Stefania Cora - AAPM: The American Association of ... · chamber , Pwall is given by the Almond -...

ACMP 25th Annual Meeting

" SMALL FIELD DOSIMETRY: MONTE CARLOASSESSMENT OF PERTURBATION AND

CORRECTION FACTORS FOR IONIZATIONCHAMBER AND SOLID STATE DETECTORS"

Stefania CoraMedical Physics Dept“San Bortolo” Hospital

VicenzaItaly

e-mail: [email protected]


Small beam definition


The definition of “ small” field inradiation dosimetry depends on:

0%

0%

0%

0%

0%

10

1. The geometr ic dimension of the field, i.e. a filed with asize less than 3x3 cm2.

2. The influence of different factors: i) the source size asprojected through the beam aper ture to the detectorlocation; ii) the size of the detector used in measurementsand iii) the electron range in the ir radiated medium.

3. The presence of air in the cavity of the detector .

4. I t does not depend on the energy of the radiation field.5. I t does not depend on the size of the detector .


Ionization chamber TG-51

• Start from ND,w

• Specify beam quality by:- %dd(10)x for photons- R50 for electrons

• Simple dose equation:Co

wDQ

Q

wNkMD

60

,⋅⋅⋅⋅⋅⋅⋅⋅====


Detectors considered

• Ionization chambers• Diamonds• Diodes• Mosfets


Ionization chamber TG-51

Co

WD

Q

WD

Q N

Nk 60

,

,====

Co

celgrflwall

water

air

Q

celgrflwall

water

air

Q

PPPPL

PPPPL

k

60

⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅

⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅

====

ρρρρ

ρρρρ

To measure

To calculate


Pwall

The wall correction factor, Pwall,accounts for the fact that the chamberwall is composed of a different materialfrom the phantom medium.

This difference in material causeschanges in the attenuation and scatter ofparticles passing through the chamberwall.

The correction Pwall applies to bothcylindrical and parallel-plate chambers.


Pwall

In electron beams, Pwall is normallyassumed to be 1.00.

For cylindrical chambers, this isjustified partially by a theoretical modeldeveloped by Nahum but for all chambersis based primarily on a lack ofinformation available regarding Pwall inelectron beams.


In photon beams, for a cylindrical ionchamber, Pwall is given by the Almond-Svensson formula:

Pwall in photon beams

(((( ))))med

air

med

air

med

wall

en

wall

air

wall

L

LL

P

⋅⋅⋅⋅−−−−++++

⋅⋅⋅⋅

⋅⋅⋅⋅====

ρρρρ

ρρρραααα

ρρρρµµµµ

ρρρραααα 1

where αααα is the fraction of ionizationfrom electrons originating in the chamberwall, 1−αααα is the fraction of ionization fromelectrons originating in the phantom.


In small beam dosimetry the cavity theory ofSpencer-Attix must be corrected because:

0%

0%

0%

0%

0%

10

1. It is valid only in condition of electronic equilibrium and foran homogeneous medium.

2. It is valid only for low energy of radiation field.

3. The range of the electrons is too large with respect the sizeof the cavity.

4. It does not take into account the effects of perturbation ofthe secondary electron fluence by the presence of thedetector.

5. The correction factors applied to the detector signal areindependent from the field size and therefore the Spencer-Attix theory does not need corrections.


Pwall for thimble chambersin photon beams


Pwall for thimble chambersin high electron beams


Pwall for thimble chambers in highelectron beams as a function of depth

1.06.0 50 −−−−⋅⋅⋅⋅==== Rdred


Pwall for PP chambersin high electron beams


Pwall for PP chambers in high electronbeams as a function of depth


The Monte Carlo method can be used to improvethe dosimetric accuracy

0%

0%

0%

0%

0%

10

1. I t can substitute the measurements in non equilibr iumconditions.

2. I t can be used to calculate the correction factors to beapplied to the measurements with detectors whenconditions for cavity theory can not be fulfilled.

3. I t can simulate the detectors.4. I t can simulate any type of radiation field.5. I t can simulate accurately the treatment head of the

linear accelerator and therefore the non-equilibr iumdosimetry of small beams in presence of heterogeneitycan be understood well.


The fluence correction – photon beams

Pfl corrects for changes in theelectron fluence spectrum due to thecavity, other than those associated withthe gradient correction.

This correction is only required inregions where full or transient chargedparticle equilibrium has not beenestablished, since by the Fano theorem,the electron spectrum is independent ofthe density of the material in regionswhere charged particle equilibrium exists


The fluence correction - electron beams

In an electron beam, density changes cancause hot or cold spots as a result of electronscattering.

