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Optical properties of monoclinic selenium
Solid State Communications,Vol.
~
PP. 543—546, 1972. Pergamon Press.
Printed in Great Britain
OPTICAL PROPERTIES OF MONOCLINIC SELENIUM J.C. Knights and E.A. Davis Surface Physics, Cavendish Laboratory, University of Cambridge
(Received 30 May 1972 by R. Loudon)
Optical absorption measurements have been made on crystals of a-monoclinic selenium at low temperatures using polarized light. Features characteristic of Mott—Wannier excitons have been observed and a direct energy gap of 2.53eV deduced.
EXPERIMENTAL PROCEDURES
these axes*.
CRYSTALS of monocliriic selenium were grown by evaporation of solutions of selenium in carbon disuiphide. Microscopic examination of the crystals using the criteria given by lizima et al.’ showed them to be of the a form. The crystals grew in the form of hexagonal platelets with thicknesses ranging from 0.041tm to 2~tm and maximum lateral dimensions of 0.2 mm. The hexagonal faces are (101) planes (using the unit 2) and the axes coplanar with this cell of Burbank face are a and b. Individual crystals were transferred to fused silica substrates and masked with brass foil or were freely suspended over masks.
RESULTS The spectral variation of the absorption coefficient measured at 290°K using unpolarized light is shown in Fig. 1. This curve represents the best fit to transmission data on eight crystals of different thicknesses — the inset shows the variation of (ah
~,)2
with photon energy.
On cooling to 80°K a broad absorption peak was observed at 2.56eV in freely mounted crystals (2.60—2.62eV in substrate mounted crystals) for one direction of polarization. Further cooling to 5°K produced marked sharpening of this peak and, as shown in Fig. 2, a well-defined shoulder appeared at 2.48 eV and a weaker feature at approximately 2.58eV. Figure 3 shows that structure also appears for the other direction of polarization.
Optical absorption measurements were made in a conventional single beam system employing phase sensitive detection. The masked crystals were mounted vertically in a helium exchange gas chamber which was in turn mounted on a liquid helium reservoir. Provision was made to rotate the crystals out of the optical path while at low temperatures to enable measurement of the incident light under identical conditions. A temperature controller, with a differential gold— iron thermocouple as sensor, was used to keep the temperature constant during measurements. Two Glan/Thompson prisms were used to determine the direction of the crystal axes in situ. and all measurements were performed with the incident light polarized along one or other of
DISCUSSION The observed room-temperature variation of the absorption coefficient with photon energy is similar to that reported previously by Caywood and Taynai; however the linear variation of * The method of determining these axes was optical and did not permit distinction between a and b.
543
544
OPTICAL PROPERTIES OF MONOCLINIC SELENIUM
log o.(cm’)
cbsorption
id
c~n:~t
/
I -
/
/
1~
~‘ol. 11, No. 4
/1
/ 5q/
2~5
3~ photon energy(eV).—.
2
~
/
5x10
25
26 27 photon energy(eV)
/
(~.hy)____________________________________
(x10~crn’l)
(b)
7 7 0” /
40•
Flo. 2. Variation of absorption coefficient with temperature in a-monoclinic selenium in the range 5—77°K. -I
)
~(cm
I
20
I
photon eriergy(eV)
10~•
B/I1~
/
.
5~10~• FIG. 1. (a) Room temperature absorption edge of
a-monoclinic selenium. 2 against photon-energy. (b) Plot of (ahv)
2---
(ahii) with h21 would seem to point to direct allowed transitions between bands separated by a gap of “ 2.53 eV, as opposed to the 2.3 eV proposed by these authors.
-
I
-
/ /
/
_
24
25
2-6
2-7 2~8 photon energy(~V)
FIG. 3. Absorption edge at 5~Kin a-mortoclinic
selenium with light polarized parallel to a and b.
