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Absorption edge of SnS2 polytypes
Solid State Communications, Vol. 54, No. 3, pp. 283-285, Printed in Great Britain.
1985.
0038-1098/85 $3.00 + .OO Pergamon Press Ltd.
ABSORPTION EDGE OF SnSa POLYTYPES R. Bacewicz, B. Palosz, W. Palosz and S. Gierlotka Jnstitute of Physics, Warsaw Technical University, Koszykowa 75,00-662 Warsaw, Poland (Received 3 1 July 1984 by M. Balkanski)
The fundamental absorption edge for the basic and large period polytypes of SnSa has been measured. The results indicate a weak dependence of the band gap on polytypism. Qualitative explanation of this fact is given. 1. INTRODUCTION VARIATION OF PHYSICAL PARAMETERS of polytype crystals with the change of their structure was reported in literature for several materials: ZnS [l] , Sic [2], CdIa [3], PbIa [4, 51. The effect of poly typism on the band structure of such materials is a problem of great interest. SnSz is a semiconductor with CdI,-type structure and it occurs in a number of structural modifications differing in the lattice period c and in the stacking of layers in the cell. The energy band structure of SnSz has been subject of theoretical and experimental investigations. Powell [6] found, from the absorption studies, the difference in the band gap of 2H and 4H polytypes of 0.1 eV for the direct gap and 0.14eV for the indirect one. These results are in keeping with the band structure calculations [7]. Acharya and Srivastava [8] reported drastic changes of the band gap between W, 4H, 24H and 24R polytypes. The aim of this note is to report the fundamental absorption edges for basic structures of SnS? : W, 4H and 18R, and for some large period polytypes. 2. EXPERIMENT The crystals of SnSa were grown from vapour phase by the method of chemical transport [9]. Growth experiments were performed in close silica ampules of inner diameter 10-l 5 mm and of length 8-13 cm. The ampules were charged with 2-3g of Sn& and with desired amount of Sn14 powder. An average concentration of the transporting agent was 8 mg cme3. Temperature of the charge was in the range 850-1020K; undercooling was IO-30 K. Golden-yellow plate shaped single crystals with dimensions from 1 x 1 x 0.01 mm3 to 10 x 20 x 0.5 mm3 were obtained, The crystals were examined by X-rays. A cylindrical camera of 43mm radius and a collimator of an aperture 0.7 mm were used. The crystals were oscillated around the a* axis in a range y- 15-30’; 7 is the angle between the incident beam (CoK radiation) and the c axis. The two basal planes of the crystal were analyzed separately. The method used
to determine the layer stackings of the polytypes of SnSz is described elsewhere [IO]. It is rare to obtain large single crystals having an uniform structure in the whole volume; frequently several polytypes occur in coalescence in crystal or a polytype occurs with disorder. The samples used in the present study had the same structure on both basal faces and it was assumed that they have similar structure in the bulk. The polytypes W, 4H, 18R and 84R were pure structures, a small amount of the structure 2H accompanied the polytypes 74H and 144R. The samples used for optical measurements were high quality as grown crystal plates of thickness ranging from 5 pm to 50 pm. The transmission was measured at room temperature, in a standard optical set-up with a grating monochromator and a photomultiplier as a detector. The reflection coefficient was taken constant for different polytypes. 3. RESULTS AND DISCUSSION The range of reliably measured absorption coefficient depends on a sample thickness (ard 2 1 condition). As the crystal thickness changes from crystal to crystal, the absorption curves measured for different polytypes cover different ranges of the absorption coefficient (Fig. 1). From this figure is seen that the absorption edges for large period polytypes are located between the curves for 2H and 4H basic polytypes. All the curves show some “convergence” effect at higher absorption level. The energy gap determined and the identification of direct and indirect electron transitions from the absorption edge data is usually made by the fitting of the classical expressions of Bardeen et al. [ 1l] . We did not use this procedure because of the limited range of the measured absorption coefficient. As a matter of fact, such an analysis seems to be questionable taking into account exciton effects which influence absorption spectra of SnSa -like semiconductors [5] . For comparison we have collected the photon energies corresponding to the absorption level of 1OOOcm” in Table 1. The energy difference between 2H and 4H
283
ABSORPTION
284 Table I. Structures
of
EDGE OF SnSa POLYTYPES
Sn& polytypes and their absorption
Vol. 54, No. 3
edges for 1000 cm-’
sample symbol
Ramsdell notation
Layer sequence of polytype cell t-o-f notation Zhdanov notation
absorption eV
a b c d
2H 4H 18R 74H*
11
0
(:2212)s (12(11),12),12(11),12121112
iflf5f
113
CflfSf
lCol4f
2.345 2.252 2.301 2.305
lf5f
l(o)2
edge
flf5flo e
84R*
(12121112(11),12122122)3
Wf
f
144R
((121112),121212111212
Wf~flo)2cflf~f1)2o
2H+4H 18R + d.
