Phonon raman scattering in nanostructured multiple quantum wells

Superlattices

and Microstructures,

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Vol. 12, No. 4, 1992

PHONON RAMAN SCATTERING IN NANOSTRUCTURED

MULTIPLE QUANTUM WELLS

P.D.Wang, C.M.Sotomayor Torres, H.McLelland, C.R.Stanley Nanoelectronics Research Centre, Departmentof Electronics and Electrical Engineering, University of Glasgow, Glasgow G12 8QQ, UK (Received 3 August 1992)

We report resonant Raman scattering and ‘hot’ carrier luminescence from dry etched GaAs-AlGaAs quantum dots, Up to 4th-order multiphonon processes were observed via photoluminescence (PL) and excitation of PL (PLE) in quantum dots for the first time. Quantum confinement effects were also found with various dot sizes. Confined and interface phonons play an important role in the carrier relaxation process. It is demonstrated that Raman scattering is mediated by zero dimensional (OD) electronic states. The measured GaAs phonon frequencies are found to map well unto the bulk LO phonon curve.

Various experimental techniques have been used to real&e the quantum dots and wires [Il. These efforts are driven mainly by predictions of attractive linear and nonlinear optical properties of these structures [2,31. Theoretical investigations have focused on the new electronic states brought about by quantum confinement interactions [5,6] in (41 and electron-phonon nanostructures. Benisty et al 161 demonstrated that the momentum relaxation of the carriers is greatly reduced. The subsequent poor luminescence is attributed to the inhibition of excited electron and hole relaxation by acoustical phonon scattering that occurs when electrons and holes are confined in a quantum dot 1.51.Wang et al [7] modelled the luminescence intensity based on the ‘intrinsic’ reduced relaxation mechanism and the carrier diffusion model. In other words, the carriers or the excitons tend to be ‘hot’with fewer channel via which to relax. On the confinement of optical phonons, several different models have been proposed so far. The original dielectric continuum (or slab mode (SM) or electrostatic) model applies electromagnetic boundary conditions. This model [8] predicts confined optical phonon modes and four interface modes in typical GaAs-AlAs system. Another different continuum model, so called guided mode (GM) model, applies mechanical boundary conditions [9,10]. Both models treat optical phonon modes as standing waves, but differ significantly on macroscopic boundary conditions, and therefore in the calculation of electron-phonon interactions. Dielectric continuum model has failed to consider the mechanical (hydrodynamic) relations between two materials at the interface. However, the lack of predication of interface modes is the strongest argument against GM model which states that the atomic

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displacement is always zero at the interface. In addition to these two macroscopic models, the microscopic lattice dynamical model has also been used [11,12,13] to calculate the electron-phonon coupling. Furthermore, based on their microscopic calculations, Huang and Zhu [ll] proposed another modified dielectric continuum model which leads to analytical expressions for the confined modes. The modified model takes into account both mechanical and electromagnetic boundary conditions. Another achievement in Huang and Zhu’s work is the demonstration of hybrid (mixed) modes when non-zero dispersion for optical phonons is considered. In this paper, we report experimental studies of deep dry etched GaAs-AlGaAs quantum dots. It is shown that up to 4th-order multiphonon resonant Raman scattering and ‘hot’ luminescence have been observed for the first time in GaAs-based nanostructures. Confined and interface phonon-polaritons play an important role in the carrier relaxation process. GaAs-AlGaAs based quantum dots were fabricated using electron beam lithography and dry etching, The starting material is a 100 period 8nm GaAs-12nm Alo.sGac7As MQW grown by MBE at 630-C. The pattern was defined by electron beam lithography (Leica Cambridge EBPG 5-HR electron beam machine at SOKeV) using HRN (high resolution negative) resist. The subsequent pattern transfer was achieved using Sick reactive ion etching (RIE). The etching power was 80 Watts at t-f of 13.56MHz producing a self bias of 280V. The etch depth was 2.lym so that all the quantum wells were etched through. We were able to fabricate quantum dots down to 200nm in lateral size with a 1O:l aspect ratio. Scanning electron microscopy @EM) reveals a dot

