Motivation

Chapter 1

Introduction and motivation

1.1 Motivation

Most of the III-V optoelectronic devices rely on junctions formed by stacks of epilayers, where the electrical current flows across the junction vertical to the sample surface. The lateral p-n junctions that are difficult to fabricate, however, are often desirable for many device applications. For example, because of their coplanar geometry, they are suitable for optoelectronic integration. Since the cross section of the lateral junction is determined by the thickness of the epilayer, the capacitance of the junction can also be much smaller than that of conventional vertical ones. Thus, the 2D lateral junctions could lead to a new family of high-frequency and optoelectronic devices [1-6]. Furthermore, lateral 2D p-n junctions are potential candidates for investigating the properties of electron spins in low-dimensional systems by optical methods [7]. On the other hand, the lateral p-i-n junction is key component in a SAW-driven single photon source devices, proposed by Foden et al [8].

1.1.1 Spin Hall Effect

The spin Hall Effect (SHE) was predicted 40 years ago [9, 10]. Theorists Dyakonov and Perel proposed that an unpolarized electrical current should lead to a transverse spin current in systems with the relativistic spin–orbit coupling. In their picture, spin–orbit coupling enters SHE via the Mott scattering of electrons on unpolarized impurities, which results in spatial separation of electrons with opposite spins directions. The effect has Hall symmetry, because the polarization axis of the spin is perpendicular to the plane of the transverse spin current and the driving longitudinal electrical current. We can simply as in figure 1.1. The SHE consists in spin accumulation at the lateral boundaries of a current-carrying conductor, the spin directions being opposite at the opposing boundaries.

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Figure 1.1. The Spin Hall Effect. An electrical current induces spin accumulation at the lateral boundaries of the sample. Spin-up electrons accumulate one side and spin-down electrons on the other side.

The term “Spin Hall Effect” was introduced by Hirsch in 1999 [11]. Indeed, it is somewhat similar to the conventional Hall Effect, where charges of opposite side accumulate at the different boundaries of the sample due to the Lorentz force, acting on moving charges in magnetic field. However, there are significant differences. First, no magnetic field is needed for spin accumulation. On the contrary, if a magnetic field perpendicular to the spin direction is applied, it will destroy the spin polarization.

Second, the value of the spin polarization at the boundaries is limited by spin relaxation.

There are two distinct mechanisms of SHE, intrinsic [12, 13] and extrinsic [9-11, 14], which differ in the role played by external impurities. The extrinsic mechanism is caused by spin-orbit coupling between Bloch electrons and impurities, whereas the intrinsic mechanism is caused by spin-orbit coupling in the band structure of the semiconductor and survives in the limit of zero disorder. The intrinsic mechanism does not depend explicitly on impurities, but it would be a serious error to think that impurities can be ignored. The intrinsic SHE proposal focused on semiconductors and suggested that the optical activity of these materials be utilized for detecting SHE. In particular, the circularly polarized electroluminescence was suggested in reference [12] and the magneto-optical Kerr effect in references [12, 13]. These methods were used in the first measurements of the SHE phenomenon [7, 15].

Wunderlich et al in reference [7] used coplanar n – p - n diodes to detect circularly polarized electroluminescence at opposite edges of the spin Hall channel, see the figure 1.2 (a). When current (Up or Down direction) was injected into hole channel, spin accumulation occurred at the boundaries of hole channel. A p-n junction current was applied simultaneously. Electron will recombined with spin-polarized hole and emitted

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polarized light. Dependence of Light polarization on current direction is shown in figure 1.2 (b). Wunderlich et al. ascribed the observed signal to the intrinsic SHE. However, impurities in their lateral diode were high, so the effect of impurities cannot be ignored.

Therefore, it would be ideal to fabricate an impurity-free lateral p-i-n diode to investigate the intrinsic SHE.

Figure 1.2. Wunderlich et al. a, Schematic of the lateral p–n junction with the channel current Ip and the diode current ILED for detecting spin accumulation.

b, Emitted light polarization of recombined light in the p–n junction for the channel and diode current flow indicated by arrows in (a).

1.1.2 SAW-driven Single photon Source

In recent years, explosive growth of the field of quantum-information science theory and metrology were the main driving forces behind the development of a novel technological tool [16, 17] - a controllable source of single photons on demand. Single photons on demand are an important resource in various areas of the emerging quantum technologies such as quantum key distribution [17-20] and all-optical quantum information processing [21]. They are the basic prerequisite for unconditional security in quantum key distribution protocols [20, 22-24] and a key ingredient for fault tolerant quantum computing schemes [18, 25, 26].

More recently, there has been an increasing interest in the surface acoustic wave (SAW)-driven single-photon sources owing to their potential applications in high-speed

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quantum communications [8, 27, 28]. In [8], Foden et al proposed that when a SAW propagates through a two-dimensional (2D) p-i-n junction, see figure 1.3 (a), a series of traveling quantum dots are formed in the i-region of the junction. Consequently, a constant stream of electron packets, which can be manipulated by a controlled split gate voltage, flows from a dimensional electron gas (2DEG) channel into a two-dimensional hole gas (2DHG) channel, where electrons and holes are recombined to create bursts of optical pulses. By controlling the split gate voltage, one can obtain a stream of single electrons to generate single photons, see figure 1.3(b). In SAW-driven single-photon source devices, the key component is a high-quality 2D p-i-n junction.

Figure 1.3 Foden et al. a, Schematic of the single-photon source. b, The conduction (CB) and valence-band (VB) edge profiles across the n-i-p junction and recombination when SAW wave propagate through.