Scintillation Detectors for Operation in High Magnetic Fields: Recent Developments Based on
NEW DEVELOPMENTS IN PHOTOCONDUCTIVE DETECTORS …
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NEW DEVELOPMENTS IN PHOTOCONDUCTIVE DETECTORS
S. Han
11th Topical Conference on High Temperature Plasma Diagnostics M o n t e e y , CA, USA May 12-16, 1996 (FULL PAPER)
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New developments in photoconductive detectors
S. Han
Los Alamos National Laboratory, NIS-5, E540, Los Alamos, NM 87545
Nearly ideal for detecting ionizing radiation, wide bandgap semiconductors present
a possibility of having outstanding radiation hardness, fast charge collection and low
leakage current that will allow them to be used in high radiation, high temperature, and
chemically aggressive environments. Over the past few years, the improvements in the
electrical quality of wide bandgap semiconductors have progressed enormously. One
particular wide bandgap semiconductor, diamond, has properties which may be ideal for
radiation detection.
Since the discovery of low pressure and low temperature deposition of diamond, the
possibility of large area diamond films have become a reality. Over the past few years,
great progress has been made in advancing the electrical quality of chemical-vapor-
deposited (CVD) diamond. Presently, unprecedented diamond wafer size of 7 in. diameter
is possible. Due to both the present electrical quality and the available size, the utilization
of diamond in radiation detection applications is not just a dream but a reality. The
progression of CVD diamond’s electrical properties in the last few years will be presented
along with what is currently possible.
Applications of CVD diamond for the National Ignition Facility 0 diagnostics will
be reviewed. In addition, a brief review concerning other possible wide bandgap
semiconductors for ICF diagnostics will be presented.
Electronic mail: han @lanl.gov
2
1. INTRODUCTION
Much of the present day radiation detection relies on silicon-based photodiodes or
p-i-n diodes. This reliance is possible because the majority of the operational environments
is nominally absent of radiation fields that may cause extensive radiation damage to the
silicon devices. In addition, silicon XUV photodiodes have high sensitivities to soft x-rays
(as high as 270 mA/W1 between 50 eV and 5 keV). and are readily available in large
quantities. A few complications with Si-photodiodes are sensitivity to optical radiation and
are easily damaged by neutrons. Another detection device for soft x-ray energies is the
vacuum x-ray diodes (XRD). Although often used for x-ray detection, XRDs have
notoriously poor and spectrally-dependent sensitivity. Therefore, a need exists for
sensitive yet spectrally flat and optically insensitive x-ray detectors. In addition, the
planned National Ignition Facility (NIF) operational environment will require that the x-ray
detectors at be radiation damage resistant, yet fast and sensitive.
A class of semiconductors called wide bandgap semiconductors offers an attractive
alternative to Si and XRD detector technologies for x-ray detection applications at NIF.
These semiconductors have bandgaps in the range 2 - >6 eV. (Thus the name for the
class.) They present a possibility of nearly ideal photoconductive detectors with
outstanding radiation resistance, fast charge collection and low leakage current. In
addition, some of these miiterials may be minimally sensitive to lo and 30 driving lasers at
NIF. One notable wide bandgap semiconductor that has been used already for z-pinch
experiments is diamond.2
Diamond has received a great attention with the advent of Chemical Vapor
Deposition (CVD). The process of CVD has allowed diamond synthesis3 under low
pressure and temperature. The resultant .material is polycrystalline. The CVD growth
method makes large area diamond fdms possible which allows monolithic integrated circuit
fabrication technology to be used in diamond photoconductive detector fabrication.
Both natural single crystal and polycrystalline diamond have been used for various
3
radiation detection purposes such as the detection of x-rays? y-rayss, high-energy charged
particles6 and neutrons.7 CVD diamond has also been shown to be an efficient UV-
imager.8 In fact, Gudden and Pohlg used a single crystal natural diamond to study its
optical absorption characteristics in 1923 because diamond was available in a large single-
crystal form with relatively high purity in comparison to other semiconductors.
