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Angular dependent negative magnetoresistance in Si-MOS (111) inversion layers
Solid State Communications, Vol. 26, pp. 701—703. © Pergamon Press Ltd. 1978. Printed in Great Britain
0038—1098/78/0615---0701 $02.00/U
ANGULAR DEPENDENT NEGATIVE MAGNETORESISTANCE IN Si—MOS (111) INVERSION LAYERS Y. Kawaguchi, H. Kitahara and S. Kawaji Department of Physics, Gakushuin University, Mejiro, Toshima-ku, Tokyo, Japan (Received 26 December 1977 by W. Sasaki) The negative transverse magnetoresistance effect was observed in n-inversion layers in Si—MOS (111) surfaces at temperatures between 1.5 and 8.3 K. The negative magnetoresistance depends only on the normal component of the magnetic field to the surface and has a saturation value at high fields. The difference between the resistivity at zero field and that at saturation field increases logarithmically with decreasing temperature such as the effect due to the s—d scattering (Kondo effect).
THE TRANSPORT PROPERTIES of a two dimensional (2D) electron gas have been extensively studied in semiconductor surface inversion layers. The 2D-nature of conduction electrons in the inversion layers is reflected well in the angular dependence of the Shubnikov—de Haas effect [1] and the weak field normal magnetoresistance [2]. The Landau level splitting in the former and the change in the resistance in the latter depend only on the normal component of the magnetic field to the surface. However, an angular independent magnetoresistance may be expected in the magnetic field effect which depends not on the motion of the conduction electrons but the property of the scattering centers such as localized spins in the Kondo effect. The authors (S.K. and Y.K.) have first observed transverse and longitudinal negative magnetoresistance effects in the naturally grown inversion layers on InAs (110) surfaces cleaved in atmospheric condition at temperatures between 5 and 10K [3]. The effects did not depend on the angle between magnetic field and the surface plane. We have explained the negative magneto-
20 K [5]. As a possible scattering mechanism to explain the negative magnetoresistance effect, we have proposed a magnetic scattering due to a magnetic moment of an orbital motion of an electron in a state other than the s-state in the 2D bound state [5]. In this article, we will describe a similar effect observed in n-inversion layers on Si (111) MOSFETS. Transverse magnetoresistance and Hall effect measurements were carried out on n-inversion layers of MOSFETs fabricated on Si (ill) surface at temperatures between 1.5 and 8.3 K, and under magnetic fields up to 1.5 T. The specimens used had oxide thickness of 800 nm, channel length of 100 jim and channel width of 500 jim. The Hall contacts were placed in the middle of the bar. The maximum mobility of the samples is 1700 cm2 V~1sec~at 4.2 K and the surface state density estimated from the threshold voltage N~= 3.5 x 1015 m2. The negative magnetoresistance was observed at electron densities, N 2. Its 9, more than magnitude at high magnetic fieldsI(Bx 1016 0.7m T) increases with increasing N 8 and become a constant 2. nearly This result agrees value well resistance onspins the basis scattering of dangling 2D electrons of 2.5% N8 of > 2Dorda x 1016and m Eisele [6]. Figure 1 shows by localized such of as the those of surface bond with the for result electrons because the resistance anomaly which is the magnetoresistance in the magnetic field applied described by Po = a log T + b has been observed perpendicular to the surface, (~P/Po)vs magnetic field simultaneously with the negative magnetoresistance curves at N 2 for different temperatures. 9 =fields 5 x 1016 m decreases quadratically. The effects. Eisele and Dorda [4] have recently reported a In the lowest (1~P/Po) negative magnetoresistance effect in Si—MOSFET (100) decrease of (L~p/p 0)becomes less steep as the field inversion layers at low temperatures between 2 and 10K. increases and passes through a minimum value at a They have concluded that the negative magnetoresistance certain field. In the higher fields (~p/p0)begins to was due to the spin scattering in connection with the increase. The magnetoresistance can be decomposed surface states, into two parts. One is an anomalous negative component, We have reported a negative magnetoresistance (~p/p0),which increases quadratically in the lowest effect which depends only on the normal component of fields and has a saturation value at higher fields. Another magnetic field B1 similarly to the ordinary positive is a normal positive component proportional to the magnetoresistance in n-inversion layers in highly Cssquare of the magnetic field. The latter predominates at adsorbed Si (Ill) surfaces at temperatures below the higher fields. The anomalous negative —
701
702
MAGNETORESISTANCE INVERSION LAYERS
\\
2.0 22 0.0
0.5 MAGNETIC FIELD
~
1.0 (Testa)
1.5
Fig. 1. Temperature dependence of transverse magnetoresistance in magnetic fields noi~a1t~ the surface at the carrier density, N9 = 5 x 10 m .
