Structure and Technological Parameters’ Effect on MISFET-Based Hydrogen Sensors’ Characteristics

Abstract

The influence of structure and technological parameters (STPs) on the metrological characteristics of hydrogen sensors based on MISFETs has been investigated. Compact electrophysical and electrical models connecting the drain current, the voltage between the drain and the source and the voltage between the gate and the substrate with the technological parameters of the n-channel MISFET as a sensitive element of the hydrogen sensor are proposed in a general form. Unlike the majority of works, in which the hydrogen sensitivity of only the threshold voltage of the MISFET is investigated, the proposed models allow us to simulate the hydrogen sensitivity of gate voltages or drain currents in weak and strong inversion modes, taking into account changes in the MIS structure charges. A quantitative assessment of the effect of STPs on MISFET performances (conversion function, hydrogen sensitivity, gas concentration measurement errors, sensitivity threshold and operating range) is given for a MISFET with a Pd-Ta₂O₅-SiO₂-Si structure. In the calculations, the parameters of the models obtained on the basis of the previous experimental results were used. It was shown how STPs and their technological variations, taking into account the electrical parameters, can affect the characteristics of MISFET-based hydrogen sensors. It is noted, in particular, that for MISFET with submicron two-layer gate insulators, the key influencing parameters are their type and thickness. Proposed approaches and compact refined models can be used to predict performances of MISFET-based gas analysis devices and micro-systems.

1. Introduction

Many types of hydrogen sensors are used in fire–explosion safety and environmental monitoring systems [1]. The microminiaturization and intellectualization of such systems based on microtechnology and nanotechnology as well as improving their performance characteristics are the main trends of their development [2]. To develop the integrated hydrogen sensors and gas-analytic lab-on-chip systems, the sensitive elements must have technological compatibility with the elements of the integrated circuits. The capacitor and transistor elements based on metal–insulator–semiconductor (MIS) structures have good compatibility with the integrated circuits’ elements [3].

Gas sensors based on MIS capacitors and field-effect transistors (MISFETs) have been studied by many investigators. A great contribution to the developments of gas-sensitive MIS devices has been made by the researchers at Linköping University since their first work in 1975 [4]. Works [5,6] described the gas sensitivity mechanisms, the kinetic modeling of hydrogen adsorption/absorption in thin films of catalytic metals and the formation of hydrogen atom dipoles in the metal–SiO₂ interfaces of MIS sensors. MIS sensors with different gate material (palladium [6], platinum and iridium [7]), with dielectric films SiO₂, Si₃N₄-SiO₂, TiO₂-SiO₂ and Ta₂O₅-SiO₂ have been investigated [8]. The semiconductors Si [4,7], GaAs [3,9] and SiC [10] were used in MIS gas sensors to detect the low concentrations of gases H₂ [6], NH₃ [7], H₂S [11], NO₂ [12] and CO [13]. The studies have shown that performance characteristics of MISFET-based hydrogen sensors depend on technological parameters [8], electrical modes [14], chip temperature [15] and external factors (e.g., irradiation [16]).

Work on the study of the hydrogen effect on the properties of thin Pd films (less than 1 micron) began long before the appearance of real MISFET, and they are still ongoing. It has been shown that under the influence of various concentrations of hydrogen in the air, the partial pressure of the surrounding gases, the temperature and type of substrate, the thickness and deposition technology of the Pd film as a result of chemical reactions, changes in the structure, density and chemical composition of palladium films can occur [8]. As a result, under certain conditions of thermo-hydrogen exposure, Pd_xH_y and PdO compounds are formed in palladium films, and the films themselves can swell and peel off from the substrate [17]. These effects lead to irreversible and/or reversible changes in the electrical conductivity of the films and the work of the electron output from Pd [3], which is the physical principle of operation of some types of hydrogen sensors.

