The simple approach to determination of active diffused phosphorus density in silicon
The diffusion of Phosphorus in silicon using a POCl₃ source has been considered. In the base of Fair-Tsai model of P-diffusion an empirical equation for calculation of active diffused phosphorus density (Qel), is proposed. In this equation, a relationship between (Qel), diffusion time, temperature a...
Збережено в:
| Дата: | 2004 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2004
|
| Назва видання: | Semiconductor Physics Quantum Electronics & Optoelectronics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/118109 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The simple approach to determination of active diffused phosphorus density in silicon / M. Sasani // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 1. — С. 22-25. — Бібліогр.: 20 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-118109 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1181092017-05-29T03:05:22Z The simple approach to determination of active diffused phosphorus density in silicon Sasani, M. The diffusion of Phosphorus in silicon using a POCl₃ source has been considered. In the base of Fair-Tsai model of P-diffusion an empirical equation for calculation of active diffused phosphorus density (Qel), is proposed. In this equation, a relationship between (Qel), diffusion time, temperature and junction depth of P-diffused layer (Xj), is presented. The value of sheet resistance (Rs), which is taken from theoretical determination at 900°C, has a good agreement with experimental result. 2004 Article The simple approach to determination of active diffused phosphorus density in silicon / M. Sasani // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 1. — С. 22-25. — Бібліогр.: 20 назв. — англ. 1560-8034 PACS: 61.72.Tt, 66.30.Lw http://dspace.nbuv.gov.ua/handle/123456789/118109 en Semiconductor Physics Quantum Electronics & Optoelectronics 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 |
The diffusion of Phosphorus in silicon using a POCl₃ source has been considered. In the base of Fair-Tsai model of P-diffusion an empirical equation for calculation of active diffused phosphorus density (Qel), is proposed. In this equation, a relationship between (Qel), diffusion time, temperature and junction depth of P-diffused layer (Xj), is presented. The value of sheet resistance (Rs), which is taken from theoretical determination at 900°C, has a good agreement with experimental result. |
| format |
Article |
| author |
Sasani, M. |
| spellingShingle |
Sasani, M. The simple approach to determination of active diffused phosphorus density in silicon Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Sasani, M. |
| author_sort |
Sasani, M. |
| title |
The simple approach to determination of active diffused phosphorus density in silicon |
| title_short |
The simple approach to determination of active diffused phosphorus density in silicon |
| title_full |
The simple approach to determination of active diffused phosphorus density in silicon |
| title_fullStr |
The simple approach to determination of active diffused phosphorus density in silicon |
| title_full_unstemmed |
The simple approach to determination of active diffused phosphorus density in silicon |
| title_sort |
simple approach to determination of active diffused phosphorus density in silicon |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2004 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118109 |
| citation_txt |
The simple approach to determination of active diffused phosphorus density in silicon / M. Sasani // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 1. — С. 22-25. — Бібліогр.: 20 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT sasanim thesimpleapproachtodeterminationofactivediffusedphosphorusdensityinsilicon AT sasanim simpleapproachtodeterminationofactivediffusedphosphorusdensityinsilicon |
| first_indexed |
2025-07-08T13:22:50Z |
| last_indexed |
2025-07-08T13:22:50Z |
| _version_ |
1837085199141175296 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics. 2004. V. 7, N 1. P. 22-25.
© 2004, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine22
PACS: 61.72.Tt, 66.30.Lw
The simple approach to determination
of active diffused phosphorus density in silicon
M. Sasani
Solid State Laser Division, Laser Research Center, AEOI, 11365-8486, Tehran, Iran
E-mail: msasani@aeoi.org.ir
Abstract. The diffusion of Phosphorus in silicon using a POCl3 source has been considered. In
the base of Fair-Tsai model of P-diffusion an empirical equation for calculation of active
diffused phosphorus density (Qel), is proposed. In this equation, a relationship between (Qel),
diffusion time, temperature and junction depth of P-diffused layer (Xj), is presented. The
value of sheet resistance (Rs), which is taken from theoretical determination at 900°C, has a
good agreement with experimental result.
Keywords: phosphorus, silicon, diffusion, sheet resistance.
Paper received 11.11.03; accepted for publication 30.03.04.
1. Introduction
Research on dopant diffusion in crystalline silicon has
provided a wealth of detailed including atomistic diffu-
sion models as well as the influence of various process
conditions in the fabrication of integrated circuits. Never-
theless, dopant distribution in new device technology can
hardly be predicted without going through several cycles
of short loop technology experiments to calibrate the dif-
fusion models used for technology computer aided de-
sign [1]. This talk addresses the question of how research
on physical models can support process simulation to
reach the goal of replacing costly experiments in the de-
velopment of new technologies. Diffusion of phosphorus,
is one of the important steps, which is used in silicon
based MEMS technology. Therefore, the presentation of
a simple equation for determination of active diffused
phosphorus density and prediction of depth junction can
be useful in silicon based MEMS technology [2].
