Semiconductor core-shell quantum dot: A low temperature nano-sensor material

Semiconductor core-shell quantum dot: A low temperature nano-sensor material Saikat Chattopadhyay, Pratima Sen, Joseph Thomas Andrews, and Pranay Kumar Sen Citation: J. Appl. Phys. 111, 034310 (2012); doi: 10.1063/1.3681309 View online: http://dx.doi.org/10.1063/1.3681309 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v111/i3 Published by the American Institute of Physics.

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JOURNAL OF APPLIED PHYSICS 111, 034310 (2012)

Semiconductor core-shell quantum dot: A low temperature nano-sensor material Saikat Chattopadhyay,1 Pratima Sen,1,a) Joseph Thomas Andrews,2 and Pranay Kumar Sen2 1

Laser Bhawan, School of Physics, Devi Ahilya University, Indore-452 017, India Department of Applied Physics, Shri G. S. Institute of Technology and Science, Indore-452003, India

2

(Received 2 August 2011; accepted 7 January 2012; published online 9 February 2012) This paper presents an analytical study of temperature dependent photoluminescence (PL) in coreshell quantum dots (CSQDs) made of most frequently used II-VI semiconducting materials. The analysis incorporates the temperature dependent radiative recombination processes in the calculation of the integrated PL intensity. The PL intensity has been derived using semiclassical density matrix formalism for the CSQDs exhibiting excitonic and biexcitonic features. The numerical estimates show that the PL intensity response and PL peak shifts are non-trivial at low temperature in such C 2012 American Institute of CSQDs and can be useful in the design of a temperature sensor. V Physics. [doi:10.1063/1.3681309] I. INTRODUCTION

Temperature is a significant fundamental thermodynamical property of matter and is required to be measured and controlled in scientific experiments as well as for industrial purpose. Luminescence thermometry is a versatile non-contact optical technique for the measurement of temperature and can overcome many of the problems and limitations of the conventional temperature measurement methods. The luminescence temperature measurement technique exploits the temperature dependent changes in the luminescence properties such as the decay lifetime of the fluorescence, the excitation spectra, and the wavelength or the energy of the fluorescence. Different luminescent materials and compounds are used as optical temperature probes including organic dyes, inorganic phosphors, and luminescent coordination complexes. Conventional phosphors with micron size grains are likely to be replaced by nanophosphors that are envisaged as potential candidate materials with much less scattering in accordance with Rayleigh’s criterion. Moreover, such nanophosphors enhance emitted light such that the detection becomes much easier and the nanoparticles have better quantum efficiency due to its confinement effect. Therefore, it is possible to design and fabricate more sensitive temperature sensors using nanoparticles.1–4 The concept of nanoparticle luminescent thermometry using semiconductor quantum dots (QDs) for a wide range of applications in low temperature environments is well known. Walker et al.2 reported the steady-state photoluminescence (PL) properties of CdSe quantum dots (QDs) for the temperature range from 100 to 315 K. Depending on PL peak shift, they have proposed that the CdSe QDs may be used as temperature indicators for temperature-sensitive coatings. Wang et al.1 analyzed the temperature response of several pure and doped semiconductor nanoparticles for the temperature ranging from room temperature to 423 K and found a linear response above the room temperature, which can be conveniently applied for temperature sensing. Ratiometric fluorescence of nanoparticles a)

Electronic mail: [email protected].

0021-8979/2012/111(3)/034310/8/$30.00

was studied by Peng et al.5 using alkoxysilanized dye as a reference and found the ratiometric fluorescence of the nanoparticles as extremely temperature sensitive near room temperature and can be suitably exploited in development of temperature nano-sensors in cellular sensing, and imaging. Very recently, a number of workers6–8 have proposed that the nanoparticles or semiconductor QDs could be used in luminescence thermometry to develop temperature sensors for various applications including medical and industrial purposes depending on their steady state photoluminescence properties. The luminescence properties of a bare semiconductor QD can be modified by using appropriate shell of an organic or inorganic material on it. In general, deposition of shell causes red-shift in PL peak and improve the PL quantum efficiency due to the proper passivation of surface dangling bonds and nonradiative recombination sites with strong confinement of electrons and holes inside the core.9 In our opinion, the thermal response of the core and shell material together will decide the temperature sensitivity of the core-shell quantum dot (CSQD). The basic requirements needed to determine the PL intensity are (i) the excitation mechanism that can generate population in various excited states of the system and (ii) radiative as well as nonradiative recombination processes that can yield the PL intensity. Furthermore, from device making point of view, it is necessary to examine the temperature sensitivity of PL intensity in different materials. In view of this discussion, we have theoretically investigated the effect of temperature on the PL intensity of different CSQDs by taking into account the temperature dependence of energy levels, dephasing mechanisms, and exciton-phonon interaction. II. THEORETICAL FORMULATIONS

