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LW4 Lecture Week 4-1

Heterojunctions

Fabrication and characterization of

p-n junctions

2

Heterojunctions: Single heterojunction

1.85eV

1.43eVEc = 0.252 eV

Ev = 0.168 eV

p-AlGaAs n-GaAs

Ec

Ev

W

0-Xp0 Xn0

Ec

Ev

Ef

Eg ~ 1.9 eV

Eg = 1.424 eV

Fig. 36. Energy band diagram for a p-n heterojunction.

Fig. 35. Energy band diagram per above calculations. N-p heterojunction.

2.9.5. Single heterojunctions: Energy band diagrams for N-AlGaAs – p-GaAs and P-AlGaAs/n-GaAs heterojunctions under equilibrium

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Energy band diagram: Double Heterojunction

N AlGaAs p GaAs

0

-xnxp

x

VF=1.0 Volt

d

P-Al

GaA

s

Fig. 39. A forward biased NAlGaAs-pGaAs-PAlGaAs double heterojunction diode.

Eg2(AlGaAs)

Eg2(p-AlGaAs)=1.85eV

Ev(n-p)

Ev(pGaAs-pAlGaAs)

p-P heterojunction1.85eV=

Ec(pGaAs-pAlGaAs)

Eg1(GaAs)

Ec(n-p)

Ec

Ev

0-Xn0 Xp0

N-p heterojunction

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.

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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

or

poA

or

NoD

pompNmNbi

xNxNq

xExE2

1=V

1

2

2

2

0

2

1

2

1

(145)

2.9.4. Forward-Biased NAlGaAs-pGaAs Heterojunction

8

0

N-AlGaAs pGaAs

X

pe

pno

ne

npo

Concentrations

np(x)=n(x)n(x)

xp-xn

Fig.34 Carrier concentrations in an n-p heterojunction

x>x> for nL

1=

xd

ndp

n22

2

n-(x)n=n pop

(73)

eB+eA=n-(x)n=n(x) L

xx

L

xx-

pop n

p

n

p )()(

x>x> for e1)-e(n=en=n(x) pL

)x--(x

kT

Vq

poL

)x--(x

n

pf

n

p

(161)

dx

ndqD+=(x)J nn

x>x> for e1)-e(L

EnDq=(x)J pL

)x-(x-

kT

Vq

n

gponn n

pf

)( 1

Hole diffusion from pGaAs to the N-AlGaAs,

(164)

Electron diffusion from N-AlGaAs to the p-GaAs side,

->x>x- for e1)-e(p=ep=p(x) NL

)x++(x

kT

Vq

NoL

)x++(x

P

Nf

P

N

(162)

dx

pdD-q=(x)J pp

e1)-e(L

pDq=(x)J L

)x+(x+

kT

Vq

p

AlGaAsNOP

P P

Nf)(

I-V Equation

9

1)-e(L

pDq+

L

nDq=)x(-J+)x(J=J kT

Vq

P

NOP

n

ponNPpn

f

)1( ,

2)(

,

2)(

kT

qVf

AlGaAsDP

AlGaAsiP

GaAsAn

GaAsin eNL

nD+

NL

nDq=J

Next we substitute the values of npo and pNo in Eq. 107

1)-e(J=J kT

Vq

s

f

,

2)(

,

2)(

AlGaAsDP

AlGaAsiP

GaAsAn

GaAsin

S NL

nD+

NL

nDq=J (170)

)1( 2

3

22

11

,

2)(

,

2)(

kTqVfKT

E

pn

pn

AlGaAsDP

GaAsiP

GaAsAn

GaAsinee

mm

mm

NL

nD+

NL

nDq=J

g )1( ,

2)(

kTqVf

GaAsAn

GaAsinn e

NL

nDq=J

I-V Equation and Current Density Plot

10

)1( ,

2)(

kTqVf

GaAsAn

GaAsinn e

NL

nDq=J

)1( 2

3

22

11

,

2)(

kTqVfKT

E

pn

pn

AlGaAsDP

GaAsiP

P eemm

mm

NL

nDq=J

g

)1( 122

3

22

11

,

2)(

,

2)(

kTqVfKT

EE

pn

pn

AlGaAsDP

GaAsiP

GaAsAn

GaAsinee

mm

mm

NL

nD+

NL

nDq=J

gg

)(2

3

11

222

),(

2),(

12

1

2 kT

EE

pn

PN

TEi

TEigg

g

g emm

mm

n

n

Here, we have used the energy gap difference DEg=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 N-AlGaAs, and it

is quite small as it has [exp-(DEg/kT)] term.

As a result, J ~ Jn(xp), and it is

In(xp)/e=0.011mA

Ln

x

Ip(-xn)/e

-xn 0

In(xp)=0.051mA

Lp=1.414x10-4cm 10µm

Ip(-xn)=5.97pA

xpNot to Scale

Ip(x<-xn)

I=Ip(-xn)+In(xp)

I-Ip(-xn)

Ip(x>xp)

Fig. 38B Current density plots.

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Carrier Confinement 02122015 L4-1 new material

N-AlGaAsr2

0 xpo-xno

p-GaAs(thickness

d)r1

NDNA

P-AlGaAsr2

d+xpo

n-AlGaAs d p-AlGaAs

p-GaAs

(NA=1015 , npo=10-1cm-3)

ni2=1014cm-3

(NA~1015 , npo~10-1*e-14cm-3)

nn

ne

ni2~1014cm-3 * e-Eg/kT

npo

ne2

n(xp+d)

Fig .41. Minority carrier concentrations in p-GaAs and in p-AlGaAs.

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.

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Energy band diagram of a double heterojunction

Eg2(AlGaAs)

Eg2(p-AlGaAs)=1.85eV

Ev(n-p)

Ev(pGaAs-pAlGaAs)

p-P heterojunction1.85eV=

Ec(pGaAs-pAlGaAs)

Eg1(GaAs)

Ec(n-p)

Ec

Ev

0-Xn0 Xp0

N-p heterojunction

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.

2L

2L

0

AlxGa1-xAs AlxGa1-xAsGaAs

∆EV

∆EC

0

V(z)

z

-EG

∆EV

-EG+∆EV

z

∆Ec = 0.6∆Eg

∆Ev = 0.4∆Eg

Fig. 42 B GaAs quantum well with finite barriers produced by AlGaAs layers.

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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: Predepositionp.143

Dt

xerfNtxN O

21),(

2

2

N ND

t X

Jt

N

BoronConcentration

atoms/cm3

x

NB

3pt

1pt2pt

123 ppp ttt

1jx 2jx 3jx

ON

Fig. 23. The impurities distribution during predeposition. Note the increasing junction depth as a function of predeposition duration.

BN

Si

BN

Si

BN

Si

BN

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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