rus
Issue #6/2025
S.V.Sidorova, S.V.Kiryanov, A.M.Naumova, E.S.Shcherbak
MODELING OF METALLIC ISLAND NANOSTRUCTURES PHYSICAL CHARACTERISTICS
MODELING OF METALLIC ISLAND NANOSTRUCTURES PHYSICAL CHARACTERISTICS
DOI: https://doi.org/10.22184/1993-8578.2025.18.6.380.390
The results of physical modeling of the functional characteristics of sensors of fields and environment based on islet nanostructures, depending on their size, are presented. The advantages of using cobalt and nickel for sensors of weak magnetic fields and aluminum with a surface layer of aluminum oxide for a gas sensor are shown. The results of the dependences of the physical parameters of the magnetic field and tunneling conductivity in the islet layers of cobalt and aluminum, respectively, on the distances between the islet nanostructures are presented.
The results of physical modeling of the functional characteristics of sensors of fields and environment based on islet nanostructures, depending on their size, are presented. The advantages of using cobalt and nickel for sensors of weak magnetic fields and aluminum with a surface layer of aluminum oxide for a gas sensor are shown. The results of the dependences of the physical parameters of the magnetic field and tunneling conductivity in the islet layers of cobalt and aluminum, respectively, on the distances between the islet nanostructures are presented.
Теги: gas sensors nanostructures physical modelling weak magnetic fields sensors газовые датчики датчики слабых магнитных полей наноструктуры физическое моделирование
Received: 8.09.2025 | Accepted: 15.09.2025 | DOI: https://doi.org/10.22184/1993-8578.2025.18.6.380.390
Original paper
MODELING OF METALLIC ISLAND NANOSTRUCTURES PHYSICAL CHARACTERISTICS
S.V.Sidorova1, Cand. of Sci. (Tech), Docent, ORCID: 0000-0002-3002-1246 / sidorova@bmstu.ru
S.V.Kiryanov1, Post Graduate, ORCID: 0009-0004-7627-2675
A.M.Naumova1, Student, ORCID: 0009-0008-1215-4855
E.S.Shcherbak1, Student, ORCID: 0009-0007-2452-3999
Abstract. The results of physical modeling of the functional characteristics of sensors of fields and environment based on islet nanostructures, depending on their size, are presented. The advantages of using cobalt and nickel for sensors of weak magnetic fields and aluminum with a surface layer of aluminum oxide for a gas sensor are shown. The results of the dependences of the physical parameters of the magnetic field and tunneling conductivity in the islet layers of cobalt and aluminum, respectively, on the distances between the islet nanostructures are presented.
Keywords: nanostructures, weak magnetic fields sensors, gas sensors, physical modelling
For citation: S.V. Sidorova, S.V. Kiryanov, A.M. Naumova, E.S. Shcherbak. Modeling of metallic island nanostructures physical characteristics. NANOINDUSTRY. 2025. Vol. 18. No. 6. PP. 380–390. https://doi.org/
10.22184/1993-8578.2025.18.6.380.390.
INTRODUCTION
Island thin films (ITFs) are a special type of structures with a number of properties that are in demand in modern technologies [1]. Due to their sensitivity to external influences and possibilities to control conductivity at the nanoscale, such films find application in various types of sensor devices [2–4].
Due to their unique properties – spin-dependent tunnelling conductivity and high sensitivity to external influences – ITFs find applications in spin-tunneling magnetoresistive (STMR) sensors and gas-sensitive sensors [2, 5–7].
Modern sensor technology is rapidly evolving towards miniaturisation, increased sensitivity and energy efficiency. Particular attention is paid to development of new functional materials capable of providing high selectivity and stability under influence of external fields and chemicals. One such solution is island thin films, which have unique properties due to their nanoscale structure and tunnelling conductivity [8–10].
ITFs find applications in the sensing layers of field and environment sensors. For example, in STMR sensors sensitive to weak magnetic fields, as well as in gas-sensitive sensors reacting to presence of molecules of substances such as ammonia. The morphology and structure of ITFs directly affect the sensitive properties of devices, which requires a thorough elaboration of their formation modes and understanding of the interaction mechanisms with external influences (fields and environment) [11, 12].
