Spin relaxation of holes in In0.53Ga0.47As/InP quantum wells
Introduction
The electron spin state is used to store information in spintronic devices. The process of information storage includes creation of an initial non-equilibrium spin state, which maintains the spin-encoded information. Spin relaxation is a process that leads the electron spin system to an equilibrium and, therefore, erases the stored information. Thus, spin relaxation is a central subject for all phenomena associated with spin. There are several known spin relaxation processes, most involving spin-orbit coupling. During the spin relaxation time τs, an electron travels a distance to the detector where the information can be read. Such a process takes place, for example, in the Datta-Das spin field-effect transistor [1]. Another way to read the spin-encoded information is by polarization-resolved photoluminescence (PL). In this case, the spin state must be unchanged during the lifetime of the photoexcited carriers. Thus, as indicated in Ref. [2], a search for electron systems that maintain spin polarization during a long time is a fundamental challenge.
A semiconductor heterostructure quantum well (QW) is a basic system for spintronic devices. The most important spin relaxation process relevant to semiconductor QWs is the Dyakonov-Perel mechanism [3] that occurs in solids without a center of symmetry. In III-V semiconductors, inversion symmetry is broken by the presence of two different atoms in the lattice primitive cell. Moreover, the symmetry is broken in heterostructures due to an asymmetric confining potential.
In the past decade, increasing interest has been demonstrated in the investigation of hole spin relaxation processes in heterostructures based on InGaAs alloys, which was stimulated by the demonstration of efficient hole spin injection in Refs. [4,5] and their promise as spintronic materials. As a result, the electron and hole spin dynamics have been investigated in InGaAs QWs by pump and probe absorption [6], time-resolved Faraday rotation [7,8], and cyclotron resonance spectroscopy [9], where a hole spin relaxation time up to 10 ms was demonstrated. Thus, spectroscopic methods are commonly used to explore spin relaxation. The intensity of the optical emission in the final state strongly depends on the relaxation of high energy excited states. In particular, the intensity of polarized emission depends on the spin relaxation [10]. In addition, the time-resolved spectroscopy allows for a direct probe of the spin relaxation time [11]. Generally speaking, optical techniques simultaneously probe both the electron and hole spin relaxation time. However, a four-fold degeneracy of the valence band in the center of the Brillouin zone, resulting in formation of the heavy hole and light hole structure of the valence band, usually causes the much faster spin relaxation time of holes as compared to that of electrons. Therefore, in most cases the time-resolved spectroscopy provides for the electron spin relaxation time, while the hole spin relaxation time is unavailable. Below we report on a new method that employes a standard polarization-resolved PL system which can be used to measure the spin relaxation time of both the electrons or holes, when they are minority carriers.
A further basic issue of spin physics is the g-factor, which defines the spin-splitting. The g-factor in lattice-matched In0.53Ga0.47As/InP heterostructures was measured in Refs. [[12], [13], [14], [15]] where the values for the effective electron g-factor was found in the range ge ≈ − (4 − 10). The only available data on the hole g-factor in an In0.53Ga0.47As/InP QW gave gh ≈ (7 − 15) [16,17]. Due to the different g-factor signs in InGaAs (negative for the electrons and positive for the holes) the effective exciton splitting is very small (typically less than 1 meV [[18], [19], [20]]). This makes it difficult to use spectroscopic techniques to study phenomena associated with the spin-splitting of carriers and, as a consequence, results in a broad range of reported g-factors.
In this work, we study the occupancy of the valence band Landau levels (LLs) by the photoexcited holes in In0.53Ga0.47As/InP QWs as a function of temperature. In this way, the hole spin relaxation processes were examined. Temperature independent spin polarization of LLs was found below 10 K, resulting in a Landau level spin memory. At higher temperatures, a thermal inter-LL activation of the photoexcited holes reduced their spin polarization. A comparison of the obtained results with the theory allowed for accurate determination of the g-factors of the holes in the In0.53Ga0.47As/InP QWs studied here. The hole spin relaxation times related to different Landau levels were obtained by using a simple formula derived in Ref. [21]. Moreover, the obtained hole spin relaxation times were compared with those measured directly by time-resolved PL. Both hole spin relaxation times were found in good agreement.
Section snippets
Experimental details
Two samples (referred to as QW1, QW2) were fabricated, consisting of a single 22.5 nm thick InxGa1−xAs/InP QW with lattice-matched composition of x = 0.53, grown on (100)-oriented InP substrates by a gas source molecular beam epitaxy system. The doping was supplied by remote Si δ-layers on both sides of the QW with 20 nm undoped spacers. An additional Si δ-layer was placed between the QW and the sample surface to screen the surface charge. The sheet electron density and the mobility measured at
Results and discussion
The energy band structure of the In0.53Ga0.47As/InP QWs, calculated by a one-electron Schrödinger-Poisson equation solver [22], is shown in Fig. 1. The band parameters used in the calculations were taken from Refs. [[23], [24], [25]]. We used a value of 0.5 eV for the Schottky barrier height [26,27]. According to the calculations, at an electron concentration higher than 2 × 1012 cm−2, two confining levels in the conduction band are occupied and separated by a gap of 24 meV. The first and
Conclusion
Processes of spin relaxation of the photoexcited holes were studied in In0.53Ga0.47As/InP QWs in a quantizing magnetic field as a function of the temperature. A good agreement of the presented results with the theory was found. No significant change in the circular polarization of the PL due to LLs was detected at a temperature lower than 10 K where a population of the spin-split valence band Landau levels is determined by the ratio of the hole lifetime and the spin relaxation time. A
Data availability statement
The data that support the findings of this study are available from the corresponding author upon reasonable request.
Significance
We report on processes of spin relaxation of non-equilibrium holes in a quantizing magnetic field investigated as a function of the temperature. Thermal occupancy of the valence band Landau levels is used to extract the hole spin relaxation time and the hole effective g-factor. Thus, a new method is proposed to determine the spin relaxation time in a simple way, avoiding sophisticated measurements necessary for direct determination of the spin relaxation time. A good agreement of the presented
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
Financial supports from the Brazilian agencies FAPESP (Grant 2015/16191-5), CNPq (Grant 305837/2015-0), CAPES (Grant PNPD 88887.336083/2019-00) and the Natural Sciences and Engineering Research Council of Canada (Grant RGPIN-2018-04015) are gratefully acknowledged.
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Cited by (1)
Inter-Landau level transfer in valence band of In<inf>0.53</inf>Ga<inf>0.47</inf>As/InP quantum well
2022, Physica E: Low-Dimensional Systems and NanostructuresCitation Excerpt :It can naturally be assumed that the recombination times τ₁₀ and τ₁₁ are close in value, which leads to t₁₀ = 0.7 ns. It should be mentioned that the obtained spin relaxation time is found in good agreement with the spin relaxation time of about 2 ns measured in similar QWs in Ref. [5]. The characteristic times obtained in this study which describe the dynamics of photogenerated holes are collected in Table 1.