hydrogen ion-sensitive field-effect transistor system

Sensors and Actuators

565

B, 7 (1992) 565-571

ion-sensitive

An extended model of the electrolyte/hydrogen field-effect transistor system Wladyslaw Institute

Torbicz

of Bioeybernetics

and Zofia Sypniewska

and Biomedical Engineering,

Polish Academy

of Science,

Warsaw (Poland)

Abstract A binding site model of the electrolyte/oxide membrane pH-ISFET system taking into account hydrogen ion exchange and physical and chemical adsorptions is given. The influence of interface parameters on the characteristics of the system is analyzed. Theoretical and experimental data are compared.

Introduction A quantitative description of interfacial processes at the boundary area between ‘metal oxides and electrolyte subjected to ISFET analysis has been undertaken by many authors. The following surface reactions occur when the metal oxide or nitride ion-selective membrane (ISM) is in contact with the electrolyte: (i) hydrogen and hydroxyl ions (primary ions) adsorption at surface binding sites (main process) [ 1,2]; (ii) physical adsorption of interfering anions and cations; (iii) chemisorption (specific adsorption) of interfering anions, cations and neutral molecules [3-61 and (iv) superficial dissolving and gelling of the oxide. The influence of processes (i) and (ii) on pHsensitive ISFETs with metal oxide membranes has been analyzed in many papers, e.g. refs. 7-9. These processes do not explain the selectivity of the metal oxide membranes to disturbing ions if a binding site model is considered. The gelling process leads to instability of the sensor and such materials are not utilized for the pH-ISFET. We present a mathematical model of the electrolyte/pH-ISFET system, based on the binding site theory and on analysis of the electrical double layer (EDL) structure, which takes into account the joint effects of hydrogen ion exchange and physical and chemical adsorptions of anions, cations and neutral molecules. This is an extension of the models presented in refs. 7-9. It enables the calculation of the pH-ISFET’s selectivity coefficients on the basis of the membrane ion exchange parameters to be made. 092%4005/92/%5.00

The theory of ion exchange on the electrolyte-insulator interface Oxides: Alz03, Ta,05, ZrOz , TiOz, Hf02 and nitrides: S&N,., and BN ‘are applied as the ISM in pH-ISFETs [lo- 151. Because of the low conductivity of the considered oxides and nitrides, as compared to that of electrolytes, it is assumed that these substances are approximately insulators so electrical conduction inside the solid phase will not be considered. The surface binding sites are the aquo complexes of the forms: positively charged SOH2+, neutral SOH, and negatively charged SO-, where S denotes the positively charged unchanging part of the surface aquo complexes [ 1,2,5,7-91. S = WWN~WI

+

(1)

Structures of binding sites at the nitride surface are discussed’ in ref. 16. \There are indications that for the S&N4 membrane there are two groups of binding sites: SiNH2+, SIN, SIN- and SiOH2+, SiOH, SiO-. The structure of the first one is similar to the structure of aquo complexes on the oxide surface. The second group of binding sites is created due to the building in of oxygen atoms into the crystal lattice of nitride in the nitride deposition process or after contacting of the nitride surface with a’ water solution. Equations describing the hydrogen ion adsorption and physical adsorption of interfering ions (creation of ion pairs) on binding sites are presented in refs. 7-9. @ 1992 -

Elsevier

Sequoia.

All rights

reserved

566

It was stated that some complexes are created on the oxide surface due to the chemisorption of anions, Ai- cations, Ki+, and neutral molecules, Ni [3-61. The chemisorption of univalent anions may occur according to the reaction [3]

112 01

describing the values of the interface parameters.

tis=I; 0 2.3RT

pH,-pH-log

2

(7)

-a+ ‘/* as/~+~(as/~)*+(~~/yl+yl-)(l-a~)l”* a(QJYI+)U- as> zz

SOH+H++Ai-

+ S’OHzAi+ + OH-

S’ = [M(OH,)]*+

(2)

(8)

(3)

In this chemical reaction the proton and anion have entered into the complex group shifting the hydroxyl ion to the electrolyte and creating a new unicharged complex. Cations, Ki+ (univalent cations will be considered) may be chemisorbed on the negative sites as an anion group OKi- with oxygen as the ligand atom according to the reaction [3]

where a+, a_ and a,, are the relative densities of the positive, negative and neutral surface complexes for the main process, respectively. ci

