X-ray detector for medical imaging with perovskite

X-ray detector

1. MODELING AND ANALYSIS OF
LEAD-FREE PEROVSKITE
PHOTOCONDUCTORS FOR
DIRECT CONVERSION X-RAY
IMAGING DETECTORS
Bangladesh University of Engineering and Technology
Department of Electrical and Electronic Engineering
Supervisor
Dr. Shaikh Asif Mahmood
Associate Professor
Department of EEE
BUET
Presented By
Naznin Sultana
Student Id: 1017062247
Department of EEE
BUET

2. Table of Contents
2
X-ray
Applications of X-ray imaging
X-ray imaging
Digital X-ray imaging
Characteristics of Ideal Photoconductor
Photoconductors in X-ray Detection
Cs
2
AgBiBr
6
(CABB) in X-ray Detection
Linear Attenuation Coefficients of Cs
2
AgBiBr
6
, MAPbI
3
and a-Se at
Different X-ray Energies
Objective of This Work
Photocurrent in X-ray Detector
Analytical Model of Photocurrent
Dark Current in Photoconductor
Initial Field Distribution in the Photoconductor
Initial Field Distribution in the CABB
Energy Level Diagram of CABB and Different Electrodes (Au, Ag, and
Al)
Photocurrent in Pristine Sample of CABB
Photocurrent in Annealed Sample of CABB
Dark current in the CABB Photoconductor
Photocurrent vs Voltage for CABB
Sensitivity of an X-ray imager
Numerical Model of Sensitivity
Numerical Model of Sensitivity in Normalized Coordinates
Results and Discussions
Conclusions
Suggestions for Future Work
03
04
05
06
07
08
09
10
11
12
13
14
15
16
17
18
19
20
21
22
23
25
26
40
41

3. X-ray
Discovered by German scientist Wilhelm Conrad R ̈ontgen on November 8,
1895.
The term R ̈ontgen radiation is also used for X-rays.
High-energy electromagnetic radiation.
High penetration properties.
Wavelength in the range of 10 picometers to 10 nanometers (30 exahertz to 30
petahertz) that correspond to energies in the range of 124 eV to 124 keV.
3

4. Medical
diagnostics
Computed tomography
Chest radiology
Fluoroscopy
Mammography
(20 keV-130 keV)
Security
Screening
Airport check
Cargo security system
Aerospace etc.
(100 keV-1 MeV)
Industrial non-
destructive testing
Food inspection (20 keV-100 keV)
Pharmaceuticals industry (<1.5
keV)
Recycling and waste sorting (20
keV-200 keV)
Identifying and quantifying
elements, crystals (1 keV-10 keV)
etc.
4
Applications of X-ray Imaging

5. X-ray source
Incident X-ray
Transmitted
X-ray

X-ray detector

Patient
Peripheral
Electronics
and A/D
converter
X-ray Imaging
Inexpensive non-invasive method of
imaging
Passing of X-rays through the
object of concern
A portion of the X-rays are either
absorbed or scattered by the
internal structures
Level of attenuation of X-ray depends
on objects or parts of objects of
different density
Incidence of attenuated X-rays on the
detector
Conversion to electrical signal from
attenuated X-ray inside the detector
Digital image generation of the object
by decoding electrical signal
5

6. Indirect Detection:
Require high synthesis
temperature, harsh
synthesis environment, and
high costs
Complex and multiple
constituents
The light scattering by the
scintillator
Direct Detection:
High sensitivity
High energy resolution
Easy integration with
readout electronics,
Better spatial resolution of
X-ray imaging
TFT Array TFT ArrayCharge readout
pixel by pixel
Photoconductor
Photodiode
Scintillator
X-ray X-ray
Conversion to
electrical charge
Conversion to
visible light
Digital image Digital image
Direct Conversion Indirect Conversion
6
Digital X-ray Imaging

7. Characteristics of Ideal
Photoconductor
•Can be easily coated onto the AMA panel
•Absorption depth δ < Device layer thickness L
•Low electron-hole pair generation energy, W
±
•No bulk recombination of electrons and holes
during drifting
•Negligible deep trapping of EHPs
•Negligible diffusion of carriers
•Lower dark current
•Longest carrier transit < Image readout time
•The properties of the photoconductor should not
change or deteriorate with time
•Uniform characteristics over the entire area
•Negligible temporal artifacts
7

8. Propertiesa-SePoly-HgI
2
Poly-PbI
2
Poly-
CdZnTe
MAPbI
3
MAPbBr
3
CsPbBr
3
CsPbI
3
Density (g/cm
3
)4.3 6.3 6 5.8 4.3 3.84.424.54
Band gap2.222.12.3 1.57 1.6 2.32.361.75
Atomic number34 6262.7 - 49 45 - -
Resistivity(Ωcm)∼10
14
∼4x10
13
∼10
12
∼10
11
10
9
~10
8
-10
9
10
9
10
9
µτ (cm
2
/V)~10
-7
~1.5x10
-5
~10
-3-
10
-4
-~10
-3-
10
-4
~2.59x10
-2
~1.32x10
-2
~3.63x10
-3
S (µCGy
-1
cm
-2
)201600120024007000003928.3556842370
LoD(nGys
-1
)550010000<52.850000 1.5<8800215219
Disadvantageous
traits
High J
D
High F
0
High
??????
±
Suitable
for low
E
High J
D
Unstable
structure
Low
dynamic
range
Toxic
Pb
Image
lag
Toxic Cd
Large area
fabrication
Unstable
structure
Toxic Pb
Halide
migration
Unstable
structure
Toxic Pb
Halide
migration
Toxic Pb
Halide
Migratio
n
Toxic Pb
Halide
Migration
8
Photoconductors in X-ray Detection

