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Electrical properties of polycrystalline NiTe thin films
Thin Solid Films - Elsevier Sequoia
ELECTRICAL THIN FILMS
S.A., Lausanne
PROPERTIES
OF
- Printed
307
in Switzerland
POLYCRYSTALLINE
NiTe
A. K. DUA AND R. P. AGARWALA
Chemistry
Division, Bhabha Atomic Research Centre, Trombay,
(Received
February
Bombay-85
(India)
8, 1971; in revised form April 28, 1971)
SUMMARY
Stoichiometric NiTe thin films have been prepared using flash evaporation technique in a dynamic pressure of less than 10e5 torr. Deposition parameters were varied in an attempt to obtain epitaxial films. Electrical properties of polycrystalline films deposited on glass substrates were studied. Resistance variation of the thin films with temperature and Hall voltage variation with magnetic field were investigated. Thickness dependence of resistivity, temperature coefficient of resistance and Hall coefficient have been experimentally determined. Several plausible explanations have been suggested to explain the results. Assuming a single free carrier model and spherical Fermi surface, relevant electrical parameters have been evaluated.
INTRODUCTION
Recently, considerable attention has been centred on the utilisation of the different characteristics of transition metal alloys and compounds. However, the physical properties of NiTe have not yet been thoroughly investigated. On the other hand there exists some contradictory data on its conductivity behaviour1*2. The present investigation describes some of the electrical and galvanomagnetic properties of nickel telluride films as a function of film thickness. EXPERIMENTAL
Nickel telluride was prepared by heating a equiatomic mixture of pure (99.999 ‘A) nickel and tellurium in vacuum at 900 “C for six days. The capsule containing the material was quenched in ice cold water. Thin films of NiTe were Thin SolidFilms,
8 (1971) 307-315
308
A. K. DUA,
Substrate
/-Soft
iron
piece
---Substrate
R. P. AGARWALA
hider
heater
.~
Spring contact -Annealing
heater
Base plate
Fig. 1. Line diagram
of the substrate
holder assembly.
prepared in a vapour deposition unit in a pressure less than lo-’ torr. A newly designed substrate holder (Fig. 1) was used to carry different substrates, which could be rotated magnetically without breaking the vacuum. This allowed six films of different thicknesses to be deposited at different temperatures in one pumpdown. Furthermore all the films could simultaneously be annealed in situ. Due to the large difference in vapour pressures of the constituents, fractional distillation took place when conventional resistive heating was used. To avoid this dissociation, the technique of flash evaporation was employed using a special powder dropper3 with provision for controlling the rate of fall of NiTe powder (20&300 mesh) on to a heated tungsten strip held at 1600 “C. The films so formed were tested for stoichiometric composition by X-ray diffraction. The film thickness was measured using a quartz crystal thickness monitor which was calibrated by multiple beam interferometry. The substrates used were either clean microscopic glass slides, or freshly cleaved mica or single crystals of rock salt. For electrical measurements, films were deposited on glass substrates which were cleaned ultrasonically in pure acetone and outgassed at - 350 “C for 30 min. A typical deposition rate was - 15 @sec. After deposition, the films were annealed at - 320 “C for nearly six hours. Resistance variation with temperature was measured in situ, the temperature being controlled to within + 1 “C using Melab’s proportional temperature controller. Other characteristic properties were measured outside the vacuum deposition system. Thin Solid Films, 8 (1971) 307-315
ELECTRICAL
PROPERTIES
Fig. 2. Electron diffraction single crystal substrate. Fig. 3. Electron diffraction substrate (other conditions
RESULTS
OF POLYCRYSTALLINE
pattern
NiTe THlN FILMS
of NiTe thin film deposited
pattern of NiTe thin film deposited being the same as in Fig. 2).
at room
temperature
at 375 “C on rocksalt
309
on rocksalt
single crystal
AND DISCUSSION
studies The deposition parameters were varied to obtain epitaxial films. In particular, the effect of different substrates, their temperature and the rate of deposition were investigated qualitatively. Electron diffraction analysis showed the films to be polycrystalline on all the three substrates used. Figures 2 and 3 show the effect of change in substrate temperature on the nature of deposit on a single crystal of rocksalt. Up to -375 “C, it appeared to favour preferred orientation but at higher temperatures the orientation effect deteriorated. This has been attributed to the onset of sublimation ofthe substrate4. Since epitaxial temperature is expected to be lowered on irradiated substrates5, NaCl single crystals were bombarded with 34 KeV, 10 mA X-rays from a copper target so as to produce colour centres. Deposition on these irradiated samples, did not produce any appreciable change in orientation. Variation of evaporation rate (5 A/set to (1)
Epitaxy
30 A/set) did not produce
a detectable
change.
