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Modelling non-ideal behaviours in H+-sensitive FETs with SPICE
Sensors and Actuators
561
B, 7 ( 1992) 561-564
Modelling non-ideal behaviours in H+-sensitive FETs with SPICE Sergio Martinoia, Biophysical
and Electronic
Massimo
Grattarola
Engineering Department
and Giuseppe
Massobrio
(DIBE), via Opera Pia I la, 16145 Genoa (Italy)
Abstract In recent
years, much work has been done to characterize ion-selective devices (ISFETs). The response of these devices to pH is commonly explained by considering H+ specific binding sites at the surface of an insulator exposed to an electrolyte. A previous generalized site-binding description is used here to model two specific aspects of the ISFET behaviour, namely: hysteresis in the response to pH, which is not predicted by the ‘standard’ site-binding theory; partial insensitivity to pH, that is, REFET structures, which are of interest as integrated reference electrodes in differential measurements. The ISFET model is implemented in SPICE and simulation results are given and compared with data reported in the literature.
Introduction
Much work has been done in the past few years to characterize ion-sensitive field-effect transistors (ISFETs) based on MOS technology, in particular ISFET pH sensors. However, some critical aspects remain to be considered, namely the reported non-ideal behaviour (i.e., drift and hysteresis) and the characterization of pH-insensitive structures to be used as integrated reference electrodes. Detailed physicochemical models of the sensing mechanism can help in understanding these phenomena. Here we propose the use of a generalized site binding model [ 11, that has been introduced into the simulation program SPICE in order to have a flexible, device-oriented tool for tackling these problems. First, the ISFET model implemented in SPICE is briefly described (a more detailed analysis can be found in ref. 1). Then, the program capabilities are specifically demonstrated by simulating slow responses (i.e., hysteresis phenomena) and pH insensitivity (i.e., REFET structures).
ISFET model implemented in SPICE
The SPICE equations defining the MOST model [2] are modified by introducing the following equations, which describe the electrochemical component in the general case of two kinds of binding sites [ 11. 0925-4005/92/$5.00
ISFET threshold voltage Vth(ISFET) = (E~x + cPlj>- (40.x- LO) L L0X YJ where qf is the Fermi potential of the semiconductor, Qss is the fixed surface state charge density, Qsc is the semiconductor surface charge density, C,, is the insulator capacitance per unit area, E,,, is the potential of the reference electrode, qlj is the liquid junction potential difference between the reference solution and the electrolyte, cpeo is the potential of the electrolyte-insulator interface, xeo is the electrolyte-insulator surface dipole potential, and cpsc is the semiconductor work function. Electroneutrality condition gd + flo + 6,,, = 0
(2)
where cd is the charge density in the diffuse layer, o0 is the charge density at the electrolyte-insulator interface, and gmos is the charge density ifi the semiconductor. Generalized site-binding relationship
co 4N,=
[H’]f - K+K_ Ns, [H+]: + K+[H+ls + K+K_ >- IV,
&it Ns @ 1992 -
(3)
Elsevier Sequoia. All rights reserved
562
where Nsi, and N”, are the silanol sites and of primary tively, N, is the total number K_ , KN+ are the dissociation is the proton concentration insulator interface.
surface densities of amine sites, respecof binding sites, K+, constants, and [H+ls at the electrolyte-
Boltzmann relationship
A
W’L = Wflb exp
-&
ye0
>
(4)
where [H+],, is the bulk H+ concentration.
As pointed out in ref. 6, if Ld is in the range 3 to 10 nm (as in our case), the influence of drift is much smaller than that of diffusion. Therefore, slow response phenomena can be estimated in terms of the diffusion process only. The addition of the buried layer modifies eqn. (2), and introduces a new equation into our model: o,j+co+o,,,os+&,(t)
where cb is the charge density of the buried layer
W+l~,r - K+K-
ob -= 4N,
[H+]&+
Slow-response phenomena
[
(2&A
evf
(8)
where q(Nsi, + N”i,) = Nb. In order to make a comparison with results obtained by other authors, an explicit definition of the hysteresis cycle is needed. The pH cycle used in our simulations is sketched in Fig. 1. A broad range of diffusion coefficients was utilized to test the model, and, as an example, a 12 10
a I
a
6 4
2
40
0
80
120
160
200
240
280
Time [min]
Fig. 1. Hysteresis
cycle considered
in the simulations.
