"SMALL FIELD DOSIMETRY: MONTE CARLO
ASSESSMENT OF PERTURBATION AND
CORRECTION FACTORS FOR IONIZATION
CHAMBER AND SOLID STATE DETECTORS"
Stefania Cora
Medical Physics Dept
“San Bortolo” Hospital
Vicenza
Italy
e-mail: stefania.cora@ulssvicenza.it
ACMP 25th Annual Meeting
Small beam definition
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The definition of “small” field in
radiation dosimetry depends on:
0% 1.
0% 2.
0%
0% 3.
4.
0% 5.
The geometric dimension of the field, i.e. a filed with a
size less than 3x3 cm2.
The influence of different factors: i) the source size as
projected through the beam aperture to the detector
location; ii) the size of the detector used in measurements
and iii) the electron range in the irradiated medium.
The presence of air in the cavity of the detector.
It does not depend on the energy of the radiation field.
It does not depend on the size of the detector.
ACMP 25th Annual Meeting
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Ionization chamber TG-51
• Start from ND,w
• Specify beam quality by:
- %dd(10)x for photons
- R50 for electrons
• Simple dose equation:
Dw = M ⋅ kQ ⋅ N D ,w
Q
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60
Co
Detectors considered
•
•
•
•
Ionization chambers
Diamonds
Diodes
Mosfets
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Ionization chamber TG-51
Q
To measure
N D ,W
kQ =
Co
N D ,W
60
L
To calculate
kQ =
ρ
L
ρ
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water
⋅ Pwall ⋅ Pfl ⋅ Pgr ⋅ Pcel
air
Q
water
⋅ Pwall ⋅ Pfl ⋅ Pgr ⋅ Pcel
air
60
Co
Pwall
The wall correction factor, Pwall,
accounts for the fact that the chamber
wall is composed of a different material
from the phantom medium.
This difference in material causes
changes in the attenuation and scatter of
particles passing through the chamber
wall.
The correction Pwall applies to both
cylindrical and parallel-plate chambers.
ACMP 25th Annual Meeting
Pwall
In electron beams, Pwall is normally
assumed to be 1.00.
For cylindrical chambers, this is
justified partially by a theoretical model
developed by Nahum but for all chambers
is based primarily on a lack of
information available regarding Pwall in
electron beams.
ACMP 25th Annual Meeting
Pwall in photon beams
In photon beams, for a cylindrical ion
chamber, Pwall is given by the AlmondSvensson formula:
α⋅
Pwall =
L
ρ
wall
air
µ
⋅ en
ρ
med
+ (1 − α ) ⋅
wall
L
ρ
L
ρ
med
air
med
air
where α is the fraction of ionization
from electrons originating in the chamber
wall, 1−α is the fraction of ionization from
electrons originating in the phantom.
ACMP 25th Annual Meeting
In small beam dosimetry the cavity theory of
Spencer-Attix must be corrected because:
0% 1.
0%
2.
0% 3.
0%
4.
0%
5.
It is valid only in condition of electronic equilibrium and for
an homogeneous medium.
It is valid only for low energy of radiation field.
The range of the electrons is too large with respect the size
of the cavity.
It does not take into account the effects of perturbation of
the secondary electron fluence by the presence of the
detector.
The correction factors applied to the detector signal are
independent from the field size and therefore the SpencerAttix theory does not need corrections.
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Pwall for thimble chambers
in photon beams
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Pwall for thimble chambers
in high electron beams
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Pwall for thimble chambers in high
electron beams as a function of depth
d red = 0.6 ⋅ R50 − 0.1
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Pwall for PP chambers
in high electron beams
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Pwall for PP chambers in high electron
beams as a function of depth
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The Monte Carlo method can be used to improve
the dosimetric accuracy
0% 1.
0% 2.
0%
0% 3.
4.
0%
5.
It can substitute the measurements in non equilibrium
conditions.
It can be used to calculate the correction factors to be
applied to the measurements with detectors when
conditions for cavity theory can not be fulfilled.
It can simulate the detectors.
It can simulate any type of radiation field.
It can simulate accurately the treatment head of the
linear accelerator and therefore the non-equilibrium
dosimetry of small beams in presence of heterogeneity
can be understood well.
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The fluence correction – photon beams
Pfl corrects for changes in the
electron fluence spectrum due to the
cavity, other than those associated with
the gradient correction.
This correction is only required in
regions where full or transient charged
particle equilibrium has not been
established, since by the Fano theorem,
the electron spectrum is independent of
the density of the material in regions
where charged particle equilibrium exists
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The fluence correction - electron beams
In an electron beam, density changes can
cause hot or cold spots as a result of electron
scattering.
