Tuning the free electron concentration in Sr-doped Bi2Se3

Journal of Physics and Chemistry of Solids 74 (2013) 746–750

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Tuning the free electron concentration in Sr-doped Bi2Se3 P. Ruleova, C. Drasar n, A. Krejcova, L. Benes, J. Horak, P. Lostak Faculty of Chemical Technology, University of Pardubice, Studentska 573, 532 10 Pardubice, Czech Republic

a r t i c l e i n f o

a b s t r a c t

Article history: Received 12 September 2012 Received in revised form 15 November 2012 Accepted 12 January 2013 Available online 21 January 2013

Single crystals of Bi2Se3 doped with strontium were grown from high purity elements. The prepared single crystals were characterized using x-ray diffraction. Inductively coupled plasma atomic emission spectroscopy (ICP-AES) was used to determine the actual concentrations of strontium in the studied samples. The transport properties were measured for all of the samples. The Seebeck coefficient, S, the Hall coefficient, RH, and the electrical conductivity, s, were measured in the temperature range from 80 K to 470 K. These data indicated acceptor-like behavior of strontium in Bi2Se3. A detailed study of the doping efficiency of strontium was performed. Interestingly, the Hall mobility of the free carriers increases markedly upon doping with Sr. This effect was qualitatively explained within a model of point defects in the crystal lattice of Bi2  xSrxSe3, which implied a decrease in the concentration of scattering centers. & 2013 Elsevier Ltd. All rights reserved.

Keywords: A. Chalcogenides B. Crystal growth D. Transport properties

1. Introduction Bi2Se3, which adopts the tetradymite structure (Bi2Se3, Bi2Te3, and Sb2Te3), is one of the constituents of room temperature thermoelectric (TE) materials [1]. Some of these materials (p-type) have been shown to form diluted magnetic semiconductors (DMS) if they are doped with some transition metals, e.g. [2,3]. Recently, it has been shown that these materials are bulk topological insulators (TI), e.g. [4–6]. These materials are degenerate semiconductors due to a high concentration of native defects that produce free carriers [7]. This concentration of free carriers affects the exploration and potential usage of these materials as topological insulators, and n-type conductivity prevents potential carrier induced ferromagnetism in Bi2Se3 based DMS [8]. Selenium vacancies are the dominant defects in Bi2Se3, and they result in electron doping on the order 1019 cm  3. In recent studies, the use of calcium was successfully demonstrated for tuning the free carrier concentration [9]. Surprisingly, doping Bi2Se3 with even very low concentrations of Ca led to p-type conductivity in this material. The acceptor characteristics of the Ca atoms were attributed to the formation of calcium-type 1 substitutional defects in place of bismuth, CaBi , which are compensated by one hole. However, this substitution involves a decrease in the concentration of selenium vacancies. According to our model, this decrease considerably reduces the electron þ2 concentration because the selenium vacancies, VSe , are compensated by two electrons. In fact, this paper provides evidence for

n

Corresponding author. Tel.: þ420 466 036 036; fax: þ 42046036124 E-mail address: [email protected] (C. Drasar).

0022-3697/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jpcs.2013.01.015

selenium vacancies and their interaction with a doping element for the first time. Doping with an electropositive element is rather uncommon within semiconductor chemistry; therefore, this topic is very interesting. We assumed that other alkali earths could induce similar effects in Bi2Se3. With the aim to provide evidence of this assumption and to perform a detailed study on the doping of Bi2Se3 with alkaline earths, we examined the next element in the periodic table, strontium. This study may be important for TE, DMS, and TI research.

2. Experimental Single crystals of Bi2  xSrxSe3, with nominal x values between 0 and 0.025, were grown by heating stoichiometric mixtures of 99.999% pure Bi, Se and 99.99% Sr (Sigma-Aldrich) in carboncoated quartz ampoules at 1073 K for 24 h. The carbon coating was necessary to prevent reactions between strontium and the quartz ampoule. The carbon coating was also used during the synthesis of undoped Bi2Se3 to maintain the same experimental conditions. The crystal growth process involved cooling from 1073 K to 923 K at a rate of 6 K per hour. The crystals were then annealed for 550 hours at 923 K in the same ampoule. Shorter annealing times may result in inhomogeneous samples. The largest obtained single crystals were up to 40 mm in length, 8 mm wide and 3 mm thick. The orientation of the single crystals was performed using the single crystal x-ray technique. For the physical properties measurements, specimens with dimensions of 15  3  (0.2–0.3) mm3 were cut from the single crystals. The doping homogeneity was examined using a position resolved

