Estimation of frequency characteristics of photodiode determined by motion of charge carriers in the space-charge region
Frequency characteristics of photodiode determined by motion of charge carriers in the space-charge region was estimated. It was shown that the current in the external circuit depends on two functions (their specific kind) of coordinates of the electric field and generation density of photodetector...
Saved in:
| Date: | 2006 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2006
|
| Series: | Semiconductor Physics Quantum Electronics & Optoelectronics |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/121625 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Estimation of frequency characteristics of photodiode determined by motion of charge carriers in the space-charge region / A.I. Danilyuk, Yu.G. Dobrovolskiy // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 3. — С. 40-43. — Бібліогр.: 7 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-121625 |
|---|---|
| record_format |
dspace |
| spelling |
nasplib_isofts_kiev_ua-123456789-1216252025-02-09T16:09:35Z Estimation of frequency characteristics of photodiode determined by motion of charge carriers in the space-charge region Danilyuk, A.I. Dobrovolskiy, Yu.G. Frequency characteristics of photodiode determined by motion of charge carriers in the space-charge region was estimated. It was shown that the current in the external circuit depends on two functions (their specific kind) of coordinates of the electric field and generation density of photodetector current. 2006 Article Estimation of frequency characteristics of photodiode determined by motion of charge carriers in the space-charge region / A.I. Danilyuk, Yu.G. Dobrovolskiy // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 3. — С. 40-43. — Бібліогр.: 7 назв. — англ. 1560-8034 PACS 85.60.Dw https://nasplib.isofts.kiev.ua/handle/123456789/121625 en Semiconductor Physics Quantum Electronics & Optoelectronics application/pdf Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Frequency characteristics of photodiode determined by motion of charge carriers in the space-charge region was estimated. It was shown that the current in the external circuit depends on two functions (their specific kind) of coordinates of the electric field and generation density of photodetector current. |
| format |
Article |
| author |
Danilyuk, A.I. Dobrovolskiy, Yu.G. |
| spellingShingle |
Danilyuk, A.I. Dobrovolskiy, Yu.G. Estimation of frequency characteristics of photodiode determined by motion of charge carriers in the space-charge region Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Danilyuk, A.I. Dobrovolskiy, Yu.G. |
| author_sort |
Danilyuk, A.I. |
| title |
Estimation of frequency characteristics of photodiode determined by motion of charge carriers in the space-charge region |
| title_short |
Estimation of frequency characteristics of photodiode determined by motion of charge carriers in the space-charge region |
| title_full |
Estimation of frequency characteristics of photodiode determined by motion of charge carriers in the space-charge region |
| title_fullStr |
Estimation of frequency characteristics of photodiode determined by motion of charge carriers in the space-charge region |
| title_full_unstemmed |
Estimation of frequency characteristics of photodiode determined by motion of charge carriers in the space-charge region |
| title_sort |
estimation of frequency characteristics of photodiode determined by motion of charge carriers in the space-charge region |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2006 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/121625 |
| citation_txt |
Estimation of frequency characteristics of photodiode determined by motion of charge carriers in the space-charge region / A.I. Danilyuk, Yu.G. Dobrovolskiy // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2006. — Т. 9, № 3. — С. 40-43. — Бібліогр.: 7 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT danilyukai estimationoffrequencycharacteristicsofphotodiodedeterminedbymotionofchargecarriersinthespacechargeregion AT dobrovolskiyyug estimationoffrequencycharacteristicsofphotodiodedeterminedbymotionofchargecarriersinthespacechargeregion |
| first_indexed |
2025-11-27T20:04:35Z |
| last_indexed |
2025-11-27T20:04:35Z |
| _version_ |
1849975254912335872 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 3. P. 40-43.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
40
PACS 85.60.Dw
Estimation of frequency characteristics of photodiode determined
by motion of charge carriers in the space-charge region
A.I. Danilyuk, Yu.G. Dobrovolskiy
Tensor ltd, 226, Chervonoarmiyska str., 58013 Chernivtsi, Ukraine
E-mail: chtenz@chv.ukrpack.net
Abstract. Frequency characteristics of photodiode determined by motion of charge
carriers in the space-charge region was estimated. It was shown that the current in the
external circuit depends on two functions (their specific kind) of coordinates of the
electric field and generation density of photodetector current.