Vol. 11, No. 4
OPTICAL PROPERTIES OF MONOCLINIC SELENIUM
The peak labelled A in Fig. 3 shows a temperature quenching typical of an exciton. Support for the excitonic nature of both this peak and that labelled B has been obtained from electrotransmission measurements made by 4 These measurements have allowed an Bordas. estimate of 20meV to be made for the binding energy of the exciton at B. If the shoulder, C, is assumed to be the n = 2 exciton in a hydrogenic series with A as the ground state, this would give a ground state binding energy of the order 30 meV for the stronger exciton. The shift in peak positions between freely and substrate mounted crystals points to a relatively high negative pressure coefficient for these excitons. This coefficient has been measured explicitly for the exciton at A by Grant.5 using hydrostatic pressure at 80°K, the result being ‘i-’ —40 x 10’ eV/bar. This value is approximately three times as large as that for the exciton in trigonal selenium6 and considerably larger than that found in other materials studied in this laboratory. a-monoclinic selenium is a molecular crystal composed of puckered SeB rings with weak intermolecular bonding. Recent calculations by Chen7 together with measurements of transport properties and ultraviolet reflectivity have been used by Dalrymple and Spear8 to propose simplified energy band schemes for both monoclinic selenium and orthohombic sulphur. These are shown in Fig.4. ______________________
orthorhomb~cSulphur E(~V)
cs
ltlt~
—
Of particular significance to the present discussion is that, on this scheme, the lowest interband transitions in monoclinic selenium occur between bands of extended states formed by intermolecular overlap. This is in contrast to the situation in sulphur, where a narrow band of states lies in 0.8eV below the conduction band, in which vibronic interaction leads to polaron formation. Chen has predicted that this band will permit the formation of strongly localized excited states and has suggested that similar states might exist in monoclinic selenium. The results presented above appear to contradict this suggestion of Chen and support the model proposed by Dairymple and Spear. Firstly, the excitons observed have low binding energies typical of Mott—Wannier type excitons. Secondly, the large pressure coefficient points to the excitons and corresponding bands being associated with intermolecular rather than intramolecular bond overlap — it might be expected that a localized ‘molecular’ exciton would be little affected by changes in intermolecular bond lengths. The only point of disagreement with reference 8 is in the value of the band-gap. The existence of an exciton at 2.48eV with a binding energy 20meV points to a band-gap of 2.50eV at 5°K. The small positive temperature coefficient deduced from Fig. 2 would place the band-gap at room temperature at 2.51—2.53eV. This is in good agreement with the intercept of 2.53eV shown in Fig. 1. The transition associated with the exciton at A is at present unidentified.
o’.-monoclintc sqtenium
-
1•~
~////~-_1~J 4043 63
______ _______ ____
__-2-3 &0
116 ~
_[
-
H.B.
jilt
CONCLUSION
-6-5
~.
~
545
~
The fundamental optical edge of a-monoclinic selenium showsabsorption characteristics 11 5
H.&~holebond C~conductionbond
FIG. 4. Energy band schemes for orthohombic sulphur and a-monoclinic selenium proposed by Dalrymple and Spear.8
typical of Coulomb-perturbed allowed transitions between bands of direct extended states. At low temperatures excitons are observed with binding energies in the range 20—30meV, the lowest transitions giving a room-temperature band-gap ‘- 2.53 eV. In agreement with the scheme proposed by Dalrymple and Spear,8 no feature characteristic of a strongly localized excitation has been observed in the region of the band edge.
546
OPTICAL PROPERTIES OF MONOCLINIC SELENIUM
Vol. 11, No. 4
REFERENCES
1.
IIZIMA S., etal. The Physics of Selenium and Tellurium, Proc. of the Int. Symp. Montreal, 1967, (edited by COOPER W.C.), Pergamon (1969).
2. 3.
BURBANK R.D., Acta C,ystallogr. 5, 236 (1952). CAY WOOD J.M. and TAYNAI J.D., J. Phys. Chem. Solids 30, 1573 (1969).
4.
BORDAS J., Ph.D. Thesis, University of Cambridge (1972).
5.
6.
GRANT A.J., unpublished work, University of Cambridge (1971). GRANT A.J., Ph.D. Thesis, University of Cambridge (1970).
7.
CHEN I., Phys. Rev. 32, 1155 (1970).
8.
DALRYMPLE R.J.F. and SPEAR W.E., J. Phys. Chem. Solids 33, 1071 (1972).
Les mesures d’absorption optique ont été effectuées sur des cristaux de sélénium a-monoclinique a basses temperatures en utilisant une lumiére polarisée. Les traits caractéristiques des excitons Mott—Wannier furent observes et un écart energetique entre deux bandes de 2.S3 eV fut deduit.