The temperature dependence of PL can be used to determine the information about energy level structure in semiconductors. In CSQDs, discrete exciton and biexciton energy states exist. The energies of these states depend on the quantum dot size as well as the band offset between the core and the shell materials. The distinct exciton and biexciton peaks

111, 034310-1

C 2012 American Institute of Physics V

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in the PL spectra can be observed only at temperatures where the binding energies of excitons/biexcitons are larger than the thermal energy. The changes in the PL peak energy and spectral-width are governed by thermally stimulated transfer processes, confining potentials, exciton/biexciton energies etc. At high temperatures where the thermal energy exceeds the exciton/biexciton binding energy, the independent charge carriers play an important role. Dawson et al.10 have shown that at elevated temperature the carrier dynamics is dominated by independent carrier relaxation. In the present theoretical formulation we have restricted ourselves to low temperatures where exciton-phonon relaxation mechanism as well as direct radiative recombination process contribute to the photoluminescence. However, we have neglected the contribution of defect states on PL intensity. The PL intensity in II–VI semiconductor quantum dots is reported to be polarization sensitive,11 and the emission intensity is proportional to the product of the probability of occupation of the excited state and the probability of empty ground state. The decay of the excited state could arise due to radiative as well as nonradiative decay mechanisms. Consequently, knowledge of initial population generated in the excited state due to photoexcitation as well as the decay processes involved are of basic importance in the calculation of PL intensity. Irrespective of the decay mechanism, the integrated PL intensity is reported to be express as12 IðTÞ ¼

I0 ; 1 þ aexpðET =kTÞ

(1)

where a and ET are the process rate parameter and activation energy, respectively. The expression for the integrated PL intensity in CSQD was given by13 IPL ðTÞ ¼

N0 s 1 þ rad eðEa =kTÞ sa

þ

srad ; sesc

(2)

with sa, srad, and sesc being the fitting parameter, radiative as well as the thermal escape rate and N0 is the initial carrier population density that can be derived from the generation rate. We assume that the radiative recombination and thermal escape rates are inversely proportional to the inhomogeneous broadening (Cinh ) and the broadening arising due to excitonacoustic phonon (cph ), exciton-LO phonon coupling (CLO ). Equations (1) and (2) have been obtained using the classical rate equations. In the present paper, we have used semiclassical treatment in which quasi-particles-like electrons, holes, excitons etc. are treated quantum mechanically while the excitation caused by the electromagnetic radiation is treated classically as waves. We have calculated the initial population by using the density matrix analysis. The activation energies used in the above Eqs. (1) and (2) correspond to the energies of the exciton and biexciton states. Accordingly, we have obtained the energies of the exciton and biexciton states in Sec. II A. In order to determine PL intensity, in Sec. II B we have taken into account the excitation of the QD by the electromagnetic radiation via the dipole type of radiation-matter interaction to obtain the population density in the excitonic/biexcitonic states. The recombination proc-

esses taking part in the deexcitation mechanism are considered in Sec. II C. Our ultimate objective to demonstrate analytically the possibility of making a low temperature nano-sensor is examined in Sec. III where we have also carried out the numerical analysis based on the theoretical formulation for three different types of CSQDs. A. Exciton and biexciton binding energies

We consider a type-I spherical core shell quantum dot with the bandgap energy of the core material being smaller than that of the shell material. The geometry and the dimensions of the dot is illustrated in Fig. 1. Here, a is the radius of the core and b is the radius of the CSQD as a whole such that the annular shell thickness is d ¼ (b - a). The two-dimensional electron and hole confinement potentials are given by14 Ve; h ðrÞ ¼

