c Pleiades Publishing, Ltd., 2016. ISSN 0005-1179, Automation and Remote Control, 2016, Vol. 77, No. 7, pp. 1301–1315. c B.I. Podlepetsky, 2015, published in Datchiki i Sistemy, 2015, No. 1, pp. 60–71. Original Russian Text
SENSORS AND SYSTEMS
Modeling of Radiation Sensitivity of Hydrogen Sensors Based on MISFET B. I. Podlepetsky National Research Nuclear University “MEPhI” (Moscow Engineering Physics Institute), Moscow, Russia e-mail:
[email protected] Received November 25, 2014
Abstract—The paper presents the electrophysical and electrical models of hydrogen and radiation sensitivities of the integrated sensors with MISFET sensing elements based on the structure Pd–Ta2 O5 –SiO2 –Si. The models take into account the influence of electrical circuits and modes, chip temperatures, surface-state density and radiation parameters on the hydrogen sensitivity of the sensors. DOI: 10.1134/S0005117916070171
1. INTRODUCTION The development of integrated sensors (IS) with sensing elements (SE) fabricated by means of microtechnology is a promising area for creation of small-sized gas-analysis devices and microsystems [1]. The hydrogen sensors used in the explosion and fire safety systems of metal mining industry, nuclear reactors, battery storage facilities, hydrogen engine vehicles and medicine attract most interest [2, 3]. The researchers from Micro and Nanoelectronics Department of “MEPhI” developed hydrogen sensors with the MIS structures Pd(Pt)–SiO2 –Si, Pd/Ti–SiO2 –Si, Pd(Pt)–Ta2 O5 –SiO2 –Si. Among the created hydrogen sensors, the best characteristics belong to the integrated cell IDV-3 containing four elements on a chip: a hydrogen-sensitive metal-insulator-semiconductor field-effect transistor (MISFET, further referred to as TSE) with the structure Pd–Ta2 O5 –SiO2 –Si and a hydrogensensitive palladium resistor, a resistor-type heating element and a test MISFET with the structure Al–SiO2 –Si (also used as a thermosensitive element in the stabilization circuit of TSE operating temperature). The structure and layout of IDV-3 were described in the papers [4, 5]. According to experimental investigations, the metrological and performance characteristics of IDV-3 depend on the technological characteristics, the thermal and electrical modes of TSE and the parameters of external influencing factors (the concentrations of other gases, the power of optical and ionized radiation) [6, 7]. In comparison with the full-scale tests of measuring devices, simulation modeling is a rather fast and cheap method for estimating the influence of different factors on the characteristics of new sensors, devices and systems. The earlier papers [6, 7] employed experimental results were used to develop the TSE models for computation of the characteristics of integrated hydrogen sensors and microsystems based on them. The influence of radiation on the characteristics of MIS structures and devices based on them was studied since the 1960s. Here some contributions belong to the researchers from Micro and Nanoelectronics Department of “MEPhI.” The results of their investigations were published in the papers [5, 8–10] and in the books [11–13]. It was shown that radiation effects and their influence on MISFET characteristics depend on different factors such as the type, energy, power 1301
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and directivity of radiation, the initial technological characteristics, temperature and electrical modes of the transistor. Numerous descriptive electrophysical models were proposed for the experimental results of radiation influence on the characteristics of MISFET and integrated circuits based on them (physicians are used to joke that “there exist as many models as defended dissertations”). Trying to create general models, to account the influence of different factors and to increase modeling accuracy, many investigators incorporate additional parameters into the models, which are often difficult to define experimentally. Actually, this complicates the models, decreases their reliability and accuracy, as well as impedes their practical usage. It is impossible to take all the aspects into consideration! Simplified mathematical models with a small number of parameters not always have a pure physical sense, but are sufficiently accurate for performing approximation of experimental dependencies with an uncomplicated parameter extraction procedure. All the models are approximate, some of them contradict each other or supplement the previous analogs. In the context of practical model usage for predicting radiation influence on the characteristics of sensors and devices, it is important to account concrete operating conditions (radiation parameters, temperature, electrical modes and their time dependence). This paper systematizes and generalizes the well-known radiation effects in MISFET. The author suggests the compact electrophysical and electrical models of ionizing radiation influence on the characteristics of MISFET with the structure Pd–Ta2 O5 –SiO2 –Si and hydrogen integrated sensors based on them. The models consider the operating conditions of the sensors. 2. PHYSICAL PRINCIPLES OF RADIATION INFLUENCE ON TSE CHARACTERISTICS The common properties of radiation effects in TSE are systematized and defined through generalizing well-known physical representations. Figure 1a shows a simplified variant of the energy band diagram whose parameters are used for analysis of electrophysical processes in the structure Pd–Ta2 O5 –SiO2 –Si. The quantities q, E0 , Ei , EC , EV and EF denote the electron charge, the vacuum level energy, the semiconductor band gap middle energy, the conduction band bottom energy, the valence band top energies of corresponding structural layers and the Fermi level energy. The numbers of corresponding layers in the MIS structure are indicated by bracketed numerals. “Ideal conditions” imply the absence of charges, zero gate voltage and zero difference of the work functions of the metal and semiconductor. The energies between the main levels which depend on the temperature and technological characteristics of the structural layers are indicated by their average values in eV, see Fig. 1a. In real TSE, there may exist charges in all structural layers and their boundaries; according to the electrical neutrality condition, the algebraic sum in electrostatic consideration equals zero. As a rule, charges have an irregular localization in the MIS structure (see Fig. 1b) and influence on electric fields, ergo TSE electrical characteristics. The insulator layers possibly contain free electrons and holes with concentrations n(x) and p(x), as well as mobile ions (e.g., H+ , Na+ ) and immobile (fixed) charges of trap-captured electrons and holes with volume densities ρI (x), ρTe (x) and ρTh (x), respectively. The total volume charge density (Fig. 1b) is defined by ρ(x) = ρI (x) + ρTh (x) − ρTe (x) + q[p(x) − n(x)].
