Advances in Photodiodes Part 5 ppt

Simulation of Small-pitch High-density Photovoltaic Infrared Focal Plane Arrays

109
concentration in zero point ( 0t
=
) is always equal to zero i.e. (0)
bgr
n =0. As the result
concentration profile of photogenerated charge carriers nearby to point 0t
=
is formed
preferably by their photogeneration with subsequent extraction into SCR. On the other hand
due to disparity
n
LP L
<
< extraction of dark minority carriers into SCR takes place from
whole thickness of p base where they have existed initially (at
b
V =0). Furthermore value of
concentration
(0) (0) 0
d
nn
=
Δ< is fixed according to expression (34) by applied bias and
algebraic value
()0
d
nLP
≤

grows with increasing of S . In other words ratio ()/(0)
dd
nLP n
is raised. This entire means that gradient of concentration of non-equilibrium dark minority
charge carriers along axis
t grows with increasing of S (Fig. 8a).

10
2
10
3
10
4
10
5
10
6
10
7
1E-10
1E-9
1E-8
1E-7
1 - I
bgr
, Θ=180
0
1
'
- I

bgr
, Θ=30
0
2 - I
d
1
'
2
1
I
bgr
, I
d
(A)
S (cm/s)

10
2
10
3
10
4
10
5
10
6
10
7
1
10

100
1 - I
bgr
(S)/I
bgr
(S=10
7
cm/s), Θ=180
0
1
'
- I
bgr
(S)/I
bgr
(S=10
7
cm/s), Θ=30
0
2 - I
d
(S)/I
d
(S=10
2
cm/s)
2
1, 1
'
I(S)/I

min
(a.u.)
S (cm/s)

(a) (b)
Fig. 9. Dark
d
I - (a) and background generated
b
g
r
I - (b) currents versus S in Hg
1-x
Cd
x
Te
(x=0.224) photodiode described by data given in Table 2. On graph (a) currents are given in
absolute units and on graph (b) – in arbitrary units when curves (a) are specified to
minimum photocurrent values
5. Photocurrent generation and collection in small-pitch high-density IRFPA
Theoretical approach was developed for the case of front-side illuminated IRFPA based on
regular structure of n
p
+
−
junctions enlaced by
g
r
n
+

- guard ring around, Fig. 10.
5.1 PV IRFPA design model
Cross-section of model PD array fragment (pixel) is shown on Fig. 10.
5.2 Photocurrent generated by sideways δ-shaped light beam
For estimation purpose let’s consider one-dimensional (along line A)
g
rm
g
r
n
p
n
p
n
+
++
−− −−
fragment (Fig. 10) of model PD array illuminated by
δ
-shaped light beam perpendicularly
to surface of array, where
m
n
+
is
n
+
- region of n
p
+

−
junction,
g
r
n
+
is
n
+
- guard ring
around n
p
+
− junction and
p
is layer (substrate) common for all pixels of PD array. Pixel is
area including
n
p
+
−
junction and limited by guard ring (Fig. 11). Model array fragment is
symmetrical regarding
m
n
+
- region (Fig. 11). For simplicity word photocurrent will mean
further photocurrent generated by pixel illuminated by proper light. Photocurrent generated
in pixel is calculated at short-circuit between lead V and Ground (Fig. 11).
Advances in Photodiodes

110

Fig. 10. Cross-section of model PD array fragment (pixel). 1 -
m
n
+
is
n
+
- region of n
p
+
−
junction with width
0
W ; 2 -
g
r
n
+
is
n
+
- guard ring with width
g
r
W ; 3 -
p
is thin layer

(substrate) common for all pixels of PD array. Spacing between periphery of n
p
+
− junction
and guard ring is marked as W . Front surface of array is irradiated by photon flux h
ν
(
δ
-
shaped light beam or uniform flux or spotlight) that is absorbed and generates photocurrent


Fig. 11. Front view of model PD array fragment. 1 -
m
n
+
is n
+
- region of
n
p
+
−
junction with
width
0
W ; 2 -
g
r
n

+
is n
+
- guard ring with width
g
r
W
; 3 -
p
is thin layer (substrate)
common for all pixels of PD array. Spacing between periphery of
n
p
+
−
junction and guard
ring is marked as W . Front surface of array is irradiated by photon flux h
ν
(
δ
-shaped
light beam or uniform flux or spotlight) that is absorbed and generates photocurrent in
pixel. One-dimensional consideration is developed along line A (illumination moves along
that line). Common
p
thin layer and
g
r
n
+

- guard ring grid are grounded. Photocurrent
generated in pixel is calculated between Ground and V diode lead connected to
m
n
+
- region
of n
p
+
− junction
Simulation of Small-pitch High-density Photovoltaic Infrared Focal Plane Arrays

111
Let’s assume:
Recombination rates of excess electrons and holes are equal to each other.

np
n
RR
τ
Δ
==
(43)
Where:
n
R and
p
R - recombination rates, n
Δ
- concentration and

τ
- lifetime of excess
electrons and holes.
Drift of excess charge carriers in electric field in
p
- region is negligible.
Band-to-band photogeneration of charge carriers at point
g
yy
=
, i.e. specific rate of
photogeneration is described by formula:
() ( )
g
gy
G
yy
δ
δ
=
×− (44)
Where: ( )
g
yy
δ
− - delta-function and G
δ
- total photogeneration rate of charge carriers.
In analyzed conditions distribution of
()ny

Δ
in
p
- region is defined by diffusion equation:

