slide1 n.
Skip this Video
Loading SlideShow in 5 Seconds..
Review of Semiconductor Physics PowerPoint Presentation
Download Presentation
Review of Semiconductor Physics

Loading in 2 Seconds...

play fullscreen
1 / 22

Review of Semiconductor Physics - PowerPoint PPT Presentation

  • Uploaded on

Review of Semiconductor Physics. Energy bands. Bonding types – classroom discussion The bond picture vs. the band picture. Bonding and antibonding Conduction band and valence band. The band picture – Bloch’s Theorem. Notice it’s a theorem, not a law. Mathematically derived. The theorem:.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

PowerPoint Slideshow about 'Review of Semiconductor Physics' - jada

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Review of Semiconductor Physics

Energy bands

  • Bonding types – classroom discussion
  • The bond picture vs. the band picture

Bonding and antibonding

Conduction band and valence band


The band picture – Bloch’s Theorem

Notice it’s a theorem, not a law. Mathematically derived.

The theorem:

The eigenstates (r) of the one-electron Hamiltonian

where V(r + R) = V(r) for all R in a Bravais lattice, can be chosen to have the form of a plane wave times a function with the periodicity of the Bravais lattice:

where un,k(r + R) = un,k(r) .


Physical picture

- Wave function


Indirect gap

- Band structure

1D case

3D case


Limitations of the band theory

Static lattice: Will introduce phonons

Perfect lattice: Will introduce defects

One-electron Shrödinger Eq: We in this class will live with this

Justification: the effect of other electrons can be regarded as a kind of background.


Semi-classic theory

Free electron

Block electron

ħkis the momentum.

ħk is the crystal momentum, which is not a momentum, but is treated as momentum in the semiclassical theory.

n is the band index.

En(k) = En(k+K)





un,k(r + R) = un,k(r)


The Bloch (i.e. semiclassic) electron behaves as a particle following Newton’s laws.

(We are back in the familiar territory.)

  • With a mass m*
  • Emerging from the other side of the first Brillouin zone upon hitting a boundary

Newton’s 1st law: the Bloch electron moves forever – No resistance?

Newton’s 2nd law:

F = dp/dt = ħdk/dt

Oscillation in dc field. So far not observed yet.


Real crystals are not perfect. Defects scatter electrons.

On average, the electron is scattered once every time period . Upon scattering, the electron forgets its previous velocity, and is “thermalized.”



Values of k

Discrete but quasi-continuous

k = 2n/L, n = 1, 2, 3, …, N

L = Na

Run the extra mile:

Show the above by using the “periodic boundary” condition.


A vacancy in a band, i.e. a k-state missing the electron, behaves like a particle with charge +q.

Run the extra mile:

Show the above.


Review of Semiconductor Physics

Carrier Statistics

  • Fermi-Dirac distribution

Nature prefers low energy.

Lower energy states (levels) are filled first.

Imaging filling a container w/ sands, or rice, or balls, or whatever

  • Each particle is still T = 0 K
  • Each has some energy, keeping bouncing around T > 0 K
  • Density of States

How many states are there in the energy interval dE at E?


1D case derived in class.

The take-home message: D(E)  E1/2


2D case

Run the extra mile

Derive D(E) in 2D.

Hint: count number of k’s in 2D.

The answer:

Or, for unit area

D(E) = constant

The take-home message:

3D case

Run the extra mile

Derive D(E) in 3D.

Hint: count number of k’s in 2D.

For unit area,

The take-home message: D(E)  E1/2


Things we have ignored so far: degeneracies

Spin degeneracy: 2

Valley degeneracy: Mc

Mc = 6 for Si


Total number of carriers per volume (carrier density, carrier concentration)

Run the extra mile

Derive the electron density n.

Hint: Fermi-Dirac distribution approximated by Boltzmann distribution.

Results for n and p are given.

p is the total number of states NOT occupied.


One way to manipulate carrier density is doping.

Doping shifts the Fermi level.

np = ni2


One small thing to keep in mind:

Subtle difference in jargons used by EEs and physicists

We use the EE terminology, of course.

Fermi level

EF = EF(T)

Same concept



Chemical potential

EF = (0)

Fermi energy

We already used  for mobility.


Before we talk about device, what are semiconductors anyway?

Classroom discussion

Why can we modulate their properties by orders of magnitude?

Classroom discussion


We have mentioned defect scattering:

Real crystals are not perfect. Defects scatter electrons.

On average, the electron is scattered once every time period . Upon scattering, the electron forgets its previous velocity, and is “thermalized.”


Any deviation from perfect periodicity is a defect. A perfect surface is a defect.



Static lattice approximation

Atoms vibrate

Harmonic approximation

Vibration quantized

Each quantum is a phonon.

Similar to the photon:

E = ħ, p = ħk

Phonons scatter carriers, too.

The higher the temperature, the worse phonon scattering.

You can use the temperature dependence of conductivity or mobility to determine the contributions of various scattering mechanisms.



 = vk

Sound wave in continuous media

Microscopically, the solid is discrete.

Phonon dispersion

Wave vector folding, first Brillouin zone.

Watch video at

Recall that

Crystal structure = Bravais lattice + basis

If there are more than 1 atom in the basis, optical phonons


Phonons in the 3D world -- Si

In 3D, there are transverse and longitudinal waves.

E = h = ħ

62 meV

15 THz

When electron energy is low, the electron only interacts with acoustic phonons,





Optical phonons and transport

At low fields,

= 38 meV

vth = 2.3 × 107 cm/s

For Si,

At high fields, vd comparable to vth

Electrons get energy from the field, hotter than the lattice – hot electrons

When the energy of hot electrons becomes comparable to that of optical phonons, energy is transferred to the lattice via optical phonons.

Velocity saturation

For Si, vsat ~ 107 cm/s



Compounds, alloys, heterostructures

InP, GaAs, …, SiC

InxGa1-xAsyP1-y, …, SixGe1-x


Band structure of alloys



  • Review of Semiconductor physics
    • Crystal structure, band structures, band structure modification by alloys, heterostructurs, and strain
    • Carrier statistics
    • Scattering, defects, phonons, mobility, transport in heterostructures
  • Device concepts
    • Heterojunction bipolar transistors (HBT)
    • Semiconductor processing
    • Photodiodes, LEDs, semiconductor lasers
    • (optional) resonant tunneling devices, quantum interference devices, single electron transistors, quantum dot computing, ...
    • Introduction to nanoelectronics

We will discuss heterostructures in the context of devices.

More discussions on semiconductor physics will be embedded in the device context.