Transcript LW2

LW4 Lecture Week 4-1
Heterojunctions
Fabrication and characterization of
p-n junctions
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Heterojunctions: Single heterojunction
2.9.5. Single heterojunctions: Energy band
diagrams for N-AlGaAs – p-GaAs and PAlGaAs/n-GaAs heterojunctions under
equilibrium
n-GaAs
p-AlGaAs
Ec = 0.252 eV
1.43eV
W
Ec
1.85eV
Eg ~ 1.9 eV
Ec
Ev = 0.168 eV
Ef
Ev
Fig. 35. Energy band diagram per above
calculations. N-p heterojunction.
Eg = 1.424 eV
Ev
-Xp0
0
Xn0
Fig. 36. Energy band diagram for a p-n
heterojunction.
2
Energy band diagram: Double Heterojunction
xp
-xn
p GaAs
0
P-AlGaAs
d
N AlGaAs
Eg1(GaAs)
N-p heterojunction
Ec(pGaAs-pAlGaAs)
Ec(n-p)
Eg2(p-AlGaAs)
=1.85eV
Ec
x
Ev(pGaAs-pAlGaAs)
VF=1.0 Volt
1.85eV= Eg2(AlGaAs)
Fig. 39. A forward biased NAlGaAs-pGaAsPAlGaAs double heterojunction diode.
Ev(n-p)
p-P heterojunction
Ev
-Xn0
0
Xp0
Fig. 42 Energy band diagram of a NAlGaAs-pGaAs-PAlGaAs
double heterostructure diode.
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Built-in Voltage in Heterojunctions
Fig. 33. Energy band diagram line up before equilibrium.
4
Built-in Voltage in Heterojunctions
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Built-in Voltage in Heterojunctions Cont.
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2.9.3.2. Built-in Voltage Method II: Gauss' Law
1
1
E mN  x N 0   Emp x po 
2
2
2
N A x 2po 
1  N D x No
 q


2   r 2 o
 r1 o 
V bi =
(145)
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2.9.4. Forward-Biased NAlGaAs-pGaAs Heterojunction
Concentrations
N-AlGaAs
pGaAs
ne
pe
np(x)=n(x)
n(x)
pno
-xn 0
npo
xp
X
Fig.34 Carrier concentrations in an n-p heterojunction
Electron diffusion from N-AlGaAs to the p-GaAs side,
Hole diffusion from pGaAs to the N-AlGaAs,
n = n p (x)- n po
2
1
d n
=
n for  > x > x p
d x 2 L2 n
(73)
p(x)= p e
+(x+ x N )
LP
= p No ( e
qV f
kT
- 1)e
+(x+ x N )
LP
for - x N > x > -
(162)
n(x)= n p (x) - n po = A e-
( x x p )
Ln
+ Be
( x x p )
Ln
J p (x) = -q D p
n(x)= n e
-(x - x p )
Ln
qV
f
= n po ( e kT - 1)e
-(x - x p )
Ln
for  > x > x p
(161)
dn
J n (x) = + qD n
dx
J n (x)=
q Dn n po ( E g1 )
Ln
qV f
( e kT - 1)e
-(x- x p )
Ln
for  > x > x p
J P (x)=
q D P p NO ( AlGaAs)
Lp
dp
dx
qV
f
( e kT - 1)e+
(x+ x N )
LP
(164)
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I-V Equation
 q Dn n po q DP p NO  qV f
( e kT - 1)
J = J n ( x p ) + J P (- x N ) = 
+
LP 
 Ln
Next we substitute the values of npo and pNo in Eq. 107
 D n ni2(GaAs ) D P ni2( AlGaAs )  qVf
 (e kT  1)
J = q
+

 L n N A,GaAs L P N D , AlGaAs 
J = J s( e
qV f
kT
- 1)
 Dn ni2(GaAs ) DP ni2( AlGaAs) 

J S = q
+

N
N
 Ln A,GaAs LP D , AlGaAs 
3

E
2
2
 Dn ni ( GaAs )
D P ni (GaAs )  mn1m p1  2  KTg
J = q
+
e


 Ln N A,GaAs LP N D , AlGaAs  mn 2 m p 2 


 qVf
 (e kT  1)


(170)
 D n ni2(GaAs )  qVf
 (e kT  1)
J n = q

 L n N A,GaAs 
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I-V Equation and Current Density Plot
3
ni2( E g 2 ,T )
ni2( E g 1 ,T )
 m m  2 ( E g 2  E g 1 )
kT
  N 2 P2  e
m m 
 n1 p1 
3

E E 
2
 Dn ni2( GaAs )
D P ni ( GaAs )  mn1m p1  2  g 2KT g 1  qVf
J = q
+
e
 (e kT  1)


