8
PHYSICAL REVIEW B VOLUME 28, NUMBER 8 15 OCTOBER 1983 Radiation-induced foil electret chamber B. G. Fallone and E. B. Podgorsak Departments of Radiation Oncology and Diagnostic Radiology, McGill University, 1650 avenue des C'edres, Montreal, Quebec H3G1A4, Canada (Received 22 February 1983; revised manuscript received 11 July 1983) Saturation current densities, extrapolated electric fields, and electret-charging and -discharging current-density profiles in an ionization electret chamber are discussed as a function of various chamber parameters, such as air-gap and polymer thickness, polarizing electrode material, exposure rate, etc. Both the saturation current density and the extrapolated electric field consist of two com- ponents; one is linear with the air-gap thickness and is attributed ta primary ionization in air, and the other exhibits exponential saturation and is attributed to air ionization caused by photoelectrons backscattered into the chamber sensitive volume from the polarizing electrode. I. INTRODUCTION Many techniques have been described for charging thin dielectric foils to form electrets. Originally, electrets were produced through thermal' (thermoelectrets) or optical (photoelectrets) charge deposition methods; recently, how- ever, isothermal charge deposition techniques have been favored because of their ease and speed; the most popular is corona charging, ' which uses an inhomogene- ous electric field to produce a discharge in air at atmos- pheric pressure. We have recently reported a new isothermal technique for forming electrets with uniform and stable charge den- sities of up to 10 C/cm . ' X rays are used to produce, in air, free-charge carriers, which drift in an electric field and get trapped on a polymer foil to form an electret. The basic relationships governing the charging and discharg- ing dynamics of this radiation-induced foil electret have been derived" using the laws of Gauss and Kirchoff, and the recently discovered hyperbolic relationship describing the saturation curves of parallel-plate ionization chambers. ' In this paper we discuss the dependence of the electret- charging and -discharging dynamics on the electret chamber parameters, such as polymer and air-gap thick- ness, polarizing electrode material, etc. The influence of these parameters on the chamber saturation current densi- ty and on the extrapolated electric field is also discussed. direct interactions of photons with air molecules and by photoelectrons which are produced by x rays in the polar- izing electrode and backscattered into the chamber- sensitive volume. The free-charge carriers drift in the chamber's effective electric field towards the appropriate electrode. In contrast to a standard ionization chamber, where the charges impinge directly onto the electrodes, in the electret chamber the charges moving in the direction of the measuring electrode are stopped and trapped on the polymer surface to form a stable foil electret. The polari- ty of the electret depends on the direction of the externally applied electric field. The initial electret-charging current is proportional to the sensitive air volume and to the x-ray exposure rate. It also depends strongly on the atomic number of the polarizing electrode reflecting the photo- emission contribution to the air ionization in the electret chamber sensitive volume. The x rays were generated by a constant potential thera- py unit (General Electric Company model no. Maximar- 100) with a maximum potential of 100 kV (peak) and an anode current of 3 mA. The half-value layer of the x-ray beam was 2.2 mm of aluminum, corresponding to an ef- fective x-ray beam energy of 28 keV. The polarizing elec- trode was at a distance of 50 cm from the target irrespec- tive of air-gap thickness. The exposure rate at that dis- tance from the target was 50 mRs 'mA II. EXPERIMENTAL ir ir ir ir ip lr ir il v 1r ir 1r is ir ir ir 1r 'ir The electret forming chamber resembles a standard parallel-plate ionization chamber as shown schematically in Fig. 1. Various metals ranging from aluminum to lead were used as the conductive polarizing electrode. The measuring electrode was made of aluminum grounded through an electrometer, and blocked by a polymer foil with a typical thickness of 100 pm. The air gap was vari- able from 1 mm to a few cm. Both electrodes were circu- lar with a diameter of 5 cm surrounded by a 1-cm wide guard ring. - The air at atmospheric pressure in the chamber- sensitive volume is ionized by electrons produced by the lead shield alumjn 0m I 1' zxuzzx 'ryggg~~ photoemjt ter 1 lucite pA FIG. 1. Schematic diagram of the electret chamber. 1983 The American Physical Society

