HgI2 As X-Ray Imager: Modulation Transfer Function Approach

International Journal of Modern Research in Engineering and Technology (IJMRET)
www.ijmret.org Volume 1 Issue 2 ǁ July 2016.
w w w . i j m r e t . o r g Page 1
HgI2 As X-Ray Imager: Modulation Transfer Function Approach
Md.Ashikuzzaman1
, Jisan Ali1
, R. Adib2
, M.M. Hossain3
,and Shaikh Asif
Mahmood4
1
Department of Electrical and Electronics Engineering, Daffodil International University,Dhaka-
1207,Bangladesh
2
Department of Technology, Harriken.com Limited,Dhaka-1213,Bangladesh
3
Department of Firmware, Relisource Technologies Limited,Dhaka-1212,Bangladesh
4
Department of Electrical and Electronic Engineering, Bangladesh University of Engineering and Technology,
Dhaka-1000,Bangladesh
ABSTRACT : The Modulation Transfer Function (MTF) of Polycrystalline Mercuric Iodide based flat panel
x-ray detectors is simulated as a function of spatial frequency. A simplified mathematical model for MTF is
applied on four different published prototypes of Polycrystalline Mercuric Iodide. Our aim was to fit curve from
MTF model with the curve from experimental data. The result of simulation from theoretical model shows a
good agreement with the measured data. We have found that deep-trapping,K-fluorescence,dependence of dark
current on temperature and exposure time are the most possible reasons for the slight mismatches between two
curves. In addition, the mobility-lifetime product for best curve fitting was also examined for each prototype.
KEYWORDS - Dark current,Deep trapping, K-fluorescence, Modulation Transfer Function, Polycrystalline,
Spatial frequency.
I. INTRODUCTION
Flat panel digital x-ray image detectors are a class
of solid-state x-ray digital radiography devices
similar in principle to image sensors used in
clinical photography[1,2]. Two types of commonly
used flat panel detectors are in practice-direct
conversion and indirect conversiosn. The direct
conversion flat panel detector consists of a
photoconductor layer sandwiched between two
electrodes; the electrode at one surface is a
continuous metal plate and the electrode at the
other surface of the photoconductor is segmented
into an array of individual square pixels held at
ground potential. A bias voltage applied to the
radiation-receiving top electrode results in an
electric field in the photoconductor.Image
irradiation causes a latent image charge
accumulation on the pixel electrodes. Some of the
x-ray generated charge carriers get trapped in the
bulk of the photoconductor layer during their drift
toward the electrodes. This trapped carrier induces
charges not only on this pixel electrode but also on
its neighboring consequently causing a lateral
spread of information and hence a loss of image
resolution[3].
Whatever photoconductor layer is used, the aim
is to obtain an image of good resolution. Resolution
refers to the ability of a radiographic imaging
system record fine detail. Obviously,detail is an
obvious pre-requisite for clinical images of
excellent quality. Mathematically, The quality of
image is determined by ―Modulation Transfer
Function‖ (MTF). MTF measures the efficiency of
an imaging system such as a detector to resolve
(transfer) different spatial frequencies of
information in an image. In other words, MTF is
the relative signal response of the system as a
function spatial frequency. In the measurement
process of MTF, mobility-lifetime product of
electrons and holes is a very important parameter
as sensitivity of photoconductor greatly depends on
the value of it.
Amorphous Selenium (a-Se), Poly crystalline-
Mercuric Iodide(Poly-HgI2), Lead Iodide(PbI2) are
the most commonly used photoconductor layer in
photo-detection. In this study, a simplified
mathematical model [4] for MTF is used on
various Published [5] prototypes of Mercuric
Iodide. The simulation results are compared to
experimental data and a good agreement is found.
At last, mobility-lifetime product for best curve
fitting is determined for each prototype.
II. MODEL AND SIMULATION
Resolution or modulation transfer function is
determined from Line Spread-Function. The Line
Spread-Function (LSF) is defined as the sum of the
spatial distribution of illuminance in the front and
the back emulsion caused by a beam of x rays
which passes through photoconductor
slit[6].Fourier transformation of the LSF gives the
corresponding modulation transfer function (MTF).
For mathematical model, we have used the Line
Spread Function (LSF) which is explained by Kabir
and others et al [4]. After fourier transform of the
Line Spread Function, it is found that [4],

      
   2 2 2
2
cos coth
( )
1 1
L L
b b t t
b b t t
F ech e Le
G f
F F L
L
 
       

      

    

   
     
  
2
2 2 2 2 2
cos coth
1
b b b b
L L
F F
b b
b b
b b b b
L
F ech e e
F
F L F
L
   
     
 

     

 
 

 
   
 
 
  
   
 
1
2
2
cos coth
1
t t
L
F L L
t t
t t
t t
L
e ech e e
F
L
F
L F

   
   


  
 
 
  
    

 
  
  
 
  
   
    
 1
b b
L
FL
b b
b b
F e e
F
 
 

  




 
  
 
 

(1)
Where, b is mobility of hole, t is mobility of
electron, b  is lifetime of hole, t  is lifetime of
electron,  is linear attenuation co-efficient , F is
the applied field , L is detector thickness.
1 L
e 
 
  is the quantum efficiency of the
detector. ω is the angular frequency and ω=2πf
where f is spatial frequency.
At zero spatial frequency, the expression for
G(f=0) is[4]:
  
  
1
(0)
1 1
L L
b b t t
b b t t
F e Le
G
L F F
 
   
     
