Approaching to an optimal value of rise time in n-well/p substrate photodiode by controlling depletion layer width
The relationship between response speed of a silicon n-well/p substrate photodiode and the depletion layer width has been investigated. Variation of both the junction capacitance and the series resistance of the photodiode with the depletion layer width have been analyzed. It is shown that the co...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2009
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irk-123456789-1188492017-06-01T03:05:28Z Approaching to an optimal value of rise time in n-well/p substrate photodiode by controlling depletion layer width Emad Hameed Hussein The relationship between response speed of a silicon n-well/p substrate photodiode and the depletion layer width has been investigated. Variation of both the junction capacitance and the series resistance of the photodiode with the depletion layer width have been analyzed. It is shown that the contribution of the time constant and the drift time in the rise time within the depletion layer can be decreased to an optimal value (less than 1ns) just for specific value of the depletion layer width and smaller value of the diffused junction area. 2009 Article Approaching to an optimal value of rise time in n-well/p substrate photodiode by controlling depletion layer width / Emad Hameed Hussein // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2009. — Т. 12, № 4. — С. 424-428. — Бібліогр.: 13 назв. — англ. 1560-8034 PACS 73.40.-c, 85.60.Dw http://dspace.nbuv.gov.ua/handle/123456789/118849 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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The relationship between response speed of a silicon n-well/p substrate
photodiode and the depletion layer width has been investigated. Variation of both the
junction capacitance and the series resistance of the photodiode with the depletion layer
width have been analyzed. It is shown that the contribution of the time constant and the
drift time in the rise time within the depletion layer can be decreased to an optimal value
(less than 1ns) just for specific value of the depletion layer width and smaller value of the
diffused junction area. |
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Article |
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Emad Hameed Hussein |
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Emad Hameed Hussein Approaching to an optimal value of rise time in n-well/p substrate photodiode by controlling depletion layer width Semiconductor Physics Quantum Electronics & Optoelectronics |
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Emad Hameed Hussein |
| author_sort |
Emad Hameed Hussein |
| title |
Approaching to an optimal value of rise time in n-well/p substrate photodiode by controlling depletion layer width |
| title_short |
Approaching to an optimal value of rise time in n-well/p substrate photodiode by controlling depletion layer width |
| title_full |
Approaching to an optimal value of rise time in n-well/p substrate photodiode by controlling depletion layer width |
| title_fullStr |
Approaching to an optimal value of rise time in n-well/p substrate photodiode by controlling depletion layer width |
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Approaching to an optimal value of rise time in n-well/p substrate photodiode by controlling depletion layer width |
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approaching to an optimal value of rise time in n-well/p substrate photodiode by controlling depletion layer width |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2009 |
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http://dspace.nbuv.gov.ua/handle/123456789/118849 |
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Approaching to an optimal value of rise time in n-well/p substrate
photodiode by controlling depletion layer width / Emad Hameed Hussein // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2009. — Т. 12, № 4. — С. 424-428. — Бібліогр.: 13 назв. — англ. |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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AT emadhameedhussein approachingtoanoptimalvalueofrisetimeinnwellpsubstratephotodiodebycontrollingdepletionlayerwidth |
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2025-07-08T14:46:38Z |
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2025-07-08T14:46:38Z |
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1837090475875500032 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 4. P. 424-428.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
424
PACS 73.40.-c, 85.60.Dw
Approaching to an optimal value of rise time in n-well/p substrate
photodiode by controlling depletion layer width
Emad Hameed Hussein
Dept. of Physics, College of Science,
Al-Mustansiryia University, Baghdad, Iraq
E-mail: emadh67@yahoo.com
Abstract. The relationship between response speed of a silicon n-well/p substrate
photodiode and the depletion layer width has been investigated. Variation of both the
junction capacitance and the series resistance of the photodiode with the depletion layer
width have been analyzed. It is shown that the contribution of the time constant and the
drift time in the rise time within the depletion layer can be decreased to an optimal value
(less than 1ns) just for specific value of the depletion layer width and smaller value of the
diffused junction area.
Keywords: silicon photodiode, n-well/p junction, p-n junction, capacitance junction,
series resistance.
Manuscript received 05.05.09; accepted for publication 10.09.09; published online 30.11.09.
1. Introduction
With the advances in technology over the past few
years, it has become possible to fabricate high speed
optoelectronic devices such as photodiode. High speed
photodiodes play an important role in optical
communication [1] and measurement systems [2], and
hence they attract attention of researchers [3-5].