Diamond photoconductive detectors have many advantages over silicon-
photodiodes . Diamond has faster response due to larger saturated carrier drift velocity10 (a
factor of 2 greater then Si) and lower dielectric constant, extremely low leakage current at
room temperature, and higher resistance to atomic displacement (displacement threshold is
approximately 43 eV,11 compared with approximately 20 eV for silicon). Due to its large
band gap, a junction is not necessary to reduce the leakage current for proper operation of
the detector at room temperature. Therefore, a detector can be made into a simple metal-
semiconductor-metal (MSM) device with a mode of operation being that of a
photoconductor,12 and is also referred to as a conductivity modulated detector13 when it is
applied to detect particles rather than photons. One main advantage of using C b diamond
films as photoconductive detectors is that the growth chemistry may be altered to
accomplish desired detector sensitivity and speed by optimizing the incorporation or
reduction of structural defects to adjust charge collection efficiency and carrier
recombination times. Furthermore, the large bandgap also serves as a'built-in filter against
the optical radiation.
II. PROPERTIES OF CVD DIAMOND
In a CVD process used to grow diamond, a mixture of methane and atomic
hydrogen is excited with an energy source such as microwave, direct current, etc. The
resultant reactive mixture is brought to a contact with a substrate. At this point both
graphitic (sp2) and diamond (sp3) bonds are formed. The excess hydrogen serves as a
preferential etchant to graphitic bonds. Resulting diamond from this growth process is
4
polycrystalline (Fig. 1) in nature primarily due to the lattice mismatch between the substrate
and the diamond film. The characteristic sp3 bonding has been verified and proven through
Raman spectroscopy with a characteristic Raman line at 1332 cm-1.14
Much of the physical and optical properties of CVD diamond is similar to single-
crystal form of diamond. However, the charge transport properties of CVD diamond can
be vastly different. This can be understood from the point of view that the charge transport
is sensitive to the imperfections in the crystal whether they are structural defects or
impurities. In the evaluation of the charge transport properties, a definition of charge
collection distance, d, is used and is defined as
d = pzE (1)
where p = carrier mobility, z = carrier lifetime, and E = applied electric field. This quantity
is used as a figure of merit in measuring the quality of the CVD films because pz product
can be a sensitive representation of the extent of defect incorporation during the growth of
the film.
Because CVD diamond film is polycrystalline, the carrier transport pioperties are
expected to degrade if the carriers are transported across grain boundaries. The extent of
degradation becomes important in the cases where the photoconductor is made to be a
surface device in the geometry very similar to Surface Acoustic Wave (SAW) devices since
the free carriers drift toward grain-boundaries where they either become trapped or
scattered. It has been shown that the grain-boundary degrades carrier transport by a factor
of 2-3.15
Since the start of the charge collection distance measurements in 1989, the value has
increased from c0.1 pm to a value greater than 100 pm (Fig. 2). This represents a factor
of 104 improvement in the quality of the CVD films. This is a result of reducing defect and
impurity incorporation in the films through improved growth processes.
The majority of the gain in the collection distance has been accomplished through
increasing the carrier lifetime. At the current state of the CVD films, the mobility is thought
5
to have reached a theoretical limit. Therefore, by reducing the concentration of
recombinatiodtrapping centers the carrier lifetime is increased thereby allowing the charge
collection distance to increase further.
111. RADIATION DAMAGE RESISTANCE OF CVD DIAMOND
One of the attractive properties of diamond is its strong bond strength. This
inherently leads to high radiation damage resistance in comparison to other tetrahedrally
bonded semiconductors. Previous work16 regarding radiation damage in diamond used
single crystal natural diamond to show that diamond radiation detectors are two orders of
magnitude more neutron-damage resistant than similar silicon radiation detectors. But, one
of the unknowns for the CVD diamond film is the influence of the polycrystallinity of the
material on the radiation damage resistance although intra-crystalline resistance should be
similar to single crystal'diamond.
In the past few years, a variety of particles has beenused in an attempt'to assess the
damage resistance of CVD diamond. The damage resistance was assessed by measuring
the charge collection distance before (do) and ifter (d) the irradiation of CVD diamond
samples at an applied electric field of 10 kV/cm. It has been shown that CVD diamond is
radiation damage resistant to 300-MeV pions with the fluence level up to 4x1014 cm-2.17
This is evidenced by the fact that the collection distance after the irradiation did not decrease
The same type of assessment was made with 500-MeV protons. In this case,
however, the current induced by the incident protons was also monitored (Fig. 4). It is
clear that the induced current due to protons reduced to the level of the current in the "dark"
when the beam is turned off and this baseline dark leakage current did not vary up to
4x1013 cm-2. In the case for a Si-photodiode in the same beam, the increase in the dark
leakage current is dramatic as a function of proton fluence in the same range (Fig. 5).
