ABSTRACT

This research work as aimed at calculating the resonant tunnelling energy of a quantum dot array which is the energy needed by a particle to tunnel through multiple barrier. A Hamiltonian of the form;

H

Was use to act on some states with different spin orientations to obtain four by four matrices. The Eigen value which was obtained can further be use to calculated the conductance in transition of the particle.

TABLE OF CONTENTS

Cover Page: ----------------------------------------------------------------------------------------------------i

The Fly Leaf---------------------------------------------------------------------------------------------------ii

Title Page------------------------------------------------------------------------------------------------------iii

Declaration----------------------------------------------------------------------------------------------------iv

Certification --------------------------------------------------------------------------------------------------v

Dedication: ---------------------------------------------------------------------------------------------------vi

Acknowledgement: ----------------------------------------------------------------------- -----------------vii

Table of contents:-------------------------------------------------------------------------------------------viii

Abstracts:------------------------------------------------------------------------------------------------------x

CHAPTER ONE:

1.1              1. Introduction ----------------------------------------------------------------------------------------1

1.2              1.2   history--------------------------------------------------------------------------------------------2

1.3              1.3   introduction to the concept of tunneling through quantum dot arrays------------------3

1.4              1.4   The Tunneling problem------------------------------------------------------------------------4

1.5              1.5   Applications of the concept of quantum tunneling----------------------------------------5

1.6              1.6   quantum dot-------------------------------------------------------------------------------------6

1.7              1.7   Quantum Confinement in Semiconductors-------------------------------------------------7

1.8              1.8   Production of Quantum Dots-----------------------------------------------------------------8

1.9              1.9  Optical properties of quantum dots ---------------------------------------------------------11

1.10          1.10 Application of quantum dots----------------------------------------------------------------12

CHAPTER TWO

2.1 resonant tunneling through quantum dot array process--------------------------------------------16

2.2 Incident electron of energy E Transmitted electron ------------------------------------------------17

CHAPTER THREE

3.0   application of hamiltonian on resonant tunneling quantum dot arrays-------------------------21

3.1   Hamiltonian to act 1-----------------------------------------------------------------------------------25

3.2   Hamiltonian to act 2-----------------------------------------------------------------------------------26

3.3   Hamiltonian to act 3-----------------------------------------------------------------------------------27

3.4   Hamiltonian to act 4-----------------------------------------------------------------------------------27

3.5   Hamiltonian to act 5-----------------------------------------------------------------------------------28

3.6 Hamiltonian to act 6-------------------------------------------------------------------------------------29

3.7 Hamiltonian to act 7-------------------------------------------------------------------------------------29

3.8 Hamiltonian to act 8 ------------------------------------------------------------------------------------30

3.9 Eigen value and Eigen vector-------------------------------------------------------------------------31 

CHAPTER FOUR

4.0   discussion of result---------- --------------------------------------------------------------------------36

CHAPTER FIVE

5.0 Recommendations---------------------------------------------------------------------------------------37

5.1 Conclusion-----------------------------------------------------------------------------------------------37             

5.2    References----------------------------------------------------------------------------------------------35