- Email: [email protected]
Hall measurements on trap states in n-channel Si MOSFETS at 77 K
Solid State Communications, Vol. 33, pp.509—5!!. Pergamon Press Ltd. 1980. Printed in Great Britain. HALL MEASUREMENTS ON TRAP STATES IN n-CHANNEL Si MOSFETS AT 77 K* B. T. Moore and D. K. Ferry Department of Electrical Engineering, Colorado State University, Fort Collins, CO 80523, U.S.A. (Received 16 July 1979 By J. Tauc) We report here on Hall studies of transport in n-channel MOSFETs at 77K. We fInd a fraction of the carriers are localized in trap states lying within the conduction band. These states are not effective as scattering centers. IN AN EARLY STUDY of n-channel inversion layers in MOSFETs, Fang and Fowler [11 found good agreement at 4.2 K between electron surface densities measured from the Hall effect and those estimated from gate capacitance. Since rH = I under these conditions, these results imply that trapping was unimportant in their study. Temperature dependent studies [2] have found
maintained by immersion in liquid nitrogen. The Hall and I—V measurements were made with pulsed sourcedrain fields, and were measured with high impedence preamplifiers and sampling oscilloscopes. In preliminary studies of these devices [5] it was thought that the differences between the measured Hall densities, ~H, and the surface density, n8, pre-
that while some devices will show Mott—Anderson type localization and some evidence for trapping at densities just above the localization edge [2, 31 in their Hall data in the 2—100 K range, most Hall measurements show that all electrons are mobile (activated conduction regime).study, we report experimental In the present results at 77 K which indicate a discrepancy between the number of carriers measured from the Hall effect and the number of carriers estimated from gate capacitance. The interpretation of this discrepancy as a measure of the Hall factor (rH> 1) is found to be inconsistent with the mobility variations seen in the device. However, one consistent explanation of this data can be developed if the presence of localized trapping states at the interface is assumed.
dicted from gate capacitance and threshold, could be used to measure the value of the Hall factor, TH. At helium temperature, Fang and Fowler [11 found rH to be unity, but this is expected because the inversion layer electrons will be degenerate at low temperatures 2. Howfor concentrantions above n8 1010 cm ever, at 77 K, the inversion layer5isxnon-degenerate and rH> I becomes possible, e.g. for ionized impurity scattering a simple calculation in 2-dimensions yields = 1.5. While this argument seems to be plausible, it is sharply contradicted by the Hall mobility, p~,variation with increasing surface density. As shown in Fig. 1, pH is found to decrease with increasing density, while calculations of mobifity vs ns for Coulomb scattering show an increase of p as n 8 increases [6, 7J, thus Coulomb scattering cannot be the dominant scattering mechanism. Finally, surface roughness scattering and phonon[7J scattering, which produce the proper p dependence have Hall factors near unity. Thus the discrepency between ~H and ns cannot be satisfactorily explainedin terms of a rH -> 1. If TH is unity, then the density of inversion layer electrons obtained from Hall measurements is the correct density ofmobile electrons and the difference between nH and n 8 may be interpreted as trappedis electronic charge. This preliminary interpretation suggested when the data is plotted in Fig. 2 as ~H VS ns The equation of the linear portion of this graph is
The devices used were fabricated with channel contacts to allow Hall and 4-point measurements directly on the carriers in3,the channel. bulk doping and there isThe no channel is p—type,Threshold Na 1015voltages cm varied among samples implant. from different wafers over the range I—2V. However, the turn-on for a particular device was sharp and well-defined at 77K. The two devices reported here had turn-on voltages of 1.3 V (6a) and 1 .9 V (6b). The number of traps near the interface has been esti2 in other studies [4]. mated at ~T 1010 devices cm The gate oxide ~ofx these apparently contains sodium ions added during growth, but attempts to change VT by drifting them to the Si—Si0 2 interface have have been been unsuccessful [41 in implying that The thesetempions may immobilized some way. erature of the samples during the present studies was
,
,
-
12H
=
~~SITH —
,
Since the slope measure is 1.01 ±.02, the value of rH is 1.0 for the region flH> 1011 cnf2. The number -~
*
Work supported by the Office of Naval Research. 509
510
HALL MEASUREMENTS ON TRAP STATES IN n-CHANNEL Si MOSFETS AT 77K
F
F
I
Vol. 33, No. 5
I /
I 01
5
Si <100> 77K
/
0
-
SAMPLE Gb
-
SAMPLE Ga
0-
/
Gb
/
/
6-
-
-
I
\\o 0
-
/J~JJ~
-
F
/ / /
,~
-
Si<100> 77K
/
II 2
a
-
F
~~0/’
0 0
F 2
F 1. 11 -2 FlO cm F
3 ~s
6
Fig. 1. Hall mobility vs measured inversion electron density. The dashed line is calculated for Coulombic scattering,
