APPLIED PHYSICS LETTERS 96, 162105 共2010兲
Modeling of porous silicon junction field effect transistor gas sensors:
Insight into NO2 interaction
G. Barillaro,a兲 G. M. Lazzerini, and L. M. Strambini
Dipartimento di Ingegneria dell’Informazione: Elettronica, Informatica, Telecomunicazioni, Università
di Pisa, Via G. Caruso 16, 56122 Pisa, Italy
共Received 27 November 2009; accepted 23 March 2010; published online 20 April 2010兲
In this paper a lumped parameter electrical model for porous silicon junction field effect transistor
共PSJFET兲 gas sensors is presented and experimentally validated. The PSJFET is an integrated
p-channel JFET device modified with a porous silicon layer, the latter acting as sensing element.
The model is described by using an analytical closed-form expression, which quantitatively links the
sensor current to the analyte concentration in the environment, and validated by using experimental
data of PSJFETs exposed to both synthetic air and NO2 with concentration of 300 ppb. Best fitting
of experimental data with the proposed model allows one to get quantitative information on the
effect of NO2 adsorption/desorption at the PS surface on electrical PS parameters, such as its
conductance and surface charge density. © 2010 American Institute of Physics.
关doi:10.1063/1.3391620兴
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Si-
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IPS
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0003-6951/2010/96共16兲/162105/3/$30.00
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Author to whom correspondence should be addressed. Electronic mail:
g.barillaro@iet.unipi.it. Tel.: ⫹39 050 2217601. FAX: ⫹39 050 2217 522.
x2
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and/or activation of the originally present boron impurities
by NO2 molecules or NO2− radicals have been proposed.
Both conductance and free-hole concentration measurements
on PS layers exposed to NO2 have been carried out to corroborate such mechanisms. However, neither direct/indirect
measurements of the PS surface charge density nor its variation upon NO2 exposure have been reported so far.
In this paper we propose an electrical model for the
PSJFET that enables a deeper understanding of chemical/
physical mechanisms regulating the sensor operation and allows gaining insight into interaction between NO2 and PS.
The PSJFET is an integrated p-channel JFET exploiting a PS
floating gate integrated on top of the p-channel to control the
JFET current upon adsorption/desorption of analytes in/from
the PS layer itself. A schematic cross-section of the PSJFET
is reported in Fig. 1共a兲, together with its lumped parameter
model 关Fig. 1共b兲兴. The n-type material has a doping density
of 1 ⫻ 1015 cm−3; the p-type material has surface doping
density NA of 1 ⫻ 1017 cm−3 which reduces to 7
⫻ 1014 cm−3 共and remains constant兲 over a depth of 0.8 ␮m.
The metallurgical junction between p- and n-type silicon is
located at 2.4 ␮m from the top.
In Fig. 1共a兲 the occurrence of two depletion regions x1
and x2 at the PS/ p-Si interface and pn junction,
S
The past decade has been characterized by a high degree
of technological advance in the field of gas sensors. Old
关e.g., polymers, metal oxides, porous silicon 共PS兲兴 and new
共e.g., carbon nanotubes兲 materials have been used for the
development of standard 共e.g., resistive, capacitive兲 and innovative 关mostly field effect transistor 共FET兲-like兴 sensors,
able to detect a number of volatile and hazardous compounds
共e.g., CO, CO2, NO2兲.1,2 Miniaturized complementary metaloxide semiconductor 共CMOS兲 gas sensing platforms, combining both sensing and electronic features on the same chip,
have been fabricated and tested.3,4 However, the basic understanding of chemical/physical mechanisms regulating gas
sensor operation has not experienced a similar progress, as
indicated, for instance, by the small number of papers on
sensor modeling.5,6 The lack of reliable quantitative models
prevents sensors from both performance simulation and optimization, and represents a bottleneck toward commercial
production and applications.
