2011 IEEE Nuclear Science Symposium Conference Record RTSD.S-245

Interpolation in a Pixellated CZT ,-Radiation

Detector Dirk Meier, IEEE, Codin Gheorghe, Tor Magnus Johansen, Sindre Mikkelsen, Gunnar Maehlum, IEEE

Abstract-We describe a method of interpolation for a pixel­lated ,,(-radiation detector made of cadmium zinc telluride (CZT) with the goal to optimize its intrinsic spatial resolution. A similar method is known from silicon strip sensors where the interpolation improves the intrinsic spatial resolution over the single-strip digital resolution.

We used a CZT crystal with a 2-dimensional matrix of anodes (pixels) on one side and a cathode on the other side. Each anode was electrically connected to a charge sensitive amplifier/shaper, which provided a pulse height output proportional to the amount of the electrical charge induced at the anodes. The amplifiers were implemented in a custom made application specific integrated circuit (ASIC) that allowed us to read out the charge from the triggering pixel and, in addition, the charge from its nearest neighbour pixels. We used 241 Am, 57 Co and 22Na radiation sources to acquire energy spectra and shadow images from a tungsten metal edge.

We observed charge sharing between pixels in about 10% and 24% of the photon interactions for 59.5 keV and 122 keV, respectively. We found that the method of interpolation did not improve the intrinsic spatial resolution in the CZT detector used, presumably due to the very small gap between pixels. Nevertheless, we consider interpolation important, since it has the potential to improve intrinsic spatial resolution either with a different method or with an anode layout that allows for more charge sharing, e.g., with larger gaps between pixels. Like in silicon sensors the method may benefit from additional electrodes in the gaps between the readout pixels.

Index Terms--,,(-radiation detector, CZT, ASIC, spatial reso­lution, interpolation, pixel

I. INT RODUCT ION

THE spatial resolution of an imaging system is an im­

portant figure of merit. Digital imaging systems for x­

and ,,(-rays employ radiation collimators providing a spatial

resolution that is determined by aperture size and length, the

magnification, and the intrinsic spatial resolution in the detec­

tor [1]. The intrinsic spatial resolution can contribute signifi­

cantly to the overall spatial resolution, especially in compact

imaging systems with small apertures and little magnification.

Our group designs digital x- and ,,(-radiation detectors with

readout electronics that is implemented in application specific

integrated circuits (ASICs) for, e.g., space science [2], [3], and

medical applications [4], [5]. The basic design of a readout

system for pixellated cadmium zinc telluride (CZT) delivers

the address of the triggering pixel and its pulse height [6].

This information allows one to measure the energy for every

photon and to count the number of photons in any energy

All authors are with Gamma Medica - Ideas (Norway) AS, http://www. gm-ideas.com

window within the acquired spectral range. The intrinsic

spatial resolution that can be achieved with this type of readout

is in principle limited by the pixel readout pitch, because only

the xy-coordinates of the triggering pixel are acquired and no

pulse height information is used for the position measurement.

The main goal of this work is to improve the intrinsic spatial

resolution in pixellated CZT ,,(-radiation detectors. To this end,

we have designed a new ASIC that provides the possibility

to acquire the pulse height from the triggering pixel, and in

addition, the pulse height from neighbour pixels due to charge

sharing.

Charge sharing has been studied in CZT with strips and pix­

els by several other groups. For example, Ref. [7] investigated

charge sharing with a model that incorporates carrier diffusion,

the range of photo/Compton-electrons and x-ray escape and

absorption. Ref. [8] used a collimated beam of radiation and

reported charge sharing between anode strips depending on

the point of interaction in the CZT, but also depending on the

photon energy. Ref. [9], [10] investigated charge sharing in

CZT with different size pixels and gaps between pixels, and

Ref. [11] discussed a model that helps for the design of anode

pixels in CZT.

In general, methods to improve intrinsic spatial resolution

by interpolation among detector elements are known for vari­

ous types of imaging detectors and charged particle trackers.