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Page 1: Radiation-induced foil electret chamber

PHYSICAL REVIEW B VOLUME 28, NUMBER 8 15 OCTOBER 1983

Radiation-induced foil electret chamber

B. G. Fallone and E. B. PodgorsakDepartments of Radiation Oncology and Diagnostic Radiology, McGill University,

1650 avenue des C'edres, Montreal, Quebec H3G1A4, Canada(Received 22 February 1983; revised manuscript received 11 July 1983)

Saturation current densities, extrapolated electric fields, and electret-charging and -dischargingcurrent-density profiles in an ionization electret chamber are discussed as a function of variouschamber parameters, such as air-gap and polymer thickness, polarizing electrode material, exposurerate, etc. Both the saturation current density and the extrapolated electric field consist of two com-ponents; one is linear with the air-gap thickness and is attributed ta primary ionization in air, andthe other exhibits exponential saturation and is attributed to air ionization caused by photoelectronsbackscattered into the chamber sensitive volume from the polarizing electrode.

I. INTRODUCTION

Many techniques have been described for charging thindielectric foils to form electrets. Originally, electrets wereproduced through thermal' (thermoelectrets) or optical(photoelectrets) charge deposition methods; recently, how-ever, isothermal charge deposition techniques have beenfavored because of their ease and speed; the mostpopular is corona charging, ' which uses an inhomogene-ous electric field to produce a discharge in air at atmos-pheric pressure.

We have recently reported a new isothermal techniquefor forming electrets with uniform and stable charge den-sities of up to 10 C/cm . ' X rays are used to produce,in air, free-charge carriers, which drift in an electric fieldand get trapped on a polymer foil to form an electret. Thebasic relationships governing the charging and discharg-ing dynamics of this radiation-induced foil electret havebeen derived" using the laws of Gauss and Kirchoff, andthe recently discovered hyperbolic relationship describingthe saturation curves of parallel-plate ionizationchambers. '

In this paper we discuss the dependence of the electret-charging and -discharging dynamics on the electretchamber parameters, such as polymer and air-gap thick-ness, polarizing electrode material, etc. The influence ofthese parameters on the chamber saturation current densi-ty and on the extrapolated electric field is also discussed.

direct interactions of photons with air molecules and byphotoelectrons which are produced by x rays in the polar-izing electrode and backscattered into the chamber-sensitive volume. The free-charge carriers drift in thechamber's effective electric field towards the appropriateelectrode. In contrast to a standard ionization chamber,where the charges impinge directly onto the electrodes, inthe electret chamber the charges moving in the directionof the measuring electrode are stopped and trapped on thepolymer surface to form a stable foil electret. The polari-ty of the electret depends on the direction of the externallyapplied electric field. The initial electret-charging currentis proportional to the sensitive air volume and to the x-rayexposure rate. It also depends strongly on the atomicnumber of the polarizing electrode reflecting the photo-emission contribution to the air ionization in the electretchamber sensitive volume.

The x rays were generated by a constant potential thera-py unit (General Electric Company model no. Maximar-100) with a maximum potential of 100 kV (peak) and ananode current of 3 mA. The half-value layer of the x-raybeam was 2.2 mm of aluminum, corresponding to an ef-fective x-ray beam energy of 28 keV. The polarizing elec-trode was at a distance of 50 cm from the target irrespec-tive of air-gap thickness. The exposure rate at that dis-tance from the target was 50 mRs 'mA

II. EXPERIMENTAL ir ir ir ir ip lr ir il v 1r ir 1r is ir ir ir 1r 'ir

The electret forming chamber resembles a standardparallel-plate ionization chamber as shown schematicallyin Fig. 1. Various metals ranging from aluminum to leadwere used as the conductive polarizing electrode. Themeasuring electrode was made of aluminum groundedthrough an electrometer, and blocked by a polymer foilwith a typical thickness of 100 pm. The air gap was vari-able from 1 mm to a few cm. Both electrodes were circu-lar with a diameter of 5 cm surrounded by a 1-cm wideguard ring. -

The air at atmospheric pressure in the chamber-sensitive volume is ionized by electrons produced by the

lead shieldalumjn 0mI 1'

zxuzzx 'ryggg~~

photoemjt ter

1

lucite

pA

FIG. 1. Schematic diagram of the electret chamber.