Vc; v 2 ðr  a2 Þ; a2

(3)

~ r being the quasi-particle position satisfying the condition a < r < b. The subscripts e, h, c, and v denote the electron, hole, conduction band, and valence band, respectively. Vc and Vv are the conduction and valence band offsets between the core and the shell. The quasi-particles in the CSQD experience strong confinement within the core due to the presence of the peripheral shell. The buffer layer further confines the electrons and holes within the shell. Hence, the particles inside the core experience a double confinement like structure. The single particle wave functions under such situation can be described using WKB approximation as14,15  ð a  8 > S > pAffiffiffiffi exp j dr for b < r < a; > j > jj > b >   > ð < a A p for a < r < a; kj dr þ /j ðrÞ ¼ pCffiffiffiffi sin 4 k > j a > >   ð > b > > S > : pAffiffiffiffi exp  jj dr for a < r < b; jj

a

(4)

FIG. 1. Schematic diagram of a core-shell quantum dot (CSQD) and dimensions as assumed in present calculation.

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with jj ¼ ikj and j ¼ e, h. AC and AS are the normalization constants for core and shell region, respectively, and sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi mVe; h ðr2  a2 Þ : kj ¼ h2 a2

hx0bx ¼ 2hx0ex  jDbx j:

(10b)

2

(5)

For a bare quantum dot, we restrict the value of the running parameter r in the range a < r < a while the contribution of shell is obtained by assigning appropriate values to the running parameter r as b < r < -a and a < r < b in the forthcoming calculations. Apart from this, the change in the physical parameters regarding energy and effective mass of electron has been incorporated in the core and shell region. The WKB wave functions defined by Eq. (4) are the single particle envelope functions. Under effective mass approximation, the total wave functions we and wh can be written as the product of the envelope function and the Bloch function (ue, uh) and given by we ða; b; re Þ ¼ /e ða; bÞ  ue ðre Þ

and

aT The term ðTþbÞ has its origin in the temperature sensitive bandgap of semiconductors and is usually given by the Varshni formula. A more appropriate form of it has been suggested by Vin˜a et al.,17,18 and all the forms show good agreement within the temperature range 15 K–300 K.19 It is worthy to mention that we have taken due care to choose the appropriate bandgap energies and Varshni parameters for both the core (re < a) and the shell (a < re < b). Dex and Dbx are the binding energies of exciton and biexciton, respectively, in a CSQD and expressed as14,20,21     e2   Dex ða; bÞ ¼ wX ða; b; re ; rh Þ  Ve þ w ða; b; re ; rh Þ 0 r  X     e2  ða; b; r ; r Þ w þ wX ða; b; re ; rh Þ  Vh þ e h  r  X

0

(11a)

(6) and

and wh ða; b; rh Þ ¼ /h ða; bÞ  uh ðrh Þ:

(7)

Here, ~ r e and ~ r h represent the position vectors of electron and hole, respectively. The interaction of near-resonant electromagnetic radiation with the QDs generates photo-induced bound one electron-hole (e-h) pairs known as excitons. In QDs, the e-h pair formation is influenced by the confinement potential in addition to the Coulombic term. Within Hartree approximation,16 the exchange ground state wave function (wX ) can be written as wX ða; b; re ; rh Þ ¼ /e ða; bÞ:ue ðre Þ  /h ða; bÞ:uh ðrh Þ:

(8)

When inter-exciton separation approaches bulk exciton Bohr radius aB, the Coulombic interaction forces existing between these excitons lead to the creation of bound two electronhole pairs well known as biexcitons similar to the case of formation of H2-molecule. Hence, the description of the interaction of radiation with such small QD system requires a three-level ladder system comprising of ground j0i, exciton jexi and biexciton jbxi states. Accordingly, we define the unperturbed Hamiltonian as 2 3 0 x0 0 (9) 0 5; H0 ¼ h4 0 xex 0 0 xbx where  hxi is the ground state energy of the ith state with the subscript i (¼ 0, ex and bx) corresponding to the ground, exciton, and biexciton states, respectively. The transition energies corresponding to these levels are temperature sensitive and given by17 hx0ex ¼   hðxex  x0 Þ ¼ hxg 

aT 2  jDex j ðT þ bÞ

(10a)

    e2  ða; b; r ; r Þ Dbx ða; bÞ ¼ we ða; b; re ; rh Þ  Ve þ w e h 0 r  e      e2    wh ða; b; re ; rh Þ  Vh þ w ða; b; re ; rh Þ 0 r  h     e2   w ða; b; re ; rh Þ þ we ða; b; re ; rh Þ  Vh þ 0 r  e       e2  ða; b; r ; r Þ :  wh ða; b; re ; rh Þ  Ve þ w e h r  h 0

