Noname manuscript No.(will be inserted by the editor)

Highly reproducible quasi-mosaic crystals as opticalcomponents for a Laue lens

Camattari Riccardo · Battelli Alessandro ·Bellucci Valerio · Guidi Vincenzo

Received: date / Accepted: date

Abstract The realization of a Laue lens for astronomical purposes involves the massproduction of a series of crystalline tiles as optical components, allowing high-efficiencydiffraction and high-resolution focusing of photons. Crystals with self-standing curveddiffraction planes is a valid and promising solution. Exploiting the quasi-mosaic ef-fect, it turns out to be possible to diffract radiation at higher resolution. In this paperwe present the realization of 150 quasi-mosaic Ge samples, bent by grooving one oftheir largest surface. We show that grooving method is a viable technique to manufac-ture such crystals in a simple and very reproducible way, thus compatible with massproduction. Realized samples present very homogenous curvature. Furthermore, witha specific chemical etch, it is possible to fine adjust one by one the radius of curvatureof the grooved samples. Realized crystals was selected for the ASI’s Laue project, thatinvolves the implementation of a prototype of a Laue lens for hard X- and soft γ-rayastronomy.

Keywords Laue lens · quasi mosaicity · grooving method · Laue project

1 Introduction

The detection of hard X-rays plays an increasingly important role in modern astron-omy. The instruments currently operating in this part of the electromagnetic spectrum,however, do not use focusing optics, i.e., the measured signal is collected directly onthe sensitive part of the detector itself.

The best technique to focus X-rays above 10 keV is Bragg diffraction. For ener-gies higher of 80 keV, it can be exploited Bragg diffraction in transmission configu-ration, the Laue geometry. In particular, a Laue lens is a concentrator conceived as an

Riccardo Camattari, Guidi Vincenzo, Battelli Alessandro, Bellucci ValerioDepartment of Physics and Earth Science, University of Ferrara, Via Saragat 1/c, 44122 Ferrara andCNR - IDASC SENSOR Lab., ItalyFax: +39 0532 974210E-mail: guidi@fe.infn.it

2 Camattari Riccardo et al.

Fig. 1 Schematic representation of a crystal plate with the coordinate system. Crystallographic orientationand QM curvature are highlighted.

ensemble of several crystals oriented in such a way that as much radiation as possibleis diffracted, through Laue geometry, towards the lens focus over a selected energyrange [1–3].

Several crystals are proposed for the realization of a Laue lens. Self-standingcrystals are mandatory for practical implementation of a focusing telescope, becausethe usage of an external device to maintain the crystal curvature leads to excessiveweight. With the aim of wide-passband focusing, a typical component under inves-tigation by the scientific community is a mosaic crystal, i.e., an aggregation of crys-tallites whose angular distribution is gaussian, spread about a nominal direction [4].However, this kind of crystals suffers 50%-maximum in reflectivity at zero absorp-tion (diffraction efficiency) and spatial resolution of diffracted photons is limitedbecause of the so-called mosaic defocusing effect [5,6]. Conversely, crystals withcurved diffracting planes (CDP) offer a continuum of possible diffraction angles overa finite range, leading to a rectangular-shape energy passband directly owing to theircurvature, while the diffraction efficiency can reach 100%.

Several techniques have been developed for the fabrication of a crystal with self-standing CDP. Such crystal can be obtained by concentration-gradient technique, i.e.,by growing a two-component crystal with graded composition along the growth axis[7–10]. However, crystals obtained by such a method are not easy to manufacture.The technique results hardly applicable for a Laue lens application, for which serialproduction of crystals should be envisaged. Crystals having CDP can also be pro-duced by applying a thermal gradient to a perfect single crystal [7], but this methodis energy consuming and not adapted to a space-borne observatory as well.

It was recently proven that CDP crystals can be obtained by grooving one faceof the crystals [11,12]. This technique is based on plastic deformation of the crystalinduced by grooving one of its largest surface [13,14]. As a result of the deformation,a permanent curvature is produced with no need for external device. Such method ischeap, simple and very reproducible, thus compatible with mass production.

