OPTICAL NONLINEARITIES OF QUANTUM - CONFINED EXCITONS IN CuBr MICROCRYSTALLITES

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OPTICAL NONLINEARITIES OF QUANTUM - CONFINED EXCITONS IN CuBr

MICROCRYSTALLITES

U. Woggon, F. Henneberger

To cite this version:

U. Woggon, F. Henneberger. OPTICAL NONLINEARITIES OF QUANTUM - CONFINED EXCI-

TONS IN CuBr MICROCRYSTALLITES. Journal de Physique Colloques, 1988, 49 (C2), pp.C2-255-

C2-258. �10.1051/jphyscol:1988260�. �jpa-00227677�

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OPTICAL NONLINEARITIES OF QUANTUM

-

CONFINED EXCITONS IN CuBr MICROCRYSTALLITES

U. WOGGON and F. HENNEBERGER

Humboldt-Universitat zu Berlin, Sektion Physik, Bereich Halbleiteroptik, Invalidenstrasse 110, DDR-1040 Berlin, D.R.G.

Abstract

-

Wut study both the linear and nonlinear optical properties of excitons in CuBr-dots for the specific sltuatkn, when the radius of the dots is 5 to 10 times larger than the bulk exciton radius.

We observe a blue shift of the exclton peak at resonant optical excitation as well as strong saturation of absorption with very large contrast and Lorentzian saturation intensities in the 100 kW/cm2 range.

The data are explained in terms of exciton

-

^excitoninteraction In the presence of quantum confinement.

1

-

INTRODUCTION

At present optical nonlinearitks related to quantum-confined excitons in semiconductors are being extensively investigated. In bulk semiconductors screening of the exciton states induced by free carriers is the dominating process, whlk the direct Interaction between the uncharged excitons is of minor importance. Recent experiments on multiple quantum wells and corresponding theoretical studies have shown /I/, that an opposite relation holds in lower dimensional systems. Another system of reduced dimensionality, which we are dealing with in the present paper, is presented by sernlconductor-doped glasses. Here small semiconductor microcrystallites are formed confining the excitons In dl three space dimensions.

In order to avoid any complications by disorder we have studied pure CuBr crystallites embedded in a silicate glass. In addition CuBr has an advantageously large exclton binding energy resulting in pronounced exciton features up to room temperature and making already small modifications due to quantum confinement experimentally observable. The samples were fabricated by the usual technique of controlled particle growth via subsequent heat treatment. The crystallite sizes were determined from X-ray diffraction and small-angle scattering measurements as well as by electron beam microscopy.

2

-

LINEAR OPTICAL PROPERTIES

The linear absorption spectrum at liquid helium temperature for three samples with different crystallite sizes is shown in Fig. 1. The spectra are dominated by two pronounced exciton peaks known from bulk CuBr and labeled Z,, and

Z3.

The quantum confinement is evidenced by the increasing shift of the peaks to higher energies. The position of the Z12 exclton In bulk CuBr has been determined from Hyper-Raman scattering experiments to be E,=2.9644 eV at T=4 K /2/

.

Thus, we observe already a substantial shift of 7 meV compared to the bulk material for the largest crystallites, the radius a of which is about ten times the CuBr exciton radius a,. For excitons in microcrystallites one has to compare the characteristic energies

-

h 2 /2@a,2

.

Ex,,=%2n2/ 2 M a 2 , and

E,,,

= ' h 2 n 2 / 2m,a2,

E x . b -

(M= me+ mh

,

p = m,mh/M for the bulk exciton binding, the quantum size effect on the exciton centre-of-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988260

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C2-256 JOURNAL DE PHYSIQUE

mass motion and on the single electron, respcrctlvely. Using mm=0.25m, and mh =1.2m, /2/ we find E

,,, =

1...6 meV a d E

,.,

^{= 6}

...