In practice, it is shown that at high concentration, the
diffusion of phosphorus (P), into silicon (Si), produces an
impurity atom distribution, which considerably differs
from the standard profile of diffusion theory [3�7]. In
order to explain the anomalous diffusion of phosphorus
pair different models have been developed. In the first
model or Fair-Tsai model, only one type of dopant-de-
fect pair namely, the dopant-vacancy pairs have been
considered [8]. Hu [9], has shown that in order to simu-
late high concentration phosphorus diffusion both dopant
interstitial and dopant vacancy pair have to be included.
The number of coupled differential equations and the
unknown parameters were still acceptable. However, in
his model no electrical charge states of species have been
taken into consideration. In the next model suggested by
Richardson and Mulvaney [10], the different charge
states of each species have also been included. This model
comprises a relatively large number of coupled differen-
tial equations, as they write one equation for each charge
state of species. Moreover, the number of unknown pa-
rameters increases rapidly with the number of consid-
ered charge state of the defects in these models. Budil
[11], has defined the total concentration for each species
as the sum of the concentrations of charged species and
the neutral one. Assuming local equilibrium for electronic
processes, he derived a pair diffusion model with only on
equation per species, considering all possible charge and
average diffusivities. In this model, however, not all-pos-
sible reactions between point defects and dopant defect
pairs have been considered. Baccus [12], has suggested a
general pair diffusion model. However, in his model there
is still a huge number of unknown parameters. Dunham
[13,14], has introduced another model with using some
of the assumptions of Baccus. In the model proposed by
Dunham, the number of parameters is reduced but the
special case of intrinsic concentrations is not automati-
cally considered. Ghaderi [15], has reduced same pa-
M. Sasani: The simple approach to determination of active diffused ...
23SQO, 7(1), 2004
rameters of Dunham s model and presented another model
for diffusion of phosphorus in silicon. But, there are sev-
eral complicate equations and unknown parameters in
all of these models. Therefore, the determination of ac-
tive diffused dopant and depth of junction as two impor-
tant parameters for evaluation of diffusion process, are
difficult. The goal of the present work is, to introduce a
simple equation for determination of active diffused phos-
phorus density (Qel), in perdeposition. According to that
equitation, the junction depth and sheet resistance has
been calculated.
2. Theory
Numerous models have been proposed to explain the
anomalous deviation from simple diffusion theory of dif-
fused phosphorus in silicon. Fair and Tsai [8], have sug-
gested a model for this purpose and have concluded that
the distribution of phosphorus in silicon during predepo-
sition has a profile, which is shown in Fig. 1. The experi-
mental results of dopant profile show that the best model
for prediction of phosphorus distribution in silicon dur-
ing predeposition process is Fair-Tsai model. According
to that model the profile of dopant distribution can be
divided into two parts, one associated with total doping
per square centimeter, Qst, and the concentration level in
this region is almost approximately constant. In the sec-
ond part that is associated with a tail region, the total
doping per square centimeter is Qtail. The Qel is sum of the
two total dopant concentrations in diffusion region (Qst
+Qtail). Also the junction depth of P-diffused layer in sili-
con is introduced as Xj. At that case, the criteria for evalu-
ation of diffusion process is determination of sheet resist-
ance (Rs). According to Fair-Tsai model the relationship
between Rs and Qel is as follows:
)108.175(
1
20
jel
s
XQq
R
××+×
= (Ω⋅cm�2) (1)
Therefore, in the Fair-Tsai model for determination
of (Rs), we need to calculate Qel. Fair [16], have also
suggested that Qel and Xj can be calculated from two fol-
lowing equations:
×+= −
K
B
tailj
c
c
erfctDXX 1
0 2 (cm) (2)
2
2
3
cm
3.0
exp1
2
1
2
−−
=
+×+
+
××=
KT
ev
D
n
nD
n
t
nQ
i
i
si
i
sel
(3)
where
+
×
+
−=
−
KT
ev
nn
nD
KT
ev
D
ie
si
tail
3.0
exp1
66.3
exp85.3
2
3
,
−
=
=
KT
ev
Di
37.4
exp2.44 and
−
=−
KT
ev
Di
4
exp44.4 (cm2s�1).
