Semiconductor core-shell quantum dot: A low temperature nano-sensormaterialSaikat 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. Related ArticlesThe resolution estimation of wedge and strip anodes Rev. Sci. Instrum. 83, 093107 (2012) Recovery improvement of graphene-based gas sensors functionalized with nanoscale heterojunctions Appl. Phys. Lett. 101, 123504 (2012) High sensitivity SQUID-detection and feedback-cooling of an ultrasoft microcantilever Appl. Phys. Lett. 101, 123101 (2012) Evaluation of rare earth doped silica sub-micrometric spheres as optically controlled temperature sensors J. Appl. Phys. 112, 054702 (2012) A new method to calculate the beam charge for an integrating current transformer Rev. Sci. Instrum. 83, 093302 (2012) Additional information on J. Appl. Phys.Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors

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Semiconductor core-shell quantum dot: A low temperature nano-sensormaterial

Saikat Chattopadhyay,1 Pratima Sen,1,a) Joseph Thomas Andrews,2

and Pranay Kumar Sen2

1Laser Bhawan, School of Physics, Devi Ahilya University, Indore-452 017, India2Department of Applied Physics, Shri G. S. Institute of Technology and Science, Indore-452003, India

(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 core-

shell 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

CSQDs and can be useful in the design of a temperature sensor. VC 2012 American Institute ofPhysics. [doi:10.1063/1.3681309]

I. INTRODUCTION

Temperature is a significant fundamental thermodynami-

cal property of matter and is required to be measured and con-

trolled 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 conven-

tional 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 tem-

perature probes including organic dyes, inorganic phosphors,

and luminescent coordination complexes. Conventional phos-

phors with micron size grains are likely to be replaced by nano-

phosphors that are envisaged as potential candidate materials

with much less scattering in accordance with Rayleigh’s crite-

rion. Moreover, such nanophosphors enhance emitted light

such that the detection becomes much easier and the nanopar-

ticles 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 tempera-

ture range from 100 to 315 K. Depending on PL peak shift,

they have proposed that the CdSe QDs may be used as tempera-

ture 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

was studied by Peng et al.5 using alkoxysilanized dye as a

reference and found the ratiometric fluorescence of the nano-

particles as extremely temperature sensitive near room temper-

ature 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 lumines-

cence thermometry to develop temperature sensors for various

applications including medical and industrial purposes depend-

ing 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 ther-

mal 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) radi-

ative 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 discus-

sion, we have theoretically investigated the effect of tempera-

ture on the PL intensity of different CSQDs by taking into

account the temperature dependence of energy levels, dephas-

ing mechanisms, and exciton-phonon interaction.

II. THEORETICAL FORMULATIONS

The temperature dependence of PL can be used to deter-

mine the information about energy level structure in semi-

conductors. In CSQDs, discrete exciton and biexciton energy

states exist. The energies of these states depend on the quan-

tum dot size as well as the band offset between the core and

the shell materials. The distinct exciton and biexciton peaksa)Electronic mail: pratimasen@gmail.com.

0021-8979/2012/111(3)/034310/8/$30.00 VC 2012 American Institute of Physics111, 034310-1

JOURNAL OF APPLIED PHYSICS 111, 034310 (2012)

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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 domi-

nated by independent carrier relaxation. In the present theo-

retical 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 in-

tensity 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. Con-

sequently, 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

1þ aexpð�ET=kTÞ ; (1)

where a and ET are the process rate parameter and activation

energy, respectively. The expression for the integrated PL in-

tensity in CSQD was given by13

IPLðTÞ ¼N0

1þ srad

saeð�Ea=kTÞ 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 exciton-

acoustic phonon (cph), exciton-LO phonon coupling (CLO).

Equations (1) and (2) have been obtained using the clas-

sical rate equations. In the present paper, we have used semi-

classical 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 activa-

tion energies used in the above Eqs. (1) and (2) correspond

to the energies of the exciton and biexciton states. Accord-

ingly, we have obtained the energies of the exciton and biex-

citon 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 consid-

ered 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 nu-

merical 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 dimen-

sions 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

d¼ (b - a). The two-dimensional electron and hole confine-

ment potentials are given by14

Ve; hðrÞ ¼Vc; v

a2ðr2 � a2Þ; (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 expe-

rience 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 struc-

ture. The single particle wave functions under such situation

can be described using WKB approximation as14,15

/jðrÞ ¼

ASffiffiffiffijjp exp

� ð�a

�b

jjdr

�for �b < r < �a;

ACffiffiffiffikj

p sin

ða

�a

kjdr þ p4

� �for �a < r < a;

ASffiffiffiffijjp exp

��ðb

a

jjdr

�for a < r < b;

8>>>>>>><>>>>>>>:

(4)

FIG. 1. Schematic diagram of a core-shell quantum dot (CSQD) and dimen-

sions as assumed in present calculation.

