nextnano^{3}  Tutorial
next generation 3D nano device simulator
1D Tutorial
ISFET (IonSelective Field Effect Transistor): SiSiO_{2} electrolyte sensor
Author:
Stefan Birner
If you want to obtain the input file that is used within this tutorial, please
submit a support ticket.
> 1DSi_SiO2_electrolyte_sensor.in

Loop over pH values from pH = 0 to pH = 14.
> 1DSi_SiO2_electrolyte_sensor_pH64.in 
pH = 6.4
This tutorial is based on the diploma thesis of Michael Bayer, TU Munich
(2004).
Acknowledgement: The author  Stefan Birner  would like to thank
Christian Uhl and Michael Bayer for helping to include the electrolyte features into nextnano³.
SiSiO_{2} electrolyte sensor
Here, we predict the sensitivity of electrolyte
gate SiSiO_{2} sensors to pH values of the electrolyte solution that
covers the semiconductor structure.
The charge density due to chemical reactions at the oxidic
semiconductorelectrolyte interface is described within the sitebinding model ($interfacestates ).
We calculate the spatial charge and potential distribution both in the
semiconductor and the electrolyte (PoissonBoltzmann equation)
selfconsistently.
The SiSiO_{2} sensor that is exposed to an electrolyte solution has the
following schematic layout:
Fig. 1: SiSiO_{2} sensor with electrolyte gate.
We simulate the structure along the z direction
so that the structure is effectively
onedimensional, i.e. laterally homogeneous.
The heterostructure is assumed to be grown along the [001]
direction and is not strained.
The file
densities/interface_densitiesD.txt gives us information about the
relevant interface charge densities:
 Interface 4 (1544 nm): Interface charge sigma_{adsorbed} that
results from the sitebinding model that describes chemical reactions at the
oxidic semiconductorelectrolyte interface. More details:
$interfacestates
$interfacestates
statenumber =
1
! between SiO2 / Electrolyte at 1544 nm
statetype
= electrolyte !
sigma_adsorbed
interfacedensity = 5.0d14
! [cm^2]  total
density of surface sites, i.e. surface hydroxyl groups
adsorptionconstant = 0.079433d0
! K_{1} = adsorption constant = 1 *
10^{1.1}
dissociationconstant = 2.511886d5
! K_{2} = dissociation constant = 1 * 10^{4.6}
$electrolyte
...
pHvalue
= 6.4d0
!
pH = lg(concentration) = 6.4 > concentration in [M]=[mol/l]
(The point of zero charge for SiO_{2} is at pH = 2.2.)
The Si region (1501 nm  1541 nm) is homogeneously ptype doped with boron
having a
concentration of 1 * 10^{16} cm^{3}.
The electrolyte region (1544 nm  9999 nm) contains the following ions:
!!
! The electrolyte (phosphate buffer, NaCl) contains five types of ions:
! 1) 7 mM singly charged anions (^{1})
< 10 mM phosphate buffer (PBS) H_{2}PO_{4}^{}
! 2) 3 mM doubly charged anions (^{2})
< 10 mM phosphate buffer (PBS) HPO_{4}^{2}
! 3) 13 mM singly charged cations (^{1+})
< 10 mM phosphate buffer (PBS) Na^{+}
! 4) 10 mM singly charged cations (Na^{+})
< 10 mM NaCl
! 5) 10 mM singly charged anions (Cl^{})
< 10 mM NaCl
!!
$electrolyteioncontent
ionnumber =
1
!
