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Excitations in solid and liquid thallous chloride
Solid State Communications,
Vol. 9, pp. 709—712, 1971.
Pergamon Press.
Printed in Great Britain
EXCITATIONS IN SOLID AND LIQUID THALLOUS CHLORIDE* H.P.R. Frederikse and W.R. Hosler National Bureau of Standards, Washington. D.C. 20234, U.S.A. (Received 8 February 1971 by E. Burstein)
The absorpti on edge of thallous chloride has been measured below and above melting point. In the crystal this edge represents the low energy tail of a strongly absorbing Wannier exciton. The similarity between the shape and temperature dependence of this absorption in the solid and in the liquid states suggests that Wannier-like excitons exist also in liquid thallous chloride.
INTRODUCTION ONE OF the major topics that has recaptured the attention of solid state scientists recently’ is the behavior of non-crystalline solids (amorphous materials, glasses) and liquids.1 2What is so intriguing is the similarity between the electrical and optical properties of the disordered and the ordered states. Quite a few materials (Ge, ~ chalcogenides, V 205, etc.) show semiconductivit~ both in the crystalline in the amorphous phase phase.~5A number of and semiconductors (e.g. Se. T1 6 ~ (This remain semiconductors on melting. that has2Te) to be contrasted with the observation several transition—metal oxides show a semiconductor—metal transition8 when the crystal undergoes only a very small structural change in the solid state.) There is some evidence that the electronic density of states of an amorphous solid or of a liquid may not be so very different from that of the crystalline form of the same material. In the case of liquid metals the nearly-free-electron model yields reasonably good results for the transport properties of charge carriers.’ Experimental studies of the optical reflectivity of several amorphous or glassy semiconductors in the range 0—10eV have shown that most of the detailed structure observed on single crystals is ‘washed out,’ but that many of the qualitative features are maintained.4 How to reconcile this *Research supported by National Aeronautics and Space Administration, U.S.A.
with the fact that the rather sharp Contour of the electronic energy dispersion curves is a direct consequence of the periodic lattice structure of crystalline solids and that this periodicity is lost inthe non-crystalline state is a very difficult problem. A considerable amount of experimental and theoretical work has been focused on the energy gap of semiconductors and insulators in their 9~ This is quite understandamorphous state~ able because the energy gap is a direct consequence of the energy band scheme, and is interpreted conventionally as the extciation of an electron from the valence (filled) band to the conduction (unoccupied) band. As far as optical properties are concerned, the experimental research efforts have been concentrated on the elements Ge, Si, Te and Se, on some Il—V compounds, and quite extensively on the chalcogenide glasses. Although the results have clearly indicated certain trends, comparison of data on different samples of the same material is difficult because most experiments have been performed on thin amorphous films; it can hardly be expected that the degree of non-crystallinity of different films is identical from sample to sample.
709
Consequently, if one wants to explore the electronic structure of disordered materials, in particular, the forbidden energy gap of non-metals there are good reasons for studying the molten
710
EXCITATIONS IN SOLID AND LIQUID THALLOUS CHLORIDE
Vol. 9, No. 10
state. Besides its reproducibility, the fact that one can compare the results gained from experiments on a liquid directly with those obtained on the solidified state is an important advantage. At first it would seem that the choice of an appropriate
temperature; hence the data below the metling point (430°C)refer to recrystallized material. These data reproduce very well the initial results obtained on a single crystal before melting. The S-shaped curve at 447°Cindicates that the sample
material is limitless. However, if one considers reasonable restrictions, it appears that the number actually shrinks considerably. The solid material should be a semiconductor or an insulator with a non-localized electronic structure. This condition excludes all molecular and Van der Waals crystals (usually organic compounds). Nearly all materials of the latter category have melting points below 100°C, while very few of the (ionic or covalent) insulators or semiconductors with long-range electronic structure melt below 200°C. A difficult aspect of many semiconductors — especially those with small energy gaps — is the free carrier absorption which can be quite high at elevated temperature, obscuring the absorption edge. If one furthermore limits the choice to substances whose melting point does not exceed 800 or 900° and whose absorption edge occurs in the visible or near u.v. spectral range (for experimental siniplicity), the number of suitable materials actually has shrunk considerably. In the remaining group. compounds containing TI appear quite frequently,
was part solid and part liquid.
