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Journal of Non-Crystalline Solids 219 (1997) 205-21 I

CdTe quantum dots by melt heat treatment in borosilicate glasses L.C. Barbosa a,*, V.C.S. R e y n o s o a, A.M. de Paula a, C.R.M. de Oliveira a, O.L. Alves b A.F. Craievich c R.E. Marotti a, C.H. Brito Cruz a, C.L. Cesar a lnstituto de Ffsica, Universidade Estadual de Campinas, Caixa Postal 6165, 13083-970 Campinas SP, Brazil b lnstituto de QMmica, Universidade Estadual de Campinas, Caixa Postal 6154, 13083-970 Campinas SP, Brazil c Laboratrrio Nacional de Luz Sincrotron, Caixa Postal 6192, 13081-970 Campinas SP, Brazil

Abstract CdTe quantu m dots in borosilicate glasses were produced and their growth kinetics, the effects of quantum confinement for electrons and phonons and the time resolved optical transmission were studied. Quantum dots in the range of 10 to 25 with a 5% size dispersion were grown. The growth kinetics were studied by small angle X-ray scattering using synchrotron light. A spherical k . p model for the electron confinement explains absorption data and selection rules, and a dielectric continuum model for the phonon confinement could explain the resonant longitudinal and surface optical phonons, as well as their overtone combinations. The time response of absorption was studied by a pump-probe measurement on the femtosecond time scale. For samples showing a large amount of surface traps the recovery time can be as fast as 300 fs, while for an almost surface trap free sample it remains on the 1-3 ps time scale. © 1997 Elsevier Science B.V.

1. Introduction

Semiconductor quantum dot (QD) doped glasses have attracted much attention due to both their unique properties brought about by the three dimensional quantum confinement and their potential for photonic applications as optical devices [1-5]. The resonant optical nonlinearities are enhanced by the three dimension quantum confinement with (R/aBohr) 3 [6], where R is the QD radius and aBohr is the semiconductor exciton Bohr radius, without the large recovering times associated with resonant effects - - the time response is still fast enough (less than 1 ps) to be used in optical devices [7]. Control of size and of size dispersion is very important to enhance optical

Corresponding author. Tel.: +55-19 788 2428; fax: +55-19 788 2427; e-mail: [email protected]

nonlinearities. Thus, an understanding of the growth kinetics is crucial. The first QDs studied in the literature were of CdSSe alloys, which caused a somewhat controversial discussion; there was doubt if the red-shifted absorption spectra were a consequence of the QD growth with the corresponding decrease in the quantum confinement or if they were the effect of the stoichiometric incorporation of Se in the alloy causing the bulk band gap to decrease. Borrelli et al. [5] answered these concerns by growing CdSe QD which showed the same behavior as the previous CdSSe doped glasses. Since then, several groups have worked with different growth techniques such as QD suspension in colloids [8], sol-gel porous glasses [9,10], rf magnetron sputtering [11] and laser ablation, isolated or combined [12], as well as different materials such as GaAs [9], CuC1 [12], CdTe [13], PbTe [14], among others. At least one optical device

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L, C. Barbosa et al. / Journal qf" Non-Crystalline Solids 219 (1997) 205-211

working at 250 gbits/s was demonstrated by Tsunetomo et al. [15] using a CdTe QD glass produced by rf magnetron sputtering combined with laser ablation. Our CdTe QD doped glasses work, begun in 1989, appeared in 1990 [13], and 1991 [16], after the 1990 [17] paper. We have studied CdTe QD growth kinetics in order to control size and size dispersion by optical absorption [18], transmission electron microscopy [16] and synchrotron small angle X-ray scattering (SAXS) [19,20] techniques; the role of the atmosphere and the semiconductor concentrations in size dispersion [21] and optical traps [22,23]; the electron and phonon confinement effects [24,25] and, finally, the time resolved properties of the samples [26]. In order to bring these kinds of glasses closer to a real application we produced PbTe QDs [14] which showed typical quantum confined spectra with quantum confined gaps in the 1.3 and 1.5 txm, today's optical communication windows. The purpose of this paper is to present an overview of the above work.

