measurement of the charge cloud shape produced by an x-ray...

Nuclear Instruments and Methods in Physics Research A 421 (1999) 90—98

Measurement of the charge cloud shape produced by an X-rayphoton inside the CCD using a mesh experiment

H. Tsunemi!,*, J. Hiraga!, K. Yoshita!,1, K. Hayashida!

! Department of Earth and Space Science, Graduate School of Science, Osaka University, 1-1 Machikaneyama-cho,Toyonaka, Osaka 560-0043, Japan

CREST, Japan Science and Technology Corporation (JST), Japan

Received 23 February 1998

Abstract

We present here the direct measurement of the charge cloud shape in the charge-coupled device (CCD) produced by anX-ray photon using a mesh technique. This technique makes use of a parallel X-ray beam and a metal mesh placed justabove the CCD. The CCD we used has a 12 lm square pixel while the mesh has many circular holes with 3.4 lm indiameter spaced at 4 times that of the CCD pixel size (multi pitch mesh). We employed the Al-K X-rays. By using thistechnique, we could unambiguously identify the interaction position of X-rays. When the X-ray enters near the pixelboundary, the charge cloud splits into two or more pixels. We obtain how much charge is collected in one pixel accordingto the interaction position of Al-K X-rays. By analyzing the split events for various part of the pixel, we can reconstructthe charge cloud shape in detail. The charge cloud shape we obtained is well expressed with an asymmetric Gaussianfunction (the horizontal width is 1.7 lm and the vertical width is 0.9 lm). The asymmetry comes from the electric field inthe CCD. ( 1999 Elsevier Science B.V. All rights reserved.

Keywords: Charge-coupled device; Mesh experiment; Sub-pixel resolution; Charge cloud shape

1. Introduction

In X-ray astronomy, a charge-coupled device(CCD) becomes a standard photon count detector[1]. It has a medium energy resolution and a good

*Corresponding author. Tel: #81 6 850 5477; fax:#81 6 850 5539 E-mail: [email protected]

1Partially supported by JSPS Research Fellowship for YoungScientists, Japan.

spatial resolution. There are several satellite pro-grams employing the CCD as an X-ray photoncount detector: ASCA [2], AXAF [3], XMM [4],ABRIXAS [5] etc.

Recently, we invented a new technique to obtainthe X-ray response of the CCD with sub-pixel res-olution [6]. The new technique consists of a metalmesh placed just above the CCD and a parallelX-ray beam. The mesh had lots of small holes withperiodic spacing. The hole was smaller than theCCD pixel size which determined the attainable

0168-9002/99/$ — see front matter ( 1999 Elsevier Science B.V. All rights reserved.PII: S 0 1 6 8 - 9 0 0 2 ( 9 8 ) 0 1 1 5 4 - 1

spatial resolution. The spacing of holes was equalto that of the CCD pixel size (single pitch mesh).This technique enabled us to restrict the inputX-ray position with sub-pixel resolution. The de-tailed gate structures were directly measured fromthe X-ray absorption feature [7,8].

In the single pitch mesh experiment, there issome ambiguity to determine the hole throughwhich the X-ray really enters. Therefore, we intro-duced an improved technique to employ the meshwhose hole spacing was a multiple of the CCD pixelsize (multipitch mesh) [9]. This enables us unam-biguously to determine the hole through which theX-ray photon really enters, resulting in the interac-tion position of various types of X-rays in detail.Then, we obtain the method to directly measure thecharge cloud shape produced inside the CCD. Thispaper describes how we obtain the cloud shapeproduced by an X-ray photon inside the CCD.

2. X-ray event grade

When the X-ray photon is photo-absorbed in theCCD, the photo-electron is produced. Then, theprimary charge cloud is formed by the photo-elec-tron. Since the energy range of interest in this paperis below 3 keV, the primary charge cloud size canbe considered as a point. The possible asymmetrydue to the polarization of X-ray [11] has nothing todo with our results.

If the photo-absorption occurs under the de-pletion region, the primary charge cloud will diffuseout in all directions. Some of them moving back-ward will be lost at the substrate of the device.Some of them moving forward will be collected intothe potential well when they reach the depletionlayer. Even in this case, the detected signal isa widespread multi-pixel cloud. Furthermore,the total charge collected in the potential well is notproportional to the incident X-ray energy. There-fore, we can easily eliminate these events bymeasuring how many pixels the charge spread. Ifwe employ the mono-energetic X-ray beam, theselection of energy also eliminates them easily.

