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Carrier mobility in single-crystal films of Bi8Te7S5
Thin Solid Films - Elsevier Sequoia S.A., Lausanne - Printed in Switzerland
105
C A R R I E R MOBILITY IN SINGLE-CRYSTAL FILMS OF BisTeTSs*
U. HERBERT GROTE AND HENN H. SOONPAA University of North Dakota, Grand Forks, N.D. 58201 (U.S.A.) (Received May 15, 1972)
Hall effect measurements on single-crystal films of BisTe7Ss show a high carrier mobility for films thin enough to be semiconducting:/~ = 1.13 m2/V sec for a film 20 atoms thick. Higher mobilities, /z = 11.7m2/V sec, are obtained from low field magnetoresistance measurements. The thickness dependence of magnetoresistance mobility is in good agreement with theory.
INTRODUCTION
BisTe7S5 can be readily cleaved into thin single-crystal films. These films come in thicknesses which are integral multiples of 9.8173 A, or five atoms 1. These five atom layers are called quintuple layers (q.l.). Since in BisTevS s we have a crystal with atomically smooth surfaces, perfectly parallel faces and a thickness known to the exact number of atoms 2-4, it presents a nearly ideal system for studying quantum size effects. In view of the good agreement with theory of our measurements of resistivity as a function of thickness 5 and temperature 6, and of our contact potential measurements 7, the galvanomagnetic measurements were expected to provide more insight into transport mechanisms in size effect quantized films. Low temperature measurements show that bulk BiaTe7S s is a semimetal and, as predicted by Sandomirskii 8, it converts into a semiconductor when a/~ < 1--in this case when the thickness becomes less than 25 atoms 6. For the studies of transport phenomena the thickness range around the semimetal to semiconductor transition is of most interest. The main problem we have encountered has been the making of good contacts. Breaks in our crystals almost invariably occur at the contacts or at the places where the thickness changes. This is to be expected from the differences in the Fermi energy as a function of thickness 7. Since all changes from one thickness to another are abrupt by at least five atoms they are accompanied by abrupt changes in Fermi energy. Consequently junctions between areas of different thickness have high resistances, and they are likely to be the first ones to yield when a current is passed through the crystal. Due to the * Paper presented at the International Conference on Thin Films, "Application of Thin Films", Venice, Italy, May 15-19, 1972; Paper 3.2. Thin Solid Films, 12 (1972) 105-109
106
u.H. GROTE, H. H. SOONPA.A
extreme thinness of our films high current densities are encountered even at low currents. Low voltages have to be used to keep current densities low, and the generated Hall voltages are often too low to be measurable across the non-ohmic contacts. EXPERIMENTAL Crystals of BisTeTS5 were mounted with epoxy resin on microscope slides and cleaved to desired thicknesses. Areas of uniform thickness, about 2 mm x 1 mm were engraved with jeweller's tools into "dog bone" samples. The wide ends of each contact were covered with colloidal graphite, on top of which silver paint was applied. Electrical contact to the silver paint was made by beryllium copper springs. Our Andonian cryostat has a temperature range from 1.4° to 350 °K. The temperature was monitored with a germanium diode in a circuit described by Huen 9. The output voltage of that circuit is directly proportional to absolute temperature, making it convenient to record the temperature. For electrical measurements the reference output signal of a PAR 220 lock-in amplifier was adjusted to 1 V peak to peak and passed through a 10sf~ resistor and the sample. The signal across the sample was fed into the differential input of a PAR 113 preamplifier, the output of