2. Experimental CdTe and PbTe QD samples were prepared by melting the matrix glass host containing (wt%) 47.66%SIO 2 + 30.52%Na20 + 16.55%B203 + 5.22 %ZnO mixed with Te and CdO dopants or SiO 2 + B203 + ZnO + K 2 0 mixed with Te and PbO dopants for 50 min at 1400°C. The molten glass was quenched by pouring onto a stainless steel plate and samples were annealed at 450°C for 3 h. At this stage we have a transparent glass with no quantum dots. The QD are produced and grown in the last heat treatment stage at temperatures ranging from 500 to 580°C for minutes or hours. In order to grow the quantum dots the furnace atmosphere was carefully controlled. It is not sufficient to have the Cd and Te embedded in the glass matrix to grow them, but that they must be in the right oxidation state (Cd 2+ and Te 2-) to form the microcrystallite. The general equation describing the oxidation state of an element M is given by [27] ( 4 / m ) M x+ + O2 ~ (4/m)M(X+,,)+ + 2 0 2 - '

(1)

where m is the number of electrons involved in the valence change of M and x + is the original valence. It is possible to achieve the right oxidation state by controlling the content of the oxygen in the furnace atmosphere. Results show that samples fabricated in air do not form QD, the oxygen content is to high and Te 2+ oxidizes to Te 4+. These glasses are transparent and do not change color with the heat treatment. Also, if the atmosphere becomes highly reduced the glasses become dark, indicating the presence of metallic Cd. In the case of PbTe we had to change the Na20 matrix component for K 2 0 in order to decrease the oxygen chemical activity in the system [28], increase the content of the strong reducing ZnO and very carefully control the atmosphere in order to grow the quantum dots. These procedures were necessary because Pb 2+ easily oxidizes to Pb 4+. Samples were characterized by small angle X-ray scattering (SAXS), photoluminescence excitation spectroscopy (PLE), Raman scattering and femtosecond pump-probe absorption. The SAXS measurements were performed at the LURE synchrotron radiation laboratory, Orsay, France, using the D24 workstation [19,20]. In these experiments we measured the intensity of the X-ray scattering as a function of the wavevector at time intervals of 5 min, while the sample was growing inside a specially built furnace. The X-ray scattering intensity versus wavevector curves were used to extract the QD's size dispersion 8, the average radius /x and the R C Guinier radius as a function of the heat treatment time. The PLE measurements were performed using a white lamp and a monochromator as the excitation source and the detection was obtained with a photomultiplier and a Spex double spectrometer. For the Raman scattering measurements we used a dye laser and an argon laser as excitation sources. The spectra were measured with a Jobin-Yvon triple spectrometer and a multichannel detector in a backscattering geometry. The transient absorption measurements were performed using a colliding pulse mode locked (CPM) dye laser, emitting 50 fs pulses at 614 nm. The pulses are amplified by a six-pass dye amplifier, and then time compressed to generated spectrally broad pulses (white spectrum pulses). A standard pump-probe set-up with the direct CPM pulses as the pump and the white spectrum pulses as the probe was used.

207

L.C. Barbosa et al./ Journal of Non-Cr)'stalline Solids 219 (1997) 205-211 '

3. R e s u l t s

i

'

i

'

i

,

i

,

i

,

E

580oC - 25 rain. ~LO II ~" ~ EL = 2.09 eV /

Time evolution of the CdTeS and CdTe QD's growth was studied by SAXS measurements. Fig. 1 shows the size dispersion as a function of the heat treatment time for two CdTeS samples with different concentrations. The size dispersions initially decrease, go through a minimum at about 10-20 min, and then increase. The average radius shows a maximum also at about 10-20 min for both samples and then decreases. For the CdTe0.6S0. 4 sample, the Guinier radius increases until about 10 rain, where it is about 30 ,~, and then stays constant, whereas for the CdTeo.6S0. 4 sample the Guinier radius increases steadily with time up to about 90 ,~. These results are presented in more details in Ref. [19]. The Guinier radius for the CdTe samples also increases steadily with time [20]. In Fig. 2 we present the Raman scattering results as a function of the sample temperature for a CdTe sample. The Raman spectrum was obtained at resonance with the first confined transition of the QD [24]. Both spectra show a main peak at the bulk CdTe longitudinal optical (LO) phonon. However,

