Enhancement of thermopower of Mn doped ZnO thin film

ARTICLE IN PRESS

Physica B 399 (2007) 38–46 www.elsevier.com/locate/physb

Enhancement of thermopower of Mn doped ZnO thin film C.K. Ghosh, S. Das, K.K. Chattopadhyay Thin Film and Nano-Science Laboratory, Department of Physics, Jadavpur University, Kolkata 700032, India Received 18 October 2006; received in revised form 24 January 2007; accepted 16 May 2007

Abstract We have studied the thermopower of Mn doped ZnO thin films experimentally for various Mn concentrations in the films and a theoretical attempt was taken to gain an insight into the origin of the enhancement of thermopower due to unbalancing of up spin and down spin electrons in the conduction band due to unfilled d-orbital of Mn. Also hopping contribution caused by partially filled d-orbital of Mn was taken into account. r 2007 Published by Elsevier B.V. PACS: 73.16.Ga; 72.20.Pa Keywords: ZnO; Thermoelectric power; Mn doping; Theoretical modeling

1. Introduction ZnO is a technologically important material due to its wide range of optical and electrical properties such as wide band gap, large excitonic binding energy, controllable electrical conductivity etc. These characteristics have made ZnO films very important for a huge range of applications such as in solar cells [1], surface acoustic waves [2], gas sensors [3], pressure sensors [4], antireflecting coating [5], transducers [6], luminescent materials [7], transparent conductors [8], heat mirrors [9], etc. The quest for diluted magnetic semiconductors (DMS) has recently attracted materials scientists, as, such semiconductors are quasiindispensable in magneto- and spin electronics. This new field of semiconductor electronics controls and hence exploits the spin degree of freedom of the electron in addition to, or in place of, its charge for several applications. Researchers have traditionally diluted mostly conventional compound semiconductors with 3d transition metals (TM) to obtain DMS as a material for magnetoand spin electronics. The presence of TM ions in these materials leads to an exchange interaction between Corresponding author.

E-mail addresses: [email protected], [email protected] (K.K. Chattopadhyay). 0921-4526/$ - see front matter r 2007 Published by Elsevier B.V. doi:10.1016/j.physb.2007.05.019

itinerant sp-band electrons or holes and the d-electron spins localized at the magnetic ions, resulting in versatile magnetic-field induced functionalities. For this purpose, magnetic ions, such as Co2+, V2+, Mn2+, Cr2+, Fe2+, etc., should be substituted for some of the metallic atoms in the semiconductor lattice to produce a semiconductor that is ferromagnetic with a Curie temperature (TC) above room temperature. After the prediction of room temperature ferromagnetism in Mn-doped ZnO by Dietl et al. [10], magnetic properties of Mn-doped ZnO have been investigated by many authors. Experimental studies give quite controversial results regarding magnetic properties of Zn1xMnxO, like ferromagnetism [11,12], antiferromagnetic coupling [13] or paramagnetism [14]. On the other hand, the thermoelectric effects provide a mean by which thermal energy can be converted into electricity and by which electricity can be used for refrigeration. Also understanding of the physical reasons for the change in thermoelectric properties due to TM doping in ZnO thin films has fundamental importance. ZnO thin films have been prepared by many techniques like thermal evaporation [15], chemical vapor deposition [16,17], radio-frequency (RF) magnetron sputtering [18], spray pyrolysis [19], pulsed laser deposition [20], sol–gel– dip-coating [21], electro-deposition [22], etc. We have used direct current sputtering technique for the synthesis of ZnO

ARTICLE IN PRESS C.K. Ghosh et al. / Physica B 399 (2007) 38–46

thin films because of its simplicity and cost effectiveness. In this work we have studied the thermopower of Mn doped ZnO thin films experimentally for various Mn concentration in the films and a theoretical attempt was taken to gain an insight into the origin of the enhancement of thermopower due to unbalancing of spin up and spin down electron in the conduction band due to unfilled d-orbital and hopping contribution caused by unfilled d-orbital of Mn. 2. Experiment

39

radiation) measurements. Compositional analysis was performed by energy dispersive analysis of X-rays (EDX, JEOL JSM 6300 Oxford-7582). Electrical characterizations (thermo-electric) of the films were done by standard method from 300 to 450 K under vacuum condition (103 mbar). The thickness of the film was measured by cross-sectional scanning electron microscope (not shown here) and was found to be 700 nm. 3. Results and discussions