Furthermore, the ratio of d to do did not decrease after the fluence level of 4x1013 cm-2
(Fig. 6) .
In an attempt to observe any decrease in d as a function of damage, 5-MeV a-
particles were then used. The relative decrease in d is approximately a factor of 1.3 at a
fluence level of 1x1013 cm-2 (Fig. 6). Even at the maximum fluence level of 1x15 cm-2,
which corresponds to 10 Grad of absorbed dose, d is only reduced by a factor of 2.5. The
reduction in d is due to the vacancy and interstitial production by the incident ions.
In all cases except for the a-particle irradiation, the ratio of charge collection
distance after to before the irradiation increases by a factor of 1.2 - 1.6. This appears to
suggest that the irradiation of the sample improves the quality of the material. This paradox
can be resolved by an hypothesis that the free charge carriers from ionization passivates the
existing carrier trapping centers thereby increasing the effective carrier lifetime. The
passivation is likely due to the large bandgap of diamond and the fact that any impurity or
defect introduces electrically active deep (>>kT) trap center. Due to the depth of the traps,
the thermal excitation of the trapped carriers back to either conduction or valence band is
unlikely thereby preventing these passivated traps from participating in further
trapping/recombination. Furthermore, a piece of evidence that supports the hypothesis is
that after an exposure to a broadband light source, the charge collection distance is reduced
to that of the unirradiated value. This fact also substantiates the extent of diamond's
radiation resistance.
IV. POLYCRYSTALLINE CVD DIAMOND-BASED TRANSMISSION
DIFFRACTION GRATING SOFT X-RAY SPECTROMETER
One of the first applications of polycrystalline CVD diamond for soft x-ray
detection appears to be in the area of time-dependent soft x-ray spectrometry at NIF to
measure time-dependent radiation temperatures of inertial confinement fusion targets. This
is due to the fact that the operational environment at NIF will be extremely harsh in terms of
6
7
radiation fields, target debris, and plasma confinement times (e100 ps). Also, the expected
radiation temperature is 300 eV** black body at NIF which is hotter than the temperatures
achieved at the Nova facility in Lawrence Livermore National Laboratory. Therefore, the
expected soft x-ray spectrum will effectively span to about 3 keV. The transport properties
of diamond that were described in sec. I along with the short soft x-ray photon absorption
length (Fig. 7), which was calculated using XCAL,19 up to 3 keV appear to be extremely
attractive for the N F environment. With this in mind, a soft x-ray spectrometer based on a
transmission grating (TG) and polycrystalline CVD diamond photoconductors has been
devised.
For the present development, only a single channel diamond photoconductor was
used in conjunction with a TG with 2000 8, period made of free-standing gold bars. The
following discussion will only concentrate on the response of the single channel detector.
Of course in the future, a monolithic multichannel CVD diamond photoconductorflG
spectrometer will be built and the response measured.
A polycrystalline CVD diamond film with the thickness of 200 pm w k purchased
from a commercial supplier.20 The film was then polished with a diamond impregnated
polishing wheel to a surface roughness of approximately 10 pm RMS. Then, a single
channel photoconductive detector with a surface metal contact structure (Fig. 8) was
fabricated on the polished side to be used as the detector for a particular x-ray energy from
TG-dispersed x-rays. The channel width on the contact structure was 75 pm with the
contact strip width being 25 pm. The applied bias was 150 VDC. More detailed
description and the fabrication of the photoconductor can be found elsewhere.21
In order to spectrally calibrate the detector and the grating, a calibrated CCD camera
was placed immediately behind the detector. The source of x-rays was laser-induced
plasma from a samarium target at the TRIDENT22 facility in Los Alamos National
Laboratory. The detector was mounted at a spatial position that corresponded to 2.5 keV x-
ray. The duration of the x-ray pulse was approximately 1.4 ns. The recording of the
8
photoconductor output was accomplished with a 7 GHz single shot transient digitizer.23
The complete schematic of the measurement system can be seen in Fig. 9.
The spectral distribution of x-rays which was recorded with the CCD camera is
shown in Fig. 10. The black shadow in the figure is the detector assembly behind the TG.
