semi physics
TRANSCRIPT
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ECE 250 – Elec t ron ic Devic es 1
Electronic Device Modeling
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ECE 250 – Elec t ron ic Devic es 2
Physics
• You should really take a semiconductor device h sics course.
• We can only cover a few basic ideas and
.
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ECE 250 – Elec t ron ic Devic es 3
Electronic Devices
• Most electronic devices are made out of semiconductors, insulators, and conductors.
• Semiconductors
– Old Days – Germanium (Ge) – Now – Silicon (Si)
– Now – Gallium Arsenide (GaAs) used for high speed
. – New – Silicon Carbide (SiC) – High voltage Schottky
diodes.
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ECE 250 – Elec t ron ic Devic es 4
Elements
• Elements in the periodic table are grouped b the number of electrons in their valence
shell (most outer shell).
– Conductors – Valence shell is mostl em t 1
electron)
– Insulators – Valence shell is mostl full
– Semiconductors – Valence shell is half full.
Or is it half em t ?
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ECE 250 – Elec t ron ic Devic es 5
Semiconductors
• Silicon and Germanium are group 4elements – the have 4 electrons in their
valence shell.
Valence
Electron
Si
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ECE 250 – Elec t ron ic Devic es 6
Silicon
• When two silicon atoms are placed close toone another the valence electrons are
shared between the two atoms, forming a
covalent bond.Covalent
bond
Si Si
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ECE 250 – Elec t ron ic Devic es 7
Si
Si
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ECE 250 – Elec t ron ic Devic es 8
SiliconSi SiSi
Si
• n mpor an proper y o e -a om
silicon lattice structure is that valenceelectrons are available on the outer edge
of the silicon crystal so that other silicon
atoms can be added to form a large single
.
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ECE 250 – Elec t ron ic Devic es 9
Si Si Si Si Si Si
Si Si Si Si Si Si
Si Si Si Si Si Si
Si Si Si Si Si Si
Si Si Si Si Si Si
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ECE 250 – Elec t ron ic Devic es 10
Si Si Si Si Si Si
Si Si Si Si Si Si
Si Si Si Si Si Si
Si Si Si Si Si Si
Si Si Si Si Si Si
º ,
state so each covalent bond position is filled.
•
material, no electrons will move because they
.=> At 0 ºK, silicon is an insulator.
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ECE 250 – Elec t ron ic Devic es 12
Si Si Si Si Si Si
Si Si Si Si Si Si
Si Si Si Si Si Si
+
Si Si Si Si Si Si
-
Si Si Si Si Si Si
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ECE 250 – Elec t ron ic Devic es 13
Si Si Si Si Si Si
Si Si Si Si Si Si
Si Si Si Si Si Si
Si Si Si Si Si Si+
-
Si Si Si Si Si Si
Since the net charge of a crystal is zero, if a
negatively (-) charged electron breaks its
bond and moves away from its original position, a positively charged “empty state”
is left in its original position.
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ECE 250 – Elec t ron ic Devic es 14
em con uc ors• As temperature increases, more bonds are
broken creating more negative freeelectrons and more ositivel char ed
empty states. (Number of free electrons is a
function of temperature.)• To break a covalent bond, a valence
l r n m in minim m n r E
called the energy band gap. (Number of free
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ECE 250 – Elec t ron ic Devic es 15
Insulators
• Elements that have a large energy band gapof 3 to 6 eV are insulators because at room
temperature, essentially no free electrons
exist.
• Note: an eV is an electron volt. It is the
is accelerated through a 1 volt potential.
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ECE 250 – Elec t ron ic Devic es 16
Electron Volt
−
joulec u
vo t coue
19 1106021
.
−
−
⎞⎛ ×=
×=
joules
coulomb19
10602.1−
×=
⎝
Also, 1 eV = 1.518 ×10-22 BTU, but who cares.
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ECE 250 – Elec t ron ic Devic es 17
Conductors
• Elements that have a small energy band gapare conductors.
