pyroelectic source modeling

8/12/2019 Pyroelectic Source Modeling

1/5

Characterization and optimization of pyroelectric X-ray sources

using Monte Carlo spectral models

Michael Klopfer, Thomas Wolowiec, Vladimir Satchouk, Yahya Alivov, Sabee Molloi n

Department of Radiological Sciences, Medical Sciences B, 140, University of California, Irvine, CA 92697, USA

a r t i c l e i n f o

Article history:

Received 5 April 2012

Accepted 23 May 2012Available online 13 June 2012

Keywords:

Ferroelectric

X-ray source

Pyroelectric

X-ray anode

Brachytherapy

a b s t r a c t

Pyroelectric X-ray sources produce emission through bulk heating of a ferroelectric crystal. In this

study, a least-square based systematic curve fitting of X-ray emission to predicted models is used to

generate an equivalent monoenergetic incident electron energy to simplify further X-ray sourceoptimization. The measured X-ray spectrum of a 1 cm3 lithium tantalite crystal cycled over 140 K are

shown to be approximated by those of an 85 keV monoenergetic electron beam. Using monoenergetic

electron sources, common configurations for transmission and directional X-ray sources are simulated

using electron targets comprised of gold, silver, copper, molybdenum and tungsten. X-ray production

efficiency depends on target material selection, incident electron energy, and target thickness for both

transmission and reflection geometries. At 20 keV, silver produced 69.7% more flux was in comparison

to copper, the least efficient target material at this energy. Conversely, at 85 keV copper outperformed

silver, the least efficient target material at this energy, by 21.6%. Pyroelectric X-ray sources can be

improved for flux and energy tuning through the use of modeling and target design. Continued

development of pyroelectric X-ray sources can lead to wide scale implementation for industrial X-ray

fluorescence and medical therapeutic applications.

& 2012 Elsevier B.V. All rights reserved.

1. Introduction

Pyroelectricity results from a spontaneous depolarization upon

bulk temperature change in a pre-polarized ferroelectric crystal,

resulting in potential differences up to several hundred keV[18].

Electron emission due to FowlerNordheim tunneling of low

pressure gas molecules near the crystal surface and correspond-

ing field acceleration has been used to generate X-rays when

accelerated electrons interact with a target [913]. Prior studies

that have demonstrated radiographic imaging and X-ray fluores-

cence analysis capabilities of pyroelectric sources indicate chal-

lenges for both flux and X-ray peak energy [1420]. During

emission, the generated crystal surface charge is depleted. Corre-spondingly, the predicted maximum charge and electron poten-

tial do not directly translate into maximum observed photon

energy as predicted by the DuaneHunt law for maximum

bremsstrahlung photon energy[21]. Previous reports indicated a

swept, packeted monochromatic emission in X-ray energy

[22,23]. Due to the low current of pyroelectric sources, once

electrons are generated, an efficient electronphoton conversion

is necessary to maximize the total flux. The efficiency of X-ray

production is dependent on incident electron energy, target

thickness, and atomic number (z). Increased target thickness

results in both increased X-ray conversion and self-attenuation

of produced photons; therefore optimization of both target

thickness and atomic number is required to maximize the X-ray

flux. Two common configurations are used for X-ray generation,

transmission and directional geometries (Fig. 1a and b). While

general studies of target design for X-ray tubes have been

performed, no systematic studies have been performed to opti-

mize the efficiency of a practical pyroelectric X-ray source[24]. In

this work, we studied the effect of target thickness on X-ray

emission efficiency by Monte Carlo simulations using the package

EGSnrc [25]. To achieve this goal, a pyroelectric crystal wasmodeled as emitting a single monochromatic electron. This

hypothesis is validated using a systematic curve fitting between

a Monte Carlo electronphoton conversion chain and an experi-

mental model. Once a reasonable expectation for incident elec-

tron energy is determined, Monte Carlo modeling is used to

simulate the X-ray emission properties for a range of common

X-ray target materials used in low power X-ray sources at various

configurations and thicknesses. In this report we first introduce

simulation details and experimental setup used to measure

pyroelectric X-ray spectrum. This is followed by presentation of

spectral determination and predictive models for simulated target

configurations.

Contents lists available at SciVerse ScienceDirect

journal homepage: w ww.elsevier.com/locate/nima

Nuclear Instruments and Methods inPhysics Research A

0168-9002/$ - see front matter& 2012 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.nima.2012.05.065

n Corresponding author. Tel.: 1 310 502 1971; fax: 1 949 824 0455.