The above ideas have led us to undertake some very simple optical experiments using the crystal TICI, in particular, the measurement of the lower part of the absorption edge at temperatures below and above its melting point (430°C).
involves both TI and Cl-ions. It has been suggested by Kunz ~ that the top of the (filled) valence band corresponds to the Tl~6s2-state, while the bottom of the (empty) conduction band is made up mainly from Tl-6s26p-states. The radius of the exciton ‘orbit’ in TlCl is of the order of 20—40 A (a* = 0.5 x /m* = 0.5 x 30/0.5 30 A), and hence a non-localized Wannier-type description seems to be favored.11 At the same time, the excitation appears to belong more to the TF ions than to the Tl~Cl ‘molecules.’ With respect to the temperature shift, Bachrach states in his thesis:’1 ‘As the temperature is raised, the exciton peak moves to higher energies; however, the peak broadens so that the edge appears to
EXPERIMENT AND DISCUSSION Thallium chloride samples were put in a rectangular quartz cell; the width of this cell was approximately 9mm while the light transversed the smaller dimension (1 mm). This cell was placed in an appropriately shaped lava oven
provided with nichrome wires and Pt—Rh thermocouples. A small vertical temperature gradient caused melting from the top down the recrystallization from the bottom up. The cell was sealed at the top (using a gold gasket) in order to prevent oxidation. The absorption edge of T1C1 at temperatures between 525°C and 27°C is shown in Fig. 1. The sequence of measurement was from high to low
Figure 2 presents the energies of the absorption edge plotted against temperature for two values 1 and of the absorption coefficient a(100cm 10 cm’). It is interesting tk note that the energy gap changes by only 0.4—0.5eV at the melting point, and that the temperature coefficients (dEg’aT)pin the solid and the liquid states are identical within the accuracy of the measurement. Our data for solid T1CI are in good agreement with the work of Bachrach.11 12 This investigator concentrated primarily on thin films measured at low temperatures and showed that the actual band edge is preceded by a strong exciton peak. He also performed some experiments on single crystals. His results and ours differ by less than 0.01 eV at room temperature. It is obvious that the absorption edges shown in Fig. 1 are the tails of the exciton peak. The question arises whether this exciton can be associated primarily with an excitation of the TI-ions or with one that
shift to lower energies.’ [For (aE~,/aT)~he quotes a value of ± 4 x 104eV/K, a figure very similar to that of the lead chalcogenides.] Having establis.hed that the absorption edges of crystalling TlCl (shown in Fig. 1) are the tails of the exciton band, we now turn our attention to the molten TICI. A glance at Figs. 1 and
Vol. 9, No. 10
EXCITATIONS IN SOLID AND LIQUID THALLOUS CHLORIDE
711
...1 I 425 Iii
z
295
4~ 447)
454
525
—
0—
El —
~
3’C
39C
400
41C
42C
430
440
450
460
~
490
490
500 50
52~ 530
540
~C
FIG. 1. Absorption edge of thallous choride at different temperatures (the numbers at the tops of the curves indicate the temperature in degrees Celsius). The curve marked (447) refers to a sample that is partly molten.
1
I I
I
exist in liquid TlCl and that the observed absorption edges again are the tails of the (broadened) exciton bands. The existence of Wannier excitons —E
—
9~ ~ —
in a molten substance has been demonstrated previously by Beaglehole for the case of liquid 14 xenon. The surprising similarity between the behavior of the liquid and of the solid leads us to the following two considerations: (a) The average co-
—
o
~
I
I __
--
__
__
-
7(0
FIG. 2. Temperature dependence of the absorption edge for two values of the absorption coefficient.
2 shows that the temperature dependence of the edge in the liquid state is very similar to that of the solid after a discontinuity of about 0.5eV at the melting point. Consequently it is logical to suggest that bound electron—hole pairs also can
ordination in the molten state is probably not very different from that in the crystal, and (b) the average cation—anion distance in the liquid is just a bit larger. The second statement is supported by measured values of the volume change ~\ir. at the melting point. It appears that ..\v,, is 20 per cent, corresponding to an average increase of the linear interionic distance of 7 per cent. .4cknowledgements — It is a pleasure to thank Dr. A.H. Kahn for helpful discussions and suggestions.