As a result of (elastic nuclear) scattering, the angular
distribution of electrons broadens with depth; a low density
cavity will consequently scatter out fewer electrons than are
scattered in, resulting in an increase in the electron fluence
towards the downstream end of the cavity in comparison with
the fluence in a uniform medium at that depth.
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The fluence correction - electron beams
The magnitude of the in-scattering perturbation
exceeds 3% for Farmer type chambers for Ez below 8
MeV.
This is one of the principal reasons why parallelplate chambers are recommended in low energy
electron beams.
In a parallel-plate chamber the diameter of the air
cavity (typically between 13 and 20 mm) is deliberately
made very much greater than its thickness (the
electrode spacing), which is 2 mm in almost all
commercial designs.
Thus most of the electrons enter the air cavity
through the front face of the chamber and only a small
fraction through the side walls.
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The fluence correction - electron beams
Well
designed
parallel-plate
chambers have a relatively wide guard
ring, 3 mm or more, which ensures that
almost no electrons entering through the
short side walls can contribute to the
chamber
signal.
Consequently,
inscattering is virtually eliminated.
The electron fluence in the sensitive
volume of such a chamber is therefore
that existing in the uniform medium at the
depth of the inside face of the front
window, which is the position of the
ff ti
i t f
tP
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The fluence correction NACP pp-chamber
electron beams
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The fluence correction
electron beams (thimble chambers)
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The gradient correction factor
One
the effects
the air
is
The of
correction
is of
larger
forcavity
steeper
to
shiftand for
the larger
effective
point
of
gradients
cavities. In
the TG-51
measurement
of the
the gradient
chamber effects
upstream
protocol,
to take
into
account
when measuring
depth-dose curves,
since there
is less attenuation
in theit
is
recommended
shift
the Pdd curve
upstream
cavity
than in to
the
phantom
medium.
For
by
0.5r for electron
beamsPanddepends
by 0.6r foron
photon
cylindrical
chambers,
the
gr
beams, where r is the radius of the cavity
dose gradient within the phantom at the
location of the cavity and on the diameter
of the cavity.
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The gradient correction factor
It should be noted that for
measurements in electron beams, at a
depth of dmax, Pgr is taken as unity since
there is no dose gradient at this depth.
For parallel-plate chambers, since the
point of measurement is at the front face
of the cavity, the gradient correction is
already taken into account and therefore
Pgr is taken as unity in both photon and
electron
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The gradient correction factor
dependence on field size and depth
PTW -chamber
–0.6·R is used as EPOM to produce the data in the
graph. Minimization results in a downstream shift of
0.29mm (10×10) and 0.48 mm (30×30) compared to the
–0.6·R prescription.
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Pcel correction factor
The central electrode correction
factor, Pcel, applies only to cylindrical
chambers, which have a central electrode
within the chamber cavity.
Pcel is used to account for the change
in ionization within the chamber due to
the presence of the central electrode.
Values are given in terms of the beam
quality, the electrode material and the
electrode radius.
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Pcel correction factor
Photon beams
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Electron beams
Uncertainties on measured absorbed-dose
calibration factors, ND;w, and on beam quality
conversion factors kQ and CQ at NRC
N DQ,W
kQ =
N D ,WCo
60
Q
N D ,W
CQ =
Nk
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Uncertainties on measured absorbed-dose
calibration factors, ND;w, and on beam
quality conversion factors kQ and CQ
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Beam quality specification of
high-energy photon beams
Measured kQ values show a spread of up to
1.1% when plotted as a function of TPR1020 where as
this spread becomes 0.4% when %dd(10)x is
used as beam quality specifier.
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Diamond detector
– Diamond is an allotrope of carbon and, as such, has an atomic
number 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 by
photons, the absorbed dose to the water phantom, Dw(p) at any point p,
is given by:
Dw ( p ) = N ⋅ Ddiam ⋅ f w
where Ddiam is the average absorbed dose in the sensitive volume
of the diamond detector and fw is a factor that depends on radiation
energy, medium of irradiation, and size of the cavity relative to the
ranges of electrons incident upon it.
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Diamond detector
For the diamond detector to behave as a Bragg–Gray cavity,
not only should the ranges of the electrons incident on the
sensitive volume of the diamond detector cavity be greater than
the size of the cavity, but also photon interactions in the cavity
should be negligible.
Even though the diamond detector sensitive volume is
physically smaller than most ionization chambers used for
radiation therapy applications its density is about 3000 times
greater than air, and so the sensitive diamond volume presents a
larger equivalent volume compared to that presented by air in most
air ionization chambers.
