Computer implementation method for simulation of energy filtered ion implantation (EFII)

Abstract

A computer-implemented method (200) for simulating energy filtered ion implantation (EFII) is provided, comprising the steps of: determining (201) at least a portion of an energy filter (25); determining (202) at least a portion of an ion beam source (5); determining (203) a simulation region (g) within a substrate (26); implementing (204) the determined at least a portion of the energy filter (25), the determined at least a portion of the ion beam source (5), and the determined simulation region (g) within the substrate (26); determining (205) a minimum distance (50) between the implemented at least a portion of the energy filter (25) and the implemented substrate (26) to enable a desired degree of lateral homogenization of energy distribution in a doping depth profile (40) of the implemented substrate (26); determining (206) a maximum expected scattering angle (a) of the energy filter (25) by simulating an energy angular spectrum for the energy filter (25); and determining (207) a total simulation volume (S v and (207) determining

Description

Technical Field

[0001] Cross - reference to related applications This application claims the benefit of and priority to Luxembourg Patent Application No. 102558, filed on February 24, 2021. The entire disclosure of Luxembourg Patent Application No. 102558 is incorporated herein by reference.

[0002] The present invention relates to a computer - implemented method for the simulation of energy - filtered ion implantation (EFII).

Background Art

[0003] In commercially - oriented micro - technological production processes, masked and / or unmasked doping elements are introduced into materials such as semiconductors (silicon, silicon carbide, gallium nitride) or optical materials (glass, LiNbO3, PMMA) by ion implantation with a predetermined depth profile in a depth range from several nanometers to several tens of micrometers.

[0004] Ion implantation is a method of achieving doping or defect profile generation in materials such as semiconductor materials or optical materials with a predetermined depth profile in a depth range from several nanometers to several tens of micrometers. Examples of such semiconductor materials include, but are not limited to, silicon, silicon carbide, and gallium nitride. Examples of such optical materials include, but are not limited to, LiNbO3, glass, and PMMA.

[0005] There is a need to generate a depth profile having a depth distribution wider than the doping concentration peak or defect concentration peak achievable by single energy ion irradiation, or to generate a doping or defect depth profile that cannot be generated by one or a few simple single energy implantations. The doping concentration peak can generally be approximated by a Gaussian distribution or more accurately represented by a Pearson distribution. However, there are also deviations from such distributions, especially when the so-called channeling effect is present in the crystalline material. Prior art methods for generating depth profiles using a structured energy filter in which the energy of a single energy ion beam is changed as the single energy ion beam passes through a microstructured energy filter component are known. The resulting energy distribution leads to the creation of ions with a depth profile in the target material. This is described, for example, in Patent Document 1. An energy filter for adjusting the depth profile in semiconductor doping applications is known from Non-Patent Document 1. Ion beam irradiation of nanostructures is known from Non-Patent Document 2.

[0006] An example of such an ion implantation apparatus 20 is shown in FIG. 1, where an ion beam 10 impinges on a structured energy filter 25. The ion beam source 5 may be a cyclotron, a radio frequency linear accelerator, an electrostatic tandem accelerator, or a single-ended electrostatic accelerator. In other embodiments, the energy of the ion beam source 5 is between 0.5 and 3.0 MeV / nucleon, or in one embodiment between 1.0 and 2.0 MeV / nucleon. In one particular embodiment, the ion beam source generates an ion beam 10 having an energy between 1.3 and 1.7 MeV / nucleon. The total energy of the ion beam 10 is between 1 and 50 MeV, in one embodiment between 4 and 40 MeV, and in a further embodiment between 8 and 30 MeV. The frequency of the ion beam 10 may be between 1 Hz and 2 kHz, for example between 3 Hz and 500 Hz, and in one embodiment between 7 Hz and 200 Hz. The ion beam 10 may be a continuous ion beam 10. Examples of ions within the ion beam 10 include, but are not limited to, aluminum, nitrogen, hydrogen, helium, boron, phosphorus, carbon, arsenic, and vanadium.

[0007] FIG. 1 shows the basic principle of the energy filter. When a single energy ion beam passes through the microstructured energy filter component, the energy of the single energy ion beam is changed according to the entry point. The resulting energy distribution of the ions leads to a change in the depth profile of the implanted material in the substrate matrix.

