InP heterostructures

Superlattices and Microstructures, Vol. 23, No. 6, 1998 Article No. sm960588

Quantum point contacts on InGaAs/InP heterostructures G. E NGELS , M. T IETZE , J. A PPENZELLER , M. H OLLFELDER ¨ ¨ T H . S CH APERS , H. L UTH Institute f¨ur Schicht- und Ionentechnik, Forschungszentrum J¨ulich (KFA) 52425 J¨ulich, Germany (Received 22 September 1994) For the first time we have observed quantized conductance in a split gate quantum point contact prepared in a strained In0.77 Ga0.23 As/InP two-dimensional electron gas (2DEG). Although quantization effects in gated two-dimensional semiconductor structures are theoretically well known and proven in various experiments on AlGaAs/GaAs and also on In0.04 Ga0.96 As/GaAs, no quantum point contact has been presented in the InGaAs/InP material with an indium fraction as high as 77% so far. The major problem is the comparatively low Schottky barrier of the InGaAs (φB ≈ 0.2 eV) making leakage-free gate structures difficult to obtain. Nevertheless this heterostructure—especially with the highest possible indium content—has remarkable properties concerning quantum interference devices and semiconductor/superconductor hybrid devices because of its large phase coherence length and the small depletion zone, respectively. In order to produce leakage-free split gate point contacts the samples were covered with an insulating SiO2 layer prior to metal deposition. The gate geometry was defined by electron-beam lithography. In this paper we present first measurements of a point contact on an In0.77 Ga0.23 As/InP 2DEG clearly showing quantized conductance. c 1998 Academic Press Limited

Key words: two-dimensional electron gas, ballistic transport, quantized conductance, split-gate point contact.

1. Motivation Compared with AlGaAs/GaAs, a two-dimensional electron gas (2DEG) based on InGaAs has a low effective mass m ∗ , high conductivity σ at room temperature, large phase coherence length l8 [7] at about 1 K and a small surface depletion zone d. These differences grow significantly with increasing indium content. A 2DEG in a strained In0.77 Ga0.23 As channel on InP substrate [4–6] is therefore very well suited for a variety of optoelectronics (E Gap ), ultrafast transistors (σ ) [9], semiconductor/superconductor hybrid devices (d) and quantum interference devices (l8 ) [7]. The latter receive more and more attention for they are believed to overcome the quantum-mechanical obstacles of further integration in nanoelectronics. This yields a strong motivation for studying InGaAs-based systems by means of point contact spectroscopy which requires adjustable split gates as emitter and collector of collimated electron beams. Recently, first point contact measurements were carried out on an indium containing layer system [3] by introducing up to 25% indium in a pseudomorphic grown Inx Ga1−x As quantum well on GaAs substrates. Split gate contacts on these 2DEGs showed quantization only at an indium fraction of x = 0.04. An 0749–6036/98/061249 + 05

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c 1998 Academic Press Limited

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2DEG

150 nm

In0.53Ga0.47As

10 nm

In0.77Ga0.23As

20 nm

InP-spacer

10 nm

InP(S)ns = 4.2 × 1017 cm–3

400 nm

InP-buffer

InP-substrate 〈100〉 s.i.

Fig. 1. MOVPE-grown layer system.

arbitrary but reproducible characteristic was found at higher values (x = 0.1 and x = 0.14). The structure with 25% indium had a considerable amount of dislocations and was relaxed. Instead of using GaAs as a substrate we used InP which enables us to increase the indium content in the conducting channel up to 77% without significant dislocation or relaxation effects. In fact, the low Schottky barrier of the InGaAs is an advantage especially for ohmic contacts between the semiconductor and superconductors such as niobium but hinders the preparation of quantized split gates. In order to enhance the barrier for transistor applications, various attempts have been made such as cap deposition of p+ -doped or wide-gap semiconductors [8] or chemical passivation of the surface InGaAs layer [9]. According to our experiments, split gates fabricated by these techniques have not shown quantization yet. Therefore a different approach has been tried successfully, namely the preparation of gate contacts by means of an insulating interlayer of SiO2 .