2.1. Target preparation

3.1. Structural property

2.2. Film deposition The sputtering system consists of a conventional vacuum system, which was evacuated to 106 mbar by a rotary and diffusion pump arrangement. ZnO thin films were deposited on corning glass substrates. Argon was used as a sputtering gas. To remove surface contamination, if any, each target was pre-sputtered for 10 min. After that, the shutter was removed to expose the substrate in the sputtering plasma. Before placing into the sputtering chamber, the glass substrates were at first cleaned by mild soap solution, then washed thoroughly in deionized water and also in boiling water. Finally, they were ultrasonically cleaned in acetone for 15 min. The summary of deposition conditions is shown in Table 1. Therefore the films were deposited on glass substrates under the same sputtering condition with only change in Mn content in the target. 2.3. Characterization The deposited films were characterized by X-ray diffraction (XRD, BRUKER D8 ADVANCE, by CuKa

Fig. 1 shows the XRD pattern of Mn doped ZnO thin films. All the three peaks (1 0 0), (1 0 1), (1 1 0) originate from hexagonal ZnO [23]. Similar pattern was observed by Roy et al. [24]. Also no peaks corresponding to doping materials, e.g., of Mn or its oxides were found in the pattern. This conclusively indicates that Mn2+ is present in the film as dopant. EDX spectrum for a 5% Mn doped ZnO sample is shown in Fig. 2. Compositional analysis clearly confirmed that Mn was present in the film and concentrations were very close to that of the nominal composition of the target material. Mn concentrations in the target material and in the film, obtained from EDX are listed in Table 2. Fig. 3 shows Mn2+ content dependence of the lattice constant of the deposited ZnO film as obtained from XRD data. Both the a- and c-axes lengths expand monotonously with Mn2+ content. Increments of lattice constants are due to larger ionic radius of Mn2+ (0.66 A) than Zn2+ (0.60 A) [25]. The modified lattice constant may be calculated upto a first-order approximation by Vegard’s

(d)

intensity (arb.units)

Commercially available ZnO powder (99.99%) and Mn powder (99.99%) were taken at 1:x (x ¼ 0.01, 0.03, 0.05, 0.07) atomic ratios and mixed thoroughly for 1 h. The mixtures were then pressed within different grooved aluminium holder of 4.5 cm diameter with a hydrostatic pressure (100 kgf cm2). These pellets were then used as the targets for sputtering and placed into the sputtering chamber by appropriate arrangements as the upper electrode. Negative terminal of the power supply was connected to the target and the lower electrode was kept at a ground potential.

(c)

(b)

Table 1 Summary of deposition parameters Electrode distance Sputtering voltage Substrate Sputtering gas Deposition pressure Deposition time

(a) 1.8 cm 2.6 kV Glass Argon 0.2 mbar 2h

20

30

40

50 60 2θ (degree)

70

80

Fig. 1. XRD pattern of Zn1xMnxO thin film deposited on glass substrate for (a) x ¼ 0.01, (b) x ¼ 0.03, (c) x ¼ 0.05 and (d) x ¼ 0.07. The curves have been vertically shifted to improve clarity.

ARTICLE IN PRESS C.K. Ghosh et al. / Physica B 399 (2007) 38–46

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Zn

Spectrum 28

O Zn

Mn Mn 0 1 2 3 4 Full Scale 536 cts Cursor: 0.000 keV

5

Zn

Mn

6

7

8

9

10 keV

Fig. 2. EDX spectrum for a ZnO film deposited from a 5% Mn containing target.

Table 2 Doping concentration (at%) in the target material and in the films Mn content in the target (at%)

Mn content in the film (at%)

1 3 5 7

0.9 2.9 4.7 6.8

law aeff ¼ (1x)aZn+xaMn, where aeff is the effective lattice constant of Zn1xMnxO, aZn and aMn are the lattice constants of ZnO and MnO lattice, respectively and x is the atomic percentage of doping. The valence state of Mn ion in ZnO was determined to be Mn2+ having spins of S ¼ 5/ 2 from electronic spin resonance measurements [26]. Thermal equilibrium limit of Mn doping has been predicted approximately 13 at% at 600 1C [27]. Here, the Mn content is well below this limit. So the Mn2+ ion is understood to have occupied the Zn site without changing the wurzite structure. By utilizing the non-equilibrium nature of growth process in plasma techniques it is possible to obtain films with higher Mn content exceeding the thermal equilibrium limit. 3.2. Thermoelectric property Thermoelectric power of any material is defined as the voltage developed between two points when a unit temperature difference is maintained between these two points. A temperature gradient between two points is accompanied by an electric field. The existence of such a field, known as ‘thermoelectric field’, is conventionally written as E ¼ S rT. The proportionally constant, S, is known as ‘thermopower’. It depends on temperature to some extent and also varies with materials.