If the photo-absorption occurs at the depletionlayer, all the primary charge cloud will be collectedin the potential well which is formed under the

Fig. 1. Various types of the event patterns or grades are ex-pected to be produced by the X-ray photon. Each small squarerepresents the CCD pixel. The dark pixels show the event pixelwhile the hatched pixels show the split pixel. The ASCA grades(0,2,3,4,6) are shown for comparison.

gates of the CCD. The primary charge cloud ex-pands through the diffusion process when it movesin the depletion layer. The diffusion length is rela-tively small [10], whereas the entire charge cloud isnot always collected into one pixel. When thephoto-absorption occurs well away from the pixelboundary, the charge cloud is collected into onepixel (single pixel) while the photo-absorption oc-curs near the pixel boundary, the charge cloud willsplit into 2—4 pixels depending on how close theinteraction position is to the pixel boundary. In anycase, we can read out all the charge through the

H. Tsunemi et al. /Nucl. Instr. and Meth. in Phys. Res. A 421 (1999) 90—98 91

read out node. The sum of the output signal isproportional to the energy of the incident X-ray.

The event is defined when the pixel output isabove the event threshold, ¹

%7%/5, as well as when it

becomes the local maximum. The split pixel is de-fined when the pixel output is above the split thre-shold, ¹

41-*5. A single event is the event having no

adjacent split pixel. Two pixel split event is theevent having only one adjacent split pixel. There-fore, there are four types of two split events: leftsplit, right split, top slit and bottom split. Most ofthe three or four pixel split events are the L-shapeor the square shape.

There are several patterns or grades showinghow the charge splits into neighboring pixels. In theASCA SIS [2], they employed eight grades basedon the patterns. Fig. 1 shows the quick summary ofthe event grades. The event grades give us someinformation on the shape of the charge cloud insideSi. Recently, a new technique was invented [6,9]using a metal mesh placed just above the CCDwhich enabled us to confine the X-ray interactionposition with sub-pixel resolution.

3. Experimental setup

Fig. 2 shows a schematic view of the experimentusing a multipitch mesh as well as a single pitchmesh. The metal mesh with holes periodicallyspaced is placed just above the CCD surface. Themesh is placed parallel to the CCD surface while itis tilted at a small angle, h. The parallel X-ray beam

Fig. 2. A schematic view of the experiment. The hole shadow isrepresented by the hatched area. (a) A single pitch mesh: themesh hole pitch is equal to that of the CCD pixel size. (b)A multipitch mesh: the mesh hole pitch is a multiple (4 in thisfigure) of the CCD pixel size.

Fig. 3. The X-ray spectrum obtained with the CCD in themultipitch mesh experiment. The continuum above 3 keV comesfrom the X-rays penetrating the metal foil while Al-K X-rayscome from those passing through the mesh hole.

is irradiated along the normal to the CCD surface.The X-rays passing through the mesh hole canreach the CCD. Therefore, the X-ray interactionposition is restricted by the mesh hole. When weobtain the X-ray event on the CCD, we can easilydetermine the interaction position of the X-rayevent.

The copper metal mesh we used is of 10 lmthickness with 3.4 lm diameter holes periodicallyspaced at 48 lm. We measured the hole diameterby averaging several holes on the SEM photo-graphs. We designed the mesh holder so that it wasplaced 1 mm above the CCD surface. The mesh wastilted about !1° from the pixel direction so thatwe could obtain a moire pattern. We employed thesame 21 m long X-ray beam line which we used [6]in the previous experiment. The applied voltage tothe X-ray generator, the UltraX-18 manufacturedby RIGAKU Corp. was about 5 kV. We used theAl target producing Al-K X-rays (1.5 keV). TheX-ray intensity was controlled so that the pile upwould not become serious in the CCD. Fig. 3shows an X-ray spectrum obtained by our system.

The transmission of copper foil of 10 lm thick-ness is 10~3 at 3 keV and lower at lower X-rayenergy. Therefore, we can say that the X-ray con-tinuum above 3 keV can penetrate the copper foilwhile all the Al-K X-rays reach the CCD onlythrough the mesh hole. Therefore, we can pick up

92 H. Tsunemi et al. /Nucl. Instr. and Meth. in Phys. Res. A 421 (1999) 90—98

the X-ray events passed through the mesh hole byselecting the X-ray energy.

