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Transmission grating spectrometer for characterization of undulator radiation
Nuclear Instruments and Methods in Physics Research A 347 (1994) 244-248 North-Holland
NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SectionA
Transmission grating spectrometer for characterization of undulator radiation D.A. Mossessian a, *, P.A. Heimann a, E. Gullikson b, R.K . Kaza a, J . Chin °, J. Akre ° 'Advanced Light Source, Accelerator and Fusion Research Division, n Center for X-Ray Optics, Materials Sciences Division, and ` Engineering Division, Lawrence Berkeley Laboratory, Berkeley, CA 94720, USA
A transmission grating spectrometer has been built to investigate undulator radiation at the Advanced Light Source. The spectrometer covers the spectral range from 10 to 620 f1 with a spectral resolution from 0.02 to 1 A (depending on the wavelength), and provides the capability to measure the spectral and angular distribution of the undulator radiation. The minimum angular resolution of the spectrometer is 10 Rrad . The absolute efficiencies of the spectrometer's optical elements have been measured with an accuracy of better than 10%, which will allow measurements of the absolute intensity of the radiation harmonics. The results of the measurements are compared to theoretical calculations of the undulator radiation based on measured magnetic field data. In this paper the design of the spectrometer, the calibration of the optical components, and test measurements with an X-ray tube are described .
1. Introduction An X-ray spectrometer has been built to characterize the radiation from the Advanced Light Source (ALS) undulators . The design of the transmission grating spectrometer (TGS) has been based upon spectrometers constructed by Molter and Ulm [1] and Tatchyn et al . [2], which were used to measure undulator radiation at BESSY and Aladdin. The spectrometer consists of two interchangeable gold transmission gratings (2000 I/mm [3] and 5000 1/mm [4]), a focusing mirror [5] at grazing incidence, and a detector (Si n-on-p photodiode [6]), which is scanned in the diffraction plane of the gratings (see Fig. 1) . The parameters of the TGS are shown in Table 1. The focusing of the spherical mirror together with a slit mounted in front of the detector makes possible the necessary spectral resolution. The angular resolution of the spectrometer is determined by the size of an aperture in front of the gratings. To measure the angular distribution of the radiation, the whole spectrometer may be translated in the vertical and horizontal directions perpendicular to the axis of the beam, while keeping the detector at a fixed wavelength . The TGS will be used to measure the spectral and angular distribution of the radiation of the ALS U5 (5 cm period) and U8 (8 cm period) undulators . The recorded spectra will be compared with the results of calculations
Corresponding author.
based on the measured magnetic field of the undulators [7]. For this comparison it is necessary to determine the absolute intensities of the radiation. For this purpose the absolute efficiencies of the detector, both gratings (for four diffraction orders) and the mirror have been measured. To test the operation of the spectrometer as a whole, spectra from an X-ray tube (K a emission lines of C and Al,O, anodes) have been recorded .
2. Spectrometer design The basic requirements of the TGS design are determined by the characteristics of the ALS undulator radiation . The spectral range of the TGS (620-10 A) is set by the operating ranges of the U5 and U8 beamlines, which are 70 to 1200 eV (177-10 A) and 20 to 300 eV (620-41 A) respectively . These beamlines utilize the first, third, and fifth harmonics of the undulator radiation. The intensity and spectral width of the fifth harmonic is especially sensitive to the effects of magnetic field errors and electron beam emittance. Consequently, the spectral resolution of the TGS is designed to be comparable with the width of the fifth harmonic from the U5 undulator, which is characterized by the largest ratio of .l/A .1 = 445 . The resolution of the TGS is determined by the width of the detector slit, the width of the mirror focus, and, in the long wavelength region, by the number of illuminated grating bars . In the short wavelength region, the 5000 1/mm transmission grating must be used to provide larger
0168-9002/94/$07 .00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0168-9002(94)00419-8
D.A . Mossessian et al. /Nuel. Instr. and Meth. in Phys . Res. A 347 (1994) 244-248
245
linear dispersion and thus better spectral resolution . The
Table 1 The parameter of the TGS
dA
d cos a
dl
mr
Photon energy range Spatial resolution Mirror coating Mirror incidence angle Mirror radius Gratings material
20-1200 eV 10 and 20 pLrad Gold 2° 29 .1 m Gold
Gratings period Detector
5000 and 2000 .k Si n-on-p photodiode
reciprocal linear dispersion of the grating is given by
where a is the diffraction angle r is the distance from the
grating to the detector, m is the diffraction order, and d is the grating period . For first order diffraction, the wavelength range of the spectrometer corresponds to the angular range 18 .059°-0 .286°. Within this range the reciprocal linear dispersion of the grating d .t/dl has a nearly con-
stant value of 4 ?r/mm. As a result, the slit width of 5 p,m o
has been chosen, corresponding to 0.02 A spectral width, which is equivalent to A/i1 A = 500 at A of 10 For the resolution of 0.02
f\
A.