In general, thermopower of any material consists of different contributions such as diffusion of electron, which according to Mott formula is proportional to temperature, and a phonon drag contribution, which depends in some different way on temperature. The diffusion contribution due to electron contains information about Fermi edge. The Fermi energy of the film can be calculated according to the following equation [28]:   kB DE f S¼ Aþ , e kT with A ¼ (5/2s) and t ¼ t0es, where kB is the Boltzmann’s constant, e the electronic charge, DEf the energy difference between Fermi level and the upper edge of the valence band, t the relaxation time for electron scattering, s is a constant which is different for different scattering mechanism and t0 is a constant, which is a function of temperature but independent of electronic charge, e. Phonon drag contribution arises from interaction between phonon and electron gas. It reduces to a very low value both at low temperature (as phonon freezes out) and at high temperature (phonon momentum is limited by phonon–phonon scattering). Thus the phonon drag contribution varies as T3 below yD/10 (where yD is Debye temperature, yD ¼ 370 K for ZnO [29]) and approximately as T 1 above yD. In doped semiconductors there may be another contribution from the variable range hopping between localized electronic states near Fermi levels. It is described by the T1/2 law of thermopower. In magnetic materials, magnon may contribute to the total thermopower by transferring magnon momentum to the electron gas. Taking all these contributions, we have an expression for thermopower vs. temperature relation as follows [30]: SðTÞ ¼ DT þ ET 3 þ þ

F ðT=yD Þ3 þ HT 1=2 G þ ðT=yD Þ4

IðT=ð2JSeff ÞÞ1=2 , K þ ðT=ð2JSeff ÞÞ2

ð1Þ

ARTICLE IN PRESS C.K. Ghosh et al. / Physica B 399 (2007) 38–46

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3.32 5.185 5.180 3.30

5.175

3.29

5.170 5.165

3.28

5.160

ZnMnO lattice constantc, A0

ZnMnO lattice constant a, A0

3.31

3.27 5.155 3.26 0.01

0.02

0.03 0.04 0.05 Mn content,at.%

0.06

0.07

Fig. 3. Dependence of lattice constant a and c on Mn of Zn1xMnxO films.

where J ¼ J1/kB is the exchange integral for the first coordination sphere and Seff the effective spin. First and second terms of Eq. (1) are the diffusion components, third term is the phonon drag component, fourth term is the variable range hopping component, last term is the magnon drag component and D, E, F, G, H, I, K are the curve fitting parameters. Doping can increase thermopower. Magnetic dopant can be used for this purpose. First, it may create a difference in number of up and down spin electron in the conduction band, which leads to enhancement of the thermopower. Secondly, since atomic number of Mn is less than Zn, substitution of Zn by Mn causes reduction in phonon energy in any vibrational mode. The reduction in phonon energy also determines the nature of the interaction between electron and phonon. Thirdly, due to the unfilled 3-d levels of dopant atom, variable range hopping also increases. Coulomb interaction between conduction electron and localized electron scatters the conduction electrons. This scattering increase with doping concentration and it is almost consistent with the found values of fitting parameter H as will be discussed later. Finally, electron–magnon interaction scatters the electron in the conduction band. This scattering increases with increasing Mn%. A similar behaviour is observed in the case sodium cobalt oxide using Hubbard model for lower magnetic impurity doping [31]. Fig. 4 shows the variation of thermoelectric power with temperature and the variation of curve fitting parameters are listed for in Table 3 for different Mn concentrations.

or O2 vacancies in the crystal. In the absence of any magnetic impurity, electrons of spin + and  are equal in number in the conduction band. In Mn-doped ZnO, we shall now consider polarization of conduction electrons originating from s–d interaction. The Hamiltonian of this interaction can be written as [32–34]    ! X X X ! ! ! ! 0 0 1 ~ N J k  k exp i k  k  R !



n

!

k0



k







kþ kþ

k  k

a !0 a !0  a !0 a !