9. Cs
2
AgBiBr
6
(CABB) in X-ray Detection
Indirect photoconductor, E
g
=~1.7 to 2.19 eV
Density=4.92 g/cm
3
The breakdown enthalpy of the Cs
2
AgBiBr
6
single crystal (SC) is greater
than zero (∆H
D
>0), stability was predicted
Mechanically stable structure, stable under moisture, heat, and light
exposure
Longer device lifetime
Free of toxic lead
Large average atomic number Z=53.1
The electron and hole effective masses of CABB are ∼0.37m
e
and ∼
0.14m
e

Since the measured effective mass for holes is smaller than that for
electrons in the cubic phase, it is expected that holes have greater
mobility than electrons.
High Resistivity=10
9
-10
11
Ωcm
Comparatively low dark current
Moderate mobility, µ= 0.5-12 cm
2
/Vs
Ionization energy=5.61 eV
S=105-1974 µCGy
-1
cm
-2
LoD =45.7-59.7 nGys
-1
Suppressed ionic migration
Very low thermal noise
9

10. 10
Linear Attenuation Coefficients of Cs
2
AgBiBr
6
, MAPbI
3
and a-Se at Different X-ray
Energies
2030405060708090100
X-ray photon energy (keV)
10
0
10
1
10
2
10
3
Cs
2
AgBiBr
6
a-Se
MAPbI
3
α ∝ Z
4
/E
3
Presence of heaviest stable element, Bi results in high Z
value of 53.1
α of Cs
2
AgBiBr
6
> α of a-Se > α of MAPbI
3
for E
ph
< 33.1
keV.
α of Cs
2
AgBiBr
6
> α of a-Se for E
ph
>36 keV

11. Objective of This Work
•To develop a numerical model of X-ray sensitivity considering the perturbed electric field due to charge
carrier trapping in the bulk and ion accumulation near the perovskite/metal interface.
•To analyze the impact of the electric field perturbation on the X-ray sensitivity of Cs
2
AgBiBr
6
X-ray
detector.
•To explore the effects of X-ray interaction and charge transport properties on the X-ray sensitivity of
Cs
2
AgBiBr
6
based detectors.
•To compare the performance of Cs
2
AgBiBr
6
based detectors with the existing a-Se based detectors in the
medical diagnostics applications.
11

12. Photocurrent in X-ray Detector
An absorber layer placed between two parallel plate
electrodes
Biasing of radiation-receiving electrode to establish a
uniform electric field across the photoconductor
Collection of photogenerated charges at the bottom
electrode
Induced photocurrent due to the movement of free charges
generated from the absorption of photons in the
photoconductor
Exponential distribution of generated EHPs
Drift due to applied electric field and diffusion of charges
due to gradient of charges
12

13. Analytical Model of Photocurrent
Assumptions:
Insufficient space charge to disturb the applied electric field.
Electric field is high enough that drift mainly contribute to
current, diffusion can be ignored.
The photocurrent density due to hole and electron transport under positive bias is given by
13

14. Dark Current in Photoconductor
A fairly small electric current that runs through photosensitive devices in the
absence of photons.
Source of noise in the photo-generated signal.
Made up of the charges generated in the detector when no outside radiation
enters the device.
Depending on the medical application, the dark current should ideally not
exceed 10–1000 pA/cm
2
.
The two main mechanisms of the dark current of an X-ray imager are:
a) Contact injection current
b) Bulk thermal generation current
Increases with the applied electric field.
Contact injection current:
??????
????
??????
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=????????????
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µ
?
??????
5
??????
?

?
?
??-
??
??????
????
??????
?
=????????????
?
µ
?
??????
6
??????
?

?
?
??.
??
Bulk thermal generation current:
??????
???
??????
?
=??????µ
?
τ′
?
??????
4
??????
?
{1−
µ
?
??????
?
?
??????
4
??????
(1−??????
?
?
µ
?

?
?
?
,
)}

,??????
?
=??????
(??)
????????????ꞷ
4
??????
?
?
?
??
?
?
??
?
,
??
??????
???
??????
?
=??????µ
?
τ′
?
??????
4
??????
?
{1−
µ
?

?
?
?
,
?
(1−??????
?
?
µ?
?
??,
)}

, ??????
?
=??????
(??)
????????????ꞷ
4
??????
?
?
?
7?
?
7
??
?,
??
Movement of ions through vacancies
and accumulation near the interfaces
results in interface electric field
elevation
14

15. ??????
5
=1+
??
?
?
,
(??????
?
?
?
+????????????−????????????−

6
)−
??
???
?
?
.
6
?
??
,
−
??
???
?
?
.
6
?
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,
−
??
???
(????
?
)

?
?
,

??????
7
=1+
??
?
?
,
(??????
?
?
?
+????????????−????????????−

6
)−
??
???
?
?
.
6
?
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,
?
−
??
???
?
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.
6
?
?
,
?

??????
6
=1+
??
?
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,
??????
?
?
?
+????????????−????????????−

6
−
??
???
?
?
.
6
?
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,
−
??
???
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.
6
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,
−
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???
{??????
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}

?
Initial Field Distribution in the Photoconductor
Free charge generation from small doses during starting
of X-ray and previous exposures
The movement of generated charges toward the electrodes
after the application of supply voltage V
The faster charge carriers will not get easily trapped and
thetrappedchargedistributionwillbeuniform.
The slower one will get easily trapped and the trapping
distribution will follow an exponential distribution.
15
∇
6
????????????
?
=
????????????
???
??????
+
????????????
?
Ɛ
α??????
??
?
−
??????
??????
∇
6
????????????
?
=
????????????
?
Ɛ
α??????
??
?
−
??????
??????
∇
6
????????????
?
=−
????????????
???
??????
+
????????????
?
Ɛ
α??????
??
?
−
??????
??????
(??????<??????<??????
??????
/??????,0)
??????
??????
/??????<??????<(??????−??????
??????
)/??????,??????
(??????−??????
??????
)/??????<??????<??????,??????