(2) Resistance variation with temperature Resistance was measured using the standard four probe method and aqua dag contacts. Its variation with temperature for two characteristic film thicknesses is shown in Fig. 4. The linear increase is indicative of the metallic character. (3) Hall efSect studies To study the Hall effect in NiTe films, a direct current was applied along the length of the film and the magnetic field used was continuous and perpendicular Thin SolidFilms,
8(1971)307-315
310
A. K. DUA.
218
-
214
-
35J 20
R. P. AGARWALA
I 60
100
140 Temperat
180
220
260
300
urePC)
Fig. 4. Variation of resistance with temperature, (1) Film thickness (2) Film thickness 250 A, TCR = 6.5 x low4 “C-l
1120 A, TCR = 9 x 10m4 “C- ’
;
to the plane of the film. To avoid the shorting of the Hall voltage, the ratio of the length to the width of each film was kept at least equal to three. For each thickness, Hall measurements were taken by changing the polarity of the magnet and the direction of the current..All the observations were performed at room temperature. Figure 5 shows the variation of Hall voltage with magnetic field. Up to -23 kilogauss, Hall voltage is proportional to the field. A further increase of field indicates a tendency of a maximum occurring in the Hall voltage as can be visualized from curve 1 (corresponding to a thickness 2645 A). However from
Magnetic
16 field ( kg 1
20
Fig. 5. Variation of Hall voltage with magnetic 125.6 mA; (2) Film thickness = 300 A; specimen Thin Solid Films, 8 (1971) 307-315
24
28
field, (1) Film thickness current 7.21 mA.
2645 A ; specimen
current
ELECTRICAL
PROPERTIES
NiTe THIN FILMS
OF POLYCRYSTALLINE
2000 Thickness
2400
2800
3200
3600
4OCO
(w)
Fig. 6. Variation of resistivity with film thickness. Open circles arc experimental represent the theoretical values on Fuchs theory with p = 0 and li = 1000 A.
points and crosses
curve 2 (thickness 300 A), it is apparent that the maximum will occur at higher fields. This behaviqur is similar to that observed by Colombani and Huet6 for bismuth thin films. (4) Magnetoresistance eflect There was no observable field up to 28 kilogauss.
change
(5) Thickness dependence of resistivity, and Hull coeficient Variations of resistivity, T.C.R. film thickness, have been respectively NiTe thin films was measured at room contacts. T.C.R. referred to values temperature
0
measurements
400
600
in the resistivity
with an applied
temperuturecoejjicient
1600
of resistance(T.C.R.)
and Hall coefficient, each as a function of plotted in Figs. 6, 7 and 8. Resistivity of temperature (- 25 “C) using indium solder between room and ice temperatures. Ice
have been made at a pressure
1200
2CCO
2400
Thickness
( !i 1
2800
- 10m3 torr.
3200
Fig. 7. Variation of T.C.R. with film thickness. Open circles are experimental represent the theoretical values on Fuchs theory with p = 0 and 1; = ICOO A. Thin Solid Films, 8 ( I97 1) 307-3 15
magnetic
3600
points
4OCO
and crosses
312
A. K. DUA.
R. P. AGARWALA
I 0
400
1200 1600 Thickness (8
800
2000
2400
2800
)
Fig. 8. Plot of Hall coefficient vs. film thickness at a magnetic field of 22.5 k gauss, open circles are experimental points and crosses represent the theoretical values on Fuchs theory with p = 0 and li = 1OOoA.