2. Preparation In this paper we report results on an MOVPE-grown layer system [4–6] of 400 nm undoped InP buffer on a semi-insulating InP h100i wafer followed by 10 nm 4.2 × 1017 cm−3 S-doped InP. A spacer of 20 nm InP separates the 10 nm strained In0.77 Ga0.23 As-channel from the dopant spike. The structure is covered with 150 nm InGaAs lattice matched to InP (Fig. 1). Quantum–Hall and Shubnikov–de Haas measurements show two-dimensional carrier concentrations n s of 4 × 1015 m2 and mobilities µ of 27 m2 V−1 s−1 at 1.4 K. Using these data the transport mean free path ltr of the 2DEG can be calculated as a function of transport relaxation time τtr and Fermi velocity vF :   p  h¯ m∗ 2π n . (1) µ ltr = s m∗ e {z } | {z } | vF

τtr

In our case ltr is 2.8 µm. To get an idea of the device geometry we need to know the average distance between any two scattering events which has to be larger than the point contact geometry. In τtr all scattering events are weighted by the scattering angle because it is the characteristic time for electron transport. Transport of electrons is strongly affected by the angle of the scattering because the momentum of an electron in current direction

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220 nm

2DEG

MESA (300 nm) PECVD SiO2 (35 nm) GATE (5 nm Cr, 50 nm Au) Fig. 2. Schematic picture of the split gate sample.

is changed more if the scattering angle is large. The distance between two transport relevant large angle scattering events is therefore larger than the distance between any two scatterings. It follows that the quantum relaxation time τq which weights all scattering events independent of angle is smaller than τtr : Z π Z π −1 −1 d2 S(2), τtr = d2 S(2)(1 − cos 2). (2) τq = 0

0

Recent work [10] shows that τq of our system is approximately one-fifth of the transport time τtr . Thus, we can estimate for our heterostructure a ballistic length of lb = vF , τq = 560 nm which is an attainable dimension for electron beam lithography. After standard wet chemical etching [12] we capped the sample with an insulating 35 nm PECVD-layer of SiO2 in order to obtain leakage-free gate contacts. AF91-etchant was used to open areas for AuGeNi ohmic contacts in the SiO2 interlayer. The Cr/Au split gates were produced with a length of 270 nm and a gate separation of 220 nm using standard electron-beam lithography (Fig. 2). The measurements were carried out in a 3 He-cryostat at temperatures of 400 mK using the lock-in technique.

3. Results Figure 3 shows the results of a resistance measurement through the point contact. The resistance grows with increasing (negative) gate voltage. Pinch off is observed at approximately −6.8 V. Due to the dielectric SiO2 material and the rather thick top InGaAs layer the curve is very smooth between 0 and −5.5 V. No specific threshold condition is observable. This threshold condition—where the gate-induced depletion zone reaches the 2DEG and the point contact built in the 2DEG is at the largest width—would yield the possibility to subtract the background resistance RB to calculate the net conductance G of the split gate. Since RB cannot be determined, the serial resistance at zero gate voltage is subtracted only. Nevertheless, the quantized conductance shown in Fig. 4 as a function of gate voltage clearly exhibits up to seven plateaus in steps of 2e2 n, n = 1, 2, 3, . . . (3) G= h indicating that n one-dimensional channels are transmitting electrons at a corresponding gate voltage. The slight deviation in step height is due to the missing correction for the gate background resistance. Since the effect of quantized conductance is well known [1, 2] and published several times in literature, no additional explanations of the fundamental features are needed here.

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30

Resistance (kΩ)

25

T = 400 mK

20 15 10 5

–6.5

–6 –5.5 Gate voltage (V)

–5

–4.5

Fig. 3. Resistance across the quantum point contact versus gate voltage.

8

Conductance (2e2 /h)

7

T = 400 mK

6 5 4 3 2 1 0 –6.5

–6 –5.5 Gate voltage (V)

–5

–4.5

Fig. 4. Conductance of the quantum point contact versus gate voltage, as obtained from the data of Fig. 3.