~
PP. 543—546, 1972. Pergamon Press.
Printed in Great Britain
OPTICAL PROPERTIES OF MONOCLINIC SELENIUM J.C. Knights and E.A. Davis Surface Physics, Cavendish Laboratory, University of Cambridge
(Received 30 May 1972 by R. Loudon)
Optical absorption measurements have been made on crystals of a-monoclinic selenium at low temperatures using polarized light. Features characteristic of Mott—Wannier excitons have been observed and a direct energy gap of 2.53eV deduced.
EXPERIMENTAL PROCEDURES
these axes*.
CRYSTALS of monocliriic selenium were grown by evaporation of solutions of selenium in carbon disuiphide. Microscopic examination of the crystals using the criteria given by lizima et al.’ showed them to be of the a form. The crystals grew in the form of hexagonal platelets with thicknesses ranging from 0.041tm to 2~tm and maximum lateral dimensions of 0.2 mm. The hexagonal faces are (101) planes (using the unit 2) and the axes coplanar with this cell of Burbank face are a and b. Individual crystals were transferred to fused silica substrates and masked with brass foil or were freely suspended over masks.
RESULTS The spectral variation of the absorption coefficient measured at 290°K using unpolarized light is shown in Fig. 1. This curve represents the best fit to transmission data on eight crystals of different thicknesses — the inset shows the variation of (ah
~,)2
with photon energy.
On cooling to 80°K a broad absorption peak was observed at 2.56eV in freely mounted crystals (2.60—2.62eV in substrate mounted crystals) for one direction of polarization. Further cooling to 5°K produced marked sharpening of this peak and, as shown in Fig. 2, a well-defined shoulder appeared at 2.48 eV and a weaker feature at approximately 2.58eV. Figure 3 shows that structure also appears for the other direction of polarization.
Optical absorption measurements were made in a conventional single beam system employing phase sensitive detection. The masked crystals were mounted vertically in a helium exchange gas chamber which was in turn mounted on a liquid helium reservoir. Provision was made to rotate the crystals out of the optical path while at low temperatures to enable measurement of the incident light under identical conditions. A temperature controller, with a differential gold— iron thermocouple as sensor, was used to keep the temperature constant during measurements. Two Glan/Thompson prisms were used to determine the direction of the crystal axes in situ. and all measurements were performed with the incident light polarized along one or other of
DISCUSSION The observed room-temperature variation of the absorption coefficient with photon energy is similar to that reported previously by Caywood and Taynai; however the linear variation of * The method of determining these axes was optical and did not permit distinction between a and b.
543
544
OPTICAL PROPERTIES OF MONOCLINIC SELENIUM
log o.(cm’)
cbsorption
id
c~n:~t
/
I -
/
/
1~
~‘ol. 11, No. 4
/1
/ 5q/
2~5
3~ photon energy(eV).—.
2
~
/
5x10
25
26 27 photon energy(eV)
/
(~.hy)____________________________________
(x10~crn’l)
(b)
7 7 0” /
40•
Flo. 2. Variation of absorption coefficient with temperature in a-monoclinic selenium in the range 5—77°K. -I
)
~(cm
I
20
I
photon eriergy(eV)
10~•
B/I1~
/
.
5~10~• FIG. 1. (a) Room temperature absorption edge of
a-monoclinic selenium. 2 against photon-energy. (b) Plot of (ahv)
2---
(ahii) with h21 would seem to point to direct allowed transitions between bands separated by a gap of “ 2.53 eV, as opposed to the 2.3 eV proposed by these authors.
-
I
-
/ /
/
_
24
25
2-6
2-7 2~8 photon energy(~V)
FIG. 3. Absorption edge at 5~Kin a-mortoclinic
selenium with light polarized parallel to a and b.