to be achieved, the image
size should be matched to the geometrical width of the slit .
The ideal image has a full width half maximum of 5 wm,
which is determined by the magnification of the mirror
(1/29) and by the vertical size of the electron beam in the undulator (o-z = 63 Wm). Calculating the effect of the spherical aberration, the source depth, and the mirror slope error (1 .5 Wrad rms) shows that these contributions are
The power density of the radiation on the grating surface should be limited because of the possibility of damaging the grating. Following the experience of M61ter and Tatchyn [1,2] the power density will be limited to 0.1
W/cm 2. During the operation of the spectrometer, the current in the storage ring must be restricted to satisfy this limit. For example, for the U5 undulator at aK of 2.5, the beam current must be <_ 0.1 mA .
smaller than the ideal image size. As a result, at a wave-
length of 10 Â, a resolution of 0.02 A is predicted. Another factor which limits the resolution is the num-
3, Optics Calibration
determined by the size of the grating aperture, which is
(gratings, detector, and mirror) is described. The calibra-
ber of illuminated grating bars. This diffraction limit is chosen according to the required angular resolution. For instance, the aperture size of 300 Rm leads to the spectral .l/AA resolution of = 1500 for 5000 1/mm grating. In this case the diffraction limit will become the main factor
determining the resolution for l > 30
X
As mentioned above, the angular distribution of the
undulator radiation can be observed by scanning the entire spectrometer in the plane perpendicular to the beam direction . For this measurement the angular acceptance of the spectrometer has to be smaller than features of the distribution . The size of the central cone from the U5 undulator at
In this section the calibration of the optical elements
tion was performed using reflectometers with two different radiation sources. The first, a laser-produced plasma, generates soft X-rays from 65 to 250
X [8].
The second
reflectometer is based on an X-ray tube with demountable anodes [9]. In this work the A1 203 , C, and Mg anodes were employed with appropriate filters to provide AIK.,
Mg K", OK ' and C K., and emission lines (8.3, 9.9, 23 .6, and 44.7 A). The spectral sensitivity of the spectrom-
eter has then been calculated as the product of the efficiencies of its elements .
10 ?r is estimated to be 17 pLrad (rms), For each grating
3.1 . Calibration of the gratings
an angular acceptance of 10 and 20 p,rad. The smaller pinhole may be chosen to observe the influence of the
The efficiencies of four orders of diffraction (both positive and negative) of both gratings have been measured (see Fig. 2) . To perform the calibration, the grating
two pinholes are available with diameters (150 and 300 Wm) which at a distance of 15 .5 m from an undulator give
electron beam emittance on the shape of the higher harmonics .
was installed in the reflectometer perpendicular to the beam in a geometry analogous to the TGS. To measure the grating efficiency the diffraction orders were scanned at a certain wavelength of the probing radiation, and then the grating was moved out of the way in order that the direct
beam intensity could be measured.
ö
dU
c :3 Nô Fig. 1. Optical layout of the transmission grating spectrometer.
The measured efficiencies have been compared with theoretical calculations . To calculate the efficiencies, the values of the grating thickness, the grating period-to-gap ratio, and the area shadowed by the support mesh are required . These parameters have been determined using an alpha-particle energy-loss technique [10] . The diffraction efficiency of the first order has been calculated for both VII. VUV OPTICS
D.A . Mossessian et al. /Nucl. Instr. and Meth. in Phys. Res. A 347 (1994) 244-248
246 a
a
z
-4,
001s Û a 4) z U
Ot ,'6' e +1
a--
a
,
1
+ -negative orders o -positive orders
z 0
50
100
",+2nd
1
r
St
eF exp{ -A (hv)ts } exp( - N-d(hv)td1 (1 I- w jLs (hv)L + 1
+ ,±4th 150
200
layer of Si0 2 ) where a part of the incident radiation is absorbed, the space charge region, where all electron-hole pairs created due to the photon absorption are separated by the internal electric field, and the back region . The photocurrent from the back region can be evaluated by considering the balance among the processes of the charge generation, diffusion, and recombination . The diode photocurrent I that is induced by the monochromatic radiation with the power F can be calculated as :
250
- eF w b
x (A)
Fig . 2. Measured efficiencies of the 5000 1/mm (a) and 2000 1/mm (b) transmission gratings. The solid curves represent calculated efficiencies of the first order of diffraction . The dashed curves connect the measured points . For the 2000 1/mm grating the efficiency of the third order is smaller than the detection limit over the whole wavelength range .
