DESIGNING AN EQUISPACED LEVEL QUANTUM WELL IN THE ULTRA TIN LAYER OF A SEMI CONDUCTOR ALLOY

ABSTRACT

A derivation of equispaced-level conduction band Hamiltonians using the coordinate-transform based procedure is presented. The procedure start with the effective-mass schrodinger equation (Luttinger and Kohn, 1995), where the local conduction-band edge is interpreted as the potential experienced by and electron in a quantum well (QW). The electron effective mass variation is proportional to the potential variation within the a QW, and the well has equispaced bound state.

In semiconductor alloy quantum wells, designs that are equispaced are difficult to come by. Milanovic and Ikonic (1996), realized the design of eqispaced level in the Ga As/ Al_x Ga_1-x  As QW system using the coordinate-transform based procedure. In this research work, an attempt has been made to extend this procedure to other semiconductor ternary alloy (A_X B_1-X C) which to the best of my knowledge, has not been done before hence this study fills a gap and is worth the effort of adding to the varieties of QW designs in existence.

Two Hamiltonians are derived, one with a confining potential that may be realizing by appropriate grading of the alloy and the other with a non-confining potential were the electron effective-mass tends to zero as Z tends to infinity  of Hamiltonian is not realizable, the aims are design an equispaced level QW in the conduction band of an ultra thin layer of a semiconductor alloy by solving the effective mass Schrodinger equation with a one dimensional harmonic oscillator (IDHO) potential, and to calculate the grading funding necessary to realized level.

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  Introduction ----------------------------------------------------------------------------------------------1

1.1                Semiconductor material for optoelectronics (quantum electrons)----------------------------4

1.2            quantum structures----------------------------------------------------------------------------------5

1.3           quantum well (qw) 2-d system ---------------------------------------------------------------------6

1.4            sub band and wave function a quantum well --------------------------------------------------11

1.5           other quantum structures --------------------------------------------------------------------------15

1.6            QWR 1-d system ----------------------------------------------------------------------------------17 QD o-d system -----------------------------------------------------------------------------------------------20

CHAPTER TWO

2.1 eqispaced conduction band model--------------------------------------------------------------------23

2.2 wave function -------------------------------------------------------------------------------------------37

2.3 conduction band offset----------------------------------------------------------------------------------40

CHAPTER THREE

3.0   presentation of results---------------------------------------------------------------------------------41

CHAPTER FOUR

4.0   discussion of result---------- --------------------------------------------------------------------------51

CHAPTER FIVE

5.0 Conclusion-----------------------------------------------------------------------------------------------53             

5.1 Recommendation ---------------------------------------------------------------------------------------56  

 5.2 References-----------------------------------------------------------------------------------------------58