Gas-sensitive sensors are widely used in ecology, industrial safety, medicine, agriculture and environmental monitoring systems [5–7]. They are required for timely detection of gas leaks, contamination assessment, and process control where the presence or concentration of certain gases is critical.
Modern applications require from such sensors high sensitivity, fast response, miniaturisation and cost-effectiveness, especially at low gas concentrations. In this context, the use of an island thin film as an active sensing layer is a promising direction in science and technology.
Due to the developed surface, inter-island gaps and high sensitivity of tunnelling conductivity to surface phenomena, ITFs allows to significantly increase the response time of the sensor to gas molecules, even at their low concentration, while maintaining relative fabrication technology simplicity.
Magnetic sensors play a key role in various industries ranging from industrial automation and transport to medicine and aerospace engineering. They are used to measure, control and record magnetic fields and object movements [2–4]. Modern requirements for such sensors include high sensitivity, performance stability, miniaturisation and cost-effectiveness.
One of the promising solutions to increase sensitivity and reduce the production cost is the use of an island thin film as the main sensing element. Such structures, due to their unique morphological and magnetic properties, make it possible to realise STMR sensors combining high sensitivity with manufacturability and possibility of large-scale production [13, 14].
The aim of the work is to model the physical characteristics of island nanostructures depending on their size.
METHODS AND MATERIALS
The choice of materials for modelling is justified by the tasks that are solved in the laboratory "Nano- and microtechnologies" of the department "Electronic technologies in mechanical engineering" of Bauman Moscow State Technical University. For example, for sensors of fields and environment the functional materials cobalt, nickel, aluminium, from which it is required to form island layers of nanometre size, are relevant. Metal oxides such as aluminium oxide and titanium oxide are used for dielectric layers that act as insulating and protective coatings. Dielectric substrates made of glass, ceramics, even polymers can be used as a basis to form the required structures for gas sensors. The requirement for insulating properties of the substrate of gas sensors is due to the need to activate the conductive properties of the island nanostructures rather than substrate conductivity. The basis for magnetic field sensors can be both dielectric substrates and semiconductor substrates. In this work, modelling was carried out for silicon substrates.
Modelling in the physical modelling environment includes the following stages: model construction, selection of materials of functional layers, setting conditions for implementation of physical phenomena, mesh construction, and calculation (Fig.1).
The spacing between islands and the number of magnetic field sensor layers will act as varying parameters for arrays of island nanostructures. For the gas sensor, only a monolayer of island structures will be formed (Fig. 2).
The models being developed for conduction are based on the fact that if two electrodes are separated by a thin insulating layer, and the layer is thin enough (nanometre-sized), current can flow between them due to the tunneling effect. The first theoretical studies of this phenomenon for low and high voltages were carried out by Sommerfeld and Bethe. Later, Holm extended the theory for intermediate voltages. However, these studies covered different voltage ranges and used different approaches, which led to the need for a unified theory.
Sommerfeld and Bethe were the first to derive equations for current density through a rectangular barrier. To obtain an analytical solution, Sommerfeld and Bethe approximated the barrier with a symmetric parabola. Later, Holm and Kirschstein, using the same method, improved Sommerfeld and Bethe’s results by using a symmetric parabola that better fitted the potential barrier. The range and applicability of this type of approximation is limited. Holm simplified the imaging potential problem for the intermediate voltage range by correcting the rectangular barrier calculations using the results obtained by Holm and Kirshtein for the low voltage case. When two metal electrodes are separated by an insulating film, equilibrium conditions require that the upper boundary of the insulator’s forbidden band is above the Fermi level of the electrodes. Thus, the insulating film creates a potential barrier between the electrodes that prevents electron tunnelling [15].
Numerical simulations of the tunnelling current distribution between metallic islands were performed to evaluate the conductive characteristics of island thin films. The Siemens conductivity model was used as the fundamental interaction, which was imposed variable on the dielectric interlayer. For all others, the conductivity was constant. Taking into account the approximations for potential barriers in the metal-dielectric-metal system, the process of electron transport in the system (between two conductors separated by tunnelling barriers) is determined by the length of the tunnelling barrier, the work of electron escape from the electrodes φ– and the applied voltage V. In such a system, depending on the value of V, two main mechanisms of tunnelling electron transport are possible. In the case of its small value (eV < φ–) there is a direct tunnelling of electrons from one electrode to another (Fig.3a), in the case of (eV > φ–) there is a cold (field) emission of electrons from one of the electrodes (Fig.3b).