Szn



þ a !0

kþ

a ! S n k 



þ a !0

k

a ! Sþ n k

 ,

þ

where N is the total number of lattice points and  ! ! J k  k0 the exchange integral between a conduction electron and d-core spin of Mn2+ ion. The exchange integral may be written as     ! ! ! 0 ~   Z exp i k  k  R ! J k~  k0 ¼ N r12 !

!

!

!

!

!

 f!0 ðr1 Þfd ðr2  Rn Þfk ðr2 Þfd ðr1  Rn Þ dt12 , k

! 0

!

where k and k are the wave vectors of conduction !

!

electron. Rn and S n represent the position of Mn2+ ion and spin operator, respectively. ak and ak are the creation and annihilation operator, respectively for conduction electron !

3.2.1. Effect of Mn on diffusion component: Polarization of conduction electrons Valence band of ZnO consists of low lying narrow peak of Zn 3-d states and O 2-p states near the Fermi level and the conduction band consists of Zn 4-s states. Additional Mn 3-d bands appeared in the band gap of ZnO. Excess charge carriers (electrons) in ZnO are due to interstitial Zn

with wave vector k and + or  spin. Here we have taken z as axis of quantization and the state of the system can be specified by giving number of electrons with each kind of !

spin for each value of k . Hamiltonian expressing s–d interaction has the diagonal element X N 1 Jð0Þðnþ  n Þ Szn ; n

ARTICLE IN PRESS C.K. Ghosh et al. / Physica B 399 (2007) 38–46

42

0.005

Thermoelectric Power (mU/K)

0 −0.005 −0.01 −0.015 −0.02 −0.025 −0.03 −0.035 −0.04 300

320

340

360 380 400 Temperature (K)

420

440

460

Fig. 4. Thermoelectric power S vs. temperature T for different Mn concentrations. (a) x ¼ 0.01 (+ +), (b) x ¼ 0.03 (   ), (c) x ¼ 0.05 ( x ¼ 0.07 (& &). The lines are theoretical fitting with Eq. (1).

) and (d)

Table 3 Variation of different fittings parameters with Mn concentrations Different doping %, x

0.01 0.03 0.05 0.07

Values of different fitting parameters D (mV/K2)

E  108 (mV/K4)

F (mV/K)

G

H (mV/K1.5)

I (mV/K)

K

0.0002 0.0003 0.0004 0.0005

3.21 1.68 3.7 3.7

1.12 0.88 1.42 1.42

0.69 0.68 0.64 0.66

0.004 0.005 0.007 0.007

0.018 0.012 0.005 0.001

1.22 1.27 2.97 2.97

where n+ and n are the total number of electrons of + and  spin, respectively. (n+n) will lower diagonal energy; hence polarize the conduction electron [34].We now consider the Hamiltonian of our complete system [35]: p2 H¼ þ H ex , 2me P ~ describes the s–d ex~n Þ~ rR sS where, H ex ¼ Jð0Þ n dð~ 

change interaction between the localized magnetic Mn2+ ions and the conduction electron, with J(0) the s–d exchange constant and the summation is performed over all Mn2+ sites. Within virtual crystal and mean field approximation, D E Hex can be written as H ex ¼ ~z =2. x is the fractional occupancy of NJð0Þx~ s z0 S D E ~z is the thermal average of Mn2+ on cationic sites. S the ~ zth component of the Mn 3d5 spin (S ¼ 5/2). Thus the levels splits due to exchange interaction between electrons in the conduction band and electron in core levels of Mn site by D  Jð0ÞSz .

In the absence of Mn, density of states (DOS) for both spins + and  are given by DðEÞ ¼ ð1=2p2 Þð8p2 me =h2 Þ3=2 E 1=2 . Average energy of electrons in conduction band for both type of spins is R1

Eg DðEÞf ðEÞE dE E¯ ¼ R 1 . E g DðEÞf ðEÞ dE

f(E) is the FD distribution function, f(E) ¼ exp((EFE)/ (kT))for weakly non-degenerate system. 3 E ¼ kT þ E g . 2 Out of a total of N electrons in conduction band, spin + and spin  both are equal in number ( ¼ N/2). Due to incorporation of x% of Mn ion, density of states are no longer same for both spin + and spin . Core spin favours the parallel spin electron in conduction band and let us

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assume that DOS for spin + does not change. Then, 2 3=2

DðE; þÞ ¼ ð1=2p2 Þð8p2 me =h Þ

ðE  E g Þ

1=2

ð1 þ x=2Þ,

E g  D=2oEoE g , DðE; þÞ ¼ ð1=2p2 Þð8p2 me =h2 Þ3=2 ðE  E g Þ1=2 ;

E4E g .

