ee105 - spring 2007 microelectronic devices and circuits lecture 2 semiconductor basics
TRANSCRIPT
EE105 - Spring 2007Microelectronic Devices and Circuits
Lecture 2Semiconductor Basics
2
Periodic Table of Elements
3
Electronic Properties of Silicon
Silicon is in Group IV (atomic number 14)– Atom electronic structure: 1s22s22p63s23p2
– Crystal electronic structure: 1s22s22p63(sp)4
– Diamond lattice, with 0.235 nm bond length Very poor conductor at room temperature: why?
(1s)2
(2s)2
(2p)6 (3sp)4
Hybridized State
4
The Diamond Structure3sp Tetrahedral Bond
A43.5
A35.2
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States of an Atom
Quantum Mechanics: The allowed energy levels for an atom are discrete (2 electrons with opposite spin can occupy a state)
When atoms are brought into close contact, these energy levels split
If there are a large number of atoms, the discrete energy levels form a “continuous” band
Ene
rgy
E1
E2
...E3
Forbidden Band Gap
AllowedEnergyLevels
Lattice ConstantAtomic Spacing
6
Silicon
Si has four valence electrons. Therefore, it can form covalent bonds with four of its neighbors.
When temperature goes up, electrons in the covalent bond can become free.
7
Electron-Hole Pair Interaction
With free electrons breaking off covalent bonds, holes are generated.
Holes can be filled by absorbing other free electrons, so effectively there is a flow of charge carriers.
8
Free Electron Density as a Function of Temperature
Eg, or bandgap energy, determines how much effort is needed to break off an electron from its covalent bond.
There exists an exponential relationship between the free-electron density and bandgap energy.
15 3/ 2 32
0 10 3
0 15 3
5.2 10 /
( 300 ) 1.08 10 /
( 600 ) 1.54 10 /
gE
kTi
i
i
n T e electrons cm
n T K electrons cm
n T K electrons cm
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N Type Doping
If Si is doped with group-V elements such as phosphorous (P) or arsenic (As), then it has more electrons and becomes N type (electron).
Group-V impurities are called Donors
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P Type Doping
If Si is doped with group-III elements such as boron (B), then it has more holes and becomes P type.
Group-III impurities are called Acceptors
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Summary of Charge Carriers
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Thermal Equilibrium (Pure Si)
Balance between generation and recombination determines no = po
Strong function of temperature: T = 300 K
2
10
( )( )
( ) ( )( ) / ( )
( ) 10 -3 cm at 300K
th opt
th
th i
i
G G T GR k n pG R
k n p G Tn p G T k n Tn T
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Majority Carrier Conc.
= Doping Conc.
Minority Carrier Conc.
(Mass Action Law)
N-Type
P-Type
Mass Action Law
The product of electron and hole densities is ALWAYS equal to the square of intrinsic electron density, regardless of doping levels
2 10 3( 300 , 10 ) K cmo o i ip n n T n
dd NNn 0
aa NNp 0
2
0i
d
np
N
2
0i
a
nn
N
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Compensated Doping
Si is doped with both donor and acceptor atoms:
– More donors than acceptors: Nd > Na N type
– More acceptors than donors: Na > Nd P type
2
2
i
i
o d a od a
o a d oa d
nn N N p
N N
np N N n
N N
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First Charge Transportation Mechanism: Drift
The process in which charge particles move because of an electric field is called drift.
Charge particles will move at a velocity that is proportional to the electric field.
Ev
Ev
ne
ph
Mobility
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Mobility vs. Doping in Silicon at 300K
Typical values 1350450
2
2
V-sec / cm V-sec / cm
n
p
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Current Flow: General Case
Electric current is calculated as the amount of charge in v meters that passes thru a cross-section if the charge travel with a velocity of v m/s.
I v W h n qI
J v n qWh
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( )
n n
p p
tot n p
n p
J E n qJ E p qJ E n q E p q
q n p E
Current Flow: Drift
Since velocity is equal to E, drift characteristic is obtained by substituting v with E in the general current equation.
The total current density consists of both electrons and holes.
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Velocity Saturation
A topic treated in more advanced courses is velocity saturation. In reality, velocity does not increase linearly with electric field. It
will eventually saturate to a critical value.
0
0
0
0
1
1
sat
sat
bE
vb
v EE
v
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Second Charge Transportation Mechanism: Diffusion
Charge particles move from a region of high concentration to a region of low concentration.
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Current Flow: Diffusion
Diffusion current is proportional to the gradient of charge (dn/dx) along the direction of current flow.
Total diffusion current density consists of both electrons and holes.
( )
n n
p p
tot n p
dnJ qD
dxdp
J qDdxdn dp
J q D Ddx dx
Diffusion Coefficient
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Example: Linear vs. Nonlinear Charge Density Profile
Linear charge density profile means constant diffusion current, whereas nonlinear charge density profile means varying diffusion current.
LN
qDdxdn
qDJ nnn dd
nn L
xL
NqDdxdn
qDJ exp
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Einstein's Relation
While the underlying physics behind drift and diffusion currents are totally different, Einstein’s relation provides a link between the two.
p
qkTD
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Resistivity of Uniformly Doped Si
1 1
n n
n
n
J E n q E
nq
nq
1
Ohm's LawV R IV E LI J tW
I V EL LJ E E
A RtW RtW RtWL L
RtW tW
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Sheet Resistance (Rs)
IC resistors have a specified thickness – not under the control of the circuit designer
Eliminate thickness, t, by absorbing it into a new parameter: the sheet resistance (Rs)
S
L L LR R
Wt t W W
“Number of Squares”
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Using Sheet Resistance (Rs)
Ion-implanted (or “diffused”) IC resistor
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Idealizations
Why does current density Jn “turn”?
What is the thickness of the resistor? What is the effect of the contact regions?