The simulation environment allows parametrization of geometric parameters, so a single model was used to study a sensor with a certain number of layers, where it is possible to specify a range of distances between islands.
When making the computational models, the following requirements for magnetic field sensors are taken into account: lateral size of cobalt islands – 140 nm, height – 70 nm; lateral size and height of nickel islands – 60 nm, height – 30 nm; distance between islands – 1...10 nm; thickness of the oxide layer above the ITF of nickel and cobalt – 5 nm. Copper electrodes have a thickness of 500 nm, silicon substrate – 20 nm (we take the surface layer of the substrate to optimise simulation time). To gas medium sensors: lateral size of aluminium islands – 60 nm, height – 30 nm; distance between islands – 2...10 nm; thickness of oxide layer – from 0.5 to 5 nm. Copper electrodes have a thickness of 500 nm, ceramic substrate – 20 nm (we take the surface layer of the substrate to optimise the simulation time).
After the calculation, a simulation map of the electric and magnetic fields and physical characteristics of the ITFs is submitted for analysis.
RESULTS AND DISCUSSION
When simulating conductivity in the layer of aluminium island nanostructures, the result is presented in the form of a 2D model showing the most stressed (high in conductivity values) areas are the places of contact between the island nanostructures (Fig.4).
It can be seen that the current density concentration is at the location where the islands are closest to each other, as this is where electrons are tunnelling through the dielectric layer of aluminium oxide.
To ensure tunnelling, the greatest thickness of the oxide layer is required, at which tunnelling occurs. After all, when interacting with the analyte gas, vacancies arise in the oxide layer, i.e., the thickness decreases and, consequently, oxygen vacancies concentration and tunnelling probability increase. For island spacing up to 10 nm in the presence of oxide layer, the current density is 5.00 · 106 A/m2 compared to the current density in the absence of oxide layer for the same island spacing of 1.55 · 106 A/m2. The conductivity modelling results showed that distribution density is higher in presence of the oxide layer, indicating that tolerance of the spacing between islands can be increased and facilitates the process of obtaining the island structure.
Conductivity of the islet layer in the gas environment changes, which is also confirmed by the modelling results. When the aluminium coatings surface is exposed to ammonia, the oxide layer is replaced by ammonium aluminate, and thickness of which can reach ~3 nm. This process reduces the work of electron yield and changes the barrier structure on the surface, which leads to a change in the conductivity of the coating.
The obtained models (Fig.5) confirmed that substitution of oxide for ammonium aluminate reduces the potential barrier and leads to an increase in the current through the film. For island structures, the effect is more pronounced due to the exponential dependence of the tunnelling current on the barrier parameters.
The growth of tunnelling current in the process of contact with gas was experimentally recorded for the islet films. This is explained by the fact that adsorption of NH3 reduces the height of tunnelling barriers between the islands, which causes an increase of current. Quantification of the current change has not been modelled yet, but the observed response confirms the high sensitivity of ITFs to the gas environment. Modelling shows that even in solid coatings the effect of NH3 is pronounced. However, it is the island films that show the greatest potential for sensitive gas sensor applications, due to a pronounced tunnelling conduction mechanism sensitive to surface chemical modifications.
The change of conductivity under a magnetic field influence underlies the operation of STMR sensors sensitive to relative orientation of magnetic moments in multilayer structures. To evaluate the behaviour of materials in a magnetic field, numerical simulations were carried out for island and solid films of cobalt and nickel (Fig. 6).
According to calculations, nickel is completely remagnetised in the selected range, while cobalt remains in the initial state, maintaining the magnetisation direction. This is a key condition for the appearance of the spin-dependent tunnelling effect.