P. Ruleova et al. / Journal of Physics and Chemistry of Solids 74 (2013) 746–750

2.866

a (nm)

0.4140

2.864 0.4135

c (nm)

2.862

0.4130

a 0.000

0.005

c

0.010 0.015 actualx

0.020

Fig. 2. a and c lattice parameters of Bi2  xSrxSe3 as a function of x.

8

S ( ΔT⊥c) (μV K -1)

-50

x=0 x=0.0007 x=0.0011 x=0.0028 x=0.0045 x=0.0181

-100 -150

4

2

-200 -250

6

100

200

300

400

500

600

σ(i⊥c) (105x Ω-1m-1)

Seebeck coefficient measurement. The variation of the Seebeck coefficient was considerably less than 5% in any sample. Diffraction patterns (CuKa, l ¼0.15418 nm) were recorded on powdered samples using a D8 Advance diffractometer (Bruker AXS, Germany) with a Bragg–Brentano Y–Y goniometer (radius 217.5 mm) equipped with a secondary beam curved graphite monochromator and Na(Tl)I scintillation detector. The scans were performed at room temperature from 10 to 801 (2Y) in steps of 0.021 with a counting time of 8 s per step. The lattice parameters were refined using the Le Bail method as implemented in the program FullProf. The transport parameters presented here include the electrical conductivity (s), the Seebeck coefficient (S), and the Hall coefficient (RH); all of these parameters were measured over a temperature range from 80 K to 470 K. These parameters were measured in the direction perpendicular to the trigonal axis, c, i.e., the electric field and thermal gradients were applied in the basal plane while the magnetic induction vector was parallel to the c axes. A conductive graphite adhesive was used to attach the current leads. Platinum wires (50 mm in diameter) were attached along the sample using thermocompression to measure the voltage drop. The Hall effect and electrical conductivity were examined using a lock-in nanovoltmeter with a 29 Hz excitation and a static magnetic field of 0.6 T. The Seebeck coefficient was determined using the longitudinal steady-state technique with a temperature difference ranging from 3 to 3.5 K. The thermal gradients were measured with the aid of fine copper–constantan thermocouples. The actual concentrations of strontium were analyzed using ICP-AES.

747

0

T (K) 3. Results and Discussion Fig. 3. Seebeck coefficient, S, and electrical conductivity, s, of Bi2  xSrxSe3 as a function of temperature.

3.1. X-ray analysis A typical x-ray diffraction pattern of Bi2  xSrxSe3 obtained for a powdered single crystal (actual x¼0.018) is shown in Fig. 1. All of the diffraction peaks can be attributed to the structure of Bi2Se3; there is no evidence of additional phases, even for the sample with the highest level of doping. The lattice parameters of the parent material, a¼0.41387 nm and c ¼2.86303 nm, are in good agreement with those in the database (PDF-4þ /ICDD). In Fig. 2, we summarize the lattice parameters as a function of the Sr concentration. In fact, we observe that the lattice parameters do 0,0,6

5

0,1,5

Sample No .15 Bi 1.982Sr 0.018Se 3

20

40 2Θ ( )

60

1,2,11

2,1,10

1,1,15 0,0,21 0,1,20 1,2,5 1,2,8

2,0,11

0,2,10

2,0,5 2,0,8

0,2,1 2,0,2 1,1,9

1,0,10

0

0,1,111,1,0

1,0,4

1

0,1,8 0,0,12

1,0,1 0,1,2 0,0,9

2

0,0,15 1,0,13

3

0,0,3

counts x 10-3 (-)

4

80

Fig. 1. X-ray diffraction pattern of a powdered Bi1.982Sr0.018Se3 single crystal.