7 mM singly charged anions
ionvalency =
1d0 !
charge of the ion: ^{1}
ionconcentration = 7d3
! Input in units of: [M] = [mol/l] = 1d3 [mol/cm³]
ionregion =
1544d0 9999d0 ! refers to region where
the electrolyte has to be applied to
ionnumber =
2
! 3 mM doubly charged anions
ionvalency =
2d0 !
charge of the ion: ^{2}
ionconcentration = 3d3
! Input in units of: [M] = [mol/l] = 1d3 [mol/cm³]
ionregion =
1544d0 9999d0 ! refers to region where
the electrolyte has to be applied to
ionnumber =
3
! 13 mM singly charged cations
ionvalency = 1d0
!
charge of the ion: ^{1+}
ionconcentration = 13d3
! Input in units of: [M] = [mol/l] = 1d3 [mol/cm³]
ionregion =
1544d0 9999d0 ! refers to region where
the electrolyte has to be applied to
ionnumber =
4
! 10 mM singly charged cations
ionvalency =
1d0 !
charge of the ion: Na^{+}
ionconcentration = 10d3
! Input in units of: [M] = [mol/l] = 1d3 [mol/cm³]
ionregion =
1544d0 9999d0 ! refers to region where
the electrolyte has to be applied to
ionnumber =
5
! 10 mM singly charged anions
ionvalency =
1d0 ! charge of the ion:
Cl^{}
ionconcentration = 10d3
! Input in units of: [M] = [mol/l] = 1d3 [mol/cm³]
ionregion =
1544d0 9999d0 ! refers to region where
the electrolyte has to be applied to
In addition to these five types of ions, the pH value (as specified in $interfacestates )
automatically determines inside the code four further types of ions, namely the
concentration of H_{3}O^{+}, OH^{} and the
corresponding anions^{} (conjugate base: [anion^{} ]
= 10^{pH}  10^{pOH} = 10^{6.4}  10^{7.6} =
3.73 x 10^{7})
and cations^{+} (conjugate acid; zero in this tutorial for pH = 6.4 because pH = 6.4
< 7). For
details, confer $electrolyteioncontent .
We have to solve the nonlinear Poisson equation over the whole device, i.e.
including the PoissonBoltzmann equation that governs the charge density in the
electrolyte region.
As for the boundary conditions we assume at the right boundary
(Electrolyte/Metal) a Dirichlet boundary condition where the electrostatic
potential phi is equal to U_{G} where U_{G} is the gate voltage
determined by an electrode in the electrolyte solution and which is constant
throughout the entire electrolyte region. In this example the applied gate
voltage is U_{G} = 0 V, i.e. the electrostatic potential in the
PoissonBoltzmann equation is fixed to 0 V. Note that the reference potential U_{G}
enters the PoissonBoltzmann equation and also the equation for the sitebinding
model at the oxide/electrolyte interface. So the Dirichlet boundary condition is
phi = 0 V. This corresponds to the fact that at the right part of the
electrolyte, i.e. at 'infinity' (at 9999 nm) the ion concentration is the
'equilibrium' (default) concentration as defined in
$electrolyteioncontent .
At the left boundary (Metal/SiO_{2}) we use a Neumann boundary
condition with a zero potential gradient that corresponds to an electric field E
= 0 V/m.
$poissonboundaryconditions
poissonclusternumber = 1
regionclusternumber = 1
boundaryconditiontype = Neumann
electricfield
= 0d0 ! 0 [V/m]
poissonclusternumber = 2
regionclusternumber = 6
boundaryconditiontype = Dirichlet
potential
= 0d0 ! phi = 0 [V]
<=> U_{G} = 0 [V]
Oxide/electrolyte interface potential as a function of pH value
The SiSiO_{2} heterostructure acts as a sensor via the semiconductorelectrolyte
interface potential that reflects sigma_{adsorbed}, the pH value and the
spatial dependence of the electrostatic potential in the solution as described
by the PoissonBoltzmann theory.
Choosing flowscheme = 30 , several
calculations are performed while sweeping over the pH value from 0 to 14.
pHvalue
= (value is overwritten internally in the program)
The file InterfacePotentialDensity_vs_pH1D.dat gives us the
information about the electrostatic potential at the oxide/electrolyte interface
for different pH values.