The modelling demonstrates a broad response even in weak magnetic fields (units of tens of μT) and the maximum change in resistance reaches 45%. It should be noted that the curve has a clear symmetrical shape with a peak at B = 0. This indicates a high sensitivity of tunnelling conductivity to the relative orientation of spins in materials with different coercivity. It is shown that island thin films have a significantly higher magnetosensitive response than solid films. This is due to tunnelling nature of the conductivity, which responds acutely to the remagnetisation of the magnetically soft layer. Such properties make ITFs an ideal candidate for use as part of highly sensitive STMR sensors capable of operating in weak magnetic fields.
To evaluate the magnetic properties of island films, numerical modelling of the remagnetisation of individual cobalt and nickel islands in an external magnetic field was carried out. The calculations were performed in a three-dimensional formulation taking into account the real geometry of the islands and distribution of magnetic induction in space (Fig.7).
Modelling showed a fundamental difference in behaviour of cobalt and nickel islands: cobalt retains stable magnetisation, whereas nickel is easily remagnetised. Such a combination of materials makes it possible to realise spin-dependent tunnelling in magnetosensitive structures with high contrast response.
Conductivity in the magnetic field of layers of ferromagnetic island thin films at their multilayer formation is caused, among other things, by the change of the magnetic field strength in the island along its height (Fig.8).
Modelling has shown that the magnetic field strength is distributed unevenly in the islet, with maximum values at the lwer point of the islet. Intensity value varies according to the law close to a damped sinusoid.
CONCLUSIONS
Physical modelling has been carried out to study the magnetic properties of cobalt islands as a function of the distance between the islands and the number of layers in the sensor. It was found that the magnetic scalar potential takes the highest values in the layers located closest to the magnet. For uniform distribution of the magnetic field strength, it is necessary to form a sensor with an even number of layers. When modelling the effect of the magnetic field on the conductivity of the island structure, a change in resistance up to –45% at ±20 μT was obtained. For solid structures, the resistance changes are weaker – up to –4% according to the model and ~–3% according to the experiment at ±1000 μT.
A model of the gas sensor in multiphysics modelling software has been constructed using the Siemens model tunneling conductivity formula, which shows the current distribution density in island nanostructures at oxide layer thicknesses from 0.5 to 5 nm: as the oxide layer increases, the current density decreases. Distribution of current density from the distance between islands with and without oxide layer is compared. The obtained dependence shows that the gas sensor on island nanostructures with an oxide layer has the best characteristics. Thus, in presence of aluminium oxide, the tolerance on the distance between islands can be extended, which will simplify the technology of island layer formation. In aluminium ITFs, increasing the substituted layer thickness on the surface leads to a sharp increase in the tunneling current, due to the exponential dependence on the barrier.
As a result of the simulations, it was found that the proper selection of geometry, materials and structure of islands allows to ensure both the magnetosensitivity of ferromagnetic island nanostructures and the gas sensitivity of aluminium island thin films.
PEER REVIEW INFO
Editorial board thanks the anonymous reviewer(s) for their contribution to the peer review of this work. It is also grateful for their consent to publish papers on the journal’s website and SEL eLibrary eLIBRARY.RU.
Declaration of Competing Interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Original paper
MODELING OF METALLIC ISLAND NANOSTRUCTURES PHYSICAL CHARACTERISTICS
S.V.Sidorova1, Cand. of Sci. (Tech), Docent, ORCID: 0000-0002-3002-1246 / sidorova@bmstu.ru
S.V.Kiryanov1, Post Graduate, ORCID: 0009-0004-7627-2675
A.M.Naumova1, Student, ORCID: 0009-0008-1215-4855
E.S.Shcherbak1, Student, ORCID: 0009-0007-2452-3999
Abstract. The results of physical modeling of the functional characteristics of sensors of fields and environment based on islet nanostructures, depending on their size, are presented. The advantages of using cobalt and nickel for sensors of weak magnetic fields and aluminum with a surface layer of aluminum oxide for a gas sensor are shown. The results of the dependences of the physical parameters of the magnetic field and tunneling conductivity in the islet layers of cobalt and aluminum, respectively, on the distances between the islet nanostructures are presented.
Keywords: nanostructures, weak magnetic fields sensors, gas sensors, physical modelling
For citation: S.V. Sidorova, S.V. Kiryanov, A.M. Naumova, E.S. Shcherbak. Modeling of metallic island nanostructures physical characteristics. NANOINDUSTRY. 2025. Vol. 18. No. 6. PP. 380–390. https://doi.org/
10.22184/1993-8578.2025.18.6.380.390.
