RESONANT MIXING BETWEEN ELECTRONIC AND OPTICAL VIBRATIONAL STATES OF A QUANTUM WELL STRUCTURE

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RESONANT MIXING BETWEEN ELECTRONIC AND OPTICAL VIBRATIONAL STATES OF A

QUANTUM WELL STRUCTURE

P. Lao, W. Tang, A. Madhukar, F. Voillot

To cite this version:

P. Lao, W. Tang, A. Madhukar, F. Voillot. RESONANT MIXING BETWEEN ELECTRONIC AND

OPTICAL VIBRATIONAL STATES OF A QUANTUM WELL STRUCTURE. Journal de Physique

Colloques, 1987, 48 (C5), pp.C5-121-C5-126. �10.1051/jphyscol:1987522�. �jpa-00226726�

JOURNAL DE PHYSIQUE

Colloque C5, suppl6ment au n0ll, Tome 48, novembre 1987

RESONANT MIXING BETWEEN ELECTRONIC AND OPTICAL VIBRATIONAL STATES OF A QUANTUM WELL STRUCTURE

P.D. LAO"), W.C. TANG, A. MADHUKAR and F. V O I L L O T ' ~ )

Departments o f Materials Science and Physics, University Of

Southern California, Los Angeles, CA 90089-0241, U.S.A.

We report the first observation of resonant mixing between electronic and optical vibrational states of a quantum well structure brought about by matching the separation between the heavy hole and light hole free excitons with the optical vibrational modes. A total of 27 peaks representing as many as 18 vibrational modes are observed i n t h e l u m i n e s c e n c e e x c i t a t i o n s p e c t r a o f t h e

G ~ A S / A ~ ~ . ~ ~ G ~ ~ . ~ ~ A S ( ~ O O ) single quantum well structure studied. This is also the first time that all four possible types of vibrational states

-

confined in the well or barrier, unconfined, and interface- have been simultaneously observed in a quantum well.

The notion that when the energy separation between two discrete electronic states or distinct electronic transitions becomes comparable to an elementary excitation of the system a resonant mixing will follow has been known for quite some time. For quantum well structures the idea was first explored1,* theoretically as a possible means of determining the coupling of confined c h a r g e carriers with the different types of optical vibrational modes via a resonant splitting of discrete Landau levels created by application of an appropriate magnetic field. While the presence of the magnetic field changes the constant density of states of two dimensionally confined carriers into discrete Landau levels, thus enhancing the resonant condition, a resonant mixing is nevertheless present even in the absence of a magnetic field2. In this paper we report the first observation of this phenomenon and, through it, also the first

(')permanent address : Department o f Physics. Fudan University. Shanghai, Chine

( 2 ) ~ r r m a n e n t address : INSA. Dipartement de CBnie Physique. Avenue de Rangueil. F-31077 ~ o u i o u s e Cedex. France

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987522

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observation of all four types of vibrational modes of a quantum well structure

-

modes con£ ined in the well, confined in the barrier layers, unconfined, and interface mode. The observations are all the more remarkable and unambiguous for they are made on a single square quantum we1 1 (SSQW)

.

The G a A s / A l O 2 32Ga0.68A.5 (100) SSQW samples were grown via molecular beam epitaxy (MBE) on our 4-400 machine, extensively modified to achieve high quality material, and consist of an intended 9 monolayer (ML) GaAs well sandwiched between 40 ML thick barrier layers, all grown on semi-insulating GaAs(100) substrate with an intervening lOOOA GaAs buffer layer. The sample growth conditions have been reported previously3, but it is worth noting that both the thicknesses of the layers and the A1 concentration were monitored via reflection-high-energy-electron-diffraction (RHEED) intensity dynamics during growth3. As such, these are known with an accuracy of + 0.1 ML and 18, respectively. Finally, growth interruption was introduced at both the interfaces defining the we113. For a single QW with such a width and barrier layer, the separation between the heavy hole and light hole band edges is theoretically expected to be near 36.5 meV, a value close to the bulk GaAs LO phonon at the

p-

point. Hence a resonant mixing is expected. The samples were examined via photoluminescence (PL)

,

PL excitation (PLE) and Raman studies in the backscattering geometry employing an ~ r + pumped dye laser with a full width at half maximum of 0.25 meV. Detection is via photon counting and the resolution is 0.2 meV.