(11b) In writing the above equations, we have taken into account the temperature influenced bandgap shrinkage in semiconductors by incorporating the Varshni contributions.17 In CSQD, band offset plays an important role in the confinement of the carriers within the core or shell materials. The temperature dependent bandgap shrinkage can also affect the band offsets and due consideration has been given to it in the present analysis. In the interaction picture, the interactions of both excitons and biexcitons with radiation are taken to be of dipole type such that the interaction Hamiltonian HI can be written as22 2 3 0 l^0ex  E 0 6 7 (12) HI ¼ 4 l^ex0  E 0 l^exbx  E 5: 0

l^bxex  E

0

^ ij (i, j ¼ 0, ex, bx) is the element of the transition Here, l dipole moment matrix operator and E [¼ E0exp (ixt)] is the excitation electromagnetic field with amplitude E0 and frequency x and it is taken to be parallel to the transition dipole ^ ij . The transition dipole moment operamoment operators l tors corresponding to the transitions between the exciton * ground states (l0ex) and biexciton * exciton states (lexbx) are defined as22,23

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Chattopadhyay et al.

^ 0ex ða; bÞ ¼ l

J. Appl. Phys. 111, 034310 (2012)

epcv j/ ða; bÞ  /h ða; bÞj; m0 x0ex e

(13a)

1 epcv j/ ða; bÞ  /h ða; bÞj3 : 2 m0 xexbx e

(13b)

and ^ exbx ða; bÞ ¼  l

Here, pcv is the interband transition momentum matrix element and is defined as24 ffi vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

 u m0 u 1 u3 me : jpct j ¼ u m0  (14) t2 2 1 þ hxg

hxg þ Dso

Here, m0 is free electron mass, me is the effective mass of electron, and Dso is the spin-orbit splitting energy for the core and shell materials of the CSQD under consideration, and  hxg is the bandgap energy. B. Population density in excitonic and biexcitonic states

Equation (15) has been solved using time dependent perturbation technique to obtain the density matrix elements of various orders. For the present formulation, we need to know the zeroth and second-order components q(0) and q2. The first order density matrix q1 does not play any role in the estimation of the PL emission intensity and are not considered henceforth. Standard mathematical procedure yields26 2 3 A 0 B (18) qð2Þ ¼ 4 0 C 0 5: D 0 F Here, ! 4X20ex 1 1 A¼ ðq000  q0ee Þ; þ (19a) x Dþ0e D 0e   4X0ex Xexbx ðq0ee  q0bb Þ ðq000  q0ee Þ B¼ þ ; (19b) x Dþ Dþ 0b 0e     1 1 1 Ax þ 4 þ þ  ðq0ee  q0bb Þ X2exbx ; C¼ x  2iCðTÞ Deb Deb (19c)

The excitation source generates the population in the exciton and biexciton states. As discussed earlier, we have considered dipole type radiation-matter interaction. With H0 and HI being the ground state and interaction Hamiltonians, the equation of motion of the density matrix q can be written as25   @q i hq_ ¼ ½ðHo þ HI Þ; q þ ih ; (15) @t relax where @q @t relax ¼ CðTÞq (T) being the temperature dependent relaxation parameter that depends on the recombination processes. We have focused our attention to the radiative and non-radiative recombination processes. The latter being dependent on the exciton-phonon interaction. Also, q is defined using a generalized 3  3 density matrix as 2 3 q00 q0e q0b (16) q ¼ 4 qe0 qee qeb 5: qb0 qbe qbb

D¼

4X0ex Xexbx x



ðq000

q0ee Þ

 Dþ 0b

þ

ðq0ee

q0bb Þ

 Dþ eb

 ;