REFERENCES
1. 2.
ZIMAN J.M., Proc. R. Soc. Lond. A318, 401 (1970). ADLER D., Electronics 43, 61(1970).
3.
FA(’~ENE.A. and FRITZXCHE H., J ..‘on-Crysralline Solids 2, 170 (1970).
712 4.
EXCITONS IN SOLID AND LIQUID THALLOUS CHLORIDE STUKE
Vol.9, No.10
J., J. Non-Crystalline Solids 4, 1 (1970).
5. DONOVAN T.M., SPICER W.E. and BENNETT J.M., Phys. Rev. Leit. 22, 1058 (1969). 6. ALLGAIER R.S., Phys. Rev. 185, 227 (1969). 7. 8.
GLASOV V.M., Liquid Semiconductors, Nauka Press, Moscow (1967); transi. Plenum Press, New York (1969). ADLER D., Rev, mod. Phys. 40, 914 (1968).
9.
COHEN M.H., J. Non.Crystalline Solids 4, 391 (1970).
10.
COHEN M.H., FRITZSCHE i-Land OVSHINSKY S.R., Phys. Rev. Leti. 22, 1065 (1969).
11.
BACHRACH R.Z., Thesis, University of Illinois, (1969).
12. BACHRACH R.Z. and BROWN F.C., Phys. Rev. B 1, 818 (1970). 13. KUNZ A.B., unpublished; quoted in reference 12, p.89. 14. BEAGLEHOLE D., Phys. Rev. Let:. 15, 551 (1965). 15.
KLEMM W.Z., Z. anorg.
ii.
allg. Chem. 152, 235 (1926).
Es wurde die Absorptionskante von Thalliumchlorid über und unter dem Schrnelzpunkt gemessen. Im Kristall stelit diese Kante den nieder-energetischen Auslauf eines stark absorbierenden Wannier Exziton dar. Die Ahnlichkeit in Form und Temperaturver lauf dieser Absorption im festen und flussigen Zustand leitet zu der Annahme dass Wannier Exzitonen auch in der Schmelze bestehen können.
Vol. 9, pp. 709—712, 1971.
Pergamon Press.
Printed in Great Britain
EXCITATIONS IN SOLID AND LIQUID THALLOUS CHLORIDE* H.P.R. Frederikse and W.R. Hosler National Bureau of Standards, Washington. D.C. 20234, U.S.A. (Received 8 February 1971 by E. Burstein)
The absorpti on edge of thallous chloride has been measured below and above melting point. In the crystal this edge represents the low energy tail of a strongly absorbing Wannier exciton. The similarity between the shape and temperature dependence of this absorption in the solid and in the liquid states suggests that Wannier-like excitons exist also in liquid thallous chloride.
INTRODUCTION ONE OF the major topics that has recaptured the attention of solid state scientists recently’ is the behavior of non-crystalline solids (amorphous materials, glasses) and liquids.1 2What is so intriguing is the similarity between the electrical and optical properties of the disordered and the ordered states. Quite a few materials (Ge, ~ chalcogenides, V 205, etc.) show semiconductivit~ both in the crystalline in the amorphous phase phase.~5A number of and semiconductors (e.g. Se. T1 6 ~ (This remain semiconductors on melting. that has2Te) to be contrasted with the observation several transition—metal oxides show a semiconductor—metal transition8 when the crystal undergoes only a very small structural change in the solid state.) There is some evidence that the electronic density of states of an amorphous solid or of a liquid may not be so very different from that of the crystalline form of the same material. In the case of liquid metals the nearly-free-electron model yields reasonably good results for the transport properties of charge carriers.’ Experimental studies of the optical reflectivity of several amorphous or glassy semiconductors in the range 0—10eV have shown that most of the detailed structure observed on single crystals is ‘washed out,’ but that many of the qualitative features are maintained.4 How to reconcile this *Research supported by National Aeronautics and Space Administration, U.S.A.