which was filtered by a PAR 210 selective amplifier and then detected by the PAR 220 lock-in amplifier. From the 220 it was fed into a Honeywell 550 X-Y recorder. Since the sample resistances were usually around 10%'L the 10sG resistor kept the sample current at 10-SA and the voltage drop across the sample was directly proportional to the resistance. With the lock-in amplifier output signal applied to the Y-terminal and the thermometer signal applied to the X-terminal, resistance v e r s u s temperature graphs were plotted directly. When the combined sample and contact resistance approached 10sty, the capacitance at the contacts became significant enough to change the phase of the maximum signal at the lock-in amplifier by 140°. In that range we measured the d.c. potential drop across the sample and across the 10sf~ resistor by a Keithley 640 electrometer, which has an input impedance of greater than 1016t2. For magnetoresistance and Hall effect measurements the reading at zero magnetic field was zeroed by the PAR 123 s.c. zero offset, which enabled us to take our readings at more sensitive scale settings. The magnetic field was produced by a 4in. Varian magnet, and for sweeping at low fields a Hewlett-Packard 6268A power supply with external programming was used. Although the electrical instrumentation worked well, our data taking was limited by the non-ohmic contacts, cryostat leaks, and sample deterioration upon thermal cycling. EXPERIMENTALRESULTS The resistivity v e r s u s temperature curves for samples of 1, 2, 4, 5 and 9 q.l. are shown in Fig. 1. The semimetal to semiconductor transition takes place Thin Solid Films, 12
(1972) 105-109
SINGLE-CRYSTAL FILMS OF
BisTeTS5
107
between 5 and 4 q.1. thicknesses. The curves of Fig. 1 when extended to higher temperatures 6, 10 show energy gaps in the semiconducting samples. Figure 2 is 100-
10, 10uINrFUPLE LAYER --2
E
> 4 X
c..
5
tO
j
o
9
260 o~'
,~o
Fig. 1. Resistivity p vs. absolute temperature in °K for samples of different thicknesses. 1 q.L = 9.8173 A or five atoms.
.
/o.L
i /":" i' " ~! ~ .... i". .
.
J
3'~
"'" k~ • '
15
'
4.O
IO~/T
Fig. 2. In p vs. 103/T, Tis in °K and thicknesses are in quintuple layers. 1 q.l. = 9.8173 A or five atoms.
taken from ref. 10. One can see the S-shape of the In p versus 1/Tcurve, where we were able to measure them at high enough temperatures before the contacts gave up. In ref. 10 (Fig. 2) the absolute values o f p were not accurately measured; therefore the temperature at which the 1 and 2 q.1. curves cross does not agree with Fig. 1. The crossing temperature, 170 °K, of ref. 11, in which the absolute values of p were measured, agrees exactly with our Fig. 1. Our Hall effect measurements have been hampered by the contacts. The highest value we have observed was for a 4 q.1. sample, which yielded a Hall mobility #n = 1.13 m2/V see at 4.2 °K. Our instrumentation can detect a magnetoresistance of A p / p < 10 -3. The only non-zero component that we have observed is with the magnetic field Thin Solid Films, 12 (1972) 105-109
108
U . H . GROTE, H. H. SOONPAA
perpendicular to the sample plane. At the low field limit a log (Ap/p) versus B plot yields a straight line with a slope usually less than the theoretical value of 2. For the semiconducting samples saturation starts at around 0.01 Wb/m 2, and it starts at progressively lower B values for thicker samples. The absolute value of Ap/p at high fields decreases monotonically with increasing sample thickness. At our highest field of B = 0 . 5 5 Wb/m 2, Ap/p= 1.1 ×10 -a for bulk samples. Carrier mobilities were calculated from Ap/p = 0.38 B2# 2 at the small B limit. In Fig. 3/~/#~ is plotted as a function of the effective thickness. The circles 2
_V__ p~
i
10
20
i
i
I
30
40
50
60
E]+b
Fig. 3. #/#~ vs. effective thickness a + b in ~. The circles are experimental values.