The grooving method can also be exploited to produce CDP crystals with theso-called quasi-mosaic (QM) effect, i.e., an intriguing effect of anisotropy in crystaldeformation [15,16]. In this configuration, the primary curvature given by the groovesgenerates a secondary curvature within the crystal due to QM effect. Usage of QMcrystals allows positioning of the crystals in a Laue lens in the same way as for mosaiccrystals, i.e., with the diffracting planes perpendicular to the major faces of the crystal

Highly reproducible quasi-mosaic crystals as optical components for a Laue lens 3

Fig. 2 Schematic representation of a cross section of a Laue lens based on QM crystals. Primary curvatureof (112) planes leads to a secondary curvature of (111) planes owing to quasi-mosaicity. In this configura-tion the (111) diffracting planes are perpendicular to the main surface of the plate. It can also be seen thecapability of primary curvature to focalize diffracted radiation while QM curvature establishes an increasein diffraction efficiency.

(Fig.1). For a Laue lens made by QM crystals, focusing can be fully provided bybending the crystals to a primary curvature equal to that of the whole lens (Fig.2). But,if the diffracting planes were perfectly flat, the reflectivity of the whole lens would bethe same as for an unbent mono-crystal, i.e., a relatively low figure. Indeed, by usingQM crystals, it is possible to encompass the focusing action due to primary curvaturewith the high reflectivity of CDP built up by quasi-mosaicity. Experimental resultsof diffraction with QM Si crystals through (111) planes have been already proved[19,20], showing that QM curvature amplifies the diffraction efficiency by more thanone order of magnitude with respect to an equivalent crystal without quasi-mosaiccurvature.

In this paper we demonstrate the feasibility of the grooving method to producea large number of Ge QM samples for practical implementation of a Laue lens, in avery reproducible and simple way. Highly homogeneous curvature is obtained in thesamples processed with our grooving technique. Moreover, we show that it is possibleto fine adjust the curvature with a very fast chemical etch. This technique has beenchosen to realize the QM Ge samples for the Laue project, supported by the ItalianSpace Agency (ASI). This is a project devoted to develop an advanced technologyfor building a petal of Laue lens with a broad energy passband (100-300 keV) andlong focal length (20 m) for space-borne Astrophysics [21,22]. The main aim is tosignificantly overcome the sensitivity limits of the current generation of gamma-raytelescopes and improve the imaging capability. It started in 2010, while it is expectedthat the prototype will be completed in summer 2013.

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Table 1 Crystal features

Material GermaniumTile size (mm3) 30×10×2

Blade type G1A 320Blade width (µm) 250

Blade rotation (rpm) 3000Blade speed (mm/s) 0.1Groove depth (µm) 1550Number of grooves 9×28Groove step (mm) 1

Primary radius of curvature along y (m) 40QM radius of curvature (m) 95.6Angular bandpass (arcsec) 4.3

Fig. 3 Photo of the a Ge sample before (a) and after (b) the manufacture. Crystallographic orientation arehighlighted.

2 Experimental

Production and optical characterization of about 150 QM Ge crystals has been carriedout at Sensor and Semiconductor Laboratory (Ferrara, Italy). Crystallographic orien-tations are indicated in Fig.3. Commercially available pure Ge wafer was diced toform 30×10×2 mm3 plates, using a high-precision dicing saw (DISCOT M DAD3220),equipped with rotating diamond blades of 250 µm width and 5 µm diamond grainsize (G1A 320). A permanent curvature was induced through the so-called groovingmethod, i.e., through the manufacture of a grid of superficial grooves on one of thelargest surfaces of the crystal. A radius of curvature of 40 m was chosen, because afocal length of f = R/2 = 20 is an ideal value for a Laue lens with long focal distance[21,22]. It is possible to calculate the ratio between QM (RQM) and primary (RQM)radius of curvature thanks to the linear theory of elasticity. It turns out to be RQM

RP=

2.39 [16]. It corresponds to a QM curvature of about 95.6 m. The angular bandpasscorresponding to this radius of curvature is 4.3 arcseconds. Main features are reportedin Tab.1.

