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Electrical size effects of thin C54-TiSi2 films grown on silicon substrates
0038-1098/88 $3.00 + .00 Pergamon Press plc
Solid State Communications, Vol. 65, No. 12, pp. 1613-1616, 1988. Printed in Great Britain.
E L E C T R I C A L SIZE EFFECTS OF THIN C54-TiSi2 FILMS G R O W N ON SILICON SUBSTRATES Jeng-Rern Yang* and Juh Tzeng Luet National Tsing Hua University, Hsinchu, Taiwan, Republic of China
(Received 26 October 1987 by I4". SasakO The temperature dependences of the Hall constant R , and resistivity Q at various thicknesses for C54-TiSi2 films grown on (1 1 1) and (1 00) silicon substrates are measured. The resistivity increases as temperature increases with a character incongruent with the Bloch-Gruneisen equation as followed by normal metals. The magnitude of R , has a fiat appearance at high temperatures (for T > 400 K), and increases as the temperature decreases and reaches a maximum value near 360 K, and then decreases to reverse the sign at low temperatures. The thinner the film thickness, the higher the temperature for sign reversal. The experimental data can be satisfactorily explained by the classical size effect and two-band model,
A L T H O U G H metallic silicides have been generally applied to very-large-scale-integrations (VLSI) as the gate and ohmic-contact materials, the mechanism of carrier transport phenomena for silicides are still largely heuristic and superficial. Titanium silicide because of its lowest resistivity in the whole refractory metal silicides and select-area etchability by self-aligned technique is considered to be a very useful material for the fabrication of three-dimensional integrated circuits [1]. Malhotra et al. [2] was the first to measure the temperature dependence of the resistivity of TiSi2 and Hall effects on Corbino disk samples. They have hastily discarded the isotropic two-band model just from a single data taken at room temperature. In this work, we have intended to measure the temperature dependence of the electrical resistivity and Hall constants of TiSi2 grown on silicon substrates with various thickness. The experimental data clearly justify the anisotropic Fermi surface and the two band conducting models. Size effect derived by Fuchs [3] is extended to two-band conductors to evaluate the transport parameters and the agreement with the existing data is good. Titanium films are electron-gun deposited on (1 1 1) and (1 00) silicon surfaces at a rate o f 2 A sec -I . The metalization is performed by isothermal annealing at 850°C under a vacuum below 1 x 10-6torr. The samples are stacked by face-to-face arrangement so that the oxidation and impurity diffusion with the
* Department of Electrical Engineering. 1" Department of Physics.
residual gases during annealing are relieved. The final stable structure of TiSi2 as examined by a transmission electron microscope (TEM) is shown to be a facecentered orthorhombic C54 phase with the three principal axes to be a0 = 8.253, b0 = 4.783 and Co = 8.54A. The grain size is about 1.5#m for the 800°C, 6 min annealed samples and growths with time obeying diffusion-limited equation. Surface morphologies indicate that many defects exist in the grain boundaries which are believed to be due to the impurity drag effect [4] and/or the thickness inhibit effect [5]. The orientation relationships of the epitaxial TiSi2 film with the substrate are (1 0 0) TiSi2//(1 1 1) Si and (1 1 0) TiSi2//(1 1 1) Si, whereas no prefered orientation is observed on (1 0 0) Si substrates [6]. 25
Ti/(111)Si BSOC1hr.
/ ~
r
20-
15-
~o->_
cz:
0
~5 1'20 1'45 ho l'ss ~20 ~4s bo ~ TEMPERATURE (K)
J20 J45 bo ~95
Fig. 1. The temperature dependence of the resistivity for TiSi2 on (1 1 1) and (1 00) silicon substrates. The film thickness is 2500/k. The solid line is the theoretical fitting by equation (1). 1613
C54-TiSi2 FILMS G R O W N ON SILICON SUBSTRATES
1614 1.6
15-
THICKNESS THICKNESS o THICKNESS • THICKNESS - THICKNESS
= THICKNESS 180A 1.5-
\ \ ~ .
o THICKNESS 260A * THICKNESS 400A • THICKNESS 700A -THICKNESS 1250A
1.4-
o
1.3-
~:
1.2-
Vol. 65, No. 12 o
10o
o ~
188A 260A 4OOA 7OOA 1250A
50LU -5.