The response of the diamond detector in megavoltage
photon beams can therefore be determined theoretically using an
intermediate cavity equation
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Diamond detector
dose contribution from photon interactions
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Diamond detector
10 MV
25 MV
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Diamond detector – electron beams
monenergetic
Philips SL75
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Diamond detector – electron beams
monenergetic
Philips SL75
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Dose-rate dependence
The relationship of conductivity to dose rate for
radiation induced conductors is given by Fowler
∝ D where
inorm = ( Dnorm )
is near 1
log (inorm ) =
⋅ log ( Dnorm )
As noted by Planskoy (1980) theory
predicts that the value of ∆ will decrease with
increasing dose rate:
0.99-0.02*log(D
)
norm
indicating that some decrease in ∆ exists
ACMP 25th Annual Meeting
Diodes
As
soon
as the
is made,
there
is initially
As
thermal
equilibrium
made
(Fermi
When
A the
newanew
thermal
diode
isjunction
equilibrium
connected
to
is established
anis
electrometer,
when
no
mechanism
conuteract
theup
diffusion
process.
This
level
lined
up!),
the
hole
diffusion
is level
exactly
no
Fermi
current
levelflows
ofto
the
unless
p-side
excess
lines
minority
withflux
Fermi
carriers
are
of
causes
carriers
todiffusion
leavesources,
the
ofopposing
its ionizing
own
matched
by
opposing
hole
flux.such
This
hole
injected
the n-side.
byan
The
external
of regions
mobile
carriers
as
(duetype,
to
leaving
behind
the
semiconductor
which
iscarriers
depleted
flux
due
to the
electric
field'depletes'
forces
holes
in
direction
radiation.
theisconcentration
The
electrical
gradient)
field
across
the
thepn
junction
onof
3 V/cm,
mobile
The
depleted
semiconductor
now
has
opposite
to
the
diffusion
direction.
The enables
electric
field
either
side
of
the
junction.
due
to φcharges.
is
greater
than
10
which
the
0
the
ionized
charge
not
compensated
the
arises
in ofimpurity
the
depletion
region
due carriers
toby the
collection
radiation
generated
minority
carrier
Thus the
depleted
regions
have
net
uncompensated
ionized
impurity
charge
(the
space
withoutcharges.
external bias.
ACMP 25th Annual Meeting
space charge.
charge).
Thus the net hole flux is now zero.
Diodes cannot be used for
absolute dosimetry
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Diodes cannot be used for
absolute dosimetry
Whenr is
the
instantaneous
rate
r isofvery
During
a not
radiation
exposure,
portion
the
When
small, many
ofdose
theaR-G
centers
are
r is carriers
very such
large
(high
injection!),
the
R-G
small When
~low
for
Co-60
beam!,
the
R-G
excess
minority
in as
the
diode
is captured
by
the
occupied
byinjection,
the
excess
minority
carriers.
In this
case,
centers
are
almost
full.
Thenot
centers
are
almost
empty
torecombination
the
minority
carriers.
R-G
centers
and
are
recombined
with
the portion
majority
the
empty
R-G
centers
may
be sufficient
to
keep
willrecombination
remain
constant
with
an increase
charge
Therefore,
the recombination
portion
remains
carriers.
the
portion
constant
with
an in
increase
of
generation,
andthe the
diode of sensitivity
willexcess
be
constantcarriers.
with
increase
∆p, and the
minority
The captured
portion
on theS excess
independent
of r lifetime
again.
minority-carrier
t anddepends
the sensitivity
do not
This
leads
to an increase∆in
sensitivity
the R-G
center
minority-carrier
p, diode
change
with
r. concentration
concentration
Nt , and
the capture
cross
section
of the
with
an increased
charge
generation
rate
because
a
minority
carrierofby
the
R-G center.
larger
fraction
the
charge
will diffuse to the junction
and be collected.
ACMP 25th Annual Meeting
Application of Burlin cavity theory to
diode detector proposed by Z. Yin
S(∆)
µen
D =α ⋅ φp,e ⋅ ⋅ dε +φe (∆) ⋅
+(1−α) ⋅ φs,γ ⋅ ⋅ε ⋅ dε
∆
ρ
ρ
ρ
L∆
The mean path length for an electron in
solid-state dosimeters is considerably shorter
than in an air cavity, so the Spencer–Attix
cavity theory is not generally valid for
computing absorbed dose (Mobit et al 1997).
ACMP 25th Annual Meeting
Application of Burlin cavity theory to
diode detector proposed by Z. Yin
6 MV
15 MV
The relative over-response of the diode detector with
increased field size can be explained simply in terms of the
higher atomic number of silicon relative to water.
By treating the primary and scattered photon spectra
separately and using Spencer–Attix and large-cavity theory
respectively it is possible to accurately predict the response of
the diode in megavoltage photon beams.
