forNWs, the net fitted curve does not match very well over the spectralwindow between 225 and 235 cm�1. It should be stressed thatsimilar mismatch between the data points and net fitted spectrum isalso observed for bulk InAs (Fig. 2) over the same spectral range.Thus, we believe that the possible spectral feature between TO andLO modes is not related to any unique characteristic of a NW (say,surface phonon modes). Such asymmetry in the LO mode at lowerwavenumber can also be observed in Ref. [11] in the Ramanspectrum of InAs NWs.

4. Internal field enhanced Raman scattering

To obtain the expression for the internal field in the NW underEM radiation, let us consider the NW to be an infinite cylinder ofradius R and dielectric constant e, surrounded by a medium ofdielectric constant em. Given an EM radiation of wavelength l andof a particular polarization, one has to solve the Helmholtzequation for a scalar function, c, in cylindrical polar co-ordinates to obtain the scattered and internal fields. The Helm-holtz equation in cylindrical polar coordinates (r,y,z) can bewritten as

1

r

@

@rr@c@r

� �þ

1

r2

@2c@y2þ@2c@z2þk2c¼ 0 ð1Þ

For single-valued functions of y the solution of the aboveequation takes the form [18]:

cnðr:y,zÞ ¼ ZnðkÞeinyeihz with (n¼ 0, 71, 72, ::::::::: ), whereZnðkÞ is the solution to the Bessel equation:

k d

dkk d

dkZn

� �þðk2�n2ÞZn ¼ 0 ð2Þ

and k¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffik2�h2

p. h is a constant, which depends on the

boundary condition that the tangential components of E and Hof the incident EM are to be continuous across the boundaryseparating the NW and the surrounding medium. k is thewavenumber corresponding to the incident radiation. In case ofplane wave excitation, incident normally on a infinite cylinder theexpression for the scalar potential becomes cnðr:y,zÞ ¼ ZnðkrÞeiny,which is independent of z. The scalar function (cn) is a generatingfunction for vector harmonics of order n, given as [18]:

Mn ¼r � ezZnðkrÞexpðinyÞ� �

,

Nn ¼1

kr �Mn: ð3Þ

where ez is the unit vector in the z-direction. Zn(kr) represents acylindrical Bessel or Hankel function. Jn(k1r) with k1¼2pm(l)/l isused for the estimation of the field inside the cylinder. Jn(k0r) andHn(k0r) with k0¼2p/l are used for the incident and scatteredwaves outside the cylinder. m(l) is the real part of the refractiveindex of the wire. The internal field can be calculated for twoindependent polarization states of incident and scattered waves(refer to Fig. 3). The plane of incidence contains the incidentdirection and the axis of the wire. In general convention, TMmode is the one for which the electric field vector is in the planeof incidence, and for the TE mode the magnetic field vector is inthe plane of incidence [19]. For these two polarization configura-tions, after expanding the expression for the electric field incylindrical polar coordinates along with the proper continuity

Fig. 1. (a) SEM micrograph of the as-grown sample; the substrate is tilted by an angle of 451 and ( b) TEM image of a typical single InAs NW.

190 200 210 220 230 240 250

T=78K NW

Bulk

Inte

nsit(

arb.

uni

t)

Raman shift(cm-1)

Fig. 2. Raman spectrum of bulk and NWs of InAs recorded at 78 K. Dotted lines are

the deconvoluted spectra for TO and LO modes. The net fitted spectrum is shown

by the solid line.

Fig. 3. Schematic diagram to show the possible polarization configurations of incident

light. z is the axis of the wire. xoz is the plane of incidence. The incident wavevector k

is shown by the solid arrow. The electric field or magnetic field vectors of the incident

light, corresponding to TM or TE mode, are shown by dashed arrows.