[0008] FIG. 1 shows that the energy filter 25 is fabricated from a film having a triangular cross-sectional shape on the right hand side, but this type of cross-sectional shape does not limit the present invention and other cross-sectional shapes may be used. Region 25 through which the upper ion beam 10-1 passes through the energy filter 25 minSince this is the minimum thickness of the film in the energy filter 25, the upper ion beam 10-1 passes through the energy filter 25 with little energy reduction. In other words, if the energy of the upper ion beam 10-1 on the left side is E1, the energy of the upper ion beam 10-1 will also have substantially the same value E1 on the right side (there is only a small energy loss due to the stopping power of the film that leads to at least some absorption of the energy of the ion beam 10 in the film).

[0009] On the other hand, the lower ion beam 10-2 passes through the region 25 where the film of the energy filter 25 is thickest max Since the energy E2 of the lower ion beam 10-2 on the left side is substantially absorbed by the energy filter 25, the energy of the lower ion beam 10-2 on the right side decreases and is lower than the energy of the upper ion beam, that is, E1>E2. As a result, the higher-energy upper ion beam 10-1 can penetrate the substrate material 30 to a greater depth than the lower-energy lower ion beam 10-2. As a result, for example, a differential depth profile occurs in the substrate material 30, which is part of a semiconductor wafer.

[0010] This depth profile is shown on the right side of FIG. 1. The dark rectangular region indicates that the ions penetrate the substrate material to a depth between d1 and d2. However, the horizontal profile shape is a special case, which can be obtained if, for example, all the energies of the ions are geometrically considered equally and the materials of the energy filter and the substrate are the same. The Gaussian curve shows an approximate depth profile that has a maximum value at a depth of d3 without the energy filter 25. It will be understood that the depth d3 is greater than the depth d2 because some of the energy of the ion beam 10-1 is absorbed by the energy filter 25.

[0011] For typical ion species (N, Al, B, P) in the energy range from 1 MeV to several tens of MeV (e.g., 40 MeV), it can be observed that low-energy ions tend to have large scattering angles, while high-energy ions tend to have small scattering angles. The reason for this different scattering behavior is the energy dependence of the stopping mechanisms below. Ions with high kinetic energy preferentially lose their energy by so-called electron stopping, i.e., excitation of the electron system of the substrate. As a result, usually only small directional deviations, i.e., small scattering angles, occur. Ions with low kinetic energy preferentially lose their energy by elastic collisions with the atoms of the substrate, so-called nuclear stopping. As a result, large-angle scattering occurs.

[0012] In one aspect regarding the simulation of the doping depth profile, in a static implantation arrangement (i.e., the filter and the substrate do not move relative to each other), the distance between the filter and the substrate plays a decisive role. As can be seen in FIGS. 6A and 6B, if the distance 50 is chosen too small, due to the low scattering of high-energy ions, there may be a transfer of the filter structure to the implanted doping depth profile. In other words, to avoid this effect, the profiles generated by a single filter unit cell or a single filter element must overlap sufficiently so that the desired degree of lateral homogenization is achieved.

[0013] In summary, for a given ion species, a given initial ion energy, a given filter design, a given substrate material, and a given filter-substrate distance, a specific energy distribution and angular distribution of the filter-transmitted ions will be generated.

[0014] In the prior art, many principles for the manufacture of the energy filter 25 are known. Usually, the energy filter 25 is made from a bulk material, and the surface of the energy filter 25 is to be etched to produce a desired pattern such as the triangular cross-sectional pattern known from FIG. 1. In Patent Document 2, an energy filter manufactured from layers of materials having different ion beam energy reduction characteristics was described. The known depth profile resulting from the energy filter depends on the structure of the layers of material as well as the structure of the surface.

[0015] A further structural principle is shown in Patent Document 3, where the energy filter includes spaced microstructural layers connected to each other by vertical walls.

[0016] The maximum output from the ion beam 10 that can be absorbed through the energy filter 25 depends on three factors: the effective cooling mechanism of the energy filter 25, the thermomechanical properties of the film on which the energy filter 25 is fabricated, and the choice of material from which the energy filter 25 is fabricated. In a typical ion implantation process, about 50% of the output is absorbed by the energy filter 25, but this can increase to 80% depending on the process conditions and filter shape.