    

  
 
2
1
1
b b b b
L L
F Fb b
b b
b b
F L
e e
L F
F
L
    
 

  

 
   
   
      

 
2 1
1
t t
L
F L Lt t
t t
t t
F L
e e e
L F
F
L

   


 


 
      
  
   
      

 1
b b
L
FL
b b
b b
F e e
F
 
 

  




 
  
 
 

(2)
Then, MTF due to bulk trapping [4] is,
 
 
 0
trap
G f
MTF f
G
 (3)
The dataset which we have used was formed
from an experiment where fabrication of
polycrystalline HgI2 film was performed by real-
time radiography using two low temperature
deposition methods—Physical Vapour
Deposition(PVD) and Particle-in-Binder(PIB)
deposition[5]. The experimenters performed PVD
deposition in a vacuum reactor where high purity
HgI2 powder was evaporated and deposited on
arrays. PIB deposition involves grains of purified
HgI2 crystals (∼6.36 g cm−3) mixed with a
polymer binder material (∼1.05 g cm−3), with a
composition ratio of 9 to 1 by weight for the two
materials[5]. In this study, we have worked on four
publicly available prototypes of Poly-HgI2 namely
PVD #4,PVD #12,PVD #16 and PIB #2 [5].
III. RESULT AND DISCUSSION
We start with the simulation of PVD #4 where
detector thickness is 210 µm and electric field
strength is .24 µm-1
. In case of PVD #4(Fig.1),
MTF values from theoretical model are very close
to experimental data at high frequency region. For
the simulation of PVD #12, detector thickness is
280 µm and electric field strength is .25 µm-1
. It is
observed from the fitting curve of PVD #12(Fig.2)
that MTF values from theoretical model shows
very good agreement with experimental data at low
frequency region.
Fig.1. Fitting a curve for PVD #4 with thickness 210 µm
and electric field strength .24 V µm
-1

and electric field strength .25 V µm-1
For the simulation of PVD #16, the detector
thickness is 280 µm and the electric field strength
is .54 µm-1
. In case of PVD #16(Fig.3), MTF
values from theoretical model are very close to
experimental data at neither low nor high frequency
region rather in the medium values of frequency.
The simulation of PIB #2 was performed at
detector thickness 615 µm and electric field .36
µm-1
. When we come to study the case of PIB
#2(Fig.4),we observe that fitting characteristics
here are almost similar to PVD #16.
Fig.4. Fitting a curve for PIB #2 with thickness 615 µm
Irregular electron-hole pair generation at the
depletion region causes dark current, resembling a
noise in photoelectric devices. We have used a
simplified model of MTF and dark current was not
taken into consideration[4]. However, the existence
of dark current would affect the experimental data
resulting in slight mismatch between experimental
curve and our model. In the MTF model, the
exposure time is not considered though dark
current generation has practical dependence on
exposure time[7]. Several studies have shown that
dark current also depends on temperature[7] which
was not taken into account in the model we
employed. These simplifications contribute to
mismatch between experimental and theoretical
data.
Some of the x-ray generated carriers are
captured by deep traps in the bulk of the
photoconductor during their drift across the
photoconductor. The random nature of carrier
charge trapping creates additional noise.This
additional noise creates signal blurring.The trapped
carriers reduce signals for the corresponding pixel
and induce charge in the neighbouring
pixels.Consequently , there is a lateral spread of
induced charges in the pixels which affects image
resolution[8]. This is an important reason for
mismatch between theoretical and practical data as
deep trapping is not considered in the mathematical
model we used.Along with the stated factors,
another reason which may contribute to the
mismatch is the K-fluorescence phenomena. K-
fluorescence is the emission of secondary x-ray
resulting from bombarding high-energy x-ray.The
K-fluorescent x-ray photon can be absorbed at a
point different from the x-ray absorption site which
deteriorates the image quality. We have used a
model which does not take into account the K-
fluorescence phenomena whereas in practical
cases, K-fluorescence phenomena has significant
effect on MTF performance[8].
The X-ray sensitivity of pixelated X-ray
detectors greatly depends on the mobility and
lifetime product of charges that move towards the
pixel electrodes and the extent of dependence
increases with decreasing pixel per unit detector
thickness[9].Table I shows the mobility-lifetime
product for best fitting of the curves.

Table 1: Summary of the mobility- lifetime product For
Best result of curve fitting in this study.
Prototype Electric
field
strength
(Vµm-1
)
Thickness
(µm)
Mobility-
lifetime
product(cm2
/V)
PVD #4 .24 210 Electron:
0.9×10
-6
Hole: 0.9×10-8
PVD #12 .25 280 Electron:10
-4
Hole: 5×10-8
PVD #16 .54 280 Electron:10
-6
Hole: 5×10-7
PIB #2 .36 615 Electron:10-6
Hole: 0.3×10-5
IV. CONCLUSION
In summary, the MTF model applied to
polycrystalline HgI2 based x-ray image detectors
shows a very good agreement with experimental
data available. Fitting Characteristics of four
prototypes are compared.The slight mismatches of
theoretical and experimental data can be attributed
to the dependence of dark current on exposure
time and temperature, carrier random charge
trapping, K-fluorescence phenomena. The
mobility-lifetime products for best fitting for four
prototypes have also been obtained.To investigate
further with more accuracy and precision, an MTF
model taking temperature dependence,multiple
exposure,deep trapping and fluorescence
phenomena into consideration could be studied.
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