Mobility studies of evaporated tellurium films

Thin Solid Films, 33 (1976) 165-171 © Elsevier Sequoia S.A., Lausanne---Printed in Switzerland

165

MOBILITY STUDIES OF EVAPORATED TELLURIUM FILMS

K. OKUYAMA Faculty of Engineering, Yamagata University, Yonezawa992 (Japan) (Received July 17, 1975; accepted September 2, 1975)

The Hall mobilities of evaporated Te films with various grain sizes were measured as a function of temperature over the range 77-330 K and were compared with theoretical values based on lattice and ionized impurity scattering. A large deviation of the Hall mobility from the theoretical values was found in Te films with a small grain size and this deviation was attributed to grain boundary scattering. The linear correlation observed between the Hall mobility at room temperature and the average grain size supports this interpretation.

1. INTRODUCTION The carrier transport properties of evaporated Te films have been investigated by several workers 1-4. Dutton et al. 1 measured the temperature dependence of the Hall mobility of Au-nucleated Te films deposited at room temperature and concluded that the predominant scattering is due to ionized impurities. Capers e t al. 2 observed a temperature dependence of the Hall mobility in the form #H = #0 exp ( - E / k T ) , which is typical of polycrystalline films where the effects of grain boundaries predominate. Okuyama et al. 4 compared the temperature dependence of the Hall mobility with theoretical values and found a large deviation. This deviation was considered to be due to grain boundary scattering. However, only Te films with a very fine grain structure (grains smaller than 0.1 lain in diameter) were used in this comparison. The aim of the present paper is to give additional data on the relationship between the Hall mobility and the crystal structure of Te films. The Hall mobilities of Te films with various grain sizes were measured as a function of temperature in the range 77-330 K, and were compared with theoretical mobilities based on the single-crystal theory. The deviation of the Hall mobility from the theoretical values was found to decrease considerably with increasing grain size. Hall mobilities at room temperature were plotted as a function of the average grain diameter in the range 0.1-1.5 Ixm, and a linear relation was obtained between them. 2. EXPERIMENTAL PROCEDURE Specimens were prepared by the thermal evaporation of Te of 99.9999 % purity onto glass substrates predeposited with Au islands. The coating ratio

166

K. OKUYAMA

(area of islands/area of substrate) was approximately 5 %. The role of the Au islands was to prevent the re-evaporation of Te when the substrate temperature was high s. Substrate temperatures were in the range 60°-270 °C and the residual pressure during deposition was 2 x 10 -6 Torr. The deposition rates and thicknesses of the Te films were 1600___400 A min -1 and 2000-4000 A, respectively. The techniques of specimen preparation and Hall effect measurement were similar to those described elsewhere s. 3. RESULTS AND DISCUSSION The Hall mobilities of Te films deposited at substrate temperatures of (a) 270 °C, (b) 170 °C and (c) 120 °C were measured as a function of temperature and are shown in Fig. 1. Electron micrographs of the surface replicas of the specimens used are shown in Fig, 2. Average values of the grain diameters were (a) 1.5 ~tm, (b) 0.4 ltrn and (c) 0.1 pan, respectively. Figure 1 shows that the Hall mobility of a large grain Te film at first increases with increasing temperature and then decreases with a further increase in temperature. This behaviour is

102

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2

10

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i

50

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100

I

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T (°K) Fig. 1. Temperature dependence of the Hall mobility for Te films with various grain sizes. The Te films were deposited at (a) 270 °C, (b) 170 °C and (c) 120 °C.

MOBILITYSTUDIESOF EVAPORATEDTe FILMS

167

characteristic of lattice scattering. On the other hand, the Hall mobility of a fine grain Te film increases monotonically with increasing temperature. The Te film with a medium grain size shows saturation in #n at around 280 K.

a

b

-~

o.skt' -

c

Fig. 2. Electronmicrographsof the surfacereplicasfor the specimensof Fig. 1. The variation of the carrier concentration with temperature is shown for the same specimens in Fig. 3. It can be seen that the carrier concentrations do not vary with temperature, irrespective of grain size, in the temperature range 77-250 K. The lower carrier concentration obtained for higher substrate temperatures during deposition is essentially due to the annealing of lattice defects which act as acceptors. 1019 c) Ts =120°C ~,LAAAA

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Fig. 3. Temperature dependence of the carrier concentration for the specimens of Fig. 1.

Since the drift mobility/~ of polycrystalline semiconducting films includes the influence of the surface mobility ~ and the mobility due to the polycrystalline nature of the films/~, in addition to the lattice scattering mobility /~L and the ionized impurity scattering mobility/~l, we can write p~! 1

=

p L I "~- p I I -~" # S I -}- # F 1

(1)

assuming that the Hall mobility is equal to the drift mobility. By subtracting from the measured Hall mobility the effect of the lattice and impurity scattering

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K. OKUYAMA

mobilities calculated o n the basis o f the single-crystal theory, # s a +/~ff 1 can be separated out. The calculation o f #~ 1 and # { 1 was done for specimens with large and small grain sizes as described elsewhere 4. The surface mobility can be written approximately as 6 /tb #" -- 1 + 2 / d

(2)

where #b is the mobility due to all scattering processes except surface scattering, 2d is the thickness o f the films assuming fiat b a n d conditions and 2 the m e a n free path o f the carriers. The m e a n free path is given by 6 2 =/~l, q

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Fig. 4. Reciprocal Hall mobility of specimen (a) and the corresponding lattice and impurity scattering mobility as a function of temperature. Fig. 5. Reciprocal Hall mobility of specimen (c) and the corresponding lattice and impurity scattering mobility as a function of temperature.