INTRODUCTION
Island thin films (ITFs) are a special type of structures with a number of properties that are in demand in modern technologies [1]. Due to their sensitivity to external influences and possibilities to control conductivity at the nanoscale, such films find application in various types of sensor devices [2–4].
Due to their unique properties – spin-dependent tunnelling conductivity and high sensitivity to external influences – ITFs find applications in spin-tunneling magnetoresistive (STMR) sensors and gas-sensitive sensors [2, 5–7].
Modern sensor technology is rapidly evolving towards miniaturisation, increased sensitivity and energy efficiency. Particular attention is paid to development of new functional materials capable of providing high selectivity and stability under influence of external fields and chemicals. One such solution is island thin films, which have unique properties due to their nanoscale structure and tunnelling conductivity [8–10].
ITFs find applications in the sensing layers of field and environment sensors. For example, in STMR sensors sensitive to weak magnetic fields, as well as in gas-sensitive sensors reacting to presence of molecules of substances such as ammonia. The morphology and structure of ITFs directly affect the sensitive properties of devices, which requires a thorough elaboration of their formation modes and understanding of the interaction mechanisms with external influences (fields and environment) [11, 12].
Gas-sensitive sensors are widely used in ecology, industrial safety, medicine, agriculture and environmental monitoring systems [5–7]. They are required for timely detection of gas leaks, contamination assessment, and process control where the presence or concentration of certain gases is critical.
Modern applications require from such sensors high sensitivity, fast response, miniaturisation and cost-effectiveness, especially at low gas concentrations. In this context, the use of an island thin film as an active sensing layer is a promising direction in science and technology.
Due to the developed surface, inter-island gaps and high sensitivity of tunnelling conductivity to surface phenomena, ITFs allows to significantly increase the response time of the sensor to gas molecules, even at their low concentration, while maintaining relative fabrication technology simplicity.
Magnetic sensors play a key role in various industries ranging from industrial automation and transport to medicine and aerospace engineering. They are used to measure, control and record magnetic fields and object movements [2–4]. Modern requirements for such sensors include high sensitivity, performance stability, miniaturisation and cost-effectiveness.
One of the promising solutions to increase sensitivity and reduce the production cost is the use of an island thin film as the main sensing element. Such structures, due to their unique morphological and magnetic properties, make it possible to realise STMR sensors combining high sensitivity with manufacturability and possibility of large-scale production [13, 14].
The aim of the work is to model the physical characteristics of island nanostructures depending on their size.
METHODS AND MATERIALS
The choice of materials for modelling is justified by the tasks that are solved in the laboratory "Nano- and microtechnologies" of the department "Electronic technologies in mechanical engineering" of Bauman Moscow State Technical University. For example, for sensors of fields and environment the functional materials cobalt, nickel, aluminium, from which it is required to form island layers of nanometre size, are relevant. Metal oxides such as aluminium oxide and titanium oxide are used for dielectric layers that act as insulating and protective coatings. Dielectric substrates made of glass, ceramics, even polymers can be used as a basis to form the required structures for gas sensors. The requirement for insulating properties of the substrate of gas sensors is due to the need to activate the conductive properties of the island nanostructures rather than substrate conductivity. The basis for magnetic field sensors can be both dielectric substrates and semiconductor substrates. In this work, modelling was carried out for silicon substrates.
Modelling in the physical modelling environment includes the following stages: model construction, selection of materials of functional layers, setting conditions for implementation of physical phenomena, mesh construction, and calculation (Fig.1).
The spacing between islands and the number of magnetic field sensor layers will act as varying parameters for arrays of island nanostructures. For the gas sensor, only a monolayer of island structures will be formed (Fig. 2).
The models being developed for conduction are based on the fact that if two electrodes are separated by a thin insulating layer, and the layer is thin enough (nanometre-sized), current can flow between them due to the tunneling effect. The first theoretical studies of this phenomenon for low and high voltages were carried out by Sommerfeld and Bethe. Later, Holm extended the theory for intermediate voltages. However, these studies covered different voltage ranges and used different approaches, which led to the need for a unified theory.
