Exciton-confined-phonon interaction in quantum dots

JOURNAL

OF

LUMINESCENCE ELSEVIER

Journal

of Luminescence

76&77

Exciton-confined-phonon Yasuaki

Masumotoa-b’*,

(1998) 189 -192

interaction in quantum dots

Tadashi

Kawazoe’.“,

Naoki

Matsuura’

Abstract

Sharp line width of excitons in CuCl quantum dots was observed by means of persistent spectral hole burning. At 2 K, the hole spectrum consists of a zero-phonon line (line width = 0.14 meV) and its acoustic phonon wing, and they are well separated from each other. With increasing the temperature T, the zero-phonon hole and its phonon side band are merged into each other and finally the hole spectrum shows broadening. Temperature-dependent hole spectra were compared with a theoretical simulation of the absorption spectra of single-sized dots. Contrary to the usual exciton broadening of the linear temperature dependence. the broadening is proportional to l/[exp(&kT) - I] at low temperature, where ci is the confined acoustic phonon energy in quantum dots. This observation demonstrates unique characteristics of the excitonphonon interaction in quantum dots. (‘ 1998 Elsevier Science B.V. All rights reserved. K~IXYI~LLS:Quantum

dot: Exciton -phonon

interaction:

Hole burning:

Electron-phonon and exciton-phonon interaction in quantum dots is unique, because electron, exciton and phonon are size-quantized in quantum dots. Continuous acoustic phonon dispersion in the bulk is converted to a set of confined acoustic phonons in dots [ 11. so that temperature broadening of exciton spectrum in dots may be changed from the linear temperature dependence observed in the bulk crystal. Recently, very sharp luminescence spectrum whose line width is less than or comparable to 0.1 meV has been reported for a couple of quantum dots by means of the single quantum-dot spectroscopy [2-51, but its origin and its temperature dependence have not been understood. In case of CuCl quantum dots, site-selective

*Corresponding author. [email protected]. I Present address: Faculty sity. Yonezawa 992, Japan.

Fax:

+ 81 298 53 6618; e-mail:

of Engineering.

Yamagata

Univer-

0022.2313’98~$19.00 I‘ 1998 Elsevier Science B.V. All rights reserved PI/ s0023-2313(97)00148-8

CuCl

laser spectroscopy, such as hole burning and fluorescence line narrowing, has been used to investigate the homogeneous line width of excitons and its temperature dependence [6.7]. However, the reported line width at low temperatures is 4 times larger than the very sharp line width observed in this report by means of persistent spectral hole burning. In this paper. we report the very sharp line width of CuCl quantum dots and its unique temperature dependence. Samples studied are nanometer size CuCl embedded in NaCl crystals. The sample preparation method and experimental procedures are the same as previously reported [S]. The absorption spectrum of CuCl quantum dots at 2 K is shown in Fig. la. The Z3 exciton absorption peak shows a blue shift of 16meV from the bulk value. corresponding to the quantized exciton shift in 3Snm radius CuCl quantum dots [9]. The absorption change spectra of the sample exposed to the very

I

I

.

I

I

.

3.22

3.2

3.24

PHOTON ENERGY (eV) spectrum of CuCl quantum dots in spectral change at 2.5. 15.30 and 50 K caused by more than 9000shots of the excitation of IOnJjcm’. The burning laser energy was changed to excite the 3.5nm radius dots with the increase of temperature Fig. 1. (a) The absorption

radius dots, the burning laser energy was changed together with the blue shift of the hole as the temperature was increased. With increasing the temperature T, the phonon side band increases and the zero-phonon hole and its phonon sideband are finally merged to each other. After that. the hole spectrum shows broadening. The temperature dependence of the full halfwidth of the hole is plotted in Fig. 2. Contrary to the usual exciton broadening of linear temperature dependence, the temperature broadening is proportional to l/[exp(b/kT) - l] below 50 K. where (Sis the confined acoustic phonon energy in quantum dots. It is the lowest-energy breathing mode of a quantum sphere expressed by 7.8/RmeV, where R (nm) is the radius of the quantum dot [ 11. In fact, the following expression was used for the fitting of the temperature-dependent full half-width of the hole 2rhole( T),

NaCI. (b) The absorption

2r,,,,(T)

= 0.17 + 3.35 x

+ 19x weak narrow-band laser are shown in Fig. 1b. They show the persistent spectral hole burning. At 2K, the hole burning photon energy was set to be 3.2194eV corresponding to 3.5nm radius CuCl dots. The hole spectrum consists of a zero-phonon line (line width = 0.14meV) and its acoustic phonon wing which are well separated from each other. After the sample is exposed to the stronger narrow-band laser (300 shots of 180 uJ/cm2), the Stokes-side confined acoustic phonon wing grows [l]. This wing comes from the light absorption by larger-sized dots than the resonantly burned dots with the emission of phonon and saturation of the growth of the resonant hole brings forth the appearance of the confined acoustic phonon side band. However, under the very low excitation intensity, the acoustic phonon wing observed in the hole spectrum shows much smaller shift than the confined phonon energy, probably because the lowest-energy tail part of the inhomogeneously broadened confined acoustic phonon wing contributes mainly at the lowest temperature. To obtain temperature-dependent hole spectra of 3.5 nm