(1 l)6 12)3 11+22 1212 + disorder
o+t f lf5f 1 + disorder
If
lf2f2f
l(o)zf
If5
2.285
tflfW3
g
h
f lfsf
l(o)6
2.320 1213
2.273 2.302
*the structure estimated approximately d. = disorder
--‘--
au-4 144R
_..-..-.
2,,+&,,
-...-...-
18Rdisordered
----
2.1
a
I
,
2.2
2.3
2.6
PHOTON
Fig. 1. Absorption
2.5
ENERGY , eV
edge for different structures of SnS2.
curves (0.09 eV) is close to the direct gap difference for these structures (0.1 eV at 273 K) as determined by Powell [6]. It increases for lower values of the absorption coefficient where indirect transitions take place and the appropriate gap difference is 0.14eV [6]. The data presented indicate that the band gap difference between various polytypes of SnS, is of the order of 0.1 eV. It is opposite to the results reported by Acharya et al. [8] who found rather drastic changes of band gaps; from 2.18eV for W, 1.89eV for 4H to 0.92eV for 24H. Those values were deduced from the
temperature dependence of conductivity and it seems that, at least, the lowest of them can be attributed to some minor density of states (perhaps extrinsic), and not to the band density which appears to be relatively weakly affected by polytypism. The present results are consistent with the YoffeRegel rule [12] , well known in physics of disordered materials: short range order is decisive for basic physical properties of solids; By virtue of this rule, one should not expect a large change of the fundamental band gap in different structural modifications of a solid if the coordination number of constituent atoms is preserved. This condition is satisfied in MX2 structures similar to Cd12: PbIa, SnSe2, SnS2, where the coordination around metal ions is always octahedral. In contrary to polytype structure of this type, there exists a number of polytype materials such as TaS2 or TaSe2 where coordination around metal is either prismatic and/or octahedral [ 131. As a result, drastic changes in the band structure of different polytypes have been observed [ 141. The decisive role of the short range order in determining the magnitude of the band gap of SnS2 is also confirmed by the absorption edge for 18R structure with some disordering, which has practically the same position as for the 18R perfectly ordered structure (curves c and h in Fig. 1). As discussed elsewhere [ 151, complex polytype structures of MX2 type may be regarded as multiphase structures i.e. the structures intermediate between the basic polytypes: 2H, 4H, and 18R for SnS2 [lo] . Table 1 gives the polytypes measured in this experiment, where the structures of polytypes are represented by stackings of Zhdanov numbers and of molecular layers t-o-f. In this notation, the symbols o, t and flf5fl represent the structures W, 4H and 18R, respectively.
ABSORPTION
Vol. 54, No. 3
EDGE OF S&
The polytypes 74H and 144R, constructed of o and flfsfl stackings, may be regarded as intermediate 2H18R structures; the polytype 84R is three phase structure having stackings o, t and flf5fl. As seen in Fig. 1 the cmves for 74H and 144R (d and f curves) lie between those for 2H and 18R (a and c), the absorption in 84R polytype (e) is intermediate between 4H and 18R (b,c). The above relations seem to confirm the multiphase model of polytype structures: the structures which are a mixture of simple structures have properties intermediate between those of components. Under these circumstances preparation of samples of desired parameters seems to be possible, however, the range of the change of the parameters is limited by the properties of component phases.