@ 1992

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profile with negligible undercut. For the optical spectroscopy, an Ar+ and a tunable Ti-sapphire lasers were used. The signal was dispersed by a Jobin-Yvon lm double spectrometer and detected by a cooled photomultiplier (PMT) operating in the standard photon counting mode. All the experiments were carried out at 5K in a continuous flow cryostat. Near backscattering geometry was employed in Raman spectroscopy. Fig.1 shows the photoluminescence excitation (PLE) spectra of three samples having 500nm, 300nm, and 25Onm dot diameters. The heavy hole 0th) and light hole (lh) exciton energies of the starting material are 1.573eV and 1589eV. The detector energy of each spectrum in Fig.1 is positioned at the corresponding hh ground state energies. A considerable blue shift measured from PLE spectra was observed with AEt=1.4, 5.8 and 9.0meV for 5OOnm. 3OOnm and 25Onm dots, respectively. Surface as well as sidewall damage was induced by long dry etching processes. Wang et al [14] performed Raman scattering studies on dry etched n+-GaAs with various etchants to assess the surface depletion layer thickness. It was shown that the top surface damage depth induced by RIE saturated at approximately -35nmf5nm. The sidewall damage, however, has a different mechanism and the sidewall depletion depth can be three or four times as high as the surface one as derived from the electrical measurements [15]. Based on above discussions, the ‘active’ dot size in our 25Onm dots is around 3Onmf10nm. Beitmann et al [16] also reported a similar dry etch damage depth in their quantum wire studies. They rely on

and Microstructures,

Vol. 12, No. 4, 7992

the estimate of the side wall damage depth in their interpretation of the quantum confinement effects as well as exciton centre of mass quantisation. In contrast to the ground states in Fig.1, the high energy peaks in the dot spectra move very slowly with AEa=15.1, 16.5 and 17.2meV for 500nm, 300nm and 250nm dots, respectively. The origin of this peak is due to the dry etch induced localised states and related defects. Further investigations are underway. The interesting and remarkable phenomena are the up to 4th order optical phonon overtones in PLE spectra. The An and B,, series extrapolates back to detection energy with a 36SmeV period. They correspond to LO phonon energy of GaAs. A corresponding Dn series is associated with TO phonons of GaAs. Cn series extrapolates 9meV above the hh ground and probably relates to the defects observed on the high energy shoulder of hh. From simple linewidth considerations, it is clear that An and Dn series arises from a multiphonon Raman scattering process while B,, and Cn are more likely exciton-related ‘hot’ luminescence. The interface phonon mode is also evidenced as a sharp peak below An series (A=-0.75meV) The insert of Fig.1 is blown-up around Al series of 25Onm diameter dot arrays. Interface phonons can be seen more clearly with some fine structures superimposed on it. Similar sharp Raman lines have also been observed in the PL. With tuning of incident photon energy, these resonate with the fundamental n=l and n=2 e-hh transitions (n denotes the quantisation in z -MBE growth- direction). If LO phonon intensity is plotted as a function of the incident photon energy, the resonant Raman profile duplicates exactly the PL spectrum. The energy position of the n=2 transition is also blue shifted by 8meVklmeV in 250nm diameter dots. This further indicates that our dots are in the quantum confinement regime.

AlAs

AI(Ga)As

’v/__A, 1.575ev 1 57

fz I

1.61

I 1.65

A3

I

0

I 1.69

I

500

m Dots

IF

,

Bulk

I Ic,L GaAs

I

3

4

3

4

IF

1.73

Excitation Energy (eV) 0

Figure 1. PLE spectra of 250nm, 300nm and 500nm quantum dots. The details of the labelling are discussed in the text. The shoulder on the high energy side of e-hh states is a defect related luminescence. The insert is blown-up of the first order Raman lmes of 25Onm dots. It can be seen clearly that some fine structures are superimposed on the interface (IF) mode. This demonstrates the mixing of optical phonons.

I

2 514

(a)

(b)

Figure 2. The schematic diagram of (a) the optical phonon energy alignment of GaAs-Al(G system and (b) the interface phonon mode calculated in a dielectric continuum model.