[0017] An example of an energy filter is shown in FIG. 2A, where the energy filter 25 is made of a triangular structured film attached to a frame 27. In a non-limiting example, the energy filter 25 can be made from a silicon-on-insulator including an insulating silicon dioxide layer 22 having a thickness of, for example, 0.2 to 1 μm sandwiched between a single piece of material, for example, a silicon layer 21 (typical thickness between 2 and 20 μm, but up to 200 μm) and bulk silicon 23 (thickness about 400 μm). The structured film is made, for example, from silicon, but may also be made from silicon carbide or another silicon-based or carbon-based material or ceramic.

[0018] To optimize the throughput of the wafer in the ion implantation process for a given ion current of the ion beam 10, and thus to use the ion beam 10 efficiently, in one aspect, only the membrane of the energy filter 25 is irradiated instead of the frame 27 in which the membrane is held in a fixed position. At least a part of the frame 27 may also be irradiated by the ion beam 10 and thus heated. In fact, the frame 27 may be completely irradiated. The membrane forming the energy filter 25 is heated, but since the membrane is thin (i.e., between 2 μm and 20 μm, but up to 200 μm), its thermal conductivity is very low. The membrane has a size between 2×2 cm 2 and 35×35 cm 2 and corresponds to the size of the target wafer. There is little heat conduction between the membrane and the frame 27. Thus, the monolithic frame 27 does not contribute to the cooling of the membrane, and the only cooling mechanism for the associated membrane is thermal radiation from the membrane.

[0019] As shown in FIG. 2B, the substrate holder 30 need not be fixed, and a device for moving the substrate 12 in the x-y plane (in the plane perpendicular to the sheet surface) can be optionally provided. Furthermore, a wafer wheel in which the substrate 12 to be implanted is fixed and rotates during implantation can also be considered as the substrate holder 30. It is also possible to move the substrate holder 30 in the beam direction (x direction) of the ion beam 10 with respect to the energy filter 25. Furthermore, heating or cooling can be optionally provided to the substrate holder 30.

[0020] Figures 3A and 3B show a typical installation of the energy filter 25 in a system for ion implantation for wafer processing. Figure 3A shows the wafer wheel 24 to which the substrate 26 to be implanted is fixed. During processing / implantation, the wafer wheel 24 is tilted 90° upward in the direction of the ion beam 10 and set to rotate. Concentric ions are thus "written" by the ion beam 10 along the wafer wheel 24. To irradiate the entire wafer area, the wafer wheel 24 is moved vertically during processing. In Figure 3B, the energy filter 25 attached in the region of the beam exit can be seen. However, the installation of the energy filter 25 in a system for ion implantation for wafer processing is not limited to a rotating setup, and a fixed setup for ion implantation for wafer processing is also possible, for example, as shown in Figure 2B.

[0021] The layout or three-dimensional structure of the energy filter 25 shown in Figures 4A to 4D shows the main possibilities of using the energy filter 25 to generate a number of doping depth profiles 40. In principle, energy filter profiles can be combined with each other to obtain a new energy filter profile and thus a doping depth profile 40.

[0022] Figures 4A to 4D show schematic diagrams of different doping depth profiles 40 (doping concentration as a function of depth in the substrate) for different-shaped energy filter microstructures (shown in side view and top view respectively). In Figure 4A, a triangular prism-shaped structure that generates a rectangular doping depth profile is shown. In Figure 4B, a smaller triangular prism-shaped structure is shown, generating a rectangular doping depth profile with a less depth distribution. In Figure 4C, a trapezoidal prism-shaped structure that generates a rectangular doping depth profile with a peak at the beginning of the profile is shown. In Figure 4D, a pyramid-shaped structure that generates a triangular doping depth profile rising to the depth of the substrate is shown.

[0023] It is known to simulate energy filtered ion implantation. However, a fundamental problem in simulating energy filtered ion implantation is that the geometric dimensions of the implantation structure are different. Energy filter structure elements are typically, for example, triangular structures made of silicon, with a height difference between the minimum and maximum film thicknesses exceeding about 1 μm and ranging from about 16 μm to 100 μm. A plurality of such structure elements arranged side by side form an energy filter. The dimensions of the energy filter structure elements in a direction perpendicular to the ion beam direction are also on the order of several micrometers to several hundred micrometers. In an actually used energy filter, the macroscopic dimensions of the energy filter film are required to range from 2×2 cm to over 17×17 cm and up to 40×40 cm. The substrate size is also in this range. On the other hand, the distance between the energy filter and the substrate is usually in the range of millimeters or centimeters.