are experimental values and the lines are calculated from Sandomirskii's8 eqn. (24) with a correction for effective thickness: # a+b 2 btoo ~ 2[(a+b)/a]+l where b is an additive constant for "effective thickness ". Best agreement between theory and experiment was obtained with ~ = 32 /~, b = - 8 . 8 6 /~, and #~ = 5.73 mZ/V sec in a least squares fit. The greatest deviation was encountered by the 3 q.1. sample, a thickness which has been found to exhibit irregularities in other experiments also 12. The/too Value is much higher than one might expect from the low magnetoresistance of the bulk material, but the scattering mechanism in the bulk material may be entirely different from that in the film. CONCLUSIONS
Resistivity and galvanomagnetic measurements are consistent with previous measurements and in agreement with existing theories. The high Hall mobility #H = 1.13 m2/V see and the magnetoresistance mobility value # = ll.Tm2/V sec for a sample 4 q.l. (just 20 atoms or 40 A) thick are quite unique. Mobilities measured for thin films of Bi 13-t5, InSb 16 and Au, Ag and Cu 17 are typically orders of magnitude below the corresponding bulk values. For BisTeTS5 the Thin Solid Films, 12 (1972) 105-109
SINGLE-CRYSTAL FILMS OF B i s T e T S s
109
Ap/p value for the thin film exceeds that of the bulk material by a factor of more
than 100. This appears to be due to the superior crystalline perfection of BiaTe 7S5, a cleaved film, compared with the perfection of deposited films, which are more distorted the thinner they are. The saturation of p(T) at high temperatures (Fig. 2) and the cross-over of the p(T) values for the 1 and 2q.l. samples at 170°K indicate a low density of states in the conduction band. Plotting In p versus l/T, three straight lines are obtained for the 1 q.l. sample. At higher temperatures there is an energy gap of greater than 0.443 eV6; in the 50°-300 °K range a relatively high concentration of donors 0.029 eV below the conduction band predominates; and below 50 °K a low concentration of donors is observed 0.000 56 eV below the conduction band. The effective thickness correction indicates a value of ti = 32 A, although the semiconductor to semimetal transition takes place between 40 and 50 A. In a plot of p77 *K/P300 °K versus thickness Ugaz 1~ observed peaks at 1, 4, 7 and 10 q.l., in agreement with our Fig. 3. ACKNOWLEDGEMENTS
It is our pleasure to acknowledge the financial support from the United States Atomic Energy Commission under Contract AT(11-1)1699. In taking low temperature measurements and in performing some calculations valuable help was provided by Mr. J. H. Marshall. REFERENCES 1 H . H . Soonpaa, Rept No. 1940, General Mills, Inc., AD-235 354, Minneapolis, 1960. 2 H . H . So0npaa, in R. Niedermayer and H. Mayer (eds.), Basic Problems in Thin Film Physics, Intern. Syrup. Clausthal-Gi~ttingen, Vandenhoek and Ruprecht, Gfttingen, 1966, p. 289. 3 H.H. Soonpaa, J. Vac. Sci. Technol., 6 (1969) 741. 4 T.O. Meyer and H. H. Soonpaa, SolidState Commun,, 6(1968) 527. 5 E. Ugaz and H. H. Soonpaa, Solid State Commun., 6 (1968) 417. 6 R.R. Schemmel and H. H. Soonpaa, Solid State Commun., 6 (1968) 757. 7 P.N. Johnson and H. H. Soonpaa, J. Phys. Chem. Solids, 32, Suppl. 1 (1971) 121. 8 V.B. Sandomirskii, Soviet Phys. JETP, 25 (1967) 101. 9 T. Huen, Rev. Sci. Instr., 41 (1970) 1368. 10 R . R . Schemmel, M. S. Thesis, Univ. of North Dakota, 1968. 11 E. Ugaz, M. S. Thesis, Univ. of North Dakota, 1968. 12 H.H. Soonpaa, Bull. Am. Phys. Soc., II-17 (1972) 254. 13 Yu. F. Ogrin, V. N. Lutskii, R, M. Sheftal, M. U. Arifova and M. I. Elinson, Radio Eng. Electron. Phys., 12 (1967) 699. 14 Yu. F. Ogrin, V. N. Lutskii and M. I. Elinson, Soviet Phys. JETP Letters, 3 (1966) 71. 15 N. Garcia, Y. H. Kao and M. Strongin, Phys. Rev., B5 (1972) 2029. 16 O.N. Filatov and I. A. Karpevich, Soviet Phys. JETP Letters, 10 (1969) 142. 17 K.L. Chopra and S. K. Bahl, J. Appl. Phys., 38 (1967) 3607.
