We discuss the concept of spin-controlled vertical-cavity surface-emitting lasers (VCSELs) and analyze it with respect to potential room-temperature applications in spin-optoelectronic devices. Spin-optoelectronics is based on the optical selection rules as they provide a direct connection between the spin polarization of the recombining carriers and the circular polarization of the emitted photons. By means of optical excitation and numerical simulations we show that spin-controlled VCSELs promise to have superior properties to conventional devices such as threshold reduction, spin control of the emission, or even much faster dynamics. Possible concepts for room-temperature electrical spin injection without large external magnetic fields are summarized, and the progress on the field of purely electrically pumped spin-VCSELs is reviewed.
Concepts for the use of the electron spin as an information carrier have become an important research field called “spintronics.” The goal of spintronic research is to exploit the carrier spin degree of freedom additionally to the charge degree of freedom in order to develop novel devices, which offer new functionalities or a better performance as their conventional counterparts. Semiconductor spintronics in general includes the search for alternative device concepts as well as the investigation of the fundamental physical processes as spin injection, spin transport, spin manipulation, and spin detection. This research area was strongly stimulated by the suggestion of the so-called spin transistor by Datta and Das in 1990 [
In this article, we first discuss the fundamentals of spin-optoelectronics and then analyze the concepts for spin injection with respect to their potential for room temperature and low magnetic field operation. Then, we discuss the concepts for spin-controlled semiconductor lasers, namely, spin-controlled vertical-cavity surface-emitting lasers (VCSELs), and analyze which properties are particularly attractive for applications. Finally, we briefly review the state-of-the-art for electrically pumped VCSELs.
Spin-optoelectronics is based on the fact that the total spin angular momentum of an electron-hole pair is directly linked to the angular momentum of a photon, which is either absorbed or emitted radiatively. This link is a consequence of the conservation of the angular momentum and is expressed by the so-called optical quantum selection rules for dipole radiation which are shown schematically for direct band-gap semiconductors in Figure
(a) Selection rules for optical transitions in direct semiconductor quantum well. The quantum numbers
As mentioned above, these selection rules directly link the spin polarization of the carriers and the polarization of the emitted or absorbed light. For example, we assume a spin polarization of 100% in the electron
In the following we assume that each hole state is sufficiently populated and thus the electron densities are the only limiting factors for optical transitions. Then the equation can be reformed to [
The situation would change completely, if split-off band related transitions were involved. If we assume, for example, an excitation with right circular polarized light with a photon energy larger than the band-gap energy
These selection rules are the basis for spin-optoelectronics because they directly link optical and carrier spin polarizations. In detail, for spin-optoelectronic devices with electrical spin injection (spin-LEDs or spin-VCSELs) they enable an estimate of the spin injection efficiency from the measured light polarization degree of the optical emission. On the other hand, they can be used also to inject carrier spin polarizations optically, by means of circularly polarized light. This is an important tool in order to investigate spin-dependent effects fundamentally, if electrical spin injection is not available.
Unfortunately the carrier spin in a semiconductor is not permanently stable like the electron charge but relaxes to equilibrium within a relatively short time called spin relaxation time. This is often a fundamental challenge for the development of spin-optoelectronic devices especially in case of the spin transport. The spin relaxation is due to many reasons like the Elliot-Yafet (EY) [
Usually, the spin relaxation time strongly decreases with temperature. In semiconductors without inversion symmetry like (100) GaAs and at low hole densities, the DP mechanism is the dominant spin relaxation mechanism at elevated temperature. Here the spin states in the conduction band for
Up to now we have concentrated on the electron spin relaxation only. Hole spins usually relax much faster than electron spins. Typical values at room temperature are in the range of 100 fs [
However, even the spin relaxation time of the electrons is typically shorter than the transport time of the carriers through a spin-optoelectronic device, for example, a spin-LED. The selection rules provide a direct link between the polarization of the spin-LED emission and the spin polarization of the carriers when they recombine. However, the longer the time is between the generation of the spin-polarized carriers (by optical absorption or electrical spin injection) the more spins relax before they recombine. This relaxation takes place both on the transport path and within the active region where the carriers recombine radiatively. Consequently, the light polarization emitted by a spin-LED only provides a lower estimate of the spin injection. Presuming a sufficient number of holes for recombination, for example, in a p-doped semiconductor, the spin relaxation within the active region can be accounted using [
Consequently, the development of electrically pumped spin-optoelectronic devices at room temperature is a huge challenge, because in standard optoelectronic devices in particular lateral carrier transport path lengths easily reach values of several micrometers. In the following section, we briefly review the concepts for electrical spin injection into semiconductors.
On the long run, spin-optoelectronic devices will only be application relevant if the spin injection can be performed electrically and when the devices operate at room temperature and without the need for high external magnetic fields which would require superconducting magnets. As we will discuss below, this implies that many of the spin injection concepts reported in the literature will never be usable in practical devices. Firstly, we briefly describe the state-of-the-art and the different concepts for spin injection into semiconductors. Again, we are concentrating on concepts which are relevant for the development of room temperature devices.