It can be seen clearly that the 5 A x-ray wavelength is subtended by the detector where the
active detector area is shown with the white outline. The response of the detector is shown
in Fig. 11. The detector reproduced the driving x-ray pulse, temporally, with high fidelity
evidenced by the fact that the FWHM of the detector response was identical to the x-ray
pulse width. What is unknown presently, however, is the noise after the falling edge. The
cause is still being examined.
Given the contrast in the CCD image, a rough estimate of the detector sensitivity
can be made. The incident power on the detector is estimated to be approximately 230
mW. Given that the signal height is approximately 150 mV, the sensitivity at 2.5 keV is
estimated to be 13 mA/W. This is a few orders of magnitude greater in sensitivity in
comparison to conventional XRDs.
In addition, a similar detector has been used to measure the spectral flatness of the
detector to a range of x-ray wavelength from 240 8, to 120 A. The measured sensitivity is
seen to be approximately flat within 10% (Fig. 12). However, the response is seen to be
different for the two different applied field strengths. This is due to the relative
contributions in the signal by photoemission and photoconduction because the detector is a
surface type. The variation in the spectral flatness in the detector sensitivity is due to
extremely short absorption depth of the x-rays of the given wavelengths. The extremely
shallowness allows for the free carriers to be diffused, across the applied electric field
lines, to the surface where they are trapped at the surface defects in addition to the bulk
carrier trapping. This is further evidenced- by the fact that the sensitivity is greater at the
shorter wavelength in Fig. 12A.
9
V. OTHER POSSIBLE WIDE BANDGAP SEMICONDUCTORS AS
PHOTOCONDUCTIVE DETECTORS FOR SOFT X-RAYS
Much of the wide bandgap semiconductor research other than CVD diamond has
been driven by the need for semiconductors to be operated at high temperatures and the
need for short wavelength optoelectronic devices such as blue/violet LEDs and blue lasers.
The two of the most advanced material for a possible x-ray detection purposes are Sic and
GaN. The properties of these materials are listed in Table 2. Reviews on these materials
can be found in Ref. 24.
In comparison to diamond, the carrier transport properties such mobilities are
inferior. But this is compensated by the fact that the purity of these materials are much
higher than CVD diamond. Furthermore, the materials can be doped either n or p type
whereas doping of diamond is only possible as a p-type. Similar to diamond, S ic and
GaN do not have native oxide layers that act as dead-layers which is a great advantage over
silicon. Furthermore, GaN has been shown to have responsivities up to 2 idvw in the
spectral range c360 nm with flat spectral resp0nsivity.x In the future, soft x-ray detectors
made from these materials should be considered and will be considered in the Los Alamos
National Laboratory's detector program.
ACKNOWLEDGMENT
I wish to acknowledge John Joseph, Dr. Ron Wagner for their assistance and the
collaborative work of the DIAMAS and RD-42 collaborations under which much of the
CVD diamond material characterization work was accomplished. My appreciation also
goes to the SPHINX staff of Sandia National Laboratories-Albuquerque, Tom Hurry of
TRIDENT facility at Los Alamos National Laboratory. I would like to thank A. Lalime and
G. Han-Lalime for their editorial assistance. Finally, some of the presented work could not
10
have been achieved without constant vigilance of Dr. James Cobble. This work was
performed under auspices of the U. S. Department of Energy by Los Alamos National
Laboratory under Contract No. W-7405-Eng-48.
1 International Radiation Detectors, 2545 West 237th St, Suite I, Torrance, CA 90505-
5529
2 See R.B. Spielman, Rev. Sci. Instrum., 63 (10) (1992) 5056; R.B. Spielman, Rev. Sci.
Instrum., 66 (1) (1995) 867
3 J. Angus and C. Hyman, Science, 241 (1988) 913; and W. Yarbrough and R. Messier,
Science, 247 (1990)) 913.
4 D. R. Kania, L. Pan, P. Bell, 0. N. Landen, H. Kornblum, P. Pianetta and M. D.
Perry, J. Appl. Phys., 68 (1) (1990) 913; R.B. Spielman, Rev. Sci. Instrum., 66 (1)
(1995) 867
5 See for example, R. J. Keddy, T. L. Nam and R. C. Burns, Phys. Med. Biol., 32(6)
(1987) 751; P. J. Fallon, T. L. Nam, R. J. Keddy, R. C. Burns and J. H. Grobbelaar,
Appl. Radiat. Isot., 41( 1) (1990) 35.