(1)
Following changes in temperature, the level of radiation and electrical fields in the MIS structure, the charges can be redistributed due to the drift and diffusion of ions, electrons, holes and charge exchange of trap centers (traps). The charge redistribution kinetics in the local structural areas depends on the concentration of free electrons n(x) and holes p(x), the energy state and volume density of traps ρT (x) which can vary under the influence of temperature and radiation (Fig. 1c). AUTOMATION AND REMOTE CONTROL
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Fig. 1. (a) The energy band diagram of the structure Pd–Ta2 O5 –SiO2 –(p-Si) and its thermodynamic equilibrium parameters under ideal conditions, (b) the structural charge distribution and the charge density function ρ(x) with hydrogen under voltage UG > 0, (c) the trap density distribution ρT (x): 1—before radiation ρT0 (x); 2—after radiation ρTM (x); A and B are the hydrogen and radiation sensitivity zones, respectively.
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The traps have the energy status ΔET in the forbidden bands of insulators and semiconductors, with division into deep and shallow, donor and acceptor ones which can be neutral or charged [11, 14]. The energy levels of traps ET are calculated from the energy boundaries of material forbidden bands: ET = (EC − ΔET ), as for the electron trap T1; or ET = EV + ΔET , as for the traps T2 (Na+ ), T3 (the hole trap) and the traps of three-valency silicon T4 (E -center) demonstrated in SiO2 by Fig. 1a. The charge status of the traps depends on the position of their energy level with respect to the Fermi level EF . The donor traps are empty (positive charged) if located higher than the level EF , and they are filled (neutral) otherwise. The acceptor traps are empty (neutral) if located higher than the level EF , and they are filled (negative charged) otherwise. For narrow bands Δx ∼ (1 . . . 10) nm with increased values of ρT (x), it is necessary to introduce averaged quantities of specific densities (per unit area), namely, the volume charge Q(x, Δx), the trap centers NT (x, Δx) (the trap density), the charged trap charges QT (x), the charges of the inversion and volume layers of the semiconductor QSI and QSD (Fig. 1b) X+ΔX
Q(x, Δx) =
X+ΔX
ρ(x)dx;
NT (x, Δx) =
X
ρT (x)dx;
(2)
X
QT (x, Δx) = ±qNT ;
QSD = qNA dD (ϕs );
QSI = ρi di (ϕs ),
where NA denotes the acceptor concentrations and ϕs represents the surface potential. In addition, it is necessary to introduce the effective insulator charge density Q0 reduced to the metal charge, and the trap energy-averaged effective density of surface-state charge Qss on the boundary SiO2 –Si (Fig. 1b): 1 Q0 = d
d
xρ( x)dx ≈ QIn1 d1 /d + QIn2 (1 − x0 /d);
(3)
0
Qss (Nss , ϕs ) ≈ Nss q(ϕs0 − ϕs )/ϕG , where ϕs0 = (Ei − EF )/q = ϕT ln(NA /ni ), ϕT = kT /q, ni are the charge carrier concentrations in the pure semiconductor,ϕG = (EC − EV )/q denotes the potential corresponding to the semiconductor forbidden band width, k means the Boltzmann constant, and T specifies the absolute temperature. The physical and mathematical support of modeling of the spatiotemporal distribution characteristics of electric charges and fields includes the following components: the electrical neutrality condition, the Poisson equation, the continuous flow equation for the electrons and holes and the continuous electrostatic induction condition [16]. The analytical solutions of these equations in general form are impossible. Therefore, modeling involves either numerical solution methods or simplified (less accurate) models on the basis of averaged spatiotemporal and energy characteristics of physical quantities and phenomena. This paper adheres to the second approach. The reason lies in rather high estimation errors of radiation parameters (energies, doses, power levels) in radiation sensitivity experiments for electronic devices: the instrumental errors are ∼ (10 . . . 15)%, while the methodic errors reach ∼ (20 . . . 30)% [13, 15]. Moreover, in the simplified models it is not difficult to relate the electrophysical and technological parameters of TSE with the electrical and metrological characteristics of sensors and devices [5]. AUTOMATION AND REMOTE CONTROL
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The kinetics of phenomena connected with filling (releasing) a spatially bounded number of vacancies having the density ρM is described by the classical equation ∂ρ = ν(t)[ρM (t) − ρ(t)], ∂t
(4)
where ρ gives the filled vacancy density, ν indicates the characteristic event frequency defining the vacancy filling rate with the density (ρM − ρ). The solutions of this differential equation depend on the parameters ν and ρM :
ρ(t) =
⎧ ρ0 + (ρM − ρ0 )[1 − exp(−νt)], ⎪ ⎪ ⎪ ⎪ ⎨ρ + νρ t,
if ν = const and ρM = const
(5.1)
if ν = const and ρM ρ(t)
(5.2)
⎪ ρ(t0 ) + CρM ln(t/t0 ), ⎪ ⎪ ⎪ ⎩
if ν = (C/t), t > t0 and ρM ρ(t)
(5.3)
0
M
ρ0 + KP t − [(KP )/ν][1 − exp(−νt)], if ν = const and ρM = ρ0 + KP t.