In Eq. 2, X0 is depth of the first region and (t) is the
diffusion time in terms of second and K is the Boltzman
constant. Also cB is the initial concentration of dopant in
the silicon before perdeposition and ck is the concentra-
tion of P at the kink in the diffusion profile (Fig. 1). In the
Eq. 3 ns is the surface concentration that can be obtained
from Fig. 2. Here ni is the intrinsic concentration that
can be determined from [17]:
Total phosphorus concentration
Electrically active phosphorus
Excess vacancy
concentration
Base-push
effect
Depth
L
o
g
c
o
n
c
e
n
tr
a
ti
o
n
KINK
TAIL
P V Dissociation
P V P + V + 2e
+
+ +
=
= x
J J≅
C � n = C
J J≅ P
T
PP
P
PV
V
V
+
+
+=
=
x
C
n
T
C n � T
Fig. 1. Phosphorus diffusion model based upon the work of Fair-
Tsai [8].
Fig. 2. Amount of inactive dopant for common dopants, solid
lines are solid solubility; dashed lines are limits of electrically
active dopant concentration.
900
10
10
20
21
1000
Tem peratu re , °CT
Im
pu
ri
ty
c
on
ce
nt
ra
tio
n
, c
m
N
1100 1200
–3
A s
P
B
B
S olu b ility l im it
E lec tr ica lly a c t iv e
A s
P
+
–
+
24
SQO, 7(1), 2004
M. Sasani: The simple approach to determination of active diffused ...
−×=
T
ni
5420
exp1017.5 20 (cm�1) (4)
Tsai [18] has proposed the equation for determina-
tion of X0. But X0 obtained from his research has some
discrepancy with experimental results. Our study has
shown this uncertainty could be compensated using the
equation given below:
t0 ×=αX (cm) (5)
where )
eV12.2
exp(057.6
TkB
−
=α
However, Fair and Tsai have presented some simpli-
fier hypotheses for providing of above equations, the cal-
culation of the sheet resistance and active diffused phos-
phorus density using Eqs 1 and 3 are difficult. Therefore,
it will be favorable to find a simple way for calculation of
Qel. In order to drive a suitable equation for Qel, we should
consider the variation of sheet resistance with respect to
diffusion time and temperature. The well-known experi-
mentally approved equation for Rs in planar silicon tech-
nology is as follows:
t
e
RR
T
a
sos = (Ω⋅cm�2) (6)
where Rso and a are two constants. In that equation, Rs is
inversely proportional to t1/2. Thus, the Qel, must be func-
tion of t1/2. On the other hand, and in the base of data
analysis process, the relationship between sheet resist-
ance and diffusion time can be shown with a mathemati-
cal function such as f (Rc)= 1)]ln([ −× ct .
According to that function, we need to define the vari-
able of lnc in terms of sheet resistance behavior for dif-
fused phosphorus in silicon, and providing an equation
for calculating the Qel. For this reason, different works
for obtaining that goal have been carried out, and it was
found that Qel can be calculated by:
( )tXtBQ jel α−−= ln (7)
where B is a constant for given temperature and t is time
(in seconds). The Xj can be given from Eq. 2. Qel for se-
veral different diffusion temperatures and times have been
calculated by using Eqs 3 and 7 and compared with ex-
perimental results given in Table 1.
3. Experiment
In order to evaluate the precision of Eq. 7, we have to
predict the sheet resistance and diffusion depth of dif-
fused layer by that equation and compare with experi-
mental results. The experiment of phosphorus diffusion
process has been carried out in Centrotherm open tube
furnace. The silicon wafers, which have been used in the
process, were P-type with 1017 atom/cm2 impurity con-
centration. For P-source, we have used POCl3 prepared
by purging of 50cc/min N2 gas bubblier. Preheating and
postheating times were 10 minutes. The sheet resistance
of diffusion region has been measured by four-point probe
technique. The variation of sheet resistance via diffusion
time was illustrated in Fig. 3. The experimental results
of sheet resistance measuring and calculation of that pa-
rameter with Eq. 7 are in good accordance. The com-
parison of the sheet resistance calculated with two differ-
ent equations 3 and 7 have been presented in Table 2.
Table 1. The variation of Qel with time in the base of two diffe-
rent Eqs 3 and 7.
Time X0, (cm) Xj, (cm) Qel Qel
(min) Eq. (7) Eq. (3)
15 4.124⋅10�6 3.76⋅10�5 1.84⋅1015 3⋅1015
30 8.388⋅10�6 5.72⋅10�5 2.517⋅1015 4.24⋅1015
60 16.78⋅10�6 8.58⋅10�5 3.436⋅1015 6.02⋅1015
T = 900°C, α = 4.67⋅10�9, ni = 5.1⋅1018, ne = 9.83⋅1019,
cB = 1⋅1017, ns = 3⋅1020, ck = 1023exp(�0.79eV/KT)
Table 2. The comparison of the sheet resistances calculated us-
ing two different Eqs 3 and 7.