Core spin does not favour antiparallel spin electron in conduction band due to exchange energy (JH), therefore DOS for spin is DðE; Þ ¼ ð1=2p2 Þð8p2 me =h2 Þ3=2 ðE  E g Þ1=2 ð1  x=2Þ, E g oEoE g þ D=2 ¼ ð1=2p2 Þð8p2 me =h2 Þ3=2 ðE  E g Þ1=2 , E g þ D=2oE. Difference in the number of spin + (n+) and spin  (n) electron is given by 2

2

2

ðnþ  n Þ ¼ ð1=2p Þð8p me =h Þx Z E g þD=2 ðE  E g Þ1=2 f ðEÞ dE E g D=2

¼ ð1=2p2 Þð8p2 me =h2 Þ3=2 xeðE F E g Þ=kT Z D=2 E 1=2 eE=kT dE D=2

43

3.2.2. Effect of Mn doping on hopping component: Enhancement of DOS for localized state near Fermi energy Potential distribution near Mn site differs from that of Zn site due to (i) differences in potential depth and (ii) spatial extension of d wave function in the neighboarhoods of respective ions. Large electron–lattice interaction near Mn site would tend to localize electrons near Mn sites and the wave function is confined in a small region of space, falling off as exp(ar). These states are called localized state and the phenomenon is known as ‘localization’. Therefore, we have a continuous DOS r(E), originating from these d levels of Mn2+ ions in the band gap region, in which all states are localized. Width of these localized states is approximately given by 2zI; z is the number of nearest neighbour and, I the transfer integral. The probability of hopping of an electron from one localized state to another depends on (a) The Boltzmann factor exp(W/kT), where W is the energy difference between any two states. (b) A factor depending on the phonon spectrum gph. (c) A factor depending on the overlap of the wave functions. The number of electrons jumping a distance ‘r’ in the direction of temperature gradient will be made up of the following two factors,

¼ IðD; TÞeðE F E g Þ=kT , IðD; TÞ ¼ ð1=2p2 Þð8p2 me =h2 Þ3=2 Z D=2 E 1=2 eE=kT dE. D=2

Same type of variation in (n+n) with respect to x can also be obtained by using Boltzmann distribution function for electron with two different types of spin. Thus energy of the system has been increased due to magnetic ion doping caused by polarization by an amount   3 DE ¼ ðnþ  n Þ kT þ E g 2   E F E g =kT 3 kT þ E g . ¼ IðD; TÞxe 2 Therefore, enhancement of thermopower in diffusion component due to unbalancing of electron in conduction band must be equal to gradient of DE: DS diff  rðDEÞ. Now,    d 3 IðD; TÞeE F E g =kT kT þ E g ¼ GðD; TÞx, dT 2    d 3 IðD; TÞeE F E g =kT kT þ E g . where GðD; TÞ ¼ dT 2

rðDEÞ ¼ x

Therefore; DSdiff  GðD; TÞx.

(i) The number of electrons involved in hopping per unit volume within a range of kT near Fermi energy, namely 2r(EF)kT and (ii) The hopping probability between two localized states separate by a distance r, in the two directions, which are given by gph exp(2arW/kT) and gph exp(2arW/k(TDT)), where DT is the difference in temperature between two localized states. The net flow of electron in the direction of low temperature is given by     W W gph exp 2ar  . 1  exp  2 DT kT kT Considering the linear variation of lattice constant with Mn2+, the variation of transfer integral may be assumed to vary with fractional occupancy of Mn2+ in cationic sites with the relation I ¼ I0 exp(lx). The number of states per unit volume within the impurity band must be equal to Mn2+ concentration. It has two effects on this, first it increases DOS, r(EF) and secondly it reduces the energy separation W between any two levels, which increases the range of hopping. It is also clear from equation that the hopping probability increases with temperature. Thermopower due to hopping is given by [36]   1 k W 2 d ln rðEÞ Shopp ¼ . 2 e kT dE E¼E F