4

tli=~=qNs

(9)

i describes the kind of surface complex pH, = - log(K,&) “*;

SO- + Ki+ Z+ SOKi

(4)

On the surface of some metal oxides neutral molecules may be chemisorbed. For example, ammonia may be adsorbed on the Ti02 surface [ 151. Some chemical reactions may be considered for this adsorption. It is assumed that the neutral ligand, Ni (NH3 for example), eliminates the H20 group from the neutral aquo complex giving a neutral surface complex: SOH+Ni

Z+ S”Ni+H,O

S” = [ M( OH,)]

6 = 2(&/&)“2

(10)

K,, K,, are the reaction equilibrium constants of the primary ions; q+ is the ratio of the concentrations of a+ to all positive surface complexes; q_. is the ratio of a_ to all negative surface complexes; q,, is the ratio of a,, to all neutral surface complexes. The relative densities of chemisorbed anions aAs, cations aks and neutral molecules aNs and relative densities of anion a,+ and cation c(kp ion pairs are given by equations:

(5) (6)

The surface complexes presented above do not exhaust all possible surface chemical groups. This problem is analyzed in refs. 3, 15 and 16. To find the surface potential, $s, dependence on the concentrations of solution components and in particular on the hydrogen ion concentration it is necessary to consider additional equations stating that [7-9, 151: (a) the sum of the concentrations of all surface complexes is equal to the density of the surface binding sites of the oxide, Ns; (b) the surface charge, bs, is the sum of the negative and positive charges of the surface complexes; (c) the EDL potentials depend on the EDL charges; (d) electrical charges in the solid-solution interface compensate charges in the semiconductor structure of the ISFET. From the equations presented above in the descriptive form we obtain, after introducing the notation given in refs. 7 and 8, the equations

aAp

=

KAip[A;Iexp(~A/~&+

1 i

aKp =

‘pAa+

1 KKi,[K:I exp( -+K/$da-

=PKa-

(11)

(12)

i

a As

-

[H+lc &is[A;b+ = bAa+

2

(13)

i

aKs

=

&

c

KKisLK?

I

Ian

=

bK%

(14) (15)

where: $0 = RTIF, KAip, KKip, KAis, KKis and KNis are the equilibrium constants of the physical and chemical adsorptions of the considered molecules aS=a+(l+PA+PA)-a-(l+PK)

43 a; Kb

a+a_ = -

(16)

(17)

The relationships presented above in which chemisorption is considered in addition to the hydrogen ion exchange and physical ion adsorption on the oxide surface are an extension of the earlier considerations [ 7, 81. An important quantity characterizing the solid/ liquid interface is the pH value corresponding to the surface charge of zero value, pH,,. This value equals pH, for the neutral interface condition and for q+ = q_.. The slope of the characteristic in the point of zero charge, pH,, is 2.3RT ’ = -7

1 l+RT/F&

(18)

where (19) C’sis the capacitance of the layer of EDL; c is the total concentration of one sign ions. As was mentioned above, the binding sites at silicon nitride ion exchange membranes are composed of two groups of binding sites of the type SiNH,, SiOH, (n = 0, 1,2). It was shown in ref. 15 that for k groups of binding sites and for electrolytes without disturbing ions the parameter pH, is equal to c N&k >I k and the slope of the characteristic is determined by eqn. ( 18) in which instead of $T one should put

PH; = c NsI(&PH* k

(21) where Nsk, & and pH& are parameters for each group of binding sites. Analytical determination of the dependence of the surface potential, &, on pH is impossible. It is done by the iterative method. Initially it is assumed that the surface charge as results from the filling of binding sites by H+ ions only. So us=ci+ - CI_ and q+ = r,r- = Q, = 1. Then for assumed c+, (a+/~_)“~ is calculated from eqn. (8), and a, from eqn. ( 17). Subsequent steps are: calculation of the diffusion layer charge, ad, from eqn. (8) and the diffusion potential, $d. From capacities and charges of EDL and potential $d, potentials $A and rjK of the compact part of EDL are calculated. Knowing these potentials it is possible to calculate the charges of ion pairs, a&, and (TKP,

surface potential, rjs, and pH. In the next steps we calculate PA, BK, BN, aAs, aKs and INS, and YI+ , qand vn, and on the end, the corrected value of us from eqn. (16). Values q+, q_ , q,, and tls calculated in the first iteration are the inputs in the second iteration. The iterative operation will end if the differences between pH quantities in subsequent steps are sufhciently small.