In addition to these effects, the following processes are considered in the models of hydrogen sensitivity of MIS capacitors and MISFET. Firstly, the hydrogen molecules adsorb on the surface of the Pd film and then dissociate into atoms. The hydrogen concentration in Pd is proportional to the concentration of adsorbed hydrogen molecules in Pd and hydrogen concentrations in air, as well as dependent on Pd temperature and the concentrations of other molecules [18]. Secondly, there is the diffusion of hydrogen atoms through the Pd film to the Pd–insulator interface [6,19]. Some hydrogen atoms form Pd_xH_y compounds, the concentration, structure and “lifetime” of which strongly depend on the chip temperature and hydrogen concentration [14]. Some hydrogen atoms penetrate to the boundary, with the dielectric either directly through the pores in the palladium film or via the tunnel mechanism through palladium grains (clusters) [5,11]. It is these atoms that form a polarized dipole layer of H in the Pd–insulator interface [6]. In work [20], based on modeling, doubts are expressed about the possibility of forming a dipole layer at the palladium–dielectric boundary. Third, there may be diffusion and drift protons in the insulator [21].

Thus, the hydrogen sensitivity of MIS devices depends on many factors. The simultaneous taking into account of all the factors is very difficult or not possible at all. In this article, the hydrogen sensitivity of the sensor characteristics was evaluated on the basis of a two-component physical model that takes into account possible changes in the work of the electron output from the gate material and changes in the MIS structure.

In recent years, based on nano- on micro-technologies, gas sensors with low sensitivity thresholds and low inertia have been developed. For example, new developments used nanostructured palladium films and Pd nanotubes [22], electrodeposited nanomaterials [23], nanoporous silicon thin films [24], integrated FET [25] and carbon nanotubes [26]. Microtechnologies, in combination with CMOS technologies [27,28], are used not only for the development of hydrogen and hydrogen-containing gas sensors [29], but also for the detection of other types of gases (e.g., CO [13,30] and NO₂ [12,31]). Note that sensor developments [13,26] are based on functionalized Single-Walled Carbon Nanotubes (SWNTs).

The researchers at National Research Nuclear University MEPhI have developed and investigated the number of discrete and integrated gas sensors (MIS capacitors, Pd and Pt resistors) with Pd (or Pt)-SiO₂-Si, Pd/Ti-SiO₂-Si, Pd (or Pt)-Ta₂O₅-SiO₂-Si structures. Experiments have demonstrated that MISFETs have the best performances compared to MIS capacitors and resistors. In addition, the integrated sensors, containing MISFET with a Pd(Ag)-Ta₂O₅-SiO₂-Si-structure (hereinafter referred to as TSE), possess the best stability and reproducibility of characteristics [21]. In recent years, we have investigated the metrological and operating characteristics of TSE (e.g., electrical modes [14], chip temperature [15] and irradiation [16]).

In this paper, we have investigated the influence of the structure and technological parameters (STPs) on the characteristics of MISFET hydrogen sensors in a general form, and for TSE, based on refined compact models, allowing us to simulate the hydrogen sensitivity of gate voltages or drain currents in weak and strong inversion modes, taking into account changes in the work of the electron output from the gate material and charges in the MIS structure. A quantitative assessment of the effect of STP on the TSE conversion function, hydrogen sensitivity, gas concentration measurement errors, sensitivity threshold and operating range is given.

2. Materials and Methods

2.1. Initial Structure and Technological Parameters of TSE

The initial structure and technological parameters, which are considered unchanged when modeling sensor characteristics, included the dimensional parameters of the structural elements, the parameters of the semiconductor and the dielectric materials listed in

Table 1. Average values of the parameters of MISFETs and parameters of used models.