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Integrating over the range of energies W which contribute to the thermopower and assuming this to be hopping energy, in case of variable-range hopping W  kðT 0 T 3 Þ1=4 . Thus, contribution to thermopower from variable-range hopping is   1=2 d ln rðEÞ . S hopp  T dE E¼E F  is constant For a fixed concentration of Mn, d lndErðEÞ E¼E F and S(T) varies as T1/2. At a fixed temperature, contribution to thermopower increases as the density of states increases near Fermi energy with different concentrations of Mn2+. The DOS for localized d-orbitals can be written as rðEÞ  b=ððE 2  E 2d Þ þ b2 Þ, Ed is the energy levels of dorbitals and b ¼ zI(x) is the half width of localized state. The slope of S(T) vs. T graph increases with Mn concentration, indicating that Fermi energy moves towards the localized impurity band and DEF are equal to 17.950, 18.989, 26.405 and 29.540 mV for x ¼ 0.01, 0.03, 0.05 and 0.07, respectively. With increasing Mn2+, EF intersects the upper edge of one of the d subbands giving rise to the large values for the corresponding derivatives of density of states. A similar behaviour was observed by Kettler et al. [37] by Mott’s s–d scattering model for FexNi80xB20. Increment of ððd ln rðEÞÞ=ðdEÞÞE¼E F depends approximately linearly on x, indicating that hopping component of thermopower, which dominates at higher temperature, also increases linearly with fractional occupancy of Mn2+ in cationic sites. Therefore, DS hopp  T 1=2 x. 3.2.3. Effect of Mn on magnon component: magnetic contribution from spin wave The variation of Curie–Weiss temperature with Mn concentration can be written as y(x) ¼ y0x approximately [38] where x is the fraction of present Mn concentration and y0 the value of Curie–Weiss temperature with x ¼ 1 (y0 ¼ 1900 K [39]). The exchange integral J(x) can be written in terms of y(x) by the following relation [40]: JðxÞ ¼

3yðxÞ , 2zS eff ðSeff þ 1Þ

where z is the number of nearest-neighbour cations, which is equal to 12 in wurtzite lattice. High spin (Seff ¼ 5/2) state Table 4 Variation of exchange integral with Mn concentration Different doping percentage, x

Value of exchange integral, Jeff (K)

Value of 2JSeff (K)

0.01 0.03 0.05 0.07

0.172 0.516 0.860 1.204

0.860 2.580 4.300 6.020

configuration is observed in other tetrahedrally coordinated Mn in II–VI semiconductors and it was confirmed by observing the Bohr magneton number, which is 5.4mB/Mn atom [41]. Since y(x) varies linearly, J(x) will also vary linearly with x, considering the value of exchange integral J(x ¼ 1) ¼ 17.2 K [41]. The value of exchange integral for different concentration of x is calculated and shown in Table 4. Thermoelectric power from magnon is given by Smag ¼

IðT=2JS eff Þ1=2 . K þ ðT=2JSeff Þ2

3.3. Thermoelectric power as a function of Mn doping Considering all these three components we may approximate the variation of thermopower with respect to Mn concentration at any temperature as SðxÞ ¼ Mx þ

Nð1=xÞ1=2 þ P. O þ ð1=xÞ2

(2)

In this expression the first term arises due to diffusion and hopping, since both varies linearly with Mn concentration and the second term arises due to magnon contribution near spin wave. P is the Mn-independent contribution to thermoelectric power that depends on undoped ZnO. Fig. 5. shows the variation of thermopower with Mn concentration in the film and the lines are theoretical fitting with Eq. (2). The corresponding curve fitting parameters are listed in Table 5. Parameter ‘D’, the diffusion contribution to the thermopower, increases with Mn+2 doping percentage. This variation is almost linear as suggested in Section 3.2.1. This variation is due to the polarization of charge carriers. Parameter ‘F’ represents interaction between electron and phonon. It decreases with increasing doping concentration. Since Mn atom has 0.036 413K 393K 373K 353K 333K

0.034 Thermoelectric power (mV/K)

44

0.032 0.030 0.028 0.026 0.024 0.022 0.020 0.018 0.01

0.02

0.03 0.04 0.05 Mn doping %.x

0.06

0.07

Fig. 5. Variation of thermoelectric power, S(T) with Mn concentration x, plotted at different temperatures.