We employed a CCD chip, N11-5-5A0N-2,a product of the Hamamatsu photonics Corp. with12 lm square pixel size. The CCD chip was cooleddown to !60°C. In our configuration, the meshwas also cooled down to the same temperature. TheCCD camera system was equipped with a mechan-ical shutter (stainless steel of 60 lm thick) to blockthe X-rays.

4. Data restoration method

Fig. 4 shows the distribution of the single eventsof Al-K X-rays on the CCD. In our experimentalsetup, the moire pattern does not directly representthe pixel structure. In the previous experimentsusing a single pitch mesh, we assumed that theCCD pixel was a perfect square shape and thatmesh holes were distributed in perfect square spac-ing. In this paper, a possible distortion effect of themesh hole distribution is taken into account.

Fig. 4. Raw images obtained by using single events. Due to themultipitch mesh, most of the X-rays appear at roughly every4]4 pixels.

The CCD pixel coordinate, X, is expressed inEq. (1)

X"CA1#a 0

0 1#bBAcos h !sin h

sin h cos h B x#Xoff,

(1)

where x denotes the mesh hole coordinate, C isa coefficient of the multipitch mesh (it is 4 in ourexperiment), a and b are expansion coefficientsalong x- and y- axis, h is a tilt angle and Xoff is anoffset. There are several reasons why the expansioncoefficient should be introduced. They are theX-ray beam divergence, the difference betweenthe thermal contraction of the mesh and that of theCCD, the production accuracy of the mesh andthe alignment of the mesh holder.

The output of the nth pixel of the CCD, Dn, is

expressed below.

Dn" P

/5) 1*9%-

M(x)E(X)dX,

where M(x) denotes the transmission of the mesh,E(X) the detection efficiency of the CCD.

The transmission of the mesh is expressed inEqs. (2)— (4)

M(x)"PH(x@)¸(x!x@) dx@ (2)

H(x)"G1 (DxD(r),

metal transmission&0 (DxD'r),(3)

where H(x) is a typical hole shape of the mesh, ¸(x)denotes the hole position on the mesh and r isa radius of the effective hole size. In our experi-mental setup, r is about 2 lm taking into accountthe diffraction of X-rays. Since the hole is period-ically spaced on the x plane, we obtain

¸(x)" +n/*/5%'%3 -!55*#%

d(x!n). (4)

Once we assume some values for a, b, h and Xoff, wecan restore a pixel image. The precise values forthese parameters are obtained by searching a set of


values which produce the largest data variance inthe restored image [6]. The practical method forthe single pitch mesh is described in Refs. [8,9]. Inthe multipitch mesh, on the contrary, there aremany pixels having no mesh hole on them as shownin Fig. 2(b). Therefore, even if we pick up the truevalues for a, b and h, we have to search the truevalue for Xoff so that the restored image is construc-ted by using pixels corresponding to the meshholes.

In this way, the image variance was maximized ata"!0.5]10~3, b"!1.3]10~3, h"!1.15°,X

0&&"2.05 and ½

0&&"0.55. We have adopted these

values for the restored images presented in theremainder of this paper. We notice that a is differ-ent from b. It means that either the hole meshspacing or the CCD pixel spacing along the x-axisis longer by 0.8]10~3 than that along the y-axis.Our results have nothing to do with this case.

5. Data analysis

5.1. Restore images for various types of X-ray events

As shown in Fig. 5, we obtained a restored imageof the ‘representative pixel (RP)’ using single events.We reproduced 3]3 RP in the figure. The pixelboundary is indicated by dashed lines. This clearlyshows that the single events occur when the interac-tion position of X-ray is well away from the pixelboundary [6—8]. The dark region represents theconvolution of the effective hole shape and theregion where the X-rays generate single events.Single events inform us of the interaction positionat which the X-ray enters somewhere in the pixel.No further information is available.

Next, we restore the RP for the two pixel splitevents which is shown in Fig. 6. The two pixel splitevents are surely produced when the X-rays enterthe boundary region making the charge cloud splitinto the adjacent pixel. The interaction position ofthe X-ray determines the ratio of how the chargecloud is split. Therefore, the split event can havefiner information on the interaction position ofX-rays. The center of gravity of the split event givesus the interaction position of X-rays with an uncer-tainity (1p) of 0.13 pixel size [9].

