Study of nanostructured layers using

Electromagnetic Analog Circuits

Master: Sergei PetrosianSupervisor: Professor Avto Tavkhelidze

IntroductionThermoelectric properties of nanograting

layersElectrical circuits as analogs to Quantum

Mechanical BilliardsComputer simulation of nanograting layerConclusion

Outline

Introduction

Nanograting and reference layers

Energy diagrams metal

Energy diagrams semiconductor

Physical and chemical properties of nano structure depends on their dimension. The properties dependes on the geometry. Periodic layer impose additional boundaryconditions on the electron wavefunction. Supplementary boundary conditions forbid some quantum states for free electrons, and the quantum state density in the energy reduces. Electrons rejected from the forbidden quantum states have to occupy the states with higher energy and chemical potential increases

Thermoelectric properties of nanograting layers

Nanograting layer Substrate

The density of states in nanograting layer minimizes G times

ρ(E) = ρ0(E)/G, where ρ0(E) is the density of states in a reference

quantum well layer of thickness L (a = 0) G is the geometry factor

Characteristic features of thermoelectric materials in respect of dimensionless figure of merit is ZT

T - is the temperature Z is given by Z = σ S2/(Ke + Kl), where S - is the Seebeck coefficient σ - is electrical conductivity Ke - is the electron gas thermal conductivity Kl - is the lattice thermal conductivity

The aim of this study is to present a solution which would allow large enhancement of S without changes in σ, κe and κl. Itis based on nanograting layer having a series of p-n junctions on the top of the nanograting layer .Depletion regionwidth is quite strongly dependant on the temperature. The ridge effective height aeff(T ) = a − d(T ) and therefore thegeometry factor of nanograting layer becomes temperature-dependent,G = G(T ).

Electrical circuits as analogs to Quantum Mechanical Billiards

For investigate the density of states in nanograting layer we used relatively new method of solving quantum billiard problem. This method employs the mathematical analogy between the quantum billiard and electromagnetic resonator.

Electric resonance circuit

We consider the electric resonance circuit by Kron’s model. Each link of the two-dimensional network is givenby the inductor L with the impedance  ZL = iωL+R where R is the resistance of the inductor and ω is the frequency. Each site of the network is grounded via the capacitorC with the impedance Zc = 1/ iωC

Square resonator model

NI Multisim Cirquits Design Suite

Using Kron’s method we built our circuit in NI Multisim software, which is used for circuits modeling. 64 subcircuits, which consist from 16 elementary cells.

4x4 elementary cell in subcirquits

R=0.01om

L=100nH

C=1nF

Simulation results in square geometry

F=2.2 MHz F=3.5MHz

Nanograting layer simulation

Simulation results in nanograting layer

F=2.5MHz F=3.7MHz

Square geometry Nanograting layer

2.2 MHz 2.5 MHz

3.5 MHz 3.7MHz

Obtained resonance frequences

First and second resonances

The Method of RLC circuits is applied to solve quantum billiard problem for arbitrary shaped contour, based on full mathematical analogy between electromagnetic and quantum problems

The circuits models were developed and simulated using NI Multisim software

Results of the simulation allow to study accurately enough the nanograting layer through computer modeling

Conclusion