3. 4. 5. 6. 7. 8. 9. 10. 11.
12. REFERENCES 1. 2.
0. Brafman & LT. Steinberger, Phys. Rev. 143, 501 (1966). WI. Knippenberg, Philips Rex Rep. 18, 161 (1963).
13. 14. 15.
POLYTYPES
285
A.M. Fernandez & O.N. Srivastava,J. Appl. Ciyst. lo,32 (1977). E. Doni, G. Grosso, G. Harbeke, E. Meier & E. Tosatti, Phys. Stat. Sol. (b) 68,569 (1975). Rao Meera & O.N. Srivastava, Solid State Commun. 35,801 (1980). M.J. Powell, J. Phys. C: Solid State Physics 10, 2967 (1977). M.J. Powell, E.A. Marseglia & W.Y. Liang.,J. Phys. C: Solid State Physics 11,895 (1978). S. Acharya & O.N. Srivastava, Phys. Stat. Sol. (a) 56, Kl (1979). H. Wiedemeier & G.J. Csillag, J. Crystal Growth 46, 189 (1979). B. Palosz, W. Palosz & S. Gierlotka, Acta Cyst., submitted. J. Bardeen, F.J. Blatt & L.H. Hall, Photoconductivity Conference, 1956, (eds. R. Breckenridge, B. Russel & E. Hahn, New York: Wiley). A.F. Yoffe & A.R. Regel in Progress in Semiconductors vol. 4, 1960, Heywood, London, p. 234. J.A. Wilson & A.D. Yoffe, Adv. Phys. 18, 193 (1969). L.F. Mattheiss, Phys. Rev. B8,3719 (1973). B. Palosz, Phys. Stat. Sol. (a) 81, 11 (1983).
1985.
0038-1098/85 $3.00 + .OO Pergamon Press Ltd.
ABSORPTION EDGE OF SnSa POLYTYPES R. Bacewicz, B. Palosz, W. Palosz and S. Gierlotka Jnstitute of Physics, Warsaw Technical University, Koszykowa 75,00-662 Warsaw, Poland (Received 3 1 July 1984 by M. Balkanski)
The fundamental absorption edge for the basic and large period polytypes of SnSa has been measured. The results indicate a weak dependence of the band gap on polytypism. Qualitative explanation of this fact is given. 1. INTRODUCTION VARIATION OF PHYSICAL PARAMETERS of polytype crystals with the change of their structure was reported in literature for several materials: ZnS [l] , Sic [2], CdIa [3], PbIa [4, 51. The effect of poly typism on the band structure of such materials is a problem of great interest. SnSz is a semiconductor with CdI,-type structure and it occurs in a number of structural modifications differing in the lattice period c and in the stacking of layers in the cell. The energy band structure of SnSz has been subject of theoretical and experimental investigations. Powell [6] found, from the absorption studies, the difference in the band gap of 2H and 4H polytypes of 0.1 eV for the direct gap and 0.14eV for the indirect one. These results are in keeping with the band structure calculations [7]. Acharya and Srivastava [8] reported drastic changes of the band gap between W, 4H, 24H and 24R polytypes. The aim of this note is to report the fundamental absorption edges for basic structures of SnS? : W, 4H and 18R, and for some large period polytypes. 2. EXPERIMENT The crystals of SnSa were grown from vapour phase by the method of chemical transport [9]. Growth experiments were performed in close silica ampules of inner diameter 10-l 5 mm and of length 8-13 cm. The ampules were charged with 2-3g of Sn& and with desired amount of Sn14 powder. An average concentration of the transporting agent was 8 mg cme3. Temperature of the charge was in the range 850-1020K; undercooling was IO-30 K. Golden-yellow plate shaped single crystals with dimensions from 1 x 1 x 0.01 mm3 to 10 x 20 x 0.5 mm3 were obtained, The crystals were examined by X-rays. A cylindrical camera of 43mm radius and a collimator of an aperture 0.7 mm were used. The crystals were oscillated around the a* axis in a range y- 15-30’; 7 is the angle between the incident beam (CoK radiation) and the c axis. The two basal planes of the crystal were analyzed separately. The method used