gratings using a model based on Fraunhofer diffraction theory [11], which includes the effect of transmission through the grating bars . Rectangular grating bars are assumed in the model . 3 .2. Detector calibration A self calibration method [12], based on theoretical calculations of the photocurrent of a semiconductor photodiode, has been applied to measure the absolute spectral sensitivities of two Si n-on-p diodes . Following this method the parameters of the diodes were determined by measuring the ratio of the detector photocurrents at two different angles of incidence . The sensitivity of the detector was then calculated using the measured parameters. The sensitivity was obtained with less than 5% uncertainty over the whole energy range . Following Krumrey and Tegeler [12], the diode can be divided into three regions : the dead layer (i .e . the shallow
(2)
where td , ,st d and ts , t-ts are the thicknesses and absorption coefficients of the dead layer and the space charge region respectively, L is the diffusion length in the back region, w is the energy of one electron-hole pair creation, and e is the electron charge . The spectral sensitivity of the diode, which is defined as the ratio s(hp)
-o--positive orders -+--negative orders
K(hu),
I
e
= - = WK(hv),
can be calculated if the three independent parameters (t,, t d , L) are known . To calculate the photocurrent when the diode is tilted, the absorption coefficient 1-c should be replaced by is/sin a, where a is the tilt angle . The ratio of photocurrents at two different angles is independent of the absolute intensity of the incident radiation . Therefore, the parameters of the diode can be calculated by fitting the measured photocurrent ratio using Eqs . (2) and (3) . However, the model can be applied to calculate the diode photocurrent only if the following conditions are satisfied : i) the reflectance at the diode surface is negligible, ii) no refraction occurs at the surface and at the interface between the different layers, iii) the sensitivity is constant over the surface of the diode . The uniformity of the diodes was evaluated by scanning the beam position over the detector surface . The inhomogenity was below 3% . The first two conditions are not fulfilled in the wavelength range from 80 to 250 X, where our calibration has been done . In this case the term exp(-gd t d ) in Eq . (2) does not correctly describe the transmission through the dead layer, and it is necessary to take into account the multiple reflection at both surfaces of Si0 2 film. In fitting the ratio of photocurrents we have calculated the transmission through the layer of SiO Z by modeling this dead layer as a thin film on an infinite substrate and taking into account the multiple reflection on both surfaces of the film [13] . The measured photocurrent ratio fitted with the calculated curve for one of the calibrated detectors is shown in Fig . 3a . The structure below 120 X results from the Si L2.3
D.A . Mossessian et at. /Nuct. Instr. andMeth. i n Phys . Res. A 347 (1994) 244-248
absorption edges. Over the calibration wavelength region the diffusion length L and space charge region thickness is does not affect the sensitivity of the diode and the value of the ratio is defined by the thickness of the dead layer td. By adjusting the value td we have been able to achieve a reasonably good fit of the measured curve. To calculate the transmitted intensity, the refractive index data from ref. [14] has been used . The measured values of td are (120 ± 5) Â for the first and (85 ± 5) Â for the second detector. To determine the diffusion length and the space charge region thickness of the diodes, the measurements of the photocurrent ratio at shorter wavelength (Al K. and Mg K~ lines) have been performed. Fitting the measured ratios with Eq . (2) results in values of L = 40 wm and is = 10 wm for the first, and L = 60 p.m and is = 15 p,m for the second detector with an uncertainty of about 50%. However, the contribution of the parameters L and ot . to the value of the sensitivity is quite small for A > 10 A. Shown
0
0.90 0 .85
247
0.9=
-W- a
0.6 ~
b
50
Fig.