2
2
()
g
nn
DG
yy
y
δ
δ
τ
∂Δ Δ
×−=−×−
∂
(45)
Where:
D
- coefficient of ambipolar diffusion.
Do solve equation (45) in intervals
/2
o
g
W
yy
<

≤
and
70
/2
g
yyy
WW
≤
≤≡ +
assuming
boundary conditions:

(/2) exp 1
op
qV
nW n
kT
⎡
⎤
⎛⎞
Δ
=× −
⎢
⎥
⎜⎟
⎝⎠
⎣
⎦
and
7

()0ny
Δ
= (46)
And stitching conditions are:

(0)(0)
gg
ny nyΔ−=Δ+
and
00
gg
yy yy
nn
DG
yy
δ
=+ =−
⎛⎞
∂Δ ∂Δ
⎜⎟
×
−=−
⎜⎟
∂∂
⎜⎟
⎝⎠
(47)
Where:
p
n - concentration of equilibrium minority charge carriers (electrons) in

p
- region.
Condition (46) means continuity of excess charge carriers’ concentration, and condition (47)
is derived relation resulted from integration of equation (45) in neighborhood of point
g
yy= . Photocurrent value
p
h
I
δ
at
0
/2yW=
is defined by formula:

ph
IqGK
δ
δ
=
×× (48)
Where:
K - coefficient of one-sided sideways photoelectric conversion defined as:

[( ) / ]
(/)
sh W d L
K
sh W L
−

=
. (49)
Where:
LD
τ
=×- ambipolar diffusion length of charge carriers.
Advances in Photodiodes

112
Graph of K versus normalized distance dWbetween
δ
-shaped light beam and periphery
of
m
n
+
- region of np
+
−
junction is presented on Fig. 12.
If sideways
δ
-shaped light beam illumination is symmetrical in relation to
n
+
- region of
np
+
− junction (i.e. junction is illuminated from left and right sides, Fig. 10) then total
photocurrent value will be two times higher than got from expression (48).

0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
d / W
L=6W
W=6L
W=3L
W=L
K

Fig. 12. Dependence of one-sided sideways photoelectric conversion coefficient
K on
normalized distance
dWbetween
δ
-shaped light beam and periphery of
m
n
+
- region

5.3 Photocurrent generated by uniform sideways and front illumination
To calculate photocurrent value
lat
p
h
I under symmetrical regarding
m
n
+
- region sideways
illumination we need integrate expression (48) with respect to
y
between /2
o
W and
W and than multiply result by coefficient 2.
In the case of uniform illumination (
()Gx const
δ
=
) we get:

2
lat lat
p
hWtot
IqG K=× × . (50)
Where:
2W
G - total sideways photogeneration rate (taking into account both left and right

sides) is defined as:

2
2
W
GGW
δ
=
×
(51)
And sideways photoelectric conversion coefficient
lat
tot
K if defined by:

2
lat
tot
LW
Kth
WL
⎛⎞
=×
⎜⎟
⎝⎠
. (52)
Assuming that photoelectric conversion coefficient is equal to 1 under front-side
illumination we can write photocurrent value
f
r

p
h
I in this case as follows:

0
fr
ph
IqGW
δ
=× × . (53)
Simulation of Small-pitch High-density Photovoltaic Infrared Focal Plane Arrays

113
As it follows from expressions (50) - (53) ratio of photocurrents generated by np
+
− junction
under uniform sideways and front-side illumination is defined by:

00
1
22
22
lat
ph
fr
o
ph
I
LW
RthathaY

WL a
I
⎛⎞ ⎛⎞
≡
=× × =× × = ×
⎜⎟ ⎜⎟
⎝⎠ ⎝⎠
(54)

/
oo
aLW
=
, /aLW
=
and
1
2
2
Yth
a
⎛⎞
=×
⎜⎟
⎝⎠
. (55)
Graph of calculated universal dependence
1
2
2

Yth
a
⎛⎞
=×
⎜⎟
⎝⎠
versus /LW is given on Fig. 13.
Herein:

(/ )
o
Ra YLW
=
× . (56)

0 2 4 6 8 10
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
L / W
Y
a

o
= L / W
o

a = L / W
R = I
lat
ph
/ I
fr
ph
= a
o
Y

Fig. 13. Graph of universal dependence
1
2
2
Yth
a
⎛⎞
=×
⎜⎟
⎝⎠
versus /LW following to (55)
5.4 Photocurrent generated by moving small-diameter uniform spotlight
Basic relation (48) allows estimating of photocurrent
p
h

I
variation when small diameter
()
s
p
ot
D
uniform spotlight is moving along surface of PD array.
To calculate photocurrent value we need integrate expression (48) with respect to
y within
uniformly illuminated region except guard ring region (
g
r
W
). Further we will limit
consideration by condition (57):

s
p
ot o
DW
≤
. (57)
Within uniform spotlight area dependence of photocurrent
p
h
I
on spot center position
c
y

will be described by formulae given further.
Case (a): Gap between
m
n
+
- region border and
g
r
n
+
- guard ring is higher than spot diameter:
Advances in Photodiodes

114

s
p
ot
WD≥ . (58)
Generation of photocurrent when spot illuminates right half of central pixel.
Let’s mark
()c
p
h
I photocurrent generated in central pixel when spot moves within interval
00
22WW yW W−− ≤≤ +
.
1a. Spot center moves within the interval:

10
02
c
y
yW r
≤
≤≡ −. (59)
In this case spot is located within
m
n
+
- region of np
+
−
junction totally. Photocurrent
()c
p
h
I is
frontal only that is:

()
fr
c
s
p
ot
ph ph
IIqGD
δ

==×× . (60)
2a. Spot center moves within the interval:

120
2/2
cspot
yyyW D
≤
≤≡ + . (61)
Spot light is appearing on the side of
m
n
+
- region and at
2c
y
y> get it away.
In the interval (61) we get:

()
()
3
12 3 2
()
(,)
c
c
ph
c
cc c

Iy
yy
LW
Fy y y y y y ch ch
qG shWL L L
δ
⎡
⎤
−
⎛⎞
⎛⎞
=−−≡−+ × −
⎢
⎥
⎜⎟
⎜⎟
⋅
⎝⎠
⎝⎠
⎣
⎦
(62)

(
)
30
2/2
spot
yW WD≡+− (63)
3а. Spot center moves within the interval:

23c
y
yy
≤
≤
. (64)
Spotlight is located totally between
m
n
+
- and
g
r
n - regions, therefore 0
fr
ph
I
=
and

()
(
)
()
()
7
27
2
()

2
c
spot
c
ph
c
c
sh D L
Iy
y
y
Fy y L sh
qG shWL L
δ
−
⎛⎞
=−≡× ×
⎜⎟
⋅
⎝⎠
. (65)
Case (a
1
): Let’s impose some condition - width of guard ring is narrower than spotlight
diameter:

g
rs
p
ot

WD
<
. (66)
4а
1
. Spot center moves within the interval:

(
)
350
2/2
cspot
yyy W WD≤≤≡ ++ . (67)
Spotlight gets away gradually from considered central pixel. Photocurrents generated in
central pixel and neighbor right side pixel will be equal to each other when
c
y
will coincide
to mid
4
y of right side guard ring (68):
Simulation of Small-pitch High-density Photovoltaic Infrared Focal Plane Arrays

115

()
(
)
40
22

gr
yW WW≡++ . (68)
In the interval (67):

()
(
)
()
()
2
5
35
2
()
2
c
c
c
ph
c
sh y y L
Iy
Fy y L
qG shWL
δ
⎡
⎤
−
⎣
⎦

=−≡×
⋅
. (69)
5a. Spot center moves beyond coordinate
5
y


5c
y
y≥ . (70)
In this case spotlight leaves central pixel entirely and no photocurrent will be generated

()
()0
c
c
ph
Iy
=
. (71)
Generation of photocurrent when spot illuminates left half of neighbor right side pixel.
Photocurrent generation in right side pixel
p
h
I
>
will take place when edge of spotlight
appears in that pixel, i.e. at condition (72):

(
)
60
2/2
cgrspot
yy W WW D≥≡ ++ − . (72)
It means that till spot’s edge hasn’t reach periphery of right side pixel and no photocurrent
is generated
6a.
6c
y
y
≤
; ( ) 0
ph c
Iy
>
=
. (73)
Photocurrent ( )
p
hc
Iy
>
and
()
()
c
c
ph

Iy
values are symmetrical about mid line of guard ring
region
4
y , i.e.:

(
)
()
4
() 2
c
p
hc c
ph
Iy I y y
>
=−. (74)
Therefore we do have the following cases:
7а
1
.
(
)
6110
2/2
cgrspot
yyy W WW D≤≤ ≡ ++ + ;
36
()

ph
с
I
Fy y
qG
δ
>
=−
×
. (75)
8а
1
.
(
)
11 10 0
22 /2
cgrspot
yyy W WWD≤≤ ≡ + + − ;
()
29
()
ph c
c
Iy
F
yy
qG
δ
>

=−
⋅
. (76)
Where:

(
)
90
2
g
r
y
WWW=++. (77)
9а
1
.
(
)
10 12 0
22
cgr
yyy
WWWr≤≤ ≡ + + +;
()
11011
()
,
ph c
cc
Iy

F
yyyy
qG
δ
>
=− −
×
. (78)
Advances in Photodiodes

116
10а
1
.
12 8c
y
yy
≤
≤ ;
()
ph c
s
p
ot
Iy
D
qG
δ
>
=

×
. (79)
Where distance between centers of
m
n
+
- regions of central and right side pixels:

80
2
g
r
y
WWW
=
++. (80)
Generation of photocurrent when spot illuminates left half of central pixel.
Let’s mark photocurrent at negative and positive coordinate
c
y
as ( )
p
hc
I
y
−
and ( )
p
hc
I

y

properly. Values ( )
p
hc
I
y
−
and ( )
p
hc
I
y
are the same in respect to zero point 0
c
y = , i.e.

(
)
(
)
p
hc
p
hc
I
y
I
y
−

=−. (81)
Therefore we do have the following cases:
11a.
1
0
c
yy
−
≤≤;
()
p
hc s
p
ot
IyqGD
δ
−
=
××
. (82)
12а.
21c
y
yy
−
≤≤−;
(
)
12 3
() ,

p
hc c c
I
yq
GF
yyyy
δ
−
=× × + + . (83)
13а.
32c
y
yy
−
≤≤−;
(
)
27
()
p
hc c
I
yq
GF
yy
δ
−
=× × + . (84)
14а.
53c

y
yy
−
≤≤−;
(
)
35
()
p
hc c
I
yq
GF
yy
δ
−
=× × + . (85)
15a.
5c
y
y
≤
− ; ( ) 0
ph c
Iy
−
=
. (86)
Generation of photocurrent when spot illuminates right half of neighbor left side pixel.
16a.