(19d)

and F¼

Ax : x  2iCðTÞ

(19e)

6 In the above equations, D6 0e ¼ x6x0ex þ iCðTÞ, Deb ¼ x 6 6xexbx þ iCðTÞ, D0b ¼ x62x0ex  Dbx þ iCðTÞ, and Xij ¼ lij E0 =2h is the Rabi frequency. In Eq. (18), the parameters A, C, and F represent the excitation intensity dependent populations in ground, exciton, and biexciton states, respectively. The occupation in the exciton level is caused by the photoinduced transition of electrons from ground state to the exciton state and relaxation of the population from the biexcitonic state to excitonic state. The former contribution is represented by the term proð0Þ portional to ðq00  qð0Þ ee Þ and the latter is represented by the ð0Þ

The diagonal elements represent the population in the ground ðq00 Þ, exciton ðqee Þ, and biexciton ðqbb Þ states while the off-diagonal elements represent the elements that undergo transitions among the states represented by their subscripts. At finite temperature T, the initial state population q(0) for ground, exciton and biexciton state are given by ð0Þ

ð0Þ

q00 ¼ 1  qð0Þ ee  qbb ;   hjDex j ð0Þ qee ¼ exp ; kB T

(17a) (17b)

and ð0Þ

qbb ¼ exp



 hðjDex j þ jDbx jÞ : kB T

(17c)

term ðqð0Þ ee  qbb Þ in Eq. (19c). In general, at room temperað0Þ

ture, ðqð0Þ ee  qbb Þ is negligibly small and one may neglect the contribution of the corresponding terms. These terms maximize and give rise to PL peak intensity at resonance with the exciton and biexcitonic transitions frequencies, respectively. The broadening of the peak is determined by CðTÞ that depends on various recombination processes. C. Radiative and nonradiative recombination processes

In the present calculations, we have incorporated the losses occurring due to radiative and nonradiative decay processes. Chen et al.27 have considered the thermal broadening of the exciton peak through the exciton-phonon interaction. The temperature dependent full width at half maximum (FWHM) was taken as

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C ¼ Cinh þ cph T þ h

J. Appl. Phys. 111, 034310 (2012)

exp



CLO 

hxLO kB T

i; 1

(20)

where, Cinh , cph , CLO , hxLO , and kB T are the inhomogeneous peak width at zero temperature, the exciton-acoustic phonon coupling strength, exciton-longitudinal optical (LO) phonon coupling strength, the LO phonon energy, and thermal energy, respectively. We have taken Cinh as temperature independent but depends on the radiative recombination process. Due to the strong overlapping of electron and hole wave functions, the radiative recombination rate in quantum dot is modified via an overlap integral parameter K and given by11 s1 rad  Cinh ¼

4e2 xn hpcv i2 K 2 : 3m20 c3 h

(21)

for the medium with background material refractive index n. For the present case K ¼ /e ða; bÞ:/h ða; bÞ. The electronphonon interaction in semiconductor nano-crystal has been addressed by Takagahara,28 where he has shown that the coupling constant cph is size dependent and is controlled not only by the electron-phonon interaction but also by exciton wave function. Valerini et al.13 have also mentioned about the enhancement in the exciton-acoustic phonon coupling constant with reduced dimensionality of the nano-crystal. They have also studied the role of different nonradiative processes in CdSe/ZnSe QDs. It has been reported that the acoustic phonon contributes significantly at low temperature.27 The values of the relevant material parameters are given in Table I. III. RESULTS AND DISCUSSION

The PL intensity IPL arises due to the radiative decay from the exciton state and is proportional to the vacancy in the ground state and the occupation in excitonic state. The usage of Eqs. (19a) and (19c) along with the mathematical definition that the net population can be expressed in terms of the product of the form C(1-A) yields     4 1 1 ð0Þ X20ex þ þ  q00  qð0Þ IPL ¼ g ee x  2iCðTÞ D0e D0e  