In interpreting the dependence ofresistivity on film thickness, it was necessary to consider several factors which contribute to the total resistivity. According to a modified form of Matthesson’s rule, the resistivity of thin, plane, parallel and continuous films could be represented as Pfilm
=
/)idealbulk
+
Pimpurity
+
Pimperfection
+
Pthickness
(1)
The last term arises because some of the mean free paths get reduced by termination at the film surface, when film thickness becomes comparable to the carrier mean free path. The observed resistivity variation with thickness in the left hand side of eqn. (I) would obviously be due to the thickness dependence of one or more terms (governed by the preparation conditions) on the right hand side of eqn (1). Considering the first three terms on the right hand side to be independent of thickness and assuming a spherical Fermi surface and the existence of scalar relaxation time, Fuchs’ has given the theoretical relation
where pi is the intrinsic resistivity, li is the intrinsic mean free path, p is the fraction of the electrons elastically scattered at the external boundary and d is the film thickness. This relation and those for T.C.R. and Hall coefficient’ have been plotted respectively (represented by crosses) in Figs. 6, 7 and 8 with p = 0, li = 1000 A and pi = the measured value for a sufficiently thick film. The sudden rise in resistivity at small thicknesses is due to the films having semicontinuous network structure resulting in a small number of conduction paths being available. One then encounters a different conduction mechanism and the theory used Thin Solid Films, 8 (197 1) 307-3 15
ELECTRICAL
PROPERTIES
OF POLYCRYSTALLINE
NiTe THIN FILMS
313
breaks down because in this region, the theoretical requirement for plane and parallel boundary surfaces is not realised. The value p = 0 is in accord with the currently accepted convention for polycrystalline films’. However it is seen that for the best fit with the experimental data, Fuchs theory requires a value of 1000 A for the mean free path whereas the value calculated from the conductivity and Hall coefficient comes to be 6 A. This discrepancy could be attributed to not fulfilling the conditions postulated during theoretical derivation. For instance, the Fermi surface may be anisotropic and the relaxation time may not be unambiguously definable”. Further correlation of size effect at small thicknesses is bound to introduce unacceptably large errors in computation. It would thus give rise to artificially of pi and Ii being independent of film thickness is large li l1 . Also the assumption i”.12,13. The mean crystallite size has been contrary to the experimental findings found1’*12 to increase with film thickness resulting in a decrease of the number of crystallite boundaries. Since the electron concentration in bulk is different to that at the interface layer of crystallites, each grain boundary will be associated with a potential barrier. These barriers will scatter conduction electrons thereby making a major contribution to pi. Hence pi and pri,,,, become a function of film thickness. This, therefore, forms an alternative physical explanation for the thickness dependence of resistivity. In fact, based on this, Mayadas et ~1.‘~ have given a theory for polycrystalline films wherein they have shown that if the average grain diameter is equal to the film thickness, then the internal size effect could give rise to macroscopic electrical and galvanomagnetic phenomena, comparable in magnitude to Fuchs size effect, even when the scattering from the external surface is negligible. In this way both the grain boundary scattering as well as the thickness size effect would contribute to the thickness dependence of resistivity. Thus, at the moment, it is difficult to derive conclusions based on any one theory. It may also be noted that the magnetic field used for the measurement of the Hall coefficient is quite large whereas the Sondheimer theory’ is valid only for very small fields. An appreciable scatter has been observed in the experimental data. This is expected since the film composition, degree of oxidation or contamination is slightly different in different runs of evaporation. It is due to the lack of rigorous and complete control of all the pertinent parameters (e.g. total and residual gas pressure, substrate and source temperature, deposition rate and substrate surface). Moreover, the accuracy of thickness measurement was limited to f 50 A, a value fairly high for the thinnest films. (6) Calculations of some of the electrical parameters The assumption of a single carrier free electron model and spherical surface made in the present investigation cannot be rigorously justified Thin Solid Films, 8 ( I97 1) 307-3 15
Fermi but is
314
A. K. DUA,
R. I’. AGARWALA
necessary to compute the electrical parameters. The free carrier model gives, carrier density n = l/R,e and the effective Hall mobility, pL,rf = IR,Ia, where e is the electronic charge; R, the Hall coefficient and 6, the conductivity. Using the above expressions and Figs. 6 and 8, effective Hall mobility and carrier density have been evaluated at different film thicknesses. Thus effective Hall mobility has been plotted as a function of carrier concentration (Fig. 9). The dependence is similar to that found by Farukhi ef al. ’ 5 for GaAs film, where the concentration has been varied intentionally by doping.
4.0
4A
48
5.2 Carrier
Fig. 9. Plot showing
the variation
5.6
density,
60
6A
68
7.2
n .1022/cm3
of effective Hall mobility
with carrier
concentration.