0~0,.0
~
0.941’
T~1.52K 90
Vol. 26, No. 11
7
~ ~,
Si-MOS(111) 44-1 180 270 360
0 I degree) Fig. 2. Angular dependence of2transverse where 0 magneto= 0~at B resistance at N8 = 5 x 1016 m face and 0 = 90°at B 1 surface.
II sur-
magnetoresistance component, (z~p/p0),at different temperatures are expressed by a function of BIT as (~p/poY= —f(B/T) in the low field region. The saturation value of(~p/p0) at high fields depends on temperature. The normal magnetoresistance component 2 where the coefficient, is described (~p/p0)f = bB b, has almostbyconstant value of(6.0 ±0.5) x l0-~T2. Similar negative magnetoresistance effects have been observed in the metallic impurity conduction region of Ge [7], Si [8] and other semiconductors [9], and are explained as the effect due to the scattering by the localized spins, The negative magnetoresistance in the present systems, however, depends only on the normal component of magnetic field to the surface. Figure 2 shows the variation of the transverse magnetoresistance with the change in the angle, 0, between the surface and the magnetic field at 1.5 K, where 0 = 0°when the field is parallel to the surface. The angular dependence of the magnetoresistance is explained as followings. Both of positive and negative magnetoresistance depend only on the normal component of magnetic field with respect to the surface,B1 = B sin 0. The positive normal component, (~p/po)~, increases with B~.On the other hand, the negative component, (~p/p0),is proportional to B~at low field limit and has a saturation value at high magnetic fields. In Fig. 2, at the lowest magnetic field (B = 0.07 2T),0.(IXP/Po) is approximately At a strong field (B = 0.9 proT) which portional to sin gives the minimum value of (~P/Po)in Fig. 1, (Z~P/Po) is almost constant except in the vicinity of 0 = 00 and 180°,where (~~fp~) decreases steeply to zero. At a strong field of B = 1.26 T, (~P/Po)has a peak value at o = 90°and 270°,where B is perpendicular to the surface, and has minimum value of about 2.6% at o = 40°,130°,230°and 320°,where B 1 is nearly 0.91 1 which gives the minimum value of(z~p/p0)= 2.6% at 1.5 K in Fig. 1.
Similar negative magnetoresistances are observed in n-inversion layers of cesium adsorbed Si (111) surfaces [5]measured and SOS—MOSFETs [10]. Dordaofand [6] have an angular dependence theEisele negative magnetoresistance in n-inversion layers in Si—MQS (100) surfaces at strong magnetic field (B = 1 .0 T) tilted up to 90°with respect to the surface. They have observed that (~p/p 0)hada constant value except in the vicinity of 0 = 00, where (z~p/po)is zero. After that they concluded that the negative magnetoresistance was due to the spin scattering. In the present surface [Si—(l11)], however, we have observed clearly that the negative magnetoresistance depends only on B1. The angular dependent effect of the negative magnetoresistance does not support a simple spin scattering model. If the present phenomena come from the localized magnetic moments, the effect similar to the Kondo effect [11] would be expected in the temperature dependence of the resistivity. In the present system, the resistivity decreases gradually with decreasing temperature and does not show the logarithmic temperature dependence. However, it would be expected that other scattering mechanisms that the magnetic scattering have a dominant contribution to the electric conduction. It is easy to seescattering whether exists the logarithmic term due discussed to a magnetic in our case. As was by Sasaki [7],the resistivity due to the magnetic scattering becomes smaller with increasing magnetic field and has saturation value at high fields, thus the difference between the resistivity at zero field and that at saturation field, ~ corresponds to the magnetic scattering due to the localized magnetic moments of the surface bound states. Figure 3 shows that L~p~t increases logarithmically with decreasing temperature. Assuming that the interaction between the conduction
Vol. 26, No. 11
MAGNETORESISTANCE INVERSION LAYERS
(s = 1), equations (1) and (2) give a best fit to the data when the number of2localized moments, Nm, and J are chosen 5.1 x iO’~m and —0.17 eV, respectively, where the density of states, DC, for 2D electron gas in Si (Ill) surfaces is 0.57 eV~.Here, the number of 2D sites in Si (111) surface is taken to be 7.83 x 1018 m2. The number of magnetic moments is about 10% of the number of the surface states, N_. This result suggests that the one-tenth of surface states have the magnetic
SIMOS(111) 441
30
.