(5)
(5.4)
As microfabrication technologies continue to develop, there appear new models and refined versions of the well-known models taking into account the technological properties of modern MISFET [16]. Many radiation effects have become classical, so it is necessary to consider them in models for new MISFET types including TSE. Let us to analyze these effects in a qualitative generalized representation. The following two primary radiation effects have a general character. 1. Radiation creates in the MIS structure structural defects (point and extensive ones) almost irreversibly increasing the density of trap centers ρT (x) in layers 1, 2 and 3 and on their boundaries (see Fig. 1c). The local variations of the trap density ΔNT (Δx) and their energy status depend on the type, energy and dose of radiation. The defects are formed during elastic interaction with the material of quick neutrons, light and heavy charged particles and gamma radiation with kinetic energies W exceeding the defect formation threshold energy WD of the given material. The parameter WD depends on radiation form and defect type (for silicon, WD ≈ 20 eV) [11, 13]. As the result of increasing NT , the life time, concentration and mobility of free carriers in the semiconductor and insulators are irreversibly reduced and the charged trap density QT can be also changed. 2. Radiation is possibly accompanied by ionization causing formation of additional (nonequilibrium) electron-hole pairs with concentrations Δn(x) = Δp(x) in the insulator and MIS structure semiconductor volumes along the track of an energy carrier (photon or particle), as well as formation of the additional traps, generally, in the discontinuity areas: on the boundaries of layers 0–1, 1–2 and 2–3 (see Fig. 1). After radiation Δn(x) rapidly decreases to zero (a reversible radiation effect), while the trap concentration can remain invariable under a constant temperature (an irreversible radiation effect). Ionization takes place under the influence of ultraviolet, roentgen and gamma radiation, light and heavy charged particles with energies exceeding the ionization threshold energy WI which depends on radiation form, forbidden gap and material density. For photoionization, this energy makes up WI = (EC − EV ), whereas for electrons in room temperature conditions it approximates WI ≈ 3.3 eV (silicon) and ≈ 18.5 eV (SiO2 ). The generation rate g = d(Δn)/dt depends on type of radiation, the radiation energy W and the absorbed dose rate P , as well as on the type, density ρ0 and structure of the material. Within the range of dose rates realized in normal operating conditions and TSE radiation tests, the generation rate has the formula g = kg P , where kg ∼ (λ/WI ), λ is the linear stopping power (λ = −dW /dx ∼ ρ0 ). For instance, under electron radiation with W ∼ 5 MeV, the parameter λ ≈ (2ρ0 ) MeV/cm and kg (SiO2 ) ≈ 8 × 1014 cm−3 Gy−1 [14]. Ionization leads to the additional current flows ΔIDI and ΔIGI through the channel and gate, respectively, as well as to accumulation of the charges QIni in the boundary areas of the insulator layers (Fig. 1b). AUTOMATION AND REMOTE CONTROL
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Note that the additional traps appear as the result of the both radiation effects; according to (2) and (3), they vary the effective charges Q0 , Qss and decrease the effective mobility μn in the TSE channel. These secondary radiation effects influence the electrical characteristics of hydrogen sensors based on TSE. 3. ELECTROPHYSICAL MODELS OF RADIATION EFFECTS The kinetics of radiation-induced trap formation. Despite different physical mechanisms of trap formation, one can suppose that the probability of their formation in the area Δx is constant and proportional to the rate P (i.e., the characteristic event frequency ν = kT P = const). Then it follows from (5.1) that NT (t, x) = NT0 (x) + [NTM (x) − NT0 (x)] × {1 − exp[−kT (x)P t]}.
(6)
The parameter kT (x) is defined experimentally and depends on the material, the physical nature of traps, radiation type and energy, yet being almost independent from the initial trap density NT0 and the rate P . In SiO2 near the boundary SiO2 –Si the average values of kT stay within the limits of (8 . . . 50) × 10−5 Gy−1 , and NTM ∼ 1013 cm−2 (under Δx ≈ 2 nm). The initial density NT0 depends on the technological factors and can take values from 109 cm−2 to 1011 cm−2 . In addition, the quantities NT0 and NTM depend on x. The maximum values of NT are in the transition areas 0–1, 1–2 and 2–3 (Fig. 1c). The traps can be the recombination centers of free carriers or capture centers. The kinetics of thermally stimulated trap annealing. After radiation, the density of traps formed due to the structural defects via elastic interactions can be decreased under high temperatures T (the so-called defect annealing). The defect annealing kinetics depends on trap type and according to (4) and (5.1) is described by NT (t) = NT0 − NTAM [1 − exp (−νD t)],
(7)
where NT0 and NTAM are the initial trap density and the maximum density of annealed traps, the characteristic event frequency is νD = kD exp[−EA /(kT )], kD denotes the annealing rate coefficient, k represents the Boltzmann constant. The parameter kD and the activation energy EA depend on trap type: e.g, for A-center traps (associations of vacancies and hydrogen atoms) and E-centers the activation energy EA constitutes 1.4 eV and 0.93 eV, respectively. After thermal dissociation, the defect components (vacancies and atoms) can discontinuously migrate and form stable compound links (other types of trap centers). Accumulation of migrated trap centers occurs in the transition structural areas. As (P xt) equals the dose D, trap formation under the influence of radiation is associated with dose effects, see (6). For high doses D > DTM ≈ 3/kT , the trap formation process reaches saturation (NT ≈ NTM ), while for low doses D < 0.1/kD the relationship (6) can be considered linear with 5% error: NT (D) = NT0 + (NTM − NT0 )kT D.