~__ 1.1_
N
_
.
.
_ ~ - ~ - - - ~
,
-10-
1-
U -15-
0
1'~ 1'45 1'70 1'S5 ~ 545 570 "~ TEMPERATURE ( K )
~
-20
~45 ~70
70
~O
1'1o
,'3o
1'so
¢70
TEMPERATURE ( K )
1'9o ~,o
lao
550 27~
Fig. 2. The temperature dependence on the resistivity Fig. 4. Temperature dependence of Hall constant for ratio at various thickness for TiSi2 on (1 0 0) Si sub- TiSi2 grown on (1 00) Si at various thickness. The solid line is the fitting by two-band size effect. strates. The leading wires for electrical measurements were attached with silver paste in form of van der Pauw pattern [7]. A compact liquid-nitrogen cryostat (Oxford DN710) and a temperature controller with a precision of 0.05% (Oxford DTC2) are implemented for the temperature dependence measurement. The temperature dependences of resistivity for thick films (~2500A)grown on (1 1 l) and (1 00) Si substrates are shown in Fig. 1. The solid lines are the theoretical plots of the Bloch-Gruneisen equation [8] OD/T
e(T) = eo + 4e'TS/04~ J 0
x xS[(e~ - 1)(1 - e-~)] -l dx,
(1)
where Q0is the residual resistivity due to crystal imperfections and impurity scatterings, Q' is a constant spe-
cifying the high temperature limit, and 0D is the Debye temperature. The best fitting of the experimental data with equation (1) implies 0D-~ 500~600K and O0 = 2 ~ 3 / ~ - c m which are compatible to the data obtained elsewhere [2]. The Fermi surface for TiSi2 is supposed to be highly anisotropic due to its elongated structure. The shortest reciprocal-lattice-vectors [0 1 0] intend to lying on the conducting plane for TiSi2 films on (l 1 1) Si substrates in which the Fermi-surface will be close to the Brillouin zone and the Umklapp phonon scattering will be dominant. It can be expected that the resistivity as shown in Fig. l for TiSi2 on (1 1 l) Si will be greater than those on the (1 00) Si substrates. The thickness dependence on the resistivity as shown in Fig. 2 was obtained by controlled chemical etching of TiSi 2 films from an original thickness of
O, 200,1.721
f
[280,L~SO0,O~Sf~)
(c,~
.
t•eo~o ,j
1 Fig. 3. The theoretical stereogram of the resistivity ratio ct at various thickness and temperatures.
(
Fig. 5. Theoretical stereogram of the Hall reduced factor fl at various temperature and thickness.
Vol. 65, No. 12
C54-TiSi 2 FILMS G R O W N ON SILICON SUBSTRATES
1250A. The resistivity increase as the thickness decreases in a manner preferentially following Fuchs size effect [3] as
1 -- e x p ( - k t ) x 1 - pexp(-kt)
dt
t
,
(2)
.1
where/~f and P-0 are the mobilities for film and bulk samples respectively, k is the ratio of the film thickness d to the bulk mean-free-path 1, and p is the carrier diffusion coefficient on the boundaries. For two-band model, the size effect due to electron and hole should be considered separately. We can define a parameter a to specify the ratio of the resistivity for thin film and bulk or
o~ = 0[/0o = (N~#¢o + Nh#ho)/(N~kte + NhPh),
(3)
where/~¢0 and #h0 are the electron and hole mobilities in bulk, respectively. The experimental values of ~ are shown in Fig. 2. The Hall constant contributed by both electrons and holes in the low field limit can be written as [9]
RH =
l (Neb 2 - Nh) e (N¢b + Nh) 2'
exponentially at low temperatures and for thin films where the size effect becomes prominant. It can be inspected from Fig. 5, the fl decreases as the temperature decreases and/or the film thickness is reduced, conclusively in congruent with the experimental data as shown in Fig. 4. The solid line is the fitting by two-band size effect. Since the band structure and the Fermi-surface of silicides are still not been attempted [10], the simple two-band model and the size effect can only successfully explain the conducting mechanism within the temperature regions of isotropic scattering (below 270 K). At high temperatures, the strong temperature dependence of the Umklapp process will overwhelm the normal process, and the thickness dependence of Hall constant can not be described by the simple Fuchs size-effect. The other effects on the electric resistivity are the Kondo effect [11, 12] due to the presence of magnetic impurities, and the phonon drag effect [13, 14]. Both of these effects has a negative temperature dependence on the resistivity and usually pronounced for short time annealed samples in which many host impurities and structure voids are present due to deficient in time for precipitation and curing.