As a result of (elastic nuclear) scattering, the angulardistribution of electrons broadens with depth; a low densitycavity will consequently scatter out fewer electrons than arescattered in, resulting in an increase in the electron fluencetowards the downstream end of the cavity in comparison withthe fluence in a uniform medium at that depth.


The magnitude of the in-scattering perturbationexceeds 3% for Farmer type chambers for Ez below 8MeV.

This is one of the principal reasons why parallel-plate chambers are recommended in low energyelectron beams.

In a parallel-plate chamber the diameter of the aircavity (typically between 13 and 20 mm) is deliberatelymade very much greater than its thickness (theelectrode spacing), which is 2 mm in almost allcommercial designs.

Thus most of the electrons enter the air cavitythrough the front face of the chamber and only a smallfraction through the side walls.




Well designed parallel-platechambers have a relatively wide guardring, 3 mm or more, which ensures thatalmost no electrons entering through theshort side walls can contribute to thechamber signal. Consequently, in-scattering is virtually eliminated.

The electron fluence in the sensitivevolume of such a chamber is thereforethat existing in the uniform medium at thedepth of the inside face of the frontwindow, which is the position of the

ff ti i t f t P


The fluence correction NACP pp-chamberelectron beams


The fluence correctionelectron beams (thimble chambers)


The gradient correction factor

One of the effects of the air cavity isto shift the effective point ofmeasurement of the chamber upstreamsince there is less attenuation in thecavity than in the phantom medium. Forcylindrical chambers, Pgr depends on thedose gradient within the phantom at thelocation of the cavity and on the diameterof the cavity.

The correction is larger for steepergradients and for larger cavities. In the TG-51protocol, to take the gradient effects intoaccount when measuring depth-dose curves, itis recommended to shift the Pdd curve upstreamby 0.5r for electron beams and by 0.6r for photonbeams, where r is the radius of the cavity


The gradient correction factor

It should be noted that formeasurements in electron beams, at adepth of dmax, Pgr is taken as unity sincethere is no dose gradient at this depth.

For parallel-plate chambers, since thepoint of measurement is at the front faceof the cavity, the gradient correction isalready taken into account and thereforePgr is taken as unity in both photon andelectron


The gradient correction factordependence on field size and depth

–0.6·R is used as EPOM to produce the data in thegraph. Minimization results in a downstream shift of0.29mm (10×10) and 0.48 mm (30×30) compared to the–0.6·R prescription.

PTW -chamber


Pcel correction factor

The central electrode correctionfactor, Pcel, applies only to cylindricalchambers, which have a central electrodewithin the chamber cavity.

Pcel is used to account for the changein ionization within the chamber due tothe presence of the central electrode.

Values are given in terms of the beamquality, the electrode material and theelectrode radius.


Pcel correction factor

Photon beams Electron beams


Uncertainties on measured absorbed-dosecalibration factors, ND;w, and on beam quality

conversion factors kQ and CQ at NRC

k

Q

WD

Q

Co

WD

Q

WD

Q

N

NC

N

Nk

,

,

,60

====

====


Uncertainties on measured absorbed-dosecalibration factors, ND;w, and on beamquality conversion factors kQ and CQ


Beam quality specification ofhigh-energy photon beams

Measured kQ values show a spread of up to1.1% when plotted as a function of where asthis spread becomes 0.4% when %dd(10)x isused as beam quality specifier.

20

10TPR


Diamond detector

– Diamond is an allotrope of carbon and, as such, has an atomicnumber Z=6.

– This is to be compared with the effective atomic number of soft tissue,Z ≅≅≅≅ 6.4

When a diamond detector is irradiated in a water phantom byphotons, the absorbed dose to the water phantom, Dw(p) at any point p,is given by:

where Ddiam is the average absorbed dose in the sensitive volumeof the diamond detector and fw is a factor that depends on radiationenergy, medium of irradiation, and size of the cavity relative to theranges of electrons incident upon it.

(((( ))))wdiamw fDNpD ⋅⋅⋅⋅⋅⋅⋅⋅====


Diamond detectorFor the diamond detector to behave as a Bragg–Gray cavity,

not only should the ranges of the electrons incident on thesensitive volume of the diamond detector cavity be greater thanthe size of the cavity, but also photon interactions in the cavityshould be negligible.

Even though the diamond detector sensitive volume isphysically smaller than most ionization chambers used forradiation therapy applications its density is about 3000 timesgreater than air, and so the sensitive diamond volume presents alarger equivalent volume compared to that presented by air in mostair ionization chambers.