1983 The American Physical Society

Page 2: Radiation-induced foil electret chamber

4754 B. G. FALLONE AND E. B. PODGORSAK

III. RESULTS AND DISCUSSION

A. Electret-charging and -discharging characteristics

The current density j (t) measured during the electret-charging or -discharging process is expressed as".

j(t)=j„,e (1+e )~, (tO f)IT 2(10 f)I0 ] IP

where j„,is the electret chamber saturation current densi-ty, and ~, the electret relaxation time, as well as tp, theelectret characteristic polarization or depolarization time,are given as follows

7=Ep( a e~ +Pe, )E*/Pj „,

1.0

0.9

0.8

0.7

0.6

0.4

0.3

0.2

0.1

tp ——win sinh[E, (0)/E*], (3)

with a and p, the air-gap and polymer thickness, respec-tively, e, and ez the dielectric constants, E* the electretchamber extrapolated electric field, ' and E, (0) the ap-plied electric field in the air gap.

In the saturation region, where E, (0))3E* and tp )7,j (t) exhibit the following behavior: At t =0 it is equal toj„,and remains equal to j„,until the effective field in theair gap falls below 3E*. Then j(t) begins to decrease, be-comes equal to (I/~2)j„, at t =tp, and exponentially ap-proaches zero as t increases further.

The electret relaxation time ~ is a function of both theelectret chamber characteristics (air-gap, polymer thick-ness and type, polarizing electrode material) and the expo-sure rate of the x-ray beam. It does not, however, dependon the magnitude of the externally applied field E, (0).

The electret characteristic polarization time tp, which isdefined as the time in which j (t) becomes equal to(I/~2)j„„ is directly proportional to r but it also de-pends in a seemingly complicated manner on E,(0). Forexperiments in the saturation region, however, we may ap-proximate Eq. (3) by

tp E,(0) —ln2, (4)

which suggests that tp/v is linearly proportional to the ap-plied field E,(0). In Fig. 2 we plot experimentally deter-mined values of tp/r as a function of E, (0)/E* for vari-ous polarizing electrode materials. The solid linerepresents a plot of Eq. (3) in excellent agreement with ex-perimental data. The tp/~ curve intercepts the abscissa atE,(0)/E*=0.88, which corresponds to tp ——0. The elec-tret polarization current density is, from Eq. (1), for tp ——0,written as

e—tIT( I + —2tlr) —I /2

and exhibits a typical exponential decay starting atj =(I/v 2)j„, for t =0.

The electret characteristic polarization or depolarizationtime tp is thus a linear function of the applied field E,(0)

time t (s)

FIG. 3. Calculated polarization or depolarization currentdensity j, normalized to j„,for various E,(0}/E* ranging from0.2 to 7.5 (&=0.59 s).

0

30

20

10

1.0

Q 9-

E O8-

Q 7C:

t) 6-

QCo

g Q4-Q

Q3-

Q 2-'P

U Q.1-

o---Pb

Ee(V/cm)

273460.383.3100

50 100 150 200 250 300

Electric Field E (V/cm)

0O~

.0rQ& d. d--Sn

rr d/PHOTOEMITTE R

ELECTRODE

Aquadag (C)Al

Cu// Sn//.g P Pb—--o-—---a--.D.o LJ

l

tanh (E/E )

I s s s s l s ~ s g I ~

0 10 30Ea(o)/ E

FIG. 2. Measured and calculated values for t0/~ as a func-tion of E,(0)/E .

FIG. 4. Current density j as a function of the applied electricfield E in an ionization chamber with an air gap a of 3.48 cm forvarious polarizing electrode materials. Exposure rate is 9R/min. The dashed curves represent calculated saturationcurves (Ref. 12) with the appropriate E .