not have a significant dependence on the Sr concentration. This result is because we are using very low concentrations of dopant and the atomic diameter of the substitutional Sr is comparable to that of Bi. 3.2. Transport parameters Figs. 3 and 4 present the measured temperature dependence of the electrical conductivity s(i?c), Hall coefficient RH(B99c), Hall mobility of free carriers mH, and the Seebeck coefficient S(DT?c). We eliminated some samples from these figures for clarity. The room temperature values of the physical parameters are summarized in Table 1 for all of the studied samples. All parameters provide evidence for the acceptor character of strontium. The temperature dependence of the parameters suggests a degenerate to nearly degenerate state of a semiconductor. However, the absolute value of the Hall coefficient tends to decrease with increasing temperature for samples with higher concentrations of strontium. This behavior is due to thermal electron-hole excitation over the band gap. The relationship mpT r provides insight about the scattering mechanism of free carriers [10]. To estimate the scattering mechanism, we performed a simplification and plotted lnmH plnðRH sÞ as a function of ln(T) in Fig. 5. The exponent r is very close to 1.5 above room temperature (solid line in Fig. 5), which indicates that scattering by acoustic phonons is the dominant mechanism. The behavior in the low temperature region can be attributed to mixed scattering by acoustic phonons and impurities. The transport parameters as a function of the Sr concentration are presented in Figs. 6 and 7. Although a considerable change in

748

P. Ruleova et al. / Journal of Physics and Chemistry of Solids 74 (2013) 746–750

μH (cm V s )

0

100

200

300

400

500

-1 -1

-2

2

x=0 x=0.0007 x=0.0011 x=0.0028 x=0.0045 x=0.0181

σ(i⊥c) (105 x Ω-1m-1)

3

-1

1000

S

-120

3

-160

2

-200

1 0

600

-240 0.000

0.005

T (K)

No. actual x 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

actual cSr [10 18cm  3]

0 0 0 0 0 0 0.0007 4.5 0.0011 6.9 0.0015 9.1 0.0022 14 0.0028 18 0.0031 20 0.0036 23 0.0044 28 0.0045 28 0.0062 39 0.0139 87 0.0181 110 0.0209 130

Rh(B99c) [cm3 C  1]

s(I?c) mH S(DT?c) [O  1 cm  1] [cm2 V  1s  1] [m VK  1]

 0.25  0.25  0.27  0.58  0.77  0.68  1.53  0.99  1.64  1.3  1.24  1.51  1.73  2.49  2.55  2.18

2630 2650 2540 2080 1620 1590 940 1250 860 980 880 850 750 510 520 580

659 662 686 1210 1250 1080 1430 1240 1410 1280 1110 1280 1290 1270 1340 1260

ln [μH (cm2V-1s-1)]

8.0

 64  63  60  85  96  101  136  117  142  130  119  131  129  137  142  149

x=0 x=0.0007 x=0.0011 x=0.0028 x=0.0045 x=0.0181

7.5

7.0

6.5

4.5

5.0

5.5 6.0 ln [T (K)]

6.5

Fig. 5. Logarithm of Hall mobility, ln mH, of Bi2  xSrxSe3 as a function of ln T. The solid line has a slope of r¼  1.5, which indicates the scattering of electrons by acoustic phonons.

the transport parameters can be observed at low doping levels, saturated values are evident at higher doping levels. The decrease of 9RH9 for the sample with the highest content of strontium might suggest (contrary to other parameters) a shift towards

0.020

2000

0 R μ

H H

μH (cm2V-1s-1)

Table 1 Room-temperature values of the Hall coefficient, RH(B99c), Seebeck coefficient, S(DT?c), electrical conductivity, s(i?c), and Hall mobility, mH of the Bi2  xSrxSe3 single crystals.

0.010 0.015 x (actual)

Fig. 6. Electrical conductivity, s, and Seebeck coefficient, S, of Bi2  xSrxSe3 as a function of the Sr concentration.

RH(B||c) (cm3C-1)

Fig. 4. Hall coefficient, RH, and Hall mobility, mH, of Bi2  xSrxSe3 as a function of temperature.