Fig. 5. The X-ray intensity map of the RP for single events withsub-pixel resolution. 3]3 RPs are shown.

Fig. 7 shows the RP for three or four pixel splitevents. We can expect that the four pixel splitevents are produced when the interaction positionof X-rays is close enough to the pixel corner so thatthe charge cloud splits into a diagonal adjacentpixel. Whereas, we can expect that the three pixelsplit events are produced when the interaction posi-tion of X-rays is a little away from the pixel cornersuch that the charge cloud does not split into thediagonal pixel.

5.2. Charge cloud shape

We should note that the event classificationby grades depends on the split threshold. If thesplit threshold is set to a small value, the appar-ent charge cloud will be large resulting in thereduction of single events. We will deal with thecharge cloud extent which is free from the splitthreshold.

Let us assume that the charge cloud shape isexpressed in the form of f (X!X

*/,½!½

*/) where

(X*/,½

*/) is the interaction position of X-ray. Then,

the output of the nth pixel, Dn(X

*/,½

*/), is given


Fig. 6. Same for Fig. 5 but for split two pixel events. (a) Right split events, (b) left split events, (c) top split events and (d) bottom splitevents

below:

Dn(X

*/,½

*/)"

Yn`1

PYn

Xn`1

PXn

f (X!X*/,½!½

*/) dX d½

(5)

where Xn,½

n,X

n`1,½

n`1is the pixel boundary of

the nth pixel. In our experiment, we can unambigu-

ously determine the interaction position inside thepixel. Therefore, we can experimentally determinethe function of D

n(X

*/,½

*/). We divide the RP into

20]20 sub-pixels. Then, we calculate all the X-rayevents belonging to each sub-pixel. We found thatthere were 300—400 X-ray events in each sub-pixel.The horizontal pixel boundary is generated by thegates of the CCD. Whereas, the vertical pixelboundary is generated by the channel stop running


Fig. 7. Same as for Fig. 5 except for four types of 3 and 4 pixelsplit events. (a) Top left corner events, (b) top right corner events,(c) bottom left corner events and (d) bottom right corner events.Each figure shows the RPs for three pixel events (left figures) andfor four pixel events (right figures).

perpendicular to the gates. The number of X-rayevents is small in the sub-pixel where the channelstop acts as an extra X-ray absorber.

Fig. 8. Dn(X

*/,½

*/), the distribution of the charge collected in the

pixel, is displayed on the X*/!½

*/plain. 3]3 pixel area is

shown. A contour of the linear scale is overlaid.

Fig. 8 shows the function of Dn(X

*/,½

*/). This

figure shows how much charge is collected into thenth pixel according to the interaction position ofthe X-ray where the nth pixel is shown in the centerpixel of the figure. We should note that this figurehas nothing to do both with the split threshold andwith the absorption feature above the depletionlayer.

Next, we obtain the relation given below bydifferentiating D

n(X

*/,½

*/) with X

*/,½

*/.

L2LX

*/L½

*/

Dn(X

*/,½

*/)"

Yn`1

PYn

Xn`1

PXn

fXY

(X!X*/, ½!½

*/)dXd½"

f (Xn`1

!X*/,½

n`1!½

*/)#f (X

n!X

*/,½

n!½

*/)

!f (Xn`1

!X*/,½

n!½

*/)

!f (Xn!X

*/,½

n`1!½

*/) (6)

Therefore, we will obtain the charge cloud shapeby differentiating the image in Fig. 8. In this


Fig. 9. A charge cloud shape obtained in our experiment isshown in 12]12 lm region. This shape is a differential functionof the image in Fig. 8. A contour of the linear scale is overlaid.The image shown here is smoothed by a Gaussian function ofthe width of p"1 lm.

calculation, we simply replace the differential equa-tion by a difference equation as described in Eq. (7).

L2LX

*/L½

*/

Dn(X

*/,½

*/)+D

n(X

i`1,½

j`1)#D

n(X

i,½

j)

!Dn(X

i`1,½

j)!D

n(X

i,½

j`1), (7)

where (Xi,½

j) represents the (i,j) sub-pixel location

in Fig. 8. An advanced method of the differential ofthe numerical calculation may produce finer resultswhich will be done elsewhere.