Page 3: Radiation-induced foil electret chamber

28 RADIATION-INDUCED FOIL ELECTRET CHAMBER 4755

for E,(0)/E* ~ 3 where the saturation condition prevails,and the initial electret polarization or depolarizationcurrent density j(0) is equal to j„,. In the region0.88&E,(0)/E*&3, the initial j(0) is between j„, and(I/v'2)j„„j exponentially decays to zero, and to is stilldefined by Eq. (3) as that time during the electret polari-zation or depolarization process in which the currentdrops to (I/i/2)j„, . For 0&E,(0)/E' &0.88, the initialj(0) is smaller than (1/V 2)j„„to &0, and j(t) rapidly de-cays to zero. In Fig. 3 we show examples of polarizationcurrent-density profiles calculated from Eq. (1) for variousvalues of E, (0)/E*.

B. Saturation current density in the electret chamber

Equation (1) gives the general shape of the radiation in-duced electret-charging or -discharging current-density

rofile, depending strongly on the saturation current den-sity j„,and the extrapolated electric field E . In order tostudy the behavior of j„,and E*, we converted the elec-tret chamber into a standard parallel-plate ionizationchamber and measured saturation curves for various po-larizing electrode materials and air gaps. As shown inFig. 4, for a given air-gap and exposure rate, j„,dependsstrongly on the atomic number Z of the polarizing elec-trode, exhibiting an almost fivefold increase when alumi-num is replaced by lead. The dashed curves represent

12current densities calculated from the relationship

j=j„,tanh(E/E'),

with the use of experimentally determined values for E*.The agreement between measured and calculated satura-tion curves is excellent.

In Fig. 5 we plot j„,(solid curves) as a function of a forvarious polarizing electrode materials. For a given ma-terial j„,increases linearly with a for large a; for small a,however, the linearity breaks down. The j„, vs a curvemay be separated into two components as

j„,(~)=j,',",(a)+j~,(~),

where the linear function j,',", is produced by charge car-riers originating from electrons released in the chamber-sensitive volume by direct interactions of photons with airmolecules, and the exponential function j~, is produced bythe photoelectrons backscattered from the polarizing elec-trode into the chamber-sensitive volume. These pho-toelectrons have a range a„of —1 cm for our x-ray p o-ho-

13ton energy at atmospheric pressure.The linear function j,',", is independent of the electrode

material and linearly dependent upon the air gap a and theexposure rate 7

jsa

0.$

0.4-C4

AI

J~gc ) 0.025 nA/cm2

Cuj~t(o )=0.27 nA/cm2

0.5

- O.4

CD0.3-

cOCO 0.2-

~~(I 0.1-

0)Ch

0-

f.o-

j~t(~) = 0.53 nA/cm&0.9

0.8-

0ca 06-

05-g$~ o..-

0.3

0.2

0.)

0

(3)

3)-

Pbis'~(~)=o. » nA/cm2

-------- (3)

-- -(2)

3

Air Gap Thickness a(cm}

- 0.2

- 1.0

-08- 0.7

-0.5

-04

-0.2

0.1

0

f ir a a for various electrode materials. Exposure rate isFICx. 5. Saturation current density j„t as a function of air gap a or va'

Curves (1) represent a plot of Eq. (11),curves (2) represent Eq. (8), and curves (3) represent Eq. (9).

Page 4: Radiation-induced foil electret chamber

4756 B. G. FALLGNE AND E. B. PQDGORSAK

1.0 I I 1 I I

o~, 0.01 j„,(a,Z, E,)=X[aa+A, 'e(Z, E )(1—e ' " )],

0 5-Eo 04™

p 0.005

0 3»8

a CO

0.2-CO

Q)

0.1

C3

0 o.o7-

a 005-(D

0( oo4-COCO

-E 0.03-OO

CL0.02-

75

LU

O—0.001 coV)

E

CL- 0.0005

0.0110

I I I I I

20 30 40 50 70 1 00

Photoemitter Atomic Number Z

0.0001

FIG. 6. Photoemission saturation current density j~, ( oo ) andphotoemission efficiency e (Ref. 1 3) as a function of polarizingelectrode atomic number The inset shows direct proportionalitybetween j~, ( ao ) and e.

where ~ is the usual proportionality constant 3.33 & 10As/cm R. Equation (8) is plotted in Fig. 5 as dashedlines (2) for an exposure rate of 9 R/min. Note. that j'„", isidentical for all electrode materials.