(8)
After high dose radiation, the density of traps formed through non-elastic interactions (e.g., intensive link break) remains almost invariable even in the case of heating. However, after low and medium dose radiation (when the density of such traps does not reach NTM ) the trap density must increase under high temperatures. This effect is specific for traps on the boundary SiO2 –Si, as their densities Nss depend on the technological factors, admixture concentrations, crystallographic orientation and the conductivity type of Si. AUTOMATION AND REMOTE CONTROL
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Fig. 2. The relationship between the formation rate of unrecombined free charge carriers in the insulator and the dose rate: 1, 2, 3 and 4 are the ranges of ultralow, low, medium and high rates, respectively.
The kinetics of radiation-induced variation in surface-state charge density taking into account formulas (3), (6) and the condition k2 = kT (d) is represented as the dose radiation effect [5] Qss (Nss (D), ϕs ) ≈ γ(D)C0 (ϕs0 − ϕs ),
(9)
γ(D) = qNss (D)/(C0 ϕG ) = q{Nss0 + (NssM − Nss0 )[1 − exp(−k2 D]}/(C0 ϕG ),
(10)
where the dielectric capacitance C0 = ε0 ε1 ε2 /(ε1 d2 + ε2 d1 ), for TSE γ ≈ 5.0 × 10−12 Nss , ([Nss ] = cm−2 ), NssM and Nss0 are the maximum and initial values of the surface-state densities. The kinetics of radiation-induced variation in effective insulator charge density. Radiationinduced additional charge carriers in the form of electron-hole pairs and/or hot electrons recombine via different mechanisms, are captured on the traps and participate in the current flows. Recombination mechanisms and rates, the trap capture rate of charge carriers depend on the type and structure of material, the stopping power of energy carriers λ, the electrical field, as well as on the hot electron density and the carrier injection level from the neighbor structural areas (e.g., the electrons from silicon to SiO2 ). The above-mentioned factors define the probability of events. For very small P and λ, the capture probability is low and almost all radiation-induced charge carriers recombine (Δn ≈ Δnr ). With the growth of the rate P and λ the quantities g = d(Δn)/dt and r = d(Δnr )/dt increase linearly. As the recombination mechanisms have physical constraints (e.g., the bounded density of recombination trap centers), under some rates P0 the growth of r(P ) slows down (dr/dP decreases, Δn > Δnr , g > r), and a part of the electrons and holes have no time to recombine, and their trap capture probability goes up. Then for the given rate P the quasi-equilibrium concentration of free (unrecombined) charge carriers Δn0 is achieved, and their capture rate equals g0 = d(Δn0 )/dt ≈ (g − r). For dose rates P > P1 , the parameter r becomes constant, g0 (P ) ≈ kg P , continues its growth and is bounded as P > P2 . More accurate models have g0 (P ) ∼ ln(P/P1 ). Figure 2 illustrates the qualitative character of the relationship g0 (P ). As the kinetics of insulator charge storage depends on the rate P , its domain can be divided into 4 ranges as follows. Within the range P ∈ (0, P0 < 1 μGy/s) the ionization currents in the semiconductor and insulator are negligibly small, the trap capture probability approximates zero, the effective insulator charge remains almost invariable (Q0 ≈ Q00 ). Within this range, radiation effects generation (e.g., the break of intensive links during ionization) possibly increases the density of protons and trap centers in the insulator and on the boundary Si–SiO2 . By-turn, this enlarges the parameter γ and the surface state charge Qss . AUTOMATION AND REMOTE CONTROL
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If P ∈ (P0 , P1 ≈ 1 . . . 20 mGy/s ], the formation rate of unrecombined free charge carriers in the insulator increases nonlinearly with the growth of P , the charges get accumulated in the insulator and the additional trap centers appear, causing appropriate variations in Q0 and Qss . The ionization gate currents are negligibly small. The range P ∈ (0, P1 ] is called the low-intensity range. Within the range of medium rates P ∈ (P1 , P2 ], the formation rate of unrecombined free charge carriers in the insulator linearly increases with the growth of P , thereby raising the trap capture rate. In this range of dose rates, variations of the charges Q0 and Qss are represented by the dose characteristics, and in the TSE operation modes it is undesired to neglect the ionization currents in the semiconductor and insulator. For high rates P ≥ P2 > 103 Gy/s, the increase of electron-hole pair generation rate with the growth of P is appreciably decelerated and g0 becomes almost independent from P due to the restrictions of ionization