(5)
where [H+lbur is the proton concentration in the buried layer, and Dew is the effective diffusion constant. In accordance with Bousse and Bergveld [6] we define Dee as: De*=-
K + [H+lbur+ K + K_ >! % s
+
Unstable responses in time have been reported for SiO*-gate ISFETs and, to a smaller extent, for A1203- and SigN4-gate ISFETs [3]. These phenomena are analyzed in detail in refs. 4 and 5 and the authors’ conclusion is that the main non-ideal effect is caused by hysteresis and not by drift. We modelled this memory phenomenon by assuming that a small fraction of binding sites is buried a few nm inside the surface, so that OH- and H+ groups can react with them at the end of a diffusion process. The data relevant to this very crude model have mostly been adapted from ref. 6. For the sake of simplicity, the various layers of the sub-surface insulator accessible to ions are lumped together into a single buried layer, which is located Ld nm (3-10) inside the insulator. The binding sites on this layer are 10% of the exposed binding sites. The diffusion of groups inside the insulator is described by the following relationship:
W+L = [H’L 1 +
(7)
=o
D KN,
where K is the reaction equilibrium constant, Nb is the surface density of buried sites, and D is the diffusion constant.
7
5
m
IO,
c
I
9i0,
0
hysteresb
width=2.2 /
\
n. E -40’ 2
4
mV
a
6
10
J 12
P"
Fig. 2. Hysteresis width (5 x 10-20cm2/s). Reduced
for an SiOJSFET V, defined as in [S].
for
a
given
DeR
563
Time per
pti unit #tap = pH
5
1.6 -
-0 '5
1.2 -
In *ii ?!
0.6 -
x ; =
0.4 0.0 1 16-021
-I I
7- 10-7-4-7
II I
1.3-020
lo-019
le-016
20mln
:
..-
_12 I
I
la-017
le-016
13
10-015
13
&[cm2/sl
Fig. 3. SiO,-ISFET hysteresis widths, according to the hysteresis cycle defined in Fig. 2, as a function of various Dem values.
PH (a)
simulation result for an SiOz-ISFET is shown in Fig. 2. Figure 3 shows the hysteresis width for an SiOz-ISFET as a function of the effective diffusion constant. The obtained hysteresis widths are somewhat smaller than those reported in the literature. The crudeness of our model, possible differences in the ‘hysteresis-cycle protocol’ and the absence in the simulation of other sources of non-ideality (i.e., drift), preclude more detailed comparisons.
0.9
0.7
o.6
REFET structures
1 , , .,:.._.; ;gq:;:i, Ion-con
According to data reported in the literature, partially pH-insensitive materials such as Teflon or Parylene can be modeled by considering the chemical equilibrium equation between the surface sites -COOH and -COH of the organic membrane and protons [7]. This equation can be obtained for our model in a straightforward way by modifying eqn. (3) into: K( COOH) N( COOH) N, [H+]s + K(COOH) > K( COH)
[H+],+K(COH)
1N .----.- N(COH)=lxlO
_I
2
00 -= qN,
=
N( COH) N,
(9)
where K(COOH) and K(COH) are the dissociation constants for the chemical reaction, and N( COOH) and N( COH) are the numbers of -COOH sites and -COH sites per unit area, respectively. The results of SPICE runs based on such a modification are given in Fig. 4(a) and (b). This
3
4
5
6
7
8
9
10
PH (b) Fig. 4. Partial pH insensitivity as a function of various -COOH (a) and -COH (b) site densities.
Figure shows the output voltage of a measuring circuit for ISFET devices as a function of pH for various -COOH site densities (Fig. 4(a)), and for various -COH site densities (Fig. 4(b)). These data show a very good agreement with those reported in ref. 7. A large region of pH insensitivity is predicted by the present ISFET model and it corresponds quite well to the reported experimental data.