Empirically, we find that j~„,(a), represented as curves(3) in Fig. 5, may be expressed as follows:

j~,(~) =j~, ( ~ )(1—e '), (9)

j~, ( oo ) =k e(Z, E ) =A, 'Xe(Z, E ),where A, is an exposure-rate-dependent proportionalityconstant, and k' is a proportionality constant independentof the exposure rate and empirically found equal to1.33 X 10 (C/R cm ) (electrons/photon)

The satUration current density j„,may thus in generalbe expressed as

where j„,( co ), the photoemission saturation current densi-ty for a &&a„ is obtained by extrapolating the measuredlinear portion of j„,(a) to a =0.

The relationship between j„,(oo ) and the efficiencye(Z, E ) for production of backscattered electrons, de-fined' as the number of backscattered electrons per in-cident photon of energy E, is shown in Fig. 6 for variouselectrode materials Z. The inset shows direct propor-tionality between j„,( oo ) and the values for F(Z,E„),i.e.,

where a and X' are constants given above, e(Z, E ) is theefficiency for production of backscattered photoelectrons,and a„(E ) is the range of photoelectrons in air at normaltemperature and pressure.

In standard ionization chambers, where low atomicnumber materials are used as the polarizing electrode,e(Z, E ) is so small that the photoemission term of j„,isnegligible in comparison with primary air ionization.With lead as polarizing electrode material, on the otherhand, the main contribution to j„,comes from the photo-emission term because of the large value of e(Z, E, ) forlead.

C. Extrapolated electric field

The extrapolated electric field E* is a parameter in thesaturation curve expression, depending on the configura-tion of the parallel-plate ionization chamber and the x-rayexposure rate. In Fig. 7 we show E* as a function of air-gap thickness a for various polarizing electrode materials.Similarly, to the j„, vs a behavior, E*(a) also has twocomponents; one, E*„,(a), is hnear for all a and is againattributed to primary ionization in air, and the other,Ez (a) exhibits an exponential saturation behavior at ap-proximately 3a, and is attributed to the photoemissionfrom the polarizing electrode. The saturation value,E~( ~ ), is obtained by extrapolating the linear portion ofthe E* vs a curve to a =0. We have shown recently ' thatE*„,(a), represented in Fig. 7 by curves (2), may be ex-pressed as

E,*;,(a)=k(aj,",", )' =kU Ira+ '

Ep (a) =Ep ( ~ )(1—e' ") .

In Fig. 8 we plot E~ ( co ) for various photoemitter ma-terials as a function: (a) of photoemitter atomic numberZ, showing a strong Z dependence of E~ ( &x ), (b) of photo-emission saturation current density j„,( oo ), showingdirect proportionality between E~ ( oo ) and j~,( ao ), and (c)of photoemission efficiency e(Z~E ), showing a linear re-lationship between E~ ( ao ) and e(Z, E,)

In general, Ez ( oo ) may thus be expressed, incorporatingEq. (10), as

E~ ( oo ) =mj ~, ( oo ) =~ &'X&(Z,E ), (14)

where m is the slope from Fig. 8(b) and A,' was defined in

where k is a universal parallel-plate ionization chamberconstant equal to 12.4X10 V/(Acm)', and Ir was de-fined above.

The subtraction of E*„,(a) from E*(a) yields Ez (a)shown as curves (3) in Fig. 7. Empirically we find thatEz (a) may be expressed, similarly to j~,(a), by an ex-ponential expression

Page 5: Radiation-induced foil electret chamber

RADIATION-INDUCED FOIL ELECTRET CHAMBER 4757

AI

Eq(~) = 4 V/cmCuEp(0o) = 25 V/cm

40- ~ 40

0

20-

o0) 10

U

Os~

0UJ

120-

g$110-0~ 100-

c5 90-

80-

70-

SnE~(~}=51 V/cm

(1) q. -

(2)

(3)I

2

(c) PbE~(~)= 71 V/cm

3)

2)

(1)0

"20

-10

- 120

-100

-70

40

30

20

10

(3)

(2)

(3)

- (2)

I

3 4 0 1 2

Ail Gyp Thickness s(cm)