Time Rs Rs Rs
(min) Eq. (3) Eq. (7) Ref. [19]
15 20.38 33.94 34
30 14.67 24.65 24.15
45 12.02 20.5 19.91
60 10.38 17.69 17.2
Fig. 3. Sheet resistance vs. diffusion time with POCl3 source.
10
15
20
25
30
20 30
T im e, m in
R
,
O
hm
/c
m
40 50 60
s
2
M. Sasani: The simple approach to determination of active diffused ...
25SQO, 7(1), 2004
4. Conclusions
Sheet resistance is being accepted as a criteria for diffu-
sion control during semiconductor device fabrication, and
it has an inversely proportional to active diffused phos-
phorus density (Qel) and junction depth (Xj). In this work,
we first presented a mathematical function (Eq. 7) for
prediction of the experimental results and parameters
included to this equation. Experimental results have
shown that Qel obtained form Eq. 7 is longer than previ-
ously proposed by the formula (equation (3) of the ref.
[16]). Hence, our equation for calculation of Qel in its
turn produces a bigger Rs, which is in better agreement
with the experimental data, including our experimental
measurements at 900°C at the diffusiion time and those
of [19, 20].
References
1. C.I. Pakes, et.al., Technology computer-aided design
modeling of single atom doping for fabrication of buried
nanostructured // Nanotechnology, 14, p. 157 (2003).
2. J. W. Judy, Microelectromechanical systems (MEMS): fab-
rication, design, and applications // Smart Mater. Struct.,
10, p. 1115 (2001).
3. S.T. Dunham, Alp H. Gencer, S. Chakravarthi // Modeling
of dopant diffusion in silicon // IEICE Trans. Electron, E82C,
p. 800 (1999).
4. D.J. Fisher, Diffusion in Silicon: 10 years of Research // Scitec
Publications Ltd., p. 159 (1998).
5. M. Yoshidal, E. Aria, Impurity diffusion in silicon based on
the pair diffusion model and decrease in quasi-vacancy for-
mation energy. Part one: Phosphorus // J. Appl. Phys., 34, p.
5891 (1995).
6. E. Antonicik, The influence of the solubility limit on diffusion
phosphorus and arsenic into silicon // Appl. Phys. A, 58, p. 117
(1994).
7. D. Mathiot, S. Martin, Modeling of dopant diffusion in sili-
con: an effective diffusivity approach including point defect
coupling // J. Appl. Phys., 70, p. 3071 (1991).
8. R.B. Fair, J.C.C. Tsai, A quantitative model for the diffusion
in silicon and the emitter dip effect // J. Electroch. Soc., 124,
p. 1107 (1977).
9. S.M. Hu, P. Fahey, R.W. Dutton, On models of phosphorus
diffusion in silicon // J. Appl. Phys., 54, p. 6912 (1983).
10. B.J. Mulvaney, W.B. Richardson, The effect of concentra-
tion-dependent defect recombination reaction on phospho-
rus diffusion in silicon // J. Appl. Phys., 67, p. 3197 (1990).
11. M. Budil, et.al., A new model of anomalous phosphorus dif-
fusion in silicon // Materials Science Forum, 38-41, p. 719
(1989).
12. B.Buccus, et.al., A study of nonequilibrium diffusion modeling
applications tom rapid thermal annealing and advanced bi-
polar technology // IEEE, Trans., Electron Dev., ED-39, p. 648
(1992).
13. S.T. Dunhan, A quantitative model for coupled diffusion of
phosphorus and point defects in silicon // J. Electroch. Soc.,
139, p. 2628 (1992).
14. F. Wittel, S.T. Dunham, Diffusion of phosphorus in Arsenic
and Boron Doped Silicon // Appl. Phys. Lett., 66, p. 1415
(1994).
15. K. Ghaderi, G. Hobler, Simulation of phosphorus diffusion in
silicon using a pair diffusion model with a reduced number
of parameters // J. Electroch. Soc., 142, p. 1654 (1995).
16. R.B. Fair, Analysis of phosphorus diffusion layers in silicon /
/ J. Electroch. Soc., 125, p. 323 (1978).
17. S. Middleman, Arthur K. Hochb, (Eds), Process engineering
analysis in semiconductor device fabrication. McGraw-Hill,
1993, p. 350.
18. J.C.C. Tsai, Shallow diffusion of phosphorus in silicon // IEEE,
Proceeding, 57, p. 1499 (1969).
19. W.E. Beadle, J.C.C. Tsai, R.D. Plummer(Eds), Quick refer-
ence manual for silicon integrated circuit technology. John-
Wiley & Sons, 1985.
20. J.D. Plummer, Peter B. Griffin, Michael D. Deal, Silicon
VLSI technology fundamental, practice, and modeling.
Prentice-Hall Inc., 2000.
|