Fitzgerald-1999 Semiconductor Electronics some III - V compounds • Dominated by many nearly identical, highly engineered junctions... 3.225 11 The p-n Junction The Diode • Note that
Trang 13.225 7
Use of Minority Carrier Diffusion Equations
• Example: Light shining on a surface of a semiconductor
hν
G at x=0 (assume infinite
absorption coefficient to simplify
example)
G
p
x
p
D
t
p
h
h − ∆ +
∂
∆
∂
=
∂
∆
∂
τ
2
2
n-type
∆p(x)? 0
Steady state solution
=0 in bulk
x
h
h
h
h
ax
ax ax
ax
ax
ax
h
h
D
a
D
Be Ae Be
a
Ae
a
Be Ae
p
D
p
x
p
τ
τ
τ
1
2
2
2
2
=
+
= +
+
=
∆
∆
=
∂
∆
∂
−
−
−
try
Now use boundary conditions of the problem:
h
D
x
Be
p
A
p
x
τ
−
=
∆
=
∴
=
∆
∞
=
0
0 ,
@ Units of length:
minority carrier diffusion length, L h
h
L
x
h
h
h
e G
p
G
B
G p
x
−
=
∆
=
∴
=
∆
=
τ
τ
τ , 0
x
x p eD
J h h ∂
∆
∂
=
© E Fitzgerald-1999
Semiconductor Electronics
some III - V compounds
• Dominated by many nearly identical, highly engineered junctions
Trang 23.225 9
Junction Fabrication Processes
© H.L Tuller, 2001
CMOS Devices
Trang 33.225 11
The p-n Junction (The Diode)
• Note that dopants move the fermi energy from mid-gap towards either the
valence band edge (p-type) or the conduction band edge (n-type)
p-type material in equilibrium n-type material in equilibrium
n~ni /Na p~ni /Nd
+
=
C
d b g
F
N
N T k E
−
=
V
a b
F
N
N T
k
EF
Ev
EF
Ev What happens when you join these together?
© E Fitzgerald-1999
-+ + + +
Holes diffuse
Electrons diffuse
+ + +
+
-+ + +
+
-+ + + +
An electric field forms due to the fixed nuclei in the lattice from the dopants Therefore, a steady-state balance is achieved where diffusive
flux of the carriers is balanced by the drift flux
E
Drift and Diffusion
Trang 4Joining p and n
Ec
EF
Ev
Carriers flow under driving force of diffusion until EFis flat
-+ + + +
Holes diffuse
Electrons diffuse
© E Fitzgerald-1999
-+ + +
+
-+ + + +
W: depletion or space charge width
Metallurgical junction
ρ E
V
Vbi
dx
x
E=∫
ε
ρ )(
dx
x
E
p a n
dx N x
n
) ( 2
a d a d bi o r p
N N N
N e
V x
+
= εε
) ( 2
a d d a bi o
N e
V x
+
a d d a bi o r
N N N N e
V
Space Charge, Electric Field and Potential
© E Fitzgerald-1999
Trang 5What is the built-in voltage Vbi?
Ec
EF
Ev
eVbi=EFn-EFp
−
−
d V
i b V
n b
n T k N
p T k
−
−
=
V
a b V b
N T k N
p T
k
=
i d a b
N N e T k V
We can also re-write these to show that eVbiis the barrier to minority carrier injection:
T k eV n
bi
e n n
−
=
T k eV p
bi
e p p
−
=
nn
np
pn
pp
eVbi
eVbi
© E Fitzgerald-1999
Qualitative Effect of Bias
• Applying a potential to the ends of a diode does NOT increase current through
drift
• The applied voltage upsets the steady-state balance between drift and
diffusion, which can unleash the flow of diffusion current
• “Minority carrier device”
Ec
EF
Ev
nn
np
pn
pp
eVbi
eVbi
T k V V e n
a bi e n n
) ( −
−
V V e p
a bi e p p
) ( −
−
=
+eVa -eVa
© E Fitzgerald-1999
Trang 6Current Flow - Recombination, Generation
© H.L Tuller, 2001
• Forward bias (+ to p, - to n) decreases depletion region, increases diffusion
current exponentially
• Reverse bias (- to p, + to n) increases depletion region, and no current flows
ideally
Ec
EF
Ev
nn
np
pn
pp
eVbi-e|Va|
Qualitative Effect of Bias
Ec
EF
Ev
nn
np
pn
pp
eVbi+e|Va|
eVbi-e|Va|
eVbi+e|Va|
-
−
=
−
+
2 2
T k qV o T k qV
d i h h a i e
a b
a
e J e
N
n L
D N
n L
D
q
J
q T k
i
i
V
I
Linear, Ohmic
Rectification, Non-linear, Non-Ohmic
V=IR
V=f(I)
Solve minority
carrier diffusion
equations on each
side and determine
J at depletion edge
© E Fitzgerald-1999
Trang 7Devices
Jedrift
Ec
E F
Jhdrift
Ev
LED/Laser
Jediff
Jhdiff
© E Fitzgerald-1999
Potential Wells - Heterojunction Lasers
Energy bands of a light-emitting diode under forward bias for a double
heterojunction AlGaAs-GaAs-AlGaAs structure
Trang 8Transistors
Bipolar (npn)
Ec
EF
Ev
emitter
base
collector
Barrier, controlled by VEB
base emitter
collector
© E Fitzgerald-1999
Field Effect
© H.L Tuller, 2001
Trang 9Transistors
FET source gate drain
x
n
CMOS
© E Fitzgerald-1999
Polycrystalline Solar Cells
minority carrier lifetime
resistivity; reduced effective mobility
Trang 10Effect of Traps (Defects) on Bands
• Trapping (Fermi level in defect) creates depleted regions around defect
+
=
C
d b
g
F
N
N T
k
E
•EFposition in semiconductor away from traps in n-type material
•EFpulled to mid-gap in defect/trap area
Ec
EF
Ev
EFpulled to trap level in defect
Etrap
Depleted regions; internal electric field
Edonor
© E Fitzgerald-1999
Other Means to Create Internal Potentials:
• Different semiconductor materials have different band gaps and electron
affinity/work functions
• Internal fields from doping p-n must be superimposed on these effects:
Poisson Solver (dE/dx=V=ρ/ε)
EF
Vacuum level
Thin films
ate Potential barriers for holes and electrons can be created
inside the material
Heterojunctions
© E Fitzgerald-1999