PS has been recently gaining increasing attention as
sensing material because of 共i兲 its huge surface-to-volume
ratio; 共ii兲 the high chemical reactivity of its surface at room
temperature; 共ii兲 the possibility of modifying its surface
chemistry with specific molecules;7 共iv兲 its compatibility
with the CMOS silicon technology.4 For instance, PS is particularly attracting for NO2 detection at sub-ppm levels,
which is addressed as one of environmental chief pollutants
by the European Environment Agency. As an example, the
PS junction FET 共PSJFET兲 is a CMOS-compatible integrated
FET-like sensor able to detect NO2 at concentrations of 100
ppb at room temperature.8
Despite the number of publications on PS-based
sensors,9,10 the interaction mechanism of NO2 with PS is still
in debate.11,12 According to the literature, NO2 molecules act
as strong acceptors at PS surface. As a consequence, hole
concentration increases after adsorption of NO2 molecules
on PS. Doping of PS by adsorbed NO2 molecules through
formation of NO2− radicals and generation of free holes,
S
x1
TE
GA
Di
Si
G
IDS
RD
IPSJFET
D
(b)
FIG. 1. 共Color online兲 共a兲 Sketch of the PSJFET sensor, consisting of a
p-channel JFET device with a mesostructured PS sensing layer on top of the
p-channel itself. The occurrence of two depletion regions, at the PS/ p-Si
interface and pn junction, extending into the p-channel is highlighted. 共b兲
Lumped parameter model of the PSJFET, taking into account both the surface charge variation and the conductance variation in the PS layer upon
molecules adsorption in PS.
96, 162105-1
© 2010 American Institute of Physics
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162105-2
Appl. Phys. Lett. 96, 162105 共2010兲
Barillaro, Lazzerini, and Strambini
x
Si
y
+ ++ ++ + + ++ ++ +
p
x1(y)
x2(y)
PS
Di
are the depletion region heights in the p-channel at the
PS/p-Si interface and pn junction, respectively, and W is the
width of the p-channel. Under the approximation of linear
graded pn junction, x2共y兲 at a distance y from the source
terminal can be expressed as a function of the channel voltage V共y兲:
n
x2关V共y兲兴 = k2关Vbi + VG − V共y兲兴1/3 ,
G
FIG. 2. 共Color online兲 Schematic cross-section of the PSJFET active region
共right underneath the PS layer兲 used to model the effect induced on the
p-channel JFET structure by the surface charge in the PS layer.
respectively, extending into the p-channel is highlighted. Actually, PS has a positive surface charge 共mostly due to adsorbed water11兲 which accounts for the presence of the depletion region x1 at the PS/ p-channel interface. Adsorption/
desorption of analytes 共e.g., NO2兲 on the PS surface modifies
such charge dependently on the analyte type and concentration in the environment. As a consequence, the width of the
depletion region in the p-channel underneath the PS also
changes, thus modulating the actual p-channel section and, in
turn, the JFET current with the analyte concentration. On the
other hand, the gate voltage can be used to change the depletion region width x2 at the pn junction, under reverse polarization, and, in turn, the actual p-channel section and JFET
current independently of the analyte type and concentration,
thus increasing the sensor flexibility. It must be highlighted
that adsorption/desorption of analytes on/from the PS surface
also affects the PS conductance and, in turn, the sensor current, as well known in the literature,11,12 in addition to the
surface charge variation effect. Surface charge and conductance variations are expected to dominate the PSJFET behavior at lower and higher concentrations, respectively. The
lumped parameter model of Fig. 1共b兲 takes into account both
these two effects, i.e., surface charge and conductance variation in the PS layer, under the assumption that they give rise
to independent contributes to the sensor current. The former
was modeled with a JFET device having a PS charged layer
on top of the conduction channel; the latter by means of a
variable resistance RPS operating in parallel to such a JFET.
The PSJFET current IPSJFET is given by the sum of the current flowing in the JFET device, IDS, and in the variable
resistance, IPS, that is IPSJFET = IDS + IPS. Finally, two resistors
RS and RD in series to the JFET/ RPS branch were also included to model both the silicon resistive paths from the
external source 共S兲 and drain 共D兲 contacts to the PSJFET
active region 共right underneath the PS layer兲, and the contact
resistances at the S and D terminals.
