The past few decades of research and development in solid-state semiconductor physics and electronics have witnessed a rapid growth in the drive to exploit quantum mechanics in the design and function of semiconductor devices. This has been fueled for instance by the remarkable advances in our ability to fabricate nanostructures such as quantum wells, quantum wires and quantum dots. Despite this contemporary focus on semiconductor quantum devices, a principal quantum mechanical aspect of the electron, its spin, has largely been ignored except in as much as it accounts for an added quantum mechanical degeneracy.
A new paradigm of electronics based on the spin degree of freedom of the electron has begun to emerge in the recent years. This field of semiconductor which is named “the spintronics” places the electron spin rather than charge at the very center of interest. The underlying basis for this new electronics is the intimate connection between the charge and spin degrees of freedom of the electron. A crucial implication of this relationship is that spin effects can often be accessed through the orbital properties of the electron in the solid state. An example of this is the spin-dependent transport measurement such as giant magneto resistance (GMR). In this manner, the information can be encoded in not only the electron’s charge but also in its spin state, i.e. through the alignment of spin up or spin down, relative to a reference such as an applied magnetic field or magnetization orientation of the ferromagnetic film. This ability offers opportunities for a new generation of semiconductor devices which combine the standard microelectronics with the spin dependent effects that arise from the interaction between the spin of a charge carrier and the
magnetic properties of the material. The advantages of these new devices would include non-volatility, increased data processing speed, decreased electric power consumption, and increased integration densities compared to conventional semiconductor devices.
Experiments to explore the transfer of a spin-polarized electric current within small devices have been ongoing for years. But attaining the same level of exquisite control over the transport of spin in micro-scale or nano-scale devices, as currently exists for the flow of charge in conventional electronic devices, remains elusive. Among the major problems of semiconductor spintronics is the understanding of spin-dependent transport in various semiconductor heterostructures.
The reason for us to choose semiconductor is that semiconductor materials offer the possibility of new device functionalities which are not realizable in metallic systems. Equilibrium carrier densities can be varied through a wide range by doping. Furthermore, the electronic properties are easily tunable by gate potentials because the typical carrier densities in semiconductor are low compared to the metals. There is a vast body of knowledge concerning semiconductor materials and processing; and these are among the most pure materials available commercially. All these attributes converge to allow definition of microelectronic devices with power gain, enabling the fan-out necessary to create massively integrated systems. In addition, recent advances have allowed optimization of interfaces between different epitaxial materials at the level of atomic-scale control. In fact, many of these processes have already been scaled up to commercial production lines. These factors which are in concert with recent advances in materials science of high-quality magnetic semiconductors now make semiconductor materials perhaps the first,
and natural choice for future spintronics applications, especially those involving large scale integration of spintronics devices.
For the real application of spintronics, Datta and Das proposed a “spin transistor” and drew the special attention to the possibility of spin injection in semiconductor systems in 1990. The structure of this “spin transistor” is shown in Figure 1.1. The idea of spin transistor proposed by Datta and Das was based on the manipulation of the spin state of the carrier by controlled spin precession. This device is similar to the conventional FET which has a drain terminal, a source terminal, and a channel which owns a tunable conductance between the source terminal and the drain terminal. However, the spin transistor is capable of injecting and accepting one spin component of the carrier contribution only. The materials of the source terminal and the drain terminal are both ferromagnetic metals and with the same alignment of electron spin orientation. The electron injects into the source terminal and gets aligned by the source terminal as the same way the drain terminal does. The current of electrons which have been aligned will flow through the channel from the source terminal to the drain terminal. It has been approved that the electrons which have been polarized are able to be manipulated via the additionally applied gate voltage. This additionally applied gate voltage will alter the spin-orbit interaction which originates from the asymmetry of the inversion in the macroscopic potential and is named the Rashba term. Further analysis to this structure will show us that the process of the control the injected electrons by applied gate voltage provides us a possibility to realize the spin device.
Figure 1.1 The Spin transistor proposed by Datta and Das
The gate control of spin splitting in quantum wells has been demonstrated in various two dimensional electron gas systems. There are considerable theoretical studies on the spin-splitting of the conduction band in zinc blende compounds.
Most III-V semiconductor materials have zinc blende lattice structure which is asymmetric with respect to inversion. Even at zero magnetic field, the intrinsic crystal fields lead to a conduction band spin splitting which is proportional to . Spin orbit coupling can also be induced by an interfacial electric field within a heterostructure. The carrier which is confined to move in an asymmetric quantum well will experience an effective magnetic field. This effective magnetic field is called the Rashba field that may induce spin precession. It is possible to tune the rate of this Rashba-field-induced precession, which will alter the built-in confinement potential. The Rashba Hamiltonian is written as
k3
z
HR =α[σ×k]⋅ˆ (1)
where α is the spin-orbit interaction parameter which is linearly dependent on Ez through the energy gap and the effective mass. is the direction of the electric field.
zˆ
The total Hamiltonian assumes that the Rashba effect dominates all other spin-coupled factors and is written as
R k
tot H H
H = + (2)
where
= ∗
m Hk k
2
2
h2 (3)
The eigenstates for the spin-up condition and the spin-down condition are then
m k k k
E± = ∗ ±α ) 2
(
2
h2 (4)
The amplitude of the spin splitting energy is 2αkF at zero magnetic field at the Fermi energy and is denoted by the notation ∆R. An electron will precess an amount ∆θ =ωLL vF in traversing a distance Lin the quantum well, where ωL =∆Rm∗L h2kF . The angle which an electron precesses through in traversing a distance L is
θ
∆ =2 2 h
L m∗α
(5)
The range of values for α given by Nitta et al. [6-7] and Heida et al. [8] is between 0.5 and 1 eVm, and gives us the corresponding energy splitting 1.5 to 6 meV. Thus, the tunability is achievable through tuning the value of
10−11
×
α by an external gate voltage.
In addition, Intel also proposed a new generation device which is the “InSb Quantum Well Transistor” recently and was built on the multi-layer epitaxial structure. The structure of the “InSb Quantum Well Transistor” is shown in Figure 1.2. In the structure as you can see in Figure 1.2, the carriers are confined within the InSb quantum well for transport. And we have found some great properties of the material InSb which make it the good candidate for the spintronics application.
Figure 1.2 The InSb quantum well transistor
It has been recognized that the spin splitting in the asymmetrical quantum well contains two distinct contributions. The first one is due to the inversion asymmetry of the bulk material. The other is the Rashba term which comes from the asymmetry in the macroscopic confining potential. This term has been used to interpret the results of different asymmetric quantum well experiments.
It is reasonable for us to believe that this is the term which provides the dominant contribution to the splitting. [1-5]
All the examples above tell us that the spintronics will have the weight in the near future. Thus, more knowledge about it is needed in urgent in the spintronics related field either to build the real devices or to continue any deeper research.
The asymmetric double well structure which we proposed in this paper provides a configuration to enlarge the spin orbit splitting of the electronic states effectively. Also we demonstrated how the spin-splitting energy will vary with different parameters for any further application in the near future.
We will organize this dissertation as several parts. Chapter 1 is the introduction and motivation of our work. Chapter 2 is the basic theories which are concerned in this work. Chapter 3 is the results of our work and will be shown in figures mainly. Chapter 4 is the conclusion of our work.
Chapter 2 Theory