100
150
200
250
The measured (a) and calculated (b) reflectivity of the gold-coated spherical mirror at 2° angle of incidence .
4.
in Fig. 3b, the calculated detector sensitivity has an uncertainty which does not exceed 5% over the wavelength range from 250 to 10 t1 . 3.3. Measurements of the mirror reflectivity
0 80 0.75 0 .70 100
150
200
X (A) b
The direct measurement of the mirror reflectivity at 2° grazing angle is difficult because of the small effective mirror size and the uncertainty in the probing beam position . To avoid these problems the intensity of the reflected radiation has been measured over a large angular range (5 °-20 ° ). Then the angular dependence has been extrapolated to 0° using the Fresnel equations for the reflectivity of thin gold film with three independent parameters-the real and imaginary parts of the refractive index and the normalization factor which makes the reflectivity at 0° equal to unity. The data obtained for the reflectivity of the mirror are shown in Fig. 4 together with the reflectivity calculated from the tabulated refractive index [14] . 4. Test measurements
X (A) Fig. 3. (a) measured (dashed line) and calculated (solid line) ratio of the first detector photocurrent at 0° and 60° angles of incidence. (b) The calculated sensitivities of the two calibrated detectors. The measured parameters of the detectors are td =120 f1, is =10 wm, L = 40 g m for the first detector (dashed line) and td = 85 is =15 p.m, L = 60 wm for the second (solid line).
The test measurements were carried out to confirm the alignment of the individual optical elements and verify the combined spectrometer efficiency . For these measurements a demountable anode X-ray tube [9] was installed in front of the TGS. The tube had a 1 by 10 mm exit slit in front of the anode. To enhance the signal from the comparatively weak and divergent source, larger apertures and slits were also installed in the TGS, including a 1 by 10 mm slit in front of the detector. The intensity from the X-ray tube can be estimated within a factor of two from the anode voltage and current. Comparison of these calculated intensities with the measured spectra (Fig . 5) shows agreement with VII. VUV OPTICS
248
D .A . Mossessian et al. /Nucl. Instr. and Meth. i n Phys. Res. A 347 (1994) 244-248 o
rials Sciences Division of the U .S . Department of Energy under Contract Number De-AC03-76SF00098 .
AI K 1st order 0 order
References
ô
e
AI K 2nd order
8
s r -30
/ o K,,st
-20
-10
0
X(A)
10
20
,
[4] 30
Fig. 5 . The spectrum of the X-ray tube with an A1 2 0 3 anode recorded during the test measurements . The negative wavelengths correspond to the negative orders of diffraction .
[5] [6] [7] [8]
the TGS calibration derived from the efficiencies of the individual optical elements. The ratios of the intensities of the different diffraction orders also agree with the results of calibration .
[10]
Acknowledgment
[11] [12] [13]
This work is supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Mate-
[9]
[14]
K . Molter and G . Ulm, Rev . Sci . Insu. 63 (1992) 1296 . R. Tatchyn, E . Kallne, A. Toor, T. Cremer and P . Csonka, Rev . Sci . Insu . 60 (1989) 1579 . Heidenhain Corp ., Dr . Johannes-Heidenhain Suasse 5, D8225 Traunreut, Germany . X-OPT, Inc ., 2426 NW 26th Place, Gainesville, FL 32605, USA . Tucson Optical Research Corp., 2105 Plumer Ave ., Tucson, AZ 85719, USA. International Radiation Detectors, 2501 W 237th St., Suite E, Torrance, CA 90505, USA. C . Wang, S . Marks and B . Kincaid, Proc. IEEE Particle Accelerator Conference, Washington, DC, May 17-20, 1993 . E.M. Gullikson, J .H . Underwood, P .C . Batson and V . Nikitin, X-ray Sci . Technol . 3 (1992) 283 . B .L Henke and M .A . Tester, Advances in X-ray Analysis, vol . 18 (Plenum, New York, 1975) . W .K . Chu, J.W . Mayer and M.A. Nicolet, Backscattering Spectrometry (Academic Press, New York 1978) . M .L. Schattenburg, Ph .D . thesis, MIT (1984) . M . Krumrey and E . Tegeler, Rev . Sci . Instr. 63 (1992) 797 . F . Stern, Solid State Physics, vol . 15 (Academic Press, New York, 1963) . B.L . Henke, E .M . Gullikson and J.C . Davis. At. Data Nucl . Data Tables 54 (1993) 181 .
NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SectionA
Transmission grating spectrometer for characterization of undulator radiation D.A. Mossessian a, *, P.A. Heimann a, E. Gullikson b, R.K . Kaza a, J . Chin °, J. Akre ° 'Advanced Light Source, Accelerator and Fusion Research Division, n Center for X-Ray Optics, Materials Sciences Division, and ` Engineering Division, Lawrence Berkeley Laboratory, Berkeley, CA 94720, USA
A transmission grating spectrometer has been built to investigate undulator radiation at the Advanced Light Source. The spectrometer covers the spectral range from 10 to 620 f1 with a spectral resolution from 0.02 to 1 A (depending on the wavelength), and provides the capability to measure the spectral and angular distribution of the undulator radiation. The minimum angular resolution of the spectrometer is 10 Rrad . The absolute efficiencies of the spectrometer's optical elements have been measured with an accuracy of better than 10%, which will allow measurements of the absolute intensity of the radiation harmonics. The results of the measurements are compared to theoretical calculations of the undulator radiation based on measured magnetic field data. In this paper the design of the spectrometer, the calibration of the optical components, and test measurements with an X-ray tube are described .
1. Introduction An X-ray spectrometer has been built to characterize the radiation from the Advanced Light Source (ALS) undulators . The design of the transmission grating spectrometer (TGS) has been based upon spectrometers constructed by Molter and Ulm [1] and Tatchyn et al . [2], which were used to measure undulator radiation at BESSY and Aladdin. The spectrometer consists of two interchangeable gold transmission gratings (2000 I/mm [3] and 5000 1/mm [4]), a focusing mirror [5] at grazing incidence, and a detector (Si n-on-p photodiode [6]), which is scanned in the diffraction plane of the gratings (see Fig. 1) . The parameters of the TGS are shown in Table 1. The focusing of the spherical mirror together with a slit mounted in front of the detector makes possible the necessary spectral resolution. The angular resolution of the spectrometer is determined by the size of an aperture in front of the gratings. To measure the angular distribution of the radiation, the whole spectrometer may be translated in the vertical and horizontal directions perpendicular to the axis of the beam, while keeping the detector at a fixed wavelength . The TGS will be used to measure the spectral and angular distribution of the radiation of the ALS U5 (5 cm period) and U8 (8 cm period) undulators . The recorded spectra will be compared with the results of calculations
Corresponding author.
based on the measured magnetic field of the undulators [7]. For this comparison it is necessary to determine the absolute intensities of the radiation. For this purpose the absolute efficiencies of the detector, both gratings (for four diffraction orders) and the mirror have been measured. To test the operation of the spectrometer as a whole, spectra from an X-ray tube (K a emission lines of C and Al,O, anodes) have been recorded .
2. Spectrometer design The basic requirements of the TGS design are determined by the characteristics of the ALS undulator radiation . The spectral range of the TGS (620-10 A) is set by the operating ranges of the U5 and U8 beamlines, which are 70 to 1200 eV (177-10 A) and 20 to 300 eV (620-41 A) respectively . These beamlines utilize the first, third, and fifth harmonics of the undulator radiation. The intensity and spectral width of the fifth harmonic is especially sensitive to the effects of magnetic field errors and electron beam emittance. Consequently, the spectral resolution of the TGS is designed to be comparable with the width of the fifth harmonic from the U5 undulator, which is characterized by the largest ratio of .l/A .1 = 445 . The resolution of the TGS is determined by the width of the detector slit, the width of the mirror focus, and, in the long wavelength region, by the number of illuminated grating bars . In the short wavelength region, the 5000 1/mm transmission grating must be used to provide larger
0168-9002/94/$07 .00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0168-9002(94)00419-8
D.A . Mossessian et al. /Nuel. Instr. and Meth. in Phys . Res. A 347 (1994) 244-248
245
linear dispersion and thus better spectral resolution . The
Table 1 The parameter of the TGS
dA
d cos a
dl
mr
Photon energy range Spatial resolution Mirror coating Mirror incidence angle Mirror radius Gratings material
20-1200 eV 10 and 20 pLrad Gold 2° 29 .1 m Gold
Gratings period Detector
5000 and 2000 .k Si n-on-p photodiode
reciprocal linear dispersion of the grating is given by
where a is the diffraction angle r is the distance from the
grating to the detector, m is the diffraction order, and d is the grating period . For first order diffraction, the wavelength range of the spectrometer corresponds to the angular range 18 .059°-0 .286°. Within this range the reciprocal linear dispersion of the grating d .t/dl has a nearly con-
stant value of 4 ?r/mm. As a result, the slit width of 5 p,m o
has been chosen, corresponding to 0.02 A spectral width, which is equivalent to A/i1 A = 500 at A of 10 For the resolution of 0.02
f\
A.
to be achieved, the image
size should be matched to the geometrical width of the slit .