(4)
where b = /~¢/#h. Within the temperature range of 150 ~ 250 K, the relaxation time of electrons and holes are both characterized by the small angle scattering, and almost have the same temperature dependence. The size effect (i.e. the scattering of carriers by the boundary as d becomes comparable or less than l), the electron with higher mobility has a longer l which meet the size effect first as the temperature decreases and the reduction of#¢ (or b) is rather prominant than /~h" Therefore Ru reverse sign at certain temperatures as shown in Fig. 4. To examine the size effect on the factor b, we can define a reduction factor fl by
A cknowledgements--This work was supported by the National Science Council of the Republic of China. The authors are indebted to Mr. I.C. Wu for his TEM measurements and to the Materials Science Center of National Tsing Hua University for providing the useful facilities. REFERENCES !. 2. 3. 4.
b = fl(t) #~o.
1615
(5)
#h0
A simultaneous solution of equations (2)-(5) for the best fitting with the experimental data implies the important parameters for TiSi2 on (1 0 0) Si substrates at 77 K which are ne = 2.2 x 1 0 2 2 c m - 3 , n h = 1.1 x 1023cm-3, p = 0.35, l~ = 900A, lh = 257A, /~ = 44.12cm2v.s. -t and/~h = 16-78cmEv-s.-m- These parameters change with temperature and are exploited to calculate the stereograms of ct(t, z) and fl(t, r). As shown in Fig. 3, the value of ~ tends to be flat at high temperatures and for thick films, and will be enhanced
5. 6. 7. 8. 9. I0.
R.T. Tung, A.F.J. Levi & J.M. Gibson, J. Vac. Technol. !14, 1435 (1986). V. Malhotra, T.L. Martin & J.E. Mahau, J. Vac. Sci. Technol. B2, 10 (1984). K. Fuchs, Proc. Cambridge Phil. Soc. 34, 100 (1938). R.W. Cahn, Physical Metallurgy, p. 1654, (Edited by K.W. Cahn) Elsevier Science Pub. B.V. (1983). R.W. Cahn, Physical Metallurgy, p. 1656, (Edited by K.W. Cahn) Elsevier Science Pub. B.V. (1983). I.C. Wu & L.J. Chen, J. Appl. Phys. 60, 3172 (1986). P.M.H. Emenger, Rev. Sci. Instrum. 44, 698 (1973). J.M. Ziman, Electrons and Phonons, Oxford University Press, London (1960). C.M. Hurd, The Hall Effect in Metals and Alloys, p. 89 Plenum Press, New York (1972). K. Lee & J.T. Lue, Phys. Lett. 125, 271 (1987).
1616 11. 12.
C54-TiSi2 FILMS G R O W N ON SILICON SUBSTRATES J. Kondo, Theory of Dilute Magnetic Alloys, Solid State Phys. 23, 184 (1969). J.R. Schrreffer, J. AppL Phys. 38, 1143 (1967).
13. 14.