The low mobility can be explained as arising due to the presence of a very high density of structural and chemical defects. Grain boundaries cause significant scattering. Some contribution to carrier density may be due to a degree of nonstoichiometry, which will be present because minimum free energy does not correspond to stoichiometric composition”. Using the bulk formulae”, relaxation time z = am/m?; Fermi energy E, = (h2/2m)(3z2n)2’3 = imu:; mean free path, 1 = TU,; carrier wave length and mobility .D = er/m (where ur is the appropriate electron 1 = h/(2mE,)“2 velocity numbers
and other symbols having their usual meanings) gives the following z = 6.1 x 10P’6sec; E, = 5.3eV; uF = 1.36 x 108cmsec~‘; 1 = 7.2A;
I = 5Aandp = 1cm2V-‘set-‘. From the carrier density, the number of effective conduction electrons per atom has been evaluated and is found to vary between 1.8 to 2.9 in the thickness range investigated. This means that it is unreasonable to apply the above relations, based on the simple band model, to the present compound. However, since the conduction nature of NiTe has remained obscure and no corresponding relations obtained, it is inevitable to use the above relations for the present analysis. ACKNOWLEDGEMENT
The authors mental work.
appreciate
Thin Solid Films, 8 ( 197 1) 307-3 15
the assistance
of V.C. George
in some of the experi-
ELECTRICAL PROPERTIES OF POLYCRYSTALLINE NiTe THIN FILMS
315
REFERENCES L. D. DUDKIN AND V.
1. VAIDANICH,in N. KH. ABRIKO~~V (ed.), Proc. 4th All Union Conf on Semicond. Materials (English translation), Consultant Bureau, New York, 1963, p.90. G. G. DVORYANKINAAND 2. G. PINSKER,KristallograJiya, 7 (19‘62) 458. A. K. DUA AND S. B.THATTE, J. Sci. Instr. (J. Phys. E), 2 (1969) 1 I 19. D. B. HOLT, &it. J. Appl. Phys., 17 (1966) 1395. T. INUZUKA AND R. UEDA, Appl. Phys. Letters, 13 (1968) 3. A. COLOMBANIAND P. HUET. in C. A. NEUGEBAUER,J. B. NEWKIRK AND D. A. VERMILYEA(eds.), Structure and Property of Thin Films, Wiley, New York.1959,p.253. K. FUCHS, Proc. Cumb. Phil. Sot., 34 (1938) 100. 8 E. H. SONDHEIMER,Adcan. Phys., I (1952) I. 9 K. L. CHOPRA AND L. C. BOBB, Acta Met., 12 (1964) 807. IO A. F. MAYADAS, R. FEDERAND R. ROSENBERG,J. Vat. Sri. Technol., 6 (1969) 690. 11 A. F. MAYADAS, J. Appl. Phys., 39 (1968) 4241. 12 H. BERGER,W. KAHLE AND G. JANICHE,Phys. Status Solidi, 28 (1968) K97. 13 F. V. SHALLCROSS,Trans. AIME, 236 (1966) 309. 14 A. F. MAYADAS, M. SHATZKESAND J. F. JANAK. Appl. Phys. Letters, 14 (1969) 345. 15 M. R. FARUKHI AND E. J. CHARLSON,J. Appl. Phys., 40 (1969) 5361. 16 R. J.HODGKINSON,J. Electronics, I (1956) 612. 17 C. KITTEL, Introduction to Solid State Physics, 2nd edn., Wiley, New York, 1956, p. 237.
Thin Solid Films, X (1971) 307-315
ELECTRICAL THIN FILMS
S.A., Lausanne
PROPERTIES
OF
- Printed
307
in Switzerland
POLYCRYSTALLINE
NiTe
A. K. DUA AND R. P. AGARWALA
Chemistry
Division, Bhabha Atomic Research Centre, Trombay,
(Received
February
Bombay-85
(India)
8, 1971; in revised form April 28, 1971)
SUMMARY
Stoichiometric NiTe thin films have been prepared using flash evaporation technique in a dynamic pressure of less than 10e5 torr. Deposition parameters were varied in an attempt to obtain epitaxial films. Electrical properties of polycrystalline films deposited on glass substrates were studied. Resistance variation of the thin films with temperature and Hall voltage variation with magnetic field were investigated. Thickness dependence of resistivity, temperature coefficient of resistance and Hall coefficient have been experimentally determined. Several plausible explanations have been suggested to explain the results. Assuming a single free carrier model and spherical Fermi surface, relevant electrical parameters have been evaluated.