  1 1 ð0Þ 2 qð0Þ þ ee  qbb Xexbx þ þ  Deb Deb    

4X20ex 1 1 0 0 (22) þ  q00  qee ;  1 x D0e Dþ 0e

where g is a constant. Since the transition energies are temperature sensitive as is evident from Eq. (10a), one can expect its influence on both the PL emission intensity and the PL peak shift. The transition energies can be modified in a CSQD by changing the shell width.14 Since the recombination processes are temperature dependent, one can expect a change in the FWHM of the PL peak with increasing temperature. These interpretations suggest that a temperature probe using a semiconductor core-shell quantum dot can be designed by calibrating the change in the PL intensity and the PL peak energy shift with respect to the ambient temperature. We have examined these features in five different types of bare and core-shell quantum dots made of II-VI semiconductor crystals. A. PL intensity as a measure of temperature

From Eqs. (10), one can notice that the PL intensity varies with temperature due to the temperature dependence of exciton/biexciton energies and recombination times. Equations (21) and (22) further suggest that the PL sensitivity in the quantum dots depends upon both the dot size and the temperature T through the different parameters like CðTÞ, Dex , Dbx etc. Lubyshev et al.29 and Xu et al.30 have shown that the thermal quenching of PL in QDs can be attributed to the thermal activation of charge carrier from the confined well to the barrier. The confinement potential in a CSQD depends on the band offset parameter that is further dependent on the bandgap of the core and the shell materials. Accordingly, we have calculated the temperature dependent PL intensity in two bare QDs viz. CdSe and ZnSe as well as in CdSe/ZnSe, CdSe/ZnS, and ZnSe/ZnS CSQDs. The excitation photon energy in each case is chosen to be temperature independent exciton resonance frequency. Figure 2 illustrates the temperature variation of the photoluminescence intensity of bare CdSe and ZnSe QDs of radius a ¼ 2.0 nm. The figure shows that ZnSe QDs, which have a larger bandgap and smaller exciton Bohr radius

TABLE I. Bandgap and Varshni parameters of the selected II–VI semiconductor materials (Ref. 19). Materials CdSe ZnSe ZnS

Bandgap (eV)

a (104 eV/K)

b (K)

1.766 2.8071 3.8652

6.96 5.58 10

281 187 600

a b

(106 eV/K2) 2.48 2.98 1.67

FIG. 2. (Color online) Temperature dependent photoluminescence intensity for bare CdSe and ZnSe quantum dots of radius a ¼ 2.0 nm under low temperature regime (5 K–78 K).

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FIG. 3. (Color online) Temperature dependent photoluminescence intensity for two core shell quantum dots having same core material (CdSe) with core radius, a ¼ 2.0 nm and different shell materials (i.e., ZnS and ZnSe) with same shell thickness, d ¼ 0.2 nm. CdSe bare quantum dot photoluminescence intensity variation with temperature is also plotted here to understand the effect of shell on a bare quantum dot at low temperature.

compared to CdSe QD, yield better PL intensity variations as compared to CdSe QDs. The temperature sensitivity of PL intensity was found to saturate above 100 K while the PL intensity decreases linearly with the lowering of the temperature below 50 K in ZnSe QDs. The improved temperature sensitivity of ZnSe QDs can be assigned to the larger value of (a/b) in this system as compared to that of CdSe (Table I). In order to examine the role of temperature sensitivity of the shell, we have obtained PL intensity of CSQDs having the same core with two different shell materials. Figure 3 demonstrates the temperature dependence of PL intensity of CdSe/ZnS and CdSe/ZnSe CSQDs as well as that of a bare CdSe QD. It is clear from the figure that coating CdSe QD with a shell made up of a semiconductor material with larger bandgap results in an increase in the PL intensity. However, coating CdSe with ZnSe exhibits sharp fall with increasing temperature below 30 K while the temperature variation is not very sharp if the CdSe QD is coated with ZnS shell. Thus a low temperature probe of CdSe/ZnSe CSQD appears to be more potential than a CdSe/ZnS CSQD probe. From the figure, it can be further seen that at temperature above 40 K, the PL intensity variations are small in both CSQDs. We define relative temperature dependent parameters arel(¼ ashell/acore) and brel(¼ bshell/bcore). From Table II, one can notice that (arel/brel) is larger in a CdSe/ZnSe CSQD as compared to that in CdSe/ZnS CSQD. This larger (arel/brel) value is TABLE II. Band offset values and effective Varshni parameters for selected II–VI core-shell quantum dots.