The ideal image has a full width half maximum of 5 wm,
which is determined by the magnification of the mirror
(1/29) and by the vertical size of the electron beam in the undulator (o-z = 63 Wm). Calculating the effect of the spherical aberration, the source depth, and the mirror slope error (1 .5 Wrad rms) shows that these contributions are
The power density of the radiation on the grating surface should be limited because of the possibility of damaging the grating. Following the experience of M61ter and Tatchyn [1,2] the power density will be limited to 0.1
W/cm 2. During the operation of the spectrometer, the current in the storage ring must be restricted to satisfy this limit. For example, for the U5 undulator at aK of 2.5, the beam current must be <_ 0.1 mA .
smaller than the ideal image size. As a result, at a wave-
length of 10 Â, a resolution of 0.02 A is predicted. Another factor which limits the resolution is the num-
3, Optics Calibration
determined by the size of the grating aperture, which is
(gratings, detector, and mirror) is described. The calibra-
ber of illuminated grating bars. This diffraction limit is chosen according to the required angular resolution. For instance, the aperture size of 300 Rm leads to the spectral .l/AA resolution of = 1500 for 5000 1/mm grating. In this case the diffraction limit will become the main factor
determining the resolution for l > 30
X
As mentioned above, the angular distribution of the
undulator radiation can be observed by scanning the entire spectrometer in the plane perpendicular to the beam direction . For this measurement the angular acceptance of the spectrometer has to be smaller than features of the distribution . The size of the central cone from the U5 undulator at
In this section the calibration of the optical elements
tion was performed using reflectometers with two different radiation sources. The first, a laser-produced plasma, generates soft X-rays from 65 to 250
X [8].
The second
reflectometer is based on an X-ray tube with demountable anodes [9]. In this work the A1 203 , C, and Mg anodes were employed with appropriate filters to provide AIK.,
Mg K", OK ' and C K., and emission lines (8.3, 9.9, 23 .6, and 44.7 A). The spectral sensitivity of the spectrom-
eter has then been calculated as the product of the efficiencies of its elements .
10 ?r is estimated to be 17 pLrad (rms), For each grating
3.1 . Calibration of the gratings
an angular acceptance of 10 and 20 p,rad. The smaller pinhole may be chosen to observe the influence of the
The efficiencies of four orders of diffraction (both positive and negative) of both gratings have been measured (see Fig. 2) . To perform the calibration, the grating
two pinholes are available with diameters (150 and 300 Wm) which at a distance of 15 .5 m from an undulator give
electron beam emittance on the shape of the higher harmonics .
was installed in the reflectometer perpendicular to the beam in a geometry analogous to the TGS. To measure the grating efficiency the diffraction orders were scanned at a certain wavelength of the probing radiation, and then the grating was moved out of the way in order that the direct
beam intensity could be measured.
ö
dU
c :3 Nô Fig. 1. Optical layout of the transmission grating spectrometer.
The measured efficiencies have been compared with theoretical calculations . To calculate the efficiencies, the values of the grating thickness, the grating period-to-gap ratio, and the area shadowed by the support mesh are required . These parameters have been determined using an alpha-particle energy-loss technique [10] . The diffraction efficiency of the first order has been calculated for both VII. VUV OPTICS
D.A . Mossessian et al. /Nucl. Instr. and Meth. in Phys. Res. A 347 (1994) 244-248
246 a
a
z
-4,
001s Û a 4) z U
Ot ,'6' e +1
a--
a
,
1
+ -negative orders o -positive orders
z 0
50
100
",+2nd
1
r
St
eF exp{ -A (hv)ts } exp( - N-d(hv)td1 (1 I- w jLs (hv)L + 1
+ ,±4th 150
200
layer of Si0 2 ) where a part of the incident radiation is absorbed, the space charge region, where all electron-hole pairs created due to the photon absorption are separated by the internal electric field, and the back region . The photocurrent from the back region can be evaluated by considering the balance among the processes of the charge generation, diffusion, and recombination . The diode photocurrent I that is induced by the monochromatic radiation with the power F can be calculated as :
250
- eF w b
x (A)
Fig . 2. Measured efficiencies of the 5000 1/mm (a) and 2000 1/mm (b) transmission gratings. The solid curves represent calculated efficiencies of the first order of diffraction . The dashed curves connect the measured points . For the 2000 1/mm grating the efficiency of the third order is smaller than the detection limit over the whole wavelength range .