Te FILMS

MOBILITY STUDIES OF EVAPORATED

169

where p is the carrier concentration, h Planck's constant and q the electronic charge. Typically, A = 60 A is obtained for p = 10is cm -a and #b = 300 cm 2 V-1 sec-1. Since the Te films used in this experiment have thicknesses of 20004000 A and hence A/dis much smaller than unity, the contribution of#s in eqn. (1) can be neglected. Therefore the deviation o f / ~ 1 from the theoretical value #L 1+ #[-- 1 should be ascribed to # f 1. 3e{ 1 25~

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0.4 0.6 0,8 AVERAGEGRAIN~

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1

1

1,0

1,2 (P,)

1.4

1.6

Fig. 6. The lIT dependence of the reciprocal mobilities due to the scattering process associated with the polycrystalline nature of the Te films. Fig. 7. Hall mobility at room temperature vs. average grain size.

Reciprocal Hall mobilities and the corresponding theoretical values are plotted for the specimens (a) and (c) in Figs. 4 and 5, respectively. Figure 4 shows that #~ 1 for a large grain Te film approaches the theoretical value in the high temperature region, while it deviates considerably from the theoretical value in the low temperature region, indicating that the predominant scattering mobility is likely to be due to #F" This deviation is especially prominent in Te films with a fine grain size, as seen in Fig. 5. In this case, a deviation of more than one order of magnitude is observed over the whole temperature range. The logarithm of # f 1, which is obtained from #~ 1_ (#L 1+#~ 1), is plotted as a function of reciprocal temperature in Fig. 6. The curves are linear, indicating a relation of the form #F =/~o exp ( - q~p/kT), with a high activation energy in the high temperature region and a low activation energy in the low temperature region. Such behaviour has frequently been observed for various polycrystalline ~emiconducting films7-9 and is interpreted in terms of the potential barriers associated with the grain boundaries. In order to explain the different activation energies observed in PbSe films, i.e. a high activation energy in the high temperature region and a low activation energy in the low temperature region, Espevik et al. 9 proposed that the former is due to the thermal excitation of carriers over the potential barrier between the grains and the latter is effectively due to the tunnelling of carriers through the barrier. The thickness of the space charge layer at the grain boundaries may be estimated from the effective Debye length Lo:

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K. OKUYAMA

LD = ~.q2 (n+p)J

(4)

where n is the electron concentration and e~ the dielectric constant of the material. From the typical values o f p = 1018 cm -3, T = 200 K and e~ = 28.0, we obtain /_~ = 43 A. Since space charge layers exist at both sides of the grain boundary, the thickness of the potential barrier through which carriers must tunnel is 86 A. This value suggests that a tunnelling phenomenon is possible. In Fig. 7 Hall mobilities at room temperature are directly related to the average grain diameter. The Hall mobilities appear to increase linearly with increasing grain size, reaching a value of 280 cm 2 V-~ sec-1 for 1.5 lain diameter. This linear correlation, which indicates grain boundary scattering to be predominant, is reasonable in a range where the grain size is relatively small. However, for large grain Te films the result is rather bewildering because lattice scattering, rather than grain boundary scattering, predominates in these films at room temperature. A possible explanation for this is a reduction of the neutral impurity centres due to an annealing effect at the elevated substrate temperatures at which large grain Te films are prepared. 4. CONCLUSION The temperature dependence of the Hall mobility of Te films with various grain sizes was measured and compared with theoretical values. It was found that #a for a large grain Te film approaches the theoretical lattice scattering mobility in the high temperature region, while in the low temperature region it deviates considerably from the calculated impurity scattering mobility. The deviation is quite large in a fine grain Te film over the whole temperature range between 77 and 330 K. From the logarithmic plot of/~f 1, a relation of the form/~v = #0 exp (-q¢/kT) was obtained. These results lead to the conclusion that the potential barriers at the grain boundaries are significant in determining the Hall mobility of a fine grain Te film over a wide range of temperatures, and in determining the Hall mobility of a large grain Te film in the low temperature region. ACKNOWLEDGMENTS

Thanks are due to Prof. Y. Kumagai of Yamagata University and Prof. M. Wada and Prof. S. Yoshida of Tohoku University for their helpful discussions. The assistance of Mr. N. Mori and Mr. R. Enomoto during the course of these experiments is also appreciated. REFERENCES 1 R.W. Dutton and R. S. Muller, Proc. IEEE, 59 (1971) 1511. 2 M.J. CapersandM. White, ThinSolidFilms, 15(1973) 5. 3 A. Goswami and S. M. Ojha, Thin Solid Films, 16 (1973) 187. 4 K. Okuyama and Y. Kumagai, Jpn. J. Appl. Phys., 12 (1973) 1884. 5 K. Okuyama and Y. Kumagai, J. Appl. Phys., 46 (1975) 1473.

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6 K.L. Chopra, Thin Film Phenomena, McGraw-Hill, New York, 1969, p. 436. 7 A. Waxman, V. E. Henrich, F. V. Shallcross, H. Borkan and P. K. Weimer, J. Appl. Phys., 36 (1965) 168. 8 H.F. van Heek, Solid-State Electron., 11 (1968) 459. 9 S. Espevik, C. Wu and R. H. Bube, J. Appl. Phys., 42 (1971) 3513.