6
0
c
yy
−
≤≤
; ( ) 0
ph c
Iy
−
=
. (87)
17а
1
.
11 6c
y
yy
−
≤≤−
;
(
)
36
()
ph c c
I
yq
GF
yy

δ
−
=× × − − . (88)
18а
1
.
10 11c
y
yy−≤≤−
;
(
)
29
()
ph c c
I
yq
GF
yy
δ
−
=× × − − . (89)
19а
1
.
12 10c
y
yy−≤≤−
;
(

)
11011
() ,
ph c c c
I
yq
GF
yy yy
δ
−
=× × − − − − . (90)
20а
1
.
812c
y
yy
−
≤≤−; ( )
p
hc s
p
ot
IyqGD
δ
−
=
×× . (91)
Case (b): Gap between
m

n
+
- region border and n
+
- guard ring is less than spot diameter:
/2
spot
WD
≤
. (92)
Generation of photocurrent when spot illuminates right half of central pixel.
21b.
1
0
c
y
y
≤
≤
;
()
fr
c
s
p
ot
ph ph
IIqGD
δ
==×× . (93)

Simulation of Small-pitch High-density Photovoltaic Infrared Focal Plane Arrays

117
22b.
13c
y
yy
≤
≤ ;
()
()
12 3
()
,
c
c
ph
cc
Iy
F
yyyy
qG
δ
=−−
⋅
. (94)
In interval (96) part of spot is located in
m
n
+

- region but spot edge does not reach guard ring.
Case (b
1
): Let’s impose some condition:
b
1
. 2( /2 )
gr spot
WD W
≤
− . (95)
23b
1
.
32c
y
yy
≤
≤ ;
()
()
42 2
()
2
c
c
ph
cc
Iy
W

Fy y y y Lth
q
GL
δ
⎛⎞
=−≡−+×
⎜⎟
⋅
⎝⎠
. (96)
24b
1
.
25c
y
yy
≤
≤ ;
()
()
35
()
c
c
ph
c
Iy
F
yy
qG

δ
=−
⋅
. (97)
25.
58c
y
yy
≤
≤ ;
()
0
c
ph
I
=
. (98)
Generation of photocurrent when spot illuminates left half of neighbor right side pixel.
26.
6
0
c
y
y
≤
≤ ; ( ) 0
ph c
Iy
>
=

. (99)
27b
1
.
610c
y
yy
≤
≤ ;
()
36
()
ph c
c
Iy
F
yy
qG
δ
>
=−
×
. (100)
28b
1
.
10 11c
y
yy
≤

≤ ;
()
410
()
ph c
c
Iy
F
yy
qG
δ
>
=−
×
. (101)
29b
1
.
11 12c
y
yy≤≤
;
()
11011
()
,
ph c
cc
Iy
F

yyyy
qG
δ
>
=− −
×
. (102)
30b
1
.
12 8c
y
yy
≤
≤ ;
()
ph c
s
p
ot
Iy
D
qG
δ
>
=
⋅
. (103)
Generation of photocurrent when spot illuminates left half of central pixel.
31.

1
0
c
yy
−
≤≤;
()
p
hc s
p
ot
IyqGD
δ
−
=
××
. (104)
32b.
31c
y
yy
−
≤≤−;
(
)
12 3
() ,
p
hc c c
I

yq
GF
yyyy
δ
−
=× × + + . (105)
33b
1
.
23c
y
yy
−
≤≤−;
(
)
42
()
p
hc c
I
yq
GF
yy
δ
−
=× × + . (106)
34b
1
.

52c
y
yy
−
≤≤−;
(
)
35
()
p
hc c
I
yq
GF
yy
δ
−
=× × + . (107)
Advances in Photodiodes

118
35.
85c
y
yy
−
≤≤−;
()0
ph c
Iy

−
=
. (108)
Generation of photocurrent when spot illuminates right half of neighbor left side pixel.
36.
6
0
c
yy
−
≤≤; ( ) 0
ph c
Iy
−
=
. (109)
37b
1
.
10 6c
y
yy
−
≤≤−;
(
)
36
()
ph c c
I

yq
GF
yy
δ
−
=× × − − . (100)
38b
1
.
11 10c
y
yy−≤≤−;
(
)
410
()
ph c c
I
yq
GF
yy
δ
−
=× × − − . (111)
39b
1
.
12 11c
y
yy−≤≤−;

(
)
11011
() ,
ph c c c
I
yq
GF
yy yy
δ
−
=× × − − − − . (112)
40b
1
.
812c
y
yy−≤ ≤−
; ( )
p
hc s
p
ot
IyqGD
δ
−
=
×× . (113)
5.5 LWIR PD array: calculation of photocurrent collection profiles
Data used in calculation of photocurrent generated in small-pitch high-density

Hg
0.776
Cd
0.224
Te PD array are given in Table 2. Junction regions thickness t was taken t(n
+
) =
0.5 μm and t(p-absorber) = 6 μm. Surface recombination rate 10
2
cm/sec.
Developed approach (57) - (113) was applied to calculate photocurrent generated in small-
pitch Hg
0.776
Cd
0.224
Te PD array. Calculated dependences of photocurrent
p
h
I generated by
spotlight in Hg
1-x
Cd
x
Te (x=0.224) PD array are shown on Fig. 14 and ratio of photocurrents
generated at uniform frontal and sideways illumination can be estimated easily from Fig. 14.
It is seen clearly that developed approach allows analytical estimation of photocurrent
generation in different close-packed PD arrays. Following to dependence presented on Fig.
13 contribution of photocurrent generated by sideways uniform illumination to total
photocurrent of pixel can be too much high at not reasonable ratios between
L , W and