An effective method of interpolation between strips has been

described for charged particle trackers made of silicon, and

the so-called "1]-method" has become common practice with

silicon strip sensors [12], [13]. For example, better than 2-f-J,m

intrinsic spatial resolution can be obtained with 50-f-J,m readout

strip pitch in 300-f-J,m thick silicon [14].

II. MET HODS

A. Detector with CZT and ASIC

We used a ,,(-radiation detector made from CZT [15] with

integrated readout [Fig. 1]. The CZT had a size of 2.54 em x

2.54 em and a thickness of 5 mm. The ASIC was wire-bonded

to a circuit board with connectors to the anode pixels in the

CZT. The ASIC contains low-noise charge sensitive amplifiers

that provide a pulse height proportional to the charge at their

inputs. The ASIC delivers the x- and y-coordinates and the

pulse height of any triggering pixel and their neighbour pixels.

A pixel generates a trigger, when the charge exceeds a pre­

programmed threshold and subsequently the ASIC multiplexes

the pulse heights from the input amplifiers to the buffer

amplifier at the output. We digitized the pulse heights using a

14-bit analog-to-digital converter (ADC). Fig. 2 illustrates the

978-1-4673-0120-6/11/$26.00 ©2011 IEEE 4550

principle of operation: The CZT has a cathode and 256 anodes,

which are each connected to an input in the ASIC. Cathode

and anodes are in the xy-plane. A negative voltage of -600 V

was applied to the cathode which provides an electric field for

the signal current along the z-direction. We operated the CZT

at a temperature of about + 15°C.

Fig. I. Top: Radiation detector made of CZT with readout ASICs underneath. Bottom: ASIC designed for the readout of CZT detectors, wire-bonded to a circuit board.

v

z�

x

y

Ii \!

------------------ ----- �'-t) ---- ------------------------. p'

E

caLhode

T

Fig. 2. Side-view drawing of pixels in the radiation detector.

B. Measurement oj the Hit Position

Fig. 3 (left) shows a drawing of the experimental setup,

with a radiation source illuminating the detector. The goal is

to develop a method that allows one to measure the position

for every l'-ray interaction in the CZT. For simplicity we

assumed an approximation where each interaction (hit) could

be associated with a point in the xy-plane. We did not

distinguish between the types of the interaction, e.g., photo

absorption, Compton scatter, pair-production, or the sequence

of interactions, neither did we use the depth-of-interaction.

Fig. 3 (right) shows a drawing of nine pixels (a cluster of

pixels), which are labeled with xy-coordinates and with the

charge they deliver to the amplifier inputs when a trigger

occurs. The center point of the triggering pixel is at (xo, Yo), while the center points of the other pixels are at (XL, Yo), etc. For every trigger, the ASIC was programmed to provide

the xy-coordinates and the charge from the nine pixels in the

cluster. It can happen that more than one pixel trigger due

to multiple interactions or maybe due to noise exceeding the

threshold. When there are more than one triggers, then each

of the triggering pixels and their neighbours were read out

sequentially. We only recorded hits from triggering pixels with

the center pixel of the hit always having a pulse height larger

than any of its neighbour pixels.

Radiation Source

/:��,------------ -n,i\\\\\ :;i \

/:' j f !\ \. \ \ ,, ' jdd��d, , �<;lqiq,1iQn',

Detector Field of View (FOV) x

Fig. 3. Left: Setup of the radiation source illuminating the detector. Right: Drawing of a cluster of pixels in the radiation detector.

We applied the following three methods to calculate the x­

and y-coordinates for every interaction. Firstly, the most basic

method is the digital method, which defines the x-coordinate

of the hit as follows:

dig def xh = xo· (1)

S· ' 1 I h d' f h h" dig def h Iml ar y, t e y-coor mate 0 t e It IS Yh = Yo, w ere

Yo is the y-coordinate of the center of the triggering pixel. The

digital method disregards by definition the magnitude of the

charge above threshold and ignores the charge in the neighbor

pixels.

