In this project we study the physical mechanisms that govern the performance of scaled-down microelectronic devices. The project is part of the EMMA program of the Academy of Finland. The consortium partners are VTT Microelectronics Centre, Physics Department, University of Jyväskylä, Optoelectronics Laboratory, Helsinki University of Technology, Laboratory of Computational Engineering (LCE), Helsinki University of Technology and Okmetic Ltd. Materials and processes will be developed to fabricate very small prototype devices for future microelectronics, namely quantum point contacts and single electron transistors. Properties of devices fabricated from different materials will be compared, and the effects of scaling down the device size will be studied to gain understanding about the consequences caused by the large surface to active volume ratios in these structures.

The material systems to be studied are Si/SiO_{2}, SiGe/Si and
InGaAs/InP. For Si/SiO_{2} structures, SOI wafers - bonded and
SIMOX - will be used as starting material. The project was started
in summer 1999. The first topics studied at LCE have focused on
modelling the Si/SiO_{2} interface and its influence on
electronic structure in the wave guide and on developing
computer programs for calculation of conductance in coherent
transport regime.

**Modeling of Electronic Structure in Silicon Quantum Wires**

Researchers: Fredrik Boxberg, Risto Virkkala, and Jukka Tulkki

We have studied strain and electronic structure
in quantum interference components made of silicon
and silicon dioxide. The research focuses on modeling
of strain, caused by thermal oxidation during the
fabrication process, and the strain induced modification
of electronic properties of the silicon/silicon oxide
constructions. The IC-technology of today is based on silicon
and only a few per cent on III-V semiconductors. However, in
silicon structures it has been difficult
to obtain phase coherence length comparable to that
of III-V semiconductors. Our goal is to
understand the electronic
properties of silicon, silicon dioxide and their interface
for optimization of Si/SiO_{2} based
quantum wire and quantum point structures.

The calculation of strain is based on the elastic continuum theory. We use a phenomenological model to account for experimentally observed strain in thin conducting silicon channels and calculate the influence of strain on electronic states by envelope wave function method. Figure 30 a) shows the calculated strain in a 240nm long quantum wire. Strains will affect the conductance band of the silicon and thereby change the electronic properties of the whole device according to our analysis. The strain will induce a three dimensional (3D) potential minimum in the wire. Figure 30 b) shows the deformation potential in the wire. The 3D minimum makes the quantum wire to function as a single electron transistor instead of a wave guide. Figure 30 c) shows the probability density of the ground state wave function in the wire. These effects are very specific to conducting channels made of silicon and silicon oxide. In the future we will extend our model to account for key features of the oxidation process itself and we will also investigate the charges existing in the isolating oxide and their influece on conductance. This will include both theoretical work and also some experiments at VTT Electronics. This project includes close cooperation with VTT Electronics.

Figure 30:
Cross sections of the quantum wire. They are all
taken along the direction of the electrical current through
the device. a) A contour plot of the induced strain in
the z-direction in the quantum wire. Dark blue indicates
a strain of about -0.01 and dark yellow corresponds to
a strain of about -0.002. b) A contour plot of the
deformation potential. The energy is given with respect
to the band edge of the conduction band. The dark blue
and dark red represent a band shift of ca. -50 meV and +10 meV
respectively. c) A visualization of the probability density
of the ground state wave function of one electron in the
quantum wire. Dark red and dark blue corresponds high and
low probability respectively. |

**Electron Transport in Silicon Quantum Wires and Point Contacts**

Researchers: Kari Maijala and Jukka Tulkki

Fabrication of nanoscale semiconductor structures opens up possibilities to develop solid state devices with fundamentally new operating principles. In these novel structures the transport of electrons and holes has to be described by quantum mechanical or semiclassical methods.

One of the prominent properties of one dimensional conducting structures called quantum wires and quantum point contacts is the quantization of conductance. The measured conductance is a nonlinear function of applied voltages and exhibits stable plateus where its value remains independent of the external field. The quantization of measurable quantities such as charge, conductance or magnetic flux is useful as transistor operation or metrological applications are considered.

Figure 31:
On the left: Quantum wire is decomposed into short sections for
computation of the conductance. On the right: Conductance of the quantum
wire in units of 2e/^{2}h. |

In this project we focus in the electron transport in silicon
nanostructures. Currently we are studying the conductance of silicon
quantum wires and quantum point contacts in the linear response
regime. We are developing computational models which are based on a
recursive Green function method. The sample is divided into small
slices (see figure 31 on the left)
which are recursively connected to each other to give the Green
function of the whole sample. Conductance of the sample (see figure
31 on the
right) is obtained from the calculated Green function and
transmission coefficients by means of a Landauer type formula
, where *g* is conductance and
*t* is the transmission matrix. Magnetotransport studies are
possible within the same framework. The method is robust and is
applicable to other nanostructures as well.