35 meV for the samples studii. whik ExVb is 104 meV for bulk CuBr /2/. This shows, that electron-hale c o r r h t b n (consistent with the exciton enhancement seen in the optical spectra) Is most Important for all smpks. But the extent to whlch the electron confinement contributes to the entire energy increases rapidly with decreasing crystallite radius and for the sampk with the smallest crystallites in Fg.1 both effects have to be consklered on the same b d . For this more complex sltuatbn we refer to a forthcoming paper and, In what follows, we concentrate on the limit a, /a c 1 appropriate to the a=l6nm sample, on whlch all further experimental data were taken

.

As has been firstly noticed by Efros and Efros /3/ the quantum confinement leads in this limiting case simply to a splitting of the bulk exciton band into discrete levels

1

^5.0,

u 4.0.

3.0.

2.0.

1.0.

while the internal motion is scarcely affected. In the present case the exciton broadening is that large that no discrete center-of-mass levels can be resolved, but as detailed in /4/, the Z1,2 absorption band of the 16nm- sample in Fig. 1 is clearly the interference of the different single transitions in 12

.

The broadening is essentially homogeneous and due to exciton-phonon interaction. The X-ray measurements have yielded that size fluctuatlons resulting in inhomogeneous broadening play a minor role for the relatively large crystallite sizes considered here.

In addition, the width of the Z1,2 line eoincides well with that of the bulk exciton / 5 / and increases gradually with rising temperature /4/. Recently-the occurrence of quantized centre-of-mass levels in CuBr microcrystallites has been directly verlfled by excitation spectroscopy in /6/.

The above discttssion has shown, that quantum size effects indeed occur in the " large" CuBr-microcrystallites studied. However. they scale down like (+L/M)E,.~ and, thus. are hardly observable for materials with smaller exciton binding energies, as for instance GaAs-dots. Next. we study the optical nonlinearities related to this specifically co~iflned excitons.

3. NONLINEAR ABSORPTION

29 311 311 12

I

Optical noniinearities of semiconductor-doped glasses have been already extensively investigated, but mostly on CdS/CdSe crystdlitea; f see e.9. /7 to 10/ and references therein) under conditions. where quantum confined excitons play only a minor role.

Fig. 2 shows tho change of the CuBr-microcrystallite absorption under excitation with dye laser pulses the frequency of which is scanned stepwise through the 21.2 exciton groundstate resonance keeping their intensity fixed. A pronounced bleaching of the exciton absorption shows up with rising intensity, which is. however.

accompanied by a blue shift of the absorption maximum. This indicates that the underlying mechanism is not two- level-like but related to many-body effects in the exciton system excited. Lattice heating causing iikewise a blue shift of the peak /4/ would imply temperature changes of more than 100 K not achievable with resonant excitation.

(The shift of the peak measured with rising bath temperature is 0.1 meV/K ) . A filling and associated blocking

=I&

Fig.1 Linear optical thickness versus photon energy for three different CuBr doped glasses at Tz1.8 K.

a46.0 nm (full curve). 12.5 nm (dashed). and 6.7 nm (dashed-dotted). Sample thickness d=200 ~ m .

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sample of Fig. 1 at liquid nitrogen temperature under excitation with 4 ns dye laser pulses of different intensities.

(1) Linear spectrum 0.0004 I, .(2) 0.151,

.

(3)0.581,.(4) I,=

20 MW/cm2. The arrows mark the different maximum positions.

An excitation-induced blue shift of the exciton peak has never been observed for bulk semiconductors, although theoretically an increase of the exciton resonance energyof EH-F