Discussion and conclusions
SPICE is a very popular program for the characterization of semiconductor devices and complex circuits. It is worth noting that we introduced the
564
ISFET device into SPICE at the physical (or physicochemical) level, instead of introducing a ‘Macromodel’. This approach should allow one to fully exploit the SPICE capabilities. As specific demonstrations, hysteresis and partial insensitivity to pH have been analyzed in this paper, on the basis of a physicochemical description of such phenomena. We think that the obtained results do prove the potentialities of the model as a tool for a deeper understanding of ISFET performances. Hopefully, thanks to the widespread use of SPICE, the proposed approach will lead to a greater standardization of ISFETs and other similar solid-state devices.
Acknowledgements
This work was supported by the National Research Council (CNR) of Italy (Target Project
MADESS) and by the Italian Ministry for the University and Research (MURST 40%). References M. Grattarola, G. Massobrio and S. Martinoia, Modeling H+ sensitive FETs with SPICE, IEEE Trans. Electron Devices, (Apr.) ( 1992) in press. P. Antognetti and G. Massobrio, Semiconductor Device Modeling with SPICE, McGraw-Hill, New York, 1988. H. Abe, M. Esashi and T. Matsuo, ISFETs using inorganic gate thin films, IEEE Trans. Elecfron Devices, ED-26 (1979) 19391944. L. Bousse, D. Hafeman and N. Tran, Time-dependence of the chemical response of silicon nitride surfaces, Sensors and Actuators, BI (1990) .361-367. L. Bousse, H. H. Van den Vlekkert and N. F. de Rooij, Hysteresis in A&O,-gate ISFETs, Sensors and Actuators B, 2 (1990) 103-I IO. L. Bousse and P. Bergveld, The role of buried OH sites in the response mechanism of inorganic-gate pH-sensitive ISFETs, Sensors and Actuators, 6 ( 1984) 65-78. 7 W. Leimbrock, U. Landgraf and G. Kampfrath, An extended site-binding model and experimental results of organic membranes for reference ISFETs, Sensors and Acfuarors B, 2 (1990) 1-6.
561
B, 7 ( 1992) 561-564
Modelling non-ideal behaviours in H+-sensitive FETs with SPICE Sergio Martinoia, Biophysical
and Electronic
Massimo
Grattarola
Engineering Department
and Giuseppe
Massobrio
(DIBE), via Opera Pia I la, 16145 Genoa (Italy)
Abstract In recent
years, much work has been done to characterize ion-selective devices (ISFETs). The response of these devices to pH is commonly explained by considering H+ specific binding sites at the surface of an insulator exposed to an electrolyte. A previous generalized site-binding description is used here to model two specific aspects of the ISFET behaviour, namely: hysteresis in the response to pH, which is not predicted by the ‘standard’ site-binding theory; partial insensitivity to pH, that is, REFET structures, which are of interest as integrated reference electrodes in differential measurements. The ISFET model is implemented in SPICE and simulation results are given and compared with data reported in the literature.
Introduction
Much work has been done in the past few years to characterize ion-sensitive field-effect transistors (ISFETs) based on MOS technology, in particular ISFET pH sensors. However, some critical aspects remain to be considered, namely the reported non-ideal behaviour (i.e., drift and hysteresis) and the characterization of pH-insensitive structures to be used as integrated reference electrodes. Detailed physicochemical models of the sensing mechanism can help in understanding these phenomena. Here we propose the use of a generalized site binding model [ 11, that has been introduced into the simulation program SPICE in order to have a flexible, device-oriented tool for tackling these problems. First, the ISFET model implemented in SPICE is briefly described (a more detailed analysis can be found in ref. 1). Then, the program capabilities are specifically demonstrated by simulating slow responses (i.e., hysteresis phenomena) and pH insensitivity (i.e., REFET structures).
