Some characteristics of a solid state detector in the soft X-ray region

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Nuclear Instruments and Methods in Physics Research A 361 (1995) 364-371 NUCLEAR

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lNSTRUhlENTS 8 METHODS c IN PHYSICS RESEARCH

ELSEVIER Section A

Some characteristics of a solid state detector in the soft X-ray region

K. Torii * , H. Tsunemi, E. Miyata, K. Hayashida

Department of Earth and Space Science. Faculry of Science. Osaka University. Machikaneyama-cho I-I. T~~yonaka. Osaka 560, Japan

Received 17 October 1094; revised form received 3 January 1995

Abstract We report here the linearity of the Si(Li) solid state detector (SSD) in the soft X-ray (1-2 keV) region, particularly

around the Si K-shell absorption edge energy (1840 eV) by using a synchrotron radiation facility. The response function of the SSD shows a big change at this energy.

We fitted the pulse height (PHI distributions with an empirical model which is a sum of two Gaussians having different parameters. Using this empirical model, we found the nonlinearity at the Si K-edge to be 8.7 ? 2.6 eV.

We introduce another type of response function in which a charge diffusion process in silicon is taken into account. The primary charge cloud is partly absorbed by the electrode when the photoabsorption occurs near the electrode, resulting in the low PH. We found that this type of response function is more appropriate in reproducing the data than the empirical model. Based on the diffusion model, we found the nonlinearity to be 1.5 + 2.6 eV. This implies that the apparent nonlinearity seen in the two Gaussian model can be attributed to the diffusion process. We conclude that there is no intrinsic nonlinearity effect in silicon at the K-edge. The diffusion effect is not applicable in the front illuminated CCD. We expect that there is no

nonlinearity in the CCD.

1. Introduction charge coupled devices (CCDI [s] which use the same principle to detect X-ray photons as the SSD.

Si(LiI solid state detectors (SSD) are widely used as In the data analysis, we need to know the performance

non-dispersive X-ray spectrometers because of their rela- of the detector in detail. In most spectroscopic X-ray

tively good energy resolution and high detection efficiency detectors, the crudest response function against the

in the soft X-ray energy region. In the fluorescence analy- monochromatic X-ray is a single Gaussian. lnoue et al. [6],

sis, the SSD has good energy resolution, enough to distin- however, reported a significant distortion of the response

guish between the K emission lines of elements with function of the Xe-filled gas scintillation proportional

adjacent atomic numbers. Higher energy resolution is counter. Similar effects have been reported in the case of

achieved by a dispersion system by sacrificing the detec- the SSD [3,7]. To model these responses, various methods tion efficiency. [8-111 have been reported.

In X-ray astronomy, the Si(Li) SSD was employed in the Einstein observatory [I] and in the BBXRT experiment [2]. It has much better energy resolution than that of conventional gas proportional counters. To distinguish the line emissions from the cosmic plasma in various ionization states, such as those in a supernova remnant, an accurate energy scale calibration is important. The SSD employed in the Einstein observatory had a similar energy resolution as SSDs used in laboratory experiments. In BBXRT. they used a mosaic SSD. Accurate energy scale calibration was performed by using characteristic X-rays from various materials [3]. The ASCA satellite [4] employs

As well as the shape of the response function, the linearity of the PH as a function of the incident X-ray energy is important for the spectroscopic study. It is well known that there is a discontinuity at the absorption edge energy in gas counters. Jahoda and McCammon [12] reported the discontinuity to be about 30 eV at the Ar L-edge using the conventional gas proportional counter. In the Xe gas counters, Koyama et al. [13] measured the discontinuity at the L absorption edge to be approximately 50 eV by using various characteristic X-rays while Lamb et al. [14] measured it by using a synchrotron radiation facility and found 59 + 7 eV at the Xe L,,,-edge, 22 f 7 eV at the Xe L,,-edge and 5 + 4 eV at L,-edge. respectively. Tsunemi et al. [15] also measured it at the K absorption edge to be 170 + 10 eV by using the synchrotron radiation facility. * Corresponding author

0168-YOO2/Y5/$OY.50 0 199.5 Elsevier Science B.V. All rights reserved

SSDI 0168-9002(95)00124-7

K. Torii et al. / Nucl. Instr. and Meth. in Phys. Rex A 361 (1995) 364-371 365

The qualitative explanation of the discontinuity at the Xe L-edge was given by Koyama et al. [13]. They thought

that the discontinuity was due to the difference of the mean ionization energy across the edge as measured by Carlson et al. [16]. Lamb et al. [14], however, failed in quantitatively explaining their measured discontinuity at the Xe L-edge by calculating the expended energy according to Ref. [16]. Their estimation of _ 250 eV is about a factor of 3 larger than the measured value. While Santos et al. [ 171 succeeded in quantitatively explaining the discontinuity at the Xe L-edge with their detailed Monte Carlo model. In their simulation, elastic and inelastic (excitation and ionization) scatterings of all the produced electrons, as well as the relaxation (Auger-Coster-Kronig transitions, fluorescence photon emission and shake-off ionization) of the initially photoionized atom are evaluated. Therefore, the discontinuity at the Xe L-edge can not be quantitatively explained by the difference of the expended energy by the initially photoionized atom.

