Basic to Solid State Physics

Course guarantor:

Ladislav Kalvoda, Eva Mihóková

Lecturer:

Ladislav Kalvoda, Eva Mihóková

Tutor:

Ladislav Kalvoda, Eva Mihóková

Supervisor:

Department of Solid State Engineering

Synopsis:

Description of fundamental properties of solids following the regular long distance ordering of atoms in a crystal lattice.

Based on the introduced bonding interaction between atoms in solids, various types of crystals and their properties are

defined. The model of crystalline lattice dynamics in harmonic approximation is described and basic thermal properties

of crystals are derived. The periodic potential of the crystal lattice is introduced and its relation to the following model

describing the energetic state of electrons in solids by means of electron energy bands explained. The special

consequences of band approach to the physical properties of solids are elucidated. The aim of the course is to

systematically introduce and interpret a broad phenomenological basis of physical properties of crystalline solids

Requirements:

Syllabus of lectures:

1. Classification of solids: description and explanation of physical nature of bonding forces between atoms in solids.

Introduction and description of other basic terms: crystal lattice, elementary cell, primitive cell, basis of the ele-

mentary cell, reciprocal lattice, Brillouin zones.

2. Description and explanation of the nature of the main types of bonds: ionic, covalent, metallic, hydrogen, van-der

Waals.

3. Vibrations of atomic lattice and their description in harmonic approximation. Explanation of basic vibration modes

observed on 1D model of linear crystal lattice formed by identical atoms.

4. Other properties of lattice dynamics in harmonic approximation. New phenomena that appear when the linear crystal

lattice contains a primitive base consisting of two different atoms. Acoustic and optical modes of waves.

5. From normal modes to phonons. Explanation of the principle of quantization of lattice vibrations.

6. Macroscopic thermal properties of solids and their microscopic nature. Specific heat of crystalline lattice: Planck

distribution law, introduction and significance of state density function (Debye model, Einstein model).

7. Beyond harmonic approximation - anharmonic interaction in crystal: theoretical description of thermal expansion

and thermal conductivity, thermal resistance of phonon gas, what are „umklapp“ processes and their importance

8. Electron properties of metals: introduction and interpretation of Fermi gas model of free electrons, Drude model,

infinite potential well, Fermi-Dirack statistics, Fermi energy, Sommerfeld model, behavior. of 3D free electron gas.

9. Specific heat of electron gas. Electrical conductivity and Ohm's law. Movement of electrons in electric and magnetic

fields. Thermal conductivity of metals.

10. Electron band structure of solids. Schrödinger equation with periodic potential, Bloch theorem. Kronig-Penny mo-

del, strong and weak potential.

11. Wave equation of electron in periodic potential. Solution of the central equation in 1D. Kronig-Penny model in

reciprocal space. Approximation of empty grid.

12. Semiconductors. Forbidden gap of energies. Direct and indirect semiconductors. Equations of motion of electrons

in the energy band. Holes. Effective mass of electrons and holes in semiconductors. Impurity conductivity: the role

of donors and acceptors, major and minor charge carriers

13. PN junction, electrical properties, curvature of energy bands, charge transport, U / I characteristic

Syllabus of tutorials:

Study Objective:

Study materials:

Key references:

[1] Ch. Kittel : Introduction to Solid State Physics, 8th ed., J. Wiley, New York 2012.

[2] A. Aharony, O. Entin-Wohlman: Introduction to Solid state Physics, World Scientific 2018.

Recommended references:

[3] M. P. Marder: Condensed Matter Physics, J.Wiley, New York 2000.

Note:

Time-table for winter semester 2024/2025:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue	roomTR:204 Mihóková E. 10:00–11:50 (lecture parallel1) Trojanova 13
Wed
Thu
Fri

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans:

• Fyzikální inženýrství - Počítačová fyzika (PS)
• Fyzikální inženýrství - Fyzikální inženýrství materiálů (PS)
• Fyzikální inženýrství - Fyzika plazmatu a termojaderné fúze (PS)
• Fyzikální inženýrství - Inženýrství pevných látek (PS)
• Fyzikální inženýrství - Laserová technika a fotonika (PS)
• Kvantové technologie (elective course)
• Vyřazování jaderných zařízení z provozu (elective course)
• Physical Engineering - Computational physics (PS)
• Quantum Technologies (elective course)
• Physical Engineering - Physical Engineering od Materials (PS)
• Physical Engineering - Plasma Physics and Thermonuclear Fusion (PS)