J.K. Panda et al. / Solid State Communications 160 (2013) 26–3128

conditions, the internal electric field can be obtained as [19]:

ETEint ¼

E0

k1

Xn ¼ 1n ¼ �1

ð�iÞneinycnin

rJnðk1rÞr�k1J0nðk1rÞy

� �ð4aÞ

ETMint ¼ E0

Xn ¼ 1n ¼ �1

ð�iÞndn Jnðk1rÞeinyz ð4bÞ

E0 is the amplitude of the incident electric field of EM radiation.The coefficients cn and dn are related to far field scatteringcoefficients an and bn by [10,19]:

cn ¼J0nðk0rÞ�anHð2Þ0n ðk0rÞ

J0nðk1rÞand dn ¼

Jnðk0rÞ�bnHð2Þn ðk0rÞ

Jnðk1rÞwith

an ¼Jnðk0rÞJ0nðk1rÞ�mJ0nðk0rÞJnðk1rÞ

Hð1Þn ðk0rÞJ0Nðk1rÞ�mHð1Þ0n ðk0rÞJnðk1rÞand

bn ¼mJnðk0rÞJ0nðk1rÞ�J0nðk0rÞJnðk1rÞ

mHð1Þn ðk0rÞJ0nðk1rÞ�Hð1Þ0n ðk0rÞJnðk1rÞ

The volume-averaged intensity of the modes per unit length isobtained by integrating the square of the electric field over thevariable r and y as [10] ITE,TM

int ¼ ð1=pR2ÞR R

0

R 2p0 9ETE,TM

int 92rdrdy.

Hence, one yields:

ITMint ¼ E2

0

Xn ¼ 1n ¼ �1

9dn92½J2

nðk1RÞ�Jn�1ðk1RÞJnþ1ðk1RÞ� ð5aÞ

ITEint ¼

E20

2

Xn ¼ 1n ¼ �1

9cn92

J2n�1ðk1RÞþ J2

nþ1ðk1RÞ�Jnðk1RÞ½Jn�2ðk1RÞJnþ2ðk1RÞ�n o

ð5bÞ

The enhanced electric field results in increase in inelasticscattering (Raman) intensity of the incident radiation. With theapproximation that the scattered frequency is not very differentfrom that of incident frequency, the ratio of the scattered intensityper unit volume (I) of the NW to that of bulk is given by

SðlÞ ¼INW=VNW

Ibulk=Vbulk

� �expt

¼ITE,TM

ðlÞIaðlÞ

" #2

ð6Þ

where VNW and Vbulk are the volumes of the NW and bulk probed bythe radiation and Ia is the average intensity of radiation within thedispersive medium. The above expression for S strongly depends onk1 and k0, and hence on l and m(l). To simulate S(l), the values ofreal part of the refractive index for different values of l for bulk InAsare taken from Ref. [20]. The data points for m over three differentregions of wavelengths have been fitted with 2nd order polynomialequations. Using these known empirical relations for m(l) for thesethree regions, the variation of S with incident wavelength (l) for TMand TE modes for different radii of the wires are plotted in Fig. 4 inthree different parts (A, B and C). Dashed lines in Fig. 4 separate thethree regions. Strong enhancement in the intensity of the scattered

J.K. Panda et al. / Solid State Communications 160 (2013) 26–31 29

signal is predicted for both modes, for certain combinations of thediameter of the NW and the excitation wavelength (note the logscale in Fig. 4(b) for the TE mode and blue curve corresponding toR¼50 nm for the TM mode). For larger diameters of the NW, asteeper enhancement condition is achieved.

Raman spectra of bulk InAs, recorded for different wavelengths ofexcitations in ðxðzzÞxÞ scattering configurations are shown inFig. 5(a). The same for NW of InAs recorded in TM configuration for

varying wavelengths of excitations are shown in Fig. 5(b). The origin oftwo extra peaks at 200 and 225 cm�1, observed for excitationwavelength 476 nm is unknown to us. It is not due to the effect oflaser heating, as the laser power on the sample for this wavelength is5 times less than the same for excitation wavelength 514 nm (forwhich they are not observed). We have fitted each spectrum of NWover the spectral range between 200 and 220 cm�1 by two Lor-entzian functions for TOl and TOh modes (not resolved in the spectrarecorded at room temperature) keeping intensity, width and peakpositions as free fitting parameters. For bulk InAs a single function