The discontinuity at the K-edge is simpler than that at the L-edge. Tsunemi et al. [15] showed that the measured discontinuity at the Xe K-edge agreed well with the calculation of the expended energy across the edge alone (without evaluating the electron-gas interactions) by tak- ing into account the photoabsorption probability at L and K edges and the escape/reabsorption probability of the fluorescent K X-rays.

Though the CCD imaging spectrometer becomes a principal detector in X-ray astronomy, such a discontinuity has not been precisely measured. We calculated the discontinuity at the Si K-edge based on the expended energy just as for the Xe K-edge [15] and found it to be about 60 eV. It is clear that this value is excluded even from the previous experiments in the literature. Recently Fraser et al. [18] studied the interaction of soft X-rays with silicon in detail from the theoretical point of view. They calculated the discontinuity of 0.2% (the equivalent width of _ 3.6 eV) at the Si K-edge. To clarify the behavior of the silicon detectors especially at around the K absorption edge, we performed an experiment and measured the characteristics of a Si(Li) SSD using the synchrotron radiation facility in the soft X-ray energy region ( _ l-2 keV1.

2. Experimentation

We used an X-ray beam line BL7A in the UVSOR

facility in the Institute for Molecular Science, Okazaki, Japan. The beam line is equipped with a double crystal monochromator. We selected a beryl crystal (2d = 15.95 A) that provided us with an X-ray energy between 830 eV and 2260 eV. The relative energy scale is controlled with a precision better than a few eV by referring to the rotation angle of the crystal. The absolute energy scale was determined by using the absorption edge of the aluminum foil.

Fig. 1 shows a schematic diagram of the experiment. The SSD we used in EGBG ORTEC (SLP-04160-S)

which is equipped with a beryllium entrance window of 12.7 pm thickness. We placed a mechanical slit between the detector and the double crystal monochromator in order to control the X-ray intensity onto the detector to be 2000-4000 counts/s which is much less than the satura- tion level of the detector. The aperture immediately in front of the detector restricted the incident X-ray position to within 0.5 mm from its center. We set the high voltage supply to the SSD to be - 1500 V through the whole experiment. After the built-in preamplifier, we used a main amplifier (Ortec 571, coarse gain 100, fine gain 0.63, shaping time 6 ps) and a multi-channel analyzer (Canberra S-20). The offset value of the system was checked by using a mercury pulser.

3. Data analysis with models

Fig. 2 shows typical PH distributions obtained for various incident X-ray energies. In some cases, clear peaks are seen due to the higher order X-rays that are much weaker than the first order X-rays. Therefore, we neglect the effect due to the higher order X-rays in our analysis. We noticed a clear peak (main peak) and a tail component next to the main peak.

There are several models proposed to fit the data, most of which are empirical [3,8-l 1,151. Among them, we chose a two Gaussian model to fit the data. The first Gaussian represents the main peak while the second Gaussian represents the tail component. Then we em-

Mechanical slit

Double crystal I monochromator

Fig. 1. Schematic view of the experiment

366 K. Torii et al. / Nucl. Instr. and Meth. in Phys. Res. A 361 (I 995) 364-371

1

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Fig. 2. Pulse height distributions are shown for various incident X-rays. (a) 1105 eV, (b) 1342 eV, (c) 1585 eV, (d) 1762 eV, (e) 1815 eV, (f) 1842 eV, (g) 1896 eV, (h) Mn K.

K. Torii et al. / Nucl. Insfr. ad Me&. in Phys. Rex A 361 11995) 364-371 367

ployed a model based on the diffusion of the primary electron cloud in the silicon crystal.

We chose the maximum likelihood method rather than the x’ method throughout our analysis [19] since the

number of events in one channel becomes small especially at the tail part.