of traps, ~T, obtained from the extension of the linear portion of the graph to n 5 =2 in 0 is good agreement with previously = 7.5 obtained ±1.0 x 1010 values cm[4]. At concentrations below nH = 1011 cm2, the data departs from the linear region. This is probably due to the lowering of the Fermi level through the energy range of the traps, consequently exciting carriers out of the traps. It should be remarked at this point that other mechanisms, such as inhomogeneous sodium distribution (hence inhomogeneous oxide charge) could cause a slow turn-on and the behavior of Fig. 2. However, the relatively sharp turn-on observed for these devices, and the similarity of behavior between devices with different turn-on voltages (different fixed charge) suggest that this is unlikely. In the remainder of this paper, we examine how such traps could occur, If the deviation from linearity for ~ <2 < 1011 cm2 is due to detrapping alone, then a difinitive value of the trap state energy is not readily obtained, However, it is likely that this deviation is due to both detrapping dynamics, a variation of rH in this region, and a band of trap states which could be moving
6
2F
9
Flail cm
Fig. 2. Hall density vs calculated surface density. Dashed line is n~ = ns. Solid line is ~H = ns—7.5x 101 cm2. slightly as they are ionized. In either case the location of the trap state is unusual in that it does not lie in the gap region. Rather, it appears that the trap states are resonant with the actual conduction band and lie very close to the bottom of the conduction band, Moreover, the nature unusual. of the potential associated traps to is somewhat If the ionized trapswith are the assumed scatter the inversion layer electrons via a screened Coulomb potential [6] then the Coulomb scattering indicated by the dashed curve in Fig. 1 results [7]. It can be seen that the actual mobility is not limited by this Coulomb scattering, so that the potential is either more heavily screened than expected or is non-Coulom. bic in nature. Hartstein and Fowler [8] have induced localized states and impurity bands by the use of mobile Na ions in the oxide. While their state location was similar to that found here for some gate voltages, as mentioned above, we find no mobile Na ions. Their scattering however, was from the simple Na positive charge [9], again in contradistinction to that found here. However, the similarities in state location in that work and this is suggestive that Na may be connected with our trap state in some manner. Most traps found in Si/SiO 2 interfaces lie within the Si bandgap [10] and much work has been done ofl these states. Laughlin et a!. [11] however, have predicted theoretically that a localized state arising from a dangling Si-bond on the oxide side of the ,
,
Vol.33, No.5
HALL MEASUREMENTS ON TRAP STATES IN n-CHANNEL Si MOSFETS AT 77K
interface would generate a trap state near the conduction band edge. Similar results were also found by White and Ngai [12] but they also found that states near the band edge could be produced by a straining of the Si—Si bond at the interface, which are subject to a configuration interaction. This suggests that these latter states could produce localization behavior with an activation energy which decreases as ns is increased. On the other hand, the dangling Si-bond is a similar defect in principle to that found in bulk Si02 ,where it is supposed that hole traps arise
REFERENCES 1.
,
from an oxygen vacancy producing a Si dangling bond [13]. It may well be that immobile Na has achieved that characteristic by breaking Si—O bonds near the interface thus producing the resonant trap discussed above. It is apparent that there is adequate theoretical basis for trap states near the conduction band edge, in general agreement with our interpretation of the experimental results reported here. Acknowledgements the authors acknowledge many helpful discussions with B.D. McCombe, P.J. Stiles, F.J. Feigi, J. Wager, C.W. Wilmsen, and C.T. White. They also gratefully acknowledge the support of NRL in preparing the devices used in this study. —
511
2. 3. 4. 5. 6. 7. 8.
9. 10. 11.
12. 13.
F.F. Fang&A.B. Fowler,Phys. Rev. 169, 619 (1968). c.~.Adhins,J. Phys. dl, 851 (1978). S. Pollit, M. Pepper & C.J. Adkins, Surf Sd. 58, 79 (1976). B.D. McCombe,(private communication). B.T.437 Moore & D.K. Ferry, Bull. Amer. Phys. Soc. 24, (1979). F. Stern & W.E. Howard, Phys. Rev. 163, 816 (1967). D.K. Ferry ,Phys. Rev. B14, 5364 (1976). A. Hartstein & A.B. Fowler,Phys. Rev. Lett. 34, 1435 (1975);J Phys. C8, L249 (l975);Proc. Intern. Conf Phys. Semiconductors, Rome 1976 p. 741. Tipografia Marves, Rome, (1976). A. Hartstein, T.H. Ning & A.B. Fowler, Surf Sci. 58, 178 (1976). B.E. DeaI,J. Electrochem. Soc. 121,198C (1974). R.B. Laughlin, J.O. Joannopoulos & D.J. Chadi, in Physics of5i02 and its Interfaces, (Edited by S.T. Pantelides) p. 321. Pergamon, New York (1978). C.T. White & K.L. Ngai (to be published). F.J. Feigl, W.B. Fowler & K.L. Yip, Solid State Commun. 14, 225 (1974).
