Electron transport in a slot-gate Si MOSFET

I. Shlimak¹, V. Ginodman¹, A. Butenko¹, K.-J. Friedland² and S. V. Kravchenko³

¹ Jack and Pearl Resnick Institute of Advanced Technology, Department of Physics, Bar-Ilan University Ramat-Gan 52900, Israel
² Paul-Drude Institut für Festkörperelektronik - Hausvogteiplatz 5-7, 10117, Berlin, Germany, EU
³ Physics Department, Northeastern University - Boston, MA 02115, USA

E-mail: shlimai@mail.biu.ac.il

Received 16 December 2007, accepted for publication 25 March 2008
Published 6 May 2008

Introduction

The fabrication of Si-MOSFET samples with a narrow gate barrier or with narrow slots in the gate [1–5] has given rise to new experimental possibilities. In particular, samples with a narrow gate barrier [1, 2] were used for investigation of the backscattering of the edge current in the quantum Hall effect (QHE) regime, while the slot-gate geometry has permitted reliable measurements of a two-dimensional electron transport in case of low electron density [6]. In this work, we use the slot-gate geometry to measure the longitudinal resistance R_xx in the QHE regime for unequal electron densities along the sample. Our aim was to reveal the influence of the spin-flip process on the electron transport when electrons on the opposite sides of the slot occupy Landau levels (LL) with different spin orientations.

Experimental results and discussion

The sample with two narrow slots (100 nm) in the upper metallic gate was similar to that described earlier in [6] (see insert in fig. 1). Application of different gate voltages V_G to the gates G₁, G₂ and G₃ permitted one to maintain different electron densities n in different parts of the sample.

The sample resistance was measured at T = 40 mK using a standard lock-in technique with the measuring current 20 nA at a frequency of 10.6 Hz. The electron mobility was μ = 2.68 m²/V · s at n = 0.83 · 10¹⁶ m⁻².

In the first series of experiments, all gates were connected. The magnetic-field dependences of the Hall (transverse) resistance R_xy measured between probes V₂–V₇ are shown in fig. 1a. The "plateaus" are clearly seen only for Landau filling factors ν ≡ hn/eB = 4 and ν = 6 corresponding to the Hall resistances 6.45 kΩ = 1/4(h/e²) and 4.3 kΩ = 1/6(h/e²), respectively. Clear "plateaus" in R_xy at ν > 6 are usually not observed in Si-MOSFET being "contaminated" by the "overshoot" effect [7, 8].

The longitudinal resistance R_xx was measured across the gap between voltage probes V₁ and V₂(R₁₂) and without the gap, between probes V₂ and V₃(R₂₃). In zero magnetic field, R₁₂ is 1.5 times larger than R₂₃ (fig. 1b) due to the distance between probes 1 and 2 being 1.5 times larger than that between probes 2 and 3. Therefore, the longitudinal resistance is not affected by the existence of the narrow slot in the gate. In other words, in our sample, the narrow slot in the upper gate does not lead to the existence of a potential barrier. It is remarkable, however, that at magnetic fields above 10 T, both resistance curves merge. This can be explained by the influence of the edge channels [9, 10], so that the length between probes becomes irrelevant.

In case of different gate voltages V_G1 ≠ V_G2 (V_G3 was always equal to V_G2), the difference in the transverse Hall voltages ΔV_H ≡ V₁₈ − V₂₇ appears. ΔV_H is added to the longitudinal voltage V_xx only on one side of the sample, depending on the gradient of the gate voltage ∇V_G, which makes the longitudinal resistance non-symmetric: for V_G1 < V_G2 at given direction of the magnetic field , ΔV_H was added to the voltage V₁₂, while for V_G1 > V_G2, V₁₂ remains unchanged (figs. 2a, b). On the opposite side of the sample, the situation is reverse: ΔV_H is added to the voltage drop V₈₇ for V_G1 > V_G2. It was shown in ref. [3] that the sample side where ΔV_H is added to V_xx is determined by the vector product . Different values of V_xx on the opposite sides of the sample mean that in order to analyze the longitudinal resistance in the case of different gate voltages, one need to subtract properly the contribution of the Hall voltage difference.

In another set of experiments, conducted at T = 300 mK, the magnetic field was fixed at 8 Tesla, while the gate voltage was varied. First, all gates were connected and V_H was measured between probes V₁ and V₈ (fig. 3, dashed line). Using the data shown in fig. 1a, one can conclude that the "plateau" at around V_G = 10 V corresponds to the filling factor ν = 6, while the "plateaus" at around V_G = 7 V and V_G = 13 V correspond to ν = 4 and ν = 8, respectively.

Figure 4a shows V_xx measured simultaneously on both sides of the sample between probes V₁–V₂ and probes V₈–V₇. V_G2 = 10 V was kept constant, while V_G1 was varied from 5 V to 15 V. In this experiment, the gradient of the gate voltage undergoes a sign change at V_G1 = 10 V. If the direction of the magnetic field is reversed, the curves trade places. The difference between the two curves ΔV_xx plotted as a function of V_G1 (fig. 3, solid line) practically coincides with V_H(V_G1). This fact allows us to subtract properly the contribution of the Hall voltage difference: one needs to take into account only the lower parts of both the curves. The result is shown in fig. 4b.

Let us discuss the curve shown in fig. 4b. Keeping V_G2 = 10 V constant means that electrons underneath the gate G₂ always occupy the sixth LL with spin "down" (see fig. 3 and the inset). When V_G1 is varied from 9 V to 11 V, electrons across the slot occupy the same (6th) LL and, therefore, have the same spin orientation. However, when 6 V < V_G1 < 8 V and 12 V < V_G1 < 14 V, the electrons underneath the gate G₁ occupy "spin up" LLs 4 and 8, respectively. At both filling factors ν = 4 and 8 (indicated in the figure by arrows), the longitudinal resistance increases compared to the ν = 6 case. Possible reason for this resistance increase is some additional scattering [11, 12] due to the necessity for electrons to flip their spins when crossing the slot.

Acknowledgments

IS thanks V. T. Dolgopolov and A. A. Shashkin for fruitful discussion and the Erick and Sheila Samson Chair of Semiconductor Technology for financial support. We are grateful to A. Bogush and A. Belostotsky for assistance.

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