with the fact that the rather sharp Contour of the electronic energy dispersion curves is a direct consequence of the periodic lattice structure of crystalline solids and that this periodicity is lost inthe non-crystalline state is a very difficult problem. A considerable amount of experimental and theoretical work has been focused on the energy gap of semiconductors and insulators in their 9~ This is quite understandamorphous state~ able because the energy gap is a direct consequence of the energy band scheme, and is interpreted conventionally as the extciation of an electron from the valence (filled) band to the conduction (unoccupied) band. As far as optical properties are concerned, the experimental research efforts have been concentrated on the elements Ge, Si, Te and Se, on some Il—V compounds, and quite extensively on the chalcogenide glasses. Although the results have clearly indicated certain trends, comparison of data on different samples of the same material is difficult because most experiments have been performed on thin amorphous films; it can hardly be expected that the degree of non-crystallinity of different films is identical from sample to sample.
709
Consequently, if one wants to explore the electronic structure of disordered materials, in particular, the forbidden energy gap of non-metals there are good reasons for studying the molten
710
EXCITATIONS IN SOLID AND LIQUID THALLOUS CHLORIDE
Vol. 9, No. 10
state. Besides its reproducibility, the fact that one can compare the results gained from experiments on a liquid directly with those obtained on the solidified state is an important advantage. At first it would seem that the choice of an appropriate
temperature; hence the data below the metling point (430°C)refer to recrystallized material. These data reproduce very well the initial results obtained on a single crystal before melting. The S-shaped curve at 447°Cindicates that the sample
material is limitless. However, if one considers reasonable restrictions, it appears that the number actually shrinks considerably. The solid material should be a semiconductor or an insulator with a non-localized electronic structure. This condition excludes all molecular and Van der Waals crystals (usually organic compounds). Nearly all materials of the latter category have melting points below 100°C, while very few of the (ionic or covalent) insulators or semiconductors with long-range electronic structure melt below 200°C. A difficult aspect of many semiconductors — especially those with small energy gaps — is the free carrier absorption which can be quite high at elevated temperature, obscuring the absorption edge. If one furthermore limits the choice to substances whose melting point does not exceed 800 or 900° and whose absorption edge occurs in the visible or near u.v. spectral range (for experimental siniplicity), the number of suitable materials actually has shrunk considerably. In the remaining group. compounds containing TI appear quite frequently,
was part solid and part liquid.
The above ideas have led us to undertake some very simple optical experiments using the crystal TICI, in particular, the measurement of the lower part of the absorption edge at temperatures below and above its melting point (430°C).
involves both TI and Cl-ions. It has been suggested by Kunz ~ that the top of the (filled) valence band corresponds to the Tl~6s2-state, while the bottom of the (empty) conduction band is made up mainly from Tl-6s26p-states. The radius of the exciton ‘orbit’ in TlCl is of the order of 20—40 A (a* = 0.5 x /m* = 0.5 x 30/0.5 30 A), and hence a non-localized Wannier-type description seems to be favored.11 At the same time, the excitation appears to belong more to the TF ions than to the Tl~Cl ‘molecules.’ With respect to the temperature shift, Bachrach states in his thesis:’1 ‘As the temperature is raised, the exciton peak moves to higher energies; however, the peak broadens so that the edge appears to
EXPERIMENT AND DISCUSSION Thallium chloride samples were put in a rectangular quartz cell; the width of this cell was approximately 9mm while the light transversed the smaller dimension (1 mm). This cell was placed in an appropriately shaped lava oven
provided with nichrome wires and Pt—Rh thermocouples. A small vertical temperature gradient caused melting from the top down the recrystallization from the bottom up. The cell was sealed at the top (using a gold gasket) in order to prevent oxidation. The absorption edge of T1C1 at temperatures between 525°C and 27°C is shown in Fig. 1. The sequence of measurement was from high to low
Figure 2 presents the energies of the absorption edge plotted against temperature for two values 1 and of the absorption coefficient a(100cm 10 cm’). It is interesting tk note that the energy gap changes by only 0.4—0.5eV at the melting point, and that the temperature coefficients (dEg’aT)pin the solid and the liquid states are identical within the accuracy of the measurement. Our data for solid T1CI are in good agreement with the work of Bachrach.11 12 This investigator concentrated primarily on thin films measured at low temperatures and showed that the actual band edge is preceded by a strong exciton peak. He also performed some experiments on single crystals. His results and ours differ by less than 0.01 eV at room temperature. It is obvious that the absorption edges shown in Fig. 1 are the tails of the exciton peak. The question arises whether this exciton can be associated primarily with an excitation of the TI-ions or with one that
shift to lower energies.’ [For (aE~,/aT)~he quotes a value of ± 4 x 104eV/K, a figure very similar to that of the lead chalcogenides.] Having establis.hed that the absorption edges of crystalling TlCl (shown in Fig. 1) are the tails of the exciton band, we now turn our attention to the molten TICI. A glance at Figs. 1 and
Vol. 9, No. 10
EXCITATIONS IN SOLID AND LIQUID THALLOUS CHLORIDE
711
...1 I 425 Iii
z
295
4~ 447)
454
525
—
0—
El —
~
3’C
39C
400
41C
42C
430
440
450
460
~
490
490
500 50
52~ 530
540
~C
FIG. 1. Absorption edge of thallous choride at different temperatures (the numbers at the tops of the curves indicate the temperature in degrees Celsius). The curve marked (447) refers to a sample that is partly molten.
