Preparation and some physical properties of Bi2Se3−xSx mixed crystals

Journal of Crystal Growth 69 (1984) 301—305 North-Holland, Amsterdam

301

PREPARATION AND SOME PHYSICAL PROPERTIES OF Bi2Se3

MIXED CRYSTALS

~

R. NOVOTNi’, P. LO~tAK,L. BENE~and J. HORAK University of Chemical Technology, 53210 Pardubice, Czechoslovakia

Received 24 April 1984; manuscript received in final form 25 September 1984

Single crystals of Bi2Se3~S~ (x = 0—0.45) were prepared by the modified Bridgman method. The homogeneity of the crystals was proved by X-ray fluorescence analysis and measurement of reflectivity spectra. Measurement of the crystal lattice parameters by the powder X-ray diffraction method showed that with increasing sulfur content the value of the lattice parameter c increases and a decreases. From the measurement of reflectivity in IR region, the electrical conductivity and the Hall coefficient, some basic physical parameters of Bi25e3_ ~ crystals were obtained which characterize the crystals as semiconductors.

1. Introduction

2. Experimental

In spite of the fact that layered crystals of A~B~ have been thoroughly studied in the last few years, only a few papers have been devoted to the Bi2Se3~S~ compounds. The phase diagram of the Bi2Se3—Bi2S3 system was studied in refs. [1—3]. According to Beglaryan and Abrikosov [1] solid solutions of Bi2S3 and Bi2Se3 are formed in the concentration region of 0—16 mol% Bi2S3 the authors [1] described also the existence of defined compounds of Bi2Se3S and BiSeS2. Neumann and Scheideger [3] found the existence of Bi2Se3—Bi2S3 solid solutions in the region of 0—6.6 mol% Bi2S3. Some physical parameters (thermal conductivity, microhardness) of polycrystalline materials of the Bi2Se3—Bi2S3 system were studied in ref. [4]. All the studies relating to the Bi2Se3_~S~ compounds [1—4]were carried out with polycrystalline samples. In our paper we describe the growth of mixed Bi2Se35S~single crystals and their characterization (lattice parameters, homogeneity) and the resuits of the study of optical and transport properties

2.1. Preparation of single crystals

Bi2Se3~S~single crystals were prepared from Bi and Se of 5N purity and S of 4.5N purity. The ____________

([mm]

100 1 2

‘

200

o

:

:

300 400

o

6 500 “

•

_____________

T[K]

1100

800

500

600

Fig. 1. A schematic picture of the furnace for the growth of Bi2Se3_~S~ mixed crystals with the temperature gradient used for the growth: (1) thermal insulation (asbestos); (2) resistance heating; (3) ceramic tube; (4) stainless-steel tube; (5) asbestos ring; (6) copper tube; (7) cooling.

0022-0248/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

302

R. Novolnj et a!.

/

Preparation and some physical properties of Bi

~

2Se3 —

synthesis of the compounds was carried out in conical quartz ampoules evacuated to iO~ Pa. The homogenization of the batches and synthesis of the compounds was carried out in a horizontal furnace at 1073 K for 48 h. The mixed crystals were grown by a vertical Bridgman method. Before pulling, the ampoules containing the melt were heat-treated at 1073 K for 24 h and when the melt filled the tip of ampoule, the ampoules were lowered through the temperature gradient shown in fig. 1 at a rate of 0.8 mm/h. This preparation gave homogeneous single crystals with well developed cleavage faces shown in fig. 2. The cleavage faces were identified by the back-reflection Laue method (fig. 3) to have the {0001 } orientation. These faces, being perpendicular to the c-axis, were always parallel with the direction of pulling, i.e. with the ampoule axis.

Fig. 2. Bi 2 Sc., ~S ~ Single crystal. 2.2.

Chemical analysis of Bi2Se?

—

,.S~crystals

The mixed crystals were analyzed using the energy-dispersive X-ray analyzer (TRACOR 2000) equipped with a Si(Li) detector (with a resolution of 148 eV at Mn Ka). The content of Bi and Se was determined experimentally and the content of S was taken as the rest to 100%. Thoroughly homogenized polycrystalline samples of Bi2Se3~S5with a known content of sulfur (x 0.0—0.5) were used as standards. In this way the composition of the studied Bi2Se3_5S,~ single crystals was found to correspond to x 0, 0.05 3, =

(, ) _______

=

of

~

lattice

parameters

The lattice parameters of the prepared single crystals were determined on powder samples by Table I Lattice parameters of Bi2Se3_~S~, crystals Sample No. 1 2 3

Fig. 3. Back-reflection Laue picture of the natural cleavage face of Bi 2Se2 74S026 single crystal.