Keywords: frequency characteristics, photodetector, charge carrier, space-charge region.
Manuscript received 17.03.06; accepted for publication 23.10.06.
1. Introduction
Characteristics of each photodiode, as a basic structure
of photodetector, in the general case are determined by
construction of photodiode. In particular, these are
characteristics of the used material, configuration of
electric fields, mobilities of charge carriers, width of the
space-charge region (SCR). In addition, characteristics
of photodiode are determined by the external applied
voltage and wave length of the used optical radiation. In
the case of its absorption, only in its SCR and at
negligibly small distances around it, for example, in a
p-i-n photodiode, frequency characteristics are deter-
mined, mainly, by the time-of-flight of the generated
charge carriers through the SCR [1-4].
As the frequency characteristics of photodiode are
one of basic, determining quality and possibilities of
every specific photodiode, the task to exactly estimate
these characteristics becomes actual for the modern
electronic technique, in particular, for constructing the
semiconductor photodiodes.
In [1, 5], the problem of kinetics of the photodiode
response related to the flight of charge carriers through
SCR was considered. However, this consideration has
not enough deep character, what does not allow to use its
results for engineering computations when constructing
the high-frequency photodiodes. In [6], considered were
the dependence of photodiode output signal and its
frequency characteristics on the input resistance and
capacity of preamplifier. This research and that of the
influence of explosive noise on the parameters of a
photodiode performed in [7] cover the specific questions
related to constructing the photodiode.
2. General case of drift of charge carriers inside the
semiconductor crystal in the electric field of SCR
We will consider a few extreme cases, when frequency
characteristics are determined by only the time-of-flight
of charge carriers through the SCR. For simplicity of
consideration, we will consider a “flat” SCR, in which
the vector of the electric field is directed along the axis
хr , i.e., the case of the “flat electric field” shown in the
figure.
xx EixEzyxE
rrrrrr
=≡ )(),,( , (1.1)
Ey = Ez = 0, (1.2)
where Ех, Ey,, Ez are the components of the electric field
vector; zyx rrr ,, are the basis vectors (axes) of the chosen
rectangular (Cartesian) co-ordinates in a three-
dimensional space; i
r
is the unit vector directed along
the axis хr .
Let one (initial) boundary of SCR coincides with
the coordinate plane { }zу rr, , and the second (final) one –
with the plane parallel to it passing through a point with
the coordinate х = х0. The accepted terms are allowed,
not violating community of consideration on the whole,
to consider a motion of charge carriers only along the
axis хr . We will choose inside the SCR two elementary
layers as flat regions parallel to the SCR scope with the
thicknesses of d x and d x' and passing in the vicinity of
points with the x' and x coordinates, respectively. Let the
charge carriers generates in the first layer with the
coordinate x'. We will consider the being found in the
second layer drifting in the field SCR charge of dx q ,
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 3. P. 40-43.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
41
xr
zr
dx
0 x′ x x0 xr
dx′
Model of “flat” SCR for estimation of frequency characte-
ristics of photodiode.
obtained by the generation on a unit area in the first
layer as responce to radiation falling onto the photodiode
crystal.
The drift velocity of this charge is equal to that of
components of its charge carriers:
xxx Ev μ
rr
= (1.3)
where xE
r
is the electric field in a point with the
coordinate х; xμ is the mobility of the considered
charge carrier in a point with the coordinate х.
We also consider that the electric field is
comparatively small, and it is possible to ignore the
mobility dependence on the electric field:
xμ = 0μ = const (x, y, z), (1.4)
where: xμ = (1.5)
and the sign “minus“ points to the direction of motion of
electrons in the electric field. When the dx q charge
moves inside the SCR, the electric current dx I = vx dx q
flows in the external circuit. From the law of energy
conservation, it is possible to write down:
xxxxx vFdvFdPd ⋅=⋅=
rr
, (1.6)
where Pdx is the power expended by the power source
on motion of the dx q charge; Fd x
r
is the force affecting
the charge in electric field.