E-mail address: [email protected] (S. Molloi).

Nuclear Instruments and Methods in Physics Research A 689 (2012) 4751
http://www.elsevier.com/locate/nimahttp://www.elsevier.com/locate/nimahttp://localhost/var/www/apps/conversion/tmp/scratch_7/dx.doi.org/10.1016/j.nima.2012.05.065mailto:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_7/dx.doi.org/10.1016/j.nima.2012.05.065http://localhost/var/www/apps/conversion/tmp/scratch_7/dx.doi.org/10.1016/j.nima.2012.05.065mailto:[email protected]://localhost/var/www/apps/conversion/tmp/scratch_7/dx.doi.org/10.1016/j.nima.2012.05.065http://localhost/var/www/apps/conversion/tmp/scratch_7/dx.doi.org/10.1016/j.nima.2012.05.065http://localhost/var/www/apps/conversion/tmp/scratch_7/dx.doi.org/10.1016/j.nima.2012.05.065http://www.elsevier.com/locate/nimahttp://www.elsevier.com/locate/nima


2/5

2. Materials and methods

2.1. Monte Carlo modeling of input electron energy

The electronphoton transport simulation package EGSnrc was

used for all Monte Carlo simulations [25]. Two types of X-ray

generation designs were simulated: a directional-geometry X-ray

source as shown in Fig. 1a, and a target perpendicular to the

electron beam as shown in Fig. 1b. A total of 108

photons at 30,60, 80, 85, 90, 100, and 120 KeV were directed in a 0.5 cm2

diameter collimated beam toward a 3 mm thick, 20 mm2 copper

target placed at 201with respect to the cathode. Beam filtration

was determined by experimental setup and was modeled by

15 cm of air, 0.25 mm of aluminum, and 2 mm of borosilicate

glass. A 5 cm2 ideal detector is modeled by the scoring plane.

Collected photons were normalized by peak energy for compar-

ison. Mean spectral energy was determined by a histogram

average of counts with respect to energy. Peak flux energy is

determined by a maximum value search after a 2 keV wide low

pass kernel is used to remove characteristic X-ray fluorescence

peaks from simulated data. Peak energy was determined by the

energy corresponding to threshold of a signal-to-noise ratio of

5 against the background[26].

2.2. Modeling of multiple anode configurations

Alternative anode configurations and materials were modeled

and evaluated for X-ray conversion, efficiency, and spectral

characteristics:

Efficency EincidentPdetected

1

In addition to prior criterion metrics, conversion efficiency (Eq.

1) is defined as the fraction of detected photons ( Pdetected) at the

scoring plane to the total incident electrons ( Eincident). A cutoff of

1 keV was used to discard low energy photons. To preserve

universality of results, no filtration was modeled between theemission source and the scoring plane. Common high-z X-ray

anode materials, including copper, molybdenum, gold, silver, and

tungsten, were chosen based on prior use in industrial or medical

X-ray sources. Directional (Fig. 1a) and transmission (Fig. 1b)

geometries were tested. Scoring planes were simulated as 20 cm2

planes immediately adjacent to the X-ray target to allow a large

acceptance angle to approximate 2p detector geometry. Direc-

tional targets were all modeled to have 2 mm thickness. This

thickness was chosen to block all transmission electrons for all

evaluated energies and can be modeled as infinitely thick.

Transmission geometry target thicknesses were varied between

1 and 10 mm. The substrate for modeled transmission geometry isomitted to eliminate the filtration effect generated by additional

material in the photon beam line. Monoenergetic electrons withenergies of 5, 8, 10, 12, 15, 20, 25, 30, 60, 85, 100, and 120 keV

were simulated to model an energy range that is observed or

modeled in prior pyroelectric experiments[19,27].

2.3. Experimental pyroelectric X-ray emission source

An experimental reference spectra were generated from a

directional geometry pyroelectric X-ray emission source (Fig. 2)

constructed from a 1 cm3 lithium tantalate monolithic crystal

with the Z-polarized face epoxy-bonded to a grounded 2 O 20 Wresistor such that a negative polarity with respect to the electron

