The oxide-electrolyte interface

As mentioned in the preceding section, when we immerse the ISFET in the pH buffer solution, the oxide/electrolyte interface will build up charges and generate an electrostatic potential. The characteristics of the ISFET are completely controlled by the properties of the oxide-electrolyte interface, and protonation/deprotonation of the gate material is influenced by the pH solution, which controls the surface potential.

But what is the charging mechanism at the surface? The site-binding model introduced by Yate et al. is the most well-known method to describe the charging mechanism at the oxide/electrolyte interface as illustrated in Fig. 2-3 and Fig. 2-4.

The surface of any metal oxide (the sensing layer) always contains hydroxyl groups, for example, in the case of silicon dioxide is SiOH groups. In this model, the oxide suface sites are assumed to be amphoteric, i.e. the amphoteric sites may donate or accept a proton from the solution, leaving a negatively charged or positively charged

surface group, respectively. The surface reactions are:

AOH ↔ AO⁻+HB⁺ (2-5)

2 B

AOH ⁺ ↔AOH H+ ⁺ (2-6) where A is the metal oxide component, such as Si, Al, Zr, Ta, and H_B represents the protons in the bulk of the solution. From these chemical reactions, it is obvious that an originally neutral surface hydroxyl site can be neutral, protonized or deprotonized depending on the pH value of the bulk solution. For this reason it is called an amphoteric site. We also have to know that there are a fixed number of surface sites per unit area, N_S

S AOH AOH2 AO

N =ν +ν + +ν − (2-7) Based on some electrochemical knowledge and math derivation, we can get the surface charge density σ_o[ /C m²]

σo =q

(

νAOH −νAO−

)

= −qB (2-8) where B is the number of negatively charged groups minus the number of positively charged groups in mole per unit area. We can see that when the number of positively and negatively charged groups on the surface is equal and consequently there will be no net charge on the surface. Under this kind of situation, we say the pH value at the point of zero charge is pHpzc. One more thing we have to know is that different operations of ISFETs (flat band condition and linear region) will yield different value of pHpzc [3].

which K_a and K_b are intrinsic dissociation constants. A detailed derivation can see

the Ref. [4,5]. Equation (2-9) shows the relation between the activity of the protons at the oxide surface

HS

a + and the surface charge density σ_o in terms of the total number of available sites N _S and the intrinsic dissociation constants K _a and K_b. After we get the surface charge density, we can find the intrinsic buffer capacity β_int, the capability of the surface to store charge as result of a small change in the H⁺ concentration, defined as

It is called “intrinsic” buffer capacity, because it is only capable of buffering small changes in the surface pH (pH ) and not in the bulk pH (_S pH ). We can see _b that the value of N , _S K and _a K are oxide dependent. More surface sites will lead _b to larger β_int. According to Ref. [4], Hydrolysis of the surface will create more surface sites and thus a rise in the intrinsic buffer capacity and the sensitivity.

Not only the surface reaction will affect the surface charge density, but also the background electrolyte will influence the surface charge density [4]. This dependence is ascribed to variations in the double layer capacitance. The surface charge σ_o is balanced by an equal but opposite charge in electrolyte, σ_dl as a result of charge neutrality. The two opposite charges, σ_{o and} σ_dl, is parallel to each other form the electrical double layer structure, and the integral electrical double-layer capacitance is named C . _{dl i,}

The relation between σ_o, σ_dl, C_{dl i,} and ϕ_o is given by

σ_dl = −σ_o = −C_{dl i o,}ϕ (2-12)

where the potential difference ϕ_o =ϕ ϕ_s− _B, the surface potential subtracts the bulk potential of the electrolyte.

But what is the detailed mechanism for the electrical double layer? The first double layer model is proposed by Helmholtz in 1879. He regards the double layer as a parallel plate capacitance structure as shown in Fig. 2-5. The plate distance “r” is taken as the ion radius and the double layer capacitance _dl Q

C =V will be a constant value, where Q is the surface charge and V is the potential difference of the double layer. But from the experiment, we can know the double layer capacitance is not a constant value, so the Hemholtz is not suitable to describe the exact double layer structure. Therefore the Hemholtz model is merely suitable for the high concentration electrolyte. Because the potential difference will be large in high concentration electrolyte, the double layer structure will be like the parallel plate capacitance.