PL 1

: 5K 'P Fig.l(a) 5K PL spectrum of a

E d g 1 7 2 8 0 e V 9 ML SSQW. Peaks PI, P2 and

P3 are doubly resonant Raman scattered peaks. (b) SK PLE spectrum for the 8 ML light h o l e r e g i o n , t a k e n w i t h detection set at 1.7280 eV if

M-m the heavy hole region. PA

i s a R a m a n p e a k S t o k e s

,,,

^{Bvl-w! I = 1,)} shifted by fl ~ * = 3 8 . 7 mev.

T h e 8 M L l i g h t h o l e i s

1.m i n o 1.m im imJ 1.- mm lm marked.

E N E W l eV 1

In fig. l(a) is shown the 5K PL spectra from such a sample. The two broad peaks centered near 1.7151 and 1.7308 eV correspond to the recombination of heavy hole to n=l electron free excitons in regions of the sample with well width of 9 ML and 8 ML, respectively. The presence of well thickness differing by

+

1ML from the intended delivery of material in samples grown with growth interruption is by now a well established phenomenon4. Of greater significance in fig.

1 (a) is the presence of the very narrow (-0.5 meV) lines indicated by Pl, P2 and P3. These are Stokes shifted by a 1 = 3 6 . 2 meV, n 2 = 3 5 . 5 meV and 3=33.3 meV and move rigidly with change in the excitation energy. The observation of these Raman lines in PL spectra is a testimony to the remarkable enhancement of Raman cross section when both incident and scattered photons are simultaneously near resonance

Fig. 2

.

5K PLE spectra with detection set at (a) 1.7294 eV and (b) 1.7323 eV in the h e a v ~ hole region. PB*, pC* and PD are additional Raman *peaks Stokes shifted by

R B

=39.0 meV,

nC*=

40.1 meV and

n

D*=4~.9 mev, respectively.

with electronic transitions. That such a double resonance condition is operative in fig. l(a) is confirmed by the PL excitation spectra shown in fig. 1 (b) for the 8 ML light* hole (lh) *free exci;on region.

One notes the presence of peaks PI

,

P z * , P3 and PA which are Stokes shifted by n 1 = 3 6 . 1 meV, fi 2=35.3 meV, h 3 = 3 3 . 7 meV and fi A =38.7 meV. While these move rigidly with the detection energy,

the peak at 1.7674 eV does not shift and is thus identified as the 8ML lh free exciton. Similar investigations of the 9 ML lh region identify its energy to be 1.7515 eV.

p7 T=5 K

J

a

f

C z

Ed=1.7323

' I I . ' .

1~38 1.766 1774 1764 1772 ENERGY (cV)

In fig. 2 we show PLE spectra taken at two typical detection energies straddling the 8 ML hh PL peak at 1.7308 eV. In spectra (a) one observes appearance of additional Raman pea5s labelled PB*, pC*, and pD*. The 8 ML lh is now coincident with PA and is the cause of its apparent greater width. In spectra (b) one has begun to lose some of the higher Stokes shift peaks. Nevertheless, as many as seven Raman peaks are clearly seen in the PLE spectra in the 8 ML lh region.

When we turn attention to the energy region between the 9 ML hh and 8 ML hh, a remarkable 27 peaks are seen in the PLE spectrum with detection set at the lowest energy end of the 9 ML hh PL line, as shown in fig. 3. Similar measurements on SSQW structures grown under identical conditions with same alloy barrier but well width different by 2 1 ML or more do not show such structure. Note that the separation of the peaks in fig. 3 from the detection energy is too small to correspond to one phonon Raman process. However, the energy separation of peaks 1 through 15 from the 9 ML lh at 1.7515 eV and of peaks 13 through 27 from the 8 ML lh at 1.7674, summarized in Table 1, corresponds well to the energy region of the optical vibrational

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Fig. 3. 5K PLE spectrum in the 9 ML heavy hole and 8 ML h e a v y h o l e r e g i o n w i t h d e t e c t i o n a t 1 . 7 0 4 0 e V . P e a k s l a b e l l e d 1 through 15 a r e a t p h o n o n e n e r g y separations from the 9 ML lh whereas peaks 1 3 t h r o u g h 2 7 a r e a t p h o n o n e n e r g y separations from the 8 ML lh.

