Unit 8
Modern Physics
Class 11 Physics
Chapter 25
Solids
Class 11 Physics – Solids Notes PDF
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Chapter Overview
The electrical behavior of a solid depends strongly on the allowed energies of its electrons. In an isolated atom, electrons occupy separate energy levels. When an enormous number of atoms come together to form a solid, these levels split into many very closely spaced levels called energy bands.
Band theory explains why some solids conduct electricity easily, why some behave as insulators, and why semiconductors have conductivity between the two. It also explains the difference between a pure semiconductor and a doped semiconductor.
Core Idea
Electrical conduction depends on the occupancy of the valence band, conduction band, and the size of the forbidden energy gap.
Chapter Scope
Energy bands, metals, insulators, semiconductors, intrinsic semiconductors, extrinsic semiconductors, and formation of n-type and p-type materials.
25.1 Energy Bands in Solids
Energy Level
In an isolated atom, electrons can possess only certain permitted energies. These discrete permitted energies are called energy levels.
Formation of Energy Bands
When many atoms are brought close together to form a solid, the outer electron clouds interact. Because each electron in the combined system must occupy an allowed quantum state, each atomic energy level splits into a huge number of closely spaced levels. These groups of closely spaced allowed levels form energy bands.
Diagram 1 — From Atomic Energy Levels to Energy Bands
A large number of closely spaced energy levels form a band in a solid.
Valence Band
The highest energy band containing valence electrons is called the valence band. Electrons in this band are generally associated with atomic bonding.
Conduction Band
The allowed energy band above the valence band is called the conduction band. Electrons in this band can move through the solid and contribute to electrical conduction.
Forbidden Energy Gap
The region between the valence band and conduction band in which no allowed electron energy state exists is called the forbidden energy gap or band gap.
Diagram 2 — Valence Band, Forbidden Gap and Conduction Band
The size and occupancy of these bands determine whether a material behaves as a conductor, semiconductor, or insulator.
25.2 Metals, Insulators and Semiconductors Using Band Theory
Metals / Conductors
In a conductor, the highest occupied band is partially filled, or the valence and conduction bands overlap. Therefore many electrons can respond to an applied electric field without needing to cross a significant forbidden gap.
Diagram 3 — Energy Bands in a Metal
Conductors have available nearby energy states, so electrons can move readily under an electric field.
Insulators
In an insulator, the valence band is full and the conduction band is empty, with a comparatively large forbidden energy gap between them. Ordinary thermal energy is usually insufficient to lift many electrons into the conduction band.
Diagram 4 — Energy Bands in an Insulator
A large forbidden gap makes electrical conduction very difficult.
Semiconductors
In a semiconductor, the valence band is normally almost full and the conduction band almost empty at low temperature, but the forbidden gap is small enough that thermal energy can promote some electrons to the conduction band.
Common elemental semiconductor examples are silicon (Si) and germanium (Ge).
Diagram 5 — Energy Bands in a Semiconductor
Because the gap is small, some electrons can be thermally excited into the conduction band.
| Property | Metal / Conductor | Semiconductor | Insulator |
|---|---|---|---|
| Band arrangement | Partially filled band or overlapping bands | Valence and conduction bands separated by a small gap | Valence and conduction bands separated by a large gap |
| Forbidden gap | Approximately zero / overlap | Small | Large |
| Charge carriers available | Many mobile electrons | Limited electrons and holes; strongly affected by temperature and doping | Very few under ordinary conditions |
| Conductivity | High | Intermediate | Very low |
| Examples | Copper, aluminium, silver | Silicon, germanium | Glass, mica, many ceramics |
25.3 Intrinsic and Extrinsic Semiconductors
Intrinsic Semiconductor
A chemically pure semiconductor is called an intrinsic semiconductor. Pure silicon and pure germanium are common examples.
At very low temperature, very few electrons are available in the conduction band. As temperature rises, thermal energy can break some covalent bonds. An electron becomes free to enter the conduction band, leaving behind a vacant state called a hole.
Diagram 6 — Electron–Hole Pair in an Intrinsic Semiconductor
In an intrinsic semiconductor, a thermally excited electron and the hole it leaves behind act as charge carriers.
- Electron concentration equals hole concentration in an intrinsic semiconductor.
- Both electrons and holes contribute to current.
- Its conductivity increases strongly with temperature because more electron–hole pairs are generated.
Extrinsic Semiconductor
A semiconductor whose electrical conductivity is deliberately increased by adding a very small controlled amount of impurity is called an extrinsic semiconductor. The process is known as doping.
Extrinsic semiconductors are of two main types: n-type and p-type.
N-Type Semiconductor
An n-type semiconductor is formed by doping silicon or germanium with a pentavalent impurity such as phosphorus, arsenic, or antimony.
Four of the impurity atom’s valence electrons form covalent bonds with neighboring silicon atoms. The fifth electron is only weakly bound and can become a free conduction electron.
- Majority carriers: electrons
- Minority carriers: holes
- Pentavalent impurity atoms are called donor impurities.
Diagram 7 — Formation of an N-Type Semiconductor
A pentavalent donor provides an additional electron that can participate in conduction.
P-Type Semiconductor
A p-type semiconductor is formed by doping silicon or germanium with a trivalent impurity such as boron, aluminium, gallium, or indium.
A trivalent impurity has only three valence electrons available for bonding, so one covalent bond lacks an electron. This vacant bond behaves as a hole.
- Majority carriers: holes
- Minority carriers: electrons
- Trivalent impurities are called acceptor impurities.
