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Theoretical foundations and results of the modeling of islet formation of thin films in vacuum
are presented. The possible groups of methods for islet thin films are considered. The dependence of thin films lateral island sizes on the technological parameters of deposition
in vacuum is shown.
are presented. The possible groups of methods for islet thin films are considered. The dependence of thin films lateral island sizes on the technological parameters of deposition
in vacuum is shown.
Теги: atomic force microscopy islet thin films thin film technology vacuum атомно-силовая микроскопия вакуум островковые тонкие пленки технология тонких пленок
It is known that the properties of thin films differ from properties of bulk materials, especially if the film thickness is very small. This "feature" is determined by the specifics of the structure of the film, which in turn depends on the processes of its formation. There are a large number of methods and processes for thin films formation, from rolling to the deposition of material on a substrate atom by atom. Most often the deposition methods are used [1].
In General, we can distinguish the following stages of thin film formation in vacuum [2]: the formation of nucleus; growth of nucleus; formation of islets; coalescence of islets; formation of channels; the growth of a continuous film. For modern science and technology, the islet films, i.e. non-continuous thin coatings, the creation of which was completed at the stage of formation of islets, are in great interest. Unique electronic, optoelectronic, and other properties of islet thin films (ITF) are associated with the fact that their size is in the nanometer range in all three dimensions. This fact determines the effect of dimensional quantization of the energy levels of electrons inside the nanostructure (islet). The behavior of electrons inside nanoscale islet is like his behavior within three-dimensional potential well [3, 8].
ITF or islet nanostructures are used in nano-electronics, optics, photonics. Their topicality is obvious and indisputable in connection with the improvement of the characteristics of the products obtained: high efficiency and durability of memory devices, a greater spectral frequency, higher performance, and, of course, smaller size of the devices.
There are two technological approaches to the creation of ITF: "top-down" and "bottom-up". "Top-down" technology implies the formation of quantum nanostructures in the processing of macro-scale object with a gradual decrease in its size. The opposite approach, "bottom-up" implies to collect, to connect and to build individual atoms and molecules into an ordered structure [3]. Let's consider the possible methods of production the ITF.
Methods of formation
of islet thin films
Lithography allows to form films of various topologies, providing high reproducibility of results (both individual and group) [3, 4], but the classical methods ensure minimum dimensions to fractions of a micrometer. However, currently the nano-lithography is actively developed, which will allow to obtain structures with sizes up to tens of nanometers.
The use of relief and developed surfaces for ITF formation has its advantages and disadvantages. With use of this methods, it is possible to achieve satisfactory reproducibility, and the result will mainly depend on the structure of the surface – pore size (for porous materials) or "globules" (for photonic crystals) [3].
As a result of consideration of the classification of methods, in terms of the ability to obtain the minimum size of the islet (up to 10 nm), for a detailed analytical review the group of methods of self-organization has been chosen. It includes molecular-beam epitaxy, gas phase epitaxy, the arc discharge, thermal evaporation, magnetron sputtering, ion-beam etching, surface melting and whirling [3].
The molecular beam epitaxy (MBE) allows to create a perfect single-crystal layers of different materials in ultrahigh vacuum conditions. In comparison with other technologies for growth of ITF this method is characterized primarily by low rate and low growth temperature [3, 5, 6]. The complexity and high cost of the technology are disadvantages of MBE
A significant advantage of the gas phase epitaxy is the high deposition rate (1 micron/min) with maintaining the high quality of the films, including the islet films [3, 4, 6], as well as the possibility of the deposition on parts of complex configuration and a large area. The disadvantages of the method include the use of aggressive media and high temperatures, and the grown layers are thicker compared with the MBE.
The arc discharge is characterized by virtually unlimited electrical power that gives the ability to sputter high-melting materials, and high coefficient of ionization of evaporated particles, which increase their energy [3, 4, 7]. The disadvantages include instability of the obtained results and the complexity of the flow control of particles.
The thermal evaporation in vacuum has the following advantages: satisfactory reproducibility of the films properties due to the high purity during the deposition; good adhesion to the substrate, especially when it is heated. The use of magnetron sputtering provides high deposition rate. The disadvantage of this method is the necessity of use of the working gas [3].
Ion beam etching allows formation of the oriented islets, i.e. with crisp boundaries arranged perpendicular to the substrate [3, 4]. It is also possible to etch virtually any substances that allows to use a wide range of materials. The uniformity of the ITF ranges from 2% to 5%. The disadvantages of this method are the expensive equipment and low selectivity of the etching.