The response of the diamond detector in megavoltagephoton beams can therefore be determined theoretically using anintermediate cavity equation


Diamond detectordose contribution from photon interactions


Diamond detector

10 MV

25 MV


Diamond detector – electron beams

monenergetic

Philips SL75


Dose-rate dependence

As noted by Planskoy (1980) theorypredicts that the value of ∆∆∆∆ will decrease withincreasing dose rate:

indicating that some decrease in ∆∆∆∆ exists

0.99-0.02*log(Dnorm)

The relationship of conductivity to dose rate forradiation induced conductors is given by Fowler

(((( )))) (((( )))) (((( ))))normnorm

∆

normnorm

∆

D∆iDi

nearis∆whereDσloglog

1

⋅⋅⋅⋅====⇒⇒⇒⇒====

∝∝∝∝


Diodes

A new thermal equilibrium is established whenFermi level of the p-side lines up with Fermi level ofthe n-side. The diffusion of mobile carriers (due tothe concentration gradient) 'depletes' the carriers oneither side of the junction.

As soon as the junction is made, there is initiallyno mechanism to conuteract the diffusion process. Thiscauses carriers to leave the regions of its own type,leaving behind the semiconductor which is depleted ofmobile charges. The depleted semiconductor now hasthe ionized impurity charge not compensated by thecarrier charges. Thus the depleted regions have netspace charge.

When a diode is connected to an electrometer,no current flows unless excess minority carriers areinjected by external sources, such as ionizingradiation. The electrical field across the pn junctiondue to φφφφ0000 is greater than 103 V/cm, which enables thecollection of radiation generated minority carrierswithout external bias.

As the new thermal equilibrium is made (Fermilevel lined up!), the hole diffusion flux is exactlymatched by an opposing hole flux. This opposing holeflux is due to the electric field forces holes in directionopposite to the diffusion direction. The electric fieldarises in the depletion region due to theuncompensated ionized impurity charge (the spacecharge). Thus the net hole flux is now zero.


Diodes cannot be used forabsolute dosimetry


Diodes cannot be used forabsolute dosimetry

During a radiation exposure, a portion of theexcess minority carriers in the diode is captured by theR-G centers and are recombined with the majoritycarriers.

The captured portion depends on the excessminority-carrier concentration ∆∆∆∆p, the R-G centerconcentration Nt , and the capture cross section of theminority carrier by the R-G center.

When the instantaneous dose rate r is verysmall ~low injection, such as for Co-60 beam!, the R-Gcenters are almost empty to the minority carriers.

Therefore, the recombination portion remainsconstant with the increase of ∆∆∆∆p, and the excessminority-carrier lifetime t and the sensitivity S do notchange with r.

When r is not small, many of the R-G centers areoccupied by the excess minority carriers. In this case,the empty R-G centers may not be sufficient to keepthe recombination portion constant with an increase ofminority carriers.

This leads to an increase in diode sensitivitywith an increased charge generation rate because alarger fraction of the charge will diffuse to the junctionand be collected.

When r is very large (high injection!), the R-Gcenters are almost full. The recombination portionwill remain constant with an increase in chargegeneration, and the diode sensitivity will beindependent of r again.


Application of Burlin cavity theory todiode detector proposed by Z. Yin

( ) ( ) ( ) εερµφα

ρφε

ρφα γ d

Sd

LD en

seep ⋅⋅⋅⋅−+∆⋅∆+⋅⋅⋅= ∫∫ ∆∆ ,, 1

The mean path length for an electron insolid-state dosimeters is considerably shorterthan in an air cavity, so the Spencer–Attixcavity theory is not generally valid forcomputing absorbed dose (Mobit et al 1997).


Application of Burlin cavity theory todiode detector proposed by Z. Yin

6 MV 15 MV

The relative over-response of the diode detector withincreased field size can be explained simply in terms of thehigher atomic number of silicon relative to water.

By treating the primary and scattered photon spectraseparately and using Spencer–Attix and large-cavity theoryrespectively it is possible to accurately predict the response ofthe diode in megavoltage photon beams.


MOSFETs

The MOSFET is a transistor with three electricalconnections. A voltage Vg applied to one connection (the gate)allows current to flow through the other two connections (sourceand drain), when biased. The main electrical parameter of aMOSFET is the threshold voltage (denoted as “ VT” ), which isdefined as the Vg value above which a current can flow throughthe drain and source of the transistor


MOSFETs

The majority-carriers in the p-n-p junction create a space chargeregion which inhibits any current from flowing between source and drain.When a negative voltage relative to the silicon substrate is applied to thegate, the minority carriers (holes, positively charged) in the substratemigrate towards the SiO2 (silicon dioxide)-silicon interface; as aconsequence, the n-type material under the gate is gradually convertedinto p-type material. When the gate voltage reaches the threshold voltagevalue (i.e. Vg = VT), the material from source to drain under the gatebecomes the same (p-type) material, and conduction between source anddrain takes place.