In our experimental setup, the charge cloudshape is smaller than the pixel size (12 lm square).Thus, we can safely assume that there is at most oneterm in Eq. (6) which is non-zero. When we differ-entiate the image of Fig. 8, we clearly obtain fourpeaks at each corner of the RP, each of whichrepresents the charge cloud shape f (X,½). Thosefour peaks are well isolated from each other. Twoare positive peaks and the other two are negativepeaks. By summing four peaks properly, we calcu-late the function of f (X,½) as shown in Fig. 9.

Since f (X,½) is a convolution of the hole shapeand the cloud shape, we can calculate the intrinsicwidth of the cloud shape. Table 1 summarizes theresults.

6. Discussion

The numerical calculation [10] shows that thefinal charge cloud size consists of two processes: theinitial charge size, 1.71]10~2E1.75lm, and the dif-fusion in the depletion layer which can be approxi-mated by &(¸/50) lm based on Fig. 4 in Ref. [10],where E is the photo-electron energy in keV and¸ is the travel distance of the electron cloud in thedepletion layer in lm. The initial charge size isexpected to be quite small for the X-ray energy wemeasured. The effective thickness of the depletionlayer of the CCD we used is about 10 lm. Takinginto account the mean absorption length of X-rayin Si, the expected charge cloud size (1p) would besub-micron scale. The expected charge cloud sizefor Al-K X-rays is about 0.1—0.2 lm.

The number of the single event and that of thesplit event will give us a rough indication of thecharge cloud size. Based on our result, the chargecloud size (the charge less than the split threshold isconsidered to be out of the cloud size) will bea quarter of the pixel size. This is inconsistent withthat derived from the above numerical calculation.

By taking into account the fact that the chargecloud size we measured is the convolution with themesh hole, the apparent charge size is expectedto be 0.9—1.7 lm as shown in Table 1 which ismuch larger than that expected from the numericalcalculation.

Table 1Charge cloud size produced by the Al-K X-ray

Al-K

Energy (keV) 1.5Mean absorption length (lm) 7.9Data width (X) (lm) 1.9(½) (lm) 1.3Intrinsic width (X) (lm) 1.7(½) (lm) 0.9


The cloud shape we obtained does not showa point symmetric structure. However, it is almostaxial symmetric both on the vertical directionand on the horizontal direction. Since the charac-teristic X-rays produced in the X-ray generatoris experimentally confirmed to be unpolarized [12],the photoelectrons are injected uniformly expectingto form a point symmetric cloud shape. The diffu-sion process during the depletion region doesnot make the cloud asymmetric. The cloud shapewe obtained is measured in two ways: the hori-zontal structure is measured based on howthe charge is split in the horizontal direction by thechannel stop while the vertical structure ismeasured based on how the charge is split in thevertical direction by the gate. Since the channelstop structure is different from the gate structure,the asymmetry of the charge cloud would comefrom the difference of the electric field. Althoughthe detailed mechanism is not clear at present, it issuggested in the previous experiment. Tsunemiet al. [11] reported the first detection of X-raypolarization using the CCD. They detected theasymmetry of the charge cloud generated by thepolarized X-ray photon by measuring the ratiobetween the number of horizontally split eventsand that of the vertically split events. They noticedthat the ratio by polarized X-rays varied accordingto the polarization direction of X-rays and that theratio by unpolarized X-rays statistically differedfrom unity. This fact can be understood if thecharge split process depends on the electric field.The detailed analysis is beyond the scope of thispaper.

7. Conclusion

We clearly show that the split event is formedaccording to the interaction position inside thepixel. When the X-ray enters well within the pixelboundary, the entire charge cloud is collected inone pixel resulting in the formation of a singleevent. When the X-ray enters near the pixel bound-ary, the electron cloud splits into the adjacentpixels. The two, three or four pixel split eventsdepend on how close the interaction position is tothe pixel boundary. We should note that it depends

on the split threshold whether the X-ray becomesa single or a split event.

We measured the collected number of electronsin one pixel, D

n, according to the interaction posi-

tion of X-rays. We should note that it has nothingto do with the split threshold. Furthermore, weobtain the charge cloud shape by differentiating thefunction of D

n. It shows an asymmetric structure.

The calculated shape we obtained comes from thethree processes: the primary charge cloud shape,the diffusion process in the depletion region and thecharge split near the pixel boundary. The asym-metry of the charge cloud shape is mainly deter-mined by the last process.

Acknowledgements

The authors are grateful to all the membersof the CCD team in Osaka university. Mr. K.Miyaguchi in Hamamatsu photonics gave ustechnical supports.

References

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