3.1. Two Gaussian model

We fit the data by using the sum of two Gaussians. The first Gaussian represents the main peak and the second Gaussian, having a smaller normalization and a lower center position, represents the tail part in the low PH region. This is one of the simplest empirical models that has been conventionally used [3,15]. Each Gaussian has three free parameters that are the center channel GC,,,, the width (the standard deviation) GW,,,, and the normalization GN,,,. There are, therefore, six free parameters in this model. In our analysis, we only used the data in the region above 60% of the main peak in order to be consistent with the diffusion model described in the next section. Some variations of this model, for example, using a skewed Gaussian for the tail part connecting smoothly to the main Gaussian [3], or adding an appropriate function for the background [ 151 are often used.

Since there is no clear explanation of the origins of these two Gaussians, we assume that the first Gaussian represents the incident X-ray energy while the second one plays as a filler between the real data and the model. The X marks in Fig. 3 show the linearity between the incident X-ray energy and the center channel of the first Gaussian.

We divided the data into two groups at the Si K-edge

energy and fitted them by a straight line separately. We

considered the deviation of the data from the straight line as a systematic error in our experiment. We found the

discontinuity at the Si K-edge energy to be 8.7 + 2.6 eV. Since the uncertainty due to the statistics is about 0.4 eV, the systematic error dominates in our results.

The value of the discontinuity could be affected by the model choice. If we take a model other than the two Gaussian model, we might obtain another value. There- fore, it is difficult to determine whether the value we

obtained here originates from the photoabsorption process in silicon or from the model itself. The typical fitting with the two Gaussian model is shown in Fig. 4a. Although the two Gaussian model is useful to represent the data empirically, we conclude that we can not determine by this model whether an intrinsic discontinuity at the Si K-edge

energy exists or not.

3.2. Diffusion model

Inoue et al. [6] reported that the response function shows a low energy tail due to the incomplete charge collection through the diffusion process inside the gas scintillation proportional counter. They explained the response function by a semi-empirical method based on the diffusion process inside the gas. A similar effect is reported in the Ge SSD [7]. We applied this method [6] to treat the diffusion process in the SSD. The charge cloud produced near the electrode was partly absorbed and formed a tail part next to the main peak.

Since our SSD is a Li-drifted type, the electric field

~TWO Gaussian Model

0 Diffusion Model

P

e

e

P

P

1000 1500 2000

Energy [eV]

Fig. 3. The linearity between the incident X-ray energy and the pulse height peak position for the two Gaussian model (X marks) and the diffusion model (circles).

368 K. Torii et al. /Nucl. Instr. and Meth. in Phys. Res. A 361 (1995) 364-371

strength in the fully depleted layer can be considered to be constant. Therefore the process is treated by the one-di- mensional diffusion equation (1) as described and com- puted in Ref. [6].

I (a) .” . T,

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1 _.a:. ! . ‘...-.. .

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a a’ ,n(x. t)=D--&x, I,-+(., t). (1)

where ntx, t) is the electron density at a distance x from the entrance window at a time t after the photoabsorption, D is the diffusion coefficient of electrons in silicon, and w is the drift velocity of the electrons. The boundary and initial conditions are given by n(0, t) = 0, n(x, 0) = N,, 6( x - xr,), where N,, is the number of electrons initially produced by the incident X-ray and x0 is the position of the photoabsorption. As shown in Ref. [6], we obtain the number of collected electrons N and its distribution f(N) d N as demonstrated below.

(2) N=N”(I -exp(-T))

Km I

dN for OININo,

otherwise,

where

PPD K-

w

Fig. 4. Examples of the data points and the best fit results for the ti and p are the mass absorption coefficient and the silicon

two Gaussian model (a) and the diffusion model (b). density respectively.

-1 I /I ._

0.5 1

Normalized Channel

Fig. 5. Data points at various incident X-ray energies normalized by their peak positions. The solid lines show the best fit curves by the

diffusion model.

K. Torii et al. / Nucl. Instr. and Meth. in Phys. Rex A 361 (1995) 364-371 369

The actual PH distribution obtained by the experiment is the convolution of Eq. (3) and the response function of the detector. The response function in this case is well

approximated by a Gaussian profile with a constant width as is common in SSD in this energy range. The obtained PH distribution for the diffusion model- is

below.

described as

(5)

The profile of the diffusion model consists of two parts: a sharp peak and a tail with a monotonic decrease towards the low energy region. Fig. 5 shows the data at various incident X-ray energies normalized by its main peak position. The best fit curves described in Eq. (5) are also superposed in the figure. Almost all the data can be well

represented by Eq. (S), particularly above the half peak position. Whereas, there is a clear discrepancy between the data and Eq. (5) below the half the peak position. Since the data in Fig. 5 are normalized by their peak position, the horizontal axis represents the depth of the location of the photoabsorption (Eq. (2)). We found that the discrepancy became clear at about 600% of the peak position which corresponds to about 600 A.