ISFET model implemented in SPICE
The SPICE equations defining the MOST model [2] are modified by introducing the following equations, which describe the electrochemical component in the general case of two kinds of binding sites [ 11. 0925-4005/92/$5.00
ISFET threshold voltage Vth(ISFET) = (E~x + cPlj>- (40.x- LO) L L0X YJ where qf is the Fermi potential of the semiconductor, Qss is the fixed surface state charge density, Qsc is the semiconductor surface charge density, C,, is the insulator capacitance per unit area, E,,, is the potential of the reference electrode, qlj is the liquid junction potential difference between the reference solution and the electrolyte, cpeo is the potential of the electrolyte-insulator interface, xeo is the electrolyte-insulator surface dipole potential, and cpsc is the semiconductor work function. Electroneutrality condition gd + flo + 6,,, = 0
(2)
where cd is the charge density in the diffuse layer, o0 is the charge density at the electrolyte-insulator interface, and gmos is the charge density ifi the semiconductor. Generalized site-binding relationship
co 4N,=
[H’]f - K+K_ Ns, [H+]: + K+[H+ls + K+K_ >- IV,
&it Ns @ 1992 -
(3)
Elsevier Sequoia. All rights reserved
562
where Nsi, and N”, are the silanol sites and of primary tively, N, is the total number K_ , KN+ are the dissociation is the proton concentration insulator interface.
surface densities of amine sites, respecof binding sites, K+, constants, and [H+ls at the electrolyte-
Boltzmann relationship
A
W’L = Wflb exp
-&
ye0
>
(4)
where [H+],, is the bulk H+ concentration.
As pointed out in ref. 6, if Ld is in the range 3 to 10 nm (as in our case), the influence of drift is much smaller than that of diffusion. Therefore, slow response phenomena can be estimated in terms of the diffusion process only. The addition of the buried layer modifies eqn. (2), and introduces a new equation into our model: o,j+co+o,,,os+&,(t)
where cb is the charge density of the buried layer
W+l~,r - K+K-
ob -= 4N,
[H+]&+
Slow-response phenomena
[
(2&A
evf
(8)
where q(Nsi, + N”i,) = Nb. In order to make a comparison with results obtained by other authors, an explicit definition of the hysteresis cycle is needed. The pH cycle used in our simulations is sketched in Fig. 1. A broad range of diffusion coefficients was utilized to test the model, and, as an example, a 12 10
a I
a
6 4
2
40
0
80
120
160
200
240
280
Time [min]
Fig. 1. Hysteresis
cycle considered
in the simulations.
(5)
where [H+lbur is the proton concentration in the buried layer, and Dew is the effective diffusion constant. In accordance with Bousse and Bergveld [6] we define Dee as: De*=-
K + [H+lbur+ K + K_ >! % s
+
Unstable responses in time have been reported for SiO*-gate ISFETs and, to a smaller extent, for A1203- and SigN4-gate ISFETs [3]. These phenomena are analyzed in detail in refs. 4 and 5 and the authors’ conclusion is that the main non-ideal effect is caused by hysteresis and not by drift. We modelled this memory phenomenon by assuming that a small fraction of binding sites is buried a few nm inside the surface, so that OH- and H+ groups can react with them at the end of a diffusion process. The data relevant to this very crude model have mostly been adapted from ref. 6. For the sake of simplicity, the various layers of the sub-surface insulator accessible to ions are lumped together into a single buried layer, which is located Ld nm (3-10) inside the insulator. The binding sites on this layer are 10% of the exposed binding sites. The diffusion of groups inside the insulator is described by the following relationship:
W+L = [H’L 1 +
(7)
=o
D KN,
where K is the reaction equilibrium constant, Nb is the surface density of buried sites, and D is the diffusion constant.
7
5
m
IO,
c
I
9i0,
0
hysteresb
width=2.2 /
\
n. E -40’ 2
4
mV
a
6
10
J 12
P"
Fig. 2. Hysteresis width (5 x 10-20cm2/s). Reduced
for an SiOJSFET V, defined as in [S].
for
a
given
DeR
563
Time per
pti unit #tap = pH
5
1.6 -
-0 '5
1.2 -
In *ii ?!