target is achieved during heating. Working vacuum level was

regulated with an adjustable leak of air to maintain 820 mTorr

dynamic pressure in accordance with documented parameters to

maximize gas amplification of electron emission [28]. Generated

electrons from the surface of the pyroelectric crystal pass an

empirically determined 0.6 cm gap to allow self-focusing and

strike a 2 mm thick copper electron target mounted at 201with

respect to the incident beam [2,22]. Generated X-rays were

passed through a 2.0 mm thick, 76 mm square borosilicate (Corn-

ing 7740) window inside a stainless steel vacuum chamber. An

Ortec NaI(Tl) detector and Ortec Trump-32 MCA were used for

spectra collection. A spacing of 50 cm was chosen between thedetector crystal face and the window of the chamber to reduce

detected multi-photon events. A Keithley 614 picoammeter was

used to measure anode current. Thermal cycling to a difference of

140 1C was provided by use of a battery-based thermostatic

controller which raised the temperature at 1.2 1C/s until the

desired temperature difference was achieved. Passive cooling to

ambient temperature was allowed between runs. X-rays emitted

during cooling were not studied in this experiment. Spectra and

current collection began at initiation of heating current and

ceased when X-ray emission stopped after final temperature is

reached. To improve counting statistics, spectra were averaged

over 5 identical runs using identical experimental parameters.

Background and energy-dependent detector quantum efficiency

corrections were made post-data averaging. Mean spectralenergy, peak energy, and peak flux energy were determined with

identical methods of those used in simulation.

Fig. 1 Fig. 2

M. Klopfer et al. / Nuclear Instruments and Methods in Physics Research A 689 (2012) 475148


3/5

3. Results

3.1. Experimental validation of spectra

InFig. 3, both simulated and experimental X-ray spectra are

shown. As seen from this figure, the experimental X-ray spectrum

from a LiTiO3 pyroelectric crystal under measured conditions

described above is shown. This spectrum had a peak energy at

27.6 keV and spanned until maximum energy at 93 keV. As can beseen from this figure, all simulated spectra showed close spectral

correlation with experimental data, indicating that the initial

assumption of a monochromatic electron beam can be used to

approximate the swept monochromatic electron beam generated

by a pyroelectric crystal. Table 1 summarizes the characteristics

of all X-ray spectra extracted fromFig. 3.

A goodness-of-fit analysis based on point-by-point least-

square RMS error (Table 1) was tested between candidate mono-

chromatic spectra at a given energy. The result showed 85 keV as

the closest representation of the measured spectra with a mini-

mum absolute error of 0.23 (Fig. 3). The generated spectra

underestimated the peak energy as observed at 93 keV by 8 keV

while overestimating the spectral peak energy and mean spectral

energy by 2.7 keV and 1.7 keV, respectively. As comparison is

made above the Compton edge for the experimental data, char-

acteristic X-rays emitted by copper are not compared such that

the spectral peak energy and flux peak energy are equivalent in

this comparison.

3.2. Optimization of electron target parameters

Simulation of directional X-ray design parameters demon-

strated that at low energies (below 30 keV), silver outperformed

other tested materials with respect to X-ray conversion efficiency,

while at high energies copper performed the best. At 20 keV an

11.3% improvement was seen by silver over copper. At 85 keV, a

54.7% improvement is seen by copper over silver. All other tested

materials performed between copper and sliver across the entire

energy range. For transmission geometry, tested targets were

used with optimum thickness for each tested energy. At 20 keV,

69.7% more flux was produced in comparison to copper, the least

efficient target material at this energy. At 85 keV, copper out-performed silver, the least efficient target material at this energy,

by 21.6%. In Figs. 4 and 5, the calculated efficiency of X-ray

emission of sources for different target materials in both direc-

tional and transmission geometries are shown. As different

thicknesses of different transmission targets have a pronounced

effect on X-ray emission, only optimized values are shown in

Fig. 5. In Fig. 6, the effect of thickness on efficiency as demon-

strated at 20 and 85 keV incident electrons is shown. In Fig. 7,the

optimized thickness values for the tested materials across multi-

ple energies are shown. In Fig. 8, the produced spectra for an

incident 100 kev monoenergetic electron beam and a common

anode thickness of 5 mm are shown.

4. Discussion

As used directly for medical imaging or brachytherapy appli-

cations, optimization of electronphoton conversion and spectral

energy properties is critical to device usefulness [29]. Likewise

XRF applications also benefit from improved X-ray flux for

shortened detection times and increased material sensitivity.