• These elements have a large number of free
electrons need very little energy to escape
.
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ECE 250 – Elec t ron ic Devic es 18
Semiconductors
• Semiconductors have a band gap energy of about 1 eV
– Silicon = 1.1 eV
– = .
– Ge = 0.66 eV
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ECE 250 – Elec t ron ic Devic es 19
Empty States
• An electron that has sufficient energy and isad acent to an em t state ma move into
the empty state, leaving an empty state
behind.
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ECE 250 – Elec t ron ic Devic es 20
Si Si Si Si Si Si
Si Si Si Si Si Si
Si Si Si Si Si Si
+This electron can
Si Si Si Si Si Si
state.
Si Si Si Si Si SiEmpty state
originally here.
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ECE 250 – Elec t ron ic Devic es 21
Si Si Si Si Si Si
Si Si Si Si Si Si
Si Si Si Si Si Si
Si Si Si Si Si Si
Empty state
Si Si Si Si Si Sinow here.
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ECE 250 – Elec t ron ic Devic es 22
Si Si Si Si Si Si
Si Si Si Si Si Si
Si Si Si Si Si Si
Si Si Si Si Si Si
Si Si Si Si Si Si
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ECE 250 – Elec t ron ic Devic es 23
Si Si Si Si Si Si
Si Si Si Si Si Si
Si Si Si Si Si Si
+
Si Si Si Si Si Si
Si Si Si Si Si Si
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ECE 250 – Elec t ron ic Devic es 24
Empty States
• Moving empty states can give theappearance that positive charges movethrough the material.
• This moving empty state is modeled as a positively charged particle called a hole.
• In semiconductors, two types of “particles”
contribute to the current: positively chargedholes and negatively charged electrons.
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ECE 250 – Elec t ron ic Devic es 25
Carrier Concentrations
• The concentrations of holes and freeelectrons are im ortant uantities in the
behavior of semiconductors.
•
of particles per unit volume, or
3cm
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ECE 250 – Elec t ron ic Devic es 26
Intrinsic Semioconductor
• Definition – An intrinsic semiconductor isa sin le cr stal semiconductor with no other
types of atoms in the crystal.
– Pure silicon
– Pure germanium
– .
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ECE 250 – Elec t ron ic Devic es 27
Carrier Concentration
• In an intrinsic semiconductor, the number of holes and free electrons are the same because they are thermally generated.
• If an electron breaks its covalent bond wehave one free electron and one hole.
• In an intrinsic semiconductor, the
concentration of holes and free electrons arethe same.
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ECE 250 – Elec t ron ic Devic es 28
Intrinsic Semiconductors
• =i
intrinsic semiconductor.
semiconductor.
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ECE 250 – Elec t ron ic Devic es 29
Intrinsic Carrier Concentration⎛ − Eg3
⎠⎝
=KT
ni
2
exp
of the semiconductor.
• g = an gap energy e
• B = material constant
⎟⎟ ⎞
⎜⎜⎛
33
#
o⋅
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ECE 250 – Elec t ron ic Devic es 30
Intrinsic Carrier Concentration⎛ − Eg3
⎠⎝
=KT
ni
2
exp
• T = temperature (ºK)
’ - º.
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ECE 250 – Elec t ron ic Devic es 31
Material Constants
Material Eg (eV)
B ( ) ( ) ⎟⎟ ⎠⎜⎜⎝ ⋅ 23
3
#
K cmo
Silicon 1.12 5.23×1015
Gallium
Arsenide
1.4 2.10×1014
Germanium 0.66 1.66×1014
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ECE 250 – Elec t ron ic Devic es 32
Important Note:
oo uses a s g y eren Notation!
