HAL Id: jpa-00227671
https://hal.archives-ouvertes.fr/jpa-00227671
Submitted on 1 Jan 1988
HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
STARK EFFECT ON A GROUND STATE EXCITON CONFINED IN THREE DIMENSIONS
M. Dagenais, W. Sharfin, J. Greene
To cite this version:
M. Dagenais, W. Sharfin, J. Greene. STARK EFFECT ON A GROUND STATE EXCITON CON- FINED IN THREE DIMENSIONS. Journal de Physique Colloques, 1988, 49 (C2), pp.C2-229-C2-232.
�10.1051/jphyscol:1988254�. �jpa-00227671�
STARK EFFECT ON A GROUND STATE EXCITON CONFINED IN THREE DIMENSIONS
M. DAGENAIS, W. F. SHARFIN* and J
.
GREENE* *Department of Electrical Engineering, University of Maryland, College Park, MD 20742, U.S.A.
* MIT Lincoln Laboratory, PO Box 73, Lexington, M A 02173, U.S.A.
* * ~ o r d Aerospace, 442 Mariott Road, Lexington, M A 02173, U.S.A.
Rksumk - L'effet Stark quantique de confinement est observk pour la premibre fois sur un exciton dont le mouvement est confink en trois dimensions ("quan- tum box"). Un dhplacement de l'ktat fundamental de I'exciton lik de l'ordre de la moitik de la largeur h mi-hauteur est observe sans klargissement apprkciable de la rksonance.
Abstract
-
The quantum confined Stark effect on an exciton confined in three dimensions (quantum box) is reported for the first time. A shift of the ground state bound exciton in CdS as large as its half-width at half-height is observed without any appreciable broadening of the resonance.We report the first measurement of the quadratic Stark shift of a bound exciton with giant oscillator strength in the direct gap CdS semiconductor. The exciton is confined in three dimensions by the potential of a neutral donor (Li or Na interstitials) which confined the exciton motion over dimensions of order of the free exciton Bohr radius (30A0). Optical transmission measurements with a single mode dye laser reveal a very narrow linewidth (8-10 GHz)' which implies a very well defined and reproducible potential well. This is in sharp contrast to previous realizations of three dimensional excitonic confinement where linewidths about 100 to 1000 times larger are commonly observed because of the large variations of the potential dimension^.^ At an electric field of 2.5 x lo4 V/cm, a relative shift of the ground state bound exciton resonance as large as its half-width at half-height is observed without any appreciable broadening of the resonance. The absolute value of the shift is very small and is measured to be about 0.1 cm-'. The bound exciton shift is about 25 times smaller than the free exciton Stark shift measured in the same experimental conditions.
Some of the very exciting recent development in experimental and theoretical solid state physics has to do with quantum confinement. Quantum size effects occur when the physical dimensions are comparable to the characteristic lengths that determine the electron behavior. Because of the possibility of demonstrating new electronic, optoelectronic and photonic devices when the dimensionality of the system is reduced, much work is presently done to confine the exciton motion to two, one and even zero dimensions. One then talks of quantum wells, quantum wires and quantum boxes respectively. Since the oscillator strength of the free exciton per molecule is proportional to the probability of finding both the electron and the hole at the same physical location, and since the overlap of the electron and hole wavefunctions increases when the dimensionality of the system is reduced, there is much to be gained in going to lower dimension systems. It can be shown
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988254
JOURNAL DE PHYSIQUE
that the bound exciton oscillator strength is enhanced compared to the free exciton - oscillator strength by a factor 8
(e) '",
where pz and M, are the free exciton reduced and total mass respectively and whereEi,,
and Eg are the free exciton and bound1 exciton binding energy.3 This factor is evaluated to be 2.6 for CdS.Bound excitons can be seen as a Coulomb-correlated electron-hole pair (exciton) weakly bound to an impurity center, and are a natural realization of a quantum box. Bound excitons have a remarkably large oscillator strength (f=9), as a result of the confinement. The wave function of the exciton weakly bound to the impurity defines a large region around the impurity, and the oscillations of the electronic polarization are coherent over the whole region. So far, very few experimental results have been reported on the Stark shifting of bound e x ~ i t o n s . ~ Our study is the first one done on a bound exciton with giant oscillator strength.