Symbols	Parameters	Values
Parameters of semiconductor and dielectric materials
ε1, ε2 and ε3	relative permittivity of Ta2O5, SiO2 and Si	25, 4 and 12
NA	concentration of acceptors in Si	5 × 1015 cm−3
µn	electron mobility in the channel	200 cm2/(V∙s)
Dimensions of structural elements
L and w	channel length and width	10 μm and 3.2 mm
d1 and d2	thicknesses of Ta2O5 and SiO2	90 nm and 80 nm
dm	thickness of the gate metal film	70 nm
Constants and derived parameters
ε0	dielectric constant of vacuum	8.85 × 10−12 F/m
k	Boltzmann constant	1.38 × 10−23 J/K
q	electron charge	1.6 × 10−19 Cl
d	thickness of the gate dielectric is (d1 + d2)	170 nm
ε	effective permittivity of the dielectric layer is (dε1ε2)/(ε1d2 + ε2d1)	7.1
C0	specific capacity of the dielectric (ε0ε)/d	37 nF/cm2
a	charge parameter in Si is (2q ε0∙ε3∙NA)1/2/C0	1.18 V1/2
b	specific steepness is (µnw C0)/L	2 mA/V2
Physical and electrical parameters
φms	output work difference potential Pd– Si	φms0 = 85 mV
T	chip temperature	400 K
φT	thermal potential (kT/q) at 400 K	33 mV
φgb	the potential of the band gap in Si	1.08 V
φs0	the potential of acceptors’ level is φT ln(NA/ni) at 400 K	0.21 V
φs	surface potential is [φ(SiO2 − Si) − φF]	0.2…0.8 V
Qte and Qss	charge densities in the dielectric and in SiO2 − Si interface	(5…100) nKl/cm2
ID	drain current	(2…300) μA
VD	voltage between the drain and the source	(0.1…0.5) V
VG	voltage between the gate and the substrate	(1…3) V
Qte and Qss	charge densities in the dielectric and in SiO2 − Si interface	(5…100) nCl/cm2
ID	drain current	(2…300) μA
VD	voltage between the drain and the source	(0.1…0.5) V
VG	voltage between the gate and the substrate	(1…3) V

. The STP values are determined using the specified materials, structure and topology of the TSE and are used to calculate the parameters C₀, a and b of the TSE characteristic electrophysical models.

The errors in the calculations of electrophysical parameters depend on the errors of the STPs, which are determined using the technological standards or errors of the measuring instruments, if the values of the STPs were determined experimentally. For example, if ε₃ is (12 ± 0.2), w is (3.2 ± 0.02) mm, L is (10 ± 0.1) μm, µ_n is (200 ± 5) cm²/(V∙s), N_A is (5 ± 0.02) × 10¹⁵ cm⁻³, then the relative errors of the parameters C₀, a and b are equal to 3.5%, 4.5% and 8.7%, respectively.

Denote the parameters with the symbol p_k ∈ {p_k} (k = 1, 2, …, 13 in

Table 2. The effect of STP p_k on the components of TSE models.

k	STP		Components of TSE Models
1	film production technologies	Pd	ΔQte (C); Δφms(C); φms0
2		Ta2O5	ΔQte(C); C0; b
3		SiO2	Qte0; Qss; C0; b
4	film thicknesses	Pd (dM)	ΔQte (C); Δφms(C)
5		Ta2O5 (d1)	ΔQte(C); Qte0; C0; b
6		SiO2 (d2)	Qte0; C0; b
7	acceptor concentration	(NA)	a; φs0; Qss
8	channel length	(L)	b
9	channel width	(w)
10	electron mobility in the channel	(µn)
11	relative dielectric permittivity	Ta2O5 (ε1)	a; b; C0
12		SiO2 (ε2)
13		Si (ε3)

). In general, the absolute and relative errors of the parameters Δp_k and δp_k are equal to ׀p_kn − p_k׀ and (Δp_k/p_kn) × 100%, respectively. The value of p_kn is the desired (nominal) value of parameter p_k or its average value, if this parameter was determined experimentally from a set of measured values.

The absolute errors of Δp_k depend on the film manufacturing technologies (for parameters with indices k ∈ {1; 2; 3; 4; 5; 6}, on photolithography technologies (for p₈, p₉), on methods of estimating their thicknesses (for parameters with indices k ∈ {4; 5; 6} and on the type and structure of the materials (for parameters with indexes k ∈ {11; 12; 13}. Typically, the values of Δw and ΔL are in the range of 0.1 to 0.5 microns, and values Δd ∈ [5 nm; 15 nm] depend on d. The relative errors δw and δL are in the range from 0.002%...0.01% to 1.1%...5%. For specific technologies of the semiconductor wafers and dielectric films production, the relative errors δε₁, δε₂, δε₃, δµ_n and δN_A usually do not exceed 2%. The relative errors of δd₁ and δd₂ are in the range of δd_min ∈ [2%; 10%] to d_max ∈ [7.5%; 30%] and are the maximum for the STPs. Consequently, the thicknesses d₁ and d₂, the dimension of which will be determined in nm, can be considered the most critical STP.