The melting of the film on the surface of the substrate is attended by the unpredictability of the shapes and sizes of islets.
The disadvantage of whirling of a colloidal solution of metal particles is a significant irregularity in the distribution of islets on the surface of the substrate. The significant advantage is ease of implementation in the case of a colloidal solution with particles of the required size [3].
Modeling of growth process of islet thin films
All theories of nucleation in thin films [1, 8] describe the first step as the collision of vapor molecules with the substrate. Three results of collision are possible: adsorption and stable fixation of molecules on a substrate; adsorption and evaporation of molecules after a finite period of time; a reflection of molecules from the substrate, like the light from the mirror. In the general case, the atoms fall on the surface of the substrate with energies, much larger kT, where T is the substrate temperature. Therefore, the question arises whether the atom can fast enough come into equilibrium with the substrate for adsorption, or it will be reflected from the substrate not giving her the whole stored energy.
Many studies are devoted to the modeling of growth of islet films. There are two theories of the formation of thin films, which describe the stages of nucleation. The capillary and atomic models of the growth of thin films are the basis for them [1, 8].
For capillary model the rate of formation of nuclei jK is calculated from the expression:
, (1)
where C is a constant that takes into account the geometrical parameters; v is the deposition rate; ΔGdes is free activation energy of desorption; ΔGsd is free activation energy of surface diffusion of adsorbed atoms; ΔG is free energy change during the formation of a critical nucleus; T is the substrate temperature; k is Boltzmann constant.
For atomic models the rate of formation of nuclei jA is calculated from the expression:
, (2)
where i* is the number of atoms in the critical nucleus; Ea is the activation energy of desorption of adsorbed atom; Ei* is the dissociation energy of the critical nucleus on the adsorbed atoms; Ed is the activation energy of surface diffusion of adsorbed atoms. The dimensional coefficient for an atomic model is defined from the expression:
, (3)
where a0 is the length of diffusion jump of an adsorbed atom (for silicon is approximately equal to the lattice constant of the substrate); y is length of the circle bounding the surface of the nucleus, which could receive atoms from the vapor phase; N0 is the density of spots, which can adsorb atoms; v1 is the frequency of desorption of adsorbed atom.
Both models in general describe the dependence of the rate j of formation of nuclei on the energy parameters. Capillary model (1) does not always give information about the size of the critical nuclei and the change of nucleation rate. The atomic model (2) is similar to capillary, but it focuses on nuclei with the size of a few atoms. The authors have chosen the atomic model of growth, since it takes into account the variation of the rate of formation of nuclei, even if the size of the nucleus changes only by one atom [1, 8].
Substituting (3) into (2), we obtain the following expression for determining the rate j [pieces/m2s] of the formation of critical nuclei:
. (4)
In order to determine the initial time of the formation of islets, we must know, when the substrate is "filled" with maximum quantity [pieces/m2] of nuclei of critical size, which is calculated by the formula:
. (5)
After this stage the growth of islets begins. Thus, it is necessary to know the time t [s] of formation of the maximum number of nuclei of critical size:
. (6)
Analysis of references has allowed to choose the values needed for calculating the parameters and with use of expression (6) to build the dependence of the time of formation of the maximum number of nuclei of the critical size on temperature of the substrate (see figure). The number of atoms in a critical nucleus for curves 1, 2, 3, 4 is 5 pieces and for curves 1`, 2`, 3`, 4` is 3 pieces.
The figure shows that the time of formation of the maximum number of critical nuclei is very small (~ 10-16 s) and the influence of the energy parameters, including substrate temperature is strong.
The dependence that defines the relationship between substrate temperature and the activation energy of desorption of adsorbed atoms is calculated for the speeds of copper deposition on silicon substrate of 10-9 kg/m2s and 10-5 kg/m2s. It was found that at a higher deposition rate (10-5 kg/m2s), the substrate temperature lower by about 100-200 K is enough for the formation of the maximum number of nuclei of critical size.
Conclusion
Theoretical studies have shown that at a higher deposition rate, lower substrate temperature is sufficient for the formation of the maximum number of nuclei of critical size. In further it is planned to conduct experimental studies of the growth of the ITF, using the defined temperature range of the substrate from 293 to 1273 K.