INTRODUCTION
Recently, considerable attention has been centred on the utilisation of the different characteristics of transition metal alloys and compounds. However, the physical properties of NiTe have not yet been thoroughly investigated. On the other hand there exists some contradictory data on its conductivity behaviour1*2. The present investigation describes some of the electrical and galvanomagnetic properties of nickel telluride films as a function of film thickness. EXPERIMENTAL
Nickel telluride was prepared by heating a equiatomic mixture of pure (99.999 ‘A) nickel and tellurium in vacuum at 900 “C for six days. The capsule containing the material was quenched in ice cold water. Thin films of NiTe were Thin SolidFilms,
8 (1971) 307-315
308
A. K. DUA,
Substrate
/-Soft
iron
piece
---Substrate
R. P. AGARWALA
hider
heater
.~
Spring contact -Annealing
heater
Base plate
Fig. 1. Line diagram
of the substrate
holder assembly.
prepared in a vapour deposition unit in a pressure less than lo-’ torr. A newly designed substrate holder (Fig. 1) was used to carry different substrates, which could be rotated magnetically without breaking the vacuum. This allowed six films of different thicknesses to be deposited at different temperatures in one pumpdown. Furthermore all the films could simultaneously be annealed in situ. Due to the large difference in vapour pressures of the constituents, fractional distillation took place when conventional resistive heating was used. To avoid this dissociation, the technique of flash evaporation was employed using a special powder dropper3 with provision for controlling the rate of fall of NiTe powder (20&300 mesh) on to a heated tungsten strip held at 1600 “C. The films so formed were tested for stoichiometric composition by X-ray diffraction. The film thickness was measured using a quartz crystal thickness monitor which was calibrated by multiple beam interferometry. The substrates used were either clean microscopic glass slides, or freshly cleaved mica or single crystals of rock salt. For electrical measurements, films were deposited on glass substrates which were cleaned ultrasonically in pure acetone and outgassed at - 350 “C for 30 min. A typical deposition rate was - 15 @sec. After deposition, the films were annealed at - 320 “C for nearly six hours. Resistance variation with temperature was measured in situ, the temperature being controlled to within + 1 “C using Melab’s proportional temperature controller. Other characteristic properties were measured outside the vacuum deposition system. Thin Solid Films, 8 (1971) 307-315
ELECTRICAL
PROPERTIES
Fig. 2. Electron diffraction single crystal substrate. Fig. 3. Electron diffraction substrate (other conditions
RESULTS
OF POLYCRYSTALLINE
pattern
NiTe THlN FILMS
of NiTe thin film deposited
pattern of NiTe thin film deposited being the same as in Fig. 2).
at room
temperature
at 375 “C on rocksalt
309
on rocksalt
single crystal
AND DISCUSSION
studies The deposition parameters were varied to obtain epitaxial films. In particular, the effect of different substrates, their temperature and the rate of deposition were investigated qualitatively. Electron diffraction analysis showed the films to be polycrystalline on all the three substrates used. Figures 2 and 3 show the effect of change in substrate temperature on the nature of deposit on a single crystal of rocksalt. Up to -375 “C, it appeared to favour preferred orientation but at higher temperatures the orientation effect deteriorated. This has been attributed to the onset of sublimation ofthe substrate4. Since epitaxial temperature is expected to be lowered on irradiated substrates5, NaCl single crystals were bombarded with 34 KeV, 10 mA X-rays from a copper target so as to produce colour centres. Deposition on these irradiated samples, did not produce any appreciable change in orientation. Variation of evaporation rate (5 A/set to (1)
Epitaxy
30 A/set) did not produce
a detectable
change.
(2) Resistance variation with temperature Resistance was measured using the standard four probe method and aqua dag contacts. Its variation with temperature for two characteristic film thicknesses is shown in Fig. 4. The linear increase is indicative of the metallic character. (3) Hall efSect studies To study the Hall effect in NiTe films, a direct current was applied along the length of the film and the magnetic field used was continuous and perpendicular Thin SolidFilms,