[0024] FIG. 5A shows a schematic view of a filter unit cell 30 of a filter structure. The energy filter 25 is composed of a single element or a single filter unit cell 30. Each unit cell 30 provides (in the simplest case) the total energy and angular spectrum of the transmitted ions. The characteristic doping depth profile 40 of energy filtered ion implantation (EFII) thus results from the irradiation of the filter unit cell 30. The side-by-side arrangement of n unit cells 30 is simply an extension, which is necessary for the irradiation of an extended substrate. See FIG. 5A. FIG. 5B shows a cross-sectional view in the y-z plane of the static irradiation situation of the energy filter 25, the ion source 5, and the substrate 26. Structures typically formed with micrometer dimensions in the y direction become a macroscopically extended energy filter, and when arranged side by side, the dimensions are up to 40 cm. As can also be seen in FIG. 5B, the same applies in the z direction. Ions are scattered while passing through the energy filter 25. During this process, the ions experience energy loss due to lateral scattering as well as the choice of shape and material, resulting in a characteristic energy-angle distribution of the ions after exiting the energy filter 25.

[0025] In the static setup according to FIG. 5B, where the energy filter 25 is arranged parallel to the substrate 26 and at a defined distance that is sufficiently large from the substrate, a desired degree of lateral homogenization of the energy distribution of the ions in the y-z plane is achieved, and thus the mapping of the microstructure of the energy filter 25 onto the substrate 26 is avoided, i.e., in the sense of a mathematical mapping function. FIG. 6A shows an arrangement in which the energy filter 25 is in contact with the substrate 26 and mapping onto the doping depth profile 40 of the energy filter 25 takes place. FIG. 6B shows an arrangement of the energy filter 25 and the substrate 26 with a "sufficient" distance 50, such that the doping depth profile 40 is homogeneously implanted laterally (y-z plane) into the substrate 26 in a plane perpendicular to the ion beam direction of the ion beam 10.

[0026] FIGS. 7A to 7C show the 1-D (z-y integration) doping depth profile 40 simulated with a filter dimension of 1000 μm×1000 μm and the 2-D profile in the x-y plane of the substrate 26. The upper plots in FIGS. 7A to 7C show the two-dimensional distribution of the doping concentration in the y-x plane. The corresponding lower representations in FIGS. 7A to 7C show the sum of the integrals along both the y-axis and the z-axis for each case.

[0027] In the following section, this irradiation arrangement of FIG. 5B will be considered in more detail as an example. In particular, the dependence of the resulting energy spectrum on the design of the injection arrangement (distance between the filter and the substrate) should be clarified based on the implanted ion concentration as a function of the location within the substrate 26.

[0028] Initial situation: The filter dimensions of the energy filter 25 are y≈1000 μm, z≈1000 μm, a plurality of unit cells (complete triangular structures) are arranged side by side, the unit cell dimensions are x = 16 μm, y≈11 μm, and are translationally symmetric in z. The implanted ions are aluminum (Al), the primary energy is 12 MeV, the filter material is equal to the substrate material and equal to silicon.

[0029] Figure 7A shows the energy filter 25 and the substrate 26 separated by 20 μm. In Figure 7A, the energy filter 25 and the substrate 26 are at a distance of fs = 20 μm from each other. The 2-D map in the x-y plane of the substrate 26 shows the mapping of the microstructure of the energy filter 25 onto the substrate 26. The lateral scattering of ions from adjacent single cells is not sufficient to achieve the desired degree of lateral homogenization along the y-axis of the doping in the substrate 26, as shown in Figure 6A.

[0030] Figure 7B shows the energy filter 25 and the substrate 26 separated by 500 μm. In Figure 7B, the energy filter 25 and the substrate 26 are at a distance of fs = 500 μm from each other. No transfer of the microstructure of the energy filter 25 onto the substrate 26 is seen. The lateral scattering of ions from adjacent single cells is sufficient to achieve the desired degree of lateral homogenization of the doping in the substrate 26. The filter-substrate distance is correctly selected in this case.