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Although electronic wave functions have been confined laterally into 3Onm diameter to show strong OD quantum confined effects, the lattice vibrations should be extended laterally to the physical sizes of the dots. Phonon confinement in z direction should be still dominant in OUT 8nm quantum wells. The theoretical investigation on the lateral phonon confinement in cylindrical quantum wires (&tm) has predicted the enhanced hybrid optical modes [17]. However, the fabrication of a regular array of those wires is currently beyond the existing technology. Since we are dealing with phonons 0.75meV below the LO phonon line, the confined modes, as well as interface modes, remain almost unchanged as long as the GaAstype LO mode of the alloy lies at sufficiently lower frequency. Otherwise, the confined modes transform into propagative optical vibrations with an energy in the optical phonon range of both GaAs and AlGaAs [181. Based on the above discussions, we can simplify the system and treat it as GaAs and AlAs as long as we study the confined modes. Fig.2 shows the schematic diagram of energy alignment of GaAs and Al(G optical phonons and the calculated interface mode [19] as a function of k// (parallel to the interface) based on the 8nm GaAs-12nm AlAs system. Fig.3 shows the similar Raman spectra taken under depolarised PLE conditions (notice the different terminology used here) for three different dot arrays. Structures superimposed on the interface phonon is more evident in smaller dots (25Onm) and in the first order. Polarisation spectra (z(x,x)z) show similar structure to those in Fig.3. Fig.4 shows the normal resonant Raman scattering spectra of 200nm and 250~1 diameter dots. Only the first order optical phonon lines have been displayed with fine structures. Fundamental LO phonon line (m=3 assigned) always participates in the second order Raman scattering. The resonant conditions correspond to the outgoing resonance with the scattered photon energy in the region of fundamental transitions (ehh). Electron-phonon interaction includes both short range deformation potential as well as Frohlich interaction associated with the macroscopic electric field of the LO and interface phonons. In the quantum dot system, the degeneracy could be completely lifted due to the three dimensional confinement. Therefore, the density of states is a g-function type. The intraband Frohlich interaction which induces the strong resonant condition in 2D cannot participate in Raman scattering process (neglecting inhomogeneous broadening). On the other hand, away from resonance, interband Frohlich interaction is weak and mostly dependent on the electron wave function penetration and hole band mixing (in large k/j). The deformation potential (DP) starts to play an important role in the Raman scattering [201 with increasing confinement. The DP only couples to the hh and lh valence bands. In order that the Raman numerator is nonvanishing, only the antisymmetric interface and confined phonons participate. Fig.3 and Fig.4 show the interface phonons close to the GaAs LO which has the antisymmetric potential (see Fig.2). Strong mixing between interface and confined modes should be expected in the rather thick (>3nm)

=

750nm E,=1.569qV

1

32

,

,

,

34 Energy

,

,

Shift E-E,

/

/ 38

36 (meV)

Figure 3. Raman spectra taken under the conventional PLE spectroscopy for three different diameter dots. The intedace and confined phonons can be observed clearly in the smaller dots and in the first order. This indicates the confined phonon effects are very important in the carrier relaxation process in the OD quantum dot system.

33

34

35

36

37

Raman Shift (meV)

Figure 4. Resonant Raman spectra for two different dot arrays. They correspond to the outgoing resonance. Some of the spectra have a luminescence background. Under resonant conditions, TO phonon modes are enhanced indicating the electron-deformation potential interaction is dominant in the OD system.

quantum well system. As a consequence, the confined phonon modes observed in our dot system should also be more antisymmetric. Moreover, for the nonvanishing Raman numerator, the odd parity pure confined modes are expected in the Raman scattering. These confined modes

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are therefore assigned to m=3,5,7,9 and 11 which can be seen clearly superimposed on the broad line of the interface mode (Fig.3 and Fig.4). According to the microscopic model ill], m=l, the half wavelength mode, changes its confined character and becomes an interface mode when the k vector changes from a strictly z axis to other directions. In the free standing dot system, the light wavevector can be coupled more strongly in the plane through the side wall than in the 2D system. The electronDP coupling in the quantum dot system also explains well the enhancement of TO efficiency under resonant conditions (see Fig.4). Under resonant conditions, the interband Friihlich coupling, the so called ‘three-band process, should be important in OD system due to the 3D quantum confinement. Calculations 16.71 show that some electron (hole) energy levels can be matched with LO phonon energy seperations. The interband term, however, will not change the assignment as discussed above. The measured phonon frequencies are found to map very well onto the theoretical 3D phonon dispersion curves by ml

q =

dFA

Where m is an integer laballing the order of the confined mode, dl is the GaAs layer thickness and A describes the penetration of the vibration mode into the barrier. A is usually assumed to be one monolayer. Das Sarma et al [21] demonstrate that, only in the thin QW samples, the confined phonon modes are important in the calculation of electron-phonon interactions. In the quantum dot system, the situation is different. The observation of phonon confinement indicates the participation of optical phonons in the carrier relaxation, although lateral phonon confinement has not been tackled. For the large dot system, as can be observed for 38Onm and 75Onm dots in Fig.3, the confined modes were barely observed. The situation is more likely to be treated as a 2D MQW system with negligible phonon confinement. In conclusion, phonon confinement in OD system is observed and shown to play an important role in the carrier relaxation processes. All observations can be explained qualitatively through the analysis of the zero dimensional electronic quantisations. The analytical determination of the Raman tensor involves the careful analysis of carrier confinement states and the hole band mixing in the OD system. It shows that phonon confinement effects are important for the future calculation of electron-phonon interactions in low dimensional nanostructures. AcknowledgementWe thank the Science and Engineering Research Council (UK) for financial support (GR/H 44714). The work was also supported by European Community ESPRIT Basic Research Action 3133. We are also grateful to Dr N.Constantinou and Professor B.K.Ridley for sending us their preprints. We

and Microstructures,

Vol. 72, No. 4, 1992

acknowledge interesting discussions with Professors S.P.Beaumont, C.D.W.Wilkinson and Dr S.Thoms. Technical support was provided by A.Ross and JGray.

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