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Hall effect studies of zinc oxide monocrystalline films
Thin Solid Films, 36 (1976) 179-182 © Elsevier Sequoia S.A., Lausanne--Printed in Switzerland
179
HALL EFFECT STUDIES OF ZINC OXIDE MONOCRYSTALLINE FILMS
D. I. D I M O V A - A L I A K O V A Institute o f Solicl State Physics, Sofia 13, bulv. Lenin 72 (Bulgaria)
(Received August 25, t975)
1. INTRODUCTION The electrical and optical properties of zinc oxide have been extensively studied in a number of laboratories in recent years l'z. Zinc oxide has a wurzite crystal structure. Most investigations agree that ZnO is a metal-excess n-type semiconductor, with interstitial zinc ions as the predominant point defects. Zinc oxide has ~ a large energy gap of 3.4 eV near 0 K. Several investigations of the Hall mobility of electrons in the c crystallographic direction have been conducted on low resistivity single crystals 3, sintered specimens 4 and thin polycrystalline films 5 of ZnO. The Hall mobility study of single-crystal ZnO performed by Hutson 3 is particularly interesting for understanding electron scattering processes in ZnO, because he was successful in interpreting the observed temperature dependence of the mobility on the basis of a combination of impurity, acoustic and optical mode scattering. In his other work 6 this author has found that the electron mobility in single-crystal ZnO is limited by piezoelectric scattering. In the present investigation the Hall mobility of electrons in "pure" zinc oxide monocrystalline thin films was measured over the temperature range 98-400 K. The data are analyzed to determine the variation of the carrier mobility with temperature. The results are interpreted in terms of the existing theories of semiconductors. 2. SAMPLEPREPARATION The monocrystalline films were grown by a vapor phase transport reaction between zinc oxide and hydrogen on an A120 3 substrate 7. The substrate temperature was about 640 °C and the temperature of the evaporation was varied from 720 °C to 790 °C. The thickness of the films was in the range 3-100/am. Investigation of the optical properties, ultraviolet refraction and luminescence, indicated that the optical spectra of the films were the same as those of zinc oxide single crystals. They were published earlier in ref. 8. The films had resistivities in the range 0.1-0.5 f2 cm. Electrical contacts to the ZnO were made by evaporating a zinc thin film and covering it with an evaporated Ag thin film. Measurements of the Hall mobility and the conductivity were performed with the equipment described earlier 5. * Paper presented at the Third International Conference on Thin Films, "Basic Problems, Applications and Trends", Budapest, Hungary, August 25-29, 1975; Paper 9-63.
180
D.I. DIMOVA-ALIAKOVA
3. E X P E R I M E N T A L RESULTS
Measurements of the conductivity and the Hall effect were made for several monocrystalline films grown at different substrate temperatures. The results of the measurement of Hall mobility are shown in Fig. 1. It can be seen that all the mobility curves have almost the same temperature dependence. The magnitude of the mobility of these samples at room temperature increases from 30 cm 2 V -1 s-1 to 100 cm z V -1 s-1 as the evaporation temperature increases from 720 °C to 790 °C. We found that the Hall mobility was very dependent on the carrier concentration, and that it decreased from 100 cm 2 V -1 s-1 to 30 cm 2 V -1 s-1 as the carrier concentration increased from 1.2 x 1017 cm -3 to 1.5 x 1018 cm -3 (Fig. 2). 200
f
"'~
""7
too
% ~
t~
so
== ~o2
:.7
,
~
,.c_
% u
io)I
20 2
4
6
8
10 103/T, *K
I
I
1017 2
s
I
10)a
I
2
concentration( cm-3 )
Fig. i. The mobility data for several samples, prepared with Tsubs = 640 °C and with the following evaporation temperatures: curve 1 , 7 1 8 °C; curve 2 , 7 4 8 °C; curve 3, 765 °C; curve 4 , 7 9 0 °C. Fig. 2. The dependence o f the Hall mobility on the carrier concentration.