[0031] Figure 7C shows the energy filter 25 and the substrate 26 at a distance of 3000 μm from each other. According to Figure 7C, when the distance between the energy filter 25 and the substrate 26 is further increased, inhomogenization of the energy distribution of the ions in the y-z plane occurs, and as a result, a gradient appears in the depth profile of the total depth doping summed along the y-axis. This inhomogenization of the energy spectrum of the ions is due to the large distance between the energy filter 25 and the substrate 26, as well as the dimensions of the ion source and the energy filter 25. As a result of both the large scattering angle of the scattered ions with a large scattering angle and the large filter-substrate distance, a plurality of strongly scattered ions no longer hit the substrate 25 and scatter past the substrate 25. Ions that scatter in this way no longer hit the substrate 25 and are thus "lost".

[0032] In actual energy filter irradiation, one aspect is to achieve a homogeneous concentration and energy distribution of ions similar to the situation shown in FIG. 7B in the lateral direction. The desired degree of lateral homogenization of the doping depth profile as well as the preservation of the complete characteristic energy spectrum are actually achieved by dynamic implantation. Here, the microstructural mapping is avoided by the relative movement from the substrate 26 to the energy filter 25, independent of the distance. Further, in practice, the loss of ions at the edge of the wafer substrate 26 is avoided by overscanning the filtered ion beam beyond the edge of the substrate 26.

[0033] In the simulation of energy filter ion implantation, a static configuration is assumed. To achieve the desired degree of lateral homogenization and avoid particle loss, the boundary condition is that the resulting energy spectrum of the simulated energy filter must be independent of the spatial coordinates y - z on the wafer. In other words, the complete energy - angle spectrum of the unit cell must be found at any y - z position on the wafer.

[0034] Ion implantation is a process "composed" of a large number of individual events. To form a typical distribution in the substrate by the statistical scattering process, a large number of single ions (usually 1×10 12 cm -2 ~1×10 15 cm -2 ) are required. The use of Monte Carlo techniques has thus become widespread in the field of ion implantation.

[0035] Therefore, simulation methods can support or shorten the development process, or facilitate the accurate design and sizing of processes and products. To enable a reasonable simulation from the perspectives of sufficient statistics, time, and cost, a method must thus be used to significantly reduce the complexity and computational effort for simulation without sacrificing accuracy while taking into account different size ratios.

[0036] Typical dimensions of the simulation regions of interest for ion implantation process simulations in semiconductor technology are perpendicular to the ion beam in a size range from a few micrometers to a few millimeters or even centimeters, and parallel to the ion beam (depth profile) in a range from a few micrometers to 100 micrometers. Typical resolution requirements in all directions are at least 5 or 10 nanometers. To achieve the required spatial resolution, these regions must be subdivided into a fine grid in the nanometer range and simulated with a corresponding large number of events to resolve the relevant characteristics with a high event density.

Prior Art Documents

Patent Documents

[0037]

Patent Document 1

Patent Document 2

Patent Document 3

Non-Patent Documents

[0038]

Non-Patent Document 1

Non-Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0039] An object of the present invention is to provide a method that enables simulation of the doping depth profile of an energy-filtered ion beam by means of a so-called “Monte Carlo” algorithm. In particular, to provide a method for efficiently simulating a complex ion implantation process such as an EFII process using the Monte Carlo method in order to reproduce the actual physical process and its effects within a substrate as accurately as possible without artifacts.

[0040] Implementing an ion implantation arrangement in a Monte Carlo simulation environment implies a high workload for implementing such an array due to the complex structure. Generally, as a result of the wide variation in the dimensions of the microscopic filter structure compared to the distance between the filter and the substrate, for example, the ratio of the “region of interest” simulation volume g of the total simulation volume S shown in FIG. 8 V becomes low. Due to the requirements for a high grid and event density in the simulation region, the total simulation volume S VThe total number of simulation events within increases, and these can only be simulated with cost - intensive computing technologies and long simulation periods.

[0041] An object of the present invention is to provide a method for incorporating the simulation of energy - filtered ion implantation into the tool landscape for technology computer - aided design (TCAD) of semiconductor electronic devices.