The surface potential is defined as the difference of the electrostatic
potential at the oxide/electrolyte interface and the reference potential U_{G}
(Here: U_{G} = 0 V).
Fig. 2: Calculated oxide/electrolyte interface potential as a function of the pH
value by using the nonlinear PoissonBoltzmann (PB) ion distribution.
For comparison the results obtained using the linear DebyeHückel (DH) ion
distribution are also shown.
As expected, in the case of zero surface potential, the PoissonBoltzmann and
the DebyeHückel results are identical.
(Electrolyte: 10 mM phosphate buffer, 10 mM NaCl)
The slope (d phi / d pH) is a characteristic property of an
oxide/electrolyte interface. Note that in Fig. 2 only the slope is relevant but not the
absolute values of the potential. A linear fit between pH = 0 and pH = 9 yields
37.7 mV/pH in agreement with experiments (P. Bergveld, A. Sibbald, Analytical
and biomedical applications of ionselectivefieldeffecttransistors, ed.
G. Svehla, Analytical Chemistry, Vol. XXIII, Elsevier, 1988).
Further below (Fig. 3) we see that the oxide/electrolyte interface charge density
saturates at high pH values (pH = [10,...,14]). This also means that this charge
density is then (almost) unaffected by the
oxide/electrolyte interface potential. Thus this quantity is then determined
purely by the PoissonBoltzmann ion distribution in the electrolyte, i.e. by the
concentration of OH^{} (and corresponding cations^{+})
that are the most present ion species at high pH values.
Oxide/electrolyte interface charge density sigma_{adsorbed} as a
function of pH value
From the file InterfacePotentialDensity_vs_pH1D.dat we also obtain
information about the oxide/electrolyte interface sheet charge density sigma_{adsorbed}
(as a function of pH value) that is determined by the amphoteric reactions at
the oxide surface.
We plot in Fig. 3 the oxide/electrolyte interface
charge density sigma_{adsorbed}:
Fig. 3: Calculated variation of the
oxide/electrolyte interface charge density sigma_{adsorbed} of the
amphoteric oxide surface with the pH value of the electrolyte solution by using
the nonlinear PoissonBoltzmann (PB) ion distribution.
Note that there is a range of pH values where the net surface charge density is
close to zero.
The calculated point of zero charge for the SiO_{2} surface is reached for pH =
2.2.
For comparison the results obtained using the linear DebyeHückel (DH) ion
distribution are also shown.
At high pH values the interface charge density
saturates at the nominal density of surface sites because at the
oxide/electrolyte interface all surface sites adsorbed the hydrogen ions from
the electrolyte solution.
interfacedensity = 5.0d14 ! [cm^2]
=> sigma_{adsorbed} = 500 * 10^{12} [e/cm^{2}]
Thus for pH values ranging from 10 to 14, the oxide/electrolyte interface
charge density is (almost) independent of both the
pH value and the electrostatic potential.
Electrostatic potential for electrolyte gate voltage U_{G} = 0
Here we plot the electrostatic potential for a pH value of 6.4.
U_{G} = 0 V,
i.e. we apply a zero gate voltage to the electrolyte. Note that U_{G} is
both the Dirichlet boundary condition for the electrostatic potential at the
right contact as well as the reference potential that enters into the
PoissonBoltzmann equation (i.e. into the exponential term of the ion charge
density).
U_{G} is constant throughout the entire electrolyte region.
U_{G} = 0 V:
poissonclusternumber = 2
regionclusternumber = 6
boundaryconditiontype = Dirichlet
potential
= 0d0 ! phi = 0 [V]
<=> U_{G} = 0 [V]
Fig. 4: Spatial electrostatic potential distribution for pH = 6.4 in the
electrolyte by using the nonlinear PoissonBoltzmann (PB) ion distribution.
For comparison the results obtained using the linear DebyeHückel (DH) ion
distribution are also shown.
(Electrolyte: 10 mM phosphate buffer, 10 mM NaCl, U_{G} = 0 V) 