0
W .
Dependences of photocurrent value
p
h
I are calculated as function of spot center position
coordinate
c
y for central and neighbor pixels of array. Condition 0
c
y
=
means that in start
position Zero of coordinate system and spot center are matched. Length (distance) is given
in units
s
p
ot
D (spot diameter). Photocurrent is calculated in units
s
p
ot
qG D
δ
×
× . It is accepted
in calculation that width of
m
n
+

- region of n
p
+
−
junction
o
W = 20 µm; width of
g
r
n
+
- guard
ring
g
r
W = 5 µm; spot diameter
s
p
ot
D = 15 µm; operating temperature 77
op
TK
=
; ambipolar
diffusion length in
p
layer L
=
48 µm. Spacing between periphery of n
p

+
−
junction and
guard ring W = 20 µm (a) and W = 5 µm (b). Photocurrent in central, neighbor right-side
and neighbor left-side pixels are presented on graphs by solid curves, dashed curves and
dash-and-dot curves properly
6. Conclusion
We have attempted to develop some general approach for simulation MWIR and LWIR PD
IRFPA including estimation of major electro-optical parameters. Estimations have shown
that extended LWIR Hg
1-x
Cd
x
Te PD with p-n junction will be potentially of 4-5 times lower
dark current value than PD with n
+
-p junction at T=77 K and 2 times lower at T=100 K.
Additionally extended LWIR Hg
1-x
Cd
x
Te PD with p-n junction will be seriously lower
Simulation of Small-pitch High-density Photovoltaic Infrared Focal Plane Arrays

119
sensitive to operating temperature increasing than PD with traditional n+-p junction. We
have shown that surface recombination rate value at back surface of thin p absorber can
have serious effect on dark current in small-size LWIR Hg
1-x
Cd

x
Te PD. We have developed
analytical expressions describing collection of photogenerated charge carriers in small-pitch
IRFPA for practical cases: uniform and small-size spotlight illumination.

-2 -1 0 1 2
0
0.2
0.4
0.6
0.8
1
I
ph
y
c
b
W
o
WW
-2 -1 0 1 2
0
0.2
0.4
0.6
0.8
1
I
ph
a

y
c
W
o
W
W

Fig. 14. Graphs of photocurrent generated in Hg
1-x
Cd
x
Te (x=0.224) PD array following to
expressions (57)-(113)
7. References
Whicker, S. (1992). “New technologies for FPA dewars”, Proceedings of SPIE, 1683, pp. 102-
112, ISBN 9780819408488, August 1992, SPIE Press, Bellingham, Washington
Triboulet, P. & Chatard, J P. (2000). “From research to production: ten years of success”,
Proceedings SPIE 4130, pp. 422-440, ISBN 9780819437754, December 2000,
SPIE
Press, Bellingham, Washington
Baker, I. & Maxey, C. (2001). “Summary of HgCdTe 2D array technology in the UK”, Journal
of Electronic Materials, Vol. 30, No. 6, (June 2001) 682-689, ISSN 0361-5235
Norton, P. (2002). “HgCdTe infrared detectors”, Opto-Electronics Review, Vol. 10, No. 3,
(September 2002) 159-174, ISSN 1230-3402
Kinch, M. (2007). Fundamentals of Infrared Detector Materials, SPIE Press, ISBN 978-0-8194-
6731-7, Bellingham, Washington
Glozman, A.; Harush, E.; Jacobsohn, E.; Klin, O.; Klipstein, Ph.; Markovitz, T.; Nahum, V.;
Saguy, E.; Oiknine-Schlesinger, J.; Shtrichman, I.; Yassen, M.; Yofis, B. & Weiss, E.
(2006). “High performance InAlSb MWIR detectors operating at 100 K and
beyond”, Proceedings SPIE 6206, pp. 6206M, ISBN 9780819462602, May 2006, SPIE

Press, Bellingham, Washington
Advances in Photodiodes

120
Kinch, M.; Brau, M. & Simmons, A. (1973). “Recombination mechanisms in 8-14 μ HgCdTe”,
J. Appl. Phys., Vol. 44, No. 4, (April 1973) 1649-1663, ISSN 0021-8979
Gelmont, B. (1980). “Auger recombination in narrow band-gap semiconductors”, Sov.
Semicond. Phys. & Tech., Vol. 14, No. 11, (November 1980) 1913-1917, ISSN 1063-
7826
Gelmont, B. (1981). “Auger recombination in narrow band-gap p-type semiconductors”, Sov.
Semicond. Phys. & Tech., Vol. 15, No. 9, (September 1981) 1316-1319, ISSN 1063-7826
Blue, M. (1964). “Optical Absorption in HgTe and HgCdTe”, Physical Review A, Vol. 134, No.
1, (January 1964) 226-234, ISSN 1050-2947
Laurenti, J.; Camassel, J.; Buchemadou, A.; Toulouse, B.; Legros, R. & Lusson, A., (1990).
“Temperature dependence of the fundamental absorption edge of mercury
cadmium telluride”, J. Appl. Phys., Vol. 67, No. 10, (May 1990) 6454-6460, ISSN
0021-8979
Schmit J., (1970). “Intrinsic carrier concentration of Hg
1-x
Cd
x
Te as a function of x and T using
k-p calculations, J. Appl. Phys., Vol. 41, No. 7, (June 1970) 2876-2879, ISSN 0021-8979
Blakemore, J. (1962). Semiconductor Statistics, Pergamon Press, ISBN 0-486-49502-7, New
York, New York
Part 2
Silicon Devices