16. Dependsontheappliedelectricfield,thedielectric
constantofthephotoconductor,thedefectdensityofthe
device,andenergybarriersforionmigration.
Theraisedinterfaceelectricfieldduetoionaccumulation
willinfluencetheinjectionofchargesfromthetwo
electrodes.
Uniformelectricfieldinthebulk
16
N
acc
=P
acc
=1x10
18
m
-3
, F
1
= ~ 1.71F
0
, F
2
= ~ 1.71F
0
F
3
= ~ F
0
L
p
=L
n
=5 µm
N
t
=0.01% of N
tc
Initial Field Distribution in the CABB

17. ϕ
M(Au)
=5.1 eV, ϕ
M(Al)
=4.28, ϕ
M(Ag)
=4.26 eV
CABB:ꭓ=3.64 eV
E
g
=~2.1 eV
E
F
=∼0.788 eV above of E
V
for p-type CABB
ϕ
s
=∼4.9 eV.
ϕ
M(Au)
>ϕ
s
> ϕ
M(Al)
>ϕ
M(Ag)
Ag/p-Cs
2
AgBiBr
6

and Al/p-Cs
2
AgBiBr
6

: Schottky contacts
Au/p-Cs
2
AgBiBr
6

: ohmic contact.
The dark conductivity (σ) of Cs
2
AgBiBr
6
is ∼10
−11
S/cm
The dark current density (=σF
0
) for ohmic contacts ~0.25
nA/cm
2
>Measured dark current ∼ 0.15 nA/cm
2
for a 2 mm
detector with 5 V bias
Ag/CABB/Ag detector: ϕ
h
=∼ (3.64+2.1-4.26) eV ∼ 1.48 eV.
ϕ
e
= ∼ (4.26-3.64) eV ∼ 0.62 eV.
Au/CABB/Au detector: ϕ
h
=∼ (3.64+2.1-5.1) eV ∼ 0.64 eV
ϕ
e
= ∼ (5.1-3.64) eV∼1.46eV.
The hole injection in Ag/CABB and the electron injection in
Au/CABB can be ignored since barrier height is greater than
1 eV.
17
Energy Level Diagram of CABB and Different Electrodes (Au, Ag, and Al)

18. N
acc
=P
acc
=1x10
18
m
-3
, F
1
= ~ 1.71F
0
, F
2
= ~ 1.71F
0
L
p
=L
n
= 5 µm
N
t
=0.01% of N
tc

Linear increase with dose rate in photocurrent density
theoretically calculated
Presence of photocurrent gain in the experimental results
Presence of dark current contributed mainly from hole
injection from the top electrode
Effective barrier height varies from 0.7 eV to 0.616 eV for
dose rate upto 140 µ
Kw
q
to fit the experimental results
The hole injection current density varies from 0.1 to 2.68
nAcm
−2
with dose rate.
The electron barrier height is much higher, hence electron
injection is insignificant.
The bulk thermal generation current density is 0.015 pAcm
−2
18
Photocurrent in Pristine Sample of CABB
0 20406080100120140
Dose rate (Gys
-1
)
0
0.5
1
1.5
2
2.5
3
Experimental results
Total Photocurrent density
Theoretical photocurrent density
h
= 3.17 cm
2
V
-1
s
-1
'
h
= 3x10
-6
s
e
= 2 cm
2
V
-1
s
-1
'
e
= 0.5x10
-6
s
F
0
= 0.0025 Vm
-1
E
av
= 30 keV
= 99.5 cm
-1
L = 2 mm

19. N
acc
=P
acc
=1x10
18
m
-3
, F
1
= ~ 1.71F
0
, F
2
= ~ 1.71F
0
L
p
=L
n
=5 µm
N
t
=0.01% of N
tc
Linear increase with dose rate in photocurrent density
theoretically calculated
Presence of photocurrent gain in the experimental results
Presence of dark current contributed mainly from hole
injection from the top electrode
Effective barrier height varies from 0.723 eV to 0.649 eV for
dose rate upto140 µ
Kw
q
to fit the experimental results
The hole injection current density reaches from 0.16 to 2.78
nAcm
−2
with dose rate
The electron barrier height is much higher; hence electron
injection is insignificant
The bulk thermal generation current density is 0.75 pAcm
−2
19
Photocurrent in Annealed Sample of CABB
0 20406080100120140
Dose rate (Gys
-1
)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Photocurrent density
Total photocurrent density
Experimental results
h
= 11.81 cm
2
V
-1
s
-1
'
h
= 5.2x10
-6
s
e
= 6.5 cm
2
V
-1
s
-1
'
e
= 0.5x10
-6
s
F
0
= 0.0025 Vm
-1
E
av
= 30 keV, = 99.5 cm
-1
L = 2 mm

20. Dark current in annealed sample > Dark current in
pristine sample due to the higher mobility in annealed
sample
20
Dark Current in the CABB Photoconductor
0 20406080100120140
Dose rate (Gys
-1
)
0
0.5
1
1.5
2
2.5
3
Dark current in pristine sample
Dark current in annealed sample
0 50100140
Dose rate (Gys
-1
)
0
1
2
3
Annealed sample
J
se
+J
sh
J
hinj
L = 2 mm
F
0
= 0.0025 V/m