‘N
703
.
20 °
moment of orbital motion of an electron in the state other than s-states. The average distance between magnetic moments is about 5.0 x 10-8 m, which is Fig. 3. Temperature dependence of I~P~t = Po P~t~almost ten times larger than the effective Bohr radius of The solid line is calculated from equations (1) and (2) the electron in a (ill) face of Si—SiC) 2 interface,? = forf=—0.l7eVandNm 5.lxIO m 1.2 x 10 m. Therefore, the surface magnetic moments are well localized. electron in a subband and a magnetic moment of an In conclusion, the temperature dependence of the orbital motion of an electron in a 2D bound state is saturation value of the negative magnetoresistance in similar to the s—d exchange interaction, the temperan-inversion layers in (111) Si—MOSFETs is well ture dependence of ~P~t is explained by the 2D version explained by the results of the theory of the electron of Hamman’s formula [3, 11, 12], scattering due to localized magnetic moments. However, the angular dependence of the negative magneto2N 2+4b1h”2 to the suggests electronthat spmsthe but due to the orbitalare motion i [a(7) / J (I) due resistance magnetic moments not o = e in zero magnetic field, where cx(fl and/i are defined by of 2D bound electrons. a(fl= 1 _2JD* In (kT/EF) andb = ir2 s(s + 1)12D*2 for the exchange interaction energy, J, and the density of states per site per one direction spin, D*. In high Acknowledgements The authors are much indebted to magnetic fields, the anomalous resistivity tends to a Professor A. Kawabata for valuable discussion, and also constant value of to A. Yagi,usSony Research for providing withCorporation silicon MOSFETs. ThisCenter, work was 10
I
1.5
2 5 TEMPERATURE (K)
10
—
—
.
—~
—
‘.
—
— —
2hNm
1
—
11 + 4bW2 I
~2j Research supportedfrom by Grant the Ministry in Aids of forEducation Fundamental and Scientific the Grant
‘
,.
8
and ~Psat =
—
Po. For the p-state of bound state
in Aid from Matsunaga Science Foundation. One of the authors (Y.K.) is obliged to the Sakokai Foundation for financial support.
REFERENCES 1.
FANG F.F. & STILES P.J.,Phys. Rev. 174,823(1968).
2.
SAKAKI H. &SUGANO T.,Japanf. App!. Phys. 42, 2053 (1971).
3. 4.
KAWAJI S. & KAWAGUCHI Y.,Proc. 9th mt. Conf Phys. Semicond., p. 780. Moscow (1968). EISELE I. & DORDA G., Phys. Rev. Lett. 32, 1360 (1974).
5. 6.
KAWAGUCHI Y., KITAHARA H. & KAWAJI S. (to be published in Surf Sd.). DORDA G. & EISELE I.,froc. 12th mt. Con,j’. Phys. Semicond., p.704. Stuttgart (1974).
7.
SASAKI W.,J. Phys. Soc. Japan 21 (Suppl.), 543 (1966).
8. 9. 10.
YAMANOUCHI C., MIZUGUCHI K. & SASAKI W.,J. Phys. Soc. Japan 22,859(1967). ISHIDA S. & OTSUKA E.,J. Phys. Soc. Japan 42,542 (1977). HATANAKA K., ONGA H., YASUDA Y. & KAWAJI S. (to be published).
11.
See for example, KONDO J., Solid State Physics (Edited by SEITZ F. & TIJRNBULL D.), Vol. 23, p. 183. Academic Press, New York (1969). HAMMAN D.R.,Phys. Rev. 174,823 (1968).