processes in the MIS structure. For high dose rates the maximum values of the charges Q0 and Qss are rapidly achieved, which correspond to the high total dose conditions. The possible operating values of P for TSE belong to the low-rate range. Radiation sensitivity studies of microelectronic devices employ simulation units with P in the medium-rate range. High rates P are achieved only in the extremal conditions (accidents at nuclear power plants or nuclear explosions) [13]. The quantitative parameters of the characteristic g0 (P ), the kinetics of insulator charge capture and relaxation depend on many factors and have a great variety of models. According to (2), for P ∈ (P1 , P2 ], constant temperatures and the TSE electrical mode parameters, the shallow trap filling rate of holes and electrons with their maximum density NTm can be described by dNT ≈ k1 P [NTm (D) − NT ], dt
(11)
where NT is the filled (charged) trap density, k1 denotes the effective filling frequency of electroneutral vacancy traps with the trap density (NTm − NT ). As a result of the nonidentical capture cross-sections and mobilities of the holes and electrons, the electrons in the electrical field rapidly leave some insulator volume ΔV ∼ Δx, thereby decreasing the probability of their recombination with the holes. Subsequently, more and more holes are captured by the free traps (the holes appear “frozen”) and increase the inner positive charge in SiO2 accumulated near the cathode (k1h > k1e ). Taking into account the expressions (3), (5)–(6), (8), (11) and that k1h > k1e and ΔQInMh > ΔQInMe , obtain the following formula of the effective charge density variation under constant P and NTm : ΔQ0 (P, t, U ) = ΔQM [1 − exp(−k1 D)],
(12)
ΔQM (P, U ) = ΔQ0M + k0 (P, U )U, where U = UG − U0 ; UG is the gate-to-substrate voltage; U0 indicates the TSE threshold voltage; the parameters ΔQ0M and k0 are defined experimentally [5, 7]. The additional accumulation of positive charge during ionization is also possible due to H–Si link breakage with formation of free protons or hole captures and their accumulation near the SiO2 –Si boundary (the hydrogen model). Based on the experimental data, the maximum densities of the effective total charge of captured holes and electrons are ΔQM > 0 and depend on the value and sign of the voltage U . For given TSE with the operating voltage U = 1 V, the parameter ΔQM ≈ 70 nC/cm2 , which corresponds to NTm ≈ 4.6 × 1011 cm−2 NTM ∼ 1013 cm−2 . The captured charges in SiO 2 having the density QIn2 > 0 are localized in the area ΔxIn ≈ (3 . . . 10) nm with the centroid at the distance x0 ≈ (10 . . . 15) nm from silicon (see Fig. 1b). AUTOMATION AND REMOTE CONTROL
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The difference of the electric field strength E2 at the points (xi + ΔxIn ) and xi makes up E2 (xi + ΔxIn ) − E2 (xi ) = E22 − E21
1 = ε0 ε2
Xi +ΔX In
ρ(x)dx = Xi
QIn2 , ε0 ε2
(13)
QIn1 = ε0 (ε2 E21 − ε1 E1 ). For a constant voltage U > 0, the growing positive charge QIn2 during radiation decreases the electrical field E21 in the basic part of SiO2 and increases the electrical field E22 near the boundary SiO2 –Si (within the interval x0 ). At the same time, the ionization current in the insulator volume j2 (E21 ) goes down, while the injected electron current from silicon j32 (E22 ) raises and the probability of recombined processes grows in comparison with the hole captures. As a result, in the high-rate range the value of QIn2 approaches its maximum QIn2M . For the operating voltages U < 2 V and small rates P , the relationship QIn2M (U ) represents an increasing linear function, see (12). In this case, E21 → 0, and QIn2 → QIn2M ≈ |QS + Qss |. With the growth of medium rates P and U > 2 V, the silicon currents increase, reducing the parameter k1 and the growth slope of QIn2M (U ). The parameter QIn2M corresponds the continuity condition of the steady-state currents j2 (E21 ) = j32 (E22 ). It follows from the above analysis that the MIS structure irregularity and the variety of radiation effects influencing its electrophysical parameters make the creation of accurate and general models impossible. Taking into account low-accuracy radiation parameters control in radiation tests, a reasonable approach lies in simplified models choice. The simplification of functional dependencies is achieved via neglecting small-order effects, piecewise-linear approximations of nonlinear dependencies and introducing effective parameter values based on averaging with respect to their spatiotemporal characteristics. The simultaneous impact of different radiation effects is considered by combining their formal representations (if the effects have an independent character) or applying complicated functions (if the effects have mutual correlations). 