8(1971)307-315
310
A. K. DUA.
218
-
214
-
35J 20
R. P. AGARWALA
I 60
100
140 Temperat
180
220
260
300
urePC)
Fig. 4. Variation of resistance with temperature, (1) Film thickness (2) Film thickness 250 A, TCR = 6.5 x low4 “C-l
1120 A, TCR = 9 x 10m4 “C- ’
;
to the plane of the film. To avoid the shorting of the Hall voltage, the ratio of the length to the width of each film was kept at least equal to three. For each thickness, Hall measurements were taken by changing the polarity of the magnet and the direction of the current..All the observations were performed at room temperature. Figure 5 shows the variation of Hall voltage with magnetic field. Up to -23 kilogauss, Hall voltage is proportional to the field. A further increase of field indicates a tendency of a maximum occurring in the Hall voltage as can be visualized from curve 1 (corresponding to a thickness 2645 A). However from
Magnetic
16 field ( kg 1
20
Fig. 5. Variation of Hall voltage with magnetic 125.6 mA; (2) Film thickness = 300 A; specimen Thin Solid Films, 8 (1971) 307-315
24
28
field, (1) Film thickness current 7.21 mA.
2645 A ; specimen
current
ELECTRICAL
PROPERTIES
NiTe THIN FILMS
OF POLYCRYSTALLINE
2000 Thickness
2400
2800
3200
3600
4OCO
(w)
Fig. 6. Variation of resistivity with film thickness. Open circles arc experimental represent the theoretical values on Fuchs theory with p = 0 and li = 1000 A.
points and crosses
curve 2 (thickness 300 A), it is apparent that the maximum will occur at higher fields. This behaviqur is similar to that observed by Colombani and Huet6 for bismuth thin films. (4) Magnetoresistance eflect There was no observable field up to 28 kilogauss.
change
(5) Thickness dependence of resistivity, and Hull coeficient Variations of resistivity, T.C.R. film thickness, have been respectively NiTe thin films was measured at room contacts. T.C.R. referred to values temperature
0
measurements
400
600
in the resistivity
with an applied
temperuturecoejjicient
1600
of resistance(T.C.R.)
and Hall coefficient, each as a function of plotted in Figs. 6, 7 and 8. Resistivity of temperature (- 25 “C) using indium solder between room and ice temperatures. Ice
have been made at a pressure
1200
2CCO
2400
Thickness
( !i 1
2800
- 10m3 torr.
3200
Fig. 7. Variation of T.C.R. with film thickness. Open circles are experimental represent the theoretical values on Fuchs theory with p = 0 and 1; = ICOO A. Thin Solid Films, 8 ( I97 1) 307-3 15
magnetic
3600
points
4OCO
and crosses
312
A. K. DUA.
R. P. AGARWALA
I 0
400
1200 1600 Thickness (8
800
2000
2400
2800
)
Fig. 8. Plot of Hall coefficient vs. film thickness at a magnetic field of 22.5 k gauss, open circles are experimental points and crosses represent the theoretical values on Fuchs theory with p = 0 and li = 1OOoA.
In interpreting the dependence ofresistivity on film thickness, it was necessary to consider several factors which contribute to the total resistivity. According to a modified form of Matthesson’s rule, the resistivity of thin, plane, parallel and continuous films could be represented as Pfilm
=
/)idealbulk
+
Pimpurity
+
Pimperfection
+
Pthickness
(1)
The last term arises because some of the mean free paths get reduced by termination at the film surface, when film thickness becomes comparable to the carrier mean free path. The observed resistivity variation with thickness in the left hand side of eqn. (I) would obviously be due to the thickness dependence of one or more terms (governed by the preparation conditions) on the right hand side of eqn (1). Considering the first three terms on the right hand side to be independent of thickness and assuming a spherical Fermi surface and the existence of scalar relaxation time, Fuchs’ has given the theoretical relation
where pi is the intrinsic resistivity, li is the intrinsic mean free path, p is the fraction of the electrons elastically scattered at the external boundary and d is the film thickness. This relation and those for T.C.R. and Hall coefficient’ have been plotted respectively (represented by crosses) in Figs. 6, 7 and 8 with p = 0, li = 1000 A and pi = the measured value for a sufficiently thick film. The sudden rise in resistivity at small thicknesses is due to the films having semicontinuous network structure resulting in a small number of conduction paths being available. One then encounters a different conduction mechanism and the theory used Thin Solid Films, 8 (197 1) 307-3 15
ELECTRICAL
PROPERTIES
OF POLYCRYSTALLINE
NiTe THIN FILMS
313
