measurement of optical bandgap energies of semiconductors
DESCRIPTION
A method for bandgap energy determination using diuse reection is presentedand compared to the traditional integrating sphere method. We have found thebandgap energies of ZnO, TiO 2 , Cu 2 O, Si, SnZrS 3 , SnZrSe 3 , Sn 2 S 3 , and BiCuOSepowders with both methods and found they agree within 0.03 eV. We havemeasured scattering from powder material in the infrared region of the spectrumwith a linear wavelength dependence. We have measured optical bowing of thebandgap energies of the SnZrS 3-x Se x system. We also describe in depth the OceanOptics spectrometer and its components.TRANSCRIPT
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T/ (1 − R)
T/ (1 − R)Exact
T/ (1 − R)
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(F (R)ω )12
ω
(F (R)ω )12
ω
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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)
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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
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θ = 0
E = E 0ei (kr − ωt )
ω k r
t
N i = n i + iκ i
N n
κ
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R01 = (n0 − n1)2 + κ1
2
(n0 + n1)2 + κ12
T 01 = 4n0n1
(n0 + n1)2 + κ12
d
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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
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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
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R03 = R02 + R23T 02T 021 − R02R23
T 03 = T 23T 02
1 − R20R23
R03 T 03
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dz
J (z ) I (z )
J (z ) z > d
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A = 1 − T − R
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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
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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)
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T/ (1 − R)
T/ (1 − R)Exact T / (1 − R)
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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 (∞ )
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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
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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
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(αω )1
p ω
α = 0
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µ
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± 10%
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