Unfortunately, realistic photodiodes have finite speed of
responsivity. So, for a fast response time, through the
fabrication process of the photodiode, impurity
concentration and operating voltage must be chosen to
give a depletion layer width so that the junction
capacitance can cause as possible as short time constant.
While many applications of photodiodes depend on
thinner depletion region, others need to maximize
thickness of the depletion region [6]. However, the series
resistance which is due to bulk and contact resistances,
and is usually only a few ohms, has an active role in the
photodiode responsivity. Almost, the contacts are
decreased by different methods like ion implantation [7]
or by using titanium silicide [8], etc. The depletion layer
is no longer dominating the series resistance as long as
the substrate width is much larger than its width and
hence a small resistivity semiconductor and small
diffused junction area are required for lowering the
series resistance. Although there are different semi-
conductor materials, silicon are commonly used to
fabricate p-n photodiodes for visible and near infrared
region [9-12], as it was chosen in this research.
2. Experimental
In n-well/p substrate photodiode the depletion region is
always wider than that for p-n junction photodiode,
because concentration levels of the n-well and the p-
substrate are relatively low. Anyhow, structure of
photodiode is essentially similar to p-n junction diode
except it has a transparent window can receive light
through it. The photodiode model adopted in this
research is similar to the model proposed by Swe and
Yeo [8]. It is a p-substrate silicon type with resistivity
ρ = 7.5 Ohm·cm and a phosphorus n-well mask was
implanted, as shown in Fig. 1. Arsenic implant and
BF2+ implant were used to form the n+ and p+ regions,
respectively, which are used as the cathode and anode
contacts, respectively. Hence, a p-n junction is formed
between p-substrate and n-well region.
3. Results and discussion
The depletion layer width at thermal equilibrium for a
one sided abrupt is given as [13]
q
KT
VV
qN
W b
S
D
22 (1)
where εs is the relative permittivity of the
semiconductor, q is the electron charge, K is the
Boltzmann constant, T is the absolute temperature, Vb is
the built-in-potential, V is the applied voltage and N is
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 4. P. 424-428.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
425
the impurity concentration (N is NA, if NA >> ND or vise
versa where NA is the accepter concentration and ND is
the donor concentration). For silicon model εS = kS·ε0,
where ε0 is the permittivity of free space (8.85 pF/m) and
kS is silicon dielectric constant (11.68). By substituting
these values and electron charge q in Eq. (1), it becomes
q
KT
VV
N
W bD
2921.12
(µm) (2)
and so we can plot the depletion layer width (WD) as a
function of impurity concentration (N) for values
changes from 1014 cm-3 to 1018 cm-3 and for different
values of (Vb – V – 2KT/q) changes from 1 V to 10 V, as
shown in Fig. 2.
Capacitance of the depletion layer of the photo-
diode is given in terms of the depletion layer width as
D
S
D
S
D W
A
W
A
C
, (3)
where A is the diffused junction area. By substituting the
value of εS in Eq. (3), it becomes
D
D W
A
C 368.103 (pF), (4)
where A is measured in mm2. From Fig. 2 the values of
WD varies approximately from 0.03 µm to 12 µm. Thus,
plotting the depletion layer capacitance as a function of
the depletion layer width for different values of A which
changes from 1 mm2 to 20 mm2 with increment of
1 mm2 gives the graph shown in Fig. 3.
Fig. 1. Side view of the photodiode.
Fig. 2. The variation of the depletion layer width as a function
of the impurity concentration at 300 K.
Fig. 3. The variation of the junction capacitance as a function
of the depletion layer width at 300 K.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 4. P. 424-428.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
426
In p-n photodiode the series resistance RS is
considered an important factor of determining its
response time, as it will be demonstrated later. The value
of RS is given as
Cn
DS
S RR
A
WW
R
, (5)
where WS is the substrate thickness which was chosen to
be 100 µm, Rn is the resistance of the n-well region and
RC is the contact resistances. As illustrated in Fig. 1 RC is
composed of Ra and Rc; the anode and cathode
resistances respectively, that is
caC RRR . (6)
Substituting Eq. (6) in Eq. (5) and rearranging it,
we get
K
DS
S R
A
WW
R
, (7)
where canK RRRR . (8)
Because of Ra, Rc and Rn characterize resistances
out of the depletion layer, their values are independent of
the values of first right term of Eq. (7). The resistance Rn
is n-well dimension dependent, so it has a constant
value. Furthermore, the values of both Ra and Rc may be
as possible as minimized during fabrication of the
photodiode, as has been mentioned above. Therefore,
they may be measured experimentally and then added to
the theoretical value of RS as a correction factor. Thus
Eq. (7) is reduced to
K
D
S R
A
W
R
075.0100
(Ohm). (9)
The dependence of RS on WD for different values of
A, which is changed from 1 mm2 to 10 mm2 with RK
about 5 Ohm, is depicted in Fig. 4.