4. DISCUSSION The scattering processes which determine the electron mobility and its temperature dependence arise from the thermal vibrations of the lattice and from impurity centers. The lattice vibrations should play the predominant role at higher temperatures, and the impurities can be expected to become more important at Ion temperatures. Typical mobility data for films of two different donor concentrations are shown in Fig. 3. The variation of mobility with temperature suggests that lattice scattering is dominant but that impurity scattering also contributes at low temperatures. The expression for electron mobility for the optical scattering mode alone as derived from perturbation theory is 3
~o~ Uo -
3
l (=,~o~01)
l<~ ~
~_,o_ ( ~o t ~ ×(ZXe z - l) ~o \ m * . / -U <~ -
(1)
HALL EFFECT IN ZnO THIN FILMS
181
2000 1000 i
60O "T
•
r
• , ~.r.7
400
'.~ ",
r'# t
2O0 L> v
100 E
/1
6O 40 20
u
600 400 200 100 60 temperature, =K
Fig. 3. The mobility data for two samples with different ionized donor concentrations (circles, 1.5 x 1017 cm-2; squares, 1.5 x 10 is cm-3) compared with a combination of the optical (#o), acoustic (#a) and piezoelectric (#p) scattering modes and ionized and neutral impurity scattering.
where a o = h2/moe2;Z = 01/T; m*n/m o = 0.27 (ref. 3); and e = 8.5 (ref. 3), the static dielectric constant for ZnO. From eqn. (1) the mobility/.to for ZnO which results from the optical scattering mode alone is shown in Fig. 3. When this is compared with the experimental results of Hall mobility the agreement is very satisfactory. The curve of go lies just above the experimental points, and therefore the addition of some other mode of scattering can be assumed. If we assume the presence of acoustic mode scattering of the form #a ~ T -a/2, we should have the total curve of #1'. Hutson6 found that the electron mobility limited by piezoelectric scattering alone in ZnO is (in cm 2 V-1 s-l)
#p'~-'50(m°~3/2(3-~) m,n]
(2)
The curve #1 = # o # p / ~ o + #p) shown in Fig. 3 shows a better agreement between theory and experiment than the theoretical curve #1' = #o#a/(#o + #a)" Impurity scattering mobilities have been computed using the Conwell-Weisskopf formula for ionized centers and Erginsoy's formula for neutral donors. The scalar effective mass rn* n = 0.27 m o was used, and the concentrations of neutrat and ionized centers were obtained from the Hall effect analysis, with the assumption of a single hydrogen-like donor level. The total mobility was obtained simply from the sum of the reciprocal values of the individual mobilities. The curves #::1 and #~2 in Fig. 3 show the total mobility compared with the experimental data for two specimens with different ionized donor concentrations. It appears that the difference between the experimental and theoretical data is greater for the specimen with the higher ionized donor concentration. However, the ionized donor concentration in this sample is so high that the distance between ionized donors is less than the wavelength of a thermal electron, a situation which probably invalidates the present theory of impurity scattering.
182
D.I. DIMOVA-ALIAKOVA
ACKNOWLEDGMENTS The author is grateful to Dr. Prof. K. V. Schalimowa and P h . D . M. M. Malov for helpful discussions. Dr. S. A. Semiletov and Dr. N. G. Riabtzev deserve special recognition for the monocrystalline films of ZnO. The present investigation was performed in the Laboratory of Semiconductor Devices in the Moscow Institute of Energy. REFERENCES 1 2 3 4 5 6 7 8
G. Hieland, E. Mollwo and F. Stockmann, Solid State Phys., 8 (1959) 191. D. G. Thomas, J. Phys. Chem. Solids, 15 (1960) 86. A. R. Hutson, Phys. Rev., 108 (1957) 222. S. E. Harrison, Phys. Rev., 93 (1954) 52. D. I. Dimova-Aliakova, Ph.D. Dissertation, Moscow, 1974. A. R. Hutson, Phys. Rev. Lett., 4 (1960) 505. R. A. Rabadanov, S. A. Semiletov and Z. A. Magomedov, Soy. Phys.-Solid State, 12 (1970) 143 M. M. Malov, D. I. Dimova-Aliakova, S. A. Kazandjev, V. A. Nikitenko and R. A. Rabadanov, Tr. Mosk. Energ. Inst., 192 (1974) 89.