4. THE ELECTRICAL MODELS OF TSE RADIATION INFLUENCE The electrical characteristics of TSE are mostly predetermined by the radiation effects connected with ionization and in the transition areas with high trap density, especially near the boundary SiO2 –Si. Changes take place in the parameters of electrical characteristics, namely, the threshold energy U0 and the transconductance b, the drain current ID and the gate current IG . The initial technological and electrophysical parameters of TSE are the following: the boron concentration in silicon NA = 5 × 1015 cm−3 ; the channel length and width L = 10 μm and z = 3.2 mm, respectively; the layer thicknesses dM = 60 . . . 80 nm, d1 ≈ d2 = 90 . . . 100 nm. The densities measured in [g × cm−3 ]: ρ00 ≈ 12, ρ01 ≈ 8.5, ρ02 ≈ 2.65, ρ03 ≈ 2.33, the effective density ρ0 ≈ 6.4. The relative permeabilities ε1 ≈ 25, ε2 ≈ 4, ε3 ≈ 12, the effective permeability ε = (dε1 ε2 )/(ε1 d2 + ε2 d1 ) ≈ 6.9. The insulator dielectric capacitance C0 = (ε0 ε)/d ≈ 30 nF/cm2 ; the effective mobility μn ≈ 200 cm2 /(V × √s); the transconductance b = (μn zC0 )/L ≈ 2.0 mA/V2 ; the semiconductor charge parameter a = 2ε3 ε0 qNA ≈ 40 (nF × V0.5 × cm−2 ). The parameters ϕ and U are measured in V, whereas the parameter Nss is measured in cm−2 . The potential corresponding to the difference of the work functions of the metal and semiconductor makes up ϕms0 ≈ 0.08. The coefficient γ ≈ 5.0 × 10−12 × Nss . For T ≈ 400 K, the parameter ϕs0 ≈ 0.36. Taking into account (9), (10) and (12), the TSE initial parameters and the results of experimental investigations of hydrogen and radiation sensitivity [3–6], a compact dependence model of the threshold voltage U0 (N, D) is suggested, see Table 1. The sensitivity parameters are chosen using the experimental data [7]. The dose characteristic of the initial threshold voltage U00 (D) = U0 (D, N = 0) is defined by the first two summands in AUTOMATION AND REMOTE CONTROL
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Fig. 3. The possible variations of the initial TSE threshold voltage the under the influence of ionizing radiation with different rates P : (1) P11 ∈ (0, P0 ]; (2) P12 ∈ (P11 , P0 ]; (3) P2 ∈ (P0 , P1 ]; (4) P31 ∈ (P1 , P2 ]; (5) P32 ∈ (P31 , P2 ]; (6) P4 > P3 . The isoline corresponding to the same dose is marked by the dashed line.
formula (14). Figure 3 shows the theoretically possible variants of the characteristics U00 (t) under different P = const. They correspond to the character of the dose characteristics U00 (D). In the infralow dose rate range, the variation ΔU00 (D = const) > 0 does not depend on the rate P . For low and medium rates, the variation is such that ΔU00 < 0 and |ΔU00 | increases simultaneously with P . In principle, variants 3 and 4 are possible under the conditions k1 > k2 and (k1 ΔU0M > k2 ΔUSSM ). The extremal case |ΔU00 | ≈ 1 V corresponds to t∗ = ln[(k1 ΔU0M )/(k2 ΔUSSM )]/P (k1 − k2 ) and is achieved at D ∗ ≈ 20 kGy. Variant 3 takes place when (ΔU0M /ΔUSSM ) ∈ (0.3; 1). The parameters U0H , ΔU0M , ΔUSSM and ΔUM depend on the temperature, while the parameter ΔU0M also depends on the voltage U (N, D) predetermined by the drain current ID (see Table 2). Figure 4 demonstrates the forecasted variations of U0 during continuous TSE operation in the radiation area with the constant rate P = 1 mGy/s. Being influenced by ionizing radiation, the hydrogen sensitivity SN = dU0 /dN starts decreasing under the dose D > D1 ∼ 750 Gy (8 days) and gradually vanishes under the dose D = D0 ≈ 16 kGy (170 days). The reduced sensitivity of Table 1. The compact model of the radiation and hydrogen sensitivity U0 Model: (14) D = P tR ; U0 (D, N, U ) = U000 − ΔU0D (D, U ) − ΔUM (D)fN (N ); ΔU0D (D, U ) = ΔU0M (U )f1 (D) − ΔUSSM f2 (D); fi (D) = 1 − exp(−ki D); fN (N ) = 1 − exp(−kN N ). Parameters
ΔU0M
Formulas and average values, V Additional parameters √ Q00 a 2ϕSD + ϕT φms0 − + (2 + γ0 )ϕs0 + ≈ 1.9 Q00 ≈ 2 nC/cm2 ; γ0 ≈ 0.1; ϕT ≈ 0.033 C0 C0 [ΔQ0M (P ) + k0 (P )(U )]/C0 ≈ (1.5 . . . 2.8) ΔQ0M ≈ 45 nC/cm2 ; k0 ≈ 25 nC/V cm2
ΔUSSM ΔUM
(γM − γ0 )ϕs0 ≈ (1.4 . . . 1.8) UM0 {1 − exp[−k3 (D0 − D)]} ≈ (0 . . . 0.5)
U000
γM ≈ 5.0 × 10−12 NSSM ≈ 5 UM0 ≈ 0.5; D0 ≈ 1.7 × 105 Gy
The sensitivity parameters: kN ≈ 15 − 3N (1/%); k1 ≈ 10−4 Gy −1 ; k2 ≈ 3 × 10−5 Gy −1 ; k3 ≈ 2 × 10−4 Gy −1 ; ϕs (U ) ≈ {[0.72+U/(2+γ)] if ϕs ∈ (0.12; 0.76]; [0.76+0.1(U −0.1)] if ϕs ∈ (0.76; 0.9]}. AUTOMATION AND REMOTE CONTROL
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Fig. 4. The TSE threshold voltage as a function of radiation time under P = 1 mGy/s: (1) N = 0 and (2) N = 2 vol. %; the time moments t1 , t2 and t3 correspond to the doses D1 , D2 and D0 , respectively.