In fact, surface grooving produces permanent plastic deformation in the neighbor-hood of the grooves [13]. Plasticization occurs in a thin layer of the crystal beneath

Highly reproducible quasi-mosaic crystals as optical components for a Laue lens 5

and beside the grooves due to the dicing process, the thickness of the plasticized layerbeing dependent on the blade and on the grooving parameters chosen. The depth ofthe plasticization for the blade that was used is about 5 µm [14]. Such plasticizedlayer transfers coactive forces to the crystal bulk, thus producing an elastic strain fieldwithin the crystal. Since a regular grid of grooves was done on the sample surface, anet curvature has been achieved.

Then, the curvature of all the samples was measured using an optical profilome-ter (VEECOT M NT1100) with 1 µm lateral and 1 nm vertical resolution. In order toaccount for the initial morphological non-planarity of the samples (wafers are gen-erally not perfectly flat), subtraction of profile before and after the grooving processwas done. Moreover, since the profile of a surface with grooves is altered by theirpresence, thus making the analysis more difficult, profilometric characterization wascarried out on the back surface of each sample.

Finally, a method to adjust the curvature has been worked out. It consist in a fastchemical etch, based on a solution of H2O2. Such solution is capable of oxidizing Gewith different speeds, depending on the crystalline phase [23]. In fact, it is possibleto selectively remove the most amorphus part of a sample, namely the material plas-ticized by the blade, lowering the state of tension and the curvature of the sample.With quick chemical etch at low H2O2 concentration, the possibility of increasingthe radius of curvature of samples of a few meters has been experimentally verified.

The production of 150 QM samples of germanium has been carried out rapidlyand in a very reproducible way. The interferometric measurement takes few minutes,less than 5 for each one. The chemical etch is very fast, it takes about one minute. Thecut process is the longest part of the production, it is about 4-5 hours long. It wouldbe possible that the process will become reproducible enough to allow skipping themorphology characterization. Currently it is necessary to measure the samples foreach step, because the experimental condition may vary in a not well controlled way.

3 Results and discussion

A series of 150 Ge QM crystals have been produced and analyzed with the profilome-ter. The measurement of the primary radius of curvature of a single sample is reportedin Fig.4. The curvatures resulting from the grooving process are very close to a spher-ical surface, because the grooves are regularly spaced and have all the same depth. Infact, to focalize the impinging photons, a cylindrical curvature would work. However,it derives from the theory of elasticity that a spherical curvature is required to obtainthe QM effect [16].

Ideally, each tile is expected to produce a diffracted spot shaped as a thin rect-angle, with 10 mm width and of thickness given by the quasi-mosaic defocusing.The defocusing can be estimated to be 2Fdetm, Fdet being the distance of the tilefrom the focal spot and m the angular distribution due to QM effect [5]. In this case2Fdetm ≃ 0.84mm.

To verify the uniformity of the curvature, subtraction of measured surface witha perfectly spherical surface having the radius of curvature equal with the averageradius of curvature (39.9 m) of the measured sample was performed. Result of sub-

6 Camattari Riccardo et al.

Fig. 4 Interferometric measurement of backside of a sample with average radius of curvature r = 39.9meters. Left side: 3d view analysis (a). Right side: Cross sections of the deformation pattern along x (b)and y directions (c), as taken on the center of the sample.

traction with the sample of Fig.4 is shown in Fig.5. Moreover, the root mean squareroughness Rq has been calculated by using Eq.1. It represent the standard deviationof the distance between the measured sample surface and the spherical surface withradius of curvature = 39.9m.

Rq =

√1

MN

M

∑i=l

N

∑i=l

Z2(xi,yi) = 13.86nm (1)

where M and N are the number of data points in the X and Y direction, respectively,of the array, and Z is the surface height.