21. Ag/CABB/Ag detector, with 3 mm thickness, applied voltage
= 5 V
N
acc
=P
acc
=1x10
18
m
-3
, F
1
= ~ 1.71F
0
, F
2
= ~ 1.71F
0
L
p
=L
n
=5 µm
N
t
=0.01% of N
tc
Linear increase with applied voltage in photocurrent density
theoretically calculated
Presence of dark current contributed mainly from electron
injection
Effective barrier height varies from 0.61 eV to 0.584 eV for
dose rate upto1471.7 µ
Kw
q
to fit the experimental results
The bulk thermal generation current density and hole
injection are insignificant
21
Photocurrent vs Voltage for CABB
02468 1012141618
Applied voltage (V)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
10
-9
Dark current
91.98Gys
-1
551.88 Gys
-1
1195.76 Gys
-1
1471.7 Gys
-1
275.94 Gys
-1
827.83 Gys
-1
h
= 6 cm
2
V
-1
s
-1
'
h
= 3x10
-6
s
e
= 3 cm
2
V
-1
s
-1
'
e
= 1x10
-6
s
E
av
= 39 keV
= 68 cm
-1
L = 3 mm

22. Sensitivity of an X-ray imager
The X-ray sensitivity (S): The collected charge per unit area per unit exposure of
radiation and is considered an important performance measure for a superior image.
High sensitivity for reduction of the risk of cancer in patients by providing superior
image contrast with low incident dosage.
High sensitivity ensures better dynamic range.
Sensitivity depends on the amount of radiation absorbed from the incident radiation,
the generation of EHPs by X-ray interactions and collection of the X-ray generated
charge is in the external circuit.
The selection of the X-ray photoconductor is highly influenced by the value of S
22

23. Numerical Model of Sensitivity
The numerical model to determine the sensitivity has been based on the following assumptions:
1) Over the complete region of the photoconductor, the material shows uniform properties.
2) The thermal equilibrium carrier concentrations are negligibly small.
3) The incident X-rays are monoenergetic and are attenuated exponentially (e
−αx′
) along the
photoconductor thickness. The generated EHPs concentration follows an exponential profile
along the detector thickness from the radiation-receiving electrode.
4) Since the generated charge profile is not uniform across the device, the diffusion of carriers is
present in the bulk at the low electric field.
5) The carrier transport is essentially one-dimensional
The continuity equations for electrons and holes in the photoconductor are The trapping rate equations for electrons and holes
Poisson’s equation in the photoconductor
The necessary initial and boundary conditions
to solve the coupled equations:
????????????′
????????????′
= ??????
?
????????????′??????′
????????????′
+??????
?
??????
6
??????′
????????????
?6
−
??????
?
??????
?
?
−??????
?
??????′??????′−??????
?
??????′??????′
?
+????????????
???
????????????′
????????????′
= −??????
?
????????????′??????′
????????????′
+??????
?
??????
6
??????′
????????????
?6
−
??????
?
??????
?
?
−??????
?
??????
?
??????′−??????
?
??????′??????′
?
+????????????
???
??????????????????′
????????????′
=
??????
?
??????
?
?
−??????
?
??????′??????′
?
????????????
??????
′
????????????′
=
??????
?
??????
?
?
−??????
?
??????′??????′
?
????????????′
????????????′
=
??????
??????
(??????
?
+??????′
?
−??????
?
−??????′
?
)
??????
??????
′??????
?
,0=??????
?
????????????
??
?
,??????
??????
′??????
?
,0=??????
?

?
??????′??????
?
,0=0,??????′??????
?
,0=0,
??????′??????,??????′=??????
?
??????
?

?
?
?
?
.
??
, ??????′0,??????′=??????
?
??????
?

?
7
?
?-
??
,
???????′????????????′
?
4
=??????

24. The drift electron photocurrent density
The drift hole photocurrent density
The diffusion electron photocurrent density
The diffusion hole photocurrent density
The total photocurrent density
The total collected charge
The sensitivity
Numerical Model of Sensitivity (contd.)
24
??????′
?
=
????????????
?
??????
?(??????′
?
4
??????′)????????????′
??????′
?
=
????????????
?
??????
?(??????′
?
4
??????′)????????????′
??????′
??
=−????????????
?
????????????′
????????????′
??????′
??
=????????????
?
????????????′
????????????′
??????′
?
=??????′
?
+ ??????′
?
+ ??????′
??
+??????′
??
Q=??????∫??????′
?
????????????′
??
4
??????=Q/AX

25. Numerical Model of Sensitivity in Normalized Coordinates
The necessary initial and boundary conditions in normalized
form to solve the coupled equations:
The continuity equations for electrons and holes in normalized
form in the photoconductor are
The trapping rate equations for electrons and holes in normalized
form
Poisson’s equation in normalized form
The normalized drift electron photocurrent density
The normalized drift hole photocurrent density
The normalized diffusion electron photocurrent density
The normalized diffusion hole photocurrent density
The normalized total photocurrent density
The normalized sensitivity
25
????????????
????????????
=
??????????????????
????????????
+??????
??
??????
6
??????
????????????
6
−
??????
??????
?
−??????
?
????????????−??????
4
????????????
?
+????????????
??/?
????????????
????????????
=−??????

??????????????????
????????????
+??????
??
??????
6
??????
????????????
6
−??????

??????
??????
?
−??????
?
????????????−??????
4
????????????
?
+????????????
??/?
????????????
?
????????????
=
??????
??????
?
−??????
4
??????

????????????
?
????????????
?
????????????
=??????

??????
??????
?
−??????
4
????????????
??????
????????????
????????????
=??????
4
(??????+??????
?
−??????−??????
?
)
???????????????????
5
4
=1
????????????,0=0 ,????????????,0=0, ??????0,??????=
?
?
?
4
??????
?

?
7
?
?-
??
,??????1,??????=
??????
?
??????
0
??????
?

?
?
?
?
.
??
,
??????
??????
??????,0=
?
?
?
4
????????????
??
?
, p
??????
??????,0 =
?
?
?
4

?
??????
?
=?(??????
5
4
??????)????????????
??????
?
=??????

