7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 1/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 2/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 3/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 4/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 5/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 6/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 7/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 8/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 9/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 10/88

T/ (1 − R)

T/ (1 − R)Exact

T/ (1 − R)

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 11/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 12/88

(F (R)ω )12

ω

(F (R)ω )12

ω

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 13/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 14/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 15/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 16/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 17/88

T Sample (λ) = S Sample (λ)S Reference (λ)

RSample (λ) = S Sample (λ)S Reference (λ)

T Sample (λ) RSample (λ)

S Sample (λ)

S Reference (λ)

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 18/88

T Sample (λ) = T Reference (λ) S Sample (λ) − S Background (λ)S Reference (λ) − S Background (λ)

RSample (λ) = RReference (λ) S Sample (λ) − S Background (λ)

S Reference (λ) − S Background (λ)

RReference (λ) T Reference (λ)

S Background (λ)

k

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 19/88

θ = 0

E = E 0ei (kr − ωt )

ω k r

t

N i = n i + iκ i

N n

κ

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 20/88

R01 = (n0 − n1)2 + κ1

2

(n0 + n1)2 + κ12

T 01 = 4n0n1

(n0 + n1)2 + κ12

d

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 21/88

d

d d

R02 = r 01 + r12t01t10e− αd eiδ

1 − r10r 12e− αd eiδ

2

T 02 = n2

n0

t01t12e− αd2 ei δ

2

1 − r10r 12e− αd eiδ

2

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 22/88

tmn = 2N mN m + N n

r mn = N m − N nN m + N n

δ = 4πn 1d

λ

R02 T 02

d

R02 = R01 + R12T 01T 10e− 2αd

1 − R10R12e− 2αd

T 02 = T 01T 12e− αd

1 − R10R12e− 2αd

T mn = nn

nm| tmn |2

Rmn = |r mn |2

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 23/88

R03 = R02 + R23T 02T 021 − R02R23

T 03 = T 23T 02

1 − R20R23

R03 T 03

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 24/88

dz

J (z ) I (z )

J (z ) z > d

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 25/88

A = 1 − T − R

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 26/88

α = 2ωκ

c =

4πκλ

c λ

κ λ

T 1 − R

− 1

= 1 − R02

T 23T 02−

R23

T 23R20

1 − R02

T 02+ T 20

R23

R02 + T 02 < 1

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 27/88

T 1 − R

= T 23T 02

1 − R02

α n1 d

T 1 − R

= |t12 |2 | t23 |2

eαd − e− αd | r12 |2

R23

T 1 − R

= e− αd

T/ (1 − R) T / (1 − R)

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 28/88

T/ (1 − R)

T/ (1 − R)Exact T / (1 − R)

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 29/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 30/88

J (z ) I (z )

1s

dr (z )dz

= r (z )2 − 2(2a − 1)r (z ) + 1

r (z ) = J (z )I (z )

a = k + s

s

r (z )

a

a = (1 + R∞ )2

4R∞

f (R∞ ) = ks

= (1 − R∞ )2

4R∞

R∞ = r (∞ )

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 31/88

k

ε

N

ε = N 2

κ = αλ4π

= εi

n

αω

= εi

n C

n κ λ εi

ω C

i = C 11

ω2 |P cv |D j

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 32/88

D j

P cv

D j = 14π3 dS k

| k (E c − E v)

P cv = ψc | − e E ·r |ψv

S k E c − E v

i = C 21

(ω )2 (ω − E Bandgap ) p

αω = C (ω − E Bandgap ) p

ω E Bandgap p

C

p

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 33/88

(αω )1

p ω

α = 0

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 34/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 35/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 36/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 37/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 38/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 39/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 40/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 41/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 42/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 43/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 44/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 45/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 46/88

µ

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 47/88

o

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 48/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 49/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 50/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 51/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 52/88

± 10%

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 53/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 54/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 55/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 56/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 57/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 58/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 59/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 60/88

± 5%

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 61/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 62/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 63/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 64/88

0.01%

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 65/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 66/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 67/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 68/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 69/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 70/88

(F (R)ω )12

ω

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 71/88

(F (R)ω )12

ω

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 72/88

(F (R)ω )12

ω

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 73/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 74/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 75/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 76/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 77/88

x = 0 I (0)

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 78/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 79/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 80/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 81/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 82/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 83/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 84/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 85/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 86/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 87/88

7/21/2019 Measurement of Optical Bandgap Energies of Semiconductors

http://slidepdf.com/reader/full/measurement-of-optical-bandgap-energies-of-semiconductors 88/88