Physics Project Report on Energy Bands in Solids

CERTIFICATE

This is to certify that the project report entitled "To Study Energy Bands in Solids" submitted by student is original and has been completed by him under my supervision.

As a student of Class XII. I did this project as a part of my studies entitled "To Study Energy Bands in Solids".

I owe a deep sense of gratitude to my Physics teacher, whose valuable advice, guidance and lovingly nurturing this project from conception to completion.

I wish to thanks Principal of our School for extending his generous patronage and constant encouragement.

Finally, I would like to thanks my respected parents for helping me economically and my friends for giving me helping hand at every step of this project.

Signature of Student

INTRODUCTION

If large number of atoms brought close to one another they begin to influence each other which cause modification in energy levels of electrons in the outer shells. To understand this let us consider single silicon crystal having n atoms. Process of splitting of levels in understood by considering the following situations.

(ii) When the inter-atomic specify r is less than d but greater than C, there is no splitting of energy levels.

(iii) When the spacing r=c, the interaction becomes appreciable, so, splitting of levels commences, but no change is energy levels of electrons.

(iv) When inter-atomic spacing r lies between b and c, energy corresponding to 3s and 2p of each atoms gets slightly changed. This reduce the energy gap. Since n number is large and energy is of few ev, the levels due to spreading of the energy are closely spaced. This collection of closely spaced levels is called energy band.

Energy band consists of three part-

i) Valence band :- In valence band there are valence electrons. This band may be partially or completely with electrons. In this band electrons are not capable of gaining energy from external electric field. Therefore electrons in this band do not contribute to the electric current.

ii) Conduction band :- In this band the electrons are rarely present. This band is either empty or partially filled with electrons. In this band the electrons can gain energy from external electric field. Thus electrons in this band contribute to the electric current.

iii) Forbidden band :- Electrons are not found in this band. This band is completely empty. Valence band and conduction band are separated by forbidden band.

There are two possible band diagrams for metals.

a) The conduction band is only partially filled with electrons. Since the lower energy levels are already filled first, to permit conduction, the electron must be raised to a position of higher energy. Since there are vacant levels in the energy band immediately above the levels, an electron can be raised to empty region with small addition of enery and thus conduction can take place. Therefore partially energy band represents a conduction band.

b) In this case, there is overlapping of valence and conduction bands, because the lowest levels in the conduction band need less energy than highest levels in the valence band. This tends the electrons in one band to overflow, as it were, into another band; and electrons in the valence bands are free to move about inside the crystal lattice and with an applied filed, contribute to electrical conduction.

The highest energy level in the conduction band occupied by electrons in a crystal, at absolute zero of temp. is called fermi level; and energy corresponding to this known as fermi energy. Under an applied field, the electrons get enough to go beyond fermi-energy and thus permit electrical conduction to take place.

Energy Band in Semiconductors

Here the two energy bands are distinctly separate with no overlapping. The forbidden gap is nearly 1ev. At aboslute zero of temp. no electron has energy to jump the forbidden band to reach the conduction band. Therefore substance is an insulator.

At room temperature, some valence electrons acquire thermal energy greater than the energy gap to reach conduction band. Thus, the crystal becomes a conductor. This is the specify property of crystal known as semiconductors. Higher the temp. greater are the chances of electrons to jump to conduction band and greatest is the conductivity. As on electron leaves the valence band, it leaves some energy level in band unfilled known as holes.

Energy Band in Insulators

In this case, there is a large energy gap(eg) approximately ~5ev depending upon the nature of the crystal. Electrons, however heated, find it practically impossible to jump this gap and thus never reach the conduction band. Thus, electrical conduction is not possible through an insulator.