Prediction of acceleration potential (V) due to the pyroelectric

effect can be done using a capacitive model[23]. In an accelerator

configuration, a paired capacitor set is used to represent the

distance of the gap (dgap) that exists between the crystal surface

and the opposing electrode:

V Q

CcrystalCgap

g DT

eoecr1=dcreo1=dgap2

whereQis the generated charge, g is the pyroelectric constant of

the material, and DTis the temperature gradient which the crystal

is cycled across.Ccrystaland Cgapare the capacitance of the system

components, eo is the permittivity of free space, ecris the crystal

relative permittivity, and dcr is the crystal thickness. When

Fig. 3

Table 1

Maximum energy

(keV)

Mean spectral

energy

Flux peak

energy

Absolute RMS

error

Experimental 35.8 27.6

60.0 30.2 24.9 0.73

80.0 36.3 29.1 0.38

85.0 37.5 30.3 0.23

90.0 40.1 30.7 0.36

100.0 43.5 31.2 0.62

120.0 48.5 33.9 0.83

Fig. 4

M. Klopfer et al. / Nuclear Instruments and Methods in Physics Research A 689 (2012) 4751 49


4/5

approximating the surface charge alone, the value of Cgap is

assumed to be negligible[8]. The observed differences in spectral

characteristics and underestimation of both current and voltage

were noted in prior estimation models[27]. From this model, the

crystal used in this study would produce 604 keV potential across

the crystal and 444 keV with respect to the electron target, placed

at a distance of 0.6 cm. This result is divergent from maximum

photon energy of 93 keV that was observed in the experimental

spectrum (Fig. 3). This constitutes observing only 20.9% of the

maximum predicted electron energy through the bremsstrahlung

and transport process. A total of 3.12 1012 accumulated elec-

trons were measured as averaged over 5 cycles constituting only

20.2% of the predicted 1.541013 generated electrons per cycle.

While confirmation of low numbers of high energy electron

emission has been made in other experiments [23], the inherent

inefficiency of the bremsstrahlung process hinders observation of

corresponding high energy photons matching the incident elec-

tron energy as predicted by the DuaneHunt law[21,30].

In conventional high flux X-ray tubes, heat capacity of the

anode must be taken into account. This traditionally limits the

anode material choice to tungsten or molybdenum. For pyro-

electric sources, the low incident electron flux can allow alter-

native elements with comparably low melting points such as

copper, gold, and silver. An increased atomic number leads to

higher bremsstrahlung generation. X-ray conversion from the

bremsstrahlung process can be estimated over a wide energy

band through the following relationship:

EbremsstrahlungEthermal

EkZ

820,000 3

where Ek is the incident electron energy in keV and Z is the

effective atomic number of the target material [26]. Correspond-

ingly, a higher elemental Z number leads to increased atomic

mass and mass attenuation[31]. As photons are generated withinthe bulk of the material, attenuation leads to reduction of emitted

photons. The effects of Compton and Rayleigh scatter also lead to

the complication of calculation for anode efficiency as energy and

path length are not conserved. The result leads to a relationship

that is bounded on the high and low ends with respect to both

target material atomic mass and thickness.

For infinitely thick electron targets in directional geometry,

silver shows the greatest efficiency of bremsstrahlung conversion

of incident electrons at low energies. At high energies, copper

performs the best. This can be explained by the competing

relationship between bremsstrahlung efficiency and X-ray mass

attenuation. Due to its low mass attenuation and low atomic

number copper shows a large absorption at low energies of the

few photons generated. In comparison, silver and molybdenum

Fig. 5

Fig. 6

Fig. 7

Fig. 8

M. Klopfer et al. / Nuclear Instruments and Methods in Physics Research A 689 (2012) 475150


5/5

outperform copper at these energies due to a greater bremsstrah-

lung despite increased self-attenuation because the conversion

events occur closer to the surface of the material, reducing the

total attenuation. In addition, silver shows enhanced conversion

efficiency at 30 keV due to Ka1,b1shell fluorescence peak at 22.96

and 24.94 keV. At higher atomic masses, silver and molybdenum

generate greater numbers of photons through more efficient

bremsstrahlung conversion. The self-attenuation of generated

photons is greater as compared to copper. The other high-zmaterialsstudied, gold and tungsten, have sufficient mass attenuation to

absorb generated photons, and despite their higher bremsstrahlung

conversion efficiency, the increased attenuation severely attenuates

generated photons. This results in lower emission efficiencies in

comparison to silver and molybdenum across the entire investigated

energy band.

For transmission geometry, generated photons need to pass

through the target material to be counted as emission. Any X-ray

production that is not directed through the material is assumed to

be lost energy. As in the directional geometry case, self-attenua-

tion of the target material leads to loss of photons. For transmis-

sion geometry, the target material must be thick enough to allow

sufficient conversion of electrons to photons, yet not too thick so

as to attenuate generated photons. This relationship is strongly

dependent on incident electron energy, especially for low energy

electrons. After target thickness values have been determined

for the optimum conversion efficiency, similar relationships for

photon production efficiency between silver and copper are

observed for high and low energies as in the directional target

simulation.

