Research on Semiconductor Quantum Structures and Physics of New Information Technologies

Optically active quantum dots (QD) and quantum wires (QWR) are compound semiconductor structures that confine both electrons and holes in a potential box having a dimension of few tens of nanometers. These semiconductor structures have exceptionally high optical quality on special transport properties, which makes them ideal for both fundamental research and technological applications. In the enclosed project descriptions we describe few topics that have been in focus during 2002.

This work includes extensive domestic and international collaboration with the following laboratories: Optoelectronics Laboratory, HUT, VTT Electronics, Instituto Nazionale di Fisica della Materia, University of Lecce, MegaGauss Laboratory, University. of Tokyo, Inst. of Industrial Science, University of Tokyo. Center for Teraherz Science, USCB.

The ever-decreasing size of the basic components of information processing will give quantum effects an important role in future technologies. Recent developments such as quantum cryptography and the idea of a quantum computer have shown that, rather than being only harmful, these effects can probably be utilized to a great extent. In communications technologies, optical transmission is setting the trend in the development of the networks. The full harnessing of the huge bandwidth provided by light still requires for replacing the switching, routing and processing electronics by all-optical components. Research on nonlinear optical materials and light-induced quantum effects will be crusial in the development of future all-optical processing technologies.

We have investigated cold atomic Fermi-gases which can be used for studing important quantum many-body effects such as superconductivity. Cold atomic gases may also serve as a source of atoms in quantum information processing applications. This research is done in collaboration with the University of Innsbruck, Austria, with Nordita, Denmark, and with the Loomis Laboratory, University of Illinois, USA. We have also participated in the University of Jyväskylä -based experimental research on the idea of using superconducting Josephson junctions as the basic processing element of a quantum computer. Related to optical communications technology, we have started a project investigating the possibilities of all-optical swithing and processing using nonlinear materials, combined with novel material structures such as photonic crystals.

Modelling of Nanoscale Semiconductor Devices

Researchers: Fredrik Boxberg, Roman Terechonkov and Jukka Tulkki

The semiconductor technology of today is mainly based on silicon. However, it has been shown very difficult to obtain long phase coherence lengths in silicon structures. For quantum mechanical operation the phase coherence is crucial. We are studying the possibilities for quantum mechanical electronics in both silicon and III-V compound semiconductor (eg GaAs) devices. We have modelled the growth process of silicon dioxide on silicon quantum wires and its effect on the electronic properties of fabricated devices. We have observed great strain-induced effects on the electronic properties of the device.

Another topic of research is the electronic and optical properties of complex III-V compound semiconductor devices. We are studying the possibility to fabricate both single photon devices (eg needed for possible quantum information processes) and laser devices. For this purpose we are developing very general tools for strain analysis and band structure calculations.

The strain in the modelled structures is due to different lattice constants of the epitaxially combined materials. The strain is of the order 10-2. Hence, the devices can be built with hardly any dislocations and we now that the strain is completely elastic. However, the strain affects though remarkably the electronic structure and it cannot be omitted from the electronic and optic model. The assumption of a dislocation-free structure is one of the corner-stones of our model. The strain and the piezoelectric field in these structures affects the position and the interband coupling of the energy bands.

The strain calculations are based on the elastic continuum theory. The full treatment of the strain in compound semiconductors leads to a electro-elastic coupled problem where the strain is coupled to the piezoelectric field. This coupling is due to the ionic atomic structure of III-V compound materials. The effect is absent in purely one material semiconductors like silicon or germanium.

The optical properties rely completely on the underlying electronic bands. From the electronic structure we can model properties like photon recombination rates, polarization of the emitted light and light amplification. We intend to extend our modeling to the time domain but so far we have only considered time independent and long term limiting properties.

We have been working on quantum wells, quantum wires and quantum dots. Figure 28 shows an 8 nm thick corrugated quantum well with a corrugation period of 13 nm. Figure 28 A and B show the electron and hole probability densities respectively, close to the fundamental energy band gap. The electronic band structure of the structure is shown in Fig. 28 C and Fig. 28 D shows schematically the geometry of the structure. The shaded layer is the InGaAs quantum well inside AlGaAs barriers. The periodic corrugation and strain induce aligned quantum wires as seen in Fig 28.