12.
0038—1098/78/0615---0701 $02.00/U
ANGULAR DEPENDENT NEGATIVE MAGNETORESISTANCE IN Si—MOS (111) INVERSION LAYERS Y. Kawaguchi, H. Kitahara and S. Kawaji Department of Physics, Gakushuin University, Mejiro, Toshima-ku, Tokyo, Japan (Received 26 December 1977 by W. Sasaki) The negative transverse magnetoresistance effect was observed in n-inversion layers in Si—MOS (111) surfaces at temperatures between 1.5 and 8.3 K. The negative magnetoresistance depends only on the normal component of the magnetic field to the surface and has a saturation value at high fields. The difference between the resistivity at zero field and that at saturation field increases logarithmically with decreasing temperature such as the effect due to the s—d scattering (Kondo effect).
THE TRANSPORT PROPERTIES of a two dimensional (2D) electron gas have been extensively studied in semiconductor surface inversion layers. The 2D-nature of conduction electrons in the inversion layers is reflected well in the angular dependence of the Shubnikov—de Haas effect [1] and the weak field normal magnetoresistance [2]. The Landau level splitting in the former and the change in the resistance in the latter depend only on the normal component of the magnetic field to the surface. However, an angular independent magnetoresistance may be expected in the magnetic field effect which depends not on the motion of the conduction electrons but the property of the scattering centers such as localized spins in the Kondo effect. The authors (S.K. and Y.K.) have first observed transverse and longitudinal negative magnetoresistance effects in the naturally grown inversion layers on InAs (110) surfaces cleaved in atmospheric condition at temperatures between 5 and 10K [3]. The effects did not depend on the angle between magnetic field and the surface plane. We have explained the negative magneto-
20 K [5]. As a possible scattering mechanism to explain the negative magnetoresistance effect, we have proposed a magnetic scattering due to a magnetic moment of an orbital motion of an electron in a state other than the s-state in the 2D bound state [5]. In this article, we will describe a similar effect observed in n-inversion layers on Si (111) MOSFETS. Transverse magnetoresistance and Hall effect measurements were carried out on n-inversion layers of MOSFETs fabricated on Si (ill) surface at temperatures between 1.5 and 8.3 K, and under magnetic fields up to 1.5 T. The specimens used had oxide thickness of 800 nm, channel length of 100 jim and channel width of 500 jim. The Hall contacts were placed in the middle of the bar. The maximum mobility of the samples is 1700 cm2 V~1sec~at 4.2 K and the surface state density estimated from the threshold voltage N~= 3.5 x 1015 m2. The negative magnetoresistance was observed at electron densities, N 2. Its 9, more than magnitude at high magnetic fieldsI(Bx 1016 0.7m T) increases with increasing N 8 and become a constant 2. nearly This result agrees value well resistance onspins the basis scattering of dangling 2D electrons of 2.5% N8 of > 2Dorda x 1016and m Eisele [6]. Figure 1 shows by localized such of as the those of surface bond with the for result electrons because the resistance anomaly which is the magnetoresistance in the magnetic field applied described by Po = a log T + b has been observed perpendicular to the surface, (~P/Po)vs magnetic field simultaneously with the negative magnetoresistance curves at N 2 for different temperatures. 9 =fields 5 x 1016 m decreases quadratically. The effects. Eisele and Dorda [4] have recently reported a In the lowest (1~P/Po) negative magnetoresistance effect in Si—MOSFET (100) decrease of (L~p/p 0)becomes less steep as the field inversion layers at low temperatures between 2 and 10K. increases and passes through a minimum value at a They have concluded that the negative magnetoresistance certain field. In the higher fields (~p/p0)begins to was due to the spin scattering in connection with the increase. The magnetoresistance can be decomposed surface states, into two parts. One is an anomalous negative component, We have reported a negative magnetoresistance (~p/p0),which increases quadratically in the lowest effect which depends only on the normal component of fields and has a saturation value at higher fields. Another magnetic field B1 similarly to the ordinary positive is a normal positive component proportional to the magnetoresistance in n-inversion layers in highly Cssquare of the magnetic field. The latter predominates at adsorbed Si (Ill) surfaces at temperatures below the higher fields. The anomalous negative —
701
702
MAGNETORESISTANCE INVERSION LAYERS
\\
2.0 22 0.0
0.5 MAGNETIC FIELD
~
1.0 (Testa)
1.5
Fig. 1. Temperature dependence of transverse magnetoresistance in magnetic fields noi~a1t~ the surface at the carrier density, N9 = 5 x 10 m .