Secondly, the center-oj-gravity method, derives the coordi­

nates of a hit by weighing the position of the pixels with the

charges measured in the neighbor pixels and defines the x­

coordinate of the hit as follows:

cog def 1 � xh = -Q � Xkqk,

x kEX (2)

where Qx = LkEX qk is the sum over the charges, e.g., in

X = {XL, xo, XR}, and the x-coordinates of the pixels located

4551

left and right of the center pixel are labeled with the sub-script L and R, respectively. In the following it is useful to define

f3 �f qR - qL

(3) x - Qx ' with the charges qL and qR in the left and right pixels,

respectively, one can rewrite Eq. 2 as follows:

x�Og = Xo + p. f3x, (4)

where P is the pixel readout pitch. A comparison of Eq. 1 and Eq. 4 shows that the term P . f3x can be understood as a correction to the digital position. The position y�og and f3y can be defined in a similar way, using the charge and position from the pixels which are located adjacent to Yo in the y-direction. According to Eq. 3, f3x and f3y falls in an interval from -0.5 to +0.5. For example, if almost all charge shares between the center pixel and its right neighbour, then qR � qo and qL � 0, and therefore, f3x � +0.5, and if almost all charge shares between the center pixel and its left neighbour, then f3x � -0.5. In practise, f3x and f3y can exceed the interval [-0.5, 0.5] because of noise.

Thirdly, Eq. 4 can be generalized to the f3-method, and the x-coordinate of the hit is defined as follows:

I Simulation of uniform illumination I I Un!fotm r •• ponse I

S(�'

Fig. 4. Simulation of the probability density function of f3 under uniform illumination of the CZT (left), the integral function S(f3) (middle), and the uniform distribution of S (right).

e.g., 241 Am point source centered far above the detector. Secondly we acquired the probability density function for f3 from all pixels. Thirdly we calculated and stored S(f3) for every pixel. Later, under operation with an unknown spatial distribution of radiation sources, we calculated the x­coordinate of the hit using Eq. 5. We applied the same method for the y-coordinate.

III. RESULT S

A. Pulse Height Spectra beta � + P S(f3 ) Xh - Xo . x , (5) We acquired pulse height distributions with the CZT de-

where

S(f3x) �f -� + �x J�X �� (f3')df3', (6)

with the probability density function dNx(f3)/df3. The second term is the cumulative distribution function, which maps a non-uniform distributed f3x into a uniform distributed S. The y-coordinate, y�eta, can be measured using the corresponding quantities in the y-direction.

C. Transformation of Random Numbers

A pixellated detector under uniform illumination with radi­ation should generate, by definition of uniformity, hits that are randomly and uniformly distributed and therefore have a uniform S(f3x) in Eq. 5. Numerically, it is well known how to transform a uniform random number into another random number with different probability [16]. We measured a non-uniform f3, knowing that it is due to a uniform random number. Therefore, we applied the inverse transformation to calculate the uniform S(f3) from the non-uniform f3. Fig. 4

illustrates the numerical procedure, starting with a Gaussian probability density function of the random variable f3 (left) and the function S(f3), which was calculated by integration of the distribution of f3. We chose a Gaussian function for illustration, because it resembles the experimental non-uniform distribution of f3 from the detector under uniform illumination. Fig. 4

(right) shows the uniform distribution of S(f3) as generated by the transformation. One can see that the distribution of S is almost uniform as expected from this method.

In practise, we applied the method as follows: Firstly we illuminated the detector uniformly using a radiation source,

tector under uniform illumination with l'-radiation from 22Na and 241 Am [Fig. 5, Fig. 6].

4000.----------------------------.

3500

3000

2500

2000

CZT pixels superimposed R 22Na _WArn _ 10SfC test pulser

Fig. 5. Pulse height distribution measured in CZT from triggering pixels under uniform illumination with '"Y-radiation from 241 Am, 22Na, and a 105 fC test pulser.

We calibrated the amplifier gain in units of keY using the photo peaks at 59.5 keY from 241 Am and 511 keY from 22Na. The energy dynamic range of the ASIC amplifiers was designed to be linear up to 3000 ke V which was validated by charge injection: the 105-fC charge is visible at about 3020 keY. The low energy threshold was at about 15 keY and

4552

1500

1000

5000

CZT pixels superimposed

.2�1Am

4 keVFWHM

D Pedestal, 1.4 keV FWHM

0�OhL..L1�OJ...J...l.�2� 0-�30�· 4!111!O-�50 60 70 pulse height from triggering pixel [keV]

Fig. 6. Close-up from Fig. 5, the pulse height distribution measured with 241 Am in CZT from triggering pixels and the pedestal.