A review of the methods of forming the ITF allows to draw a conclusion that the most advantageous from the point of view of the determinant criterion (minimal size) is molecular-beam epitaxy, which provides high reproducibility and other advantages. But it is not industrial technology and demands a lot of time for implementation.
As acceptable methods in terms of availability the thermal evaporation and magnetron sputtering are chosen. These technologies have a wide range of modes and the possibility of varying the structural elements that will allow to achieve the desired result in the formation of the ITF.
In General, we can distinguish the following stages of thin film formation in vacuum [2]: the formation of nucleus; growth of nucleus; formation of islets; coalescence of islets; formation of channels; the growth of a continuous film. For modern science and technology, the islet films, i.e. non-continuous thin coatings, the creation of which was completed at the stage of formation of islets, are in great interest. Unique electronic, optoelectronic, and other properties of islet thin films (ITF) are associated with the fact that their size is in the nanometer range in all three dimensions. This fact determines the effect of dimensional quantization of the energy levels of electrons inside the nanostructure (islet). The behavior of electrons inside nanoscale islet is like his behavior within three-dimensional potential well [3, 8].
ITF or islet nanostructures are used in nano-electronics, optics, photonics. Their topicality is obvious and indisputable in connection with the improvement of the characteristics of the products obtained: high efficiency and durability of memory devices, a greater spectral frequency, higher performance, and, of course, smaller size of the devices.
There are two technological approaches to the creation of ITF: "top-down" and "bottom-up". "Top-down" technology implies the formation of quantum nanostructures in the processing of macro-scale object with a gradual decrease in its size. The opposite approach, "bottom-up" implies to collect, to connect and to build individual atoms and molecules into an ordered structure [3]. Let's consider the possible methods of production the ITF.
Methods of formation
of islet thin films
Lithography allows to form films of various topologies, providing high reproducibility of results (both individual and group) [3, 4], but the classical methods ensure minimum dimensions to fractions of a micrometer. However, currently the nano-lithography is actively developed, which will allow to obtain structures with sizes up to tens of nanometers.
The use of relief and developed surfaces for ITF formation has its advantages and disadvantages. With use of this methods, it is possible to achieve satisfactory reproducibility, and the result will mainly depend on the structure of the surface – pore size (for porous materials) or "globules" (for photonic crystals) [3].
As a result of consideration of the classification of methods, in terms of the ability to obtain the minimum size of the islet (up to 10 nm), for a detailed analytical review the group of methods of self-organization has been chosen. It includes molecular-beam epitaxy, gas phase epitaxy, the arc discharge, thermal evaporation, magnetron sputtering, ion-beam etching, surface melting and whirling [3].
The molecular beam epitaxy (MBE) allows to create a perfect single-crystal layers of different materials in ultrahigh vacuum conditions. In comparison with other technologies for growth of ITF this method is characterized primarily by low rate and low growth temperature [3, 5, 6]. The complexity and high cost of the technology are disadvantages of MBE
A significant advantage of the gas phase epitaxy is the high deposition rate (1 micron/min) with maintaining the high quality of the films, including the islet films [3, 4, 6], as well as the possibility of the deposition on parts of complex configuration and a large area. The disadvantages of the method include the use of aggressive media and high temperatures, and the grown layers are thicker compared with the MBE.
The arc discharge is characterized by virtually unlimited electrical power that gives the ability to sputter high-melting materials, and high coefficient of ionization of evaporated particles, which increase their energy [3, 4, 7]. The disadvantages include instability of the obtained results and the complexity of the flow control of particles.
The thermal evaporation in vacuum has the following advantages: satisfactory reproducibility of the films properties due to the high purity during the deposition; good adhesion to the substrate, especially when it is heated. The use of magnetron sputtering provides high deposition rate. The disadvantage of this method is the necessity of use of the working gas [3].
Ion beam etching allows formation of the oriented islets, i.e. with crisp boundaries arranged perpendicular to the substrate [3, 4]. It is also possible to etch virtually any substances that allows to use a wide range of materials. The uniformity of the ITF ranges from 2% to 5%. The disadvantages of this method are the expensive equipment and low selectivity of the etching.
The melting of the film on the surface of the substrate is attended by the unpredictability of the shapes and sizes of islets.
The disadvantage of whirling of a colloidal solution of metal particles is a significant irregularity in the distribution of islets on the surface of the substrate. The significant advantage is ease of implementation in the case of a colloidal solution with particles of the required size [3].