Interferometric measurements of the sample curvatures worked out at LSS havealready validated in previous X-ray diffraction experiments at ESRF (beamline ID15A)and ILL (beamline DIGRA), with energies above 150 keV [11,12,19]. In these ex-periments, the FWHM of the recorded rocking curves corresponded to the curvatureof the sample as measured with the profilometer.

The series of 150 samples have been produced with a radius of curvature slightlylower with respect to the desired value of 40 meters, because of the sample over-bentcan be adjusted one by one at the value of 40 meter thanks to the chemical etch. Infact, during the production, some features are difficult to control. For example, thereis an uncertainty on the crystals thickness, which can vary from sample to sample.The consequence is a partial reproducibility on the final curvature. Indeed, for eachsample the curvature is homogeneous, but the resulting radius of curvature may varyfrom sample to sample. Although the distribution of primary radius of curvature isintentionally not symmetric, a fit with a gaussian has been worked out. It results thatthe distribution has mean = 36.6 m and standard deviation = 6.6 m. The distributionof the measured curvature radius for all the samples, recorded along [111] direction,is reported in Fig.6.

Highly reproducible quasi-mosaic crystals as optical components for a Laue lens 7

Fig. 5 Subtraction between the measured sample with a spherical surface with radius r = 39.9 meters.Left side: 2d view of subtracted data (a). Right side: Cross sections of the subtraction pattern along x (b)and y directions (c), as taken on the center.

Fig. 6 Distribution of primary radius of curvature, measured along [111] direction on the 150 crystal tilesproduced, before the chemical etch. The red dashed line shows the best fit Gaussian distribution.

Then, the chemical etch based on H2O2 has been experimentally verified. Theetching can oxidize and remove a very thin layer of crystal. The removal of materialin the region of the grooves causes a relaxation of the tensile state, allowing thesample to relax its curvature. In Tab.2 an example has been reported. 60 seconds ofetching has been performed, obtaining a relaxation of the curvature of about 4 meters,starting from 36.8 to 40.3. With shorter etch it would be possible to obtain lower valueof relaxation.

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Table 2 Adjustment of the curvature in a Ge grooved sample

Chemical etch solution of H2O2Initial radius of curvature along [111] 36.8 m

Concentration 2.5 ml in 100 ml of waterEtch duration 60 s

Final radius of curvature 40.3 mTemperature room

Fig. 7 Expected reflectivity for the fabricated Ge samples. The top curve is the theoretical reflectivity of anon-grooved CDP block of germanium having dimensions identical to those of our tiles. The bottom curveshows the theoretical reflectivity of the grooved tiles, which takes into account the fact that a fraction ofcrystal is removed during the manufacture process.

The expected reflectivity for these crystals is the value predicted by the diffrac-tion theory for curved diffracting planes. However, a portion of sample is removedduring the manufacture, thus it must be taken into account that the grooves occupyabout 32.5% of the samples volume. The curvature should be uniform throughout thesamples, both in the blocks between the grooves and below the grooves. The expectedreflectivity is reported in Fig.7.

4 Conclusions

Production time of an individual tile currently takes 4-5 hours, mostly consisting ofautomated operations, i.e., mass production of QM crystals for building a Laue lenscan be envisaged. However, much more time can be saved, once all the process willbe optimized.

It has been shown that the samples obtained in such a way result to have a high-homogeneous curvature. Moreover, with the chemical etch, it turns be possible to fineadjust one by one the radius of curvature of the samples, preserving the homogeneityof bending. Grooving turns out to be an elective method for a quick production of a

Highly reproducible quasi-mosaic crystals as optical components for a Laue lens 9

large number of self-standing bent samples, that is a mandatory issue for a concreterealization of a Laue lens.

The Ge samples are currently being tested at LARIX facility, with X-ray diffrac-tion on the QM (111) planes. When all these experimental data will be acquired, theprototype of the Laue lens will be assembled and tested at the LARIX laboratories toform the petal lens.

Acknowledgements The authors are grateful to ASI for financial support through the Laue project.

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