2.2. Metrological Characteristics of TSE

To assess the influence of various factors on the characteristics of the sensors and systems being developed based on MISFETs, simulation modeling can be used, which is considered a fast and inexpensive method compared to full-scale tests of sensors with various STPs. In simulation modeling, the type, structure and values of STPs and the parameters of the models are chosen arbitrarily. In this paper, the characteristics of the TSE with the parameters specified in Table 1 were studied.

A fragment of the structure, the schematic designation of the n-channel TSE and a potentiometric circuit of its embedding for measuring the gas concentration C are shown in Figure 1 and Figure 2.

The main metrological characteristics of TCE include: conversion function (dependence V as function of C); differential S_d and integral S sensitivities being equal to dV/dC and ΔV/ΔC; absolute ΔC and relative δC errors of measurement C; the sensitivity threshold C_th; minimum relative error δC_min; the boundaries of the working range C₁ and C₂, limited by a given error δC_max and finally C_max.

As previous studies [16,21] have shown, the conversion function of a TSE can be represented in general form as V (C) is [V₀ − ΔV(C)], where the initial value of V (at C = 0) is equal to V₀. In general, the output signals V of MISFETs-based sensors are formed as a result of the embedding of one or more transistors in various measurement circuits. In this paper, the main components of the models are determined using experimental studies of one TSE in the mode with a constant current I_D and the voltage V_D as shown in Figure 2b. In this case,

V (C) = V_G (C) = V_G0 − ΔV_G (C) and S_d = dV_G/dC,

(1)

V_G0 (φ_s) = φ_s + a·{φ_s + φ_T·exp[(φ_s − 2φ_s0)/φ_T)]}^1/2 + φ_ms0 − [Q_te0 + Q_ss (φ_s)]/C₀.

(2)

For modeling the characteristics of TSE sensors, the following expression can be used to approximate the conversion function in the range of hydrogen concentrations from 0.005 vol.% to 1.5 vol.% [16]:

ΔV_G(C) = ΔQ_te(C)/C₀ − Δφ_ms(C) = ΔV_m · [1 − exp(−k_C·C)] > 0.

(3)

Then, the sensitivity of S_d is equal to [−k_C·ΔV_m · exp(−k_C·C)]. The maximum relative error of measuring the gas concentration δC in the general case is represented as

δC = 100% × ΔC/C = 100% × [Δ(C)·|S_d| + ΔV + Δ(V)]/(C|S_d|),

(4)

where Δ(C) is the absolute error of the specified gas concentration during sensor calibration, ΔV is the error voltage measurements and Δ(V) being equal to Δ(ΔV_G) is the absolute voltage error associated with an absolute error of the parameter p_k and is approximately equal to [dV_G/dp_k]·Δp_k. Then, after sensor calibration the sensitivity threshold C_th is (ΔV/|S_dmax|), minimum relative error is δC_min and the boundaries of the working range C₁ and C₂ can be determined as solutions of Equations (5) and (6). The value of δC_min is δC (at C is C^*), where C^* is the solution of the following equation:

d(δC)/dC = 0.

(5)

The values of C₁ and C₂ are solutions of Equation (6) with respect to C at a given δC_max greater than δC_min:

δC_max = 100% × [Δ(C)|S_d| + ΔV + Δ(V)]/(C|S_d|),

(6)

C_max = (1/k_C) · ln (ΔV_m/ΔV).

(7)

These transcendental equations will be solved using numerical methods. The testing n-channel MISFET based on the Pd-Ta₂O₅-SiO₂-Si structure was fabricated on a single chip (2 × 2 mm²) together with a (p–n) junction temperature sensor and heater resistor by means of conventional n-MOS technology. Technological processes are detailed and presented in [14,21].

3. Results

3.1. Influence of Film Manufacturing Technology and Thicknesses on the Components of the Conversion Function

The experimental studies demonstrated that the MISFET hydrogen sensitivity depends on several effects, which occur in regions of the (ambient gas)–metal–dielectric structure. The probability of various effects depends on the following factors: chip temperature; partial pressure of hydrogen; material, chemical composition, structure, manufacturing technology and thickness of the gate film and the pressure of the gas medium [4,13,18,22,23]. The presence of a large number of influencing factors complicates and/or make it impossible in principle to simulate the influence of the material, the technology of production and the thickness of the shutter film on the metrological characteristics of MISFETs. The degree of this influence can only be determined experimentally. The morphology (crystalline, polycrystalline, amorphous, nanoparticles, etc.) of palladium films may affect the hydrogen sensitivity of sensors based on Pd film resistors or MIS structures as shown, for example, in [21,22].