In general, the alignment of spins upon injection into a semiconductor implies the presences of a magnetic layer somewhere in the vicinity of the contact of the spin-optoelectronic device. The straightforward approach would be to use ferromagnetic contacts, for example, iron contacts. In a ferromagnetic metal like iron, the density of states at the Fermi level has both s- and d-character. The exchange interaction in the ferromagnet leads to a spin splitting of the d-states and therefore to a different density of states for spin-up and spin-down states at the Fermi level [
Schematics of the exchange field induced spin-splitting of the d-like density of states in a ferromagnetic metal.
But with a normal ohmic contact between the magnetic iron contact and the semiconductor, the large conductivity mismatch [
Many ferromagnetic metals, in contrast, have Curie temperatures far above room temperature. But other problems appear for spin injection from ferromagnetic metals. As mentioned above, the conductivity mismatch between metal and semiconductor prevents spin injection via ohmic contacts. This problem can be solved using tunnel contacts either via Schottky contacts or via isolating tunnel barriers as, for example, MgO. In tunnel contacts the tunnel rates for the electrons are proportional to the product of the densities of states of the materials on both sides of the tunnel barriers [
Spin injection at room temperature has indeed been successfully realized both with Schottky barriers [
Optimized structure for a room temperature spin-LED. The design combines a Fe/Tb-multilayer contact structure with spontaneous perpendicular magnetization, a highly efficient MgO tunnel barrier for spin injection, a minimized electron path length, and InAs QDs with enhanced spin lifetime at room temperature (a), (b) depicts the schematic energy diagram of the spin-LED in growth direction. Spin-polarized electrons will be injected from the lowest Fe layer of the Fe/Tb multilayer contact into
However, even this optimized spin-LED will probably not become relevant for applications other than the characterization and optimization of spin injection contacts. This is because LEDs are generally too slow for information technology. Moreover, the injection efficiencies that could be obtained even in the best case are still rather low. In contrast, spin-controlled lasers might offer a much higher application potential. In the following section, we will analyze this potential.
The first step on the way to a spin-polarized laser is to identify a qualified laser concept. Principally a choice has to be made, whether an edge- or a vertical-emitting geometry suites best. Figure
Comparison between spin-VCSEL (a) and spin-edge emitter (b).
Altogether, because of the above-mentioned fundamental disadvantages of edge-emitting concepts a VCSEL seems to be the most qualified concept for a spin-polarized laser at room temperature. Thus, the challenge of a more complicated spin injection concept has to be faced.
As a consequence of the long vertical spin transport path, room temperature spin-VCSELs with electrical spin injection are not available yet. Thus, at this stage, the potential of spin-VCSELs at room temperature has to be analyzed theoretically or with alternative experimental techniques. Since the selection rules shown in Figure
The idea that spin-controlled lasers might offer a much higher potential than spin-LEDs arises from the fact that lasers show a dynamical behavior much different from that of LEDs. One important example affects the influence of the spin relaxation in the active region. In spin-LEDs the effective circular polarization degree will be reduced. This reduction is usually accounted for by the factor
The dynamic behavior of spin-polarized laser can be investigated theoretically using a spin-dependent rate-equation model. Several different models have been used in the literature for this purpose [
In the SFM the light field is coupled to two population inversion variables [
One important difference between a spin-laser and a spin-LED is the nonlinearity of a laser at the laser threshold which enables a kind of amplification of spin information with a spin-controlled carrier injection. Figure
Schematical illustration of the optical gain as a function of photon energy in a VCSEL with conventional unpolarized pumping (a) and for a small spin polarization of the carriers in the active region (b). The spin-polarized pumping leads to separation of the gain spectra for the
Unpolarized inversion
Spin-polarized inversion
The anisotropic pumping leads to a small spin polarization of the carriers in the active region. We assume here a small excess in the occupation of the
In these experiments, a Ti : sapphire laser was taken for optical pumping an InGaAs/GaAs-QW-VCSEL-structure at room temperature. The spin injection was obtained by pulsed excitation with a pulse length of 80 fs. Figure
Circular polarization degree as a function of the carrier spin polarization in the active region (a). The experiments have been obtained at room temperature for pulsed excitations and show a good agreement with theoretical results based on the SFM for a spin relaxations time of 40 ps. (b) shows the calculated laser characteristics for a carrier spin polarization of 0% and 50%.
Accordingly, a spin-VCSEL has two threshold carrier densities
A closer look onto the experimental details of the work done on purely optically pumped spin-VCSELs indicates problems that might occur in electrically pumped devices, too. In order to obtain the effects like spin amplification and threshold reduction great care had to be taken to ensure a perfectly circularly symmetric pump spot. Otherwise additional anisotropic carrier density and temperature effects introduce parasitic anisotropies into the cavity, which lead to a coupling of both circular polarized laser modes and result in linearly polarized laser emission. Such cavity anisotropies like birefringence and dichroism are known to have an enormous impact on the polarization dynamics of electrically pumped VCSEL [
Setup for hybride excitation and spin control of a commercial VCSEL device. (SMF) single mode fiber, (POL) linear polarizer, (QWP) quarter wave plate, (M) mirror, (HWP) half wave plate, and (BP) bandpass.