Thus, from our studies it is seen that the choice of target

material and target thickness for the most efficient X-ray emis-

sion depends on the energy range to be used. These factors have

to be taken into account when designing a particular X-ray

source.

5. Conclusions

Through the course of this study we simulated pyroelectric

X-ray emission for various common electron-target materials and

multiple incident energies to find maximum electronphoton

conversion efficiencies. Reduction of the modeling of the complex

packeted emission properties of pyroelectric sources leads to

simplified device modeling. The results of studies on anode

designs show that the highest efficiency of X-ray emission

depends on target material as well as on incident electron energy.

The work presented can be used to guide further design for

experimental and commercial pyroelectric X-ray sources for

industrial and medical applications.

Acknowledgments

The authors would like to thank Dr. James Brownridge and Dr.

Yaron Danon for the insightful discussions that helped us bringthis project to fruition. We would also like to thank Crystal

Technologies for the donation of the crystals used during the

course of these experiments.

References

[1] J. Geuther, et al., Physical Review Letters 96 (2006) 054803.[2] N. Kukhtarev, et al., Journal of Applied Physics 96 (2004) 6794.[3] G. Rosenman, Ferroelectrics 126 (1992) 305.[4] O. Peleg, et al., Journal of Applied Physics 97 (2005).[5] V.D. Kugel, et al., Journal of Physics D: Applied Physics 28 (1995) 2360.[6] J.D. Brownridge, S. Raboy, Journal of Applied Physics 86 (1999) 640.[7] J.A. Geuther, Y. Danon, Journal of Applied Physics 97 (2005).[8] S.T. Liu, D. Long, Proceedings of the IEEE 66 (1978) 14.[9] J.D. Brownridge, Nature 358 (1992) 287.

[10] I.V. Strigushenko, Fizika Tverdogo Tela 22 (1980) 625.[11] J.F. Nye, Physical Properties of Crystals, Oxford University Press, New York,

1984.[12] Q. Peng, R.E. Cohen, Physical Review B 83 (2011).[13] G.I. Rosenman, et al., Physica Status Solidi BBasic Research 120, 667670

(1983).[14] J. Kawai, et al., X-Ray Spectrometry 34 (2005) 521.[15] H. Ida, J. Kawai, Spectrochimica Acta Part B 60 (2005) 89.[16] G. Pauley, Indiana University, 2011.[17] H. Ida, J. Kawai, Analytical and Bioanalytical Chemistry. 379 (2004) 735.[18] H. Ida, 2004.[19] Amptek, Amptek Announces the COOL-X X-Ray Generator with Pyroelectric

Crystal, Press Release, May 17, 2002.[20] B. Rosenblum, et al., Applied Physics Letters 25 (1974) 17.[21] Hunt, Physical Review A 6 (1915) 116.[22] J.D. Brownridge, et al., Applied Physics Letters 78 (2001) 1158.[23] J. Geuther, Rensselaer Polytechnic Institute, 2007.[24] A. Ihsan, et al., Nuclear Instruments and Methods in Physics Research Section

BBeam Interactions with Materials and Atoms 264 (2007) 371.[25] E. Mainegra-Hing, I. Kawrakow, Medical Physics 33 (2006) 2683.[26] S.J.A. Bushberg J.T., E.M. Leidholdt Jr., J.M. Boone, The Essential Physics of

Medical Imaging, 2nd ed., Lippincott Williams & Wilkins, Philadelphia, 2002,pp. 278279.

[27] T.Z. Fullem, et al., Radiation Research 172 (2009) 643.[28] J.D. Brownridge, S.M. Shafroth, Applied Physics Letters 83 (2003) 1477.[29] A. Ihsan, et al., Nuclear Instruments & Methods in Physics Research Section

B-Beam Interactions with Materials and Atoms 269 (2011) 1053.[30] W. Duane and T. Shimizu, Proceedings of the National Academy of Sciences of

the United States of America 5, 198-200 (1919).[31] J.H. Hubbell and S.M. Seltzer, NIST Report No. NISTIR 5632 (1995).

M. Klopfer et al. / Nuclear Instruments and Methods in Physics Research A 689 (2012) 4751 51

pyroelectic source modeling

Documents