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CE 124A
ECE 124A
LSI Principles
VLSI Principles
Lecture 7
pn
pnjunction Diode, MOS Capacitor and MOS
junction Diode, MOS Capacitor and MOSFET
FET
Prof. Kaustav Banerjee
Electrical and Computer Engineering
ail:
[email protected] ucsb edu
Email: [email protected]
Lecture 7, ECE 124A, VLSI Principles
Kaustav Banerjee
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View Full Document Semiconductor Physics Tutorial:
Key Points to Remember…
ond Model
Bond Model
Nearest neighbor atoms covalently bonded with
valence electrons (=4 for Si)
At absolute zero temperature….no free electrons
As temp. increases, thermal energy (kT) causes
ome of the covalent electrons to break loose
to
some of the covalent electrons to break loose….to
become conduction electrons.
.(
intrinsic
)
Absence of an electron causes a “void” or a “hole”
Dopantswith an extra (one less) electron contribute
toward increasing the number of conduction
electrons (holes):
ntype and ptype (extrinsic)
Lecture 7, ECE 124A, VLSI Principles
Kaustav Banerjee
semiconductors
Semiconductor Physics Tutorial:
ey Points to Remember
Key Points to Remember…
Band Model
When many atoms are brought together….discrete energy levels
are replaced with bands of energy states separated by
gaps…due to
Pauli Exclusion Principle
At absolute zero, most of the lower energy bands are completely
filled….and upper energy bands are completely empty….thus no
conduction…like a full or empty bottle of water!
alence band
due to the valence electrons (mostly bound)
Valence band
: due to the valence electrons (mostly bound)
Conduction band
: due to the conduction electrons
Top edge of valence bandE
V
ottom edge of conduction band 
Bottom edge of conduction bandE
C
Band gap: E
G
= E
V
–E
C
(=1.1 eV in Si)
how to measure E
G
?
Energy band diagrams are drawn w.r.t electrons….
onor (acceptor) energy levels are drawn close to the
Lecture 7, ECE 124A, VLSI Principles
Kaustav Banerjee
Donor (acceptor) energy levels are drawn close to the
conduction (valence) band edges….
why?
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ey
ey oints to Remember…
oints to Remember…
Key
Key Points to Remember…
Points to Remember…
Band Model
Effective mass concept….
Acceleration = F/m
=
qE/m
e
(for electrons);
=
qE/m
h
(for holes)
A more complete description of the electrons in a crystal is
based on their wave characteristics
Electron wave function (
) is a solution to the 3dimensional
Schrodinger’s equation:
H
=
E
Solution is of the form:
= exp (±
k.r
);
where
k
is the wave vector
2
the electron wavelength)
= 2
π
/
λ
(
λ
is the electron wavelength)
k
is a function of energy,
E
Effective mass
of electrons/holes are related to the
curvature
of
e E
curves
why?
the E k curves….
.why?
Density of states: D(E)
= number of states/
Δ
E x Volume
Effective density of states in valence (N
v
) and conduction (N
c
)
ands…
Lecture 7, ECE 124A, VLSI Principles
Kaustav Banerjee
bands…
Thermal equilibrium and Fermi function
FermiDirac
distribution function: 1/(1 + exp (EE
F
)/kT)
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This note was uploaded on 12/04/2010 for the course ECE 134 taught by Professor York during the Fall '08 term at UCSB.
 Fall '08
 York

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