Figure 2 represents the simplified cross-section of the
PSJFET active area used to model the effect induced on the
JFET structure by the surface charge in the PS layer. It shows
the PS layer, with its positive charge, on top of the JFET
structure, the PS-induced depletion region x1, and the depletion region x2 due to the pn junction.
For small VDiSi values the voltage drop across the elemental section of the p-channel is given by the following:
dV共y兲 = IDSdR共y兲 =
IDS␳
dy,
W关h − x1共y兲 − x2共y兲兴
共1兲
where ␳ and h are the resistivity and the metallurgical height
of the p material underneath PS, respectively, x1共y兲 and x2共y兲
共2兲
where Vbi is the built-in voltage of the pn junction, VG is the
electrical gate voltage, and k2 is a constant which depends on
the doping profile of the pn junction.
As to the depletion region at the PS/p-Si interface, the
PS layer is described as an ideal homogeneous insulator with
a uniformly distributed fixed positive charge density
QPS共C兲共C / cm3兲, whose value depends on the analyte concentration C. In order to compensate for such a charge, a
depletion region forms in the p-channel. As no electrical contacts are placed on top of PS, the latter was assumed acting
as a floating gate, thus inducing a depletion region whose
height x1共y兲 is constant along the p-channel and modulated
by the analyte concentration, as follows:
x1共y兲 =
QPS共C兲
tPS ,
qNA
共3兲
with q elementary charge and tPS thickness of PS.
By substituting Eqs. 共3兲 and 共2兲 in Eq. 共1兲 and then integrating it over the channel length L, between source 关y = 0,
V共0兲 = VSi兴 and drain 关y = L, V共L兲 = VDi兴, the IDS current is
obtained, as follows:
IDS = k1共VDi − VSi兲 + 共3/4兲k2关共Vbi + VG − VDi兲4/3
− 共Vbi + VG − VSi兲4/3兴,
共4兲
where k1 depends on QPS as follows:
k1 =
冉
冊
W
QPS
h−
tPS .
␳L
qNA
共5兲
Equation 共4兲 holds for drain voltage values lower than
VDi_sat, which corresponds to the pinch-off of the JFET for a
given gate voltage VG and PS charge density QPS:
VDi_sat = Vbi + VG − 共k1/k2兲3 .
共6兲
The pinch-off occurs when h = x1共y兲 + x2共y兲, for a certain y
value. This causes the current to reach its saturation value,
which is independent of any further increase in the drain
voltage, as follows:
IDS_sat = k1共VDi_sat − VSi兲 + 共3/4兲k2关共Vbi + VG − VDi_sat兲4/3
− 共Vbi + VG − VSi兲4/3兴.
共7兲
In case the Early effect for FETs needs to be taken into
account, the right hand-side of Eqs. 共4兲 and 共7兲 must be multiplied by 关1 + ␭共VDi − VSi兲兴, where ␭ is the inverse value of
the Early voltage.
The model is completed by taking into account the leakage current IPS through the PS layer, which also depends on
the analyte concentration C:
IPS = GPS共C兲共VDi − VSi兲,
共8兲
where GPS共C兲 is the PS conductance. The use of Eq. 共8兲
implicitly supposes that the Ohm law holds for PS, at least in
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162105-3
Appl. Phys. Lett. 96, 162105 共2010兲
Barillaro, Lazzerini, and Strambini
(a)
(b)
FIG. 3. 共a兲 Experimental IV curves 共solid lines兲 and best fitting curves
共dotted lines兲 of a PSJFET exposed to synthetic air, at several VGS values.
共b兲 Experimental IV curves 共solid lines兲 and best fitting curves 共dotted lines兲
of a PSJFET exposed to 300 ppb of NO2, at several VGS values.
the voltage range of this work, as experimentally verified
共unpublished results兲.