Sommerfeld and Bethe were the first to derive equations for current density through a rectangular barrier. To obtain an analytical solution, Sommerfeld and Bethe approximated the barrier with a symmetric parabola. Later, Holm and Kirschstein, using the same method, improved Sommerfeld and Bethe’s results by using a symmetric parabola that better fitted the potential barrier. The range and applicability of this type of approximation is limited. Holm simplified the imaging potential problem for the intermediate voltage range by correcting the rectangular barrier calculations using the results obtained by Holm and Kirshtein for the low voltage case. When two metal electrodes are separated by an insulating film, equilibrium conditions require that the upper boundary of the insulator’s forbidden band is above the Fermi level of the electrodes. Thus, the insulating film creates a potential barrier between the electrodes that prevents electron tunnelling [15].
Numerical simulations of the tunnelling current distribution between metallic islands were performed to evaluate the conductive characteristics of island thin films. The Siemens conductivity model was used as the fundamental interaction, which was imposed variable on the dielectric interlayer. For all others, the conductivity was constant. Taking into account the approximations for potential barriers in the metal-dielectric-metal system, the process of electron transport in the system (between two conductors separated by tunnelling barriers) is determined by the length of the tunnelling barrier, the work of electron escape from the electrodes φ– and the applied voltage V. In such a system, depending on the value of V, two main mechanisms of tunnelling electron transport are possible. In the case of its small value (eV < φ–) there is a direct tunnelling of electrons from one electrode to another (Fig.3a), in the case of (eV > φ–) there is a cold (field) emission of electrons from one of the electrodes (Fig.3b).
The simulation environment allows parametrization of geometric parameters, so a single model was used to study a sensor with a certain number of layers, where it is possible to specify a range of distances between islands.
When making the computational models, the following requirements for magnetic field sensors are taken into account: lateral size of cobalt islands – 140 nm, height – 70 nm; lateral size and height of nickel islands – 60 nm, height – 30 nm; distance between islands – 1...10 nm; thickness of the oxide layer above the ITF of nickel and cobalt – 5 nm. Copper electrodes have a thickness of 500 nm, silicon substrate – 20 nm (we take the surface layer of the substrate to optimise simulation time). To gas medium sensors: lateral size of aluminium islands – 60 nm, height – 30 nm; distance between islands – 2...10 nm; thickness of oxide layer – from 0.5 to 5 nm. Copper electrodes have a thickness of 500 nm, ceramic substrate – 20 nm (we take the surface layer of the substrate to optimise the simulation time).
After the calculation, a simulation map of the electric and magnetic fields and physical characteristics of the ITFs is submitted for analysis.
RESULTS AND DISCUSSION
When simulating conductivity in the layer of aluminium island nanostructures, the result is presented in the form of a 2D model showing the most stressed (high in conductivity values) areas are the places of contact between the island nanostructures (Fig.4).
It can be seen that the current density concentration is at the location where the islands are closest to each other, as this is where electrons are tunnelling through the dielectric layer of aluminium oxide.
To ensure tunnelling, the greatest thickness of the oxide layer is required, at which tunnelling occurs. After all, when interacting with the analyte gas, vacancies arise in the oxide layer, i.e., the thickness decreases and, consequently, oxygen vacancies concentration and tunnelling probability increase. For island spacing up to 10 nm in the presence of oxide layer, the current density is 5.00 · 106 A/m2 compared to the current density in the absence of oxide layer for the same island spacing of 1.55 · 106 A/m2. The conductivity modelling results showed that distribution density is higher in presence of the oxide layer, indicating that tolerance of the spacing between islands can be increased and facilitates the process of obtaining the island structure.
Conductivity of the islet layer in the gas environment changes, which is also confirmed by the modelling results. When the aluminium coatings surface is exposed to ammonia, the oxide layer is replaced by ammonium aluminate, and thickness of which can reach ~3 nm. This process reduces the work of electron yield and changes the barrier structure on the surface, which leads to a change in the conductivity of the coating.
The obtained models (Fig.5) confirmed that substitution of oxide for ammonium aluminate reduces the potential barrier and leads to an increase in the current through the film. For island structures, the effect is more pronounced due to the exponential dependence of the tunnelling current on the barrier parameters.