The influence of various factors on characteristics of the electrolyte/insulator system Primary and counterion adsorption In all calculations presented in this paper it is assumed that capacities of EDL are CA = C, = 140 uF cmm2, Cs = 17.5 uF cmP2 [2,7-91. The total capacity of EDL, C-r, depends on the total ion concentration, c, according to eqn. (19) and, for c = 0.1 mol dcrn3, C, = 14.1 uF cmP2. The influence of N,, K, and Kb on $(pH) characteristics has been analyzed by many authors and is shown in Fig. 1. The saturation of these curves appears even for small values of Ns density. This is due to the filling of all binding sites by positive charges (a+ = 1, c+ = 1) or negative charges (c(_ = 1, as = - 1) for the values of pH not very far from pH,. For oxides applied as ion exchange membranes of ISFETs the density Ns is of the order of (0.2 . . . 5) x 1014cmP2 for Si02, (0.8 . . . 1) x 10” cmW2for A&O3 and Ta205 and 1.2 x 10” cm-* for titanium group metal oxides [ lo- 151. It results from eqns. ( 18) and ( 19) that the slope of the characteristic is close to the Nernstian one and the characteristic is linear for p=----9NsGF $1

CTRT

(22)

The concentration of ion pairs created on the insulator surface depends on the equilibrium constants KA,, and KKP and on the total concentration of ions of one sign, c. Ion pair surface charges, a&, and cIKp, increase the surface charge, as, but because of the cancelling of the electrical field directed into a semiconductor structure by the counterions of the ion pairs, the influence of physical adsorption on the $,(pH) characteristic should be negligible. This is confirmed by the relationship rjs( pH) presented in Fig. 2(a) for the given K,, K,, . The saturation of these curves (ccs= l), not shown

568

Qce(pCI)

I

-6

-2

-4

0

2

4

6

8

1

-6

1

-4

I

-2

1

0

I

2

I

4

I

6

8

pH- pi-k

PH- P*

Fig. 1. c(ls(pH) and ccs(pH) dependences for KAp = KKp = 0.1,c =O.l mol dcm-s and Ka, Kbr N, respectively: (curve 1); IO-‘a, IO-’ 6, 1.2 x IO’scm-* (curve 2); IO-*, 10ms6, 5.0x IO” cm-’ (curve 3).

-6

-4

-2

0

2

4

6

8

-6

-4

-2

0

- CC-blip -

-6

-2

-4

0

4

6

10ms6, 1.2x 10’5cm-2

8

pH- pkk

pH-PHr ds+toHb--

2

IO-s,

ddbiH)-

2

4

6

- -

8

o%plpi+----

II

-6

’

’

-4

-2

&Kp(@-i)-

0

’

’

’

2

4

6

’ 8

Fig. 2. The influence of KAp and K,, on the interface quantities $s, us, a,, a_, a,, aAp. aKp for K, = IO-“, c = 0.1 mol dcm-3; KAp = KKp = IO (curve I), I (curve 2), 0.1 (curve 3), 0.01 (curve 4).

in the picture, takes place far above the considered pH range. Interfering ion and neutral molecules chemisorption

Measurements show that the presence of the ions differing from the potential-determining ions in an electrolyte introduce the saturation to the $s(pH) characteristics. The counterion adsorption discussed above does not explain this shape of

Kb= 10-36,

Ns = 1.2~ lO’5,

characteristic. Conformity of theoretical and experimental data is obtained after accounting for chemisorption. The influence of the chemisorption equilibrium constant, KKs, (it is assumed that KAs = 0) on insulator-electrolyte interface parameters, for a 1:1 electrolyte and for one kind of interfering cation of constant concentration, is presented in Fig. 3. The densities of the surface charge, Q, and

a3

-

@ \-;T,,,

569

I

1

0.2 0.1 -

_____-

ao._-__-____

-------_

1

-a4 -

2

-o.2-a3 -

, -6

3

4

-4

-2

0

2

4

6

8

6

8

pH-pHz

cC+CpHk----

-6

-4

-2

CC-CpH1 -

0

2

4

-6

-4

-2

dc*p(pH)-----

QCKP(PH~

-

: :

4

aaol: ;L : :

:

3

:

o.oo ----

LI

1

-6

-4

‘. ‘8.