0~0,.0
~
0.941’
T~1.52K 90
Vol. 26, No. 11
7
~ ~,
Si-MOS(111) 44-1 180 270 360
0 I degree) Fig. 2. Angular dependence of2transverse where 0 magneto= 0~at B resistance at N8 = 5 x 1016 m face and 0 = 90°at B 1 surface.
II sur-
magnetoresistance component, (z~p/p0),at different temperatures are expressed by a function of BIT as (~p/poY= —f(B/T) in the low field region. The saturation value of(~p/p0) at high fields depends on temperature. The normal magnetoresistance component 2 where the coefficient, is described (~p/p0)f = bB b, has almostbyconstant value of(6.0 ±0.5) x l0-~T2. Similar negative magnetoresistance effects have been observed in the metallic impurity conduction region of Ge [7], Si [8] and other semiconductors [9], and are explained as the effect due to the scattering by the localized spins, The negative magnetoresistance in the present systems, however, depends only on the normal component of magnetic field to the surface. Figure 2 shows the variation of the transverse magnetoresistance with the change in the angle, 0, between the surface and the magnetic field at 1.5 K, where 0 = 0°when the field is parallel to the surface. The angular dependence of the magnetoresistance is explained as followings. Both of positive and negative magnetoresistance depend only on the normal component of magnetic field with respect to the surface,B1 = B sin 0. The positive normal component, (~p/po)~, increases with B~.On the other hand, the negative component, (~p/p0),is proportional to B~at low field limit and has a saturation value at high magnetic fields. In Fig. 2, at the lowest magnetic field (B = 0.07 2T),0.(IXP/Po) is approximately At a strong field (B = 0.9 proT) which portional to sin gives the minimum value of (~P/Po)in Fig. 1, (Z~P/Po) is almost constant except in the vicinity of 0 = 00 and 180°,where (~~fp~) decreases steeply to zero. At a strong field of B = 1.26 T, (~P/Po)has a peak value at o = 90°and 270°,where B is perpendicular to the surface, and has minimum value of about 2.6% at o = 40°,130°,230°and 320°,where B 1 is nearly 0.91 1 which gives the minimum value of(z~p/p0)= 2.6% at 1.5 K in Fig. 1.
Similar negative magnetoresistances are observed in n-inversion layers of cesium adsorbed Si (111) surfaces [5]measured and SOS—MOSFETs [10]. Dordaofand [6] have an angular dependence theEisele negative magnetoresistance in n-inversion layers in Si—MQS (100) surfaces at strong magnetic field (B = 1 .0 T) tilted up to 90°with respect to the surface. They have observed that (~p/p 0)hada constant value except in the vicinity of 0 = 00, where (z~p/po)is zero. After that they concluded that the negative magnetoresistance was due to the spin scattering. In the present surface [Si—(l11)], however, we have observed clearly that the negative magnetoresistance depends only on B1. The angular dependent effect of the negative magnetoresistance does not support a simple spin scattering model. If the present phenomena come from the localized magnetic moments, the effect similar to the Kondo effect [11] would be expected in the temperature dependence of the resistivity. In the present system, the resistivity decreases gradually with decreasing temperature and does not show the logarithmic temperature dependence. However, it would be expected that other scattering mechanisms that the magnetic scattering have a dominant contribution to the electric conduction. It is easy to seescattering whether exists the logarithmic term due discussed to a magnetic in our case. As was by Sasaki [7],the resistivity due to the magnetic scattering becomes smaller with increasing magnetic field and has saturation value at high fields, thus the difference between the resistivity at zero field and that at saturation field, ~ corresponds to the magnetic scattering due to the localized magnetic moments of the surface bound states. Figure 3 shows that L~p~t increases logarithmically with decreasing temperature. Assuming that the interaction between the conduction
Vol. 26, No. 11
MAGNETORESISTANCE INVERSION LAYERS
(s = 1), equations (1) and (2) give a best fit to the data when the number of2localized moments, Nm, and J are chosen 5.1 x iO’~m and —0.17 eV, respectively, where the density of states, DC, for 2D electron gas in Si (Ill) surfaces is 0.57 eV~.Here, the number of 2D sites in Si (111) surface is taken to be 7.83 x 1018 m2. The number of magnetic moments is about 10% of the number of the surface states, N_. This result suggests that the one-tenth of surface states have the magnetic
SIMOS(111) 441
30
.