− ⎟ ⎠
⎜⎝
=KT
BT ni exp3
33
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ECE 250 – Elec t ron ic Devic es 33
Book Material Constants
Material Eg (eV) B ( ) ( ) ⎟⎟ ⎠
⎞
⎜⎜⎝
⎛
⋅36
#
K cmo
Silicon 1.12 5.4×1031
34
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ECE 250 – Elec t ron ic Devic es 34
Example
• Find the intrinsic carrier concentration of free electrons and holes in a silicon
semiconductor at room temperature.
35
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ECE 250 – Elec t ron ic Devic es 35
MathCAD
eV 1.602 1019−⋅ coul⋅( ) 1⋅ volt⋅≡ K B 86.2 10
6−⋅ eV⋅:=
⋅:=
Bsi 5.23 1015⋅
1
cm3
K 1.5⋅
⋅:=
Egsi 1.12 eV⋅:=
ECE 250 El t i D i 36
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ECE 250 – Elec t ron ic Devic es 36
MathCAD
ni Bsi T1.5
⋅ exp
si−
2 K B⋅ T⋅⋅:=
10 1= .
cm3
The concentration of silicon atoms in anintrinsic semiconductor is 5×1022 atoms/cm3.
ECE 250 El t i D i 37
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ECE 250 – Elec t ron ic Devic es 37
Extrinsic Semiconductors
• Since the concentrations of free electronsand holes is small in an intrinsic
semiconductor, only small currents are
ossible.• Impurities can be added to the
of free electrons and holes.
ECE 250 El t i D i 38
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ECE 250 – Elec t ron ic Devic es 38
Extrinsic Semiconductors
• An impurity would have one less or onemore electron in the valance shell than
silicon.
•would come from group 3 or group 5
.
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ECE 250 Elec t ron ic Devic es 40
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ECE 250 – Elec t ron ic Devic es 40
Si Si Si Si Si Si
Si Si Si Si Si Si
Si Si P Si Si Si
-
Si Si Si Si Si Si
Si Si Si Si Si Si
ECE 250 Elec t ron ic Devic es 41
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ECE 250 – Elec t ron ic Devic es 41
Extrinsic Semiconductors
• The group 5 atom is called a donorim urit since it donates a free electron.
• The group 5 atom has a net positive charge
move.
,created without adding holes.
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ECE 250 – Elec t ron ic Devic es 43
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ECE 250 Elec t ron ic Devic es
Extrinsic Semiconductors
• The most common group 3 impurity is boron which has 3 valence electrons.
• Since boron has only 3 valence electrons,
its neighbors leaving one open bond
.
ECE 250 – Elec t ron ic Devic es 44
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ECE 250 Elec t ron ic Devic es
Si Si Si Si Si Si
Si Si Si Si Si Si
Si Si B Si Si Si
Si Si Si Si Si Si
Si Si Si Si Si Si
ECE 250 – Elec t ron ic Devic es 45
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ECE 250 Elec t ron ic Devic es
Extrinsic Semiconductors
• At room temperature, silicon has freeelectrons that will fill the o en bond
position, creating a hole in the silicon atom
whence it came.• The boron atom has a net negative charge
,
atom cannot move.
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ECE 250 – Elec t ron ic Devic es 47
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Extrinsic Semiconductors
• Since boron accepts a valence electron, it iscalled an acce tor im urit .
• Acceptor impurities create excess holes but
.
• A semiconductor doped with an acceptor
p-type semiconductor.
ECE 250 – Elec t ron ic Devic es 48
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Carrier Concentrations
• For any semiconductor in thermale uilibrium n =n 2 where
• no = the concentration of free electrons.
o .
• ni = the intrinsic carrier concentration
⎟ ⎞⎜⎛ −= Eg BT ni exp23
ECE 250 – Elec t ron ic Devic es 49
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Extrinsic Carrier Concentrations
• For an n-type semiconductor with donor im urities the concentration of donor
impurities is Nd with units #/cm3.
• ,electrons in the n-type semiconductor is
o .