100 ke V for all channels with 241 Am and 22Na, respectively. The 22N a spectrum has photo peaks at 511 ke V and 1275 ke V with the expected Compton scatter in the CZT and events from scatter in the environment. The 241 Am spectrum is difficult to see on the large dynamic range scale and it is therefore magnified in the close-up view Fig. 6. The 241 Am spectrum has a photo peak at 59.5 keY and entries about 23 keY and 27 keY below the photo peak due to x-ray escape from Cd and Te, respectively. For the 59.5-keV photo peak we measure about 4-keV full-width-half-maximum (FWHM) , which is better than previous measurements with the same type of CZT but different readout [17]. A measurement with all CZT pixels connected to the readout but without any charge from radiation gives the pedestal [Fig. 6]. The pedestal data is distributed around zero and has a full-width-half-maximum of 1.4 keY. Using 4.6 eV to create an electron-hole pair in CZT, one computes the electronic noise per readout channel connected to the detector of about 130 electrons equivalent noise charge root mean square (ENC RMS).

B. Charge Sharing

Fig. 7 shows the correlation of pulse heights acquired from the triggering center pixel (qo) and the neighbour pixel with the largest pulse height (q1), acquired with ,),-radiation from 241 Am. The largest neighbour pulse height was measured in one of the eight neighbour pixels surrounding the triggering pixel.

We counted the number of events that fall in between the lines shown in the figure. The majority of events have a neighbour pixel pulse height near zero, that is, all charge (Q) appears in the triggering pixel and no charge is shared with a neighbour, i.e., q1 :::::: 0 and qo = Q. However, there is a significant number of events distributed along a

r---------------------------------� ... ,�

,.

triggering pixel pulse height [ADe]

Fig. 7. Measurement of the pulse height in the neighbour pixel with the largest charge versus the pulse height in the trifgering center pixel under illumination with ')'-radiation from 2 1 Am.

straight line, q1 = f(qo), with a negative slope of one, i.e., f(qo) = -qo + Q. We identify the entries with q1 > 15 keY with events that share charge between two pixels. Using 241 Am, we measured about 10% of charge sharing events in the 5-mm thick CZT at 1.6-mm pixel pitch. A measurement with 57 Co under the same conditions has 24% of charge sharing events. It appears that the number of charge sharing events increases for higher photon energy, probably due to the larger range of the photo electron at higher photon energy.

C. Calibration for Interpolation

We measured the distribution of f3x and f3y for all pixels according to Eq. 3 and computed the cumulative distribution functions [Fig. 8]. The events without charge sharing generate a normal distribution of f3x, f3y around zero with a width determined by the electronic noise from three pixels. The events with charge sharing generate a few entries in the interval from -0.5 to +0.5. If the charge would share linearly depending on the position between two pixels, then one would expect a uniform f3x-distribution. If there were additional electrodes in between the readout pixels, then one would expect a multi­modal distribution of f3x, as it is known from silicon strip detectors. However, since the distribution of f3x is relatively narrow with only a few entries from charge sharing, one cannot expect much improvement in the intrinsic spatial resolution over the digital resolution.

We used the integral functions to compute S(f3x) for every event according to Eq. 6. Fig. 9 shows the measured values S(f3x) versus f3x for all pixels superimposed. The measure­ments of S(f3x) allows one to compute the sub-pixel position according to Eq. 5.

D. Planar Shadow Image

We placed a 3-mm thick piece of solid tungsten about 2 mm over the detector covering about 14 pixels. The 241 Am source was located about 15 cm above the detector. The tungsten absorbed almost all photons at 59.5 keY and cast a shadow image onto the detector. The edge of the tungsten defined a straight line diagonally across the detector. Fig. 10 shows the shadow images acquired and processed with the digital method (top) and the f3-method (bottom).

