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147.
Miki,
H., Omura,
Y.,
Ohmameuda,
T.,
Kumon,
M.,
Asada,
K.,
Izumi,
K.,
Sakai,
T.,
and Sugano,
T.
IEDM Tech. Dig.,
1989, Paper 34.7.1, p. 906.
148. Yamazaki, K., et
al.
Ext. Abstracts ofthe 8th Inter-
nat. Workshop on Future Electron Devices-Three
Dimensional
ICs
and Nano-Meter Functional
Devices, Kochi Prefecture, Japan,
1990, p. 105.
149. Aibara,
R.,
et al.
Ext. Abstracts
of
the 8th Inter-
nat. Workshop on Future Electron Devices-
Three Dimensional ICs and Nano-Meter Func-
tional Devices, Kochi Prefecture, Japan,
1990,
p. 113.
21
Optoelectronics
Revised
and
Expanded
by
Gregory
E.
Stillman
The Optical Spectrum
21-2
Radiometry
21-3
Terms and Definitions
Blackbody Radiation
Interaction
of
Optical Waves With Matter
21-9
Reflectance
Absorptance
Transmittance
Refraction
Optical Sources
21-10
Tungsten Lamps
Fluorescent Lamps
Arc Lamps
Light-Emitting Diodes
High-Intensity Visible LEDs
Superluminescent Diodes
Semiconductor Lasers
Optical Detectors
21-14
Terms
and
Figures
of
Merit
Characterization
of
Detectors
Ultimate Sensitivity
of
Detectors
Thermal Detectors
Quantum Detectors
Spectral Response
of
Semiconductor Detectors
21
-1
21
-2
REFERENCE DATA FOR ENGINEERS
RADIO
GAMMA^
I
ULTRA-
I
IKFRARED
11
RAYS
,
I
VlOLET
I
I
I
EHF SHF UHF VHF HF
MF
LF VLF
.I
I1
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
Optoelectronics is the technological marriage of the
fields of optics and electronics. It includes the genera-
tion and evaluation of electromagnetic radiation in the
optical wavelength range and its conversion into electri-
cal current or signals, the interaction of light with
matter, radiometry, and the characteristics of sources
and detectors.
THE OPTICAL SPECTRUM
The optical spectrum is generally defined to encom-
pass electromagnetic radiation with wavelengths in the
range from
10
nm to lo3
pm,
or frequencies in the
range from 300 GHz to 3000 THz (Fig.
1).
Other units are often used to describe the optical
spectrum, as discussed below. For engineering calcula-
tions, three significant figures usually give sufficient
accuracy. More precise values of the constants can be
obtained from
NBS/NIST
data.
Wavelength
h:
1
pm
=
10-3
mm
=
io3
nm
=
io4
A
Frequency (v
or
f).
1 cm-' (wave number)
=
30 GHz
=
3
X
10"
Hz
v1
cA
V
(wave number)
=
-
=
-
(cm-')
Photon energy
(E):
where the velocity of light in free space is
c
=
3
x
10'0
cnds
and Planck's constant
h
is
h
=
6.63
X
J.s
The optical spectrum is divided into three major
categories, as follows.
Ultraviolet:
Wavelengths shorter than those in the
visible spectrum and longer than for
X
rays are collec-
tively designated ultraviolet (UV). Ultraviolet is
cia@
fied according toowavelength as extreme (LOO-2000
A),
far (2000-3000
A),
or near (3000-3700
A).
Ultraviolet
is also sometimes designated as short-wave or long-
wave.
Visible:
Those wavelengths in the approximate range
3700-7500
A
can be perceived by the human eye and
are therefore collectively designated as visible light.
Visible light is classified according to the various colors
its wavelengths elicit in the mind of a standard observFr.
The major color categories
are
violet (3700:4550
A),
blue (4560-4?20
A),
green (4930-577q
A),
yellow
(5780-5970
b),
orange (5980-6220
A),
and red
(6230-7500
A).
Infrared:
Those wavelengths longer than those in the
visible spectrum and shorter than microwaves are col-
lectively designated infrared
(IR).
Infrared is classified
according to its wavelength as near (0.75-3 pm),
middle (3-6 pm), far (6-15
pm),
and extreme or
submillimeter
(15
pm-1
mm), although different au-
thors often use slightly different wavelength ranges for
these classifications.