Because the Helmholtz model only considers the electrostatic force, therefore it can not model the relation between the double layer capacitance and electrolyte concentration. In the beginning of 20th century, Gouy and Chapman proposed the idea of a diffuse layer to interpret the capacitive behavior of an electrode/electrolyte interface as shown in Fig. 2-6. This model made significant improvements by introducing a diffuse model of the electrical double layer, in which the potential at a surface decreases exponentially due to adsorbed counter-ions from the solution. They think that the ions in the solution are not only electrostatically attracted to the electrode surface but also the attraction is consumed by the random thermal motion which acts to equalize the concentration through the solution. The ions concentration in the electrolyte will obey the Boltzmann equation:

i

( )

i^{oexp i x}

C x C z q

kT φ

⎛− ⎞

= ⎜ ⎟

⎝ ⎠ (2-13) where φ_x is the potential at any distance x with respect to the bulk of the solution,

i( )

C x and C_i^o are the molar concentration of species i at a distance x and in the bulk of the solution, respectively. Z is the magnitude of the charge on the ions. The _i relation between ionic activity (a ) and ions concentration (_i c ) is _i a_i = × , where f c_{i i} f is activity coefficient. In diluted electrolyte i f will be approached unity. _i However, the Gouy-Chapman model has one major drawback. The ions are considered as point charge that can approach the surface arbitrarily close in this model.

This will cause unrealistic high concentrations of ions near the surface at high values of ϕ_o [4]. Hence, the Gouy-Chapman model is only suitable for low concentration electrolyte. This implies that the electrical double layer structure have to combine the Hemholtz and Gouy-Chapman model in certain way.

In 1924, Stern combined these two double layer models, named Gouy-Chapman-Stern model. The Gouy-Chapman-Stern model, which combines the Helmholtz single adsorbed layer with the Gouy-Chapman diffuse layer, is most widely used to describe the electrical double layer structure in ISFET literature. The model describes that some of the ions in the electrolyte are next to the electrode surface and because of the finite ions size, the ions couldn’t approach the surface arbitrarily close. The other ions are distributed in the electrolyte according to the Boltzmann equation and form a charge diffuse layer in the electrolyte. There is a distance, x_H, which is the closest plane for the centers of the ions. Hence, the diffuse layer is starting from x_H, and will possess the same amount of charge σ_{dl (of} opposite sign) as oxide surface charge σ_o, because the Helmholtz layer is not containing any charge, as shown in Fig. 2-7 and Fig. 2-8. In Gouy-Chapman-Stern model, the double layer capacitance consists of a series network of a Hemholtz layer capacitance (Stern capacitance) and a diffuse layer capacitance. The difference between ϕ_o and ϕ₁ is the potential difference across the Stern capacitance and the

Stern capacitance has a value of ^{r o 2}

H

x F m

ε ε _{⎡ ⎤}

⎣ ⎦ . By the Gouy-Chapman-Stern model, we can get the critical parameter：differential double layer capacitance C , the _dif ability of the double layer to store charge in response to a small change in the potential, defined as

stated here, but of its inverse. The derived inverse C is made up of two _dif components in series:

2.2.3 Theory for the pH sensitivity of ISFET

From above discussions, the sensitivity of the pH ISFET is related to the intrinsic buffer capacity β_int and the differential capacitance C . By site-binding model and ^dif

Gouy-Chapman-Stern model, we can get the values of β_{int and} C , respectively. _dif The pH sensitivity is the change of the insulator-electrolyte potential, ϕ_o, on the change of the bulk pH, ^o

pHB

ϕ

∂

∂ . This expression is derived from a separate treatment of both sides of the double layer, i.e., the gate insulator and the electrolyte [8].

Combining equation (2-10) and equation (2-14), we can get the effect of a small

在文檔中 以pH-ISFET元件為基礎之尿素感測器之製造與研究 (頁 37-42)