ARTICLE IN PRESS C.K. Ghosh et al. / Physica B 399 (2007) 38–46 Table 5 Variation of different fittings parameters with different temperature Temperature (K)

M (mV/K)

N (mV/K)

O

P (mV/K)

333 353 373 393 413

0.17078 0.22607 0.20417 0.23546 0.22588

0.00063 0.00068 0.00074 0.00078 0.00083

1.47338 1.80746 1.96999 2.12874 2.75705

0.01727 0.01476 0.01729 0.01593 0.01833

45

and the hopping component is due to the hopping of electrons between localized states that arises from Mn 3-d levels in the band gap. An equation relating the thermopower of ZnO with Mn concentration in the films is obtained which shows good fitting with experimental data. The found variation of fitting parameters also supports the above theoretical reasoning. Acknowledgements

smaller atomic number than Zn atom, Mn atom will contribute less energy to the lattice vibrational energy than the energy contribution from Zn atom. Parameter ‘H’, the variable range hopping contribution, increases with Mn doping. This increment is almost linear with doping as suggested in Section 3.2.2. The parameter H that represents variable range hopping contribution to thermoelectric power is negative and also its absolute value increases with increasing Mn concentration in the films. From the expression of DOS of localized states rðEÞ 

Shopp

b , ðE  E 2d Þ þ b2 2

we obtain   1=2 d ln rðEÞ T dE E¼E F T

1=2

! 2E F . ðE 2F  E 2d Þ þ b2

The negative value of fitting parameter H indicates that absolute value of E 2d must be greater than that of ðE 2F þ b2 Þ. In the absence of Mn doping, electrons of two different kind of spin are equal in number and Mn doping creates a difference in this number by exchange interaction between as suggested in Section 3.2.1, i.e. incorporation of Mn favours electron having same kind of spin in conduction band and doesnot favor electron of opposite spin. This leads to a net reduction of the number of charge carrier in conduction band and to a shift in Fermi energy level. Also the width of localized states varies doping concentration, x, as b ¼ 2zI0elx as suggested in Section 3.2.2. Therefore the increment in Mn doping concentration leads to larger negative contribution to the thermopower from hopping component. The good fitting of the experimental data with Eq. (2) indicates the thermopower of Mn-doped ZnO can be described by Eq. (2). 4. Conclusions It has been observed that, thermoelectric power of Mn doped ZnO thin films increases with Mn2+ almost linearly. The main reason for this approximately linear variation is due to the major contribution originating from diffusion and hopping component. Enhancement in diffusion component is due to polarization of conduction electrons