6
Methodology for Design, Measurements and

Characterization of Optical Devices on
Integrated Circuits
G. Castillo-Cabrera
1,3
, J. García-Lamont
2
and M. A. Reyes-Barranca
3

1
Superior School of Computing (ESCOM), National Polytechnic Institute (IPN),
2
Institute of Basic Science and Engineering, CITIS, Hidalgo State University,
3
Electrical Engineering Department, SEES, CINVESTAV-IPN,
Mexico
1. Introduction
The main application of optical devices is image processing which is a research field still in
study for a wide variety of applications, such as video digital cameras for entertainment use,
pattern recognition based in artificial neural networks, real time object tracking, clinical uses
for repair by stimulation parts of visual system and artificial vision for application in silicon
retinas, among others. So, it is important to evaluate the performance of available integrated
photo-sensor devices used in these applications, considering issues as noise, resolution,
processing time, colour, etc. Actually, there are several technologies available for integration
of photo devices, commonly CCD, BiCMOS and GaAs. Although all of them are usually
applied in image acquisition systems, there are still some performance aspects that should
be optimised, as voltage levels, leakage currents, high fabrication costs, etc., so research is
still being done to overcome these limitations. Standard CMOS integrated circuit technology
is also an attractive alternative, since devices like phototransistors and photodiodes can be
implemented as well. The foremost advantage of CMOS devices is its availability in

standard technology. It should be mentioned that this technology has also some limitations
but since fabrication of CMOS integrated circuits has low costs, exploration of the potential
of new technologies for image processing is still an interesting field. Besides, algorithms can
be implemented along for tasks such as border detection (space vision), movement detection
(space-time vision), image enhancement (image processing vision) and pattern classification
or recognition (neuro-fuzzy vision).
Considering the state of the art (Aw & Wooley 1996; Storm & Henderson, 2006; Theuwissen,
2008), as well as clinic approaches (Zaghloul, & Boahen, 2004), in this work, a chip was
designed and fabricated, with two possible photo-sensor structures: p+/N-well/p-substrate,
for phototransistors and N-well/p-substrate, for photodiodes, through the standard 1.5µm
AMI’s- , N-Well technology. In the future, it is the intention to design a second chip that
must include electronics for image processing with pulse frequency modulation (PFM), once
the characterization gives enough information about the performance of the stages studied.
A complete description is given.
Advances in Photodiodes

124
2. Devices Involved, type of structures
After the CCDs, the new generations of optical devices are based in standard CMOS
technology. Experimental study based is here presented, about two typical structures in the
field of art, namely, phototransistor and photodiodes which were designed and fabricated
through the standard 1.5µm AMI’s- technology. Technically those are known as “structures
P+/N-Well/P-substrate” and “structures N-Well/P-substrate” respectively, which are
presented by Fig. 1.


(a) (b)
Fig. 1. Optical devices, (a): P+/N-Well/P-substrate, (b): N-Well/P-substrate
In the former, Fig. 1(a), P+/N-Well/P-substrate, the P+/N-Well is being an active junction
as well as N-Well/P-substrate junction. An active junction is one in which two

semiconductors with different conductivity, “p” and “n” type, are joined and electrically
interacting. N-Well is a diffused region n-type on substrate. P+ on N-Well is an implanted
material and also serves as low resistive ohmic contact. N+ on N-Well is an n-type
implanted region and solely is used as low resistive ohmic contact. P+ on P-substrate is an
implanted p+-type material and is used as low resistive ohmic contact. Terminals E, B and C
are Emitter, Base and collector respectively in the phototransistor.
In the last one, Fig. 1(b), N-Well/P-substrate, there is only one active junction. N+ and P+
are implanted regions which does low resistive ohmic contact with N-Well and P-substrate
respectively.
Both, structures P+/N-Well/P-substrate and N-Well/P-substrate, symbols are presented by
the Fig. 2.


(a) (b)
Fig. 2. Symbols for optical structures (a): P+/N-Well/P-substrate, (b): N-Well/P-substrate
3. Circuital architecture of pixel for characterization
3.1 Components of architecture
Fig. 3 presents the pixel architecture which has resulted efficient for optical devices
characterization. It consists in optical device, four transistors, a source of current and buffer
Methodology for Design, Measurements
and Characterization of Optical Devices on Integrated Circuits

125
for readout. The common source amplifier consists, in M1 transistor and current source Isc,
and it is used to handle the photocurrent. M2 is row select transistor and is not part of
amplifier strictly speaking, however its position play an important role on this architecture,
as will be shown in section 4. Photocurrent, from optical device, is integrated at the parasitic
capacitance of the p-channel transistor M1, between node 2 and substrate, which is tied to
ground. Assuming that photocurrent is constant, the relation of integrated voltage can be
obtained by using the relation

qCV
=
⋅ in the parasitic capacitance.

t
1
int
C
0
Vidt
Δ
=
∫
(1)
where

dq
dt
i = (2)
MSHUT along with signal VSHU controls the exposition time
Δ
t. MREST along with signal
VRES have as function to reset the nodes 1 and 2 at level Vreset. Optical devices can be
P+/N-Well/P-substrate or N-Well/P-substrate structures. BUFFER OUTPUT provides
power to avoid disturbance during readout.