breaks down because in this region, the theoretical requirement for plane and parallel boundary surfaces is not realised. The value p = 0 is in accord with the currently accepted convention for polycrystalline films’. However it is seen that for the best fit with the experimental data, Fuchs theory requires a value of 1000 A for the mean free path whereas the value calculated from the conductivity and Hall coefficient comes to be 6 A. This discrepancy could be attributed to not fulfilling the conditions postulated during theoretical derivation. For instance, the Fermi surface may be anisotropic and the relaxation time may not be unambiguously definable”. Further correlation of size effect at small thicknesses is bound to introduce unacceptably large errors in computation. It would thus give rise to artificially of pi and Ii being independent of film thickness is large li l1 . Also the assumption i”.12,13. The mean crystallite size has been contrary to the experimental findings found1’*12 to increase with film thickness resulting in a decrease of the number of crystallite boundaries. Since the electron concentration in bulk is different to that at the interface layer of crystallites, each grain boundary will be associated with a potential barrier. These barriers will scatter conduction electrons thereby making a major contribution to pi. Hence pi and pri,,,, become a function of film thickness. This, therefore, forms an alternative physical explanation for the thickness dependence of resistivity. In fact, based on this, Mayadas et ~1.‘~ have given a theory for polycrystalline films wherein they have shown that if the average grain diameter is equal to the film thickness, then the internal size effect could give rise to macroscopic electrical and galvanomagnetic phenomena, comparable in magnitude to Fuchs size effect, even when the scattering from the external surface is negligible. In this way both the grain boundary scattering as well as the thickness size effect would contribute to the thickness dependence of resistivity. Thus, at the moment, it is difficult to derive conclusions based on any one theory. It may also be noted that the magnetic field used for the measurement of the Hall coefficient is quite large whereas the Sondheimer theory’ is valid only for very small fields. An appreciable scatter has been observed in the experimental data. This is expected since the film composition, degree of oxidation or contamination is slightly different in different runs of evaporation. It is due to the lack of rigorous and complete control of all the pertinent parameters (e.g. total and residual gas pressure, substrate and source temperature, deposition rate and substrate surface). Moreover, the accuracy of thickness measurement was limited to f 50 A, a value fairly high for the thinnest films. (6) Calculations of some of the electrical parameters The assumption of a single carrier free electron model and spherical surface made in the present investigation cannot be rigorously justified Thin Solid Films, 8 ( I97 1) 307-3 15
Fermi but is
314
A. K. DUA,
R. I’. AGARWALA
necessary to compute the electrical parameters. The free carrier model gives, carrier density n = l/R,e and the effective Hall mobility, pL,rf = IR,Ia, where e is the electronic charge; R, the Hall coefficient and 6, the conductivity. Using the above expressions and Figs. 6 and 8, effective Hall mobility and carrier density have been evaluated at different film thicknesses. Thus effective Hall mobility has been plotted as a function of carrier concentration (Fig. 9). The dependence is similar to that found by Farukhi ef al. ’ 5 for GaAs film, where the concentration has been varied intentionally by doping.
4.0
4A
48
5.2 Carrier
Fig. 9. Plot showing
the variation
5.6
density,
60
6A
68
7.2
n .1022/cm3
of effective Hall mobility
with carrier
concentration.
The low mobility can be explained as arising due to the presence of a very high density of structural and chemical defects. Grain boundaries cause significant scattering. Some contribution to carrier density may be due to a degree of nonstoichiometry, which will be present because minimum free energy does not correspond to stoichiometric composition”. Using the bulk formulae”, relaxation time z = am/m?; Fermi energy E, = (h2/2m)(3z2n)2’3 = imu:; mean free path, 1 = TU,; carrier wave length and mobility .D = er/m (where ur is the appropriate electron 1 = h/(2mE,)“2 velocity numbers
and other symbols having their usual meanings) gives the following z = 6.1 x 10P’6sec; E, = 5.3eV; uF = 1.36 x 108cmsec~‘; 1 = 7.2A;
I = 5Aandp = 1cm2V-‘set-‘. From the carrier density, the number of effective conduction electrons per atom has been evaluated and is found to vary between 1.8 to 2.9 in the thickness range investigated. This means that it is unreasonable to apply the above relations, based on the simple band model, to the present compound. However, since the conduction nature of NiTe has remained obscure and no corresponding relations obtained, it is inevitable to use the above relations for the present analysis. ACKNOWLEDGEMENT
The authors mental work.
appreciate
Thin Solid Films, 8 ( 197 1) 307-3 15
the assistance
of V.C. George
in some of the experi-
ELECTRICAL PROPERTIES OF POLYCRYSTALLINE NiTe THIN FILMS
315
REFERENCES L. D. DUDKIN AND V.
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