The reproducible occurrence of distinct quantization steps in all our samples is interesting when compared with the only other available measurements of split gate point contacts on indium containing systems. As mentioned before, Mace et al. [3] used strained InGaAs quantum wells on GaAs substrates. It was suggested that the mobilities of these samples were limited by alloy disorder as predicted by Walukiewicz et al. [11], with τalloy as the corresponding relaxation time: x(1 − x) , (4) A x is the atomic percentage of the group III compounds and A a constant for the particular heterostructure. −1 = τalloy

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For heterostructures with an indium content of x = 0.1 and above the measured point contact characteristics showed an arbitrary but reproducible structure instead of the 2e2 / h plateau spacing. This was explained to be due to alloy disorder and interface roughness. The pattern was found to fade at temperatures above 750 mK. Since the mobility of our sample is also known [6] to be limited by alloy scattering and when taken into account the fact that eqn (4) is a parabola with its maximum at x = 0.5, an indium percentage of x = 0.77 should produce a similar or even stronger arbitrary pattern in a point contact measurement. Our data were taken at temperatures of 400 mK with a current heating of the same magnitude and thus thermal smearing would be a possible explanation for the missing alloy scattering substructure. However, since our conductance steps are very well resolved, temperature is not the dominant factor for the deviation in our characteristics compared with the results of Mace et al. It is most probable that the deviation is due to differences in crystal quality and interface roughness between the MBE grown pseudomorphic InGaAs and our 2DEG grown by MOVPE. In conclusion, our new topic is quantized conductance shown in a point contact of the Inx Ga1−x As–InP– 2DEG with an indium fraction as high as 77%. No additional models are needed to explain the measured characteristics. In particular, no assumptions have to be made concerning interface roughness and alloy disorder which is surprising when compared with former measurements on heterostructures with a low indium content. The presented point contacts provide the basis for further detailed mesoscopic studies of strained InGaAs/InP heterostructures.

References [1] — B. J. van Wees, H. van Houten, C. W. J. Beenakker, J. G. Williamson, L. P. Kouwenhoven, D. van der Marel, and C. T. Foxon, Phys. Rev. Lett. 60, 848 (1988). [2] — D. A. Wharam, T. J. Thornton, R. Newbury, M. Pepper, H. Ahmed, J. E. F. Frost, D. G. Hasko, D. C. Peacock, D. A. Ritchie, and G. A. C. Jones, J. Phys. C21, L209 (1988). [3] — D. R. Mace, M. P. Grimshaw, D. A. Ritchie, C. J. B. Ford, M. Pepper, and G. A. C. Jones, J. Phys.: Condens. Matter. 5, L227 (1993). [4] — D. Gr¨utzmacher, R. Meyer, P. Balk, C. Berg, Th. Sch¨apers, H. L¨uth, M. Zachau, and F. Koch, J. Appl. Phys. 66, 697 (1989). [5] — H. Hardtdegen, R. Meyer, H. Løken-Larsen, J. Appenzeller, Th. Sch¨apers, and H. L¨uth, J. Cryst. Growth 116, 521 (1992). [6] — H. Hardtdegen, R. Meyer, M. Hollfelder, Th. Sch¨apers, J. Appenzeller, H. Løken-Larsen, Th. Klocke, Ch. Dieker, B. Lengeler, and H. L¨uth, J. Appl. Phys. 73, 4489 (1993). [7] — J. Appenzeller, Th. Sch¨apers, H. Hardtdegen, B. Lengeler, and H. L¨uth, IRRM Proceedings, 6th Internat. Conf. on Indium Phosphide and Related Materials, 516 (1994). [8] — P. Kordo˘s, M. Marso, R. Meyer, and H. L¨uth, J. Appl. Phys. 72, 1 (1992). [9] — K. C. Hwang, S. S. Li, C. Park, and T. J. Anderson, J. Appl. Phys. 67, 6571 (1990). [10] — D. Uhlisch, diploma thesis, RWTH Aachen, Germany (1994). [11] — W. Walukiewicz, H. E. Ruda, J. Lagowski, and H. C. Gatos, Phys. Rev. B30, 4571 (1984). [12] — S. Adachi, Solid State Sci. Technol. 129, 609 (1980).