Formula Sheet Optical Devices - Electronic Devices - Electronics and Communication

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Electronic Devices: Optical Devices F orm ula Sheet
for GA TE
Basic Concepts
• Energy of a Photon : Energy asso ciated with a photon of ligh t.
E =hf =
hc
?
where h is Planc k’s constan t (6.626×10
-34
Js ), f is frequency (Hz ), c is sp eed of ligh t
(3×10
8
ms
-1
), ? is w a v elength (m ).
• Energy Bandgap : Minim um energy required for electron transition in semiconduc-
tors.
E
g
=
hc
?
threshold
where ?
threshold
is the threshold w a v elength for photon e mission/absorption.
Photo dio des
• Photo curren t : Curren t generated due to inciden t ligh t.
I
p
=?q
P
hf
where I
p
is photo curren t (A ), ? is quan tum e?iciency , q is electron c harge (1.602×
10
-19
C ), P is optical p o w er (W ), f is photon frequency .
• Resp onsivit y : Ratio of photo curren t to inciden t optical p o w er.
R=
I
p
P
=
?q
hf
(AW
-1
)
• Dark Curren t : Curren t in the absence of ligh t (dep ends on temp erature and mate-
rial).
Ligh t-Emitting Dio des (LEDs)
• Optical P o w er Output : P o w er emitted b y an LED.
P
out
=?
ext
·I·
E
g
q
where ?
ext
is external quan tum e?iciency , I is forw ard curren t (A ), E
g
is bandgap
energy (eV ).
• W a v elength of Emission : Determined b y the bandgap.
?=
hc
E
g
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Page 2


Electronic Devices: Optical Devices F orm ula Sheet
for GA TE
Basic Concepts
• Energy of a Photon : Energy asso ciated with a photon of ligh t.
E =hf =
hc
?
where h is Planc k’s constan t (6.626×10
-34
Js ), f is frequency (Hz ), c is sp eed of ligh t
(3×10
8
ms
-1
), ? is w a v elength (m ).
• Energy Bandgap : Minim um energy required for electron transition in semiconduc-
tors.
E
g
=
hc
?
threshold
where ?
threshold
is the threshold w a v elength for photon e mission/absorption.
Photo dio des
• Photo curren t : Curren t generated due to inciden t ligh t.
I
p
=?q
P
hf
where I
p
is photo curren t (A ), ? is quan tum e?iciency , q is electron c harge (1.602×
10
-19
C ), P is optical p o w er (W ), f is photon frequency .
• Resp onsivit y : Ratio of photo curren t to inciden t optical p o w er.
R=
I
p
P
=
?q
hf
(AW
-1
)
• Dark Curren t : Curren t in the absence of ligh t (dep ends on temp erature and mate-
rial).
Ligh t-Emitting Dio des (LEDs)
• Optical P o w er Output : P o w er emitted b y an LED.
P
out
=?
ext
·I·
E
g
q
where ?
ext
is external quan tum e?iciency , I is forw ard curren t (A ), E
g
is bandgap
energy (eV ).
• W a v elength of Emission : Determined b y the bandgap.
?=
hc
E
g
1
Solar Cells
• Short-Circuit Curren t : Curren t under zero v oltage.
I
sc
=qAG(L
n
+L
p
)
where A is the area (m
2
), G is generation rate (m
-3
s
-1
), L
n
and L
p
are diffusion
lengths for electrons and holes.
• Op en-Circuit V oltage : V oltage when no curren t flo ws.
V
o c
=
kT
q
ln
(
I
L
I
0
+1
)
where k is Boltzmann’s constan t (1.381×10
-23
JK
-1
), T is temp erature (K ), I
L
is
ligh t-generated curren t, I
0
is rev erse saturation curren t.
• Fill F actor : E?iciency of p o w er deliv ery .
FF=
P
max
I
sc
V
o c
• E?iciency : Ratio of output p o w er to inciden t p o w er.
? =
P
max
P
in
=
FF·I
sc
·V
o c
P
in
Lasers
• Threshold Curren t : Minim um curren t for lasing.
I
th
=
qV
?
i
t
(N
tr
+
1
Gg
0
)
where V is activ e v olume, ?
i
is in ternal quan tum e?iciency , t is carrier lifetime, N
tr
is
transparency carrier densit y , G is confinemen t factor, g
0
is gain co e?icien t.
• Optical Gain : Gain required for lasing.
g =Gg
0
(N -N
tr
)
where N is carrier densit y .
Key Notes
• Standard v alues: h = 6.626 × 10
-34
Js , c = 3 × 10
8
ms
-1
, q = 1.602 × 10
-19
C ,
k =1.381×10
-23
JK
-1
.
• Use SI units for GA TE calculations.
• F or photo dio des and solar cells, consider material prop erties (e.g., silicon, GaAs) for
bandgap and e?iciency .
• Chec k for temp erature dep endence in solar cell parameters.
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