1. Master: Sergei Petrosian Supervisor: Professor Avto Tavkhelidze

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

3. 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 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

4. Nanograting layer Substrate  The density of states in nanograting layer minimizes G times  ρ(E) = ρ 0 (E)/G, where ρ 0 (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 S 2 /(K e + K l ), where  S - is the Seebeck coefficient  σ - is electrical conductivity  K e - is the electron gas thermal conductivity  K l - is the lattice thermal conductivity

6. The aim of this study is to present a solution which would allow large enhancement of S without changes in σ, κ e and κ l. 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 a eff (T ) = a − d(T ) and therefore the geometry factor of nanograting layer becomes temperature-dependent, G = G(T ).

7. 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 Z L = 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 Z c = 1/ iωC

9. 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.

10. R=0.01om L=100nH C=1nF

11. F=2.2 MHz F=3.5MHz

13. F=2.5MHz F=3.7MHz

15. Square geometryNanograting layer 2.2 MHz2.5 MHz 3.5 MHz3.7MHz First and second resonances

16.  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