Basically, the deposition technology and thickness of metal film d_m can affect the conversion function components ΔQ_te(C) and Δφ_ms(C). In the investigated TSE Pd film (d_m is 70 ± 5 nm) was prepared using laser evaporation in vacuum 2·10⁻³ Pa in the substrate’s temperature range of 300–400 °C. For this technology, at thicknesses d_m that is less than 80 nm, the palladium film has a porous structure. Therefore, it can be assumed that the hydrogen sensitivity and response time will be independent of d_m and of its deviations Δd_m from the nominal values of d_mn. For other technologies (for example, with thicknesses of nanostructured Pd films less than 30 nm), the response time decreased, and the sensitivity can be increased at low concentrations (~5–50 ppm) with a decrease in d_m [32]. Quantitative analysis of the effect of the Pd films’ characteristics on the hydrogen sensitivity of the TSE requires special experimental studies, which have not been observed in this work.

Deposition technologies and the thicknesses of dielectric films d₁ and d₂ can affect the conversion function components V_G0 and ΔV_m, which according to (2) and (3) are inversely proportional to specific capacity C₀:

V_G0 = φ_s + 0.085 + {41·[φ_s + 0.033·exp((φ_s − 0.42)/0.033)]^1/2 − 5}/C₀ (V),

(8)

ΔV_m = ΔQ_tem/C₀ − Δφ_msm = 15/C₀ + 0.11 (V),

(9)

C₀ = (ε₀ε₁ε₂)/(ε₁d₂ + ε₂d₁),

(10)

where in engineering physical models (8) and (9), the dimensions of the potentials are the volts, charge density is nCl/cm², capacitance is nF/cm² and thicknesses is nm. With an increase in the hydrogen concentration, the work of the electron output from Pd decreases, and therefore you have a negative value Δφ_ms(C) [3]. The absolute ΔC₀ and relative δC₀ being equal to 100% × ΔC₀/ΔC₀ errors for C₀ are, respectively, equal to:

ΔC₀ = ε₀[ε₂d₁(Δε₁·ε₂ + 2Δε₂·ε₁) + ε₁d₂(Δε₂·ε₁ + 2Δε₁·ε₂) + ε₁·ε₂(Δd₂·ε₁ + Δd₁·ε₂)]/(ε₁d₂ + ε₂d₁)²,

(11)

δC₀ = [δε₁(2ε₁d₂ + ε₂d₁) + δε₂(2ε₂d₁ + ε₁d₂) + δd₂·ε₁d₂ + δd₁·ε₂d₁]/(ε₁d₂ + ε₂d₁),

(12)

where Δε₁, Δε₂, Δd₁ and Δd₂ and δε₁, δε₂, δd₁ and δd₂ are the absolute and relative errors of the corresponding values. For the values, ε₁ is 25 and ε₂ is 4, and the dependences of the components C₀ and δC₀ on thicknesses of d₂ at different values of d₁ are shown in Figure 3.

In the process of forming metal and dielectric films at a constant temperature Tp of the silicon wafer (substrate), their thicknesses depend on the time of the process t and on the temperature-dependent growth rate of the film v_i. For example, when creating a SiO₂ film via silicon oxidation in dry oxygen, the dependence of d₂(t) for various Tp is shown in Figure 4 (based on Figure 8a in [32]). At the initial stage of silicon oxidation (up to d₂ is about 30 nm), the thickness of the SiO₂ film is proportional to the oxidation time t; with further oxidation, the thickness of d₂ is proportional to (t)^1/2. If the oxidation of silicon in dry oxygen is carried out at a temperature of 1100 °C, then the thickness d₂ is v₁·t (nm) at t ∈ [0; 10 min] and d₂ = 30 + v₂·(t)^1/2 (nm) when the t is greater than 10 min, where v₁ and v₂ are equal to 4.0 nm/min and 8.5 nm·min ^½; [t] is min.