The Li ion is implanted in the surface region about several hundred A into the SSD where the electric field is reduced. Then, the charge cloud produced in this region is lost easily through the electrode. This loss is more than that expected from Eq. (1). Therefore, we did not use the

data region below about 60% of the sharp peak in our analysis. In this way, we fitted the data with the diffusion model function (5). The free parameters are the peak position N,,, normalization A, the standard deviation of the Gaussian (T, and K. Though the likelihood has not significantly improved compared with the two Gaussian model, the data are well reproduced with the diffusion model except at the channel region less than about 60% of the peak position (see Fig. 4b).

We obtained the relation between the peak position and the incident X-ray energy. Circles in Fig. 3 show the linearity between the incident X-ray energy and the center channel of the sharp peak. We divided the data into two groups at the Si K-edge energy and fitted them by a straight line separately. We derived a systematic error in our experiment just as we did in the two Gaussian model fitting. We found the discontinuity at the Si K-edge energy to be 1.5 + 2.6 eV.

4. Discussion

We analyzed the data by using two models: one is a two Gaussian model and the other is a diffusion model.

Since the two Gaussian model is an empirical one, there is no physical meaning. We will focus on the diffusion model.

4.1. PH distribution

The diffusion model is based on the charge diffusion process in silicon. The discrepancy in the low PH region in the diffusion model can be attributed to the fact that the

model does not take into account the Li implanted region near the electrode. Using Eq. (4) and the following relation, we find the linear relation between p and K.

V w=@=cL~~.

where E is the the electric field strength. We use the following parameters: the silicon density, p = 2.34

[g/cm3], the applied high voltage, V= 1500 [VI, the depletion layer thickness, d, the dielectric constant of silicon,

E = 12, the mobility of electrons at the liquid nitrogen temperature, pe, and the diffusion coefficient at the liquid nitrogen temperature, D = pe kT/e. Therefore, we get the following in our experiment.

A = 2 = 3.7 x 10-S D

II 1.4 X 10’ cm’s_’

-1 X

WL,

2.1 X lo4 cm2 V-‘SK’ [g cm-‘]

(7)

Fig. 6 shows the best fit values of A as a function of incident X-ray energy. The data point denoted by a circle

shows the result from Mn Ka X-rays (5890 eV). All the data points show smooth variation on the incident X-ray energy and show almost constant values. We should note that d is given as 0.441 cm in the manufacturer’s catalog, but this is difficult to confirm.

/ t

0 L-I- -uLL_ r-l_ L- -l 1000 1500 2000

Enrrgy (eV]

Fig. 6. A values determined from our data are shown according to

the incident X-ray energy. The data point at 5.9 keV is also shown

by a circle for comparison.

370 K. Torii et al. / Nucl. Instr. and Meth. in Phys. Res. A 361 (I 995) 364-371

We noticed in Fig. 6 that the data point just above the Si K-edge energy shows a higher value than its neighbors.

This can be attributed to the inadequacy of the mass absorption coefficient used in our fitting. In our calculation, we assumed the mass absorption coefficient was expressed by a simple power law function of the incident X-ray energy excepting the edge structure. We calculated the mass absorption coefficient with the above assumption by using the published data points [20]. As a result, the structures due to the extended X-ray absorption fine structure (EXAFS) or X-ray absorption near edge structure (XANES), which show a sharp peak and a wavy structure just above the K-edge for crystalline silicon [21], are not taken into account. Therefore, the data point just above the K-edge energy may represent the fine structure of the absorption coefficient. Our absolute energy scale calibra-

tion is not enough to calculate the precise mass absorption coefficient due to EXAFS and XANES. We can say, however, that the result is qualitatively consistent with the

constant value of A at all incident X-ray energies we have studied.

4.2. Linearity

In the diffusion model, a sharp peak represents the complete charge collection events. We found the disconti-

nuity to be 1.5 _t 2.6 eV. The incomplete charge collection events can be represented by a tail part next to the main peak that can be empirically approximated by an extra function. However, if we fit the sharp peak with a Gauss- ian profile, the Gaussian will be affected by the type of the function employed for the incomplete charge collection

events. Therefore, the discontinuity we obtained based on the two Gaussian model does not represent the intrinsic property of the silicon. Since we get no discontinuity based on the diffusion model, we conclude that there is no measurable discontinuity for the complete charge collec-

tion events. As described in Section I, it is well known that there is

a discontinuity at the edge energies in the gas counters. We applied the diffusion model to the data obtained by the

Xe-filled gas proportional counter [15]. The resultant discontinuity of 170 f 10 eV at the Xe K-edge is the same as obtained with the two Gaussian model. In this case, if we use appropriate values [22] for Eq. (4), K is estimated to be about 4 X lop4 and 2 X 1O-3 for just below and above the Xe K-edge, respectively. These values are several tens of times smaller than those of SSD in which case K is about 9 X 10e3 and 1.5 X 10-i for just below and above the absorption edge, respectively. Therefore, the apparent position of the main peak is not affected by the model employed in the case of the Xe-filled gas proportional counter mainly due to its low density of the detector material.