Thus, the work (1.6) is the scalar product of the
parallel vectors of the force and velocity: vF rr
↑↑ .
We note that
Pd x = IdU x0 , (1.7)
where U0 is the external applied to SCR voltage equal to
the difference of potentials on the SCR scope,
Fd x
r
= xxdE qr , (1.8)
dt
xd
dt
xdivx
rrr
== , (1.9)
dt
xdvx
r
r
= , (1.10)
as well as the charge carriers from the first layer into the
second one (come behind the time) equal to the time of
motion of charge carriers between the layers on the area
xΔ = ( )0xx −′ that is:
)()( ttqdtqd xx ′−′= , (1.11)
where
0
''''
≥==′ ∫ ∫
′ ′
x
x
x
x xxE
xd
v
xdt
μ
r
r
r
r
(1.12)
is the time of the charge motion from the x′ point to the
x ′′ one in the considered time point t. Then, Eq. (1.7) can
be written down as follows:
xxxxxx vEqdvFdIdU rrrr
⋅⋅=⋅=0
or
)()()()(0 tvtEttqdtIdU xxxx
rr
⋅′−′= . (1.13)
The charge )( ttqd x ′−′ is created when absorption
of radiation by the charge carriers takes place, that is
why
)()( 0 ttNdettqd xx ′−′=′−′ , (1.14)
where 0e is the charge of one carrier of the considered
type with its sign; )( ttNd x ′−′ is the quantity of the
electron-hole pairs given rise by the absorbed radiation
in the first layer in the time domain ( )dttttt +′−′− ; .
It is obvious that
ν
νν
νγ
ν
ddtxd
x
tt
h
ttNd x ⋅⋅′⋅
∂′∂
′−Φ∂
⋅=′−′ ∫
)()()(
2
1
, (1.15)
where )(νγ is the quantum yield on the set wavelength;
νh is the energy of one absorbed quantum;
dt
x
tt
⋅
∂′∂
′−Φ∂
ν
)(2
is the energy in the single range of the
wave taken in the first layer in the time of dt; )( tt ′−Φ
is the flux of the radiation absorbed in a crystal.
For convenience of calculation, we will take sine
similar modulation of radiation for a basis, that is:
,~)( Φ+Φ=Φ t )const(t=Φ , tωsin~
0Φ=Φ , where
Φ is the unvariable (including background) component
of the absorbed flux; Φ~ is the variable component of the
flux; 0Φ is an amplitude of the variable component in
xμ for holes,
nμ− for electrons,
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 3. P. 40-43.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
42
the absorbed flux; ωt = 2πf is the modulation frequency
of the photoelectric signal (current).
Then, it is possible to write down Eq. (1.14) as
follows:
dtxddt
hx
eqd x ′⋅Φ+Φ
∂
∂
⋅
′∂
∂
⋅=′ ∫ νω
νν
νγ
ν
)sin()(
00
1
(1.16)
and after rearrangements to derive
,~
sin
0
00
qdqd
dtxdtI
x
qdqd
xx
xx
′+′=
=⋅′⋅⋅
′∂
∂
+′=′ ω
(1.17)
where ν
νν
νγ
d
h
e
I
∂
Φ∂
= ∫ 00
0
)(
is the effective (internal)
amplitude of variable by the component of the generated
photocurrent; )(сonst0 tqd x =′ .
As the invariable component can be dropped
without sacrificing the community of consideration
when estimating the frequency properties of the
photodetector, further we will consider only the variable
component, therefore:
dtIdxddttI
x
qd xx ⋅′=′⋅⋅⋅
′∂
∂
=′ ωsin~
0 , (1.18)
×⋅⋅=′ )()(
0
xvxE
U
1Idd xxxx
rr
=′⋅⋅′−⋅
′∂
∂
× xddtttI
x
)(sin0 ω (1.19)
xdI
x
ttdtxvxE
U
1
xx ′⋅
′∂
∂
⋅′−⋅⋅⋅⋅= 0
0
)(sin)()( ω .