(see Table 1)

-

V)

. C _e

-

?? e

. *

-

-

$

>

t

vt z

W I-

f

Table 1 . ASSIONEIENT OF YLE P U K S UF FItiUHE 3

, ^{I I 1}

1.7080 17180 1.7280 17380 ENERGY ( e V )

modes of the SSQW expected on the basis of presently known behavior of the GaAs and A10,32Ga0.68As optical phonon branches. A detailed discussion of the identification of each of these peaks is both, beyond the scope of the length restrictions on the paper and not yet possible since neither the X-point values nor the dispersion f r o m p t o X of the two-mode behavior of the optical phonon branches of the A10,32Ga0.68As alloy are known. What can, however, be said without ambiguity 1s that given that both overlapping and non-overlapping energy regions exist between the optical phonons of bulk GaAs and AlO. 32Ga0. 68Ast the peaks observed above 36.2 mev (the P-point LO of GaAs) correspond to modes confined in the alloy barrier layers and arise from the AlAs-like LO and TO branches. Similarly, peaks between 34.7 meV ( P - p o i n t energy of the GaAs-like LO mode of Alga ,Gap. 7As) and 36.2 rneV represent modes confined in GaAs well and arise rom the GaAs LO branch. The peak at 35.5 meV (also P2 of figs. 1 and 2) is, however, likely to be an interface phonon since its energy coincides well with the intersection5 of the real parts of the dielectric function of GaAs and A1oe32Ga0.68As. Peaks in the region of 34.7 meV down to near 30.2 meV (the best available estimate for the X-point value of the GaAs-like LO mode of the alloy) correspond to modes of the entire SSQW structure (i.e. unconfined) due to the overlapping nature of the LO and TO branches of the well and barrier layers. A possible exception is the 33.3 meV mode (peak P3 of figs. 1 and 2) which' is just barely away from the overlapping region between the TO branch of the well and the GaAs-like TO branch of the alloy. It could thus be a confined TO mode of the well.

Finally, peaks below 30.2 meV are confined modes of the barrier arising from the GaAs-like TO branch.

We ascribe the remarkable observation of this structure in the PLE spectra to the dramatic modification of the usually constant density of electronic states by resonant mixing between the lh+one of each vibrational mode of the SSQW and the corresponding hh band.

This is schematically shown in fig. 4. It is perhaps worth noting

( 1

^RESONANT M I X I N G

( (

^REGIME

I

^{RESONINCE REGIME} ;

I I _ OML HH BMLHH OYL LH BMLLH

Fig. 4. shows schematically the regime of resonant mixing b e t w e e n t h e l h + o n e vibrational mode of the SSQW a n d t h e c o r r e s p o n d i n g hh band.

that this is a purely quantum mechanical phenomenon which does not require any thermal excitation of phonons. Indeed, once it is recognized that this structure in the density of states of coupled (electronic + vibrational) states is inherently present in such a system then it becomes also possible to appreciate that many of the conventional notions and associated terminology of Raman scattering

C5-126 JOURNAL DE PHYSIQUE

may need to be extended to correctly describe strongly mixed electron and phonon states.

This work was supported by the U.S. Army Research Office and Air Force Office of Scientific Research.

REFERENCES:

1. A. Madhukar and S. DasSarma, Surf. Sc.

98,

135 (1980).

2. S. DasSarma and A. Madhukar, Phys. Rev.

g,

2823 (1980).

3. F. Voillot, J.Y. Kim, W.C. Tang, A. Madhukar and P. Chen, Superlattices and Microstructures (In Press).

4. See, for example, F. Voillot, A. Madhukar, W.C. Tang, M.

Thomsen, J.Y. Kim and P. Chen, App. Phys. Letts.

50,

194 (1987) and references therein.

5. O.K. Kim and W.G. Spitzer, Jour. App. Phys.

50,

4362 (1979).