Modeling of growth process of islet thin films
All theories of nucleation in thin films [1, 8] describe the first step as the collision of vapor molecules with the substrate. Three results of collision are possible: adsorption and stable fixation of molecules on a substrate; adsorption and evaporation of molecules after a finite period of time; a reflection of molecules from the substrate, like the light from the mirror. In the general case, the atoms fall on the surface of the substrate with energies, much larger kT, where T is the substrate temperature. Therefore, the question arises whether the atom can fast enough come into equilibrium with the substrate for adsorption, or it will be reflected from the substrate not giving her the whole stored energy.
Many studies are devoted to the modeling of growth of islet films. There are two theories of the formation of thin films, which describe the stages of nucleation. The capillary and atomic models of the growth of thin films are the basis for them [1, 8].
For capillary model the rate of formation of nuclei jK is calculated from the expression:
, (1)
where C is a constant that takes into account the geometrical parameters; v is the deposition rate; ΔGdes is free activation energy of desorption; ΔGsd is free activation energy of surface diffusion of adsorbed atoms; ΔG is free energy change during the formation of a critical nucleus; T is the substrate temperature; k is Boltzmann constant.
For atomic models the rate of formation of nuclei jA is calculated from the expression:
, (2)
where i* is the number of atoms in the critical nucleus; Ea is the activation energy of desorption of adsorbed atom; Ei* is the dissociation energy of the critical nucleus on the adsorbed atoms; Ed is the activation energy of surface diffusion of adsorbed atoms. The dimensional coefficient for an atomic model is defined from the expression:
, (3)
where a0 is the length of diffusion jump of an adsorbed atom (for silicon is approximately equal to the lattice constant of the substrate); y is length of the circle bounding the surface of the nucleus, which could receive atoms from the vapor phase; N0 is the density of spots, which can adsorb atoms; v1 is the frequency of desorption of adsorbed atom.
Both models in general describe the dependence of the rate j of formation of nuclei on the energy parameters. Capillary model (1) does not always give information about the size of the critical nuclei and the change of nucleation rate. The atomic model (2) is similar to capillary, but it focuses on nuclei with the size of a few atoms. The authors have chosen the atomic model of growth, since it takes into account the variation of the rate of formation of nuclei, even if the size of the nucleus changes only by one atom [1, 8].
Substituting (3) into (2), we obtain the following expression for determining the rate j [pieces/m2s] of the formation of critical nuclei:
. (4)
In order to determine the initial time of the formation of islets, we must know, when the substrate is "filled" with maximum quantity [pieces/m2] of nuclei of critical size, which is calculated by the formula:
. (5)
After this stage the growth of islets begins. Thus, it is necessary to know the time t [s] of formation of the maximum number of nuclei of critical size:
. (6)
Analysis of references has allowed to choose the values needed for calculating the parameters and with use of expression (6) to build the dependence of the time of formation of the maximum number of nuclei of the critical size on temperature of the substrate (see figure). The number of atoms in a critical nucleus for curves 1, 2, 3, 4 is 5 pieces and for curves 1`, 2`, 3`, 4` is 3 pieces.
The figure shows that the time of formation of the maximum number of critical nuclei is very small (~ 10-16 s) and the influence of the energy parameters, including substrate temperature is strong.
The dependence that defines the relationship between substrate temperature and the activation energy of desorption of adsorbed atoms is calculated for the speeds of copper deposition on silicon substrate of 10-9 kg/m2s and 10-5 kg/m2s. It was found that at a higher deposition rate (10-5 kg/m2s), the substrate temperature lower by about 100-200 K is enough for the formation of the maximum number of nuclei of critical size.
Conclusion
Theoretical studies have shown that at a higher deposition rate, lower substrate temperature is sufficient for the formation of the maximum number of nuclei of critical size. In further it is planned to conduct experimental studies of the growth of the ITF, using the defined temperature range of the substrate from 293 to 1273 K.
A review of the methods of forming the ITF allows to draw a conclusion that the most advantageous from the point of view of the determinant criterion (minimal size) is molecular-beam epitaxy, which provides high reproducibility and other advantages. But it is not industrial technology and demands a lot of time for implementation.
As acceptable methods in terms of availability the thermal evaporation and magnetron sputtering are chosen. These technologies have a wide range of modes and the possibility of varying the structural elements that will allow to achieve the desired result in the formation of the ITF.
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