[0042] An object of the present invention is to provide a computer - implemented method that greatly improves the efficiency of Monte Carlo simulation of an energy - filtered implantation process, that is, reduces the effort for model implementation, reduces the complexity of computer simulation, and ultimately shortens the calculation time or reduces the requirements for computer hardware performance. For a geometric simulation model, the present invention improves the ratio of the simulation area g to the total simulation volume S V . According to the present invention, it becomes possible to reduce the number of simulation events while maintaining a high event density within the simulation area g. As a result, the simulation time can be saved.

[0043] Therefore, there is a need to improve the method for simulating energy - filtered ion implantation.

Means for Solving the Problems

[0044] According to a first aspect of the present invention, a computer-implemented method for the simulation of energy-filtered ion implantation (EFII) includes determining at least a part of an energy filter, determining at least a part of an ion beam source, determining a simulation region within a substrate, implementing the determined at least a part of the energy filter, the determined at least a part of the ion beam source, and the determined simulation region within the substrate, determining a minimum distance between the implemented at least a part of the energy filter and the implemented substrate to enable a desired degree of lateral homogenization of the energy distribution in the doping depth profile of the implemented substrate, determining a maximum predicted scattering angle of the energy filter by simulating an energy-angle spectrum for the energy filter, and defining a total simulation volume. Thereby, the simulation volume S v is provided to be as small as possible and the simulation volume S v is provided in a simplified manner. It is further possible to provide a static filter and substrate arrangement independent of the static or dynamic actual implantation setup. Thus, this method enables the implementation of shape simplification by considering the energy-angle distribution and related geometric constraints.

[0045] In one aspect of this method, the minimum distance between the energy filter and the substrate is between 100 μm and 1000 μm in the simulation of the EFII process of Al ions at a kinetic primary energy of 12 MeV.

[0046] In another aspect of this method, the energy filter based on the determined maximum predicted scattering angle determines the number of filter unit cells arranged adjacent to each other.

[0047] In another aspect of this method, the simulation region analyzed within the substrate is between 1 μm and 500 μm in any direction.

[0048] According to a second aspect of the present invention, a computer-implemented method for the simulation of energy filter ion implantation (EFII) includes steps of approximating an energy filter in at least one basic element, selecting at least one of the at least one basic element to enable assembly of a desired shape and material composition of the simulated energy filter from the selected basic element, determining an energy angle spectrum for the selected at least one basic element, determining a virtual ion beam source based on the determined energy angle spectrum of the selected at least one basic element, and simulating the implantation effect within a simulation region in a substrate. This enables separation of a more complex simulation task into determining a virtual ion beam source (i.e., an EFIIS source) and subsequent simulation of the ion implantation effect for any substrate. This method enables a simulation in a series of process steps associated with a simulation that reduces the overall simulation volume and thus improves the efficiency of performing the simulation. Therefore, this method also enables simulation of more complex energy filters. This is a result of an improved ratio of the simulation region g to the total simulation volume S v and the simulation volume is independent of each other in steps of determining the virtual ion beam characteristics and simulating the simulation region g with a predefined virtual ion beam. This enables better simulation efficiency even when the dimensions of the energy filter and the simulation region are very different. Further, the event density and grid density of two process steps of this method can be determined independently of each other, thereby enabling optimization of the simulation according to requirements.

[0049] In one aspect of this method, at least one basic element is at least a part of at least one energy filter element, a filter unit cell of an energy filter, or one of a set of discrete energy filters.

[0050] In one aspect of this method, the energy filter is triangular, pyramidal, inverted pyramidal, or of a free form.

[0051] In another aspect of this method, the filter unit cell of the energy filter is composed of a plurality of basic elements of different shapes, different material compositions, or different layer structures.

[0052] In one aspect of this method, the implantation effect is one of defect generation, doping profile, and masking effect.

[0053] In another aspect of this method, a new filter shape, selection of a new filter material, new layer composition of the energy filter, new primary ions, new primary ion energy, new primary ion implantation angle, and a new virtual ion beam source are determined.

[0054] In one aspect of this method, this method includes the step of storing at least one basic element in a database.

[0055] In one aspect of this method, this method includes the step of storing a virtual ion beam source in a database.