gratings using a model based on Fraunhofer diffraction theory [11], which includes the effect of transmission through the grating bars . Rectangular grating bars are assumed in the model . 3 .2. Detector calibration A self calibration method [12], based on theoretical calculations of the photocurrent of a semiconductor photodiode, has been applied to measure the absolute spectral sensitivities of two Si n-on-p diodes . Following this method the parameters of the diodes were determined by measuring the ratio of the detector photocurrents at two different angles of incidence . The sensitivity of the detector was then calculated using the measured parameters. The sensitivity was obtained with less than 5% uncertainty over the whole energy range . Following Krumrey and Tegeler [12], the diode can be divided into three regions : the dead layer (i .e . the shallow
(2)
where td , ,st d and ts , t-ts are the thicknesses and absorption coefficients of the dead layer and the space charge region respectively, L is the diffusion length in the back region, w is the energy of one electron-hole pair creation, and e is the electron charge . The spectral sensitivity of the diode, which is defined as the ratio s(hp)
-o--positive orders -+--negative orders
K(hu),
I
e
= - = WK(hv),
can be calculated if the three independent parameters (t,, t d , L) are known . To calculate the photocurrent when the diode is tilted, the absorption coefficient 1-c should be replaced by is/sin a, where a is the tilt angle . The ratio of photocurrents at two different angles is independent of the absolute intensity of the incident radiation . Therefore, the parameters of the diode can be calculated by fitting the measured photocurrent ratio using Eqs . (2) and (3) . However, the model can be applied to calculate the diode photocurrent only if the following conditions are satisfied : i) the reflectance at the diode surface is negligible, ii) no refraction occurs at the surface and at the interface between the different layers, iii) the sensitivity is constant over the surface of the diode . The uniformity of the diodes was evaluated by scanning the beam position over the detector surface . The inhomogenity was below 3% . The first two conditions are not fulfilled in the wavelength range from 80 to 250 X, where our calibration has been done . In this case the term exp(-gd t d ) in Eq . (2) does not correctly describe the transmission through the dead layer, and it is necessary to take into account the multiple reflection at both surfaces of Si0 2 film. In fitting the ratio of photocurrents we have calculated the transmission through the layer of SiO Z by modeling this dead layer as a thin film on an infinite substrate and taking into account the multiple reflection on both surfaces of the film [13] . The measured photocurrent ratio fitted with the calculated curve for one of the calibrated detectors is shown in Fig . 3a . The structure below 120 X results from the Si L2.3
D.A . Mossessian et at. /Nuct. Instr. andMeth. i n Phys . Res. A 347 (1994) 244-248
absorption edges. Over the calibration wavelength region the diffusion length L and space charge region thickness is does not affect the sensitivity of the diode and the value of the ratio is defined by the thickness of the dead layer td. By adjusting the value td we have been able to achieve a reasonably good fit of the measured curve. To calculate the transmitted intensity, the refractive index data from ref. [14] has been used . The measured values of td are (120 ± 5) Â for the first and (85 ± 5) Â for the second detector. To determine the diffusion length and the space charge region thickness of the diodes, the measurements of the photocurrent ratio at shorter wavelength (Al K. and Mg K~ lines) have been performed. Fitting the measured ratios with Eq . (2) results in values of L = 40 wm and is = 10 wm for the first, and L = 60 p.m and is = 15 p,m for the second detector with an uncertainty of about 50%. However, the contribution of the parameters L and ot . to the value of the sensitivity is quite small for A > 10 A. Shown
0
0.90 0 .85
247
0.9=
-W- a
0.6 ~
b
50
Fig.
100
150
200
250
The measured (a) and calculated (b) reflectivity of the gold-coated spherical mirror at 2° angle of incidence .