to determine the layer stackings of the polytypes of SnSz is described elsewhere [IO]. It is rare to obtain large single crystals having an uniform structure in the whole volume; frequently several polytypes occur in coalescence in crystal or a polytype occurs with disorder. The samples used in the present study had the same structure on both basal faces and it was assumed that they have similar structure in the bulk. The polytypes W, 4H, 18R and 84R were pure structures, a small amount of the structure 2H accompanied the polytypes 74H and 144R. The samples used for optical measurements were high quality as grown crystal plates of thickness ranging from 5 pm to 50 pm. The transmission was measured at room temperature, in a standard optical set-up with a grating monochromator and a photomultiplier as a detector. The reflection coefficient was taken constant for different polytypes. 3. RESULTS AND DISCUSSION The range of reliably measured absorption coefficient depends on a sample thickness (ard 2 1 condition). As the crystal thickness changes from crystal to crystal, the absorption curves measured for different polytypes cover different ranges of the absorption coefficient (Fig. 1). From this figure is seen that the absorption edges for large period polytypes are located between the curves for 2H and 4H basic polytypes. All the curves show some “convergence” effect at higher absorption level. The energy gap determined and the identification of direct and indirect electron transitions from the absorption edge data is usually made by the fitting of the classical expressions of Bardeen et al. [ 1l] . We did not use this procedure because of the limited range of the measured absorption coefficient. As a matter of fact, such an analysis seems to be questionable taking into account exciton effects which influence absorption spectra of SnSa -like semiconductors [5] . For comparison we have collected the photon energies corresponding to the absorption level of 1OOOcm” in Table 1. The energy difference between 2H and 4H
283
ABSORPTION
284 Table I. Structures
of
EDGE OF SnSa POLYTYPES
Sn& polytypes and their absorption
Vol. 54, No. 3
edges for 1000 cm-’
sample symbol
Ramsdell notation
Layer sequence of polytype cell t-o-f notation Zhdanov notation
absorption eV
a b c d
2H 4H 18R 74H*
11
0
(:2212)s (12(11),12),12(11),12121112
iflf5f
113
CflfSf
lCol4f
2.345 2.252 2.301 2.305
lf5f
l(o)2
edge
flf5flo e
84R*
(12121112(11),12122122)3
Wf
f
144R
((121112),121212111212
Wf~flo)2cflf~f1)2o
2H+4H 18R + d.
(1 l)6 12)3 11+22 1212 + disorder
o+t f lf5f 1 + disorder
If
lf2f2f
l(o)zf
If5
2.285
tflfW3
g
h
f lfsf
l(o)6
2.320 1213
2.273 2.302
*the structure estimated approximately d. = disorder
--‘--
au-4 144R
_..-..-.
2,,+&,,
-...-...-
18Rdisordered
----
2.1
a
I
,
2.2
2.3
2.6
PHOTON
Fig. 1. Absorption
2.5
ENERGY , eV
edge for different structures of SnS2.