ECE 250 – Elec t ron ic Devic es 50
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Extrinsic Carrier Concentrations
• Since no po=ni
2
for any semiconductor inthermal equilibrium, and
• For an n-type semiconductor, no ≈ Nd
d
io
N
n p
2
=
• Where po is the concentration of holes in then-type semiconductor.
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ECE 250 – Elec t ron ic Devic es 53
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Current in Semiconductors
• The two processes that cause free electronsand holes to move in a semiconductor aredrift and diffusion.
• Drift – the movement of holes and electronsdue to an electric field
• Diffusion – the movement of holes and
electrons due to variations inconcentrations.
ECE 250 – Elec t ron ic Devic es 54
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Drift Current
• Assume that an electric field is applied to toa semiconductor.
• This field acts on holes and electrons.
ECE 250 – Elec t ron ic Devic es 55
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Drift Current-Electrons
• Electrons – The Electric
field creates a force in the E r
opposite direction of the
electric field – Attractive.dn
vs −
e • vdn is the drift velocity of
electrons.n J
r
•n
s e curren ens y
due to electrons.n-type
ECE 250 – Elec t ron ic Devic es 56
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Drift Current-Electrons
• The electrons acquire a drift velocity of r
s
•
ndn −=
n units of cm2/(volt-sec).
• n .
• For low-doped silicon, a typical number is= 2 -n .
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ECE 250 – Elec t ron ic Devic es 58
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Drift Current Density-Electrons
• Current = charge per unit time (coul/sec).• =
specific area = amps/unit area = coul/(sec-
2
ECE 250 – Elec t ron ic Devic es 59
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Drift Current Density-Electrons
E enenv J ndnn μ =−=• e = the charge on an electron = 1.602×10-19
coulombs.• n=concentration of electrons = #/cm3.
= 3.
223
chargecharge ampcmenvdn ===
secseccm cmcm⋅
ECE 250 – Elec t ron ic Devic es 60
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Drift Current - Holes
• Holes – The Electric field
creates a force in the E r
same direction of the
electric field.dp
vr+
h • vdp is the drift velocity of
holes. p J
r
• p
s e curren ens y
due to holes.n-type
ECE 250 – Elec t ron ic Devic es 61
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Drift Current-Holes
r
s
• Where μ p is the mobility of holes with units pdp =
o cm vo -sec .
• The units of vdp are cm/sec.
• For low-doped silicon, a typical number isμdp=480 cm2/volt-sec.
ECE 250 – Elec t ron ic Devic es 62
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Mobility - Aside
• Note that μn> μ p.
• .
• P-type and n-type devices operate the same.
, - .
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ECE 250 – Elec t ron ic Devic es 64
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r r
dpvh
r
dnvs −
e
r
p n J
n-type n-type
Drift current due to holes and electrons is in the same direction.
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ECE 250 – Elec t ron ic Devic es 66
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Ohm’s Law
• Another form of Ohm’s law is J=σE• .
• Noting that
E ep E en J pn
rrr
μ μ +=
• andrv
ECE 250 – Elec t ron ic Devic es 67
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Conductivity
We can find the conductivity of a
semiconductor as
pn epenσ +=
ECE 250 – Elec t ron ic Devic es 68
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(Cover Them)
ECE 250 – Elec t ron ic Devic es 69
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Excess Carriers
• So far we have assumed that thesemiconductor is in stead state.
• Suppose that we shine light on a
.• If the photons have sufficient energy, valence
create pairs of free electrons and holes.
ECE 250 – Elec t ron ic Devic es 70
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Excess Carriers
called excess holes (δ p) and excess free.
• When excess holes and free electrons are
create , t ese concentrat on o o es an
free electrons increase above the thermal
equ r um va ue
n = n + δn = + δ
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ECE 250 – Elec t ron ic Devic es 72
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Excess Carriers
• Generation – Creates free electrons – hole
airs.
• Recombination – Eliminates free electrons
.• Excess Carrier Lifetime – The mean time
exist before recombination.