Figure 28

Figure 28: (A) Electron and (B) hole probability densities in a corrugated quantum well. (C) The modeled energy diagram. (D) A schematic model of the simulated AlGaAs/InGaAs quantum well.

Energy Band Structure Calculations

Conductance and optical properties of electronic and photonic devices are governed by the electronic structure of the active materials of the components. Due to the fast electron relaxation, we pay attention only to the electronic states near the band edge. This motivates the use of the k.p-theory.

In this project we have developed numerical methods for calculation of electronic structure in semiconductor quantum wells, wires and dots. Considering the basis composed of the high s- and p-orbitals and taking into account the electron spin we derived the 8x8 Luttinger-Kohn hamiltonian to be discretised. The strain effects calculated separately using ANSYS library are included to this hamiltonian. Finite differences method is used to discretise the hamiltonian in such a way that the final matrices are symmetrical [1]. Closed, open or cycle boundary conditions are included to take into account the finite geometry of the semiconductor structures.

Special libraries are required to diagonalise the obtained matrices which size may be of the order up to 1000000 by 1000000. We are using PARPACK library to parallize the eigenvalue problem to run it on the cluster systems.

[1] O. Stier, Electronic and Optical Properties of Quantum Dots and Wires
(Wissenschaft und Technik Verlag Berlin, 2001).

Modelling Optical Components for Access Networks

Researchers: Jani Oksanen and Jukka Tulkki

With the long haul network backbone transformed into an optical information highway, the transfer capacity is mostly limited by the electronic bottlenecks in the access and metropolitan area networks. The undisputed success of the optical fibres in the network backbone encourages to resolve the bottlenecks by passing to optical solutions in the other parts of the networks as well. This solution, however, requires all-optical components which do not exist commercially (or at all) at present.

Metropolitan area networks include a large number of separate connections, which makes fast switching devices and inexpensive laser transceivers essential. The goal of this project is to create models and new ideas for the components needed in expanding the optical network.

Figure 29

Figure 29: The calculated absorption spectrum of a quandum dot laser.

Figure 30

Figure 30: Schematic representation of the linear optical amplifier including a waveguide and a vertical microcavity with highly reflecting distributed Bragg reflectors (DBR).

Figure 31

Figure 31: The coupling between the signals, vertical cavity laser (VCL) and carriers of the system. a) The signal of Ch. 1 as a function of time at different positions along the amplifier. The weak self modulation of the signal is seen at the output. b) The constant signal of Ch. 2 at different positions. The weak cross modulation of Ch. 1 is seen at the amplifier output. c) The relaxation oscillation of the carrier density caused by changes in the signal powers. d) The photon density fluctuations in the VCL mode captures most of the disturbances.

We have investigated the differences of the quantum well and dot lasers with respect to their chirp under direct current modulation. This is done by evaluating the changes caused by the current modulation to the refractive index of the laser waveguide. The basic mechanism causing the chirp is the relation between the refractive index and the absorption of the medium. When a laser is modulated with current, the carrier concentration in the lasers changes in time. The changes in carrier density alter the gain, which further induces changes in the refractive index. And as the refractive index changes the wavelength of the optical field that 'fits' in the laser cavity changes.

The refractive index changes corresponding to a change in the carrier density can be tracked using the Kramers-Kronig relation stating that the the refractive index at a given wavelength depends on an integral of the absorption spectrum of the material. It has been shown that the quasi-equilibrium is a good approximation of the carrier distribution under lasing conditions, and if the carrier distribution in the material is known, also the absorption spectrum can be calculated. This enables to evaluate the linewidth enhancement factor at a given carrier density and wavelength even without a dynamical model.

To evaluate the actual chirp, it is necessary to use dynamical equations to find out just how much the current modulation changes the carrier density of the laser. The simplest model is the two-level rate equations describing the relation between carrier density and the laser field. After the amplitude of the carrier density fluctuation is known it becomes a simple task to evaluate the chirp, provided the refractive index spectrum is known.

It turns out that, in addition of having a low threshold current, the quantum dot lasers can add very low chirp - an order of magnitude lower than corresponding quantum well lasers - to the signal, even when modulated directly with current. In practice this might remove the need of costly external modulators in the laser transmitters.