OPTOELECTRONICS
21
-3
RADIOMETRY
Terms and Definitions
Radiometry is the science of measurement of optical
radiation at any wavelength, based simply on physical
measurements. Radiant energy cannot be measured
quantitatively directly, but must always be converted
into some other form such as thermal, electrical, or
chemical. Radiometry applies over the entire electro-
magnetic spectrum, not just the optical region. The
terms used
to
describe radiant power in radiometry are
summarized in Table
1.
All the terms used in radiome-
try are defined in terms of energy. When certain
quantities are considered as a function of wavelength or
frequency, the adjective “spectral” is used to modify
the term, and the symbol for the quantity is followed by
the appropriate spectral symbol,
A,
v,
or
V,
in parenthe-
ses. When the spectral concentration of a quantity is
considered, it is also described by the adjective spectral,
but in this case the symbol is subscripted with the
appropriate spectral quantity; for example the spectral
radiant excitance can be given as
WA
in units of
W.m-2.pm-’.
Blackbody Radiation
Any surface of a body with a temperature greater than
absolute zero
(T
=
0
K) is a source of radiation. The
term “blackbody” applies to a thermal radiator that
absorbs completely all incident electromagnetic radia-
tion regardless of the wavelength, the direction of
incidence, or the polarization. Such a radiator also has
the maximum emission possible for any wavelength and
in any .direction for a thermal radiator in thermal
equilibrium at a given temperature. Kirchhoffs law
states that for any body (all materials) in an isothermal
enclosure at temperature
T,
the ratio of the radiant
excitance (emittance),
W,
to
the absorptance,
a,
is
equal
to
the radiant excitance of a blackbody,
Wbb,
at
the same temperature:
W(T)/a
=
wbb(T)
Planck’s law gives the blackbody spectral power for
unpolarized radiation emitted at temperature
T
between
the wavelengths
A
and
A
+
dA
as
WA(A, T)dA
=
2m2hhm5
(ehclAkT
-
l)-’
dA
=
CldA/A5(eC2’AT
-
1)
where,
k
=
1.38
X
J-K-l is Boltzmann’s
C,
=
2nc2h
=
3.74
x
lo4
W.~m-~.pm~,
C2
=
ch/k
=
1.44
x
lo4
pm.K.
Fig.
2
shows the variation of
WA(A,
T)
with
A
for
various values
of
T.
The integral
of
WA(A,
T)dA
over
all
constant,
wavelengths gives the Stefan-Boltzmann law for total
blackbody radiant excitance
wbb(T)
in W/cm2,
wbb(T)
=
Wn(h,
T)dA
=
(2r5k4/15c2h3)T4
=
(T4C1/15C*4)T4
=
UT4
where
a
=
5.67
X
W.C~-~.K-~ is the Stefan-
Boltzmann constant. The blackbody spectrum has a
pronounced maximum at a particular wavelength
A,
for
a given temperature
T,
and the relationship
A,T
=
C2/4.9651
=
2897.8
pm*K
is known as Wien’s displacement law.
Planck’s law can also be specified in terms of
frequency or wave number instead of wavelength, and
these relations result in slightly different forms of
Wien’s displacement law.
For
calculations it is often
convenient to use the dimensionless quantity
x
=
hc/AkT
=
hv/kT
=
CZ/AT
for which Planck’s law becomes
WJx, T)dx
=
(15uT4/a4)[x3dn/(ex
-
l)]
The energy flux per unit area for wavelengths lying
between
x,
and
x2
can easily be calculated using the
series expansions below:
=
(15aT4/r4) x3dx/(e”
-
1)
where
=
hc/AokT
=
C2/A,T
and the energy flux per unit area for wavelengths
between
A2
and
A,
is given by
WhA
=
(15aT4/n4)
2
(~“/n~)[(nx)~
+
3(n~)~
+
6nx
+
61
1
n=l
x2
for
xi
2
2.
TABLE
1.