MOSFETs

Principle of radiation detectionWhen the MOSFET is exposed

to ionizing radiation, electron-hole pairsare created in the SiO2 layer. If Vg > 0during irradiation, holes are trapped atthe Si/SiO2 interface; as a consequence,the previous VT value can no longerswitch “ ON” the MOSFET. An increaseof VT by ∆∆∆∆VT (voltage shift) is requiredfor current to pass through the drain tothe source. The resulting ∆∆∆∆VT isproportional to the absorbed dose andits amplitude per unit dose defines theMOSFET sensitivity in mV/cGy [95]. VTis the quantity directly measured, sothat the absorbed dose results from thefollowing

SV

Dose t∆∆∆∆====

Where S is the sensitivity

SV

Dose t∆∆∆∆====


MOSFETs

The threshold voltage of the single MOSFET is affectedby temperature (4-5 mV/°°°°C) and by the cumulated dose, asboth reduce Nox , thus limiting the accuracy of measurement inclinical situations.

These effects are significantly negligible for devicesmade of two identical MOSFETs fabricated on a similar siliconchip (dual-MOSFET) and operated at different gate biases.Indeed, as the measured difference of VT between the twotransistors is a measure of the radiation dose, this effectivelyreduces the temperature dependence to less than 0.015 mV/°°°°C,as well as other drift effects, such as dependence on cumulateddose, which affect both MOSFETs in the same manner


MOSFETs

Energy dependenceEnergy dependence of the response was studied

especially for photon beams. It is constant within ±±±± 2-3% over a wide range of electron (5-21 MeV) and photon(4-25 MV) therapy beams.

Below 0.6 MeV the MOSFET response increaseswith decreasing energy. Indeed, for quasi-monoenergetic low x-ray energies (12-208 keV),MOSFET sensitivity was found to be 4.3 times higher at33 keV than at 6-MV

Similarly to diodes, this has been attributed to thesecondary-electron stopping power ratios of silicon towater, producing peak sensitivity at incident energy ofapproximately 30 keV .


MOSFETs

Fading effectMOSFET response increases with increasing the

time between irradiation and readout, and after about 10hours it starts decreasing.

This is due to slow movement of the holes insidethe dioxide layer, and to delayed release of trappedholes.

For TN MOSFETs a 3 % fading following irradiationwas observed within the first 5 hours and thereafter itremained stable up to 60 hours.

Fading up to 2 % for readings within 1-10 minfollowing irradiation was reported for Sicel OneDosesensors. As to Sicel implantable MOSFETs, fadingsignificantly influences dose readings, as determinedby Beddar et al. and Briere et al.


MOSFETsReproducibilitySensor reproducibility depends on the amount of the ∆∆∆∆VT,which depends on both absorbed dose and sensitivity.For exposures causing about 100 and 150 mV ∆∆∆∆VT, singleand dual-MOSFETs showed a reproducibility of 3-4 %and 2 % (2σσσσ), respectively. For higher ∆∆∆∆VT, e.g. 300 mV,sensor reproducibility improves to ≤≤≤≤ 1% (2σσσσ). Therefore,for a given absorbed dose, sensor reproducibilityimproves with increasing sensitivity. Due to the earlyMOSFET saturation caused by a higher sensitivity, thechoice of the set (tox, Vg) should be optimized for everyapplication.

As to the maximum inter-variability for a batch of20 TN MOSFETs, it was reported to be 5 % .Manufacturing reproducibility of less than 1% wasreported for NMRC prototypes


MOSFETsAngular dependence

As the shape of the MOSFET is not spherical, the secondaryelectron distribution may vary for different beam directions, thuscausing possible angular dependence of the response.

The anisotropy of response for TN standard sensors, underCPE conditions is less than ±±±± 2.5 % at 6 MV photon beams.

For 6-9 MeV electron beams, TN MOSFET response in full-buildup setup was verified to have angular dependence within ±±±±

2% and to show no dependence on dose rate

Stefania Cora - AAPM: The American Association of ... · chamber , Pwall is given by the Almond -...

Documents

Transcript of Stefania Cora - AAPM: The American Association of ... · chamber , Pwall is given by the Almond -...