4

5

6

7

8

9

10

11

12

450 500 550 600 650 700 750 800

10-5

10-4

10-3

10-2

10-1

100

R=30nm

x106

For TM mode

Wavelength(nm)

R=50nmC

B

A

R=22nm

Rat

io(S

)

Fig. 4. Variation in the square of the ratio of scattered intensity per unit volume of the

NWs for (a) TM mode and (b) TE mode of radiation. The short dashed line shows the th

references to color in this figure legend, the reader is referred to the web version of th

Raman shift (cm-1)190 200 210 220 230

501

514

647

568

530

520

*

496

488

476

457

Inte

nsity

(arb

. uni

t)

*

Fig. 5. Raman spectra of (a) bulk and (b) NWs of InAs, recorded at varying excitation wa

bulk and NWs for 476 nm excitation wavelength.

for TO mode is used keeping the peak position, width and intensityas free fitting parameters. In Fig. 6 we have plotted (symbols) the

ratio of the intensity (i.e. S�VNW/VBulk) of the TOh mode in TM

configuration for NWs to TO mode of bulk InAs, as obtainedexperimentally. The solid line is the simulated S convolutingEq. 5(a) in Eq. (6) with a Gaussian function with mean radius as22 nm and the standard deviation 0.85 nm to include the sizedistribution of the NWs, as observed from TEM measurements. Ashift by 10 nm (from 504 nm to 514 nm�48 meV) towards thehigher wavelength was necessary to match the experimental datapoints. In order to rationalize this shift of 48 meV we recall that thesolid lines correspond to the results of the simulations for the InAsnanostructure assuming the same electronic properties of bulk InAs,which is in a ZB phase. There are quite a few reports in the literature,where the electronic band structure of the WZ phase of InAs hasbeen calculated [21–24]. In a recent article, [11] it was shown thatthe band gap related resonant Raman intensity of the TO mode of theInAs NW down-shifts by 110 meV from that of the corresponding

10-6

10-5

10-4

10-3

10-2

10-1

100

0.1

1

10

100

450 500 550 600 650 700 750 800

Wavelength(nm)

Rat

io(S

)

x106

For TE mode

R=50nmR=30nm

CBA

R=22nm

NW to that of bulk (S(l)) with wavelength of radiation for different radii of InAs

ree regions, A, B and C, over which S has been simulated. (For interpretation of the

is article.).

190 200 210 220 230

457

476

488

496

501514

520

530

568

647

Inte

nsity

(arb

. uni

t)

Raman shift (cm-1)

* *

velengths (in nm at right). The * marks are two unidentified lines observed in both

5

6

7

450 500 550 600 650

0.1

0.2

0.3

0.4

0.5

0.6

Wavelength (nm)

Rat

io(S

)

[Int

ensi

ty R

atio

(S*VNW/VBulk

)]ex

pt

475 500 525Wavelength(nm)

Inte

nsity

(arb

.uni

t)

Fig. 6. Variation of (INW/Ibulk)expt ie (S�VNW/VBulk) and simulated S with wave-

length in TM configuration. Experimental data points are shown by symbols. The

solid line is the simulated S convoluting Eq. (5a) in Eq. (6) with a Gaussian function

to include the size distribution of the NWs. Inset of the figure shows the variation

of integral intensity of TOh modes of the InAs NWs (blue dots) and bulk (green

dots) with wavelength of excitation. (For interpretation of the references to color

in this figure legend, the reader is referred to the web version of this article.)

1.8 2.0 2.2 2.4 2.6 2.8

0.0

0.1

0.2

0.3

0.4

Wavelength (nm)

Energy (eV)

I LO

/IT

O

444478518565621690

1.8 2.1 2.4 2.7-0.1

0.0

0.1

0.2

0.3

0.4

Energy (eV)

I LO

/IT

O

Bulk

Fig. 7. Variation of intensity ratio of LO and TO modes with incident excitation

energy in NWs. Inset of the figure shows the same for bulk InAs. The solid lines are

the guide to the eye. Error bars at last two points are large because of low intensity

of the TO mode.

