PHY2024 
Condensed Matter I 
201213 

Dr V.V. Kruglyak 


Delivery Weeks: 
T2:0111 

Level: 
5 (NQF) 

Credits: 
15 NICATS / 7.5 ECTS 

Enrolment: 
87 students (approx) 

Description
This module will explain how electrons, and other waves, propagate within crystalline materials and
affect their properties. The properties of periodic structures are discussed, particularly the
relationship between real space and reciprocal space and the representation of elastic and inelastic
scattering in both spaces. Both phonons and electrons are profoundly influenced by the crystal
structure in which they propagate. The last section of this module considers the transport of
electrons in the freeelectron and nearlyfreeelectron approximations, which give a good
description of the behaviour of electrons in metals and semiconductors. The vibrational excitations
of the crystal lattice (phonons) are of particular importance to the properties of insulators.
Module Aims
Condensed matter physics, particularly in the solidstate, underpins modern technology and is also
important because it provides the physical realisation of much fundamental physics. This module aims
to give the student a firm grounding in the traditional areas of the subject but also to introduce
some of the latest developments in one and twodimensional systems that are being studied in the
research groups at Exeter.
Intended Learning Outcomes (ILOs)
A student who has passed this module should be able to:

Module Specific Skills and Knowledge:
 explain how elastic scattering by a crystal is treated using the concept of the reciprocal
lattice and how calculations separate factors which depend on the lattice and on the basis
and solve problems relating to representative solid state materials;
 describe the features of the vibrations of monatomic and of diatomic linear chains and
explain the significance of dispersion curves in three dimensions;
 discuss the scattering of phonons, and in particular the occurrence of Umklapp scattering of
phonons near the Brillouin zone edge;
 describe the free electron model and apply it in calculations;
 use the nearly free electron model to account for the occurrence of
energy gaps at the Brillouin zone edges, and the consequent
behaviour of the group velocity and effective mass of the electrons;
 explain qualitatively band theory and the concepts of Brillouin zone, density
of states, Fermi energy, effective mass and holes;
 state Bloch's theorem, and sketch Ek diagrams;
 describe acceptors, donors and the basic optical transitions in semiconductors;
 distinguish between extrinsic and intrinsic properties of semiconductors;
 define drift, diffusion and thermal conduction and the relations between them for metals,
semiconductors and degenerate semiconductors;
 explain how to construct a Fermi surface;

Discipline Specific Skills and Knowledge:
 apply thermodynamics, electromagnetism and quantum mechanics to the soldstate;
 use mathematical abstraction to represent and solve problems involving
periodic structures;

Personal and Key Transferable / Employment Skills and Knowledge:
 solve problems requiring spatial reasoning;
 use a range of resources to develop an understanding of topics through independent study;
 meet deadlines for completion of work for problems classes and develop appropriate
timemanagement strategies.
Syllabus Plan

Introduction
Brief historical survey.

Bragg scattering
 Crystal Sructures (Revision)
 General features of scattering by solids
 Scatteredwave amplitude
 Laue conditions for diffraction
 Reciprocal lattice and Brillouin zones
 Structure factor
 Examples: Xray diffractometer; transmission electron microscope

Freeelectron model
 Freeelectron Fermi gas
 Energy dispersion in kspace
 Reduced and extended zones
 Effective mass
 Density of states
 Electrondistribution function; Fermi level
 Heat capacity

NearlyFreeElectron Model
 Effect of crystal potential on the freeelectron picture
 Bloch electron
 Origin of energyband gaps
 Holes

Band Picture for Classification of Solids
 Formation of energy bands in solids
 Band picture for insulators, semiconductors and metals

Fermi surfaces
 Fermi surfaces in metals
 Harrison's construction of the Fermi sphere

Intrinsic and Extrinsic Semiconductors
 Donor and acceptor levels in semiconductors; ionization
energy of a donor electron, and the Bohr radius
 Freechargecarrier concentration and the Fermi level
at different temperatures
 The significance of the Fermi level;
band structure of a pn junction
 Elementary Optical Properties of Semiconductors: Fundamental absorption; direct and indirect
transitions; absorption coefficient; recombination

Phonons
 Lattice vibrations of the monatomic linear chain
 Diatomic linear chain.
 Lattice vibrations of threedimensional crystals
 Longitudinal and transverse phonons;
 Plotting of dispersion relations
 Heat Capacity

Transport Properties (Electrical and Thermal)
 Relaxation times: phonon/lattice; electronic
 Drift and diffusion in semiconductors; the Einstein relation
 Thermal conduction in semiconductors and insulators
 Drift and thermal conduction in metals
 The WiedemannFranz law

Introduction to Nanostructures and Nanomaterials
 Quantum Wells, Wires and Dots
 Carbon nanotubes
 Graphene
Learning and Teaching
Learning Activities and Teaching Methods
Description 
Study time 
KIS type 
22×1hour lectures 
22 hours

SLT 
5×6hour selfstudy packages 
30 hours

GIS 
8×2hour problems sets 
16 hours

GIS 
Problems class support 
8 hours

SLT 
Tutorial support 
3 hours

SLT 
Reading, private study and revision 
71 hours

GIS 
Assessment
Weight 
Form 
Size 
When 
ILOS assessed 
Feedback 
0% 
Exercises set by tutor 
3×1hour sets (typical) 
Scheduled by tutor 
116 
Discussion in tutorials

0% 
Guided selfstudy 
5×6hour packages 
Fortnightly 
116 
Discussion in tutorials

10% 
8 × Problems sets 
2 hours per set 
Weekly 
116 
Marked in problems class, then discussed in tutorials

15% 
Midterm test 
30 minutes 
Weeks T2:06 
115 
Marked, then discussed in tutorials

75% 
Examination 
120 minutes 
May/June assessment period 
115 
Mark via MyExeter, collective feedback via ELE and solutions. 
Resources
The following list is offered as an indication of the type & level of information that
students are expected to consult. Further guidance will be provided by the Module Instructor(s).
Core text:
Supplementary texts:
ELE:
Further Information
Prior Knowledge Requirements
Prerequisite Modules 
Properties of Matter (PHY1024) 
Corequisite Modules 
none 
Reassessment
Reassessment is not available except when required by referral or deferral.
Original form of assessment 
Form of reassessment 
ILOs reassessed 
Time scale for reassessment 
Whole module 
Written examination (100%) 
115 
August/September assessment period 
Notes: See Physics Assessment Conventions.
KIS Data Summary
Learning activities and teaching methods 
SLT  scheduled learning & teaching activities 
33 hrs 
GIS  guided independent study 
117 hrs 
PLS  placement/study abroad 
0 hrs 
Total 
150 hrs 


Summative assessment 
Coursework 
10% 
Written exams 
90% 
Practical exams 
0% 
Total 
100% 

Miscellaneous
IoP Accreditation Checklist 
 SS03 Phonons and heat capacity
 SS04 Crystal structure and Bragg scattering
 SS05 Electron theory of solids to the level of simple band structure
 SS06 Semiconductors and doping

Availability 
unrestricted 
Distance learning 
NO 
Keywords 
Physics; Electronic; Semiconductor; Fermi; Phonons; Lattices; Energy; Properties; Crystal; Bands; State. 
Created 
01Oct10 
Revised 
01Oct11 