?(??????
5
4
??????)????????????
??????
??
=??????
??
?
????????????
????????????
5
4
????????????
??????
??
=−??????
??
?
????????????
????????????
5
4
????????????
??????
?
=??????
?
+??????
?
+ ??????
??
+??????
??
S
normalized
=??????∫??????
?
????????????
?
4

26. Results
and
Discussions
26

27. Effect of Electric Field on Charge Distribution
The transit time reduces with an increase in the electric field.
The drift hole concentration reaches the maximum value of
3.8x10
15
m
−3
and 3x10
15
m
−3
at 0.4 mm and 0.2 mm,
respectively from the radiation-receiving electrode, at electric
field 1 V/µm and 0.1 V/µm, respectively
The drift electron concentration reaches the maximum value of
5.3x10
15
m
−3
and 1.8x10
15
m
−3
, respectively near the top
electrode, at electric field 1 V/µm and 0.1 V/µm, respectively
Trapped hole distribution is almost uniform along the
detector thickness due to lower transit time. The trapped
electron distribution follows the exponential interaction
profile of the X-rays.
The trapped hole concentration increases from ∼2x10
15
m
−3
to ∼1.4x10
16
m
−3
for electric field decrease from 1 V/µm to
0.1 V/µm. The trapped electron concentration near the top
electrode increases from ∼8x10
16
m
−3
to ∼1x10
17
m
−3
for
electric field decrease from 1 V/µm to 0.1 V/µm.
27
0 0.20.40.60.8 1 1.21.41.61.8 2
Distance from top electrode (mm)
10
6
10
8
10
10
10
12
10
14
10
16
10
18
10
20
Trapped hole distribution at 0.1 V/m
Trapped electron distribution at 0.1 V/m
Trapped hole distribution at 1 V/m
Trapped electron distribution at 1 V/m
h
= 11.81 cm
2
V
-1
s
-1
'
h
= 5.2x10
-6
s
e
= 6.5 cm
2
V
-1
s
-1
'
e
= 0.5x10
-6
s
E
av
= 30 keV, = 99.5 cm
-1
X = 0.2 Gy
L = 2 mm
0 0.20.40.60.8 1 1.21.41.61.8 2
Distance from top electrode (mm)
10
0
10
5
10
10
10
15
Hole distribution at 0.1 V/m
Electron distribution at 0.1 V/m
Hole distribution at 1 V/m
Electron distribution at 1 V/m
h
= 11.81 cm
2
V
-1
s
-1
'
h
= 5.2x10
-6
s
e
= 6.5 cm
2
V
-1
s
-1
'
e
= 0.5x10
-6
s
E
av
= 30 keV, = 99.5 cm
-1
L = 2 mm
X = 0.2 Gy

28. Effect of Electric Field on Electric Field Distribution
Neartheelectrodes,accumulatedionsperturbtheapplied
electricfield,andtheelectricfieldiselevatedto∼1.77times
theappliedelectricfield.
Theelectricfieldacrossthephotoconductorisaffectedby
thedriftandtrappedcharges,andtheelectricfielddecreases
belowtheappliedelectricfieldinthebulkofthe
photoconductor.
Thelowestpointofthedistributedfieldis0.975timesthe
appliedelectricfieldfor0.1V/µm,duetothepresenceof
hightrappedchargeconcentration.
Forhigherfield,transittimeisreduced,andthetrapped
chargeconcentrationismuchlower,yieldinganearly
uniformelectricfieldinthedevice.
28
0 0.10.20.30.40.50.60.70.80.9 1
Normalized distance from top electrode
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
Uniform electric field
F
0
= 0.1 V/m
F
0
= 1 V/m
h
= 11.81 cm
2
V
-1
s
-1
'
h
= 5.2x10
-6
s
e
= 6.5 cm
2
V
-1
s
-1
'
e
= 0.5x10
-6
s
E
av
= 30 keV, = 99.5 cm
-1
X = 0.2 Gy
L = 2 mm

29. Effect of Charge Carrier Diffusion on Sensitivity
For smaller applied electric fields,
the diffusion of charge carriers is
visible, although not significant.
Diffusion of charges can be ignored.
29
0.02 0.030.040.050.060.070.080.090.1
Applied electric field (V/m)
80
100
120
140
160
180
200
220
240
With diffusion
Without diffusion
h
= 11.81 cm
2
V
-1
s
-1
'
h
= 5.2x10
-6
s
e
= 6.5 cm
2
V
-1
s
-1
'
e
= 0.5x10
-6
s
E
av
= 30 keV, = 99.5 cm
-1
X = 0.2 Gy
L = 2 mm

30. Effect of Electric Field on Sensitivity
Theappliedelectricfieldisvariedupto5Vµm
−1
.
Withtheincreaseoftheelectricfield,thesensitivity
increasesasthedriftvelocityforfreecarriersincreases.
Increaseofsensitivitywiththeappliedelectricfieldatthe
lowelectricfields,duetothedecreaseoftransittime.
Saturationofthecollectedchargeatalargeelectricfield
causessensitivitysaturation.
At5Vµm
−1
:
S=∼634µCGy
−1
cm
−2
withchargeinjection
S=∼621µCGy
−1
cm
−2
,whenignored,whichis2%lower.
Highersensitivityassumingcarrierinjectionbecausethe
injectedchargesaddtothetotalcollectedcharges.
30
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Applied electric field (V/m)
0
100
200
300
400
500
600
700
No ion accumulation and charge injection
Ion accumulation with charge injection
h
=11.81 cm
2
V
-1
s
-1
, '
h
=5.2x10
-6
s
e
=6.5 cm
2
V
-1
s
-1
, '
e
=0.5x10
-6
s
E
av
=30 keV, = 99.5 cm
-1
L = 2 mm
X = 0.2 Gy