-~_

4 "1"=30C

S°lf ,

~

~lOK J

I

,

I

,

100 ]20 140 160 ]so 200 22o Raman Shift (cm -1) Fig. 2. Raman scattering spectra at room temperature (T = 300 K) and at 10 K in resonance with the first absorption peak. The intensity was normalized to the peak intensity of the LO-phonon and the spectra were vertically shifted tor clarity.

the low temperature spectrum shows thinner and better resolved peaks, presenting the LO phonon and also the first surface phonon SO~.

0,35

I

- - * - - CdTe

0.30

---*--- CdTe

S

0.6 0.4

g

S

,'

0.3 0.7 t

0.25

0.10

,'

/

2

.X

II i

.A"

I

[

I

4

5

6

i 1 . 2 + 0.1 ps

0.04

.,A"

.K~ o.ls

,/'

~,,

0.02

jeje -role-*

0.00

O.lO

".,¢2././

0.05

-0.02

~-e

~ = L4+ 0.2 ps

O

-0.04 o.oo

[

0.06

/

0.20

L e~ e',

I

0.08

t /

t-,

I

0.12

1,

0

I,

I

10

J

I

20

I

Heat Treatment

I

30

i Time

I

40

i

#

50

i

60

[mini

Fig. 1. Quantum dot size dispersion obtained with SAXS measurements in the Synchrotron Light Radiation Laboratory at LURE, France, as a function of the annealing time.

-I

0

1

2

3

T i m e D e l a y (ps)

Fig. 3. Ultrafast response of absorption against time delay between pump and probe pulses (symbol: measured, full lines: fittings) for CdTe QD doped glasses prepared as discussed in Ref. [22,23] with one heat treatment at 570°C.

L.C. Barbosaet al./ Journalof Non-CrystallineSolids219 (1997)205-211

208

Fig. 3 presents a typical pump-probe result showing the ultrafast time dependence of the absorption spectra for our recently grown CdTe samples. The differential transmission signal (DTS) is plotted against the time delay between pump and probe. The symbols are the measured data and the lines are fittings to obtain the recovery times. We obtained recovery times of order of 1 ps.

where tr is the surface tension (surface interface energy/area), gQD and gm are the Gibbs free energy per atom in the QD and in the matrix, VQt) is the volume of one atom in the QD and a is the lattice parameter of a zincblend crystal structure. The maximum of the free energy in Eq. (3) happens for qr

n= 6 4. Discussion

Several groups have studied the quantum dot growth kinetics and it is agreed that the process takes place in a supersaturated glass solid solution through homogeneous nucleation followed by a diffusion limited growth which ends in coalescence [29]. These processes are well studied [30-34]. In this paper we discuss in more detail the fundamental concepts in this field, which could give us some clear insights of the growth kinetics in our QD samples. In the first stage, the nucleation stage, the embryos grow from the ions (Cd 2+ and Te 2-) embedded in the matrix in a series of steps of absorption/emission of one atom. There is an atom flux only between dots differing in the number of atoms by one atom. Let Z,(t) be the number of quantum dots per volume with n atoms in the time t and I, the rate of atoms transfer between the n-atoms QD to the (n + 1). The rate equation for the size distribution Z, is then

OZ. Ot" =I"

3(I,Z,)

1Z, i - I,Z,

On

(2)

To calculate I, we must examine the absorption/emission of atoms of an n-atoms QD. The Gibbs free energy variation to capture one atom has to take into account the work done by the surface tension to increase the area of the QD, and the change in energy between the isolated atom and the same atom inside the QD crystal. This change in the free energy can be written as AG = 4-rrR2cr - ~-wR43 gQD -- gm

vQo 9,tr) t/3

= --~

o-aZn2/3--(gQD--gm)n,

(3)

oa 2

gQD

gm

(4)

However, the change in the free energy is not independent of the QD size, because the equilibrium concentration of the crystal and dispersed atoms depend on the radius of the QD [33]. Following the Gibbs-Thomson relation,

gQD--gm =go+kBTln[NeNq-~n('~)) 1,

(5)

where go is a constant, T is the temperature and Neq(n) is the equilibrium concentration of atoms in the matrix with a n-atoms dot. The equilibrium concentration as a function of the dot size is given by

exp

kBTn~/3

.

