Transcript Study of nanostructured layers using electromagnetic analog circuits

Master: Sergei Petrosian
Supervisor: Professor Avto Tavkhelidze
 Introduction
 Thermoelectric
properties of nanograting layers
 Electrical circuits as analogs to Quantum Mechanical
Billiards
 Computer simulation of nanograting layer
 Conclusion
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
Nanograting layer
Substrate
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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
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Z is given by Z = σ S2/(Ke + Kl), where
 S - is the Seebeck coefficient
 σ - is electrical conductivity
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Ke - is the electron gas thermal conductivity
 Kl - is the lattice thermal conductivity
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The aim of this study is to present a solution which would allow large
κ
κ
enhancement of S without changes in σ, e and 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 aeff(T ) = a − d(T ) and therefore the
geometry factor of nanograting layer becomes temperature-dependent,
G = G(T ).
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 twodimensional 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
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 Multisim Cirquits Design Suite
R=0.01om
L=100nH
C=1nF
F=2.2 MHz
F=3.5MHz
F=2.5MHz
F=3.7MHz
Square geometry
Nanograting layer
2.2 MHz
2.5 MHz
3.5 MHz
3.7MHz
First and second resonances
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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