Vol. 65, No. 12
R. Suri, A.P. Thakoor & K.C. Chopra, J. Appl. Phys. 46, 2574 (1975). R.P. Huebener, Phys. Rev. 146, 502 (1966).
Solid State Communications, Vol. 65, No. 12, pp. 1613-1616, 1988. Printed in Great Britain.
E L E C T R I C A L SIZE EFFECTS OF THIN C54-TiSi2 FILMS G R O W N ON SILICON SUBSTRATES Jeng-Rern Yang* and Juh Tzeng Luet National Tsing Hua University, Hsinchu, Taiwan, Republic of China
(Received 26 October 1987 by I4". SasakO The temperature dependences of the Hall constant R , and resistivity Q at various thicknesses for C54-TiSi2 films grown on (1 1 1) and (1 00) silicon substrates are measured. The resistivity increases as temperature increases with a character incongruent with the Bloch-Gruneisen equation as followed by normal metals. The magnitude of R , has a fiat appearance at high temperatures (for T > 400 K), and increases as the temperature decreases and reaches a maximum value near 360 K, and then decreases to reverse the sign at low temperatures. The thinner the film thickness, the higher the temperature for sign reversal. The experimental data can be satisfactorily explained by the classical size effect and two-band model,
A L T H O U G H metallic silicides have been generally applied to very-large-scale-integrations (VLSI) as the gate and ohmic-contact materials, the mechanism of carrier transport phenomena for silicides are still largely heuristic and superficial. Titanium silicide because of its lowest resistivity in the whole refractory metal silicides and select-area etchability by self-aligned technique is considered to be a very useful material for the fabrication of three-dimensional integrated circuits [1]. Malhotra et al. [2] was the first to measure the temperature dependence of the resistivity of TiSi2 and Hall effects on Corbino disk samples. They have hastily discarded the isotropic two-band model just from a single data taken at room temperature. In this work, we have intended to measure the temperature dependence of the electrical resistivity and Hall constants of TiSi2 grown on silicon substrates with various thickness. The experimental data clearly justify the anisotropic Fermi surface and the two band conducting models. Size effect derived by Fuchs [3] is extended to two-band conductors to evaluate the transport parameters and the agreement with the existing data is good. Titanium films are electron-gun deposited on (1 1 1) and (1 00) silicon surfaces at a rate o f 2 A sec -I . The metalization is performed by isothermal annealing at 850°C under a vacuum below 1 x 10-6torr. The samples are stacked by face-to-face arrangement so that the oxidation and impurity diffusion with the
* Department of Electrical Engineering. 1" Department of Physics.
residual gases during annealing are relieved. The final stable structure of TiSi2 as examined by a transmission electron microscope (TEM) is shown to be a facecentered orthorhombic C54 phase with the three principal axes to be a0 = 8.253, b0 = 4.783 and Co = 8.54A. The grain size is about 1.5#m for the 800°C, 6 min annealed samples and growths with time obeying diffusion-limited equation. Surface morphologies indicate that many defects exist in the grain boundaries which are believed to be due to the impurity drag effect [4] and/or the thickness inhibit effect [5]. The orientation relationships of the epitaxial TiSi2 film with the substrate are (1 0 0) TiSi2//(1 1 1) Si and (1 1 0) TiSi2//(1 1 1) Si, whereas no prefered orientation is observed on (1 0 0) Si substrates [6]. 25
Ti/(111)Si BSOC1hr.
/ ~
r
20-
15-
~o->_
cz:
0
~5 1'20 1'45 ho l'ss ~20 ~4s bo ~ TEMPERATURE (K)
J20 J45 bo ~95
Fig. 1. The temperature dependence of the resistivity for TiSi2 on (1 1 1) and (1 00) silicon substrates. The film thickness is 2500/k. The solid line is the theoretical fitting by equation (1). 1613
C54-TiSi2 FILMS G R O W N ON SILICON SUBSTRATES
1614 1.6
15-
THICKNESS THICKNESS o THICKNESS • THICKNESS - THICKNESS
= THICKNESS 180A 1.5-
\ \ ~ .
o THICKNESS 260A * THICKNESS 400A • THICKNESS 700A -THICKNESS 1250A
1.4-
o
1.3-
~:
1.2-
Vol. 65, No. 12 o
10o
o ~
188A 260A 4OOA 7OOA 1250A
50LU -5.