[0056] In another aspect of this method, the method includes parametrically analyzing a masking structure on a substrate to optimize the masking thickness, material composition, and masking layout, and to optimize the 3D doping profile within the substrate affected by the masking structure. The mask structure can significantly affect the 3D doping profile through its composition, thickness (partial transparency), and the angle of its "bevel" (partial implantation at a flat angle). These effects can be very well analyzed by the method according to the invention, or the doping profile and the mask can be optimized.

[0057] In one aspect of this method, the optimization of the masking structure and / or the 3D doping profile on the substrate is performed using Monte Carlo simulation. The mask structure can significantly affect the 3D doping profile through its composition, thickness (partial transparency), and the angle of its "bevel" (partial implantation at a flat angle). These effects can be very well analyzed by the method according to the invention, or the doping profile and the mask can be optimized.

[0058] The present invention will now be described with reference to the drawings. It will be understood that the aspects of the invention described in the drawings are merely examples and in no way limit the scope of protection of the claims. The present invention is defined by the claims and their equivalents. It will be understood that the features of one aspect of the present invention can be combined with the features of a different aspect of the present invention. The present invention will become more apparent when reading the following detailed description of a plurality of examples as part of the disclosure in consideration of the accompanying drawings.

Brief Description of the Drawings

[0059]

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Mode for Carrying Out the Invention

[0060] FIG. 8 shows a schematic diagram of a static simulation model of energy filter ion implantation (EFII) according to a first aspect of the present invention. The energy-angle distribution characteristics of the static simulation model of EFII correspond to the representation of the geometric boundary conditions required to accurately reproduce the actual implantation conditions and the energy-angle spectrum. FIG. 8 shows the dimensions of the ion source obtained from the area-wide scanning process of the ion beam during implantation. The EFII process can be simulated within a Monte Carlo simulation environment. As seen in FIG. 8, the distance 50 (fs) between the filter and the substrate should be at least dimensioned at a distance 50 where the scattering of ions leads to the desired degree of lateral homogenization of the energy distribution and no structural transfer of the microstructure of the energy filter to the substrate 26 is seen in one implementation. In the simulation of the EFII process of Al ions at a kinetic primary energy of 12 MeV, this minimum distance 50 is fs = 500 μm according to FIG. 7B.

[0061] The maximum predicted scattering angle α of the filter unit cell 30 should be determined. For this purpose, the energy angle spectrum for a given filter unit cell 30 is simulated and the maximum scattering angle α (which is still experienced by a relevant number of ions) is determined. In particular, when the number of ions simulated is large, there will always be a plurality of ions having a scattering angle close to 90°. Thus, the angle α can also be defined in a way that the angle α does not include the relevant portion of the scattered ions, that is, scattered ions with a scattering angle larger than the angle α that make up less than 1% or 2% of the total number of ions in total. This reduces the accuracy but simplifies the simulation. As shown in FIG. 8, using this maximum angle α, the total width of the filter model, that is, how many filter basic cells have to be arranged side by side with each other is calculated. To ensure that the entire angular spectrum of the ions hits the simulation region g, the characteristic energy filter injection profile is generated in the simulation region g. In the simulation of the EFII process of Al ions with a primary kinetic energy of 12 MeV and the distance 50 between the energy filter 25 and the substrate 26 being fs = 500 μm, as can be seen in FIG. 16, the maximum scattering angle α is about 70°. FIG. 8 shows the widths of the energy filter 25 and the ion source 5. The analyzed region in the substrate 26 (that is, the simulation region g) is given by g = 2 μm. The required total width of the ion beam source 5 and the energy filter 25 is thus L = 2749 μm. The analyzed region in the substrate 26 (that is, the simulation region g) can also be between 1 μm and 500 μm.

[0062] The total dimension of the simulation is calculated by the formula L = l + g, and the width l of the ion beam source 5 and the energy filter 25 is calculated by the following formula, l / 2 = f s tan(α) where α = the maximum scattering angle, and f s = the distance 50 between the energy filter 25 and the substrate 26.