Thin Solid Films, 12 (1972) 105-109
105
C A R R I E R MOBILITY IN SINGLE-CRYSTAL FILMS OF BisTeTSs*
U. HERBERT GROTE AND HENN H. SOONPAA University of North Dakota, Grand Forks, N.D. 58201 (U.S.A.) (Received May 15, 1972)
Hall effect measurements on single-crystal films of BisTe7Ss show a high carrier mobility for films thin enough to be semiconducting:/~ = 1.13 m2/V sec for a film 20 atoms thick. Higher mobilities, /z = 11.7m2/V sec, are obtained from low field magnetoresistance measurements. The thickness dependence of magnetoresistance mobility is in good agreement with theory.
INTRODUCTION
BisTe7S5 can be readily cleaved into thin single-crystal films. These films come in thicknesses which are integral multiples of 9.8173 A, or five atoms 1. These five atom layers are called quintuple layers (q.l.). Since in BisTevS s we have a crystal with atomically smooth surfaces, perfectly parallel faces and a thickness known to the exact number of atoms 2-4, it presents a nearly ideal system for studying quantum size effects. In view of the good agreement with theory of our measurements of resistivity as a function of thickness 5 and temperature 6, and of our contact potential measurements 7, the galvanomagnetic measurements were expected to provide more insight into transport mechanisms in size effect quantized films. Low temperature measurements show that bulk BiaTe7S s is a semimetal and, as predicted by Sandomirskii 8, it converts into a semiconductor when a/~ < 1--in this case when the thickness becomes less than 25 atoms 6. For the studies of transport phenomena the thickness range around the semimetal to semiconductor transition is of most interest. The main problem we have encountered has been the making of good contacts. Breaks in our crystals almost invariably occur at the contacts or at the places where the thickness changes. This is to be expected from the differences in the Fermi energy as a function of thickness 7. Since all changes from one thickness to another are abrupt by at least five atoms they are accompanied by abrupt changes in Fermi energy. Consequently junctions between areas of different thickness have high resistances, and they are likely to be the first ones to yield when a current is passed through the crystal. Due to the * Paper presented at the International Conference on Thin Films, "Application of Thin Films", Venice, Italy, May 15-19, 1972; Paper 3.2. Thin Solid Films, 12 (1972) 105-109
106
u.H. GROTE, H. H. SOONPA.A
extreme thinness of our films high current densities are encountered even at low currents. Low voltages have to be used to keep current densities low, and the generated Hall voltages are often too low to be measurable across the non-ohmic contacts. EXPERIMENTAL Crystals of BisTeTS5 were mounted with epoxy resin on microscope slides and cleaved to desired thicknesses. Areas of uniform thickness, about 2 mm x 1 mm were engraved with jeweller's tools into "dog bone" samples. The wide ends of each contact were covered with colloidal graphite, on top of which silver paint was applied. Electrical contact to the silver paint was made by beryllium copper springs. Our Andonian cryostat has a temperature range from 1.4° to 350 °K. The temperature was monitored with a germanium diode in a circuit described by Huen 9. The output voltage of that circuit is directly proportional to absolute temperature, making it convenient to record the temperature. For electrical measurements the reference output signal of a PAR 220 lock-in amplifier was adjusted to 1 V peak to peak and passed through a 10sf~ resistor and the sample. The signal across the sample was fed into the differential input of a PAR 113 preamplifier, the output of which was filtered by a PAR 210 selective amplifier and then detected by the PAR 220 lock-in amplifier. From the 220 it was fed into a Honeywell 550 X-Y recorder. Since the sample resistances were usually around 10%'L the 10sG resistor kept the sample current at 10-SA and the voltage drop across the sample was directly proportional to the resistance. With the lock-in amplifier output signal applied to the Y-terminal and the thermometer signal applied to the X-terminal, resistance v e r s u s temperature graphs were plotted directly. When the combined sample and contact resistance approached 10sty, the capacitance at the contacts became significant enough to change the phase of the maximum signal at the lock-in amplifier by 140°. In that range we measured the d.c. potential drop across the sample and across the 10sf~ resistor by a Keithley 640 electrometer, which has an input impedance of greater than 1016t2. For magnetoresistance and Hall effect measurements the reading at zero magnetic field was zeroed by the PAR 123 s.c. zero offset, which enabled us to take our readings at more sensitive scale settings. The magnetic field was produced by a 4in. Varian magnet, and for sweeping at low fields a Hewlett-Packard 6268A power supply with external programming was used. Although the electrical instrumentation worked well, our data taking was limited by the non-ohmic contacts, cryostat leaks, and sample deterioration upon thermal cycling. EXPERIMENTALRESULTS The resistivity v e r s u s temperature curves for samples of 1, 2, 4, 5 and 9 q.l. are shown in Fig. 1. The semimetal to semiconductor transition takes place Thin Solid Films, 12
(1972) 105-109
SINGLE-CRYSTAL FILMS OF
BisTeTS5
107
between 5 and 4 q.1. thicknesses. The curves of Fig. 1 when extended to higher temperatures 6, 10 show energy gaps in the semiconducting samples. Figure 2 is 100-
10, 10uINrFUPLE LAYER --2
E
> 4 X
c..