The growth of tunnelling current in the process of contact with gas was experimentally recorded for the islet films. This is explained by the fact that adsorption of NH3 reduces the height of tunnelling barriers between the islands, which causes an increase of current. Quantification of the current change has not been modelled yet, but the observed response confirms the high sensitivity of ITFs to the gas environment. Modelling shows that even in solid coatings the effect of NH3 is pronounced. However, it is the island films that show the greatest potential for sensitive gas sensor applications, due to a pronounced tunnelling conduction mechanism sensitive to surface chemical modifications.
The change of conductivity under a magnetic field influence underlies the operation of STMR sensors sensitive to relative orientation of magnetic moments in multilayer structures. To evaluate the behaviour of materials in a magnetic field, numerical simulations were carried out for island and solid films of cobalt and nickel (Fig. 6).
According to calculations, nickel is completely remagnetised in the selected range, while cobalt remains in the initial state, maintaining the magnetisation direction. This is a key condition for the appearance of the spin-dependent tunnelling effect.
The modelling demonstrates a broad response even in weak magnetic fields (units of tens of μT) and the maximum change in resistance reaches 45%. It should be noted that the curve has a clear symmetrical shape with a peak at B = 0. This indicates a high sensitivity of tunnelling conductivity to the relative orientation of spins in materials with different coercivity. It is shown that island thin films have a significantly higher magnetosensitive response than solid films. This is due to tunnelling nature of the conductivity, which responds acutely to the remagnetisation of the magnetically soft layer. Such properties make ITFs an ideal candidate for use as part of highly sensitive STMR sensors capable of operating in weak magnetic fields.
To evaluate the magnetic properties of island films, numerical modelling of the remagnetisation of individual cobalt and nickel islands in an external magnetic field was carried out. The calculations were performed in a three-dimensional formulation taking into account the real geometry of the islands and distribution of magnetic induction in space (Fig.7).
Modelling showed a fundamental difference in behaviour of cobalt and nickel islands: cobalt retains stable magnetisation, whereas nickel is easily remagnetised. Such a combination of materials makes it possible to realise spin-dependent tunnelling in magnetosensitive structures with high contrast response.
Conductivity in the magnetic field of layers of ferromagnetic island thin films at their multilayer formation is caused, among other things, by the change of the magnetic field strength in the island along its height (Fig.8).
Modelling has shown that the magnetic field strength is distributed unevenly in the islet, with maximum values at the lwer point of the islet. Intensity value varies according to the law close to a damped sinusoid.
CONCLUSIONS
Physical modelling has been carried out to study the magnetic properties of cobalt islands as a function of the distance between the islands and the number of layers in the sensor. It was found that the magnetic scalar potential takes the highest values in the layers located closest to the magnet. For uniform distribution of the magnetic field strength, it is necessary to form a sensor with an even number of layers. When modelling the effect of the magnetic field on the conductivity of the island structure, a change in resistance up to –45% at ±20 μT was obtained. For solid structures, the resistance changes are weaker – up to –4% according to the model and ~–3% according to the experiment at ±1000 μT.
A model of the gas sensor in multiphysics modelling software has been constructed using the Siemens model tunneling conductivity formula, which shows the current distribution density in island nanostructures at oxide layer thicknesses from 0.5 to 5 nm: as the oxide layer increases, the current density decreases. Distribution of current density from the distance between islands with and without oxide layer is compared. The obtained dependence shows that the gas sensor on island nanostructures with an oxide layer has the best characteristics. Thus, in presence of aluminium oxide, the tolerance on the distance between islands can be extended, which will simplify the technology of island layer formation. In aluminium ITFs, increasing the substituted layer thickness on the surface leads to a sharp increase in the tunneling current, due to the exponential dependence on the barrier.
As a result of the simulations, it was found that the proper selection of geometry, materials and structure of islands allows to ensure both the magnetosensitivity of ferromagnetic island nanostructures and the gas sensitivity of aluminium island thin films.
PEER REVIEW INFO
Editorial board thanks the anonymous reviewer(s) for their contribution to the peer review of this work. It is also grateful for their consent to publish papers on the journal’s website and SEL eLibrary eLIBRARY.RU.
Declaration of Competing Interest. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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