Signs of the vectors in (1.19) vanish due to a
parallel xxx veEF rrr
↑↑⋅= 0 , that is scalar product
xxxx veEveE ⋅⋅=⋅⋅ 00
rr
. Taking (1.10) into account,
.
)(sin)(
0
0
IddxdI
x
ttxdxE
U
1Idd
xx
xxx
′=′⋅
′∂
∂
×
×′−⋅⋅⋅=′ ω
(1.20)
Also it is obvious that
∫=
0
0
0
x
x xdEU . (1.21)
In the general case, within the framework of the
assumptions accepted by us in relation to the type of
modulation of the photoelectric signal, the increase of
current in an external circuit (current of photoelectric
signal) can be presented as follows:
.)
)(
(sin
)(
)(
'
0
0
0
∫
∫
⋅′⋅
′∂
∂
⋅−×
×′
x
x x
''
x
x
x
xx
xdxd
x
I
xE
xdt
xdxE
xE
I= dd
'' μ
ω r
r
(1.22)
Here, the current in the external circuit depends on
two functions of coordinates of the electric field and
generation density of current of photoelectric signal, and
this current value depends on the specific type of these
functions.
By the extreme cases being of practical interest for
us, there are the cases:
• even strength of the electric field Ex = E0 = const;
• even density of the volume charge
0εε
enEx =∇ ;
• local, including superficial, generations of current
of the photoelectric signal )( 00
0 xI
x
I δ=
′∂
∂ , where ( )0xδ
is an ordinary delta function;
• even on the volume of current generation of the
photoelectric signal
0
00
x
I
x
I
=
′∂
∂ .
Four rearranged functions give four combinations
inherent to four really possible situations. Simplicity of
the derived expressions make them very comfortable for
computations when constructing the photodiodes, and
generality of the used presentations provides the high
calculation accuracy, confirmed by the subsequent
measurements of parameters.
3. Conclusions
It was shown that the current in the external circuit
depends on two functions (their specific kind) of
coordinates of the electric field and generation density of
current of photoelectric signal, fully determined by total
parameters of material of photodetector and absorbed
radiation.
Simplicity, generality and accuracy of the obtained
expressions make them suitable for the use to calculate
and construct new photodiodes.
References
1. S.M. Sze, Physics of semiconductor devices, vol. 2.
Mir, Moscow, 1984 (in Russian).
2. V.P. Astakhov, D.A. Gindin, V.V. Karpov,
K.V. Sorokin, About influence of resistance of
surface channel on dark current of quadrant p-i-n
photodiodes on silicon // Prikladnaya fizika No 2,
p. 79-85 (1999) (in Russian).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2006. V. 9, N 3. P. 40-43.
© 2006, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
43
3. Yu.R. Nosov, Photodetectors in optoelectronics //
Electronnaya tekhnika, ser. 2, 4(183), p. 33-36
(1986) (in Russian).
4. A.A. Ashcheulov, V.M. Godovanjuk, Yu.G. Dob-
rovolsky et al., Silicon p-i-n photodiode with little
value of dark current // Proc. SPIE 3890, р. 119-
124 (1999).
5. V.M. Yurgenman, M.A. Trishenkov, Photodiode
response kinetics in carrier transit through the
space-charge region // Radiotekhnika i elektronika
ХХІІ, issue 6, p. 1028 (1977) (in Russian).
6. V.M. Hodovaniouk, I.V. Doktorovych, V.K. Bu-
tenko, V.H. Yuryev, Yu.G. Dobrovolsky, Silicon
photodiode and preamplifier operation charac-
teristic properties under background radiation
conditions // Semiconductor Physics, Quantum
Electronics and Optoelectronics 8(1), p. 83-86
(2005).
7. Yu.G. Dobrovolsky, Explosion noise of silicon
photodiodes // Fizika i khimiya tverdogo tela 6(2),
p. 307-310 (2005) (in Russian).
|