~__ 1.1_
N
_
.
.
_ ~ - ~ - - - ~
,
-10-
1-
U -15-
0
1'~ 1'45 1'70 1'S5 ~ 545 570 "~ TEMPERATURE ( K )
~
-20
~45 ~70
70
~O
1'1o
,'3o
1'so
¢70
TEMPERATURE ( K )
1'9o ~,o
lao
550 27~
Fig. 2. The temperature dependence on the resistivity Fig. 4. Temperature dependence of Hall constant for ratio at various thickness for TiSi2 on (1 0 0) Si sub- TiSi2 grown on (1 00) Si at various thickness. The solid line is the fitting by two-band size effect. strates. The leading wires for electrical measurements were attached with silver paste in form of van der Pauw pattern [7]. A compact liquid-nitrogen cryostat (Oxford DN710) and a temperature controller with a precision of 0.05% (Oxford DTC2) are implemented for the temperature dependence measurement. The temperature dependences of resistivity for thick films (~2500A)grown on (1 1 l) and (1 00) Si substrates are shown in Fig. 1. The solid lines are the theoretical plots of the Bloch-Gruneisen equation [8] OD/T
e(T) = eo + 4e'TS/04~ J 0
x xS[(e~ - 1)(1 - e-~)] -l dx,
(1)
where Q0is the residual resistivity due to crystal imperfections and impurity scatterings, Q' is a constant spe-
cifying the high temperature limit, and 0D is the Debye temperature. The best fitting of the experimental data with equation (1) implies 0D-~ 500~600K and O0 = 2 ~ 3 / ~ - c m which are compatible to the data obtained elsewhere [2]. The Fermi surface for TiSi2 is supposed to be highly anisotropic due to its elongated structure. The shortest reciprocal-lattice-vectors [0 1 0] intend to lying on the conducting plane for TiSi2 films on (l 1 1) Si substrates in which the Fermi-surface will be close to the Brillouin zone and the Umklapp phonon scattering will be dominant. It can be expected that the resistivity as shown in Fig. l for TiSi2 on (1 1 l) Si will be greater than those on the (1 00) Si substrates. The thickness dependence on the resistivity as shown in Fig. 2 was obtained by controlled chemical etching of TiSi 2 films from an original thickness of
O, 200,1.721
f
[280,L~SO0,O~Sf~)
(c,~
.
t•eo~o ,j
1 Fig. 3. The theoretical stereogram of the resistivity ratio ct at various thickness and temperatures.
(
Fig. 5. Theoretical stereogram of the Hall reduced factor fl at various temperature and thickness.
Vol. 65, No. 12
C54-TiSi 2 FILMS G R O W N ON SILICON SUBSTRATES
1250A. The resistivity increase as the thickness decreases in a manner preferentially following Fuchs size effect [3] as
1 -- e x p ( - k t ) x 1 - pexp(-kt)
dt
t
,
(2)
.1
where/~f and P-0 are the mobilities for film and bulk samples respectively, k is the ratio of the film thickness d to the bulk mean-free-path 1, and p is the carrier diffusion coefficient on the boundaries. For two-band model, the size effect due to electron and hole should be considered separately. We can define a parameter a to specify the ratio of the resistivity for thin film and bulk or
o~ = 0[/0o = (N~#¢o + Nh#ho)/(N~kte + NhPh),
(3)
where/~¢0 and #h0 are the electron and hole mobilities in bulk, respectively. The experimental values of ~ are shown in Fig. 2. The Hall constant contributed by both electrons and holes in the low field limit can be written as [9]
RH =
l (Neb 2 - Nh) e (N¢b + Nh) 2'
exponentially at low temperatures and for thin films where the size effect becomes prominant. It can be inspected from Fig. 5, the fl decreases as the temperature decreases and/or the film thickness is reduced, conclusively in congruent with the experimental data as shown in Fig. 4. The solid line is the fitting by two-band size effect. Since the band structure and the Fermi-surface of silicides are still not been attempted [10], the simple two-band model and the size effect can only successfully explain the conducting mechanism within the temperature regions of isotropic scattering (below 270 K). At high temperatures, the strong temperature dependence of the Umklapp process will overwhelm the normal process, and the thickness dependence of Hall constant can not be described by the simple Fuchs size-effect. The other effects on the electric resistivity are the Kondo effect [11, 12] due to the presence of magnetic impurities, and the phonon drag effect [13, 14]. Both of these effects has a negative temperature dependence on the resistivity and usually pronounced for short time annealed samples in which many host impurities and structure voids are present due to deficient in time for precipitation and curing.