-80

σ

4

S(ΔT⊥c) (μVK-1)

RH(B||c) (cm C )

2

-40

5

2000

1000

-2

0.000

0.005

0.010 0.015 x (actual)

0.020

Fig. 7. Hall coefficient, RH, and Hall mobility, mH, of Bi2  xSrxSe3 as a function of the Sr concentration.

p-type conductivity. Although it was possible to prepare p-type samples, they were inhomogeneous. These samples exhibited a transition temperature (p-type to n-type) at approximately 370 K. Several attempts were performed, but we have not yet succeeded in preparing completely homogeneous p-type samples. Perhaps a prolonged annealing is necessary to prepare these samples. Interestingly, we observed an extraordinary increase in the mobility upon Sr-doping. This result strongly indicates an increase in the free carrier relaxation time, which is largely due to the decrease in the concentration of scattering centers (although in some cases, this might be partially ascribed to a shift in the carrier concentration [11] or a complex band structure [12]). Therefore, introducing Sr-related point defects must induce a decrease in the concentration of native defects in Bi2Se3, as discussed below. To address this point, examining the doping efficiency of strontium, Z ¼ Dn/DcSr, is helpful (Dn and DcSr is the variation in the electron and strontium concentration between two samples, e.g. Dn ¼n1(Bi2  xSrxSe3) n2(Bi2  xSrxSe3)). Rather than assuming both majority and minority carriers, we calculated the free carrier concentration using n ¼ gA/RHe, where the structure factor, g ¼1 for a single valley model [13,14]. This simplification could be debatable at higher temperatures because of the increasing Hall coefficient, which indicates a rise of minority carriers (Fig. 4). The Hall factor, A, is very close to unity [15]. However, we believe that this simplification yields the best estimate for all n-type samples at room temperature, even for those with the lowest carrier concentration. We assumed a simplified parabolic single valley model in the extrinsic regime and used data published in [14] to

3.3. Point defects - doping efficiency of Sr in Bi2Se3 In this section, we discuss the interaction of Sr with the parent Bi2Se3. All transport parameters indicate the acceptor behavior of strontium. However, it is apparent that the doping efficiency, Z ¼ Dn/DcSr, is not a constant within the examined doping region. With the aim to shed light on this issue, we discuss the doping efficiency in the framework of a point defect model. Bi2Se3 prepared from a stoichiometric melt always exhibits an excess of Bi accompanied by the formation of native point defects. þ2 1 Selenium vacancies, VSe , and bismuth antisites, BiSe , are crucial native defects in Bi2Se3 [17]. Because the selenium vacancies are dominant, this material is an n-type semiconductor with a concentration of free electrons given by the equation þ2 ½Bi1 e ¼ 2½V Se Se :

ð1Þ

However, the substitutionally incorporated strontium atom is compensated by a hole because of its valence 2Sr þ 3Se ¼ 2Sr1 Bi þ Bi2 Se3 þ2h

þ

ð2Þ

Therefore, within this ordinary model, each strontium atom produces 1 hole. To verify this model, we plotted the variation of the electron concentration, n, as a function of the strontium concentration, cSr, in Fig. 8. The derivative of this function provides the local doping efficiency. However, the situation in this case is simple. Two almost linear regions can be observed in this dependence. For the low content of strontium (a decrease by Dn ffi 2  1019 cm  3), the doping efficiency is Z ¼ Dn/DcSr ffi 2, while for the high strontium concentration it is Z2 ffi0. However, this result contradicts Eq. (2), which predicts that the efficiency is equal to 1 and is independent of the concentration. Divergence towards higher and lower values of Z indicates that there are other processes occurring. The anomalous value of Z, which is greater than 1 for x r0.001, involves an interaction of strontium with native defects [7]. The defect structure of Bi2Se3 belongs to hybrids of Schottky and antistructure disorder [18]. Most likely, the concentration of selenium vacancies is decreased upon doping due to shift of equilibrium [7], þ2 3 BiBi þ VSe þ 2e 3Bi1 Se þVBi þ4h