The error δd₂ is (δv₂ + 100% × Δt/t) or δd₂ is (δv₂ + 50% × Δt/(t)^1/2), where δv₂ depends on the dispersion of the plate temperature ΔTp. The value of Δt is determined by the time parameters of the temperature response Tp (t) when the plate is introduced into the core with the constant temperature and partial pressure of oxygen, or by the time parameters of establishing a constant partial pressure of oxygen after oxygen is introduced into the placement zone of the plate heated to the operating temperature Tp and the time of oxygen pressure drop. Usually, δv₂ < 0.5% and Δt ∈ (0.5; 2) min. For a given thickness d₂, the error δd₂ can be estimated as δd₂ being less than the value of [0.5% + 425Δt/(d₂ − 30)]. For example, if d₂ is 50 nm and Δt is 30 s, then the value of δd₂ < 11.1%, and if d₂ is 80 nm and Δt is 30 s, then the value of δd₂ < 4.75%.

Thus, the thicknesses and dielectric permittivities of dielectric films determine the capacitance C₀, which can be considered a key parameter affecting the TSE conversion function.

3.2. Influence of Material’s Parameters and Topological Dimensions of Elements on Conversion Function Components

The material’s parameters (ε₃, N_A, µ_n) and topological dimensions (L, w) affect parameters a and b, which depend on the value of C₀. According to (2), the conversion function component V_G0 depends on the variables parameters a and φ_s. Then, the absolute error ΔV_G0 with small deviations Δa and Δφ_s a from their average values can be presented as:

ΔV_G0 = (∂V_G0/∂φ_s)Δφ_s + (∂V_{G0 /}∂a)Δa = 0.01·(K_φ·φ_s·δφ_s + K_a·a·δa),

(13)

K_φ = 1+ 0.5a(1+ exp m)/(φ_s + φ_T·exp m)^1/2; K_a = (φ_s + φ_T·exp m)^1/2; m = (φ_s − 2φ_s0)/φ_T.

(14)

Parameter a depends on values of ε₃, N_A and C₀, and the potential φ_s depends on the given values of I_D and V_D. According to the simplified TSE electrical model [15], the dependence I_D (V_G) at φ_s > 2φ_s0 has two sections: parabolic when I_D ∈ [I_D0; I_D1] and φ_s ∈ [2φ_s0; φ_s1], and linear when value of I_D is greater than I_D1 being equal to (I_D0 + 0.5bV_D²). In principle, the entire range of changes in the drain current I_D and gate voltage V_G corresponding to the inversion mode can be used to measure the hydrogen concentration. Usually, the values of the set current are within the error range: I_D is I_Dn ± ΔI_D.

In practice, the electric mode of strong inversion (at φ_s > φ_s1) is chosen, in which the measurement errors ΔV_G0 and δC are minimal. For example, when V_D is 0.2 V (I_D1 is 42 μA) and I_D is equal to (20 ± 2) μA, the value of V_G0 is (1.16 ± 0.01) V, and when I_D is equal to (100 ± 2) μA, the value of V_G0 is (1.25 ± 0.005) V. Then, the values of I_D and fluctuations of Δφ_s are represented as:

I_D = b·{a·V_D·[(φ_s + φ_T exp m) ^1/2 − φ_s^1/2] − 0.5V_D²}; Δφ_s ≈ 2ΔI_D·(φ_s + φ_T exp m)^1/2/[a·b·V_D·(1 + exp m)].

(15)

The dependences of the potential φ_s on the current I_D at different V_D and on values of V_G0 at different C₀ are shown in Figure 5. The relative errors of conversion function components a and b are equal to:

δa = δC₀ + 0.5(δε₃ + δN_A) = 4.5% and δb = δC₀ + δµ_n + δw + δL = 8.7%.

(16)

Quantitative values of a and b are given for the investigated TSE. Average values of the parameters of the conversion function for different C₀ and (w/L) are presented in

Table 3. Average values of parameters for different C₀ and (w/L) at I_D is 0.1 mA and V_D is 0.2 V.