1

1 exp(d/kT) 1 exp(d/kT)

- 1

1’

- 1

(1)

where 6 is 2.2meV and the optical phonon energy A is set to be 23.4meV. The agreement between experimental data and the fitting curve is good. This means that the temperature broadening of the exciton line width is dominated by the interaction between confined excitons and thermally activated confined acoustic phonons. This observation demonstrates unique characteristics of the exciton phonon interaction in quantum dots. With the increase of the radius of the dots, the hole line width starts broadening at lower temperature. This feature can be explained by the temperature broadening model of excitons interacting with the thermally activated confined acoustic phonons, because 6 is inversely proportional to R. Unique size-dependent and temperature-dependent exciton line width for CuCl quantum dots is observed. Following Takagahara’s formulation [ 10,l l] of the interaction between the exciton and the confined acoustic phonons in semiconductor quantum dots. the absorption spectrum of the exciton

I

CuCl in NaCl

:’ ...,:.., 0

10-l loo

IO'

IO2

TEMPERATURE

(K)

Fig. 2. Log-log plot of the temperature-dependent hole width. Sohd circles are the experimental results. Solid line is calculated by the expression Eq. (I) shown in the text. Dashed lines y. and /j show the acoustic phonon contribution and the optical phonon contribution, respectively. Open circles are the line width of the simulated hole spectra of 3.5 nm radius CuCl dots.

phonon

coupled

system

is given as [12]

(hc,, - E” + .GB)[ _ YJlr _ S h 2

with S,(f)

=

1

(;'j/h(Oj)'e

yn(htoj)

S = S+(O) + S_(O). and

+ f *

$1.

ELR = 2 ;-f/h,.

Here litoi are the confined acoustic phonon energies, E,) the adiabatic exciton energy, n(h~f)j) the phonon occupation number, ;‘II the longitudinal relaxation rate and ;‘, is the coupling constant between the exciton and the phonon given by the matrix element of the exciton-phonon coupling Hamiltonian. As it is difficult to obtain ;‘j from the first principles. we treat ;lj as an empirical parameter. The values of parameters used for the numerical calculations are ;‘I1 = 0.07meV and Z,;,i = O.O36(meV)‘. Here we consider the same value for ;‘; each mode. Reflecting on the relation

between the radius of dots and confined acoustic phonon energy, 7.8,!RmeV. the phonon inhomogeneous distribution is assumed to be a Gaussian with centered energy of (i = 2.2 meV and standard deviation of u = I .O meV for 3.5 nm radius dots. Here, we introduce the cut-off at 6 i 2.1 meV to avoid the divergence of S,(t). Phonon inhomogeneous distribution is used. because single-sized dots have different shapes and different surrounding circumstances. Highly oscillatory integrand in Eq. (2) prevents us to integrate it. Therefore. we calculate it in the low-temperature limit (a) and in the high-tempcrature limit (b). The boundary between (a) and (b) is about 10 K. In region (a), I(;!,,~h~,jj)‘c’ i(,l,f

[n(h~~~j)

+

~

~

~]I

~

1.

so that we can calculate I((!,) by expanding the exponential function in Eq. (2) in powers of S,(t) and S-(r). Hence. the S+(t)“S~(t)“’ term gives the Lorentzian side band due to n-phonon emission and rn-phonon absorption process. The numerical calculation is performed by taking up to the thirdorder terms of S+(t) and S_(t). The numerical results of the absorption spectra for T = 2 and 5 K are shown in Fig. 3a. We can reproduce the sharp zero-phonon line. In region (b). each phonon side band is unresolved and their envelope function will give the absorption spectrum. The formula to calculate the envelope function is given in Ref. [l I] by expanding S,(t) up to 1’. The numerical results of the absorption spectra for T = 20, 30 and SOK are shown in Fig. 3b. As we calculate the envelope function of the absorption spectra. we cannot ivell reproduce the sharp zero-phonon line overlapping with the acoustic phonon band. However. the increase of the width of the absorption spectrum is obtained as the temperature increases. Comparing Fig. 3 with Fig. 1b, we tind qualitative agreement between the theorq and the experiment is good. Especially. the feature that hole spectrum turns to a unified broad band at 30K is understood. because an absorption spectrum hecomes an envelope function in the temperature regime of(b). Further, we plotted the full half-width of the simulated hole spectra. a convolution

Y. Masumoto et al. / Journal

ofLuminescence

76& 77 (1998) 189-192

broad acoustic phonon band. However, it is still beyond our calculation technique and is left for future study. We note that the present calculation as empirical parameters. The detailed caltreats culation of these parameters from first principles is also left for study. yj

References Cl1 S. Okamoto, PI K. Brunner, c31 c41

PHOTON Fig. 3. Simulated absorption quantum dots. The calculation in the text.

ENERGY

(eV)

line shape of 3.5 nm radius CuCl formula and used parameters are

integral Z(o) * I(o), in Fig. 2. The simulated result agrees with the experimental results. The simulation in the intermediate regime between (a) and (b) will probably reproduce the characteristic absorption spectrum of a sharp line superposed on the

c51 161 c71 ca c91 Cl01 Cl11 Cl21

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