Vol. 11, No. 4
OPTICAL PROPERTIES OF MONOCLINIC SELENIUM
The peak labelled A in Fig. 3 shows a temperature quenching typical of an exciton. Support for the excitonic nature of both this peak and that labelled B has been obtained from electrotransmission measurements made by 4 These measurements have allowed an Bordas. estimate of 20meV to be made for the binding energy of the exciton at B. If the shoulder, C, is assumed to be the n = 2 exciton in a hydrogenic series with A as the ground state, this would give a ground state binding energy of the order 30 meV for the stronger exciton. The shift in peak positions between freely and substrate mounted crystals points to a relatively high negative pressure coefficient for these excitons. This coefficient has been measured explicitly for the exciton at A by Grant.5 using hydrostatic pressure at 80°K, the result being ‘i-’ —40 x 10’ eV/bar. This value is approximately three times as large as that for the exciton in trigonal selenium6 and considerably larger than that found in other materials studied in this laboratory. a-monoclinic selenium is a molecular crystal composed of puckered SeB rings with weak intermolecular bonding. Recent calculations by Chen7 together with measurements of transport properties and ultraviolet reflectivity have been used by Dalrymple and Spear8 to propose simplified energy band schemes for both monoclinic selenium and orthohombic sulphur. These are shown in Fig.4. ______________________
orthorhomb~cSulphur E(~V)
cs
ltlt~
—
Of particular significance to the present discussion is that, on this scheme, the lowest interband transitions in monoclinic selenium occur between bands of extended states formed by intermolecular overlap. This is in contrast to the situation in sulphur, where a narrow band of states lies in 0.8eV below the conduction band, in which vibronic interaction leads to polaron formation. Chen has predicted that this band will permit the formation of strongly localized excited states and has suggested that similar states might exist in monoclinic selenium. The results presented above appear to contradict this suggestion of Chen and support the model proposed by Dairymple and Spear. Firstly, the excitons observed have low binding energies typical of Mott—Wannier type excitons. Secondly, the large pressure coefficient points to the excitons and corresponding bands being associated with intermolecular rather than intramolecular bond overlap — it might be expected that a localized ‘molecular’ exciton would be little affected by changes in intermolecular bond lengths. The only point of disagreement with reference 8 is in the value of the band-gap. The existence of an exciton at 2.48eV with a binding energy 20meV points to a band-gap of 2.50eV at 5°K. The small positive temperature coefficient deduced from Fig. 2 would place the band-gap at room temperature at 2.51—2.53eV. This is in good agreement with the intercept of 2.53eV shown in Fig. 1. The transition associated with the exciton at A is at present unidentified.
o’.-monoclintc sqtenium
-
1•~
~////~-_1~J 4043 63
______ _______ ____
__-2-3 &0
116 ~
_[
-
H.B.
jilt
CONCLUSION
-6-5
~.
~
545
~
The fundamental optical edge of a-monoclinic selenium showsabsorption characteristics 11 5
H.&~holebond C~conductionbond
FIG. 4. Energy band schemes for orthohombic sulphur and a-monoclinic selenium proposed by Dalrymple and Spear.8
typical of Coulomb-perturbed allowed transitions between bands of direct extended states. At low temperatures excitons are observed with binding energies in the range 20—30meV, the lowest transitions giving a room-temperature band-gap ‘- 2.53 eV. In agreement with the scheme proposed by Dalrymple and Spear,8 no feature characteristic of a strongly localized excitation has been observed in the region of the band edge.
546
OPTICAL PROPERTIES OF MONOCLINIC SELENIUM
Vol. 11, No. 4
REFERENCES
1.
IIZIMA S., etal. The Physics of Selenium and Tellurium, Proc. of the Int. Symp. Montreal, 1967, (edited by COOPER W.C.), Pergamon (1969).
2. 3.
BURBANK R.D., Acta C,ystallogr. 5, 236 (1952). CAY WOOD J.M. and TAYNAI J.D., J. Phys. Chem. Solids 30, 1573 (1969).
4.
BORDAS J., Ph.D. Thesis, University of Cambridge (1972).
5.
6.
GRANT A.J., unpublished work, University of Cambridge (1971). GRANT A.J., Ph.D. Thesis, University of Cambridge (1970).
7.
CHEN I., Phys. Rev. 32, 1155 (1970).
8.
DALRYMPLE R.J.F. and SPEAR W.E., J. Phys. Chem. Solids 33, 1071 (1972).
Les mesures d’absorption optique ont été effectuées sur des cristaux de sélénium a-monoclinique a basses temperatures en utilisant une lumiére polarisée. Les traits caractéristiques des excitons Mott—Wannier furent observes et un écart energetique entre deux bandes de 2.S3 eV fut deduit.