Diagram 8 — Formation of a P-Type Semiconductor
A trivalent acceptor creates a missing bond electron, represented as a mobile hole.
| Property | Intrinsic | N-Type | P-Type |
|---|---|---|---|
| Purity | Pure semiconductor | Doped semiconductor | Doped semiconductor |
| Typical dopant | None | P, As, Sb | B, Al, Ga, In |
| Dopant valency | — | Pentavalent | Trivalent |
| Impurity role | — | Donor | Acceptor |
| Majority carrier | Electrons and holes in equal numbers | Electrons | Holes |
| Minority carrier | Not described by majority/minority distinction | Holes | Electrons |
| Conductivity | Lower than appropriately doped material | Higher than intrinsic material | Higher than intrinsic material |
Key Terms
| Term | Meaning |
|---|---|
| Energy level | A discrete permitted energy of an electron in an isolated atom. |
| Energy band | A large group of extremely closely spaced allowed electron energies in a solid. |
| Valence band | The highest band containing valence electrons. |
| Conduction band | A band in which electrons can move through the solid and contribute to conduction. |
| Forbidden energy gap | The energy region between allowed bands in which no electron states are permitted. |
| Intrinsic semiconductor | A pure semiconductor. |
| Hole | A vacancy created when an electron leaves a valence-bond state; it behaves as a positive charge carrier. |
| Doping | Controlled addition of a small impurity concentration to modify semiconductor conductivity. |
| Donor impurity | A pentavalent dopant that supplies an extra conduction electron. |
| Acceptor impurity | A trivalent dopant that creates a hole by accepting an electron into an incomplete bond. |
Important Exam Questions
Short-Answer Questions
- What is an energy level?
- What is an energy band?
- Define valence band, conduction band, and forbidden energy gap.
- Why is a metal a good conductor according to band theory?
- Why is an insulator a poor conductor according to band theory?
- What is a semiconductor? Give two examples.
- Define intrinsic semiconductor.
- What is meant by a hole in a semiconductor?
- What is doping?
- What is a donor impurity? Give examples.
- What is an acceptor impurity? Give examples.
- State the majority and minority carriers in n-type and p-type semiconductors.
- Why does the conductivity of an intrinsic semiconductor increase with temperature?
- Why is an n-type semiconductor electrically neutral despite having excess conduction electrons?
Long-Answer Questions
- Explain qualitatively how discrete atomic energy levels form energy bands when atoms combine to form a solid.
- Explain valence band, conduction band, and forbidden energy gap with a labelled diagram.
- Differentiate metals, semiconductors, and insulators on the basis of band theory with suitable diagrams.
- Explain the formation and conduction mechanism of an intrinsic semiconductor.
- Explain how an n-type semiconductor is formed. State its majority and minority carriers.
- Explain how a p-type semiconductor is formed. State its majority and minority carriers.
- Differentiate intrinsic, n-type, and p-type semiconductors.
Conceptual Questions
- Why can a semiconductor conduct more easily than an insulator although both may have a filled valence band at low temperature?
- Why does adding a very small amount of impurity greatly change semiconductor conductivity?
- Can a hole exist as an ordinary free positive particle inside the crystal? Explain its physical meaning.
- A silicon sample is doped with phosphorus. Identify its type and majority carrier.
- A germanium sample is doped with boron. Identify its type and majority carrier.
- Why do electrons and holes occur in equal numbers in a pure intrinsic semiconductor?
Diagram Questions
- Draw the formation of energy bands from discrete atomic energy levels.
- Draw and label valence band, forbidden gap, and conduction band.
- Draw separate energy-band diagrams for conductor, semiconductor, and insulator.
- Draw an intrinsic semiconductor showing an electron–hole pair.
- Draw an n-type semiconductor lattice showing a pentavalent donor and extra electron.
- Draw a p-type semiconductor lattice showing a trivalent acceptor and hole.
One-Minute Revision
- Isolated atoms have discrete energy levels; solids have closely spaced energy bands.
- The valence band contains valence electrons.
- The conduction band contains mobile conduction electrons.
- The forbidden energy gap contains no allowed electron states.
- Metals have a partially filled band or overlapping valence and conduction bands.
- Insulators have a comparatively large forbidden energy gap.
- Semiconductors have a small energy gap and intermediate conductivity.
- Silicon and germanium are common elemental semiconductors.
- An intrinsic semiconductor is chemically pure.
- Thermal excitation in an intrinsic semiconductor creates electron–hole pairs.
- Doping produces an extrinsic semiconductor.
- Pentavalent donor doping produces n-type semiconductor.
- Electrons are majority carriers in n-type material.
- Trivalent acceptor doping produces p-type semiconductor.
- Holes are majority carriers in p-type material.
Diagram Practice
- Draw three isolated atomic energy levels and show how each becomes a band in a solid.
- Redraw the basic valence-band / band-gap / conduction-band diagram from memory.
- Draw side-by-side band diagrams of a conductor, semiconductor, and insulator.
- Draw an intrinsic silicon lattice and mark one thermally generated electron–hole pair.
- Draw an n-type lattice using phosphorus as donor impurity and label the extra electron.
- Draw a p-type lattice using boron as acceptor impurity and label the hole.
Syllabus Coverage Checklist
| NEB/CDC Chapter 25 scope | Covered |
|---|---|
| 25.1 Energy bands in solids — qualitative ideas | Yes |
| Distinguish energy level and energy band; formation of energy bands | Yes |
| 25.2 Metals, insulators and semiconductors using band theory | Yes |
| 25.3 Intrinsic and extrinsic semiconductors | Yes |
| Formation of n-type semiconductor | Yes |
| Formation of p-type semiconductor | Yes |
| Related conceptual questions | Yes |
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