0.6 -
x ; =
0.4 0.0 1 16-021
-I I
7- 10-7-4-7
II I
1.3-020
lo-019
le-016
20mln
:
..-
_12 I
I
la-017
le-016
13
10-015
13
&[cm2/sl
Fig. 3. SiO,-ISFET hysteresis widths, according to the hysteresis cycle defined in Fig. 2, as a function of various Dem values.
PH (a)
simulation result for an SiOz-ISFET is shown in Fig. 2. Figure 3 shows the hysteresis width for an SiOz-ISFET as a function of the effective diffusion constant. The obtained hysteresis widths are somewhat smaller than those reported in the literature. The crudeness of our model, possible differences in the ‘hysteresis-cycle protocol’ and the absence in the simulation of other sources of non-ideality (i.e., drift), preclude more detailed comparisons.
0.9
0.7
o.6
REFET structures
1 , , .,:.._.; ;gq:;:i, Ion-con
According to data reported in the literature, partially pH-insensitive materials such as Teflon or Parylene can be modeled by considering the chemical equilibrium equation between the surface sites -COOH and -COH of the organic membrane and protons [7]. This equation can be obtained for our model in a straightforward way by modifying eqn. (3) into: K( COOH) N( COOH) N, [H+]s + K(COOH) > K( COH)
[H+],+K(COH)
1N .----.- N(COH)=lxlO
_I
2
00 -= qN,
=
N( COH) N,
(9)
where K(COOH) and K(COH) are the dissociation constants for the chemical reaction, and N( COOH) and N( COH) are the numbers of -COOH sites and -COH sites per unit area, respectively. The results of SPICE runs based on such a modification are given in Fig. 4(a) and (b). This
3
4
5
6
7
8
9
10
PH (b) Fig. 4. Partial pH insensitivity as a function of various -COOH (a) and -COH (b) site densities.
Figure shows the output voltage of a measuring circuit for ISFET devices as a function of pH for various -COOH site densities (Fig. 4(a)), and for various -COH site densities (Fig. 4(b)). These data show a very good agreement with those reported in ref. 7. A large region of pH insensitivity is predicted by the present ISFET model and it corresponds quite well to the reported experimental data.
Discussion and conclusions
SPICE is a very popular program for the characterization of semiconductor devices and complex circuits. It is worth noting that we introduced the
564
ISFET device into SPICE at the physical (or physicochemical) level, instead of introducing a ‘Macromodel’. This approach should allow one to fully exploit the SPICE capabilities. As specific demonstrations, hysteresis and partial insensitivity to pH have been analyzed in this paper, on the basis of a physicochemical description of such phenomena. We think that the obtained results do prove the potentialities of the model as a tool for a deeper understanding of ISFET performances. Hopefully, thanks to the widespread use of SPICE, the proposed approach will lead to a greater standardization of ISFETs and other similar solid-state devices.
Acknowledgements
This work was supported by the National Research Council (CNR) of Italy (Target Project
MADESS) and by the Italian Ministry for the University and Research (MURST 40%). References M. Grattarola, G. Massobrio and S. Martinoia, Modeling H+ sensitive FETs with SPICE, IEEE Trans. Electron Devices, (Apr.) ( 1992) in press. P. Antognetti and G. Massobrio, Semiconductor Device Modeling with SPICE, McGraw-Hill, New York, 1988. H. Abe, M. Esashi and T. Matsuo, ISFETs using inorganic gate thin films, IEEE Trans. Elecfron Devices, ED-26 (1979) 19391944. L. Bousse, D. Hafeman and N. Tran, Time-dependence of the chemical response of silicon nitride surfaces, Sensors and Actuators, BI (1990) .361-367. L. Bousse, H. H. Van den Vlekkert and N. F. de Rooij, Hysteresis in A&O,-gate ISFETs, Sensors and Actuators B, 2 (1990) 103-I IO. L. Bousse and P. Bergveld, The role of buried OH sites in the response mechanism of inorganic-gate pH-sensitive ISFETs, Sensors and Actuators, 6 ( 1984) 65-78. 7 W. Leimbrock, U. Landgraf and G. Kampfrath, An extended site-binding model and experimental results of organic membranes for reference ISFETs, Sensors and Acfuarors B, 2 (1990) 1-6.