The grid outlines the CZT pixels (readout anodes) of 1.6-mm pitch. The radiation illuminated almost all pixels (several

4553

�40.--------------------==-----.1 � "C uniform illumination � u, "C120 from 24'Am .S

pixel .t (x,y)=(8,B) 100 . PDF

80 -CDF

60

40

20

0.8] .!:j 0.7 �

0.6 g 0.5 0.4 0.3 0.2 0.1

o -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0 P.

Fig. 8. Measurement of the probability distribution (PDF) dN /d/3x and the cumulative distribution function (CDF) for a typical pixel.

-;. 0.6 "'-in

0.4

0.2

0

-0.2

-0.4

-0�.6 -0.4 -0.2 o

3.5 3 2.5 2 1.5

0.5 0.2 0.4 0.6 0

P.

Fig. 9. The measured S(/3x) versus /3x, superimposed for all channels in the detector.

1000 counts per pixel) except the upper right corner where the tungsten absorbed the photons leaving only a few counts per pixel. The variation in the number of counts among pixels in the illuminated region is typical for this type of CZT. As expected, using the digital method (top) we can only approx­imate the tungsten edge with a "staircase" pattern defined by the 1.6-mm pixel pitch, which indicates no improvement in intrinsic spatial resolution. The ,B-method (bottom) allowed us to create an image with sub-pixel bins. We chose a bin size of 200 /-Lm x 200 /-Lm, however, we still observe the "staircase" pattern from 1.6-mm pitch.

Fig. 11 compares the three methods using a bin size of 25 /-Lm x 25 /-Lm. The grid outlines the pixels of 1.6-mm pitch. The digital methods (top) assigns every hit position to a pixel center and all counts are summed up in the numbers given. The tungsten absorbs most of the photons and causes the low number of counts in the upper right corner of the detector. The center-of-gravity method (middle) creates an image with a peak in each pixel center and many events distributed in bins along the pixel center lines. The tungsten edge appears as a "staircase" pattern in the upper right corner of the detector. The

Edge Shadow Image, Digital, 1:1 � 2,5 E

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10,5

9.5

8.5

7.5

6.5

x [1,6mmj

1 Edge Shadow Image, l.Pixel.�, 8:11

x [1,6mmj

Fig. 10. Shadow images of a tungsten edge acquired in the CZT detector under illumination with radiation from 241 Am. The same data is shows for I bin per pixel (top) using the digital method and 8 x 8 bins per pixel (bottom) using the /3-method.

,B-method (bottom) creates an image with a broad distribution across all bins in each pixel and the tungsten edge appears as a staircase pattern. We used the same number of events in each image, and therefore the counts per bin decrease as the events are distributed over more bins.

IV. DISCUSSION

We described three methods to measure the posItIOn of hits in a pixellated CZT ,-radiation detector with the goal to improve the intrinsic spatial resolution. The benchmark is set by the digital method that uses the xy-coordinate of the pixel with the largest pulse height and provides an intrinsic spatial resolution equal to the pixel pitch. The other two methods (center-of-gravity and ,B-method) allow one to interpolate the position between the pixel with the largest pulse height and its neighbours. Using the two methods of interpolation, we could not yet improve the intrinsic spatial resolution. This result may have several reasons:

4554

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5.5 6.5 7.5 8.5 9.5 10"5 11.5 II x [1.6mm]

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Fig. I I. Shadow images of a tungsten edge acquired in the CZT detector under illumination with radiation from 241 Am, using the digital method (top), the center-of-gravity method (COG, middle), and the ,a. method (bottom). All images are have 64 x

64 bins per 1.6 mm x 1.6 mm pixel.