Experiments on several PSJFET sensors were performed
to verify the validity of the model. The PSJFETs, fabricated
according to,13 have a gate contact on the back-side of the
chip and interdigitated comb-finger source and drain contacts
on the front-side. Both source and drain contacts have ten
fingers, each one 100 ␮m in length. The distance between
adjacent source and drain fingers is 50 ␮m. A meandershaped PS layer with equivalent width 共W兲 of 3875 ␮m,
length 共L兲 of 10 ␮m and thickness 共tPS兲 of 0.8 ␮m is produced between source and drain contacts. The sensors were
then exposed to either synthetic air or synthetic air/NO2 mixture at different NO2 concentrations 共100, 300, and 500 ppb兲,
while keeping the flow rate in the test chamber constant at
200 SCCM and the chamber temperature at 30⫾ 0.1 ° C. For
any device the IPSJFET − VDS characteristics were measured at
several VGS values after 3tR from exposure of the sensor to
any new concentration, where tR is the response time of the
sensor 共less than 5 min兲. Solid lines in Fig. 3 represent measured IV curves, in synthetic air 关Fig. 3共a兲兴 and at 300 ppb of
NO2 关Fig. 3共b兲兴, for several VGS values. The PSJFET shows a
FET-like behavior, exhibiting both linear and saturation regions depending on the VDS voltage. The effect of the gate
terminal is of reducing 共in module兲 the PSJFET current as
VGS increases. On the other hand, the IPSJFET current significantly increases as the NO2 concentration increases. On the
basis of the proposed model, such a behavior can be explained by supposing 共i兲 a reduction in the positive PS surface charge and, in turn, in the depletion region x1, and/or 共ii兲
an increase in the PS conductance with the NO2 concentration.
Quantitative information on these two effects were obtained by best fitting experimental IV curves with the described model, using k1, GPS and k2 as fitting parameters. To
check the robustness of the model, different experimental
curves measured in synthetic air and in the presence of 300
ppb of NO2, at different VGS values 共0, 0.1, 0.2, 0.5, and 1 V兲
were considered. A value of 25 ⍀, estimated by sensor geometrical dimensions and doping profiles, was employed for
the series resistances RS and RD. Due to the channel length, ␭
was set to 0 V−1. Parameters k1 and GPS are expected to be
ideally independent of the VGS voltage, while significantly
changing with the NO2 concentration. On the other hand, k2
only depends on the geometrical characteristics and doping
profiles of the JFET structure, so that it is expected to be
independent of both NO2 concentration and gate voltage VGS.
Dotted lines in Fig. 3 represent theoretical curves resulting from best fitting experimental curves with the following
parameters: k1 = 0.99⫻ 10−3 ⫾ 9.57⫻ 10−6 A V−1, GPS = 9.75
⫻ 10−6 ⫾ 4.00⫻ 10−6 S,
k2 = 7.80⫻ 10−4 ⫾ 4.20
−6
3/4
in
air;
and
k1 = 1.24⫻ 10−3 ⫾ 2.01
⫻ 10 A V
−5
−1
−5
⫻ 10 A V , GPS = 9.43⫻ 10 ⫾ 5.49⫻ 10−6 S, k2 = 7.89
⫻ 10−4 ⫾ 1.29⫻ 10−5 A V3/4 in NO2. Good agreement between calculated and measured curves is achieved both in the
linear and saturation region, whereas a slight mismatch can
be seen in the transition region.14 As expected, k1 and GPS
are significantly dependent on NO2, while k2 is not.
A variation in the PS conductance from 9.75 to 94.3 ␮S
results upon exposure of the sensor to 300 ppb of NO2, together with, from Eqs. 共3兲 and 共5兲, a reduction ⌬x1
= 130 nm of the depletion region under the PS layer. This
latter corresponds, from Eq. 共3兲, to a reduction ⌬QPS = 1.2
⫻ 1014 q cm−3 in the positive PS charge density, from QPS
= 9.96⫻ 1014 q cm−3 in air to QPS = 8.76⫻ 1014 q cm−3 at
300 ppb of NO2, where q is the elementary charge. This data
are in good agreement with the literature on conductometric
PS gas sensors,11,12 for which a strong increase in the PS
conductance is reported after exposure to NO2, together with
the formation of a low concentration of NO2− radicals on the
PS surface, which is here quantitatively estimated in 9.6
⫻ 109 q cm−2 for 300 ppb of NO2.
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The reduced accuracy in the transition region is due to the simplified
approach 共linear-graded approximation兲 used in describing the doping profile across the pn junction.
1
2
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