 Ln N A,GaAs LP N D , AlGaAs  mn 2 m p 2 



Here, we have used the energy gap difference Eg=Eg2-Eg1. From Eq. 174 we can see that the
second term, representing hole current density Jp which is injected from p-GaAs side into NAlGaAs, and it is quite small as it has [exp-(Eg/kT)] term.
As a result, J ~ Jn(xp), and it is
I=Ip(-xn)+In(xp)
 Dn n
J n = q
 L n N A,GaAs
2
i ( GaAs )
In(xp)=0.051mA
 qVf
 (e kT  1)


3

 D P ni2( GaAs )  mn1m p1  2  Eg

 e KT
J P = q


 L P N D , AlGaAs  mn 2 m p 2 

I-Ip(-xn)
Ip(x>xp)

 qVf
 (e kT  1)


Ip(x<-xn)
In(xp)/e=0.011mA
Ip(-xn)=5.97pA
Not to Scale
Ip(-xn)/e
-xn
0 xp
-4
Lp=1.414x10 cm
Fig. 38B Current density plots.
Ln
10µm
x
10
Carrier Confinement
N-AlGaAs
r2
p-GaAs
(thickness
d)
r1
ND
NA
-xno
0
xpo
02122015 L4-1 new material
P-AlGaAs
r2
Thus, the addition of P-AlGaAs at
x=xp+d forces the injected electron
concentration quite small. That is, it
forces all injected carrier to recombine
in the active layer. This is known as
carrier confinement.
d+xpo
p-GaAs
(NA=1015 , npo=10-1cm-3)
ni2=1014cm-3
nn
ne
ne2
n(xp+d)
n-AlGaAs
d
npo
p-AlGaAs
(NA~1015 , npo~10-1*e-14cm-3)
ni2~1014cm-3 * e-Eg/kT
Fig .41. Minority carrier concentrations in p-GaAs and in p-AlGaAs.
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Energy band diagram of a double heterojunction
Eg1(GaAs)
N-p heterojunction
Ec(pGaAs-pAlGaAs)
Ec(n-p)
Eg2(p-AlGaAs)
=1.85eV
Ec
Ev(pGaAs-pAlGaAs)
1.85eV= Eg2(AlGaAs)
Ev(n-p)
p-P heterojunction
Ev
-Xn0
0
Xp0
Fig. 42 Energy band diagram of a NAlGaAs-pGaAs-PAlGaAs double
heterostructure diode.
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2.9.8 Double heterojunction with a quantum well
By reducing the thickness of p-GaAs layer to 50-100Å, we obtain a quantum well
double heterostructure as shown schematically in Fig. 42B, page 173.
AlxGa1-xAs
AlxGa1-xAs
GaAs
∆EC
∆Ec = 0.6∆Eg
∆Ev = 0.4∆Eg
L
∆EV
2
0
L
V(z)
0
z
-EG
z
2
∆EV
-EG+∆EV
Fig. 42 B GaAs quantum well with finite barriers produced by AlGaAs layers.
13
Photon confinement in a waveguide region formed by double heterojunction layers
(p.170)
When electron and holes recombine in the GaAs layer, they produce photons.
AlGaAs layers have lower index of refraction than GaAs layer. As a result it forms a
natural waveguide.
In the laser design example, we have mentioned various methods for the calculation of
modes in such a slab waveguide. Also we need to calculate the confinement factor G of
the mode. Confinement factor also determines the JTH. Generally, the confinement factor
becomes smaller as the thickness of the active layer becomes narrower. This also depends
on the index of refraction difference between the active and the cladding layers.
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2.8. Fabrication of Diodes
Interfacing of an n- and a p-type semiconductor forms a p-n junction (or
diode). Experimentally, this is done by one of the following methods
including:
•diffusion of p- impurities in n-Si,
•ion implantation of donor atoms in p-Si (generally this is followed by
annealing to eliminate the damage to the lattice caused by high energy
implantation), and
•epitaxial growth (depositing a p- layer on n-type substrate). In the case
of diffusion or ion implantation, the impurity or dopant concentration is
higher in the top layer than the substrate.
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Diffusion from an infinite source: Predeposition
p.143
N
   J
t
N
2 N
D
t
X 2
BN BN BN BN
Si Si Si
x 

N ( x, t )  N O 1  erf

2 Dt 

NO
Boron
Concentration
atoms/cm3
t p 3  t p 2  t p1
t p1
x j1
t p2
t p3
NB
x j 2 x j3
x
Fig. 23. The impurities distribution during predeposition. Note the
increasing junction depth as a function of predeposition duration.
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Junction depth measurements
Figure 24. (a) Sample before Diffusion (Width polished side up)
(b) Sample after Diffusion (p-type)
(c) Sample after back etch of p-Si diffused Layer.
Figure 25. Dicing and Mesa Formation
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Electrical Characterization of p-n diodes
Figure 26. (a) Left: Circuit connections for current source and voltage
meter. (b) Right: Sample after Diffusion (p-type)
Figure 27. C-V measurements
Figure 29. Solar cell
measurements
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