034310-2 Chattopadhyay et al. J. Appl. Phys. 111, 034310 (2012)

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with jj¼ ikj and j¼ e, h. AC and AS are the normalization

constants for core and shell region, respectively, and

kj ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffimVe; hðr2 � a2Þ

�h2a2

s: (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 run-

ning parameter r as �b< r< -a and a< r< b in the forth-

coming 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 approxi-

mation, 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

weða; b; reÞ ¼ /eða; bÞ � ueðreÞ (6)

and

whða; b; rhÞ ¼ /hða; bÞ � uhðrhÞ: (7)

Here,~re and~rh represent the position vectors of electron and

hole, respectively.

The interaction of near-resonant electromagnetic radia-

tion 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 approxima-

tion,16 the exchange ground state wave function (wX) can be

written as

wXða; b; re; rhÞ ¼ /eða; bÞ:ueðreÞ � /hða; bÞ:uhðrhÞ: (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 electron-

hole 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

H0 ¼ �hx0 0 0

0 xex 0

0 0 xbx

24

35; (9)

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 sensi-

tive and given by17

�hx0ex ¼ �hðxex � x0Þ ¼ �hxg �aT2

ðT þ bÞ � jDexj (10a)

and

�hx0bx ¼ 2�hx0ex � jDbxj: (10b)

The term aT2

ðTþbÞ has its origin in the temperature sensitive

bandgap of semiconductors and is usually given by the Var-

shni formula. A more appropriate form of it has been sug-

gested by Vina 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, respec-

tively, in a CSQD and expressed as14,20,21

Dexða; bÞ ¼ wXða; b; re; rhÞ Veþe2

�0r

� ���������wXða; b; re; rhÞ

�

þ wXða; b; re; rhÞ Vhþe2

�0r

� ���������wXða; b; re; rhÞ

� (11a)

and

Dbxða; bÞ¼ weða; b; re; rhÞ Veþe2

�0r

� ���������weða; b; re; rhÞ

�

� whða; b; re; rhÞ Vhþe2

�0r

� ���������whða; b; re; rhÞ

�

þ weða; b; re; rhÞ Vhþe2

�0r

� ���������weða; b; re; rhÞ

�

� whða; b; re; rhÞ Veþe2

�0r

� ���������whða; b; re; rhÞ

� :

(11b)

In writing the above equations, we have taken into account

the temperature influenced bandgap shrinkage in semicon-

ductors by incorporating the Varshni contributions.17 In

CSQD, band offset plays an important role in the confine-

ment 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

HI ¼ �0 l0ex � E 0

lex0 � E� 0 lexbx � E�

0 lbxex � E 0

264

375: (12)

Here, lij (i, j¼ 0, ex, bx) is the element of the transition

dipole moment matrix operator and E [¼ E0exp (ixt)] is the

excitation electromagnetic field with amplitude E0 and fre-

quency x and it is taken to be parallel to the transition dipole

moment operators lij. The transition dipole moment opera-

tors corresponding to the transitions between the exciton *ground states (l0ex) and biexciton * exciton states (lexbx)

are defined as22,23

034310-3 Chattopadhyay et al. J. Appl. Phys. 111, 034310 (2012)

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l0exða; bÞ ¼ epcv

m0x0exj/�eða; bÞ � /hða; bÞj; (13a)

and

lexbxða; bÞ ¼ � 1

2

epcv

m0xexbxj/�eða; bÞ � /hða; bÞj3: (13b)

Here, pcv is the interband transition momentum matrix ele-

ment and is defined as24

jpctj ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3

2m0

m0

me� 1

�2

�hxgþ 1

�hxg þ Dso

� �vuuuut : (14)

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 biexcitonicstates

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

�i�h _q ¼ ½ðHo þ HIÞ; q� þ i�h@q@t

� �relax

; (15)

where @q@t

� relax¼ 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 de-

pendent on the exciton-phonon interaction. Also, q is defined

using a generalized 3� 3 density matrix as

q ¼q00 q0e q0b

qe0 qee qeb

qb0 qbe qbb

24

35: (16)

The diagonal elements represent the population in the ground

ðq00Þ, exciton ðqeeÞ, and biexciton ðqbbÞ 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

qð0Þ00 ¼ 1� qð0Þee � qð0Þbb ; (17a)

qð0Þee ¼ exp��hjDexj

kBT

� �; (17b)

and

qð0Þbb ¼ exp��hðjDexj þ jDbxjÞ

kBT

� �: (17c)

Equation (15) has been solved using time dependent pertur-

bation 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 consid-

ered henceforth. Standard mathematical procedure yields26

qð2Þ ¼A 0 B0 C 0

D 0 F

24

35: (18)

Here,

A ¼ 4X20ex

x1

Dþ0e

þ 1

D�0e

!ðq0

00 � q0eeÞ; (19a)

B ¼ 4X0exXexbx

x�ðq0

ee � q0bbÞ

Dþ0b

þ ðq000 � q0

eeÞDþ0e

� �; (19b)

C ¼ 1

x� 2iCðTÞ Axþ 41

Dþeb

þ 1

D�eb

� �ðq0

ee � q0bbÞX2

exbx

� �;

(19c)

D ¼ 4X0exXexbx

xðq0

00 � q0eeÞ

Dþ0b

þ ðq0ee � q0

bbÞDþeb

� �; (19d)

and

F ¼ �Axx� 2iCðTÞ : (19e)

In the above equations, D60e ¼ x6x0ex þ iCðTÞ, D6

eb ¼ x6xexbx þ iCðTÞ, D6

0b ¼ x62x0ex � Dbx þ iCðTÞ, and Xij

¼ lijE0=2�h is the Rabi frequency.