TSE after high radiation doses can be explained by the degrading absorptive-desorptive properties of the palladium-insulator gas-sensitive area as the result of its structural disturbances induced by radiation. TSE looses operability as the extremum point D ∗ is reached (250 days). The differential dose sensitivity of the TSE threshold voltage decreases with the growth of the absorption dose and almost vanishes as DM ≈ 100 kGy: SD = dU0 /dD = ΔUSSM k2 exp(−k2 D) − ΔU0M k1 exp(−k1 D). The threshold values of D and P are computed under the absolute voltage error ΔV = 1 mV. The dose threshold for U0 is defined as Ds = ΔV /|SDM | ≈ 3.76 Gy. The dose rate threshold Ps can be found via the TSE operation time tR in the conditions of radiation: Ps = Ds /tR ≈ 0.42 μGy/s (for tR = 100 days). The dose rate thresholds for the drain and gate currents depend on the TSE circuit and the voltages UD and UG . Table 3 combines the calculated parameters of dose characteristics for the working ranges of TSE hydrogen sensitivity and the corresponding thresholds. As the dose characteristics of the working ranges of TSE hydrogen sensitivity are restricted by the dose D0 < D ∗ , the primary threshold voltage U00 may only decrease under radiation. The variations of the primary threshold voltage U00 under radiation can reach the order of the variations ΔU0N Table 2. The calculation formulas of the drain current ID in different TSE modes ID = f (U, UD ), No., mode, ϕS (V) ∈ U = UG0 + ΔUG − U000 (N, D) + ΔU0D (D, U ) + ΔUM (D)fN (N ) 1. Depletion, (0.12; 0, 36] I0 exp{U/[(2 + γ)ϕT ]}[1 − exp(−UD /ϕT )] + ΔID0 , I0 ≈ b(ϕT )2 2. Weak inversion, (0.36; 0, 72] ΔID0 ≈ qkg P (UD /L)zdI (μn τn + μp τp ); b(D) = b0 /{1 + ηΔNssM [1 − exp(−k2 D)]} 3. Medium inversion, (0.72; 0.85] 4. Strong inversion, (0.85; 0.9]
b (U )2 + I0 + ΔID0 , UD ≥ UDH is the flat area 2n nUD b U− UD + I0 + ΔID0 , UD < UDH is the steep domain; 2 2(ID − I0 − ID0 ) UDH = U/n = nb
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PODLEPETSKY Table 3. The calculated parameters of the dose characteristics Parameter, units of measure Notation Value Initial value of U0 (for D = 0 and N = 0), V U000 1.92 ± 0.02 Primary value of U0 (for N = 0) U00 U0H − ΔU0D Maximum variation of U00 under the influence of ionizing ΔU0D max 0.85 ± 0.05 radiation for U = 1 V, V Threshold dose for U0 , Gy Ds 3.8 ± 0.2 D1 730 ± 30 Boundary dose for the constant hydrogen sensitivity area, Gy Dose decreasing hydrogen sensitivity by two times, kGy D2 10.2 ± 0.2 Dose decreasing hydrogen sensitivity to zero, kGy D0 15.5 ± 0.5 D∗ 21 ± 2 Dose corresponding to the extremum value of U00 , kGy Threshold dose for b(U = 2 V), Gy Db 17 ± 2 Ps 0.42 ± 0.02 Threshold value of P for U0 , μGy/s Threshold value of P for ΔID0 (UD = 1 V), Gy/s PD 0.60 ± 0.03 Threshold value of P for IG (UG = 5 V), Gy/s PG >2 Table 4. The operating conditions of the sensors, modes and events Events The electrical modes of TSE Gas, fN (N ) Radiation, tR Active (working modes)—no. 2, 3, 4— =0 =0 {UD > 0, UG > [U0 − (2 + γ)ϕs0 ]} >0 Passive (“waiting” modes)— no. 5—(UD = 0 and UG = 0); no. 6—(ID = 0 and IG = 0)
>0
=0 >0
Notation A B C D
The crystal temperature T must be considered, as representing an important influencing factor regulated by a heating element. The typical values of the crystal temperature: 1) T ∼ 25◦ C (storage mode)—for the events A and B and “waiting” modes; 2) T ∼ 130◦ C—for the events C and D and working modes; 3) T ∼ 250◦ C (special annealing) for the events A, C and “waiting” modes.
under the influence of hydrogen. These variations are irreversible and explained by an increase in the positive charge Q0 and the negative charge Qss (actually, the first effect prevails). Radiation influence on TSE is studied experimentally through measuring the voltage-current characteristics ID = F (IG ) in the subthreshold and superthreshold modes and calculating the parameters U0 , b and γ based on them. Such an approach becomes inadmissible for the practical usage of TSE as the SE of a hydrogen sensor: it requires much time and special equipment. In sensors and devices, TSE is included in measuring circuits, where the output signals Uout are connected with the variations of U0 and b. Two types of circuits are often chosen [16], namely, circuit no. 1 {Uout = UG ; (ID , UD , U ) = const} or circuit no. 2 {Uout = UD ; UG = UG0 = const}. The quantitative changes of the transformation function parameters Uout (N ) depend on the TSE electrical modes (see Table 2) which are defined by circuit type and electrical parameters (the working values of ID or UG0 ). Computational formula choice depends on the operating conditions of the sensors, see Table 4. Figures 5 and 6 show the graphs of Uout (N ) for the sensors before and after radiation in the both types of circuits. Clearly, after radiation the graphs of Uout (N ) are shifted down for the both types of circuits. Under the influence of radiation in doses D ≤ 750 Gy, the hydrogen sensitivities of the sensor based on circuit no. 1 remain invariable. On the other hand, the hydrogen sensitivity of the sensor based on circuit no. 2 is increased with the growth of absorption dose during TSE operation in the flat area of the voltage-current characteristic. AUTOMATION AND REMOTE CONTROL
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Fig. 5. The transformation functions (ID = 0.3 mA): the doses D: (1) 0; (2) 500 Gy; (2) 2 kGy.
