Study of nanostructured layers using Electromagnetic A nalog C ircuits

1. Study of nanostructured layers usingElectromagnetic Analog Circuits Master: Sergei Petrosian Supervisor: Professor AvtoTavkhelidze

2. Outline • Introduction • Thermoelectric properties of nanograting layers • Electrical circuits as analogs to Quantum Mechanical Billiards • Computer simulation of nanograting layer • Conclusion

3. Introduction Nanograting and reference layers Energy diagrams metal Physical and chemical properties of nano structure depends on their dimension. The properties dependes on the geometry. Periodic layer impose additional boundary conditions 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 Energy diagrams semiconductor

4. 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

5. 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

6. The aim of this study is to present a solution which would allow large enhancement of Swithout changes in σ, κe and κl. It is based on nanograting layer having a series of p-n junctions on the top of the nanograting layer .Depletion region width is quite strongly dependant on the temperature. The ridge effective height aeff(T ) = a − d(T ) and therefore the geometry factor of nanograting layer becomes temperature-dependent, G = G(T ).

7. 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.

8. Electric resonance circuit We consider the electric resonance circuit by Kron’s model. Each link of the two-dimensional network is given by 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 capacitor C with the impedance Zc= 1/ iωC

9. Square resonator model 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. NI MultisimCirquits Design Suite

10. 4x4 elementary cell in subcirquits R=0.01om L=100nH C=1nF

11. Simulation results in square geometry F=3.5MHz F=2.2 MHz

12. Nanograting layer simulation

13. Simulation results in nanograting layer F=2.5MHz F=3.7MHz

15. Obtained resonance frequences First and second resonances

16. Conclusion • 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