The authors wish to thank Department of Science and Technology, Government of India, for financial support. One of us (CKG) wishes to thank Council for Scientific and Industrial Research (CSIR), Government of India, for awarding him a Junior Research Fellowship (JRF) during the execution of the work. SD wishes to thank University Grants Commission (UGC), Government of India, for awarding him a Senior Research Fellowship (SRF) during the execution of the work. References [1] C. Lee, K. Lim, J. Song, Sol. Energy Mater. Sol. Cells 43 (1996) 37. [2] H.S. Kang, J.S. Kang, J.W. Kim, S.Y. Lee, J. Appl. Phys. 95 (2004) 1246. [3] S.P.S. Arya, O.N. Srivastava, Cryst. Res. Technol. 23 (1988) 669. [4] L.B. Wen, Y.W. Huang, S.B. Li, J. Appl. Phys. 62 (1987) 2295. [5] S. Major, K.L. Chopra, Sol. Energy Mater. 17 (1988) 319. [6] J.K. Srivastava, L. Agrawal, B. Bhattacharyya, J. Electrochem. Soc. 11 (1989) 3414. [7] H.C. Pan, B.W. Wessels, Mater. Res. Soc. Symp. Proc. 152 (1989) 215. [8] K.L. Chopra, S. Major, D.K. Pandya, Thin Solid Film 102 (1983) 1. [9] Z.C. Jin, C.G. Granqvist, Proc. SPIE 21 (1987) 827. [10] T. Dietl, H. Ohno, F. Matsukara, J. Cibert, D. Ferrand, Science 287 (2000) 1019. [11] P. Sharma, A. Gupta, K.V. Rao, F.J. Owens, R. Sharma, R. Ahuja, J.M.O. Guillen, B. Johansson, G.A. Gehring, Nat. Mater. 2 (2003) 673. [12] S.W. Jung, S.J. An, G.C. Yi, Appl. Phys. Lett. 80 (2002) 4561. [13] T. Fukumara, Z. Jin, M. Kawasaki, T. Shono, T. Hasegawa, S. Koshiharam, H. Koinuma, Appl. Phys. Lett. 78 (2001) 958. [14] A. Tiwari, C. Jin, A. Kvit, D. Kumar, J.F. Muth, J. Narayan, Solid State Commun. 121 (2002) 371. [15] P. Petrou, R. Sing, D.E. Brodie, Appl. Phys. Lett. 35 (1979) 930. [16] P. Soulette, S. Bethke, B.W. Wessels, H. Pan, J. Cryst. Growth 86 (1988) 248. [17] Z. Fu, B. Lin, J. Zu, Thin Solid Film 402 (2002) 302. [18] T. Minami, H. Nato, S. Takata, Jpn. J. Appl. Phys. 23 (1984) L280. [19] M.S. Tomar, F. Garcia, Thin Solid Film 90 (1982) 419. [20] H. Agura, A. Suzuki, T. Matsushita, T. Aoki, M. Okuda, Thin Solid Film 445 (2003) 263. [21] M. Ohyama, H. Kozuka, T. Yoko, Thin Solid Film 306 (1997) 78. [22] S. Peulon, D. Lincot, Adv. Mater. 8 (1996) 166. [23] JCPDS Powder Diffraction File Card No. 05-0664. [24] V.A.L. Roy, A.B. Djurisic, H. Liu, X.X. Zhang, Y.H. Leung, M.H. Xie, J. Gao, H.F. Lui, C. Surya, Appl. Phys. Lett. 84 (2004) 756. [25] C.J. Cong, L. Liao, J.C. Li, L.X. Fan, K.L. Zhang, Nanotechnology 16 (2005) 981–984. [26] P.B. Dorain, Phys. Rev. 112 (1958) 1058. [27] C.H. Bates, W.B. White, R. Roy, J. Inorg. Nucl. Chem. 28 (1966) 397. [28] R.K. Wilderson, A.C. Beer, Semiconductors and Semimetals, vol. 8, Academic Press, New York, 1971.

ARTICLE IN PRESS 46

C.K. Ghosh et al. / Physica B 399 (2007) 38–46

[29] S. Adachi, Handbook on Physical properties of Semiconductors, vol. III, Kluwer Academic Publishers, Dordrecht, 2004. [30] T. Gron, A. Krajewski, J. Kusz, E. Malicka, I.O. Kozlowsa, A. Waskowska, Phys. Rev. B 71 (2005) 035208. [31] W. Koshibae, S. Maekawa, Physica B 329–333 (2003) 896–897. [32] T. Kauys, Prog. Theoret. Phys. Japan 16 (1956) 45. [33] A.H. Mitchell, Phys. Rev. 105 (1957) 1439. [34] K. Yosida, Phys. Rev. 106 (1957) 893. [35] W. Yang, K. Chang, F.M. Peeters, Appl. Phys. Lett. 86 (2005) 192107. [36] N.F. Mott, E.A. Davis, Electronic Processes in Non-Crystalline Materials, Clarendon Press, Oxford, 1979.

[37] W.H. Kettler, S.N. Kaul, M. Rosenberg, Phys. Rev. B 39 (1984) 6140. [38] E. Chikoize, Y. Dumont, F. Jomard, D. Ballutaud, P. Galtier, O. Gorochov, D. Ferrand, J. Appl. Phys. 97 (2005) 10D327. [39] T. Fukumara, Z. hengwu Jin, M. Kawasaki, T. Shono, T. Hasegawa, S. Koshihar, H. Koinuma, Appl. Phys. Lett. 78 (2001) 958. [40] J.H. Kim, H. Kim, D. Kim, Y.E. Ihm, W.K. Choo, J. Appl. Phys. 92 (2002) 6066. [41] M.H. Kane, K. Shalini, C.J. Summers, R. Varatharajan, J. Nause, C.R. Vestal, Z.J. Zhang, I.T. Ferguson, J. Appl. Phys. 97 (2005) 023906.