Fig. 6. The transformation functions (UG0 = 1 V): the doses D: (1) 0; (2) 1kGy; (3) 5 kGy; (4) 10 kGy.
In circuit no. 1 the initial value UoutH depends on the selected working drain current ID which defines ϕs , the electric field strength E22 and the maximum variation during radiation of the positive charge ΔQM . In this case, the charge Qss depends only on the parameter γ(D). The variation of the primary output voltage is ΔUout0 = ΔU0 . The growth of ID increases E22 , ΔQM , UoutH , SD and the span of the dose characteristic of the initial value ΔUout0 (D). Moreover, higher drain current ID intensifies the influence of surface-state charge variations (induced by radiation) on the characteristics Uout0 (D): the greater is ΔNssM , the stronger is this phenomenon. For reducing the influence of radiation on the characteristics Uout0 (D), it is recommended to choose the values ID ≈ 0.02 mA and UD ≈ 1 V. In circuit no. 1, the initial value UoutH depends on the working voltage UG0 , for which several operation modes of TSE are considered: 1) initially closed (modes 1 and 2) and then opened under AUTOMATION AND REMOTE CONTROL
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the influence of hydrogen and/or radiation (curve 2 in Fig. 6); 2) initially opened in the flat area of the voltage-current characteristic in mode 3; 3) initially opened in the flat area of the voltagecurrent characteristic in mode 4 (under the influence of hydrogen and/or radiation TSE remains either in the flat area or possibly moves to the steep area of the voltage-current characteristic). All operation modes above have the features that, under UG0 = const, the parameters ϕs and E22 are not constant. In this case, the charge Qss depends on the parameter γ and can also changed due to the variation of ϕs . The dose characteristics Uout0 (D) and hydrogen sensitivity depend on the voltage UG0 . For improving hydrogen sensitivity in circuit no. 2 under radiation influence, it is recommended to choose the value UG0 ≈ 2.0 V.
5. CONCLUSION Using radiation effects analysis, it has been demonstrated that the irregularity of the MIS structure and the variety of radiation influences on the spatiotemporal characteristics of its electrophysical parameters make it impossible and even unreasonable in practice to develop general and accurate models. Taking into account the low-accuracy radiation control of experimental investigations on the radiation sensitivity of MISFET, the paper has suggested the simplified models, where the number of parameters is decreased through neglecting the small-order effects and introducing the effective values of the electrophysical parameters. The simultaneous actions of different radiation effects has been properly considered by combining their formal representations (for the additive effects, i.e., the effects of an independent character) or involving complicated mathematical functions (in the case of any mutual correlations of the radiation effects). The paper has also proposed the compact models of ionizing radiation influence on the TSE characteristics (MIS transistor sensing elements based on Pd-Ta2 O5 -SiO2 -Si). The multiple-factor conditions of sensor operation are incorporated in the models (chip temperature, absorption dose rate, the electrical modes of TSE, the type and electrical parameters of a measuring circuit). The threshold values of the doses, dose rates, the electrical parameters of TSE and measuring circuits defining the applicability ranges of the associated formulas have been defined. The connection of the electrical and metrological characteristics of the sensors with the physical parameters of TSE established within the framework of the models allows their usage for predicting the operability of gas analyzers in the conditions of higher radiation level. The examples of calculated changes in the hydrogen sensor working range under low-intensity prolonged radiation and the transformation functions for the two types of the TSE circuits have been presented. The degree of ionizing radiation influence on the TSE sensor characteristics depends on the operating conditions (ionizing radiation rate, measuring time and modes) being predetermined by the application domains and intended purpose of the devices. For doses D > Ds ≈ 3.8 Gy, the radiation variations of Uout0 (D) should be taken into account; when D ∈ (D1 ; D0 ], it is necessary to consider the reduced hydrogen sensitivity. In most cases, P < 0.1 mGy/s and hence the influence of radiation should not be neglected if tR > 15 hours. For instance, concentration monitoring systems for hydrogenous gases in mines and hydrogen engine aircrafts operate in such modes. In near space P ≈ (20 ÷ 70) mGy/s, and the threshold dose is accumulated within a month. In most real operating conditions of the sensors, the dose limit can be accumulated within more than 5 years; such periods appreciably exceed the continuous operation time of a hydrogen sensor (∼ 120 days). Therefore, radiation can be treated as a weak influencing factor. The previous irradiation of TSE by doses up to 1 kGy can be used for improving the operating characteristics of integrated hydrogen sensors, viz., reducing radiation sensitivity, increasing the stability of hydrogen sensitivity and lowering power consumption via nullifying UG0 in circuit no. 2 as the initial value U00 ≈ 0. AUTOMATION AND REMOTE CONTROL
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