1. Despite their success in silicon strip detectors, the two methods of interpolation cannot be used in CZT detectors. There are important differences between silicon strips and CZT detectors, which might prohibit the success in CZT. Most important, the signal from CZT detectors is due to the motion of electrons only, which means that the pulse height in large electrodes, e.g. on the cathode, depends on

the depth-of-interaction. Yet, the pulse height on the anode is relatively independent of the depth-of-interaction due to the segmentation of the anode in many relatively small pixels. By design of the CZT detector, only one pixel collects the full charge, while the adjacent pixels collect only a small amount of charge when the electrons move over the gap between pixels. However, it is well known that moving electrons induce a "transient" current in several adjacent pixels [18]. Therefore, the methods described here, might be useful with a different shaping time in the neighbour pixel readout, that would allow one to measure the maximum transient current instead of the charge, and then use the recorded pulse heights to interpolate between pixels.

2. The two methods are not suitable for this type of CZT detector, but might be suitable for other types of detectors, e.g., with larger gaps between pixels. In the CZT we observe that the interactions that cause charge sharing occur in the gaps between pixels. In order to increase the amount of charge sharing one might want to modify the design of the anode and enlarge the gaps while retaining the pixel pitch. In silicon detectors, the methods of interpolation are successful because the strips are very small compared the pitch. However, CZT pixels with large gaps lose charge when electrons move over the gaps. Like in silicon detectors, the method may require additional electrodes with a defined impedance in between the readout pixels to provide cross coupling between the readout channels. The suitable impedance between the gap pixels and the readout pixels would cause an induced charge in the readout pixels.

Besides improved intrinsic spatial resolution, the neighbour pixel readout promises other benefits for spectroscopy. For example, summing the charges from the triggering pixel and from neighbours, one can increase the number of entries in the photo peak and reduce the number of entries in the low-energy tail of the energy spectra by a few percent.

V. SUMMARY

We described a method of interpolation for a pixellated CZT ,),-radiation detector with the goal to optimize the intrinsic spatial resolution. To this end we designed and manufactured an application specific integrated circuit for the readout of CZT pixel detectors. The important new feature allows one to read out the pulse height from triggering pixels and neighbour pixels. The amplifiers have a very large dynamic range that is linear up to 105 fC (�3020 keY in CZT), while the equivalent noise charge is as low as 130 e RMS (� 1.4 ke V FWHM at the pedestal with the CZT pixels connected to the amplifier inputs). Using the new readout for the CZT detector, we acquired energy spectra from ,),-radiation sources. We observed charge sharing between pixels in about 10% and 24% of the photon interactions with 241 Am and 57 Co, respectively. We described two method of interpolation. The experimental work did not yet show an improved intrinsic spatial resolution. We discussed how one could use the methods of interpolation with the same detectors but different shaping time in the neighbour pixels. These tests are in principle possible with the same readout electronics and will be done in the near future.

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We also discussed a different anode layout with larger gaps between readout pixels and intermediate electrodes similar to silicon detectors. In summary, the neighbour pixel readout still holds the promise to provide additional information that could improve the intrinsic spatial resolution over digital resolution.

VI. ACKNOW LEDGMENT S

We gratefully acknowledge the support from the Research Council of Norway, Scattefunn project numbers 199238 and 206782.

REFERENCES

[1] S.R. Cherry, lA. Sorenson, M.E. Phelps, "Physics in Nuclear Medicine", Saunders, 3rd edition (2003).

[2] C. Budtz-JjlIrgensen 1. Kuvvetli, Y. Skogseide, K. Ullaland, N. 0stgaard, "Characterization of CZT detectors for the ASIM mission", Nuc!. Sci. Symp. , Conf. , IEEE, Dresden, October 2008. Available on 27. Oct. 2011 at http://web.ift.uib.no/�nikostlpapers/R04-5_MIC08.pdf

[3] S. Ishikawa, S. Saito, H. Tajima, T. Tanaka, S. Watanabe, H. Odaka, T. Fukuyama, M. Kokubun, T. Takahashi, Y. Terada, S. Krocker, S. Christe, S. McBride, and L. Giesener, "Fine-Pitch Semiconductor Detector for the FOXSI Mission", Trans. Nuc!. Sci. , IEEE, 58, 4, 2011.

[4] D.J. Wagenaar, J. Zhang, T. Kazules, T. Vandehei, E. Bolle, S. Chowd­hury, K. Pamham, B.E. Patt, "In Vivo Dual-Isotope SPECT Imaging with Improved Energy Resolution", Nuc!. Sci. Symp. Conf. , IEEE, 6 (2006) 3821 - 3826.

