Summary
Summary Solid State physics
- Course
- Institution
Providing classic notes of solid state physics with examples and answers. Quality content for perfect study and very helpful for exams.
[Show more]
Seller
Follow
shrishnemane
Content preview
Unit - IV---------------------------------------------------------
Solid State Physics
---------------------------------------------------------
Que.1. Explain Opening of band gap due to
internal electron diffraction and hence
explain formation of bands in solids [6]
When an electron moves through a lattice of
positive ions, it experiences varying potentials.
The potential of an electron at the positive ion
site is zero and is, maximum in between two
ions as shown in figure below. The dotted line is representing the motion for a
free electron. As electron is moving in a
periodic potential, it appears that there are gaps
which open in energy spectrum at an integer of
These gaps correspond to energy bands inside
the solids. Thus, the energy level of electron in
the crystal lattice is discrete.
Formation of Bands:
1. In a single isolated atom, the electrons in
each orbit have definite energy associated with
it. But in case of solids all the atoms are close
to each other, so the energy levels of outermost
orbit electrons are affected by the neighboring
atoms.
2. Band formation is preferred in solids as
atomic spacing is very small. In liquids and
gases as atomic spacing is much larger as
Kronig and Penney approximated these compared to solids so band formation is not
potentials inside the crystal to the shape of preferred.
rectangular steps. 3. When two single or isolated atoms are bring
close to each other, then the outermost orbit
electrons of two atoms are interact or shared
with each other i.e. the electrons in the
outermost orbit of one atom experience an
attractive force from the nearest or neighboring
atomic nucleus. Due to this the energies of the
electrons will not be in same level, the energy
The energies of electrons can be known by levels of electrons are changed to a value which
solving Schrödinger’s wave equation in such a is higher or lower than that of the original
lattice. energy level of the electron.
By solving the Schrödinger’s wave equation 5. However, the energy levels of inner orbit
using Bloch theorem, we get Energy vs electrons are not much affected by the presence
K (momentum) diagram of neighboring atoms.
1 Sinhgad COE, Engineering Physics
, Que.2. Explain in brief how free electron theory it can be shown that 𝑘/σ𝑇=1.11x10-8
theory explains electrical conductivity and WΏ/K2.
thermal conductivity of solids, and relation
between electrical and thermal conductivity This number is also known as Lorentz’s
of solids (Wiedemann–Franz law). What are number. This number is based on
the limitations of this theory? [4] calculations as per Maxwell-Boltzman
distribution for electrons. If Fermi-Dirac
The electrons present in the outermost orbitals statistics is applied to electrons, this number
of the atom, determine the electrical properties is modified to 2.45x10-8 WΏ/K2., which
of the solid. The electron theory of solids agrees quite well with experimental
explains the structures and properties of solids findings.
through their electronic structure. The electron 6. Advantages (Success) of Free Electron
theory is applicable to all solids. The theory is Theory
developed in three phases: i) It verified Ohm’s law
ii) It explains electrical and thermal
1. This theory was developed by Drude and conductivities of metals.
Lorentz in 1900 and hence is also known as iii) It derived Wiedemann-Franz law (i.e.
Drude-Lorentz theory. According to this relation between electrical conductivity
theory, a metal consists of electrons which and thermal conductivity.
are free to move about in the crystal like iv) It explains optical properties of metals.
molecules of a gas in a container.
7. Disadvantages (Limitations) of Free
2. Neglecting the electron-electron interaction Electron Theory
and the electron-ion interaction, it appears
i) The phenomenon such as photoelectric
as if the electrons move in a confined box
effect, Compton effect, black body
with periodic collision with ions in the
radiations, etc could not be explained
lattice. This idea is utilized to explain many
properties of metals satisfactorily such as ii) The theoretical values of specific heat
electrical conductivity, Ohm’s law, thermal and electronic specific heat as calculated
conductivity etc. from this theory do not agree with
experimental values
3. Electrical conductivity of metal: It can be iii) Electrical conductivity of
shown that Electrical conductivity = semiconductors or insulators could not be
explained.
𝜎=𝑛𝑒𝜇, where n is electron density, e is
charge on electron and µ is the mobility of iv)Wiedemann-Franz law deviates at low
electrons. temperature.
v) Ferromagnetism could not be explained
4. Thermal Conductivity: Thermal by this theory.
conductivity is the property of material’s vi) The theoretical value of paramagnetic
ability to conduct the heat. From free susceptibility is greater than experimental
electron theory, it can be shown that value.
thermal conductivity𝐾=k𝐵𝑛𝑣λ/2, where kB
is Boltzmann constant. Que.3. Explain terms (a) valence band (b)
conduction band (c) band gap energy. [4]
5. Wiedemann-Franz Law:
The Wiedemann–Franz law states that the There are number of energy bands in solids but
ratio of the electronic contribution to the three of them are very important. These three
thermal conductivity (K) and the electrical energy bands are important to understand the
conductivity (σ) of a metal is proportional behavior of solids. These energy bands are -
to the temperature (T). From free electron
2 Sinhgad COE, Engineering Physics
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller shrishnemane. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $8.99. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
81298 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now