There are three factors defining the response time
of a photodiode: draft time tdrift, diffusion time tdiff and
time constant tRC. The total rise time is determined by:
2
diff
2
drift
22 )()()()( tttt RCr , (10)
where the time constant is given as
))((2.2 SDLSRC CCRRt , (11)
where RL is the load resistance, and CS is the stray
capacitance which can be minimized by using short
leads. Thus, Eq. (11) becomes
DLSRC CRRt )(2.2 . (12)
Substituting Eq. (4) and Eq. (9) in Eq. (12) results
.
075.0100
2274096.0
D
LK
D
RC
W
A
RR
A
W
t
(13)
Fig. 4. The dependence of the series resistance on the depletion
layer width.
The drift time tdrift for silicon is given as
d
D
V
W
t drift , (14)
where Vd is the average drift velocity of the carriers
which is 1·107cm/s for silicon at 300 K. By substituting
this value in Eq. (14), it becomes
m01.0drift DWt (ns). (15)
Figure 5 illustrates the variation of tRC with the
depletion layer width for different values of load
resistance from 10 to 50 Ohm and the diffused junction
area of 5 mm2 as well as the variation of tdrift with the
depletion layer width.
Because the research concerns what happens inside
the depletion layer, the diffusion time (tdiff) is out of our
study. So, plotting 2
drift
2 )()( ttRC has just been
adopted and shown in Fig. 6.
Figure 7 illustrates superposition of the two graphs
of tRC and tdrift to produce the third graph denoted by
2
drift
2 )()( ttRC which is the first two terms of tr in
Eq. (10).
As shown in Fig. 2 the depletion layer width much
decreases with increasing the impurity concentration and
decreasing reverse applied potential and vice versa. That
is because increasing or decreasing of the concentration
of diffusing charge carriers between both sides of the
junction. Of course, the narrowest depletion layer causes
largest capacitance when the area of the diffused layer is
so large, as illustrated in Fig. 3. On the other hand, since
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 4. P. 424-428.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
427
the substrate thickness is always much larger than the
depletion layer thickness, the last one has no longer
effect on the series resistance. Therefore, with minimum
value of the contacts resistance, the series resistance may
be changed few milliohms, as shown in Fig. 4. Thus, the
time constant of the photodiode, which is due to series
resistance and its total capacitance as well as the load
resistance, depends on the depletion layer width. With
small value of the load resistance and small diffused
junction area, the time constant may be minimized by
increasing the depletion layer width due to its effect on
the junction capacitance, as has been stated.
Fig. 5. The variation of tRC and tdrift with the depletion layer
width.
Fig. 6. The variation of 2
drift
2 )()( ttRC with the depletion
layer width.
Fig. 7. The variation of 2
drift
2 )()( ttRC with the depletion
layer width.
In contrast, the drift time increases linearly with the
depletion layer width, because of decreasing the electric
field within it, and intersects the time constant curves, as
illustrated in Fig. 5. So, adding their quadratic values
results in the curves shown in Fig. 6 in which the
minimum value of each curve lies at the same point of
their intersection. That means, the minimum values of
them lie at specific values of the depletion layer width.
Returning to Fig. 7, for RL = 10 Ohm and A =
5 mm2, one can see that the plot of the square root of
quadratic tRC plus quadratic tdrift is a curve starts from the
highest value of tRC corresponding to the minimum value
of the depletion layer width and finishes at the highest
value of tdrift corresponding to the maximum value of the
depletion layer width. Also, its minimum value (0.59 ns)
lies at the intersection of both curves, i.e. at 42.4 µm.
Further, for A = 1 mm2 the minimum value becomes
0.31 ns at depletion layer width of 21.8 µm.
4. Conclusions
Since the junction capacitance of the photodiode is
dependent on the depletion layer thickness, the diffused
junction area and the applied reverse bias, the minimum
value of contribution of both the time constant and the
drift time in rise time, are obtained at specific value of
the depletion layer width which is corresponding to
smaller diffused area, and larger applied reverse bias.
Furthermore, for values less than that value of the
depletion layer the contribution of the time constant
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2009. V. 12, N 4. P. 424-428.
© 2009, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
428
dominates the rise time value whereas the contribution
of the drift time dominates the rise time for values more
than the specific value of the depletion layer. In other
words, it is possible to reach an optimal value of the rise
time by controlling the depletion layer thickness through
the fabrication process of the photodiode.
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