INTRODUCTION TO QUANTUM THEORY OF SOLIDS

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INTRODUCTION TO QUANTUM THEORY OF SOLIDS

• By
• Sushama Baag

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CHAPTER OBJECTIVE
LECTURE-1

• This chapter provides the basic concepts and
  terminology for understanding
• semiconductors.
• Importance is given to the concepts of energy
  band ,
• 2 kinds of electrical charge carriers called
  electrons and holes
• and how the carrier can be controlled with
  addition of dopants.
• Another important fact is the Fermi distribution
  function and
• concept of Fermi level.
• The electron and hole concentration are closely
  linked to Fermi level.
• Mastery of the terms , concepts and models
  presented here will prepare
• you for understanding not only the many
  semiconductor devices that
• are in existence today but also many more that
  will be invented in the future.

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Before the How , Ask Yourself Why

• Before we dive in, well take a moment to explain
  exactly why were so interested in, and dependent
  on semiconductors in the first place.
• Semiconductors are so important to our electronic
  devices simply bcoz their properties can be
  easily and substantially manipiulated.

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FORMATION OF ENERGY BANDS

• Electrons in individual atoms can exist only at
  exact specified energy levels.
• But the Pauli Exclusion Principle says that two
  electrons cannot exist in the same space at the
  same time.
• So when we bring together billions of atoms, the
  electrons move their orbits ever-so-slightly, so
  that each one is different.
• When we combine all these orbits, each different
  by a miniscule amount, the result is the
  formation of a band of energy levels, in which
  an electron can exist virtually anywhere

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Characteristics of Energy Bands

• Energy bands become wider as the distances
  between atoms become shorter.
• The higher the energy level, the wider is the
  corresponding energy band that it splits into.

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Energy Band In Silicon

• The actual band splitting in a crystal is much
  more complicated than shown in the figures above.
• Let us consider an isolated Si atom(At. No.14).
• 1s2 2s2 2p6 3s2 3p2

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Energy Bands at different Principal Quantum
Numbers