179
HALL EFFECT STUDIES OF ZINC OXIDE MONOCRYSTALLINE FILMS
D. I. D I M O V A - A L I A K O V A Institute o f Solicl State Physics, Sofia 13, bulv. Lenin 72 (Bulgaria)
(Received August 25, t975)
1. INTRODUCTION The electrical and optical properties of zinc oxide have been extensively studied in a number of laboratories in recent years l'z. Zinc oxide has a wurzite crystal structure. Most investigations agree that ZnO is a metal-excess n-type semiconductor, with interstitial zinc ions as the predominant point defects. Zinc oxide has ~ a large energy gap of 3.4 eV near 0 K. Several investigations of the Hall mobility of electrons in the c crystallographic direction have been conducted on low resistivity single crystals 3, sintered specimens 4 and thin polycrystalline films 5 of ZnO. The Hall mobility study of single-crystal ZnO performed by Hutson 3 is particularly interesting for understanding electron scattering processes in ZnO, because he was successful in interpreting the observed temperature dependence of the mobility on the basis of a combination of impurity, acoustic and optical mode scattering. In his other work 6 this author has found that the electron mobility in single-crystal ZnO is limited by piezoelectric scattering. In the present investigation the Hall mobility of electrons in "pure" zinc oxide monocrystalline thin films was measured over the temperature range 98-400 K. The data are analyzed to determine the variation of the carrier mobility with temperature. The results are interpreted in terms of the existing theories of semiconductors. 2. SAMPLEPREPARATION The monocrystalline films were grown by a vapor phase transport reaction between zinc oxide and hydrogen on an A120 3 substrate 7. The substrate temperature was about 640 °C and the temperature of the evaporation was varied from 720 °C to 790 °C. The thickness of the films was in the range 3-100/am. Investigation of the optical properties, ultraviolet refraction and luminescence, indicated that the optical spectra of the films were the same as those of zinc oxide single crystals. They were published earlier in ref. 8. The films had resistivities in the range 0.1-0.5 f2 cm. Electrical contacts to the ZnO were made by evaporating a zinc thin film and covering it with an evaporated Ag thin film. Measurements of the Hall mobility and the conductivity were performed with the equipment described earlier 5. * Paper presented at the Third International Conference on Thin Films, "Basic Problems, Applications and Trends", Budapest, Hungary, August 25-29, 1975; Paper 9-63.
180
D.I. DIMOVA-ALIAKOVA
3. E X P E R I M E N T A L RESULTS
Measurements of the conductivity and the Hall effect were made for several monocrystalline films grown at different substrate temperatures. The results of the measurement of Hall mobility are shown in Fig. 1. It can be seen that all the mobility curves have almost the same temperature dependence. The magnitude of the mobility of these samples at room temperature increases from 30 cm 2 V -1 s-1 to 100 cm z V -1 s-1 as the evaporation temperature increases from 720 °C to 790 °C. We found that the Hall mobility was very dependent on the carrier concentration, and that it decreased from 100 cm 2 V -1 s-1 to 30 cm 2 V -1 s-1 as the carrier concentration increased from 1.2 x 1017 cm -3 to 1.5 x 1018 cm -3 (Fig. 2). 200
f
"'~
""7
too
% ~
t~
so
== ~o2
:.7
,
~
,.c_
% u
io)I
20 2
4
6
8
10 103/T, *K
I
I
1017 2
s
I
10)a
I
2
concentration( cm-3 )
Fig. i. The mobility data for several samples, prepared with Tsubs = 640 °C and with the following evaporation temperatures: curve 1 , 7 1 8 °C; curve 2 , 7 4 8 °C; curve 3, 765 °C; curve 4 , 7 9 0 °C. Fig. 2. The dependence o f the Hall mobility on the carrier concentration.
