Carrier Concentrations
Introduction
Knowledge of carrier concentrations are key in
SC devices, esp. wrt to available energy states
FermiDirac Statistics
definition: a means to describe the concentration of
electrons with respect to available energy le
Atomic Structure and Quantum Mechanics
Introduction
The Particle in a Box problem shows that the
SWE can be used to describe the interaction of
particles with potential fields, which could be
electrons with nuclei.
The problem is that atoms arent so sim
Quantum Mechanics  Intro
Definition  A method to explain the behavior of small
particles (e.g., electrons) because these particles dont
follow classical mechanics.
Classic experiments leading to quantum mechanics:
Plancks observations of emitting bodi
Charge Carriers in Semiconductors
Electrons and Holes
In pure semiconductors, at 0K, the valence band is
full and the conduction band is empty
As T> 0K, some electrons will gain sufficient
energy to cross the gap into the conduction band,
leaving empty
Semiconductor Device
Introduction
Semiconductor: A group of materials having
electrical conductivities between metals and
insulators
Characteristics
conductivities can be varied by changes in
temperature
optical excitation
impurity incorporation (do
Chapter 4
Introduction
Excess charge carriers
For operational SC devices, these carriers are in
excess of those generated thermally.
Generation mechanisms
Electron bombardment
Optical excitation
Objectives of Chapter 4
Characterize optical absorpti
Capacitance in the PN Junction
Capacitance types:
Junction capacitance (Cj)
Due to the dipole in W
Somewhat analogous to a parallelplate capacitor
Dominant in reversed biased situations
Sometimes called the depletion capacitance
Charge Storage Capaci
Transient and AC Conditions
Transients
Definition: time dependent conditions
Typical case: simple switching from forward to
reverse bias
Relevance: Most devices are used in switching
operations or are used for processing ac signals
Time variation in
Carrier Injection
Minority carrier concentration on each side of the
transition region will vary with the applied bias.
With respect to hole concentration:
Without biasing: pp/pn = e(qV/kT) in the bulk
With biasing:
p(xp0)/p(xn0) = exp[q(V0V)/kT]
wher
PN Junctions
Introduction
Simplest construction: step junction (sharp interface)
Generalities:
Differences in doping on each side of the junction causes
a potential difference between the two sides
For equilibrium conditions
Net current flow = 0
T
Diffusion of Carriers
Diffusion
Definition: the net flow of carriers from regions of
high carrier concentration to low concentration
Physical processes associated with diffusion
Random thermal motion
Scattering from lattice impurities
Its a timedep
The Transition Region
Generalities
W is composed of both ntype and ptype material and
encompasses the physical junction.
W is completely depleted of charge carriers
The Efield set up by uncompensated dopants in this region
serves to sweep out any m
Biasing a Schottky Contact
Forward Biasing
The contact potential decrease to V0 Vf
Reverse Biasing
Contact potential increases to V0 + Vr
The diode equation:
I = I0(eqV/kT 1) where I0 exp(qB/kT)
Generalities:
Forward biasing current in these conta
Current entering and leaving a volume xA.
Injection of holes at x = 0, giving a steady state hole distribution p(x)
and a resulting diffusion current density Jp(x).
Drift and diffusion of a hole pulse in an ntype bar:
(a) sample geometry;
(b) position an
Charge Carriers in Semiconductors
Effective Mass
Definition  an expression for the mass of an
electron that takes into account its interaction
with the lattice.
Its an accounting construct that simplifies the
calculations, since its easier to create a ma
Bonding Forces and Energies in Solids
Introduction
From Chapter 2, electrons in individual atoms are
restricted to certain, well defined energy levels.
Since solids are just collections of atoms, the
same should true for electrons in solids, but, as it
Case EECS 321  Spring 2014  Lecture 18 Notes  Feb. 28, 2014
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Name: ke EECS 321 Spring 2017
Exam #4
1._ Consider an nchannel Si MOSFET transistor made on a substrate with a doping concentration of
1 x 1018/crn3. The gate is made from heavily phosphorusdoped polysilicon. The thickness of the gate
insulator is 10 nm.
You are advised to put your initials on all attached sheets.
Name: EECS 321 Spring 2017
Exam #2
Note: For Si, the bandgap is 1.12 eV and the intrinsic carrier concentration at 300K is 1.5 x 1010/cm3
1. Consider a piece of silicon that is 5 pm in length
Be sure to put your name on all attached sheets.
Name: km; EECS 321 Spring 2017
Exam #1
Note: For Si, the bandgap is 1.12 eV and the intrinsic carrier concentration at 300K is 1.5 x low/cm3
1. Calculate: (1) the atomic density, (2) the mass density and
Current entering and leaving a volume xA.
Injection of holes at x = 0, giving a steady state hole distribution p(x)
and a resulting diffusion current density Jp(x).
Drift and diffusion of a hole pulse in an ntype bar:
(a) sample geometry;
(b) position an