Parameters →	δC0, %	a, V	δa, %	w/L Is 0.003			w/L Is 0.006
↓ C0, nF/cm2				b, mA/V2	δb, %	ΔVG0, mV	b, mA/V2	δb, %	ΔVG0, mV
30	2.1	1.37	3.1	1.62	7.3	6	3.24	7.0	3
40	3.6	1.02	4.6	2.16	8.8	4.6	4.32	8.5	2.3
50	5.5	0.82	6.5	2.70	10.4	3.7	5.4	10.1	1.8

. As an example, Figure 5 shows the coordinates of the points corresponding to the values V_G0 being equal to 1.2 V, 1.4 V and 1.7 V for different V_D and a given drain current of 1 mA.

3.3. Influence of Specific Capacity on the Main Metrological Characteristics of TSE

The quantitative assessment of the effect of STPs on the initial value of the output signal, hydrogen sensitivity, absolute and relative errors in measuring gas concentration, the sensitivity threshold, the maximum concentration and the hydrogen concentration range for a given maximum relative error is given. The calculations used engineering physical models obtained on the basis of selected electrophysical and electrical models. The dependences of δC(C) and the average values of metrological characteristics for different C₀ are presented in Figure 6 and in

Table 4. Average values of metrological characteristics for different C₀ at δC_max being equal to 7%.

MC →	VG0, V	ΔVm, V	kC, 1/(vol.%)	Sdmax, V/(vol.%)	δCmin, %	Cth, ppm	C1, ppm	C2, ppm	Cmax, ppm
↓ C0, nF/cm2
30	1.55	0.61	8	4.88	4.9	2.0	50	1410	8016
40	1.52	0.42		3.36	5.5	2.9	90	1210	7550
50	1.48	0.32		2.56	6.1	3.9	160	960	7210

.

4. Discussion

The analysis of the data obtained allows us to draw the following conclusions.

• All the considered STPs of the TSE (p_k in Table 2) affect the components of the conversion function on which the main metrological characteristics depend.
• The deposition technology and thickness of the metal film dm can affect the conversion function components ΔQ_te(C) and Δφ_ms(C) on which the sensor’s hydrogen sensitivity and the response time depend. A quantitative analysis of the effect of the Pd films technological characteristics on TSE hydrogen sensitivity requires special experimental studies. In the investigated TSE, the Pd film has a porous structure. Therefore, it can be assumed that the hydrogen sensitivity and response time will be independent of d_m and of its deviations Δd_m from the nominal values of d_mn.
• The values of V_G0 and ΔV_G0 depend on N_A, C₀ and the given electrical parameters I_D and V_D. With the growth of I_D and V_D, the error ΔV_G0 decreases. As a result of the calibration of the measuring device, the zero error is determined by the error ΔV_G0 or the instrumental error of the voltage measurement ΔV (in the examples considered, ΔV is 1 mV).

5. Conclusions

Refined compact electrophysical and electrical models are proposed that link the drain current, the voltage between the drain and the source, the voltage between the gate and the substrate with the structure and technological parameters (STPs) of an n-channel MISFET as a sensitive element of a hydrogen sensor (TSE). The method of the analytical assessment of the effect of STPs on the main metrological characteristics of a TSE is proposed. A qualitative assessment is given of the influence of the metal gate film manufacturing technology, the technology of manufacturing the gate dielectric films and their thicknesses, the concentration of impurities in the semiconductor, the length and width of the channel and the mobility of electrons in the channel on the metrological characteristics of TCE.

Using the example of a TSE with a Pd-Ta₂O₅-SiO₂-Si structure, manufactured according to a specific technology, a quantitative assessment of the effect of STPs on the initial value of the output signal, hydrogen sensitivity, absolute and relative errors in measuring gas concentration, the sensitivity threshold and the hydrogen concentration range for a given maximum relative error is given. The calculations used engineering physical models obtained on the basis of selected electrophysical and electrical models.

The degree of influence of each STP and their errors on the components of the conversion function and the main metrological characteristics of a TSE is shown. It has been established that for a specific technology of manufacturing TSEs (in particular, for MISFET with submicron two-layer gate insulators), the key influencing parameters are their type and thickness. Proposed approaches and models can be used to predict performances of MISFET-based gas analysis devices and micro-systems and also to solve the inverse problem determining the STPs according to the specified metrological characteristics.

In contrast to works [22,29], in which structures with ultrathin single-layer dielectric films were studied, this work shows the significant effect on the hydrogen sensitivity of sensors of submicron thicknesses of MISFET dielectrics.