(a) (b)
Fig. 3. (a) Architecture of pixel, (b) Optical device
Transistors MSHUT and MREST operate as switches in order to integrate the photocurrent

generated in the photo-sensor at a given time and operation frequency. Fig. 4 shows the
waveforms of their respective gate voltages. Integration time
Δ
t, takes place while MSHU is
on and MRES is off. During this time, the photocurrent is converted to voltage at the gate of
transistor M1 (node-2 in Fig. 1). The relation between the integrated voltage and
photocurrent is expressed in Eq. (1), assuming that the photocurrent is uniform in time. The
DC voltage source, Vreset, is the reference voltage from which integration of the
photocurrent is carried out.
Advances in Photodiodes

126
3.2 Signals of control


Fig. 4. Waveform of signals shutter and reset

(
)
/
int
ICV T
ph T
=
ΔΔ (3)
where:
p
h
I : photocurrent from the photo-device.
T

C : capacitance at node-2
int
ΔV
: integrated voltage in
T
C
(
int
/
measured
VV AvΔ=Δ
)
TΔ : integration time
Av : amplifier’s gain
In addition, Vreset sets the quiescent point of the amplifier. Fig. 4 shows the input voltage
pulses applied to the gate of MRES and MSHUT, respectively.
Since the objective of this work is to propose a methodology for the characterization of
photo-devices and pixel architectures, the design was made considering those parameters
affecting the performance of pixels and the way they will be measured. The design was
carried out with the more simple architecture. Unlike what was reported with current
amplifiers in the current-mode readout configuration (Philipp et al 2007), the amplifier is
configured for voltage-mode operation in this work. From results obtained with this design,
useful information can be processed and analysed considering a specific application,
regarding factors such as the spectral response and silicon integration area of
p+/N-well/p-
substrate
phototransistors and N-well/p-substrate photodiodes, as well as integration time,
integrated voltage, transistors’ aspect ratio and reference voltage used, for instance.
Considerations about technology parameters, is important also in the definition of the
dependence of the response and the architecture operation upon the photo-device structure.

Here, we present the electronic design, layout, simulations and some measurements on the
fabricated chip. This prototype was made using the 1.5µm AMI’s technology. The chip
contains five pairs of phototransistors and five pairs of photodiodes, with one instance of
each pair covered with metal for dark current characterization purposes. Results reported
Methodology for Design, Measurements
and Characterization of Optical Devices on Integrated Circuits

127
here are only from those devices having an area of (9µm)x(9µm). Bigger photo-devices were
also measured, but as they saturated the amplifier, no useful results were obtained. A
drawing is given in the Fig. 5 which is showing the fabricated array.


Fig. 5. Drawing for the array of optical devices
4. Circuit analysis
Now, doing reference to the Fig. 3, some design criteria for the circuit are defined. (1)
Transistors MREST and MSHUT are used as switches, so their sizes can be drawn with
minimum dimension features allowed by the technology. (2) Channel modulation effects
must be avoided with M1, therefore its channel length should be at least five times the
minimum dimension allowed. (3) For proper operation of the amplifier, it is recommended
to choose a stable current source for biasing, thus, a cascode configuration was selected and
designed for sourcing 20µA. (4) By adjusting the current source and Vreset the voltage gain
of the amplifier it is varied, giving a useful degree of freedom for the characterization of the
architecture and different devices, including the possibility another kind of not optical
integrated sensors. (5) Transistor M2 it is inserted into the amplifier since it is a standard
way for selecting row within an array. However, the role of M2 on the amplifier here
proposed must be analyzed. (6) Finally, a standard buffer circuit is used for provide of
power to the output.
Fig. 6 (a) shows the schematic of the cascode current source used for biasing the amplifier.
Transistors involved in the amplifier are M1, M2, M4 and M6. Fig. 6 (b) shows the

equivalent circuit for the amplifier and the cascode current source, used to find a
mathematical relationship between the voltage gain and the size of M2.
From Figure 4(b),
s
r is the channel resistance of M2; here, subscripts 01, 04 and 06 are
identifiers for transistors M1, M4 and M6, respectively. A circuit analysis gives the following
expression for the output voltage,
out
V :

01 1 2 04 3 06 2
0
s
ri ri ri ri
+
++= (4)

21 11ms
g
ii
g
v
−
= (5)
Advances in Photodiodes

128

(a) (b)

Fig. 6. Cascode source current (a) schematic, (b) equivalent circuit

23 44m
g
s
ii
g
v
−
= (6)

01 1 2out s
vriri
−
=+ (7)

04 3 06 2out
vriri=+ (8)
Equations from (4) up to (8) are mesh equations from which the next expression is obtained:

02 out
Ri v
=
(9)
Where

0 04 4 06 04 06m
Rr grr r
=
++ (10)

12 11ms
g
ii
g
v
−
+= (11)

01 1 2sout
ri ri v
+
=− (12)
And by using (11) and (12),
2
i can be obtained:

01 1 1
2
01
ms
g
out
s
rg v v
i
rr
−
=
+

(13)
From (9) and (10), the voltage gain of the amplifier is deduced:

01 1 1
0
01
msg out
out
s
rg v v
Rv
rr
−
⎛⎞
=
⎜⎟
⎜⎟
+
⎝⎠
(14)
Methodology for Design, Measurements
and Characterization of Optical Devices on Integrated Circuits