(4)
where b = /~¢/#h. Within the temperature range of 150 ~ 250 K, the relaxation time of electrons and holes are both characterized by the small angle scattering, and almost have the same temperature dependence. The size effect (i.e. the scattering of carriers by the boundary as d becomes comparable or less than l), the electron with higher mobility has a longer l which meet the size effect first as the temperature decreases and the reduction of#¢ (or b) is rather prominant than /~h" Therefore Ru reverse sign at certain temperatures as shown in Fig. 4. To examine the size effect on the factor b, we can define a reduction factor fl by
A cknowledgements--This work was supported by the National Science Council of the Republic of China. The authors are indebted to Mr. I.C. Wu for his TEM measurements and to the Materials Science Center of National Tsing Hua University for providing the useful facilities. REFERENCES !. 2. 3. 4.
b = fl(t) #~o.
1615
(5)
#h0
A simultaneous solution of equations (2)-(5) for the best fitting with the experimental data implies the important parameters for TiSi2 on (1 0 0) Si substrates at 77 K which are ne = 2.2 x 1 0 2 2 c m - 3 , n h = 1.1 x 1023cm-3, p = 0.35, l~ = 900A, lh = 257A, /~ = 44.12cm2v.s. -t and/~h = 16-78cmEv-s.-m- These parameters change with temperature and are exploited to calculate the stereograms of ct(t, z) and fl(t, r). As shown in Fig. 3, the value of ~ tends to be flat at high temperatures and for thick films, and will be enhanced
5. 6. 7. 8. 9. I0.
R.T. Tung, A.F.J. Levi & J.M. Gibson, J. Vac. Technol. !14, 1435 (1986). V. Malhotra, T.L. Martin & J.E. Mahau, J. Vac. Sci. Technol. B2, 10 (1984). K. Fuchs, Proc. Cambridge Phil. Soc. 34, 100 (1938). R.W. Cahn, Physical Metallurgy, p. 1654, (Edited by K.W. Cahn) Elsevier Science Pub. B.V. (1983). R.W. Cahn, Physical Metallurgy, p. 1656, (Edited by K.W. Cahn) Elsevier Science Pub. B.V. (1983). I.C. Wu & L.J. Chen, J. Appl. Phys. 60, 3172 (1986). P.M.H. Emenger, Rev. Sci. Instrum. 44, 698 (1973). J.M. Ziman, Electrons and Phonons, Oxford University Press, London (1960). C.M. Hurd, The Hall Effect in Metals and Alloys, p. 89 Plenum Press, New York (1972). K. Lee & J.T. Lue, Phys. Lett. 125, 271 (1987).
1616 11. 12.
C54-TiSi2 FILMS G R O W N ON SILICON SUBSTRATES J. Kondo, Theory of Dilute Magnetic Alloys, Solid State Phys. 23, 184 (1969). J.R. Schrreffer, J. AppL Phys. 38, 1143 (1967).
13. 14.
Vol. 65, No. 12
R. Suri, A.P. Thakoor & K.C. Chopra, J. Appl. Phys. 46, 2574 (1975). R.P. Huebener, Phys. Rev. 146, 502 (1966).