=

(13 x/ 3 )E, .ba; n, follows in Hartree- Fock approximation for the interacting exciton gas of density n, /11/. Apparently, there is a perfect compensation between the Hartree-Fock contribution and the negative correlation energy (screening) in 30. As has been stressed in /t/ this balance is disturbed in lower dimensional systems, since screening is here strongly reduced due to the restricted mobility of the e&ctrcm*hok pairs. In fact, excitation-induced blue shifts have been observed for the first time on 20 confined excitons in GaAs/GaAIAs AE (me!/)- multiple quantum wells /12/. In /13/ such a blue shift has been also predicted for excitons confined to microcrystalliter, just for the situation of interest a, <a. It occurs via an increase of the exciton radius caused by free carrier screening effectuating a stronger confinement. However, under the conditions studied here free carriers are practically not present. Therefore, we have calculated the Hartree-Fock shift EH-F,C of an exciton system confined to a microcrystallite /4/. The general treatment follows straightforward the 3 0 one /It/. The result for a macroscopic population of the lowest centre-of-mass level is plotted in Fig. 3. For the sampie studied experimentally we get a Hartree-Fock blue shift of about 3/4 of the bulk one. However. this value may not be directly compared with the experimental shift. because the actual density of excitons created depends on the excitation wavelength due to the different linear absorption levels. In addition, n, varks strongly across the sample in direction of the excitation beam because of the large optical thickness (ad ~ 6 ) . To enable a comparison we have sdved numerically the propagation equation of the light intensity coupled to that of the exciton density /4/. In the absorption coefficient all discrete centre-of-mass levels, the oscillator strength of which decays like l/n2

,

have been included and homogeneously broadened with

. ' I

Nonlinearity has been accounted for by modifying the linear exciton peak absorption and resonance energy. respectively. according to

with the characteristic densities ns and ne for the saturable absorption and the blue shlft, respectively. After proper normation of the different quantities and using the linear absorption data of the sunple studied the only free parameter remaining Is the r a t b n s /nB

.

The calculations ykM In a quite direct manmr a value of n

s *

0.1 n e

.

The corresponding nonlinear spectra are shown in Flg. 4. Good agreement with the experiment is seen.

From the results in Fig. 3 we obtain a value of about 0.09 a;3 a: 3x10'~ for n e yklding then n s s 3x10'~ cni3

.

This means that a few ten excitons are sufficient to bleach fully the extiton absorption of the microcrystallite, although it can formally contain several hundreds. For the bulk materhl it holds n s * 0.045a;~ %

2 ~ 1 0 ' ~ c m -3/ 14/

.

Therefore, we conclude that excitons confined to mlcrocrystalllt~ under the condltkn studied give rise to larger optical nonlinearitles than in the correspondlng bulk semiconductor. While the slngle exciton b still weakly influenced by the confinement. the effect on the exciton-axciton interaction is considerably stronger, since the characterlrtlc length of the letter is larger then the exciton radius. A theoretical study In the frame of a x s - treatment /15/ has led to the same concluskn.

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C2-258 JOURNAL

DE

PHYSIQUE

a, /a ( l og. scale 1 -

Fig. 3 Calculated Hartree-Fock shift EH-F,C versus confinement for two mass ratios. EH-~,C is given in units of the bulk shift EH-F=(13n/3)Ex,baz n x .

Fig.4 Calculated nonlinear absorption spectra. I, is given in units of honsd/r

.

r is the exciton life-time.

Parameters according to the experiment: a,d =8 and l"/ E ^x.b=0.1.

At the low energy-side of the resonance the total absorption bleaching observed is a combined effect of both saturation and Mue shift

.

The contribution of the blue shift is maximum in the region of maximum slope of the linear absorption band at h o % E x

- ^r.

Here almost complete saturation of absorption and a large switching contrast of more than 20 is found. Accounting for the finite optical thicknessof the sample Lorentzian saturation intensity (Including now both processes) of about 200 kw/cm2 is estimated. Excitons are present also at room temperature in CuBr-mirocrystallltes and. indeed. saturable absorption with no significant difference to low temperature is observed /4/. This shows that effective optical switches at room temperature can be achieved with the help of quantum confined excitons in semiconductor microcrystallites

.

REFERENCES

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h g . H.. Acadsnoic Press, 1987.

/2/ Hiinerlage, 8.. Rosster, U.. Vu D y Phach, Bkas, A., and Grun, J.B., Phys. Rw.B 22,(1980) 797 and refe- rences therein.

/3/ Efros, ALL., and Efros, A.L.,

Rz.

Tekh. Pduprw. 16,(1982) 1209.

/4/ Hennekrger. F.. Woggon. U., Puts, J., and Splegdberg, Ch., Appl. Phys. B 45,(1988).

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/lo/

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