Materials

VBO CBO aðshellÞ bðshellÞ b ¼ a ¼ (eV) (eV) rel aðcoreÞ rel bðcoreÞ

CdSe/ZnSe (Ref. 31) 0.23 CdSe/ZnS (Ref. 32) 0.6 ZnSe/ZnS (Ref. 33) 0.58

0.75 1.44 0.03

0.802 1.437 1.792

0.666 2.135 3.209

arel brel

1

(10 )

12.04 6.73 5.58

FIG. 4. (Color online) Temperature dependent photoluminescence intensity variation at low temperature (5 K–78 K) in CdSe/ZnS, ZnSe/ZnS, and ZnSe.

responsible for larger temperature sensitivity of the CdSe/ ZnSe CSQDs. To examine the contribution of temperature sensitivity of core, we have obtained PL intensity of CSQDs having same shell with different core materials. In Fig. 4, the PL intensity variation as a function of temperature has been plotted for CdSe/ZnS, ZnSe/ZnS, and ZnSe QDs. We changed the core material keeping the shell to be the same as ZnS to examine the explicit PL response in the core material at low temperature. The figure reveals that the sensitivity of CdSe/ ZnS CSQDs is better. The reason for this can again be attributed to (arel/brel) ratio as is evident from Table II. B. PL peak shift as a measure of temperature

Most of the available literatures show that the excitation sources selected for experimental study of PL spectra in II-VI semiconductor QDs are Ti:sapphire laser or Arþ laser. We consider the excitation of the QDs by using a Ti:sapphire laser. The PL spectra for all the five samples (two bare and three core-shell QDs) are plotted in Fig. 5. The inset in the figures have been plotted for the bare QDs. It is found that the PL intensity in CSQDs can be increased by nearly an order of magnitude through the proper choice of the shell material. This finding establishes the utility of a shell on the core of the QDs. The figures also exhibit red shifts in the PL peaks with increasing temperature. The redshift has been calculated and found to be around 1013 s-1 for the temperature range 10 K-75 K. Both Valerini et al.13 and Walker et al.2 have experimentally observed the redshift in PL peak with increasing temperature. Walker et al.2 suggested that significant temperature dependence of luminescence combined with its insensitivity to oxygen quenching establishes CdSe/ ZnS QDs as optical temperature indicator. On the basis of the theoretical analysis made in the present paper, we find that the temperature probe using CSQD can be made by calibrating the probe via PL intensity variations as a function of temperature. Although the analysis made in the present paper have been carried out for a single quantum dot, in practice

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interaction based relaxation times for calculating the PL intensity. It is observed that an increase in temperature leads to redshift of the PL peak. Also the PL intensity decreases with increasing temperature. The numerical analysis has been made for CdSe and ZnSe bare quantum dots as well as CdSe/ZnS, CdSe/ZnSe, and ZnSe/ZnS CSQDs. It is found that the presence of a shell improves the PL intensity. Also the matching of core and shell materials is important for making a nano-sensor. After examining the effect of temperature sensitivities of core (CdSe/ZnS, ZnSe/ZnS) and shell materials (CdSe/ZnSe, CdSe/ZnS) on the temperature dependent PL intensity, we observe that the ratio of the relative parameters defined in terms of (arel/brel) plays a significant role in the selection of the core/shell materials for making a low temperature nanosensor using a core-shell II-VI semiconductor quantum dot. ACKNOWLEDGMENTS

The financial support received from the Department of Science and Technology (DST), New Delhi, India is gratefully acknowledged by the authors. 1

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FIG. 5. (Color online) Temperature dependent PL spectra for three different CSQDs (i) CdSe/ZnSe CDQS and CdSe bare QD (inset), (ii) CdSe/ZnS CSQD and CdSe bare QD (inset), (iii) ZnSe/ZnS CSQD and ZnSe bare QD (inset).

one comes across an ensemble of quantum dots that can be restricted to about 5% during their growth using latest techniques in nano-technology. Consequently, the effect of size variation may be neglected without sacrificing the qualitative accuracy of the result. In conclusion, we have examined the possibility of using II-VI semiconductor quantum dots as low temperature nanosensor. The expression for the PL intensity has been obtained using density matrix formalism. We have incorporated the temperature variations in the bandgap and the exciton-phonon

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