In the present work, the electric field is applied in the direction of propagation of the incident laser beam. The electrodes were evaporated on two glass substrates spaced by a hollow insulating washer to form a small cavity containing the 15.5pm thick CdS sample. The sample assembly was then immersed in superfluid liquid helium. A krypton ion pumped dye laser operating at -487 nrn of linewidth of 0.3 cm-l was used in conjunction with a Burleigh wavemeter to accurately monitor the laser wavelength. Precise transmission measurements were performed at different electric fieldsand the data were analyzed and fitted according to a method that was previously de~cribed.~
Since the crystals are photoconductive, it is necessary to apply a square-wave voltage to the plates with a time interval less than the effective dielectric relaxation time of the crystal to avoid polarization effects. For the n = 1 exciton and for the bound exciton, the stark-effect is dominated by the simple hydrogenic Stark effect in th.e effective-mass approximation. The Stark shifts are proportional to the square of the applied electric field. A bipolar square wave voltage of up to 125 volts was applied to the electrodes. The period of the square wave voltage was 10 ps and, according to Thomas and Hopfield: was sufficiently short to avoid any screen-out effect by nccumulation of charges. At the maximum applied electric field (2.5 x
lo4
V/cm), a shift of (0.1 f 0.03) cm-' toward higher energies is detected for the bound exciton resonance. This shift should be compared to a shift of 2.5 cm-' for the free exciton resonance measured in the same conditions. The 0.1 cm-' shift of the bound exciton resonance toward higher energies is shown in Fig. 1. For the fit, the laser spectral profi!e was assumed to have a gaussian lineshape with a width 2a = 0.3 cm-' and the bound exciton lineshape was assumed to be Lorentzian with a full width at half maximum (FWHM) of 0.27 cm-I. Assuming a gaussian lineshape :for the bound exciton leads to similar results. No apparent broadening of the resonance due to field ionization is detected. Higher electric fields were applied to the sample, but each time the electrodes were ripped off by the strength of the applied electric field. We note that the free exciton shift is in agreement with the standard predictions for the ground state shift of a hydrogenic atom when the direction of the applied electric field is properly taken into a c ~ o u n t . ~ A very well defined quadratic shift of the free exciton resonance toward lower energies is observed.The evaluation of the bound exciton Stark shift from first principles is not an easy task because it is a four-body problem. In order to get a qualitative descriptio:n of the physics, we can imagine the bound exciton as being a hydrogen molecule. A covalent bond is formed by the electron belonging to the impurity donor (Li or Na) and the electron belonging to the exciton. To a large extent, the exciton still conserves its identity. In fact, a deuteron model is often used to explain the large oscillator strength of the bound e ~ c i t o n . ~ When an electric field is applied of a bound exciton, two things happen. First, the electric field tries to break the covalent bond in order to minimize the two dipole energies. By doing so, the binding energy of the bound exciton is reduced. Second, the exciton ground
+ &
(8, +
t +
t
Stark shift: 125 V .applied+ +
c
.O 0.75-
V)
.- V)
E
V) c +
2
0 0.50
-
0 I0.25
(3 experiment
+
theoryI t
4 . @ '
e
m
(3 experiment
d
+
theory-
?:m =+4
(4
++* *++,
?+?++%++, , F* .+, e e ++I++'
f%l*f*' '9, +d+t+e4
m y '
'2,-,*"
@ l + + + , , z * ' + ~ ~ '*:,I+'
r"
I I I I I I I I +Figure 1 The I2 bound exciton in CdS at an applied electric field of 2.5x104V/cm. A shift of (O.lf 0.03) cm-I toward higher energies is observed.
20528 20530 20532 20534 20536
state shifts toward lower energies, as expected for any hydrogenic systems in the presence of an electric field. As a result of these two opposing effects, the total shift of the bound exciton resonance is less than the free exciton shift. In addition, it is experimentally found that the free exciton shift is overly compensated and that the resulting shift of the bound exciton resonance is toward higher energies.
JOURNAL DE PHYSIQUE
A bound exciton is a good system for studying the physics of confinement in a low-dimensional system and for understanding the advantages of confinement in enhancing optical nonlinearities in semiconductors. Saturation behavior, degener- ate four-wave mixing, and optical bistability measurements near bound excitons have already been reported.'?'
REFERENCES
1. M. Dagenais, Appl. Phys. Lett., 43, 742 (1983).
2. L. Brus, IEEE J. Quantum Electr. QE-22, 1909 (1986).
3. M. Dagenais and W.F. Sharfin, J. Opt. Soc. Am. B2,1179 (1985); E.I. Rashba and G.:E. Gurgenishivili, Sov. Phys. Solid State 4, 759 (1962); G.D. Sanders and Y . 4 . Chang, Phys. Rev. B28,5887 (1983).
4.
B.S.
Razbirin, I.N. Ural'tsev, and A.A. Bogdanov, Sov. Phys. Solid State, 15, 604 (1973); G.F. Glinskii and A.N. Pikhtin, Sov. Phys. Semicond., 9, 1393 (1975); H. Kukimoto, S. Shionoya, S. Toyotomi, and K. Morigaki, J. Phys. Soc.Japan, 28, 110 (1970); E. Hanamura, J. Phys. Soc. Japan, 28, 120 (1970);
M.V. Lebedev and V.G. Lysenko, Sov. Phys. Solid State, 24,1721 (1982).
5. M. Dagenais and W.F. Sharfin, Opt. Eng. 25, 219 (1986); M. Dagenais and W.F. S h d n , Phys. Rev. Lett. 58, 1776 (1987).
6. D.G. Thomas and J.J. Hopfield, Phys. Rev., 124, 657 (1961).
7. L.I. Sdtiff, Quantum Mechanics, in Chapter 33 (McGraw-Hill, London, 1968) 544pp.; H.E. White, Introduction to Atomic Spectra, i n Chapter 20 (McGraw- Hill, New York, 1934) 457 pp..
8. M. Dagenais and W.F. Sharfin, Appl. Phys. Lett. 46,230 (1985); M. Dagenais and W.F. S h d n , in Optical Bistability 111, edited by H.M. Gibbs, P. Mandel, N. Peyghambarian and S.D. Smith (Springer Verlag, New York, 1986) p. 122.