31. For low electric field with high dose:
Sensitivityconsideringchargeinjectionislowercomparedto
sensitivityignoringchargeinjection.
Theaccumulatedionsneartheelectrodeslowersthebulk
electricfield,carriertrappingincreases,andlowersthe
chargecollection.
Theelevatedinterfaceelectricfieldcausesmorecharge
injectionfromtheelectrodes,although,thechargeinjection
isinsignificant.
For high electric field with high dose:
The charge injection is significant due to the electric
field elevation at the interfaces from ion accumulation,
and overall the charge collection increases.
31
0.080.0820.0840.0860.0880.090.0920.0940.0960.0980.1
Applied electric field (V/m)430
432
434
436
438
440
442
444
446
No ion accumulation and charge injection
Ion accumulation with charge injection
h
= 11.81 cm
2
V
-1
s
-1
, '
h
= 5.2x10
-6
s
e
= 6.5 cm
2
V
-1
s
-1
, '
e
= 0.5x10
-6
s
E
av
= 30 keV, = 99.5 cm
-1
X = 5 Gy
L = 2 mm0.030.0310.0320.0330.0340.0350.0360.0370.0380.0390.04
Applied electric field (V/m)
230
240
250
260
270
280
290
300
No ion accumulation and charge injection
Ion accumulation with charge injection
h
= 11.81 cm
2
V
-1
s
-1
, '
h
= 5.2x10
-6
s
e
= 6.5 cm
2
V
-1
s
-1
, '
e
= 0.5x10
-6
s
E
av
= 30 keV, = 99.5 cm
-1
X = 5 Gy
L = 2 mm
Effect of Injection current on Sensitivity

32. Trapped charge concentration
increases with lifetime reduction
Drift charge concentration
increases with lifetime increase
Effect of Hole Trapping on Charge Distribution
32
0 0.20.40.60.8 1 1.21.41.61.8 2
Distance from top electrode (mm)
10
8
10
9
10
10
10
11
10
12
10
13
10
14
10
15
10
16
'
h
= 1 s
'
h
= 10 s
'
h
=
h
= 11.81 cm
2
V
-1
s
-1
e
= 6.5 cm
2
V
-1
s
-1
'
e
= 0.5x10
-6
s
E
av
=30 keV, = 99.5 cm
-1
X = 0.2 Gy
L = 2 mm
F
0
= 0.1 V/m
0 0.20.40.60.8 1 1.21.41.61.8 2
Distance from top electrode (mm)
10
12
10
13
10
14
10
15
10
16
10
17 '
h
= 1 s
'
h
= 10 s
'
h
=
h
= 11.81 cm
2
V
-1
s
-1
e
= 6.5 cm
2
V
-1
s
-1
'
e
= 0.5x10
-6
s
E
av
=30 keV, = 99.5 cm
-1
X = 0.2 Gy
L = 2 mm
F
0
= 0.1 V/m

33. Trappedchargeconcentration
increaseswithlifetimereduction
Driftchargeconcentration
increaseswithlifetimeincrease
Effect of Electron Trapping on Charge Distribution
33
0 0.20.40.60.8 1 1.21.41.61.8 2
Distance from top electrode (mm)
10
6
10
8
10
10
10
12
10
14
10
16
'
e
= 0.1 s
'
e
= 1 s
'
e
= 10 s
h
=11.81 cm
2
V
-1
s
-1
e
=6.5 cm
2
V
-1
s
-1
'
h
=10x10
-6
s
E
av
=30 keV, = 99.5 cm
-1
X = 0.2 Gy
L = 2 mm
F
0
= 0.1 V/m
0 0.20.40.60.8 1 1.21.41.61.8 2
Distance from top electrode (mm)
10
8
10
10
10
12
10
14
10
16
'
e
= 0.1 s
'
e
= 1 s
'
e
= 10 s
h
= 11.81 cm
2
V
-1
s
-1
e
= 6.5 cm
2
V
-1
s
-1
'
h
= 10x10
-6
s
E
av
= 30 keV, = 99.5 cm
-1
X = 0.2 Gy
L = 2 mm
F
0
= 0.1 V/m

34. Charge collection decreases with more carrier trapping
Sensitivity increases with decreasing levels of hole
trapping
S = 572.5 µCGy
-1
cm
-2
, ??????
?
?
=1 µ?????? , 5 V/µm
S = 642 µCGy
-1
cm
-2
, ??????
?
?
=10 µ?????? , 5 V/µm
S = 649.5 µCGy
-1
cm
-2
, no hole trapping , 5 V/µm
??????
?
?
>10 µ??????, negligible effect of hole lifetime on
sensitivity
Effect of Charge Carrier Trapping on SensitivityEffect of Charge Carrier Trapping on Sensitivity
34
Charge collection decreases with more carrier trapping
Sensitivity increases with decreasing levels of electron
trapping
S = 635 µCGy
-1
cm
-2
, ??????
?
?
=0.1 µ?????? , 5 V/µm
S = 642.6 µCGy
-1
cm
-2
, ??????
?
?
=1 µ?????? , 5 V/µm
S = 643.6 µCGy
-1
cm
-2
, ??????
?
?
=10 µ??????, 5 V/µm
Negligible effect of electron lifetime on sensitivity, since
radiation receiving electrode is positively biased.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Applied electric field (V/m)
100
200
300
400
500
600
700
'
e
= 0.1 s
'
e
= 1 s
'
e
= 10 s
h
=11.81 cm
2
V
-1
s
-1
e
=6.5 cm
2
V
-1
s
-1
'
h
=10x10
-6
s
E
av
=30 keV, = 99.5 cm
-1
X = 0.2 Gy
L = 2 mm
F
0
= 0.1 V/m
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Applied electric field (V/m)
0
100
200
300
400
500
600
700
'
h
=
'
h
= 10 s
'
h
= 1s
h
= 11.81 cm
2
V
-1
s
-1
e
= 6.5 cm
2
V
-1
s
-1
, '
e
= 0.5x10
-6
s
E
av
= 30 keV, = 99.5 cm
-1
X = 0.2 Gy
L = 2 mm