of

x 0.00 0.053 0.26 0.44

a (A) 4.1343 4.1354 4.1248 4.112~

c

(A) 28.6115 28.606~ 28.551~ 28.468~

V 3) (A 423.52 423.67 420.69 416.90

R. Novotnj’ et a!. / Preparation and some physical properties of Bi

2 Se3 —

X-ray diffraction analysis using a HZG-4B diffractometer (VEB Freiberger Prazisionsmechanik, DDR). The diffraction maxima were measured by a step procedure using a step of 0.01°.The measurement was carried out in the range of 29 5—100~ with Cu Ka radiation in the range of 5—45° and Ka1 radiation in the range of 45—100°; the Kfl radiation was removed by a Ni filter. The calibration of the diffractometer was carried out with polycrystalline Si. The obtained diffraction lines were indexed according to ref. [5] and the values of the lattice parameters a and c of the mixed crystals were calculated by the least squares method. The calculated values of the lattice parameters and the unit cell volume are shown in table 1.

S~

303

1 23 4 5 6

—i~i

1 2—4---oj

~

~—+--°

I

I

5__f_~

=

6_4..o/ 7

2 34 56

2.4. Reflectivity measurements

The reflection spectra of Bi2Se35S~ single crystals were measured in the wavelength range of 2—25 ~tm using an infrared spectrophotometer Perkin-Elmer, model 684. The measurement was carned out on natural cleavage faces (0001 } of the crystals at room temperature with unpolarized light at an angle of incidence on the sample of 6.5°. The results of the reflectivity measurement in the plasma resonance region of Bi2Se3.~5S~ crystals for the orientation E I c are shown in fig. 4. The

I

I

I

I

~ [tim] Fig. 5. Reflectivity spectra of Bi2Se256S0~crystal measured at 294 K on the natural crystal face along the axis of the crystal growth. The curves were shifted relative to each other in order 4

8

12

to eliminate the overlap of the curves.

reflectivity measurement was used also for checking the homogeneity of the prepared single crystals. A perfect homogeneity of the crystals is manifested in fig. 5 by the results of the reflectivity measurement along the length of the Bi2Se256S044 crystal.

80

2.5. Measurement of transport coefficients

70

On theconductivity, samples ofHall dimensions of 8positions Xmeasured 3 X 0.1—0.3 3 the electrical conductivity was in Electrical coefficient and of R (A) mm

R 1%]

Table 2 30

minimum of Bi 2Se3...~S~ crystals at 300 K

20 4

6

I I _____________ 8 10 12

I

14

___

16 __________ 18 A

[~jm]

Sample No.

X

~

1

0.00

(Q’cm~) 2600

2 3 ~

0.053 0.26 0.44

2835 3236 3428

3/A.s) RH(BIIc) (cm 0.237

(tim) Amin

0.208 0.173 0.158

12.4 11.9 10.5

13.1

Fig. 4. Reflectivity spectra of Bi 2Se3.~S~ single crystals in the region of plasma resonance frequency measured at 294 K: x = 0.000 (curve I), x = 0.053 (curve 2), x = 0.260 (curve 3), x = 0.440 (curve 4).

R. Novotn~et a!.

304

/

Preparation and some physical properties of Bi

2Se3... ~

the direction perpendicular to the trigonai c axis ~ The Hall coefficient R~ was measured for the magnetic induction B ii c at room temperature using the AC method with 170 Hz and B 1.1 T. The values of o~, R~(Bic) and the results of the chemical analysis and the position of the reflectivity minimum are shown in table 2.

frequency dielectric constant, k is the absorption index, ca is the frequency of radiation, ~ is the plasma resonance frequency and TOPi is the optical relaxation time. By fitting the measured reflectivity spectra R(X) with a theoretical curve, the values of e~,oi~,and T°~were estimated. From the value of as,, the ratio of N/rn1 was determined using the relation 2, (4) ca~(EJ c) (Ne2/E~om1)~

=

3. Results and discussion The Bi 2Se3.. ~S5single crystals prepared by the described method can be easily cleaved along the trigonal c-axis; with increasing sulfur content their hardness increases. The natural cleavage faces (0001) possess a mirror-like appearance. The reflectivity measurement on the natural cleavage faces along the crystal length gives the same value of the minimum of R(X) and also the same course of R(X) in the plasma resonance region (fig. 4j; only at the tip of the crystal there is a small gradient of concentration of current carriers. These results can be taken as evidence of crystal homogeneity and perfect distribution of sulfur in the bulk crystal. The homogeneity of the distribution of Se and S in the crystals was confirmed also by the X-ray fluorescence analysis. The reflectivity spectra R(X) for the samples 1—4 were evaluated using the Drude—Zener [6] theory expressed by the following relations:

=

where N is the free-carrier concentration, rn1 is the effective mass in the direction perpendicular to the c-axis. The results obtained from the analysis of the reflectivity spectra, i.e. e~, N/rn1 and Tor’t are shown in table 3. From the obtained ~ values we can see that an increase in the sulfur content in the Bi2Se3.~S~ crystals decreases slightly the high-frequency dielectric constant. For pure Bi2Se3, ~ = 29.8 while for Bi2Se256Se044, c~ 27.8. This result is in accordance with a concept according to which an increase in ionieity due to the incorporation of S atoms into the Bi2Se3 crystals results in a decrease of the refractive index. If we take the approximation that the conduction band in Bi2Se3.~S~ crystals can be described by the single-valley model used for n-Bi2Se3 [7] and we consider the presence of only one type of current carrier, neglecting thus a possible splitting of the conductivity band, then we can use the relations: ~,

=

n2_k2={1_{(a/wp)2+(1/~pT0N)2I~},(1)

R~1=A]~, 2nk = c/~aT°~ [(/)2 + (l/capT0~i)2J R = (n — 1)2 + k2/(n + 1)2 + k2,

where n is the refractive index,

E,z

—

(2)

(5)

(6)

t, (N/m1)eR~ =A1(m1) for the calculation of A~js,A

(3)

is the high-

From the values of

1/m1 and ‘r~. N/rn1

and electrical con-

Table 3 Parameters of Bi2Se3...~S~ crystals calculated from transport coefficients and optical measurements Sample No. I

x

e~

N/rn ~ 3) (1026 1.73 m

(102 m2 V~s1)

(—)

A1/m ~

(10~~s)

0.00

w~(E ~ c) (10w 1.36 s~)

(10~~ s)

(—) 29.8

6.0

6.16

6.57

5.3

2 3 4

0.53 0.26

29.1 28.4 27.8

1.43 1.52 1.71

1.87 2.06 2.55

5.8

5.6

5.90 5.60

4.2

5.42

6.23 5.71 6.45

5.4 5.5 4.8

0.44

/ Preparation and some physical properties of Bi2Se3 — ~S5

R. Novotn5~e a!.

ductivity a1, the relaxation time T& was 2 ), where e isalso the calculated (Tet = a1 (m1/N )(1/e electron charge). The value of TOP( decreases slightly with increasing sulfur content, whereas T& has nearly the same value in the whole concentration region. As can be seen from the results of the calculations shown in table 3, with increasing sulfur content the mobility of current carriers decreases; a decrease in the value of A1~tis associated both with increasing concentration of current carriers and with increasing energy gap E5 of the Bi 2Se3_~S5crystals due to the substitution of Se atoms by S atoms. This substitution is associated with a decrease in the value of the lattice parameter c in the direction of the tnigonal axis, and moreover, with a decrease in the parameter a (table 5). Therefore, the unit cell volume V also decreases with increastng S content. In the lattice of n-type Bi2Se3 we can suppose the presence of selenium vacancies [8], because the measured density is lower than the theoretical one. Therefore, if the sulfur atoms are positioned in the anion sublattice of the Bi2Se35S5 crystals, we can explain the increase in the concentration of free electrons with increasing sulfur content in these .

.

305

crystals in the created following The of sulfur vacancies perway: S atom in number Bi 2Se3..5S5 crystals is higher than the number of selenium vacancies created per Se atom, i.e. [V~’J/[Sse]> [Vs~j/[Sese]. Therefore, during the growth of Bi2Se3~S~mixed crystals, under the described conditions, with increasing sulfur content the total concentration of vacancies increases and thus the concentration of free electrons compensating positive charges of the vacancies also increases.

References [1] ML. Beglaryan and N.Ch. Abrikosov, Doki. Akad. Nauk SSSR 128 (1959) 345. [2] J.B. D’yachkova, Tr. Inst. Mineral. Geokhim. Kristallok-

him. Redkikh Elementov 7 (1961) 150. [3] G. Neumann and B. Scheideger, Helv. Phys. Acta 40 (1967) 293.

[4] N.Ch. Abrikosov and V.F. Bankina, Izv. Akad. Nauk SSSR, Neorg. Mater. 15 (1979) 1097. [5] H. Gobrecht, K.-E. Boerets and 0. Pantzer, Z. Physik 177 (1964) 68. [610. Madelung, in: Handbuch der Physik, Vol. 20, Ed. S. Flugge (Spnnger, Berlin, 1957). . [7] H. Kohler and G. Landwehr, Phys. Status Sohdi (b) 45 (1971) K109. [81IF. Bogatyrev, A. Vatko, L. Tich~,and J. Horkk, Phys. Status Solidi (a) 22 (1974) K63.

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