J.K. Panda et al. / Solid State Communications 160 (2013) 26–3130

bulk material due to the decrease in E1 gap of the WZ phase of theformer. In the inset to Fig. 6, the intensity of the TO mode of NW andbulk InAs, as measured by us, has been plotted using blue and greensymbols for different laser excitation wavelengths. As expected fromthe electronic band structure and results reported in Ref. [11], wealso observe the resonance of the TO mode of the NW and bulk InAsat 513 nm and 491 nm (difference�108 meV). Thus, if we take intoaccount this 108 meV downshift of the resonance energy, we canconclude that the 48 meV downshift of the maxima in internal fieldinduced enhancement of Raman scattering in NWs, as observed inFig. 6, is not a manifestation of band-gap resonance alone. A crucialrole is played by the material property, m(l), in determining internalfield induced Raman scattering for the dielectric NW. Here we wouldlike to mention that in the above simulation the optical absorptioncoefficients for NW at different wavelengths are not included due tounavailability of the data in the literature. We assume it to be sameas that of bulk and its effect cancels out in estimating the ratio, S.

5. Contributions of DP and EO effect in Raman scatteringof NW

In Fig. 7 we compare the intensity ratio (r) of LO and TOmodes for bulk and NW of InAs with varying incident excitationenergy. Here, we assume that though the probed region varieswith change in wavelength, its effect should not contribute to theintensity ratio of the phonon modes appreciably. It should berecalled that this ratio corresponds to relative contribution ofdeformation potential and electro-optic effect in the inelasticscattering (Raman) of light in polar semiconductor [25]. Increas-ing of I(LO)/I(TO) ratio at different temperature with variation ofexcitation energy shows DP and EO contribute strongly near theresonance [26]. For the excitation energy below the energy of theE1 gap the relative contribution of DP and EO effect on intensity ofthe phonon modes is not expected to alter appreciably. Thus, the

value of r is nearly same till 2.5 eV and 2.4 eV for bulk and NWs,as observed in Fig. 7. However, near resonance, the ratio increaseswith the increase of the excitation energy due to enhancedcoupling of electric field of electromagnetic radiation with pho-nons. For the excitation energy well above the band gap, the ratiodecreases for bulk InAs (shown in the inset of Fig. 7), while forNWs we find that there is a monotonic increase in r beyond theband gap, with further increase in excitation energy (till 2.8 eV).To explain this anomalous behavior of r in NWs, we refer to theelectronic band structure of WZ and ZB phases of the NW asobtained from ab-initio calculation. [11] At the E1 gap (G-A) ofthe WZ phase, there are closely spread electronic energy states(within the range of 0.4 eV) in the valence band. This increasesthe range of excitation energy (2.4 eV to 2.8 eV in Fig. 7), overwhich the strong coupling of the electric field of electromagneticradiation with the phonon mode can be obtained. However, at theE1 gap (G-L) of the ZB phase, such degeneracy in energy states islifted. Hence a relatively sharp resonance in r is observed for thebulk system.

6. Conclusions

In conclusion, we have demonstrated a strong resonance effectdetermined by the increase in electric field intensity of electro-magnetic radiation in InAs NWs yielding a large enhancement ininelastic scattering of light from InAs NWs. We have also provideda classical explanation for the enhancement effect in our cylind-rical NWs. These findings demonstrate how an efficient couplingof visible radiation with such semiconductor nanostructures canbe achieved. The giant field enhancement in InAs NWs harnessthe potential of using these semiconductor nanostructures infuture semiconductor nanotechnology, in sensor engineeringand photonic devices, where efficient coupling with electromag-netic radiation is desirable. In addition, we have compared therelative contribution of DP and EO effect in NWs and bulk InAs forvarying excitation energies.

J.K. Panda et al. / Solid State Communications 160 (2013) 26–31 31

Acknowledgments

AR and JKP thank Central Research Facility at IIT Kharagpur forthe availability of Raman spectrometer. This work was partlysupported by MIUR under PRIN 2009 prot. 2009HS2F7N_003.

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