‘N
703
.
20 °
moment of orbital motion of an electron in the state other than s-states. The average distance between magnetic moments is about 5.0 x 10-8 m, which is Fig. 3. Temperature dependence of I~P~t = Po P~t~almost ten times larger than the effective Bohr radius of The solid line is calculated from equations (1) and (2) the electron in a (ill) face of Si—SiC) 2 interface,? = forf=—0.l7eVandNm 5.lxIO m 1.2 x 10 m. Therefore, the surface magnetic moments are well localized. electron in a subband and a magnetic moment of an In conclusion, the temperature dependence of the orbital motion of an electron in a 2D bound state is saturation value of the negative magnetoresistance in similar to the s—d exchange interaction, the temperan-inversion layers in (111) Si—MOSFETs is well ture dependence of ~P~t is explained by the 2D version explained by the results of the theory of the electron of Hamman’s formula [3, 11, 12], scattering due to localized magnetic moments. However, the angular dependence of the negative magneto2N 2+4b1h”2 to the suggests electronthat spmsthe but due to the orbitalare motion i [a(7) / J (I) due resistance magnetic moments not o = e in zero magnetic field, where cx(fl and/i are defined by of 2D bound electrons. a(fl= 1 _2JD* In (kT/EF) andb = ir2 s(s + 1)12D*2 for the exchange interaction energy, J, and the density of states per site per one direction spin, D*. In high Acknowledgements The authors are much indebted to magnetic fields, the anomalous resistivity tends to a Professor A. Kawabata for valuable discussion, and also constant value of to A. Yagi,usSony Research for providing withCorporation silicon MOSFETs. ThisCenter, work was 10
I
1.5
2 5 TEMPERATURE (K)
10
—
—
.
—~
—
‘.
—
— —
2hNm
1
—
11 + 4bW2 I
~2j Research supportedfrom by Grant the Ministry in Aids of forEducation Fundamental and Scientific the Grant
‘
,.
8
and ~Psat =
—
Po. For the p-state of bound state
in Aid from Matsunaga Science Foundation. One of the authors (Y.K.) is obliged to the Sakokai Foundation for financial support.
REFERENCES 1.
FANG F.F. & STILES P.J.,Phys. Rev. 174,823(1968).
2.
SAKAKI H. &SUGANO T.,Japanf. App!. Phys. 42, 2053 (1971).
3. 4.
KAWAJI S. & KAWAGUCHI Y.,Proc. 9th mt. Conf Phys. Semicond., p. 780. Moscow (1968). EISELE I. & DORDA G., Phys. Rev. Lett. 32, 1360 (1974).
5. 6.
KAWAGUCHI Y., KITAHARA H. & KAWAJI S. (to be published in Surf Sd.). DORDA G. & EISELE I.,froc. 12th mt. Con,j’. Phys. Semicond., p.704. Stuttgart (1974).
7.
SASAKI W.,J. Phys. Soc. Japan 21 (Suppl.), 543 (1966).
8. 9. 10.
YAMANOUCHI C., MIZUGUCHI K. & SASAKI W.,J. Phys. Soc. Japan 22,859(1967). ISHIDA S. & OTSUKA E.,J. Phys. Soc. Japan 42,542 (1977). HATANAKA K., ONGA H., YASUDA Y. & KAWAJI S. (to be published).
11.
See for example, KONDO J., Solid State Physics (Edited by SEITZ F. & TIJRNBULL D.), Vol. 23, p. 183. Academic Press, New York (1969). HAMMAN D.R.,Phys. Rev. 174,823 (1968).
12.