-40

-20

-10

4 0

FICx. 7. Extrapolated electric field E as a function of polarizing electrode materials. Exposure rate is 9 R/min. Curves (1)represent Eq. (15), curves (2) Eq. (12), and curves (3) represent Eq. (13).

the preceding section.The general relationship for the extrapolated field

E*(a,Z, E ) is now given by

E*(a,Z,E, ) =k'aX' +m'e(Z, E)X

a/a~(E„))—where m'=mA, '=1.33)&10 Vcm ' (R/s) ' (electrons/photon) ', and k'=kv ~=22.6 Vcm (R/s) '~ . Theextrapolated field E* thus consists of two terms: one,determined by the primary ionization in air, is dominantfor chambers with low atomic number electrodes, and theother, determined by photoemission from the polarizingelectrode, is dominant at high atomic number polarizingelectrodes.

D. Polarization current-density profiles

The time dependence of the electret polarization currentdensity during the electret-charging process is described

by Eq. (1). In this section we discuss the general proper-ties of polarization current-density profiles based on thesaturation current density j„, and extrapolated field E*.In Figs. 9 and 10 we show various calculated polarizationcurrent-density profiles obtained in the electret chamberwith a lead polarizing electrode and with various air gapsa ranging from 0.18 to 3.48 cm for an applied field E, (0)equal to 5E* (Fig. 9) and a constant applied voltage Vo of500 V (Fig. 10). The insets to both figures give relevantparameters, such as E*,E, (0), and j„,as a function of a.The extrapolated fields E* were obtained from measuredsaturation curves for various air gaps and agree well withdata calculated from Eq. (15). The electret relaxationtimes ~ and characteristic polarization times to were cal-culated from Eqs. (2) and (3), respectively

The condition E,(0)=5E" in Fig. 9 ensures that theelectret chamber is initially in the saturation region for allair gaps and the initial polarization current density isequal to the standard saturation current density j„,. Aplot of measured j„,(a) for a lead electrode was shown inFig. 5(d) in excellent agreement with data calculated fromEq. (11). Combining Eqs. (2) and (4) we get

Page 6: Radiation-induced foil electret chamber

4758 B. G. FALLONE AND E. B. PODGORSAK 28

60-

40-

Eo(a@~+pe, )E* E,(0)tp= —ln2

pjsat(16)

Eo 2Q-

0~0.001 0.002 0.003

photoemission Efficiency0.004

ILL

oILU

m 60-(II

III w

0n. 4Q-tg

LU

III 20COCO

E 0eO0

I I I I I I0.2 0.4 0.6 0.8

photoemission Saturation Current Density j p (~) (r)A/cm )sat

60-

40-

20-Cu

L

snlK

(a)

10 20 30 40 50 60 70 80Photoemitter Atomic Number Z

FICJ. 8. Photoemissive extrapolated electric field E~ ( oo ) as afunction (a) of polarizing electrode atomic number Z, (b) ofphotoemission saturation current density j„,(ao), and (c) ofphotoemission efficiency.

the characteristic electret polarization time, which at leastfor small air gaps gives a fairly good indication of thetime needed to charge the electret to its maximum chargedensity o,„. At larger gaps, however, the current profilebecomes less and less steep and the time needed to fullycharge the electret is much longer than tp, which is stilldefined as the time where j= (1/V 2)j„,.

Figure 10 shows polarization current-density profilesfor a constant external voltage Vo of 500 V applied acrossair gaps of various thicknesses. The chamber is in thesaturation region for the three small air gaps since forthem E,(0) & 3E'. The current profiles start at j„„remain constant for a while depending on to, and then ex-ponentially drop to zero. The areas under all three pro-files are identical and equal to the maximum surfacecharge density. For the air gaps of 2.38 and 3.48 cm,however, the chamber is not in the saturation region, theinitial current density is lower than j„,and starts an im-mediate decay towards zero. The areas under the currentprofiles, however, are also equal to o,„, indicating thatthe electret becomes fully charged even in situations wheresaturation conditions do not prevail in the electretchamber. It is evident from Fig. 10 that the time requiredto fully charge the electret under these conditions can be-come quite large.