4.
in Fig. 3b, the calculated detector sensitivity has an uncertainty which does not exceed 5% over the wavelength range from 250 to 10 t1 . 3.3. Measurements of the mirror reflectivity
0 80 0.75 0 .70 100
150
200
X (A) b
The direct measurement of the mirror reflectivity at 2° grazing angle is difficult because of the small effective mirror size and the uncertainty in the probing beam position . To avoid these problems the intensity of the reflected radiation has been measured over a large angular range (5 °-20 ° ). Then the angular dependence has been extrapolated to 0° using the Fresnel equations for the reflectivity of thin gold film with three independent parameters-the real and imaginary parts of the refractive index and the normalization factor which makes the reflectivity at 0° equal to unity. The data obtained for the reflectivity of the mirror are shown in Fig. 4 together with the reflectivity calculated from the tabulated refractive index [14] . 4. Test measurements
X (A) Fig. 3. (a) measured (dashed line) and calculated (solid line) ratio of the first detector photocurrent at 0° and 60° angles of incidence. (b) The calculated sensitivities of the two calibrated detectors. The measured parameters of the detectors are td =120 f1, is =10 wm, L = 40 g m for the first detector (dashed line) and td = 85 is =15 p.m, L = 60 wm for the second (solid line).
The test measurements were carried out to confirm the alignment of the individual optical elements and verify the combined spectrometer efficiency . For these measurements a demountable anode X-ray tube [9] was installed in front of the TGS. The tube had a 1 by 10 mm exit slit in front of the anode. To enhance the signal from the comparatively weak and divergent source, larger apertures and slits were also installed in the TGS, including a 1 by 10 mm slit in front of the detector. The intensity from the X-ray tube can be estimated within a factor of two from the anode voltage and current. Comparison of these calculated intensities with the measured spectra (Fig . 5) shows agreement with VII. VUV OPTICS
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D .A . Mossessian et al. /Nucl. Instr. and Meth. i n Phys. Res. A 347 (1994) 244-248 o
rials Sciences Division of the U .S . Department of Energy under Contract Number De-AC03-76SF00098 .
AI K 1st order 0 order
References
ô
e
AI K 2nd order
8
s r -30
/ o K,,st
-20
-10
0
X(A)
10
20
,
[4] 30
Fig. 5 . The spectrum of the X-ray tube with an A1 2 0 3 anode recorded during the test measurements . The negative wavelengths correspond to the negative orders of diffraction .
[5] [6] [7] [8]
the TGS calibration derived from the efficiencies of the individual optical elements. The ratios of the intensities of the different diffraction orders also agree with the results of calibration .
[10]
Acknowledgment
[11] [12] [13]
This work is supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Mate-
[9]
[14]
K . Molter and G . Ulm, Rev . Sci . Insu. 63 (1992) 1296 . R. Tatchyn, E . Kallne, A. Toor, T. Cremer and P . Csonka, Rev . Sci . Insu . 60 (1989) 1579 . Heidenhain Corp ., Dr . Johannes-Heidenhain Suasse 5, D8225 Traunreut, Germany . X-OPT, Inc ., 2426 NW 26th Place, Gainesville, FL 32605, USA . Tucson Optical Research Corp., 2105 Plumer Ave ., Tucson, AZ 85719, USA. International Radiation Detectors, 2501 W 237th St., Suite E, Torrance, CA 90505, USA. C . Wang, S . Marks and B . Kincaid, Proc. IEEE Particle Accelerator Conference, Washington, DC, May 17-20, 1993 . E.M. Gullikson, J .H . Underwood, P .C . Batson and V . Nikitin, X-ray Sci . Technol . 3 (1992) 283 . B .L Henke and M .A . Tester, Advances in X-ray Analysis, vol . 18 (Plenum, New York, 1975) . W .K . Chu, J.W . Mayer and M.A. Nicolet, Backscattering Spectrometry (Academic Press, New York 1978) . M .L. Schattenburg, Ph .D . thesis, MIT (1984) . M . Krumrey and E . Tegeler, Rev . Sci . Instr. 63 (1992) 797 . F . Stern, Solid State Physics, vol . 15 (Academic Press, New York, 1963) . B.L . Henke, E .M . Gullikson and J.C . Davis. At. Data Nucl . Data Tables 54 (1993) 181 .