We have also studied a new kind of semiconductor amplifiers that have a stabilizing laser field perpendicular to the amplified signal. The analysis is based on a stochastic rate equation model coupling the signal and perpendicular laser field photon densities to the carrier density of the laser. These differential equations are solved numerically to see the effects of the stabilizing field to the amplification. Due to the compact size, customizable amplification spectrum, integrability and current injection, these amplifiers are ideal for signal amplification, because their signal degradation is small.

Future topics include switching, adjustable wavelength lasers and other related components. Also the electronic structure calculations of the material research group are to be used in the future simulations.

Photonic Crystals

Researchers: Anu Huttunen and Päivi Törmä*
*Department of Physics, University of Jyväskylä.

Photonic crystals are periodic dielectric structures. The periodicity causes bandgaps for light to appear, i.e., light with a certain wavelength cannot travel in the crystal. Photonic crystals are a very attractive solution to various problems in telecommunications. The periodicity, and thus the bandgap, can be in either one, two or three dimensions. A widely used example of a one-dimensional photonic crystal is the Bragg grating. Two-dimensional photonic crystals embedded with defects could be used, e.g., as a waveguide for integrated optics and three-dimensional photonic crystals as a microcavity.

Photonic crystals may become the key material for integrated optics. Then they are demanded to have as small size as possible. Thus we study thin slabs of one- and two-dimensional photonic crystals. Band structures and eigenmodes, and thus the functioning of the photonic crystal change markedly, when the finite height and the surrounding material is taken into account. We also study photonic crystals made of Kerr-nonlinear materials, which means that the material properties are dependent on the local light intensity. Thus the bandstructure of the nonlinear photonic crystal, i.e., the transmission as a function of the frequency, can be changed dynamically by applying a high-intensity control pulse. This phenomenon could be used for fast all-optical switching in optical telecommunications. We have developed an iterative Fourier-method to calculate the bandstructures. To study light propagation in the structures we use a finite difference time domain (FDTD) method in collaboration with VTT Electronics.

Figure 32a Figure 32b

Figure 32: On the left cross section of a one-dimensional photonic crystal slab and a gaussian pulse propagating along it. On the right the shape of one component of the eigenmode in the region marked with a square.

Cold Degenerate Atomic Fermi Gases

Researchers: Mirta Rodriguez, Gheorghe-Sorin Paraoanu1 and Päivi Törmä1
1Department of Physics, University of Jyväskylä

The remarkable achievement of Bose-Einstein condensation (BEC) in alkali gases has stimulated the trapping and cooling of also the Fermionic isotopes. The regime of quamtum degeneracy has been achieved for 40K and 6Li by several experimental groups.

Atomic gases can be efficiently and accurately manipulated. They are dilute and weakly interacting thus offering the ideal tool for studying fundamental quantum statistical and many-body physics.

The most prominent phenomena for the fermionic samples would be the superfluid BCS transition. When fermionic atoms in two different hyperfine states are trapped they may have an attractive interaction between them caused by s-wave scattering. According to theoretical predictions, the system then lowers its energy by the formation of atomic Cooper-pairs and becomes a superfluid.

We are studying different manisfestations of superfluidity in these novel systems:

  1. The vortex core size reflects the typical coherence length of the system. We have analyzed the single vortex solution for the order parameter very close to the transition temperature, and studied how the trapping potential affects the healing length of the system. We found that the healing length differs essentially from that of metallic superconductors due to the trapping effects.

  2. We have proposed the use of on-resonant or near-resonant light to probe the order parameter in order to detect the superfluid transition and the Cooper-pair coherence across different regions of the superfluid. The possibility of exciting collective modes by the probing laser light has also been considered.

  3. We have reformulated the josephson effect between two superfluids when it is possible to couple in a different way the two atoms forming the pair.

A purely quantum transport phenomena such as Bloch oscillations can also be observed in these Fermi gases when they are loaded in a periodic optical potential.

Figure 33

Figure 33: Proposed laser scheme to observe the josephson current between two superfluid atomic Fermi gases. In these systems one more degree of freedom will be experimentally available and one can couple with different "voltages" atoms in "spin up" and "spin down" states.