maintained by immersion in liquid nitrogen. The Hall and I—V measurements were made with pulsed sourcedrain fields, and were measured with high impedence preamplifiers and sampling oscilloscopes. In preliminary studies of these devices [5] it was thought that the differences between the measured Hall densities, ~H, and the surface density, n8, pre-
that while some devices will show Mott—Anderson type localization and some evidence for trapping at densities just above the localization edge [2, 31 in their Hall data in the 2—100 K range, most Hall measurements show that all electrons are mobile (activated conduction regime).study, we report experimental In the present results at 77 K which indicate a discrepancy between the number of carriers measured from the Hall effect and the number of carriers estimated from gate capacitance. The interpretation of this discrepancy as a measure of the Hall factor (rH> 1) is found to be inconsistent with the mobility variations seen in the device. However, one consistent explanation of this data can be developed if the presence of localized trapping states at the interface is assumed.
dicted from gate capacitance and threshold, could be used to measure the value of the Hall factor, TH. At helium temperature, Fang and Fowler [11 found rH to be unity, but this is expected because the inversion layer electrons will be degenerate at low temperatures 2. Howfor concentrantions above n8 1010 cm ever, at 77 K, the inversion layer5isxnon-degenerate and rH> I becomes possible, e.g. for ionized impurity scattering a simple calculation in 2-dimensions yields = 1.5. While this argument seems to be plausible, it is sharply contradicted by the Hall mobility, p~,variation with increasing surface density. As shown in Fig. 1, pH is found to decrease with increasing density, while calculations of mobifity vs ns for Coulomb scattering show an increase of p as n 8 increases [6, 7J, thus Coulomb scattering cannot be the dominant scattering mechanism. Finally, surface roughness scattering and phonon[7J scattering, which produce the proper p dependence have Hall factors near unity. Thus the discrepency between ~H and ns cannot be satisfactorily explainedin terms of a rH -> 1. If TH is unity, then the density of inversion layer electrons obtained from Hall measurements is the correct density ofmobile electrons and the difference between nH and n 8 may be interpreted as trappedis electronic charge. This preliminary interpretation suggested when the data is plotted in Fig. 2 as ~H VS ns The equation of the linear portion of this graph is
The devices used were fabricated with channel contacts to allow Hall and 4-point measurements directly on the carriers in3,the channel. bulk doping and there isThe no channel is p—type,Threshold Na 1015voltages cm varied among samples implant. from different wafers over the range I—2V. However, the turn-on for a particular device was sharp and well-defined at 77K. The two devices reported here had turn-on voltages of 1.3 V (6a) and 1 .9 V (6b). The number of traps near the interface has been esti2 in other studies [4]. mated at ~T 1010 devices cm The gate oxide ~ofx these apparently contains sodium ions added during growth, but attempts to change VT by drifting them to the Si—Si0 2 interface have have been been unsuccessful [41 in implying that The thesetempions may immobilized some way. erature of the samples during the present studies was
,
,
-
12H
=
~~SITH —
,
Since the slope measure is 1.01 ±.02, the value of rH is 1.0 for the region flH> 1011 cnf2. The number -~
*
Work supported by the Office of Naval Research. 509
510
HALL MEASUREMENTS ON TRAP STATES IN n-CHANNEL Si MOSFETS AT 77K
F
F
I
Vol. 33, No. 5
I /
I 01
5
Si <100> 77K
/
0
-
SAMPLE Gb
-
SAMPLE Ga
0-
/
Gb
/
/
6-
-
-
I
\\o 0
-
/J~JJ~
-
F
/ / /
,~
-
Si<100> 77K
/
II 2
a
-
F
~~0/’
0 0
F 2
F 1. 11 -2 FlO cm F
3 ~s
6
Fig. 1. Hall mobility vs measured inversion electron density. The dashed line is calculated for Coulombic scattering,