ACMP 25th Annual Meeting
MOSFETs
The MOSFET is a transistor with three electrical
connections. A voltage Vg applied to one connection (the gate)
allows current to flow through the other two connections (source
and drain), when biased. The main electrical parameter of a
MOSFET is the threshold voltage (denoted as “VT”), which is
defined as the Vg value above which a current can flow through
the drain and source of the transistor
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MOSFETs
The majority-carriers in the p-n-p junction create a space charge
region which inhibits any current from flowing between source and drain.
When a negative voltage relative to the silicon substrate is applied to the
gate, the minority carriers (holes, positively charged) in the substrate
migrate towards the SiO2 (silicon dioxide)-silicon interface; as a
consequence, the n-type material under the gate is gradually converted
into p-type material. When the gate voltage reaches the threshold voltage
value (i.e. Vg = VT), the material from source to drain under the gate
becomes the same (p-type) material, and conduction between source and
drain takes place.
ACMP 25th Annual Meeting
MOSFETs
Principle of radiation detection
When the MOSFET is exposed
to ionizing radiation, electron-hole pairs
are created in the SiO2 layer. If Vg > 0
during irradiation, holes are trapped at
the Si/SiO2 interface; as a consequence,
the previous VT value can no longer
switch “ON” the MOSFET. An increase
of VT by ∆VT (voltage shift) is required
for current to pass through the drain to
the source. The resulting ∆VT is
proportional to the absorbed dose and
its amplitude per unit dose defines the
MOSFET sensitivity in mV/cGy [95]. VT
is the quantity directly measured, so
that the absorbed dose results from the
following
Dose =
∆ Vt
S
Where S is the sensitivity
ACMP 25th Annual Meeting
Dose =
∆ Vt
S
MOSFETs
These effects are significantly negligible for devices
threshold voltage of the single MOSFET is affected
made The
of two
identical MOSFETs fabricated on a similar silicon
by temperature (4-5 mV/°C) and by the cumulated dose, as
chip (dual-MOSFET) and operated at different gate biases.
both reduce Nox , thus limiting the accuracy of measurement in
Indeed, as the measured difference of VT between the two
clinical situations.
transistors is a measure of the radiation dose, this effectively
reduces the temperature dependence to less than 0.015 mV/°C,
as well as other drift effects, such as dependence on cumulated
dose, which affect both MOSFETs in the same manner
ACMP 25th Annual Meeting
MOSFETs
Energy dependence
Energy 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 increases
with
decreasing
energy.
Indeed,
for
quasimonoenergetic low x-ray energies (12-208 keV),
MOSFET sensitivity was found to be 4.3 times higher at
33 keV than at 6-MV
Similarly to diodes, this has been attributed to the
secondary-electron stopping power ratios of silicon to
water, producing peak sensitivity at incident energy of
approximately 30 keV .
ACMP 25th Annual Meeting
MOSFETs
Fading effect
MOSFET response increases with increasing the
time between irradiation and readout, and after about 10
hours it starts decreasing.
This is due to slow movement of the holes inside
the dioxide layer, and to delayed release of trapped
holes.
For TN MOSFETs a 3 % fading following irradiation
was observed within the first 5 hours and thereafter it
remained stable up to 60 hours.
Fading up to 2 % for readings within 1-10 min
following irradiation was reported for Sicel OneDose
sensors. As to Sicel implantable MOSFETs, fading
significantly influences dose readings, as determined
by Beddar et al. and Briere et al.
ACMP 25th Annual Meeting
MOSFETs
Reproducibility
Sensor 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, single
and dual-MOSFETs showed a reproducibility of 3-4 %
and 2 % (2σ), respectively. For higher ∆VT, e.g. 300 mV,
sensor reproducibility improves to ≤ 1% (2σ). Therefore,
for a given absorbed dose, sensor reproducibility
improves with increasing sensitivity. Due to the early
MOSFET saturation caused by a higher sensitivity, the
choice of the set (tox, Vg) should be optimized for every
application.
As to the maximum inter-variability for a batch of
20 TN MOSFETs, it was reported to be 5 % .
Manufacturing reproducibility of less than 1% was
reported for NMRC prototypes
ACMP 25th Annual Meeting
MOSFETs
Angular dependence
As the shape of the MOSFET is not spherical, the secondary
electron distribution may vary for different beam directions, thus
causing possible angular dependence of the response.
The anisotropy of response for TN standard sensors, under
CPE conditions is less than ± 2.5 % at 6 MV photon beams.
For 6-9 MeV electron beams, TN MOSFET response in fullbuildup setup was verified to have angular dependence within ±
2% and to show no dependence on dose rate
ACMP 25th Annual Meeting