6M. Franklin, A. Fry, K. K. Gan, S. Han, H. Kagan, D. Kania, R. Kass, S. K. Kim,
R. Malchow, F. MOKOW, S. Olsen, W. F. Palmer, L. S. Pan, F. Sannes, S. Schnetzer,
R. Stone, Y. Sugimoto, G. B. Thomson, C. White and S. Zhao, NIM, A315 (1992) 39.
7 T. G. Miller, NIM, 43 (1966) 338.
M. A. Plano, M. I. Landstrass, S. Han, S. McWilliams and D. R. Kania, Proc. 3rd Int.
Symp. on Diamond Materials, The Electrochemical Society, Inc., Pennington, New
Jersey, 93-17 (1993) 986.
9 B. Gudden and R. Pohl,.Z. Physk, 17 (1923) 331.
10 RD42 Collaboration, CERNDRDC 94-2 1, DRDC-P56, 1994.
11 J. Koike, D. M. Parkin and T. E. Mitchell, Appl. Phys. Lett., 60(12) (1992) 1450.
12 R. Bube, Photoconductivitv of Solids, Robert E. Krieger, Huntington, NY, 1978.
11
13 S. Han, R.S. Wagner, J. Joseph, M.A. Plan0 and M. Dale Moyer, Rev. Sci. Inst. 66
(12) (1995) 5516.
9 S ee for example J.E. Field, The Properties of Diamond, Academic Press, London,
1979.
15 S. Han and R.S. Wagner, Appl. Phys. Lett., accepted for publication, 1996.
16 S.F. Kozlov, R. Stuck, M. Hage-Ali, anbd P. Siffert, IEEE Trans Nuc Sci, NS22
(1975) 160.
17 C. Bauer, et al, NIh4 paper
18 J.D. Kilkenny, M.D. Cable, C.A. Clower, B.A. Hammel, V.P. Karpenko, R.L.
Kauffman, H.N. Kornblum, B. J. MacGowan, W. Olson, T.J. Orzechowski, D. W.
Phillion, b. Chrien, B. Failor, A. Hauer, R. Hockaday, J. Oertel, R. Watt, C. Ruiz, G.
Cooper, D. Hebron, R. Leeper, J. Porter, and J. Knauer, Rev. Sci. Instrum., 66 (1)
(1995) 288.
19 XCAL, Oxford Research Group, 5737 Clinton Ave, Richmond CA 94805.
20 St. GobaidNorton Diamond Films, Northboro, MA.
21 S. Han, R.S. Wagner, J. Joseph, and E. Gullikson, to be appeared in NUC. Inst.
Meth.-A, 1996.
22 N.K. Moncur, R.P. Johnson, R.G. Watt, and R.B. Gibson, Applied Optics, 34 (21)
(1995) 4274-4283.
23 Tektronix 7250 Transient Digitizer.
24 See for example: The entire issue of Proc. of IEEE, 79 (5) (1991);
25 M. Asif Khan, J.N. Kuznia, D.T. Olson, J.M. Van Hove, M. Blasingame, L.F. Reitz,
Appl. Phys. Lett., 60 (23) (1992) 2917
- -----
FIGURES AND TABLES
Table 1: Properties of diamond in comparison to Si and G a s .
Table 2: Properties of Sic polytypes and GaN in comparison to diamond.
Figure 1: : Scanning electron micrograph of the growth surface of the diamond film used
to fabricate the detectors. The mean grain size of the film on the growth surface was
measured to be 51 pm.
Figure 2: A history of charge collection distance improvement.
Figure 3: The leakage and proton beam induced current for a CVD diamond detector as a
function of 500-MeV proton fluence: A) up to 5 x 1012 cm-2 and B) up to 4 x 1013 cm-2.
It is clear from the data that the leakage currents do not increase with the cessation of the
proton irradiation.
Figure 4: The ratio of charge collection distances before and after the irrdiation as a
function of 500-MeV proton fluence.
Figure 5: The leakage and proton beam induced current for a Si photodiode as a function
of 500-MeV proton fluence. The increasing current is due to the proton damage of the
photodiode.