4. DISCUSSION The scattering processes which determine the electron mobility and its temperature dependence arise from the thermal vibrations of the lattice and from impurity centers. The lattice vibrations should play the predominant role at higher temperatures, and the impurities can be expected to become more important at Ion temperatures. Typical mobility data for films of two different donor concentrations are shown in Fig. 3. The variation of mobility with temperature suggests that lattice scattering is dominant but that impurity scattering also contributes at low temperatures. The expression for electron mobility for the optical scattering mode alone as derived from perturbation theory is 3
~o~ Uo -
3
l (=,~o~01)
l<~ ~
~_,o_ ( ~o t ~ ×(ZXe z - l) ~o \ m * . / -U <~ -
(1)
HALL EFFECT IN ZnO THIN FILMS
181
2000 1000 i
60O "T
•
r
• , ~.r.7
400
'.~ ",
r'# t
2O0 L> v
100 E
/1
6O 40 20
u
600 400 200 100 60 temperature, =K
Fig. 3. The mobility data for two samples with different ionized donor concentrations (circles, 1.5 x 1017 cm-2; squares, 1.5 x 10 is cm-3) compared with a combination of the optical (#o), acoustic (#a) and piezoelectric (#p) scattering modes and ionized and neutral impurity scattering.
where a o = h2/moe2;Z = 01/T; m*n/m o = 0.27 (ref. 3); and e = 8.5 (ref. 3), the static dielectric constant for ZnO. From eqn. (1) the mobility/.to for ZnO which results from the optical scattering mode alone is shown in Fig. 3. When this is compared with the experimental results of Hall mobility the agreement is very satisfactory. The curve of go lies just above the experimental points, and therefore the addition of some other mode of scattering can be assumed. If we assume the presence of acoustic mode scattering of the form #a ~ T -a/2, we should have the total curve of #1'. Hutson6 found that the electron mobility limited by piezoelectric scattering alone in ZnO is (in cm 2 V-1 s-l)
#p'~-'50(m°~3/2(3-~) m,n]
(2)
The curve #1 = # o # p / ~ o + #p) shown in Fig. 3 shows a better agreement between theory and experiment than the theoretical curve #1' = #o#a/(#o + #a)" Impurity scattering mobilities have been computed using the Conwell-Weisskopf formula for ionized centers and Erginsoy's formula for neutral donors. The scalar effective mass rn* n = 0.27 m o was used, and the concentrations of neutrat and ionized centers were obtained from the Hall effect analysis, with the assumption of a single hydrogen-like donor level. The total mobility was obtained simply from the sum of the reciprocal values of the individual mobilities. The curves #::1 and #~2 in Fig. 3 show the total mobility compared with the experimental data for two specimens with different ionized donor concentrations. It appears that the difference between the experimental and theoretical data is greater for the specimen with the higher ionized donor concentration. However, the ionized donor concentration in this sample is so high that the distance between ionized donors is less than the wavelength of a thermal electron, a situation which probably invalidates the present theory of impurity scattering.
182
D.I. DIMOVA-ALIAKOVA
ACKNOWLEDGMENTS The author is grateful to Dr. Prof. K. V. Schalimowa and P h . D . M. M. Malov for helpful discussions. Dr. S. A. Semiletov and Dr. N. G. Riabtzev deserve special recognition for the monocrystalline films of ZnO. The present investigation was performed in the Laboratory of Semiconductor Devices in the Moscow Institute of Energy. REFERENCES 1 2 3 4 5 6 7 8
G. Hieland, E. Mollwo and F. Stockmann, Solid State Phys., 8 (1959) 191. D. G. Thomas, J. Phys. Chem. Solids, 15 (1960) 86. A. R. Hutson, Phys. Rev., 108 (1957) 222. S. E. Harrison, Phys. Rev., 93 (1954) 52. D. I. Dimova-Aliakova, Ph.D. Dissertation, Moscow, 1974. A. R. Hutson, Phys. Rev. Lett., 4 (1960) 505. R. A. Rabadanov, S. A. Semiletov and Z. A. Magomedov, Soy. Phys.-Solid State, 12 (1970) 143 M. M. Malov, D. I. Dimova-Aliakova, S. A. Kazandjev, V. A. Nikitenko and R. A. Rabadanov, Tr. Mosk. Energ. Inst., 192 (1974) 89.