THE EFFECT EFFECT * J.E. FURNEAUX Naval
ON THE QUANTUM
and T.L. REINECKE
Science 142 (1984) 1X6- 18X North-Holland. Amsterdam
10 July 1983; accepted
The Quantum Hall Effect has been studied in silicon metal-oxideesemiconductor field effect transistors (MOSFETs) in which there are positive ions (Na+) that can be drifted across the oxide. When mobile ions are drifted up to the oxide-semiconductor interface, the oxide charge N,,, and the interface potential fluctuations increase [l]. In this way we have been able to study the effects of systematic, well-characterized changes in the interface charge and in the associated localized electron states on the Quantum Hall Effect. These systems exhibit Quantum Hall plateaus corresponding to the filling of valley levels, spin levels and complete Landau levels in the two-dimensional inversion layer electron gas. At a constant field of 13 T and temperature of T = 1.35 K, we have measured the resistivity components p, ~. p_,~ and dp, ,/dn and dp,,./dn where n is the two-dimensional carrier density. These data were used to study the Quantum Hall plateau widths and positions as functions of added interface charge and of channel mobility p. The amount of added interface charge was determined from the shifts in the threshold voltage by AN,, = CAy,/e where C is the capacitance per unit area of the MOSFET. These data are shown in figs. 1 and 2. The Hall plateau widths fall on universal curves linear in l/p at high mobilities as seen in fig. 1 where the mobilities p are measured at 4.2 K and H = 0. The parameter l/p provides a measure of scattering in the inversion layer . A notable feature of these data is the difference is behavior between the plateaus associated with the full Landau levels and the plateaus associated with the full spin levels. The spin plateaus grow in width more slowly than the Landau level plateaus. A similar behavior is observed as a function of A N,,x for high mobility samples (pB > 12) . A remarkable feature of these data is seen in fig. 2 where the extrapolated apparent positions in gate voltage of the different kinds of plateaus are shown. For AN,,, < 4 X 10” cm-“, the full Landau level positions do not move with * Partially
by an Office of Naval Research
0039-6028/84/$03.00 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
T. L. Reinecke
/ Effect of interface charge on QHE
aI I OS2VPB
Fig. 1. The normalized widths of the Hall plateaus versus normalized inverse widths of the spin plateaus; (b) the widths of the Landau plateaus. The density nondegenerate Landau level is no = 3.146 X 10” cm m2, The different symbols substrate biases: (0) + 1 V, (0) 0 V, (A) - 1 V. (0) - 2 V. (U) - 4 V, (A) - 8
mobility: (a) the associated with a indicate different V.
respect to the conductivity threshold. On the other hand, the positions of the spin levels move with respect to those for filled Landau levels and increase with increasing interface charge. The positions of the valley levels behave similarly to those for spin levels . We propose that the behavior of the Hall plateau widths and positions observed here can be understood in terms of specific features of scattering and
J. E. Furneaux,
T. L. Reinecke
/ Effect of’ inierface
Fig. 2. The normalized positions of the p,, minima relative to the conductivity thresholds versus added interface charge AN,,. The upper curve gives the spin and valley level positions the lower curve the Landau level positions. The dashed curve indicates the region for which electrons associated with the impurities are banded and where the measurement of AN,, is reliable.
V,, and the less
localization at the interface. The tendency for all plateau widths to increase with increased interface charge is consistent with a picture in which the mobility edges move toward the centers of each band giving more localized states in the band edges. In order for there to be an apparent shift in a p,, minimum, it is necessary not only that the adjacent band tails overlap but also that the increased overlap be asymmetrical. Such an asymmetrical overlap is consistent with the asymmetrical band shapes found for a two-dimensional electron gas in the presence of attractive scattering centers , and may also be related to relative energy shifts expected for the spin levels because of their orthogonality to electron wavefunctions localized at charged impurities.
References [l]  (31 
A. Hartstein and A.B. Fowler, Phys. Rev. Letters 34 (1975) 1435. H.L. Stiirmer, D.C. Tsui and A.C. Gossard, Surface Sci. 113 (1982) 32. J.E. Furneaux and T.L. Reinecke, to be published. H. Aoki, J. Phys. Cl0 (1977) 2583; Cl1 (1978) 3823.