35. Effect of Photoconductor Thickness on SensitivityEffect of Photoconductor Thickness on Sensitivity
Sensitivityincreaseswithincreaseofphotoconductor
thickness
Sensitivitydecreasesbeyondoptimumthicknessdueto
carriertrapping
S
max
=453µCGy
-1
cm
-2
,L
opt
=350 µm,0.1V/µm
S
max
=590µCGy
-1
cm
-2
,L
opt
=500 µm,0.5V/µm
S
max
=622.7µCGy
-1
cm
-2
,L
opt
=550 µm,1V/µm
Optimumthicknessincreaseswithappliedelectricfield
duetotransittimereduction
Athighappliedelectricfieldmaximumsensitivitystarts
tosaturate
35
0 1002003004005006007008009001000
Device thickness (m)
300
350
400
450
500
550
600
650
700
750
F
0
= 0.1 V/m
F
0
= 0.5 V/m
F
0
= 1 V/m
h
=11.81 cm
2
V
-1
s
-1
, '
h
=5.2x10
-6
s
e
=6.5 cm
2
V
-1
s
-1
, '
e
=0.5x10
-6
s
E
av
=30 keV, = 99.5 cm
-1
X = 0.2 Gy

36. Effect of Dose on Charge DistributionEffect of Dose on Charge Distribution
Trapped charge concentration
increases with dose
Drift charge concentration
increases with dose
36
0 0.20.40.60.8 1 1.21.41.61.8 2
Distance from the top electrode (mm)
10
4
10
6
10
8
10
10
10
12
10
14
10
16
10
18
10
20
Hole concentration for 0.2 Gy
Electron concentration for 0.2 Gy
Hole concentration for 1 Gy
Electron concentration for 1 Gy
h
= 11.81 cm
2
V
-1
s
-1
, '
h
= 5.2x10
-6
s,
e
= 6.5 cm
2
V
-1
s
-1
, '
e
= 0.5x10
-6
s
E
av
=30 keV, = 99.5 cm
-1
, F
0
= 0.1 V/m, L = 2 mm
0 0.20.40.60.8 1 1.21.41.61.8 2
Distance from the top electrode (mm)
10
6
10
8
10
10
10
12
10
14
10
16
10
18
Hole concentration for 0.2 Gy
Electron concentration for 0.2 Gy
Hole concentration for 1 Gy
Electron concentration for 1 Gy
h
= 11.81 cm
2
V
-1
s
-1
, '
h
= 5.2x10
-6
s,
e
= 6.5 cm
2
V
-1
s
-1
, '
e
= 0.5x10
-6
s
E
av
=30 keV, = 99.5 cm
-1
, F
0
= 0.1 V/m, L = 2 mm

37. Effect of Dose on Field DistributionEffect of Dose on Field Distribution
The elevation near the top and bottom electrodes is 1.76
times the applied electric field for 0.2 µGy, which is mainly
due to the ion accumulation, rather than the drift and trapped
charges and the lowest point reaches 0.975 times of applied
electric field in the bulk with almost uniform distribution.
Since an increase in exposure increases the trapped and drift
charges in the detector, the elevation near the top and bottom
electrodes are ∼1.77 and ∼1.85 times the applied electric
field, and the lowest point reaches 0.89 times of applied
electric field for 1 µGy.
37
0 0.10.20.30.40.50.60.70.80.9 1
Normalized distance from top electrode
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
0.2 Gy
1 Gy
Unifrom electric field
h
= 11.81 cm
2
V
-1
s
-1
'
h
= 5.2x10
-6
s
e
= 6.5 cm
2
V
-1
s
-1
'
e
= 0.5x10
-6
s
E
av
= 30 keV, = 99.5 cm
-1
F
0
= 0.1 V/m
L = 2 mm

38. Effect of Dose on SensitivityEffect of Dose on Sensitivity
Sensitivityincreaseswithincreaseofdoseduetomore
photogeneratedcarriers
Sensitivitydecreasesbeyondoptimumdosewhencarrier
trappingdominatesduetopresenceofexcessfreecarrier
Athighappliedelectricfieldsensitivityalmostsaturates
andcarriertrappingisinsignificantforanydose
S
max
=583µCGy
-1
cm
-2
,Dose=10 µGy,1V/µm
S
max
=463µCGy
-1
cm
-2
,Dose=7µGy,0.1V/µm
S
max
=359.5µCGy
-1
cm
-2
,Dose=4.5 µGy,0.05V/µm
38
0123456789 10
X-ray dose (Gy)
150
200
250
300
350
400
450
500
550
600
650
F
0
= 0.05 V/m
F
0
= 0.1 V/m
F
0
= 1 V/m
h
= 11.81 cm
2
V
-1
s
-1
, '
h
= 5.2x10
-6
s
e
= 6.5 cm
2
V
-1
s
-1
, '
e
= 0.5x10
-6
s
E
av
=30 keV, = 99.5 cm
-1
L = 2 mm

39. CABB: 2677 µCGy
−1
cm
−2
for 5 V/µm
A-Se: 2026 µCGy
−1
cm
−2
for 5 V/µm
32 % increase in sensitivity for CABB compared to a-Se
The sensitivity obtained for Cs
2
AgBiBr
6
is much higher than a-Se
due to its larger charge transport properties and greater
absorption coefficient.
CABB: 189 µCGy
−1
cm
−2
for ∼4 V/µm.
a-Se: 179 µCGy
−1
cm
−2
at ∼5 V/µm.
The increase in sensitivity is 5.58% for CABB from a-Se.
Cs
2
AgBiBr
6
in Medical DiagnosticsCs
2
AgBiBr
6
in Medical Diagnostics
39
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Applied electric field (Vm
-1
)
0
20
40
60
80
100
120
140
160
180
200
Cs
2
AgBiBr
6
a-Se
E
av
= 20 keV
L = 200 m
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Applied electric field (V/m)
0
500
1000
1500
2000
2500
3000
a-Se
Cs
2
AgBiBr
6
E
av
= 60 keV
L = 1 mm

