Spin-dependent electron transport in semiconductors.
My thesis work was funded by the Gaspard Monge international grant.
To get the manuscript of my PhD thesis, click here.
Current technologies are based on electronics for transmitting, processing and receiving information. It is the movement of electrons inside semi-conductors (like Silicon) that is used as a way of representing and transferring digital information. The transistor, invented in 1948, is the fundamental component of processors, having two states of operation (representing a "1" or a "0" ) according to the resistance that opposes to the movement of electrons across a channel. Nowadays, the miniaturization of electronic components have achieved a density of some millions of transistors over a squared millimeter! This has allowed to improve the speed and performance of electronical devices for the last 60 years. However, the miniaturization of transistors is reaching some fundamental limits, for example because of the problem of evacuating the heat dissipated by currents on such a small surfaces.
The electron not only has a charge, but also another fundamental property called spin, which is a quantized physical quantity that can only have two values when a measurement is performed: 'up' or 'down'. It is therefore an excellent candidate to represent digital information!. Spintronics is an emergent technology whose objective is to use the spin of the electrons (and not only their charge) to create new devices, with lower power consumption than our current transistors.
Different physical processes are important to understand in order to conceive a spintronic device. First of all, we should be capable of aligning the electron's spin either in the "up" or "down" direction (we call this process "spin orientation") to represent information. In a non-magnetic semiconductor at equilibrium, the number of electrons with spin "up" and "down" are equal, we say that they are unpolarized. On the other hand, if all of the electrons have the same spin, then we say that they are 100 % polarized. After this spin orientation, we need to transport this information from one point to the other within the semi-conductor. For this, we need to consider the fact that the transport of charge and spin may differ strongly. Indeed, different spin transport phenomena have been demonstrated in the last 15 years, such as the spin-Coulomb drag and the Spin Hall Effect. The goal of my thesis was to better understand spin transport in semi-conductors by taking into account the Pauli principle.
Spin transport and the Pauli principle
During my PhD, I studied diffusive transport of polarized electrons in Gallium Arsenide (GaAs). When a conduction electron moves inside the crystal, its momentum changes randomly because of the different scattering mechanisms that can affect its movement. The longer the characteristic time of scattering is, further the electron can diffuse and therefore separate from its initial position during its lifetime in the conduction band. In our experiments, electrons are excited in the conduction band and spin-polarized by the absorption of a circularly polarized laser beam, which is tightly focused in a surface of approximately 1/4th of a squared micron. Electrons diffuse over all directions during their lifetime in the conduction band, moving away from the excitation spot. When electrons leave the conduction band, they emit light whose circular polarization degree is proportional to the electronic spin polarization at the time of emission. I studied this luminescence coming from the spin polarized electrons. Thanks to a special microscope, it is possible to build an image of the spatial electron distribution, and at the same time, of their spin polarization as a function of space.
Typically, electrons loses their spin polarization as a function of time during their movement in the semi-conductor, because of different processes that can relax their spin orientation within and during scattering events. The figure below shows images of the spatially resolved spin-polarization for different excitation powers in p-doped GaAs at 15 K. As the excitation power increases, the concentration of electrons in the conduction band also increases.
At weak excitation power (from 72 nanowatts to 0.45 milliwatts), the electron polarization is maximum at the position where they are originally excited by the laser spot, and then it exhibits a monotonic decrease as a function of the distance traveled by the electrons. Eventually, the information contained in the electron polarization is completely lost after some tens of microns.
However, we have shown that electron polarization can actually increase during diffusion, as long as the excitation power is high enough. This is a consequence of a fundamental quantum law, known as the Pauli exclusion principle, which says that it is impossible for two electrons to occupy the same quantum state (which is characterized by its wave function and its spin orientation). For a scattering mechanism to be effective, the final state should be available, which is generally true at low electron density. On the other hand, if the density of electrons with a given spin (for example, "up") is of the same order of magnitude than the density of accessible states (approximately 1017 cm-3 in GaAs), then the final state during a scattering event will be probably occupied by an electron of the same spin, in which case this event is forbidden by quantum mechanics and won't happen. These spin "up" electrons will travel further than the spin "down" electrons, which are less in number. This explains the figures obtained at 1.89 and 2.55 milliwatts, in which we see a progressive increase of the spin polarization from the centre up to a distance of 2 microns. Eventually, the concentration of electrons at higher distances becomes again smaller than the concentration of available states, the spin polarization will start to decrease again as it should.
Even though the Pauli principle has been known for almost a century, and its consequences have been observed in very different systems (chemical bonds, atomic gases, neutron stars), its effects on spin polarized transport in solids have never been explicitly observed until now. The experimental observation of this Pauli blockade is important because it should modify all of the other observed phenomena on spin polarized transport (such as the spin hall effect) at high electron density. The next step would be to explore lower dimensional systems (quantum wells or nano-wires), in which this effects should be stronger because of the quantum confinement of electrons.
Phys. Rev. Lett. 111, 246601 - Published 9 December 2013
F. Cadiz, D. Paget, and A.C.H. Rowe
On the press:
Researchers in the Condensed Matter Physics Laboratory (École polytechnique / CNRS) have revealed a new spin filter effect in semiconductors
Press release, published December, 2013
F. Cadiz, SPIE Optics & photonics, San Diego convention center, 17th-22nd August, 2014
A.C.H. Rowe, Condensed matter in paris, 24th-29th August, 2014
Here is a video of drift and diffusion of photoelectrons in a Hall bar resolved by microluminescence imaging.