curves (0.09 eV) is close to the direct gap difference for these structures (0.1 eV at 273 K) as determined by Powell [6]. It increases for lower values of the absorption coefficient where indirect transitions take place and the appropriate gap difference is 0.14eV [6]. The data presented indicate that the band gap difference between various polytypes of SnS, is of the order of 0.1 eV. It is opposite to the results reported by Acharya et al. [8] who found rather drastic changes of band gaps; from 2.18eV for W, 1.89eV for 4H to 0.92eV for 24H. Those values were deduced from the
temperature dependence of conductivity and it seems that, at least, the lowest of them can be attributed to some minor density of states (perhaps extrinsic), and not to the band density which appears to be relatively weakly affected by polytypism. The present results are consistent with the YoffeRegel rule [12] , well known in physics of disordered materials: short range order is decisive for basic physical properties of solids; By virtue of this rule, one should not expect a large change of the fundamental band gap in different structural modifications of a solid if the coordination number of constituent atoms is preserved. This condition is satisfied in MX2 structures similar to Cd12: PbIa, SnSe2, SnS2, where the coordination around metal ions is always octahedral. In contrary to polytype structure of this type, there exists a number of polytype materials such as TaS2 or TaSe2 where coordination around metal is either prismatic and/or octahedral [ 131. As a result, drastic changes in the band structure of different polytypes have been observed [ 141. The decisive role of the short range order in determining the magnitude of the band gap of SnS2 is also confirmed by the absorption edge for 18R structure with some disordering, which has practically the same position as for the 18R perfectly ordered structure (curves c and h in Fig. 1). As discussed elsewhere [ 151, complex polytype structures of MX2 type may be regarded as multiphase structures i.e. the structures intermediate between the basic polytypes: 2H, 4H, and 18R for SnS2 [lo] . Table 1 gives the polytypes measured in this experiment, where the structures of polytypes are represented by stackings of Zhdanov numbers and of molecular layers t-o-f. In this notation, the symbols o, t and flf5fl represent the structures W, 4H and 18R, respectively.
ABSORPTION
Vol. 54, No. 3
EDGE OF S&
The polytypes 74H and 144R, constructed of o and flfsfl stackings, may be regarded as intermediate 2H18R structures; the polytype 84R is three phase structure having stackings o, t and flf5fl. As seen in Fig. 1 the cmves for 74H and 144R (d and f curves) lie between those for 2H and 18R (a and c), the absorption in 84R polytype (e) is intermediate between 4H and 18R (b,c). The above relations seem to confirm the multiphase model of polytype structures: the structures which are a mixture of simple structures have properties intermediate between those of components. Under these circumstances preparation of samples of desired parameters seems to be possible, however, the range of the change of the parameters is limited by the properties of component phases.
3. 4. 5. 6. 7. 8. 9. 10. 11.
12. REFERENCES 1. 2.
0. Brafman & LT. Steinberger, Phys. Rev. 143, 501 (1966). WI. Knippenberg, Philips Rex Rep. 18, 161 (1963).
13. 14. 15.
POLYTYPES
285
A.M. Fernandez & O.N. Srivastava,J. Appl. Ciyst. lo,32 (1977). E. Doni, G. Grosso, G. Harbeke, E. Meier & E. Tosatti, Phys. Stat. Sol. (b) 68,569 (1975). Rao Meera & O.N. Srivastava, Solid State Commun. 35,801 (1980). M.J. Powell, J. Phys. C: Solid State Physics 10, 2967 (1977). M.J. Powell, E.A. Marseglia & W.Y. Liang.,J. Phys. C: Solid State Physics 11,895 (1978). S. Acharya & O.N. Srivastava, Phys. Stat. Sol. (a) 56, Kl (1979). H. Wiedemeier & G.J. Csillag, J. Crystal Growth 46, 189 (1979). B. Palosz, W. Palosz & S. Gierlotka, Acta Cyst., submitted. J. Bardeen, F.J. Blatt & L.H. Hall, Photoconductivity Conference, 1956, (eds. R. Breckenridge, B. Russel & E. Hahn, New York: Wiley). A.F. Yoffe & A.R. Regel in Progress in Semiconductors vol. 4, 1960, Heywood, London, p. 234. J.A. Wilson & A.D. Yoffe, Adv. Phys. 18, 193 (1969). L.F. Mattheiss, Phys. Rev. B8,3719 (1973). B. Palosz, Phys. Stat. Sol. (a) 81, 11 (1983).