COMMON
RADIOMETRIC
TERMINOLOGY
N
4
Equation
h
Symbol Term Description Units
U
Radiant Energy transferred by
energy electromagnetic waves
J
U
Radiant energy Radiant energy per unit
density volume
J.c~-~
u
=
dUidV
radiant energy
W
P
=
dUidt
P
Radiant flux Rate of transfer
of
W
Radiant
Radiant flux emitted per
W
=
dPidA
emittance unit area
of
a source W.cm-2
Number of photons emitted
emittance
per second per unit area
intensity solid angle W.sr-l
J
=
dPidQ
Radiant photon
Phot0ns.s-'
aK2
Q
J
Radiant
Radiant flux per unit
N
Radiance Radiant flux per unit
H
Irradiance
Radiant flux incident per
solid angle per unit area W.cm-2.sr-'
N
=
Wiw
unit area W.cm-'
length interval at a particular
wavelength W.pm-'
PA
=
dPldA
H
=
dPidA
Spectral radiant
Radiant flux per unit wave-
PA
flux
n
rn
n
particular wavelength W.cm
-'
.pm
-I
WA
=
dWidA
rn
QA
Spectral radiant Radiant photon emittance per
n
photon emittance unit wavelength interval at a
rn
particular wavelength Photons.s-'.cm-'.pm-'
QA
=
dQidA
2
Spectral radiant Radiant intensity per unit wave-
c)
rn
JA
0
NA
NA
=
dNidA
P
Spectral Irradiance per unit wavelength
HA
interval at a particular wave-
e
(Radiant) Ratio
of
radiant emittance of a
WA
Spectral radiant Radiant emittance per unit
emittance wavelength interval at a
intensity
length interval at a particular
wavelength W.sr-'.pm-'
JA
=
didA
interval at a particular
s
6
s
Spectral radiance
Radiance per unit wavelength
wavelength
W.cm
-2.
sr
-
I
.
pm
-
I
irradiance
n
c)
2
rn
reflectance to incident radiant flux (Numeric)
rn
7
(Radiant) Ratio
of
transmitted radiant
n
transmittance flux to incident radiant
flux
(Numeric)
v)
length Wxm-2.pm-'
HA
=
dHidA
emissivity
source to that of a blackbody at
the same temperature (Numeric)
absorptance to incident radiant flux (Numeric)
I
(Y
(Radiant) Ratio
of
absorbed radiant flux
e
(Radiant)
Ratio
of
reflected radiant
flux
OPTOELECTRONICS
21
-5
103
102
101
100
*
g
10-
1
g
z
F
*-
10-3
10-4
N
1
s
10-2
-
k2
10-5
10-6
10-7
10-8
10-
1
100
10'
102
A
IN MICROMETERS
Fig.
2.
Blackbody spectral radiant emittance,
WA(h,
T),
for different blackbody temperatures.
A
similar expression can be derived for values of
xi
<
2
using
Wo-Ao(T)
=
uT4
(1
-
(15/,rr4)x2
[1/3
-
xo/S
+
~:/60
-
~0415
040
+
x2/272 160
-
x2/13 305 600
+
. .
.I}
which converges rapidly
for
xo
<
2.
Similar relations for the number of quanta or photons
emitted by a body at temperature
T
can be obtained by
dividing
WA(A,
T)
by the energy of the quanta at
wavelength
A,
hclh,
as
QA(A,
T)dA
=
(C3/A4)[dA/(eC2'AT
-
l)]
where
C3
=
Cl/hc
=
271~.
The variation of
QA(A,
T)
with
A
for several temperatures is shown in Fig.
3.
The
relation corresponding to Wien's displacement law
relating the wavelength of maximum quanta emission
A',
to the temperature is
A',T
=
3669.73
pm.K
for
A',
in micrometers, and the Stefan-Boltzmann law
for the total number of photons emitted per unit area in
blackbody radiation is
Qbb(T)
=
(rT4/2.75kT
=
LT'
T3
where
LT'
=
1.49
X
10" ~-'.cm-*.K-~. These rela-
tions are summarized in Table
2.
Since the blackbody radiant emission and radiant
photon emission are both functions of
AT,
it is possible
to plot a single normalized curve of blackbody radiant
emission as a function of
AT
that makes possible a
simple determination of the fraction
of
the peak emis-
sion at any value of
AT,
as well as the fraction of the
total radiant emittance below
AT
(Le., for values of
A0