„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 nanometer-sized 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

This results in plane-wave solutions for the motion of the electron in the x-and y-directions,

where obeys the one-dimentional schrodinger equation for a particle in an infinite square well

0, .....0( )

,.....

for z dV z

otherwise

( ) ( )yxik yik xr e e z

2

( ) ( ) ( )2 *

pV z z E z

m

( )z

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

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 :

The total energy of the electron is the sum of this quantized energy and the kinetic energy due to its (x,y)-motion

nk

d

2 2 2

22 *n

h nE

m d

22 2( )

2 *n x y

hE E k k

m

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 shape-dependent and where some of the most fascinating aspects of nano begin

There are three confinements regimes that exist: Strong confinement

Intermediate

Weak In all cases a is the critical dimension of the nanostructure ( - carrier’s

Bohr radius)

In nanostructures >>>

optical and electrical properties are therefore dominated by confinement effects

e ha a a

h ea a a

,e ha a a

,e ha a

,e ha a a

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 core-shell 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 kp 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 :

Where h=6.62x js is Planck’s constant,p=mv is the objects momentum,and m –is its associated mass

h

p

3410

Centripetal force of an electron circling an infinitely heavy positively charged,nucleus with their mutual Coulomb force:

Relationship between the wavelength of the particle and its associated Bohr radius

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.

2 2

204

mv q

r r

2n r

Solving for the radius r, gives a generic Bohr radius:

where is the dielectric constant of the material

let us connect the de Broglie wavelength to the Bohr radius just found

An associated velocity :

Associated electron de Broglie Wavelength :

finally :

illustrating that electron’s de Broglie wavelength and its Bohr radius are essentially the same thing

2 202

4 n hr

mq

2

04ee e

h qv

m a h

202

2e

e e e

hh h

p m v m q

2e ea