5
tO
j
o
9
260 o~'
,~o
Fig. 1. Resistivity p vs. absolute temperature in °K for samples of different thicknesses. 1 q.L = 9.8173 A or five atoms.
.
/o.L
i /":" i' " ~! ~ .... i". .
.
J
3'~
"'" k~ • '
15
'
4.O
IO~/T
Fig. 2. In p vs. 103/T, Tis in °K and thicknesses are in quintuple layers. 1 q.l. = 9.8173 A or five atoms.
taken from ref. 10. One can see the S-shape of the In p versus 1/Tcurve, where we were able to measure them at high enough temperatures before the contacts gave up. In ref. 10 (Fig. 2) the absolute values o f p were not accurately measured; therefore the temperature at which the 1 and 2 q.1. curves cross does not agree with Fig. 1. The crossing temperature, 170 °K, of ref. 11, in which the absolute values of p were measured, agrees exactly with our Fig. 1. Our Hall effect measurements have been hampered by the contacts. The highest value we have observed was for a 4 q.1. sample, which yielded a Hall mobility #n = 1.13 m2/V see at 4.2 °K. Our instrumentation can detect a magnetoresistance of A p / p < 10 -3. The only non-zero component that we have observed is with the magnetic field Thin Solid Films, 12 (1972) 105-109
108
U . H . GROTE, H. H. SOONPAA
perpendicular to the sample plane. At the low field limit a log (Ap/p) versus B plot yields a straight line with a slope usually less than the theoretical value of 2. For the semiconducting samples saturation starts at around 0.01 Wb/m 2, and it starts at progressively lower B values for thicker samples. The absolute value of Ap/p at high fields decreases monotonically with increasing sample thickness. At our highest field of B = 0 . 5 5 Wb/m 2, Ap/p= 1.1 ×10 -a for bulk samples. Carrier mobilities were calculated from Ap/p = 0.38 B2# 2 at the small B limit. In Fig. 3/~/#~ is plotted as a function of the effective thickness. The circles 2
_V__ p~
i
10
20
i
i
I
30
40
50
60
E]+b
Fig. 3. #/#~ vs. effective thickness a + b in ~. The circles are experimental values.