of traps, ~T, obtained from the extension of the linear portion of the graph to n 5 =2 in 0 is good agreement with previously = 7.5 obtained ±1.0 x 1010 values cm[4]. At concentrations below nH = 1011 cm2, the data departs from the linear region. This is probably due to the lowering of the Fermi level through the energy range of the traps, consequently exciting carriers out of the traps. It should be remarked at this point that other mechanisms, such as inhomogeneous sodium distribution (hence inhomogeneous oxide charge) could cause a slow turn-on and the behavior of Fig. 2. However, the relatively sharp turn-on observed for these devices, and the similarity of behavior between devices with different turn-on voltages (different fixed charge) suggest that this is unlikely. In the remainder of this paper, we examine how such traps could occur, If the deviation from linearity for ~ <2 < 1011 cm2 is due to detrapping alone, then a difinitive value of the trap state energy is not readily obtained, However, it is likely that this deviation is due to both detrapping dynamics, a variation of rH in this region, and a band of trap states which could be moving
6
2F
9
Flail cm
Fig. 2. Hall density vs calculated surface density. Dashed line is n~ = ns. Solid line is ~H = ns—7.5x 101 cm2. slightly as they are ionized. In either case the location of the trap state is unusual in that it does not lie in the gap region. Rather, it appears that the trap states are resonant with the actual conduction band and lie very close to the bottom of the conduction band, Moreover, the nature unusual. of the potential associated traps to is somewhat If the ionized trapswith are the assumed scatter the inversion layer electrons via a screened Coulomb potential [6] then the Coulomb scattering indicated by the dashed curve in Fig. 1 results [7]. It can be seen that the actual mobility is not limited by this Coulomb scattering, so that the potential is either more heavily screened than expected or is non-Coulom. bic in nature. Hartstein and Fowler [8] have induced localized states and impurity bands by the use of mobile Na ions in the oxide. While their state location was similar to that found here for some gate voltages, as mentioned above, we find no mobile Na ions. Their scattering however, was from the simple Na positive charge [9], again in contradistinction to that found here. However, the similarities in state location in that work and this is suggestive that Na may be connected with our trap state in some manner. Most traps found in Si/SiO 2 interfaces lie within the Si bandgap [10] and much work has been done ofl these states. Laughlin et a!. [11] however, have predicted theoretically that a localized state arising from a dangling Si-bond on the oxide side of the ,
,
Vol.33, No.5
HALL MEASUREMENTS ON TRAP STATES IN n-CHANNEL Si MOSFETS AT 77K
interface would generate a trap state near the conduction band edge. Similar results were also found by White and Ngai [12] but they also found that states near the band edge could be produced by a straining of the Si—Si bond at the interface, which are subject to a configuration interaction. This suggests that these latter states could produce localization behavior with an activation energy which decreases as ns is increased. On the other hand, the dangling Si-bond is a similar defect in principle to that found in bulk Si02 ,where it is supposed that hole traps arise
REFERENCES 1.
,
from an oxygen vacancy producing a Si dangling bond [13]. It may well be that immobile Na has achieved that characteristic by breaking Si—O bonds near the interface thus producing the resonant trap discussed above. It is apparent that there is adequate theoretical basis for trap states near the conduction band edge, in general agreement with our interpretation of the experimental results reported here. Acknowledgements the authors acknowledge many helpful discussions with B.D. McCombe, P.J. Stiles, F.J. Feigi, J. Wager, C.W. Wilmsen, and C.T. White. They also gratefully acknowledge the support of NRL in preparing the devices used in this study. —
511
2. 3. 4. 5. 6. 7. 8.
9. 10. 11.
12. 13.
F.F. Fang&A.B. Fowler,Phys. Rev. 169, 619 (1968). c.~.Adhins,J. Phys. dl, 851 (1978). S. Pollit, M. Pepper & C.J. Adkins, Surf Sd. 58, 79 (1976). B.D. McCombe,(private communication). B.T.437 Moore & D.K. Ferry, Bull. Amer. Phys. Soc. 24, (1979). F. Stern & W.E. Howard, Phys. Rev. 163, 816 (1967). D.K. Ferry ,Phys. Rev. B14, 5364 (1976). A. Hartstein & A.B. Fowler,Phys. Rev. Lett. 34, 1435 (1975);J Phys. C8, L249 (l975);Proc. Intern. Conf Phys. Semiconductors, Rome 1976 p. 741. Tipografia Marves, Rome, (1976). A. Hartstein, T.H. Ning & A.B. Fowler, Surf Sci. 58, 178 (1976). B.E. DeaI,J. Electrochem. Soc. 121,198C (1974). R.B. Laughlin, J.O. Joannopoulos & D.J. Chadi, in Physics of5i02 and its Interfaces, (Edited by S.T. Pantelides) p. 321. Pergamon, New York (1978). C.T. White & K.L. Ngai (to be published). F.J. Feigl, W.B. Fowler & K.L. Yip, Solid State Commun. 14, 225 (1974).