. . . .24 . . . . .. . . . . .

1

i

1

1

1

L

-2

0

2

4

6

8

Fig. 3. The influence of KKS on the interface l), 10 (curve 2), 1 (curve 3), 0 (curve 4).

a2. a0 ?---

11 -6

1

1

i

I

1

I

1

-4

-2

0

2

4

6

B

pH-pHz

characteristics

for

KAp= KKp = 0.1, KAr= KNs= 0;other parameters

the main process complexes, CX,, tl_ and a, decrease with the increase of the cation chemisorption equilibrium constant, KKs, value. The saturation point, pHsat, of the $s(pH) curve depends on the KKsvalue. The value of pH,,, enables us to calculate the selectivity coefficient KHK of the ISFET for measuring the hydrogen ion activity, aH, of an electrolyte containing interfering cations of activity ak. For univalent cations =

aHsat

’

/aK

8

a6 y” y a4 -

P+Pk

&K

6

as.

\42,3,4 I

,“a02 ‘d

4

oC~s(oH)

I

d

2

A.0 .

I 0 0 I

: :

ao6.

0

pH- pHz

pH- pHz

(23)

Calculated values of the selectivity coefficients for

as for Fig. 2;

KKs= 100(curve

curves 1, 2 and 3 are 8.37 x lo-‘, 1.05 x lo-’ and 1.05 x 10V8, respectively. Due to the chemical adsorption of neutral molecules, neutral surface complexes block a part of the binding sites (Fig. 4(d)). In contrast to the cation chemisorption, which causes saturation of the $s( pH) characteristic, the chemisorption of neutral molecules introduces non-linearity near the pH, point (Fig. 4(a)), which is stronger for higher KNs values. If this process is irreversible, the blocking of binding sites may appear even for low KNs values, when the membrane surface is subjected to the electrolyte for a longer time.

570

-0.4-6

I

1

-4

1

-2

1

0

I

2

I

4

I

6

4

-6

8

-4

-2

pli- PHZ ccc*ipH)-----

2

4

@ 1.v I

4

I

t

1

-4

1 0

1

-2

8

I

a.2

11 -6

6

CcnlpH)

cG(pH)-

I

r

0

pH-pHr

I

2

1

4

1

6

II 8

-6

-4

-2

pH-pwz

0

2

4

6

pH-pH=

A.0 -

O.RS 4 o.Ao h % 0.05 0.

42

.3* A2 4=._:::, ’ .. ‘. . . ‘.*‘.Z. %_ -

11 -6

1

-4

4

s Q6 3 0.4

I

I , I I

-

0

42.

1

-2

;

0

1

2

I.__..__.______. ’ 1 c. 4 6 8

3 \

I

2

aor---

11 -6

1

-4

pH-pHz

1

-2

i

0

1

2

1

4

1

6

1

8

PH- P*

Fig. 4. The effect of KNpon the interface characteristics for the parameters of Fig. 3, for cN = 0.01 mol dcne3 and KAr= KKs= 0;KNs= 1 (curve 1), 10 (curve 2), IO2 (curve 3), lo3 (curve 4).

Discussion and conclusions

The results presented in this paper enable the examination of all important reactions in the insulator-electrolyte interface responsible for the generation of interface potential, which is the output signal of ISFETs. The iterations for the counting of the interface parameters are efficient for a very wide range of reaction equilibrium constant values if the main process and physical adsorption are considered. Introducing chemisorption into consideration

leads to a decrease of the stability range of this algorithm, which is smaller for the larger 6, KAP, KKp and KKs values. The influence of pH, and KNs on this stability is negligible. Comparison of the experimental and theoretical characteristics AUo,(pH) = A$(pH) of the TiOz gate pH-ISFET are presented in Fig. 5 for 0.1 mol dcrnm3acetic acid, without disturbing metallic ions (white squares) and with these ions of concentration 0.1 mol dcme3 (black squares), titrated with HCl, for decreasing pH, and with Tris, for increasing pH. Data related to Li+, Na+ and

571

References 1 D. E. Yates, S. Levine and T. W. Healy, Site-binding model of the electrical double layer at the oxide/water interface, J. Chem. Sot., Faraday Truns. I, 70 (1974) 1807-1818. 2 J. Davis, R. James and J. Leckie, Surface ionization and complexation at the oxide/water interface, I, J. CoNoid Interface Sci., 63 (1978) 480-499. 3 S. M. Ahmed, in J. W. Diglle (ed.), Oxide and Oxide Films, Vol.