40. ConclusionsConclusions
AnumericalmodeloftheX-raysensitivitybasedonthesemiconductor
continuityequations,trappingrateequations,andPoisson’sequation
consideringtheperturbationoftheappliedelectricfieldduetothe
accumulationofionsnearthemetal/photoconductorinterfacesunderthe
influenceofbiasvoltageandcarriertrappinginthebulk.
PresenceofphotocurrentgainfortheAu/Cs
2
AgBiBr
6
/Audetectorduetothe
presenceofdarkcurrentsoriginatingmainlyfromholeinjection.
Theelectroninjectioncurrentandbulkthermalgenerationcurrentare
insignificant.
Thetrappedchargeconcentrationincreaseswiththedecreaseoftheapplied
electricfield,whereasthedriftchargeconcentrationhastheoppositeeffect.
Theinjectedchargesincreasethetotalcollectedcharges,thesensitivityis
higherwhencarrierinjectionisconsidered.However,forhighexposureand
verylowelectricfieldoppositeresultisobserved.
Theeffectofcarrierdiffusionisnegligible.
Thelevelofholetrappinghasasubstantialimpactonsensitivitycomparedto
electrontrapping.
Theoptimumphotoconductorthicknessis∼350-550µm.
ThesensitivityforchestradiologyandmammographyishigherforCABB
thana-Se.
40

41. Suggestions for Future WorksSuggestions for Future Works
i)The injection current reduction by implementing a blocking layer
between the electrode and the photoconductor. The inclusion of the
blocking layer in the numerical model will help investigate the future
optimization of the device.
ii)The subsequent exposures to the detector generate deep trap centers in
the device. The inclusion of the X-ray-induced deep trap centers in the
numerical model will help improve the performance of the
Cs
2
AgBiBr
6
based detectors in the future.
iii)The numerical model is based on a p-type photoconductor, it can be
extended to analyze the properties and performance of an n-type
photoconductor
iv)A thorough assessment of image quality may be accomplished by
investigatingthe MTF (Modulation Transfer Function) and DQE
(Detective Quantum Efficiency) along with the sensitivityof lead-free
perovskite photoconductors.
41

42. 42
PublicationsPublications
NazninSultana,ShaikhAsifMahmood,“SensitivityAnalysisofaCs
2
AgBiBr
6
X-rayImage
Detector”,11thInternationalConferenceonElectricalandComputerEngineering(ICECE)2020,
Dhaka,Bangladesh,DOI:10.1109/ICECE51571.2020.9393130, AwardedBestPaperin
Electronics
NazninSultana,ShaikhAsifMahmood,“InvestigationofNonlinearPhotocurrentinDouble
PerovskiteX-rayDetectors”,Inpreparationforsubmission.
NazninSultana,ShaikhAsifMahmood,“NumericalModellingofSensitivityinDoublePerovskite
X-rayDetectors”,Inpreparationforsubmission.

43. 43
Acknowledgements
Dr. Shaikh Asif Mahmood (Supervisor)
Associate Professor EEE, BUET, Dhaka
Dr. Aynal Haque
Head and Professor
Dept. of EEE, BUET, Dhaka
Dr. Samia Subrina
Professor
Dept. of EEE, BUET, Dhaka
Dr. Mahbub Alam
Associate Professor
Dept. of EEE, BUET, Dhaka
Dr. M. Mofazzal Hossain
Professor (External)
Dept. of EEE, ULAB, Dhaka

44. 44
•W. Pan, H. Wu, J. Luo, Z. Deng, C. Ge, C. Chen, X.-H. Jiang, W.-J. Yin, G. Niu, L. Zhu, L.
Yin, Y. Zhou, Q. Xie, X. Ke, M. Sui, and J. Tang, “Cs
2
AgBiBr
6
single crystal X-ray
detectors with a low detection limit,” Nature Photonics, vol. 11, pp. 726–732, 2017.
•H. Zhang, Z. Gao, R. Liang, X. Zheng, X. Geng, Y. Zhao, D. Xie, J. Hong, H. Tian, Y.
Yang, X. Wang, and T. ling Ren, “X-ray detector based on allinorganic lead-free
Cs2AgBiBr6 perovskite single crystal,” IEEE Transactions on Electron Devices, vol. 66, pp.
2224–2229, 2019.
•M. Z. Kabir, “Modeling of X-ray photoconductors for X-ray image detectors,” Ph.D.
dissertation, Aug 2005.
•A. Hoq, D. Mamsapuram Panneerselvam, and M. Kabir, “Sensitivity reduction mechanisms
in organic perovskite X-ray detectors,” Journal of Materials Science: Materials in
Electronics, vol. 32, pp. 16 824–16 830, 2021.
•Mahmood and M. Z. Kabir, “Dark current mechanisms in stabilized amorphous selenium
based n-i detectors for X-ray imaging applications,” Journal of Vacuum Science and
Technology, vol. 29, p. 031603, 2011.
•H. Huang and S. Abbaszadeh, “Recent developments of amorphous selenium based X-ray
detectors: A review,” IEEE Sensors Journal, vol. 20, pp. 1694–1704, 2020.
•S. O. Kasap and J. A. Rowlands, “Direct-conversion flat-panel X-ray image sensors for
digital radiography,” Proc. of the IEEE, vol. 90, pp. 591 – 604, May, 2002
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45. Thank You
45