1
I I
I
exist in liquid TlCl and that the observed absorption edges again are the tails of the (broadened) exciton bands. The existence of Wannier excitons —E
—
9~ ~ —
in a molten substance has been demonstrated previously by Beaglehole for the case of liquid 14 xenon. The surprising similarity between the behavior of the liquid and of the solid leads us to the following two considerations: (a) The average co-
—
o
~
I
I __
--
__
__
-
7(0
FIG. 2. Temperature dependence of the absorption edge for two values of the absorption coefficient.
2 shows that the temperature dependence of the edge in the liquid state is very similar to that of the solid after a discontinuity of about 0.5eV at the melting point. Consequently it is logical to suggest that bound electron—hole pairs also can
ordination in the molten state is probably not very different from that in the crystal, and (b) the average cation—anion distance in the liquid is just a bit larger. The second statement is supported by measured values of the volume change ~\ir. at the melting point. It appears that ..\v,, is 20 per cent, corresponding to an average increase of the linear interionic distance of 7 per cent. .4cknowledgements — It is a pleasure to thank Dr. A.H. Kahn for helpful discussions and suggestions.
REFERENCES
1. 2.
ZIMAN J.M., Proc. R. Soc. Lond. A318, 401 (1970). ADLER D., Electronics 43, 61(1970).
3.
FA(’~ENE.A. and FRITZXCHE H., J ..‘on-Crysralline Solids 2, 170 (1970).
712 4.
EXCITONS IN SOLID AND LIQUID THALLOUS CHLORIDE STUKE
Vol.9, No.10
J., J. Non-Crystalline Solids 4, 1 (1970).
5. DONOVAN T.M., SPICER W.E. and BENNETT J.M., Phys. Rev. Leit. 22, 1058 (1969). 6. ALLGAIER R.S., Phys. Rev. 185, 227 (1969). 7. 8.
GLASOV V.M., Liquid Semiconductors, Nauka Press, Moscow (1967); transi. Plenum Press, New York (1969). ADLER D., Rev, mod. Phys. 40, 914 (1968).
9.
COHEN M.H., J. Non.Crystalline Solids 4, 391 (1970).
10.
COHEN M.H., FRITZSCHE i-Land OVSHINSKY S.R., Phys. Rev. Leti. 22, 1065 (1969).
11.
BACHRACH R.Z., Thesis, University of Illinois, (1969).
12. BACHRACH R.Z. and BROWN F.C., Phys. Rev. B 1, 818 (1970). 13. KUNZ A.B., unpublished; quoted in reference 12, p.89. 14. BEAGLEHOLE D., Phys. Rev. Let:. 15, 551 (1965). 15.
KLEMM W.Z., Z. anorg.
ii.
allg. Chem. 152, 235 (1926).
Es wurde die Absorptionskante von Thalliumchlorid über und unter dem Schrnelzpunkt gemessen. Im Kristall stelit diese Kante den nieder-energetischen Auslauf eines stark absorbierenden Wannier Exziton dar. Die Ahnlichkeit in Form und Temperaturver lauf dieser Absorption im festen und flussigen Zustand leitet zu der Annahme dass Wannier Exzitonen auch in der Schmelze bestehen können.