Though the discontinuity at the Xe K-edge can be explained from the point of view of the difference of final

ionization states across the absorption edge [15], the same argument does not quantitatively explain the discontinuity

at the L-edge [14]. While Dias et al. [23] succeeded in quantitatively explaining the discontinuity at the L-edge of Xe gas by extensive Monte Carlo simulation.

One of the reasons of this disagreement may be qualitatively understood as the difference of the state of the detector material of gas and crystal. The final state of Xe gas is a highly ionized ion as measured by Carlson et al. [16], while the final charge spectra of silicon shown in Ref. [16] is not the measured value but interpolated from the measurement of various gasses. In the case of the crystal, the final state is thought to be not as highly ionized as the gasses, because “lack” of electrons in one atom would be easily supplied by surrounding atoms through the valence band. Therefore, the expended energy itself and the difference of it across the absorption edges in the crystal would be smaller than what is expected from the gas.

Fraser et al. [18] studied a silicon detector in detail

especially to understand the precise response function of X-ray CCD from the theoretical point of view. Their calculation includes i) electron-phonon interaction; ii) valence band ionization; iii) excitation of plasmons; iv) core L-shell ionization; and v) core K-shell ionization; for the process of the electron energy loss following the X-ray absorption and the atomic relaxation. Their prediction of the discontinuity at the Si K-edge is 0.2% or the equivalent

width of - 3.6 eV which agrees well with our experimen-

tal result. This good agreement shows that the discontinuity of the silicon detector is not only due to the difference of the energy expenditure at the initially photoionized silicon atom but also due to the difference of the compli- cated interactions of electrons (five mechanisms as described above) with silicon crystal at below, and above the

edge.

4.3. Comparison between the SSD and the CCD

We measured the characteristics of the Si(Li) SSD in detail. Since the CCD is made of silicon, similar effects may be expected in the CCD. Following the photoabsorption, the primary electron cloud is repelled from the electrode by the electric field in the SSD. In the front-illuminated CCD, the primary electron cloud is pulled to the electrode by the electric field. Since there is an insulation layer between the electrode and the depletion layer, no charge is lost by the diffusion. In this way, we can expect the PH distribution of the front-illuminated CCD to have a small tail part due to the effect described in this paper. While the tail in the front-illuminated CCD is due rather to the charge split effect among the pixels. The incomplete charge collection due to the diffusion effect will occur in the back-illuminated CCD. This is a similar effect in the SSD. A tail next to the main peak is reported at the low energy region 1241. We expect that there is no discontinuity

K. Torii et al. / Nucl. Instr. and Meth. in Phys. Res. A 361 (1995) 364-371 371

around the Si K-edge energy in the CCD although the [3] J.C. Luchner and E.A. Boldt, Nucl. lnstr. and Meth. A 242

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5. Conclusions

(41

El

Y. Tanaka, H. Inoue and S.S. Holt, Publ. Astron. Sot. Japan

46 (1994) L37.

We used the diffusion model to analyze the PH distributions in the soft X-ray region of the SSD. The PH distribution consists of two parts: the complete charge collection events and the incomplete charge collection events. The former made a sharp peak while the latter formed a tail next to the main peak. This dual-component curve can be well understood by using the diffusion model.

161

I71

181

[91

[lOI

[Ill

[121

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The linearity of the peak position of the sharp peak was examined in the energy range including the Si K-edge energy. We found the discontinuity at the Si K-edge energy to be 1.5 f 2.6 eV. Though the obtained value is much smaller than what is expected from the simple calculation used in the case of gas counters [15], it may be attributed to the difference in the structure of electron energy levels in the gas and in the crystal. The expected discontinuity from detailed Monte Carlo simulation by Fraser et al. [18] agrees well with our results.

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The authors express their thanks to all the member of the CCD group in Osaka University as well as the operat- ing staff at the UVSOR facility. The experiment was performed under the Joint Studies Program of the Institute for Molecular Science. This work was partly supported by the Grant-in-Aid for scientific research (05242103 and 06452023). The manuscript was read by Amy Lesser.

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Documents

Some characteristics of a solid state detector in the soft X-ray region