„ZnO nanodots and nanowires“
Jarji Khmaladze – Ivane Javakhishvili Tbilisi State University,
Faculty of Exact and Natural Sciences
Tbilisi -2012
nanostructures – structures having at least one dimension between
1 and 100 nm – have received steadily growing interests as a result
of their peculiar and fascinating properties, and applications
superior to bulk samples.
quantum confinement of electrons by the potential wells of nanometersized structures may provide one of the most powerful means to control
the electrical, optical, magnetic and thermoelectric properties of a solid
state functional material
Advantages of nanostructures are connected to size
effect - dependence of properties on structure
size.
Because of new controlling parameters (size and
shape), a number of desired properties of materials,
which could not be achieved in bulk samples, are
expected to be realized in nanostructures.
What does Nanostructure actually represent?
semiconductor
Nanostructure
represents
nano
size
semiconductor material of smaller band-gap embedded in
material with higher band- gap.
In this case quantum confinement in material with smaller gap
takes place – electrons are localized in nano size region.
Three main type of nanostructures:

Quantum wells-2D structures– 1D
confinement

Quntum wires -1D structures – 2D
confinement

Quantum dots – 0D structures – 3D
confinement
The simplest quantum mechanical model for
confined electron – electron in potential
well with infinite barrier
Potential is constant within the well and infinite outside the well
 0, fo r .....0  z  d
V (z)  
  , .....o th er w is e
This results in plane-wave solutions for the motion of the electron in the
x-and y-directions,
ik x x ik y y
 (r )  e e  ( z )
where  ( z ) obeys the one-dimentional schrodinger equation for a
particle in an infinite square well
 p2

 V ( z )   ( z )  E ( z )

 2m *

As is well known the general solution of this equation must be a linear
combination of sines an cosines chosen to satisfy the boundary
conditions imposed by the well.Since wave function must vanish at
z=0,the solutions must be of the form sin(kz) and since it must also
vanish at z=d,we must choose k to be
n
k 
d
For any positive integer (n=1,2,….).This restriction results in the
quantization of the energy.The energies associated with the motion
of the electron along the z-direction are :
h  n
2
2m * d
2
2
En 
2
The total energy of the electron is the sum of this quantized energy and
the kinetic energy due to its (x,y)-motion
EEn
h
2
2m *
(k x  k y )
2
2
Excitons



An exciton is a bound state of an electron and hole which are
attracted to each other by the electrostatic Coulomb force. It is
an electrically neutral quasiparticle that exists in insulators,
semiconductors and in some liquids
An exciton can be formed when a photon is absorbed by a
semiconductor. This excites an electron from the valence band
into the conduction band. In turn, this leaves behind a localized
positively-charged hole The electron in the conduction band is
then attracted to this localized hole by the Coulomb force
In low dimensional nanostructures exciton binding energy
dramatically increases
CONFINEMENT REGIMES

In nanoscale materials of appropriate symmetry the confinement of individual
electrons and holes dominates at small enough sizes.it is therefore in this regime
where the optical and electrical properties of materials become size-and shapedependent and where some of the most fascinating aspects of nano begin
There are three confinements regimes that exist:
Strong confinement a  a , a

Intermediate


e
h
Weak
In all cases a is the critical dimension of the nanostructure ( a e , a h
Bohr radius)

In nanostructures >>>


e
h
ah  a  ae
aa a
- carrier’s
a  ae , ah
optical and electrical properties are therefore dominated by confinement effects
Research subject and objectives



Why nanowires?
Nanowires are one-dimensional (1D) objects with space
confinement in two dimensions. They are distinguished by higher
(with respect to quantum dots) photoluminescence efficiency,
strongly linear polarized emission, significantly faster carrier
relaxation (3).
In the framework of the project it is planned to calculate band
structure and energy levels in freestanding and core-shell ZnO
nanowires of different size. Excitonic effects are going to be
studied taking into account enhancement of Coulomb
interaction by the penetration of an electric filed of carriers into
a surrounding medium (dielectric confinement).
Research plan



Calculation of electronic structure of ZnO
freestanding nanowires of different sizes without
accounting excitonic effects.
Calculation of electronic structure of ZnO coreshell nanowires of different sizes, different depth
and shape of confinement potential without
accounting excitonic effects
Investigation of excitonic effects in ZnO
Nanowires of both type.
Research methods





Single particle states of electrons and holes will be calculated in the
frame of multi-band k p theory, which is one of the powerful tool for
calculation of band states as bulk as nano crystals .
As ZnO is wide gap semiconductor, mixing only between valance
band states are going to be taken into account.
Core –shell nanowires will be modeled by using confinement
potential of different depth and shape (parabolic type).
Electron- hole Coulomb interaction will be studied in the frame of
configuration
interaction method
Compliance of research methods
with the objectives of the
project

In the framework of the project i plan to obtain complete picture of
electronic structure of freestanding and core-shall nanowires.
Calculation of electronic structure is a hot topic, as it creates a
background for prediction of optical and electrical behavior of
material, excitonic effects will also be studied in details. Space and
dielectric confinement makes excitonic effects especially important
in investigation of optical spectra of low dimensional systems
Thanks a lot!
Connecting the de Broglie wavelength to the Bohr Radius
According to de Broglie,the wavelength
associated with each object is :
 
h
p
 34
Where h=6.62x
js is Planck’s
constant,p=mv is the objects
momentum,and m –is its associated
mass
10
Centripetal force of an electron circling an infinitely heavy
positively charged,nucleus with their mutual Coulomb force:
mv
r

2

q
2
4  0 r
2
Relationship between the wavelength of the particle and
its associated Bohr radius
n   2 r

n- is an integer(an integer number of electron
wavelenght must fit into the circumference of a classic
Bohr orbit if it is to be allowed.
Solving for the radius r, gives a generic Bohr radius:
4   0 n h
2
r 
where

mq
2
2
is the dielectric constant of the material
let us connect the de Broglie wavelength to the Bohr radius just found
ve 
An associated velocity :
h
q

2
me ae
4 0 h
Associated electron de Broglie Wavelength :
e 
finally :
h
p
h

m e ve

2  0 h
meq
2
2
 e  2 a e
illustrating that electron’s de Broglie wavelength and its Bohr radius are
essentially the same thing