Figure 6: The ratio of charge collection distances before and after the irrdiation as a
function of 5-MeV a-particle fluence.
Figure 7: The (Ue) photon attenuation.length in diamond as a function of photon energy as
calculated with XCAL.
Figure 8: A schematic diagram of the detector geometry.
Figure 9: The current waveform out of the detector recorded with a 7 GHz transient
digitizer.
Figure 10: A CCD output of the spectral distribution of the incident x-rays. The black
shadow is the detector assembly and the round circle outlined in white is the detector active
area. The area subtended x-ray wavelength of 5 A. Figure 11: A schematic of the measurement system used to evaluate the single-channel
13
CVD diamond photoconductor/transmission grating system.
Figure 12: Sensitivity and quantum efficiency of a diamond photoconductor as functions
of x-ray wavelength and applied bias voltage: A) 300 V and B) 100 V. The sensitivity of
the photoconductor is flat within +lo% over the entire spectral range.
~-
14
Property Diamond Silicon Gallium Arsenide
Mass Density [g/cm3 ]
Atomic Charge
Band Gap [eV]
Electron Mobility [cm2 Nls]
Hole Mobility [cm2 N/s]
Saturation Velocity [pdsec]
Energy to create e-h pair [ev]
3.5
6
5.5
1800
1200
220
13
Cohesive Energy [eV/atom] 7.37
Breakdown Field [v/cm] 107
Resistivity [ a -cm] > l o l l
Thermal Conductivity w/m/K] 1000-2010
Dielectric Constant 5.7
2.33
14
1.12
1350
480
82
3.6
4.63
3x105
2.3~10
150
11.9
5.32
31,33
1.43
8500
400
80
4.2
4x 1 O5
1 .ox 10
45
13.1
TABLE 1
15
I
L. 6H-Sic Diamond GaN
Band gap (eV) 2.2 2.9 5.5 3.4
Electron Mobility (cm *N-sec)
Hole Mobility
Breakdown Field (MVlcm)
Saturated Drift Velocity (IO 7 cm/sec)
1000 600 1800 900
40 1200
0.3
2
lo
2.2
150 (?)
5 (?)
2.2
Table 2
16
Figure 1
17
1000
100
10
1
0.1
0.01
* 4.- .
1989 1990 1991 1992 1993 1994 1995 1996 1997
Year
Figure 2
.
18
30
25
20
1 5
1 0
5
0
Beamon
Beam Off
-2 P 0 cm
400 800
Time (min)
1200
25 309
1600 !
12 -2 5x10 cm
12 -2 t
5x10 cm Time (min)
Figure 3
.
19
60
40
20
-
-
- 0
0
i i i 1 1 i Beam -On
Beam-Off 3 I
Proton Huence (cm- '1
Figure 4
20
2.5 1 I 1 I I I I
lo7
I o Irradiation Run-2 A Irradiation Run-1
lo8
.
10' 1o1O lo1 10l2 10'~ Proton Huence (ern-')
Figure 5
10'~
21
1.2
1 .o
0.8
0.6
0.4
0.2
1 1 1 1 1 1 1 1 ~ I I 1 1 1 1 1 1 ~ I I 1 1 1 1 1 1 ~ I 1 1 1 1 1 1 1 ~ 1 1 1 1 1 1 1 1 ( 1 1 1 1 1 1 1
P
Figure 6
0.001
0.0001
1.0-
10- lo00 100
Photon Wavelength
Figure 7
23
Diamond Substrate
Metal ContacVStrips
Metal ContacVStrips
Figure 8
24
hnL - IBias, Suppl y 1
-
Vacuum Boundary
Figure 9
25
Figure €0
26
0.20
0.1 5
F v 0.10
0.00
-0.05 0
I L
5 1 0 1 5
Time (ns) 20 2 5
Figure 11
.z a 3.0 1 .o
0.8 2.5
P 2.0 m
0.6 1.5 e
3! 0.4 2 0 3
1 .o v
0.0 120 140 160 180 200 220 240
Wavelength (A)
(0
'0 F
Y x
wl > U .- .- c. .- rn c Q) v)
8ool
2oot[ 1 0 120 140 160 180 200 220 240
Wavelength (A)
0.20
0.15 p . F h b) 0.10 . E! ? 0 3
0.05.
0.00
Figure 12