(6)

For small QDs where the N e q ( n ) > Nm, N m is the actual concentration, there is an atom flux outwards from the QD which tends to redissolve it. The opposite happens for the larger ones. The critical n is the one where NCq(nc) = Nm, and can be expressed in terms of the supersaturation degree A = ( N m N,)/N~ as

)3

nc =

kBT ln--O + A)

(7)

where N~ = Neq(~) exp( - go/kBT) is the equilibrium concentration with a R = oc QD. The supply of atoms to the QD, however, is not instantaneous, and depends on the diffusion of the elements in the matrix to feed the QD surface. This creates a concentration gradient around each QD. Assuming a stationary flux, the concentration at the

L C. Barbosa et al./Journal of Non-Crystalline Solids 219 (1997) 205-211

e-

.e

N

Rcl

R~2

Quantum Dot radius Fig. 4. The equilibrium concentration of the atoms dispersed in the matrix as a function of the QD radius for three different temperatures. N m is the actual concentration in the glass and R cr and Re2 are the critical radius for this concentration Nm at temperatures T I and T2, respectively.

distance r of the QD, N ( r ) , is given by N ( r ) = N m - [N m - N(r = R)](R/r) leading to a diffusion flux Ii,(R)--4wRD[Nm -N(R)], where D is the diffusion coefficient and R is the QD radius. If the diffusion time is longer than the time for the QD to enter in equilibrium with its surroundings the N ( r = R) above is just the equilibrium concentration given by Eq. (6) and can be used to show that On Ot

(6.rr2)E/3Da2nl/3

×

Nm - N, exp

kBTnl/3

.

(8)

Considering this equation together with the rate equation, Eq. (2), and taking into account that the Nm = N o - F m Z n, which establishes that the total number of atoms per volume in the matrix is N o and constant, we have a complete set of equations to study the growth dynamics of the QD's distribution evolution in time. Fig. 4 illustrates these discussions. For a given Nm the critical number increases with temperature and there is no QD formation at all if the concentration is below N, value for some temperatures. The total number of atoms in the matrix has to be constant, so the concentration N~ continuously de-

209

creases as the QDs grow, making the critical size increasingly larger. It is possible to suddenly change the temperature, from T~ to T 2, for example, making the critical radius instantaneously higher, as was done in the double annealing process [18]. There is also the possibility to change the temperature to a value where the N, is higher than Nm, from T2 to T~, for example. In this case all QDs will redissolve. A possible advantage of using this method comes from the fact that the smaller particles redissolve faster than the larger ones, which can be used to compress the particle size distribution. The following features can be intuitively taken out from the set of equations: first we notice that I,, has a positive slope for n < n~ and negative for n > n c. However, in the beginning, there is no QD, so Z, has a much stronger negative slope than the positive I,, slope, otherwise there is no QD embryo formation. This nucleation process tries to establish an equilibrium distribution where Zoq(n) = Nmexp(-AG/KT). This population falls down exponentially until the n c is reached, where it starts to grow indefinitely to infinite. This clearly means that the equilibrium situation will never happen. When the time evolves and the distribution starts to show a positive slope Z,,+~ >Z~ at the critical size, the growth process starts. If, in this phase, the amount of atoms taking from the matrix is much smaller than the initial concentration, the dots just grow in the diffusion only regimen and show a t ~/2 oc R growth law. When the concentration Nm in the matrix starts to decrease, the critical radius increases and the smaller particles tend to redissolve, feeding the larger ones with their atoms, which is the coalescence process. This stage shows a t 1/3 c t R growth law [35-37]. The Guinier radius, whose average weights more than the larger QDs, steadily increases with time indicating that QDs are always growing. The average radius shows a maximum and starts to decrease. The only way for the average radius to decrease while the larger QDs continue to grow is by the appearance of new small QDs. This would also increase the size dispersion as shown in Fig. 1. These results lead to the conclusion that nucleation and growth occur simultaneously. Efforts to avoid simultaneous nucleation and growth includes annealing at 460-490°C to produce