are experimental values and the lines are calculated from Sandomirskii's8 eqn. (24) with a correction for effective thickness: # a+b 2 btoo ~ 2[(a+b)/a]+l where b is an additive constant for "effective thickness ". Best agreement between theory and experiment was obtained with ~ = 32 /~, b = - 8 . 8 6 /~, and #~ = 5.73 mZ/V sec in a least squares fit. The greatest deviation was encountered by the 3 q.1. sample, a thickness which has been found to exhibit irregularities in other experiments also 12. The/too Value is much higher than one might expect from the low magnetoresistance of the bulk material, but the scattering mechanism in the bulk material may be entirely different from that in the film. CONCLUSIONS
Resistivity and galvanomagnetic measurements are consistent with previous measurements and in agreement with existing theories. The high Hall mobility #H = 1.13 m2/V see and the magnetoresistance mobility value # = ll.Tm2/V sec for a sample 4 q.l. (just 20 atoms or 40 A) thick are quite unique. Mobilities measured for thin films of Bi 13-t5, InSb 16 and Au, Ag and Cu 17 are typically orders of magnitude below the corresponding bulk values. For BisTeTS5 the Thin Solid Films, 12 (1972) 105-109
SINGLE-CRYSTAL FILMS OF B i s T e T S s
109
Ap/p value for the thin film exceeds that of the bulk material by a factor of more
than 100. This appears to be due to the superior crystalline perfection of BiaTe 7S5, a cleaved film, compared with the perfection of deposited films, which are more distorted the thinner they are. The saturation of p(T) at high temperatures (Fig. 2) and the cross-over of the p(T) values for the 1 and 2q.l. samples at 170°K indicate a low density of states in the conduction band. Plotting In p versus l/T, three straight lines are obtained for the 1 q.l. sample. At higher temperatures there is an energy gap of greater than 0.443 eV6; in the 50°-300 °K range a relatively high concentration of donors 0.029 eV below the conduction band predominates; and below 50 °K a low concentration of donors is observed 0.000 56 eV below the conduction band. The effective thickness correction indicates a value of ti = 32 A, although the semiconductor to semimetal transition takes place between 40 and 50 A. In a plot of p77 *K/P300 °K versus thickness Ugaz 1~ observed peaks at 1, 4, 7 and 10 q.l., in agreement with our Fig. 3. ACKNOWLEDGEMENTS
It is our pleasure to acknowledge the financial support from the United States Atomic Energy Commission under Contract AT(11-1)1699. In taking low temperature measurements and in performing some calculations valuable help was provided by Mr. J. H. Marshall. REFERENCES 1 H . H . Soonpaa, Rept No. 1940, General Mills, Inc., AD-235 354, Minneapolis, 1960. 2 H . H . So0npaa, in R. Niedermayer and H. Mayer (eds.), Basic Problems in Thin Film Physics, Intern. Syrup. Clausthal-Gi~ttingen, Vandenhoek and Ruprecht, Gfttingen, 1966, p. 289. 3 H.H. Soonpaa, J. Vac. Sci. Technol., 6 (1969) 741. 4 T.O. Meyer and H. H. Soonpaa, SolidState Commun,, 6(1968) 527. 5 E. Ugaz and H. H. Soonpaa, Solid State Commun., 6 (1968) 417. 6 R.R. Schemmel and H. H. Soonpaa, Solid State Commun., 6 (1968) 757. 7 P.N. Johnson and H. H. Soonpaa, J. Phys. Chem. Solids, 32, Suppl. 1 (1971) 121. 8 V.B. Sandomirskii, Soviet Phys. JETP, 25 (1967) 101. 9 T. Huen, Rev. Sci. Instr., 41 (1970) 1368. 10 R . R . Schemmel, M. S. Thesis, Univ. of North Dakota, 1968. 11 E. Ugaz, M. S. Thesis, Univ. of North Dakota, 1968. 12 H.H. Soonpaa, Bull. Am. Phys. Soc., II-17 (1972) 254. 13 Yu. F. Ogrin, V. N. Lutskii, R, M. Sheftal, M. U. Arifova and M. I. Elinson, Radio Eng. Electron. Phys., 12 (1967) 699. 14 Yu. F. Ogrin, V. N. Lutskii and M. I. Elinson, Soviet Phys. JETP Letters, 3 (1966) 71. 15 N. Garcia, Y. H. Kao and M. Strongin, Phys. Rev., B5 (1972) 2029. 16 O.N. Filatov and I. A. Karpevich, Soviet Phys. JETP Letters, 10 (1969) 142. 17 K.L. Chopra and S. K. Bahl, J. Appl. Phys., 38 (1967) 3607.
Thin Solid Films, 12 (1972) 105-109