129
Defining the next ratio:

0
01
s
R

K
rr
=
+
(15)

01 1 1ms
g
out out
r
g
vKvKv
−
= (16)
And since

1s
g
in
vv
=
−
out
in
v
Av
v
=
(17)

Finally the voltage gain is obtained:

01 1
1
m
K
Av r g
K
=−
+
(18)
When
1K >> , the gain can be approximated to:

01 1m
Av r g
≅
− (19)
This is only possible if
s
r is sufficiently small, from (15). So, assuming that
01 04 06
rrr==
from (10) and (11), the size of M2 must be such that
s
r will result very small, compared with
01
r ,
04
r and

06
r . With an iterative procedure, the aspect ratio /WL of M2 was made large
enough such that
s
r does not have a strong influence over the amplifier’s operation (Baker et
al 2005). So, for the technology used the calculated aspect ratio for M2 was, 64.8Wm
μ
=
and 2.4Lm
μ
= . Then, considering these design outlines, the operation of the circuit based on
M2 can be traduced in a convenient performance evaluation. As a result of the above design
considerations, this basic analysis of the equivalent circuit reveals that the role of the row-
select transistor is important for the proper operation of the amplifier. The voltage gain in
(19) can be estimated using the following expressions (Baker et al 2005):

01
1
D
r
I
λ
=
⋅
(20)

()
1
2
W

mD
L
gKPI= (21)
Using values of
KP and
λ
, from the 1.5μm AMI technology, the maximum voltage gain
was estimated as: 35Av dB
=
.
4.1 Simulation
Once the sizes of transistors used in the pixel were calculated, simulations with PSPICE
were made to confirm the behavior of the circuit. Fig. 7 shows the gain range that can be
achieved with the amplifier, going from 10dB to 32dB. Beside this, Input voltage, which is
provided with Vreset, goes from 2.2V up to 3.5V, taken as parameter RCASC in the source
current, Fig. 6(a).
Advances in Photodiodes

130

Fig. 7. Transfer function simulated
In order to evaluate temporal response, input voltage was adjusted to 3.5V, which belong to
the gain of 32dB. Fig. 8 shows a simulated temporal response. Time of integration is of 0.9ms
and time of reset is 0.1ms, according with the waveforms of VSHU and VRES seen in the
Fig. 4. Level of photocurrent for simulation was taken of 10pA, from Reginald-Krishna's
model (Perry 1996).


Fig. 8. Temporal response structure P+/N-Well/P-substrate
4.2 Layout

Cross section and layout are given in Fig. 9 and 10, for P+/N-Well/P-substrate and N-
Well/P-substrate structures, respectively.
Methodology for Design, Measurements
and Characterization of Optical Devices on Integrated Circuits

131

(a) (b)
Fig. 9. P+/N-Well/P-substrate structure (a) Cross section (b) Layout
We can see two junctions in the Fig. 9. As it was been established in the Fig. 3, terminal of
“emitter” is periodically reset at CD level of Vreset, which is also the amplifier´s point of
operation. Terminal of “base” is tied to VDD which is power supply. “Collector” is tied to
ground. Both junctions are biased in reverse way. Base-emitter junction is to (5V-Vreset) and
base-collector junction to (5V-0V).


(a) (b)
Fig. 10. N-Well/P-substrate structure (a) Cross section (b) Layout
Photodiode, structure N-Well/P-substrate given in Fig. 10, only has two terminals. Terminal
of cathode is reset to Vreset periodically and anode is tied to ground. So, it is biased in
reverse way.
The phototransistor’s “base” has the same dimensions of the photodiode’s anode ring,
(9µm)x(9µm). So, both has the same active surface. The photocurrent generated is collected
by the phototransistor’s emitter and the same happens with the cathode of the photodiode.
5. Results
An array, which has been drawn in the Fig. 5, was fabricated and it is shown in the Fig. 11.
Advances in Photodiodes

132

Fig. 11. Fabricated array of devices, microphotography
At the bottom of each column we can see a block, which comprise both, cascode source
current Isc and BUFFER OUTPUT. First left column has different size of not covered
phototransistors, P+/N-Well/P-substrate structures. Second column of left to right consists
of P+/N-Well/P-substrate structures, similar sizes that first left column but covered with
metal 2 (process AMI of 1.5µm). Third and fourth columns of left to right are not covered
and covered N-Well/P-substrate structures respectively, photodiodes. Transfer function
measured, of amplifier is given in the Fig. 12.


Fig. 12. Experimental transfer function of amplifier
Methodology for Design, Measurements
and Characterization of Optical Devices on Integrated Circuits

133
Experimental transfer function of amplifier is quite fitted to the criteria design. Fig. 12 shows
one of these functions. During the procedure of calibration, in a first set of measurements it
was saw a strong response in the case photodiodes. So, in order to carry out measurements,
the amplifier gain was set at 10dB in case of photodiodes measurements, while
phototransistors at 32dB, in order to have a good reading without saturated response. It is
clear that response of the photodiode, shown in Fig. 13 tend to be much larger than
phototransistors, Fig. 14. This is an indication that the integrated current within the
photodiode is higher compared to that of the phototransistor, even with the same incident
illumination power.


Fig. 13. Measurements of the temporal response in the N-Well/P-substrate structures
(photodiodes)

Fig. 14. Measurements of the temporal response in the P+/N-Well/P-substrate structures
(phototransistors)