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L. C. Barbosa et al. / Journal of Non-Crystalline Solids 219 (1997) 205-211

a large number of nuclei, and the second step at 540-560°C, to only grow nuclei [22,23]. A series of samples which showed size dispersion with standard deviation of the order of 6% resulted [22,23]. It is clear from the growth kinetics discussion that this double annealing method suddenly increases the critical radius, by increasing the temperature. As a consequence the larger particles, close to the new critical radius, start to grow faster while the smaller particles tends to redissolve, breaking up the continuous distribution of sizes of the QDs. After this break up the total number of QDs remains the same and the quickly redissolving of the small nucleus provides atoms for the growth of the larger QDs. In this case the average radius can only grow with time which is consistent with our results. The simplest model to calculate the quantum confinement effects considers spherical particles with an infinitely high potential at the sphere surface, and independent electron and hole bands. This simple effective mass approximation model [1] is the most used quantum confinement model. Nonetheless this model does not explain all the quantum confined transitions observed. To obtain all the observed transitions we considered a more complete model taking in account the mixing of electron and hole bands [25], which we denoted k .p spherical model. This model is based on the Kane's k . p model and considers the complete Luttinger Hamiltonian. The total angular momentum F (the sum of the Bloch functions J and the envelope functions L angular momenta) is used as a basis for writing the k .p operator. On this basis the Hamiltonian is block diagonal with blocks defined by F = 1/2, 3 / 2 , 5 / 2 , . . . . By diagonalizing each blocks we obtain the quantum confined levels. The main differences introduced by the k - p spherical model are the mixing of the hole bands and a lowering of the electron levels which is due to nonparabolicities effects caused by the band mixing. The transition energies obtained from this model explain well all the observed transitions measured by photoluminescence excitation [25]. Raman scattering for CdTe nanocrystals clearly show confinement effects on the phonon spectra as a function of the quantum dot size. We observed the longitudinal optical (LO) phonon modes, surface phonons (SO) and some of their overtone combina-

tions. Surface phonon scattering intensity increases as the quantum dot size decreases. Confinement effects were observed by changing the laser excitation energy, and thus tuning to resonance with the optical transitions for quantum dots of different sizes within their broad size distribution in semiconductor doped glasses. These results can be explained by considering the difference in the dielectric functions of the CdTe nanocrystals and the surrounding glass matrix in the dielectric continuum model [24]. The absorption recovery time in the order of 1 ps for the new samples is longer than the first observed 300 fs recovery time of our first CdTe samples [26]. These different results may be explained in view of the fact that these new samples do not have the broad infrared luminescence band that the previous one had, because they are supposed to be trap .free samples [22,23]. The fact that the ultrafast time decays are greater means that the deep traps, associated with that luminescence, must have a predominant role in this decay process. Elimination of traps left samples with slower response times but in the ps range.

5. Conclusions Controlling growth temperatures and times leads to obtaining CdTe quantum dots in borosilicate glasses with a size dispersion of only 5%. These samples are almost surface trap free. The quantum confinement effects on the electron and phonon as a function of size are clearly seen. The electron quantum confinement is explained by a spherical k , p model and the pbonon confinement is well explained by a dielectric continuum model. The absorption recovery times depend mostly on the density of surface traps. For samples showing large amounts of surface traps the recovery time is as fast as 300 fs while, for an almost surface trap free sample, it remains in the 1-3 ps time scale.

Acknowledgements The authors acknowledge Conselho Nacional de Desenvolvimento Cientffico e Tecnol6gico (CNPq), Funda~o de Amparo ?a Pesquisa do Estado de S~o

L. C. Barbosa et al. / Journal of Non-Crystalline Solids 219 (1997) 205-211

Paulo (FAPESP), Programa de Apoio ao Desenvolvimento Cientffico e Tecnol6gico (PADCT) and Telocornunica~es Brasileiras S / A Telebras for financial support.

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