[5] C.B. Hruska, S.w. Phillips, D.H. Whaley, D.J. Rhodes, M.K. O'Connor, "Molecular Breast Imaging: Use of a Dual-Head Dedicated Gamma Camera to Detect Small Breast Tumors", American J. Roentgenology, 191 (2008).

[6] S. Mikkelsen, D. Meier, G. Mrehlum, B. Sundal, J. Talebi, A. Helland, N. Ostgaard, Y. Skogseide, K. Ullaland, "Low- Power and Low-Noise Multi-Channel ASIC for X-ray and Gamma-Ray Spectroscopy", 2nd International Workshop on Analog and Mixed Signal Integrated Circuits for Space Applications (AMICSA), 31 August - 2 September 2008, Cascais/Sintra, Portuga!. Available on 27. Oct. 2011 at http://web.ift. uib.no/�nikostlpaperslProceedings-AMICSA_2008-08-25. pdf

[7] Y. Du, Z. He, W. Li, G.F. Knoll, D.K. Wehe, "Monte Carlo Investigation of the Charge Sharing Effects in 3-D Position Sensitive CdZnTe Gamma Ray Spectrometers", Trans. Nuc!. Sci. , IEEE, 46 (1999) 4.

[8] E. Kalemci and J.L. Matteson, "Investigation of charge sharing among electrode strips for a CdZnTe detector", Nuc!. Instr. Meth. A478 (2002) 527-537.

[9] C.M.H. Chen, S.E. Boggs, A.E. Bolotnikov, W.R. Cook, F. Harrison, S.M. Schindler, "Numerical Modeling of Charge Sharing in CdZnTe Pixel Detectors", Trans. Nuc!. Sci. , IEEE, 49 (2002) p.270.

[10] K. Wangerin, Y. Du, F. Jansen, "CZT Performance for different Anode Pixel Geometries and Data Corrections", Nuc!. Instr. Meth. A648 (2011) S37-S41.

[11] K. Iniewski, H. Chen, G. Bindley, 1. Kuvvetli, C. Budtz-JjlIorgensen, "Modeling Charge-Sharing Effects in Pixellated CZT Detectors", Nuc!. Sci. Symp. Conf. , IEEE, NM2-3, (2007).

[12] E. Belau, R. Klanner, G. Lutz, E. Neugebauer, HJ. Seebrunner, A. Wylie, T. Bahringer, L. Hubbeling, P. Weilhammer, J. Kemmer, U. Katz, M. Riebesell, "Charge Collection in Silicon Strip Detectors", Nuc!. Instr. Meth. 214 (1983) 253-260.

[13] G. Lutz, "Semiconductor Radiation Detectors, Device Physics", Springer, 2001.

[14] C. Colledani, W. Dulinskia, R. Turchetta, F. Djama, A. Rudge, P. Weil­hammer, "A submicron precision silicon telescope for beam test pur­poses", Nuc!. Instr. Meth. 372 (1996), 3, 379-384.

[15] Endicott Interconnect, Detection and Imaging Systems, 373 Saxonburg Blvd. , Saxonburg, PA 16056, United States.

[16] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, "Numerical Recipes in C, The Arti of Scientific Computing", Cambridge University Press, 2nd Edition, 1994.

[17] G. Maehlum, K.I. Dietzel, D. Meier, M. Szawlowski, B. Sundal, T. Van­dehei, DJ. Wagenaar, B.E. Patt, "Study of Cadmium Zinc Telluride (CZT) Radiation Detector Modules under Moderate and Long-term Variations of Temperature and Humidity", Nuc!. Sci. Symp. Conf. , IEEE, 2007.

[18] J.C. Kim, S.E. Anderson, W. Kaye, SJ. Kaye, Y. Zhu, F. Zhang, Z. He, "Study on effect of charge sharing events in common-grid pixelated CdZnTe detectors", Nuc!. Sci. Symp. Conf. , IEEE, 2009.

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