In Eq. (18), the parameters A, C, and F represent the ex-

citation 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 relaxa-

tion of the population from the biexcitonic state to excitonic

state. The former contribution is represented by the term pro-

portional to ðqð0Þ00 � qð0Þee Þ and the latter is represented by the

term ðqð0Þee � qð0Þbb Þ in Eq. (19c). In general, at room tempera-

ture, ðqð0Þee � qð0Þbb 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 recombinationprocesses

In the present calculations, we have incorporated the

losses occurring due to radiative and nonradiative decay proc-

esses. 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

034310-4 Chattopadhyay et al. J. Appl. Phys. 111, 034310 (2012)

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C ¼ Cinh þ cphT þ CLO

exp�hxLO

kBT

�� 1

h i ; (20)

where, Cinh, cph, CLO, �hxLO, and kBT 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 in-

dependent but depends on the radiative recombination pro-

cess. 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

s�1rad � Cinh ¼

4e2xn

3m20c3�hhpcvi2K2: (21)

for the medium with background material refractive index n.

For the present case K ¼ /�eða; bÞ:/hða; bÞ. The electron-

phonon 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 tempera-

ture.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

IPL ¼ g4

x� 2iCðTÞ X20ex

1

Dþ0e

þ 1

D�0e

� �qð0Þ00 � qð0Þee

��

þ 1

Dþeb

þ 1

D�eb

� �qð0Þee � qð0Þbb

�X2

exbx

�

� 1� 4X20ex

x1

Dþ0e

þ 1

D�0e

� �q0

00 � q0ee

� � �; (22)

where g is a constant. Since the transition energies are tem-

perature 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 recombina-

tion processes are temperature dependent, one can expect a

change in the FWHM of the PL peak with increasing temper-

ature. 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 temper-

ature. 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 sensitiv-

ity 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 exci-

tation photon energy in each case is chosen to be temperature

independent exciton resonance frequency.

Figure 2 illustrates the temperature variation of the pho-

toluminescence intensity of bare CdSe and ZnSe QDs of ra-

dius a¼ 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 semicon-

ductor materials (Ref. 19).

Materials Bandgap (eV) a (10�4 eV/K) b (K)ab

(10�6 eV/K2)

CdSe 1.766 6.96 281 2.48

ZnSe 2.8071 5.58 187 2.98

ZnS 3.8652 10 600 1.67

FIG. 2. (Color online) Temperature dependent photoluminescence intensity

for bare CdSe and ZnSe quantum dots of radius a¼ 2.0 nm under low tem-

perature regime (5 K–78 K).

034310-5 Chattopadhyay et al. J. Appl. Phys. 111, 034310 (2012)

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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 in-

tensity decreases linearly with the lowering of the tempera-

ture 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 fig-

ure, 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

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 in-

tensity variation as a function of temperature has been plot-

ted 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 attrib-

uted 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 cal-

culated 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 signifi-

cant 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 cali-

brating 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

FIG. 3. (Color online) Temperature dependent photoluminescence intensity

for two core shell quantum dots having same core material (CdSe) with core

radius, a¼ 2.0 nm and different shell materials (i.e., ZnS and ZnSe) with

same shell thickness, d¼ 0.2 nm. CdSe bare quantum dot photolumines-

cence intensity variation with temperature is also plotted here to understand

the effect of shell on a bare quantum dot at low temperature.

FIG. 4. (Color online) Temperature dependent photoluminescence intensity

variation at low temperature (5 K–78 K) in CdSe/ZnS, ZnSe/ZnS, and ZnSe.

TABLE II. Band offset values and effective Varshni parameters for selected

II–VI core-shell quantum dots.

Materials

VBO

(eV)

CBO

(eV)arel ¼ aðshellÞ

aðcoreÞ brel ¼bðshellÞbðcoreÞ

arel

brel

(10�1

)

CdSe/ZnSe (Ref. 31) 0.23 0.75 0.802 0.666 12.04

CdSe/ZnS (Ref. 32) 0.6 1.44 1.437 2.135 6.73

ZnSe/ZnS (Ref. 33) 0.58 0.03 1.792 3.209 5.58

034310-6 Chattopadhyay et al. J. Appl. Phys. 111, 034310 (2012)

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one comes across an ensemble of quantum dots that can be

restricted to about 5% during their growth using latest tech-

niques 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 nano-

sensor. 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

interaction based relaxation times for calculating the PL in-

tensity. 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 nano-

sensor 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 grate-

fully acknowledged by the authors.

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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).

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