So far, we have only discussed time averaged stationary effects. But, besides spin amplification, spin control, and threshold reduction in continuously operating spin-VCSELs, dynamical effects might be even more promising. For example, it was predicted that spin-VCSELs might be considerably faster than their conventional counterparts. First fundamental investigations by Hallstein et al. confirmed this potential [
The results for a pulsed spin injection into the
Dynamics of the total intensity (a) and the circular polarization degree (b) of an electrically pumped VCSEL after additional spin injection using a short right circularly polarized light pulse. Theoretical calculations based on the SFM are depicted ((c), (d)).
The ability for enhance speed and modulation bandwidth is a very promising advantage of spin-VCSELs, which is attractive for a lot of applications, for example, high-speed optical data communication technology. Accordingly, a lot of work has been concentrated on this issue, and several other concepts have been presented, recently. Lee et al. investigated the small-signal modulation properties of both circularly polarized laser modes in a spin-polarized VCSEL, theoretically [
However, even though a lot of progress has been made in emphasizing the advantages of spin-polarized laser devices in comparison to conventional ones and a lot of promising properties have already been identified, a device with superior performance in comparison with conventional devices is still missing. One important challenge which has to be solved is the realization of efficient electrically pumped spin-VCSELs at room temperature. The current state of technology for electrically pumped VCSELs will be discussed in the next section. However, another important problem is that most concepts for spin-VCSELs are restricted to an operation near the laser threshold. This can be an important drawback on the way to realistic applications, because here the efficiency and the power of a laser are low and the laser dynamics is inherently slow. Accordingly, the search for other spin-dependent properties which are not restricted to this current region is one of the most relevant tasks in the near future. Anyway, the usable current region can be significantly enhanced by improving the spin polarization degree. Here the development of spin-VCSELs using (110) GaAs quantum wells might deliver an important progress due to the long spin relaxations time in this material. Recently the first optically pumped spin-VCSEL grown on (110) GaAs substrate and operating at room temperature could be demonstrated by Iba et al. [
All electrically pumped spin-polarized VCSEL devices published so far have been developed at the University of Michigan, USA. The first device was presented in 2005 by Holub et al. [
Taking the difficulties due to hole spin injection and MCD in the cavity into account, the next concept for an electrically pumped spin-VCSEL consequently based on electron spin injection contacts. This concept was realized by Holub et al. in 2007 [
Circular polarization degree (a) and threshold current reduction (b) as a function of the magnetic field in an electrically pumped spin-VCSEL at 50 K. The VCSEL design is displayed in the inset of (b). The spin-VCSEL based on electron spin injection utilizing a Fe/AlGaAs Schottky tunnel contact design. (from [
In order to optimize the spin-VCSEL concepts for an operation at elevated temperatures, the next concept published by Basu et al. in 2008 based on InAs/GaAs quantum dots as active gain medium [
Though impressive progress has been made concerning the development of electrically pumped spin-VCSELs, a device operating at room temperature is still missing. However, the realization of this goal is absolutely necessary to develop spin-VCSELs in order to benefit from the potential for superior performance in comparison to conventional devices in the near future. Thus, additional intensive research effort is required in this field in the next years. But the already demonstrated results are encouraging and raise the hope that this goal can be reached soon.
In this paper we review the state-of-the-art of spin-controlled VCSELS with a particular focus on the most promising concepts for real devices. After discussing the fundamentals of spin-optoelectronics we discuss the concepts for electrical spin injection into semiconductor light-emitting diodes (LEDs). However, spin-controlled lasers are generally more attractive for applications than spin-controlled LEDs. Lasers have much faster dynamics than LEDs and the nonlinearity of the laser at threshold potentially enables a strong amplification of spin-dependent effects. Among the different concepts for semiconductor lasers, VCSELS are most attractive for spin-control because of their vertical device architecture and circular symmetry. Fundamental studies confirm that spin-VCSELs promise to have lower thresholds than their conventional counterparts and that they enable spin-control of the output polarization. But their most promising advantage is that they might be much faster than their conventional counterparts. For practical applications, the interaction of the spin effects with cavity anisotropies like birefringence and dichroism might enable enormously high modulation frequencies. Recently, Li et al. and Gerhardt et al. [
The greatest challenge in the field of spin-VCSELs still remains the realization of room temperature operation with pure electrical spin injection. Further massive effort will have to be invested into the engineering of appropriate spin injectors, injection paths in the semiconductor, and of materials with weak spin relaxation such as (110) GaAs, for example. Additionally a successful integration of efficient spin injection contacts with perpendicular magnetization, providing low switching fields would be an important issue towards realistic applications. However, there has been considerable progress in this area of electrically pumped VCSELs in the past few years. Together with the above-mentioned high potential of spin-VCSELs it can thus be expected that spin-controlled VCSELs remain a scientifically stimulating research area with growing application potential within the next decade.
The authors thank the German science foundation for financial support within the SFB 491. Helpful discussions with and technical support from T. Ackemann, C. Brenner, M. Li, and H. Höpfner are greatfully acknowledged.