1, Marcel Dekker, New York, 1972, Ch. 4, pp. 3199517. 4 F. J. Hingston, A. M. Posner and J. P. Quirk, Competitive adsorption of negatively charged ligands on oxide surfaces, Discuss. Faraday Sac., 52 (1971) 334-351. 5 H. P. Boehm, Acidic and basic properties of hydroxylated metal oxide surfaces, Discuss. Faraday Sot., 5.2 (1971) 264-289. 6 J. Westall and H. Hohl, A comparsion of electrostatic models for the oxide/solution interface, Adu. Colloid Interface Sci., 12 (1980) 0

2

4

6

8

A0

PH Fig. 5. Comparison of the experimental and theoretical characteristics of TiO, gate pH-sensitive ISFET. K. = IO-‘.“, Kb = 10-4.2, KAp=KKp=O.l, KAs=KNr=O. c=O.lmoldcm-3.

K+ ions are similar so they are not distinguished in this Figure. Chlorides of the above mentioned metals were used as the source of disturbing ions. It may be seen from Fig. 5 that the experimental curve AUos(pH) is saturated for the presence of these disturbing ions in the solution whereas it is unsaturated if they are absent. The theoretical curve was calculated for Ns = 1.2 x lOI cm-‘, C’s= 17.5 uF cme2 pH, = 5.8, KAP= KKp = 0.1 and for K, = 10-7.4 and Kb = 10-4.2 to fit the experimental slope of the characteristic, drawn with a full line. It is worth remembering that KAp and KKp values have a negligible influence on the slope of the characteristics, which for experiment is equal to 57.3 mV pH-‘. The saturation of the A Uos(pH) curve appears for pH = 8 and it corresponds to KKs = 10.

265-294. 7 L. Bousse, N. F. De Rooij and P. Bergveld, Operation of chemi-

cally sensitive field-effect sensors as a function of the insulatorelectrolyte interface, IEEE Trans. Electron Deoices, ED-30 (1983) 1263-1270. 8 L. Bousse, N. F. De Rooij and P. Bergveld, The influence of

counter-ion adsorption on the &,/pH characteristics of insulator surfaces, Surface Sci., 135 (1983) 479-496. 9 A. Van Den Berg, P. Bergveld, D. N. Reinhoudt and E. J. Sudhher, Sensitivity control of ISFETs by chemical surface modification, Sensors and Actuators, 8 (1985) 129-148. 10 T. Matsuo, M. Esahi and H. Abe, pH ISFETs using A&O,, S&N., and SiO, gate thin films, IEEE Trans. Electron Devices, ED-26 (1979) 1856-1857. 11 T. Matsuo and M. Esahi, Methods of ISFET fabrication, Sensors and Actuators, I (1981) 77-96.

12 T. Akiyama, Y. Ujihira, Y. Okabe, T. Sugano and E. Niki, Ion-sensitive field effect transistors with inorganic gate oxide for pH sensing, IEEE Trans. Electron Devices, ED-29 (1982) 19361941. 13 D. Sobczynska and W. Torbicz, ZrO, gate pH-sensitive field effect tansistor, Sensors and Actuators, 6 (1984) 93- 105. 14 D. Sobczynska, W. Torbicz, A. Olszyna and W. Wtosinski, Borazon-gate pH-sensitive field effect transistor, Anal. Chim. Acfa, 171 (985) 357-361. 15 W. Torbicz, Theory and Properties of Field Transistors as Biochemical Sensors, Ossehneum, Wroclaw, 1988 (in Polish).

16 D. N. Furlong, D. E. Yates and T. W. Healy, in S. Trasatti (ed.), Electrodes of Conductive Metallic Oxides, Part B, Elsevier, Amsterdam, 1981, p. 367.