þ

ð3Þ

749

2

2

n Δn 0

0

0.0

0.5

1.0

cSr 0.00

Δn (1019cm-3)

ensure that the concentration of minority carriers is negligible in all n-type samples. Indeed, under these assumptions, the room temperature concentration of minority holes is at least three orders of magnitude lower compared to that of the concentration of electrons, even in the sample with the lowest electron concentration (sample No.16, p E2.1015 cm  3 and n E3.1018 cm  3, respectively). Despite the simplification, this result supports the usage of the relationship n ¼1/RHe. Furthermore, we used considerably smaller concentration increments, Dn, for estimating the strontium doping efficiency. This process reduces potential error in this estimation. Interestingly, the concentration of electrons in the parent Bi2Se3 is not comparable with that published in a similar study [9]. In the previous study, although the samples were prepared using 5N elements, the starting pure Bi2Se3 exhibits an unusually low concentration of electrons (n E8.1017 cm  3), and thus, anomalous physical properties. This result partially explains the crossover to p-type conductivity, even for the significantly low nominal Ca-doping. For unknown reasons, we obtained pure Bi2Se3 that always had different properties (n E2.5.1019 cm  3); however, these properties were in good agreement with those in former studies, e.g. [15,16]. This remarkable point is worth further exploration.

n (1019cm-3)

P. Ruleova et al. / Journal of Physics and Chemistry of Solids 74 (2013) 746–750

1.5

(1020cm-3)

0.01 x (actual)

0.02

Fig. 8. Electron concentration, n, and variation of the electron concentration, Dn, as a function of the Sr concentration.

This effect was clearly observed in Bi2Se3 upon doping with calcium[9]. Generally, strontium as an electropositive element polarizes the host structure inducing an increase in the point defect formation energy, and thus, a decrease in their concentration. The disappearance of selenium vacancies and bismuth antisites might induce a decrease in the lattice parameters and the unit cell volume due to the recovery of bonds on the formerly vacant Se-sites, which would decrease the lattice dimensions. Although the a parameter did not vary with the Sr-content, the c parameter exhibited a small decrease (see Fig. 2). A value of Z considerably less than 1 indicates that strontium forms either uncharged defects or forms two types of defects that mutually cancel their doping effects. The substitutional defect 1 SrBi might be, for example, compensated by strontium interstitials, Sriþ 1, that produce electrons; such processes cannot be excluded. However, the mobility increases further for x4 0.001, which suggests another scenario. Therefore, we assume that even very small concentrations of Sr are able to reduce the selenium vacancies in accordance with the results published in [9]. However, at higher strontium concentrations up to x¼0.011, the 1 bismuth antisites, BiSe , next to the vacancies are also being depleted, i.e. the equilibrium constant given by Eq. (3) varies. This healing process is in agreement with both the increase of mobility (Fig. 7) and the reduced doping efficiency of strontium. For a wide concentration range above x ¼0.011, the mobility and electron concentration remain approximately constant, which suggests a simultaneous depletion of antisites and the formation 1 of substitutional defects, SrBi .

3.4. Thermoelectric properties The power factor, PF ¼ sS2, as a function of temperature is shown in Fig. 9 for some samples. The PF increases with increasing strontium content up to x¼0.01, where the concentration of free electrons reaches an optimum value for TE properties. The maximum PF ffi 0.0017 WK  2m  1 is located at approximately T¼370 K for samples with medium concentrations of strontium. The decrease of the PF at higher temperatures is associated with the band gap excitation of electrons and holes. Using the extrapolated thermal conductivity of pure Bi2Se3 from [15], k ffi 3 Wm  1K  1, we obtained ZT(T¼370 K) ffi0.2, which is a value that is far too low compared to state-of-the-art materials used for TE applications, e.g. [19,20] and references therein.

P. Ruleova et al. / Journal of Physics and Chemistry of Solids 74 (2013) 746–750

σS2 (10-3 WK-2m-1)

750

x=0 x= 0. 0007 x= 0. 0011 x= 0. 0028 x= 0. 0045 x= 0. 0181

1.5

1.0

0.5 100

200

300

400

500

600

T (K) Fig. 9. Power factor, sS2, of Bi2  xSrxSe3 as a function of temperature.

4. Conclusions We prepared a series of Bi2  xSrxSe3 single crystals with nominal x values ranging between 0 and 0.025. X-ray diffraction analyses excluded the presence of additional phases. Analysis of the transport and thermoelectric properties reveal strontium to be an acceptor in Bi2Se3. A strong interaction of strontium with native defects in the host structure is demonstrated on varying the doping efficiency. Strontium doped single crystals that crossover to p-type conductivity were inhomogeneous on a large scale. Strontium is a notable doping element for tuning the electron

concentration in Bi2Se3 since it matches the structure and increases the mobility of free carriers in Bi2Se3.

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