In Fig. 11 we compare the calculated [Eq. (I)] and mea-sured polarization current profiles for various polarizingelectrode materials, for an air gap of 0.18 cm and for three

0.9

O,y

0.7—

POLARIZlNG ELECTRODE Pb

a(cm) E'(V/cm) E (0)= 5E'(V/cm)

0.6

C= 0S-N~

0.4—

0.18 0.68I 5 j

O.3&

0)~ 02—D

0.1—

0.180.681.682.383.083.48

3.08

2142648094

100

105210320400470500

3.48 air gap a {cm

I I0 5

I I I10 15 20 25 30 45

Time (s)FIG. 9. Calculated time dependence of the electret-charging or -discharging current j for a lead polarizing electrode with various

air gaps a. The electret chamber was initially under saturation conditions since E,(0)=5E for all a.

Page 7: Radiation-induced foil electret chamber

28 RADIATION-INDUCED FOIL ELECTRET CHAMBER 4759

0 A

air gap a {cm)

~1.682.

E*(V/cm) E (o) (v/cm) ') (nA/cm )sat

0.7

O0.6—

O~0 5

0.4—

gO

3

0.3—0)

O0.2—

0.1—

0 I I I I

10 15 20 25

Time (s)FIG. 10. Calc lu ated time dependence of the electret-charging

or -discharging current j for a lead polarizing electrode withvarious air gaps a. The externally applied voltage Vp was 500 Vfor all air gaps.

applied fields E,(0) equal to approximately 5E*, 10E,and 20E . We notice that for E,(0)-5E' the agreementbetween calculated and measured profiles is excellent; forlarge applied fields, however, the calculated curve is con-siderably steeper than the measured one. This discrepancymay be attributed to the electret chamber, .where a break-down in saturation characteristics may occur at very highvoltages, or to the electret-charging characteristics whichmay depend on charge densities already trapped on thepolymer surface.

IV. CONCLUSION

A new isothermal technique for production of stablefoil electrets has been developed recently. X rays are usedto create free charges which are subsequently trapped on apolymer foil to form the electret. The apparatus closelyresembles a parallel-plate ionization chamber used in radi-ation dosimetry. The measured electret-charging and- ischarging current-density profiles agree well with pro-iles calculated using the laws of Gauss and Kirchoff in

conjunction with the recently discovered hyperbolic rela-tionship describing the saturation curves of parallel-plateionization chambers. The profiles are given in terms ofthe electret chamber saturation current density and of theextrapolated electric field, both depending on the chamberphysical parameters, such as air-gap and polymer thick-ness, polarizing electrode material, x-ray exposure rate,etc. General relationships for the saturation current den-sity and the extrapolated field were given, showing that

0.6—Co 05

~ 0.4—

0 1 2

1.0

0.9I—

08~0.7—

~ 0.6—COIO

~~ 0.5~~~

0.4

3 4 5 6 7 8 9 10 11 12 13 14I i I I r-

Time t(s)

3 4 5

Time t(s)

0.02

p,p15

0.010

0.005

0.25

0.20

o.i5

0.10

0.05

0

0.14—

0. i0—

0.06CV

O0.02

0~~O~M

Q)

0.35

0.25—

0.15

0.05—

I

2 3 4 5

Time t(s)

Time t(s)

1.0

—0.9

—0.8

—0.7

—0.6

—l0.5

—0,4

—0.3

—0.2

—0.1

7I 0

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

FICi. 11. Theoretical ((dashed) vs measured (solid) polarization current densities as a function of time ftrode materials and externally applied fields E (0). Th

ensi ies as a unction of time for various polarizing elec-ie s, . e air-gap thickness a was 0.18 cm, exposure rate 9 R/min.

Page 8: Radiation-induced foil electret chamber

B. G. FALLONE AND E. B. PODGORSAK 28

the two consist of two components, one linear with theair-gap thickness and attributed to primary ionization inair, and the other exhibiting an exponential saturation andattributed to air ionization caused by photoelectrons back-scattered into the chamber sensitive volume from the po-larizing electrode.

ACKNOWLEDGMENTS

We would like to thank Dr. Richard Heese for helpfuldiscussions. This work was supported in part by the Med-ical Research Council of Canada under Grant No. MA-6960.

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