[0063] Figure 9 shows a flowchart of a computer-implemented method 200 according to a first aspect of the present invention for simulation of energy filter ion implantation (EFII). The method 200 for simulation of energy filter ion implantation (EFII) includes a step 201 of determining at least a part of an energy filter 25, a step 202 of determining at least a part of an ion beam source 5, a step 203 of determining a simulation region g within a substrate 26, and a step 204 of implementing the determined at least a part of the energy filter 25, the determined at least a part of the ion beam source 5, and the determined simulation region g within the substrate 26. The simulation environment is, for example, a Monte Carlo simulation. The method 200 includes a step 205 of determining a minimum distance 50 (fs) between the implemented at least a part of the energy filter 25 and the implemented substrate 26 to enable a desired degree of lateral homogenization of the energy distribution in the doping depth profile 40 of the implemented substrate 26, a step 206 of determining a maximum predicted scattering angle α of the energy filter 25 by simulating an energy angle spectrum for the energy filter 25, and a step 207 of defining a total simulation volume S V (see the dotted line in FIG. 8), and further includes a step 207.

[0064] For example, in method 200, in the simulation of the EFII process of Al ions with a primary kinetic energy of 12 MeV, it is further required that the minimum distance 50 (fs) between the energy filter 25 and the substrate 26 be between 100 μm and 1000 μm. Method 200 further includes that in the simulation of the EFII process of Al ions with a primary kinetic energy of 12 MeV and a minimum distance 50 of 500 μm, the maximum predicted scattering angle α of the filter unit cell 30 is 70°. Method 200 further includes that the simulation region g in the substrate 26 is 2 μm in one dimension. Method 200 further includes that the full width l of the energy filter 25 according to the determined maximum predicted scattering angle α is the number of filter unit cells arranged adjacent to each other. For example, the minimum distance 50 (fs) between the energy filter 25 and the substrate 26 can also be 0 μm (without homogenization), up to 1000 μm beyond 100 μm, or up to several millimeters (fully homogenized). For light ions (hydrogen) and very high energies and large filter structures (e.g., thickness 100 μm), a distance 50 greater than 1000 μm is required.

[0065] FIG. 10 shows a schematic side view of an energy filter to be simulated. A computer-implemented method 300 according to a second aspect of the present invention includes a first process step of selecting one or more basic elements 25a-1, 25a-2, … 25a-n. The basic elements 25a-1, 25a-2, … 25a-n are, for example, energy filter elements 25a (shown in FIG. 11A), filter unit cells 30, or a set of discrete energy filter elements 25a (shown in FIG. 11C). The selection is made such that the desired shape and material composition of the entire simulated energy filter 25 can be assembled from these basic elements. FIGS. 11A to 11D show examples demonstrating the possibility of selecting or defining the basic elements 25a-1, 25a-2, … 25a-n. FIGS. 11A to 11D show schematic side views of the basic elements 25a-1, 25a-2, … 25a-n approximated from the simulated energy filter 25. FIG. 12 shows a schematic side view of a simulated composite energy filter provided with a filter unit cell 30. As shown in FIG. 11D, the triangular structure of the energy filter element 25a can be approximated by n adjacent discrete filter membrane pieces 25a-1, 25a-2, 25a-3, … 25a-n.

[0066] FIGS. 13A to 13B show a simulation model of an energy filter ion implantation EFII with approximated geometric conditions according to a second aspect of the present invention. FIGS. 13A and 13B show a schematic view of a geometric simulation model of the method 300 and the continuation of the simulation. However, the present invention is not limited to a series of simulations and may be a single simulation.

[0067] As shown in FIG. 14, a method 300 according to a second aspect of the present invention for simulation of energy filter ion implantation (EFII) approximating geometric conditions includes, as a first process step, a step 301 of approximating an energy filter 25 in at least one basic element 25a-1, 25a-2, …, 25a-n, a step 302 of selecting at least one of the at least one basic element 25a-1, 25a-2, …, 25a-n to enable assembly of a desired shape and material composition of the simulated energy filter 25 from the selected basic element 25a-1, 25a-2, …, 25a-n, and a step 303 of determining an energy angle spectrum for the selected at least one basic element 25a-1, 25a-2, …, 25a-n. The at least one basic element 25a-1, 25a-2, …, 25a-n is at least a part of at least one energy filter element 25a, a filter unit cell 30 of the energy filter 25, or one of a set of discrete energy filters 25. The energy filter 25 can be, for example, triangular, pyramidal, inverse pyramidal, or free-form. The filter unit cell 30 of the energy filter 25 is composed of a plurality of basic elements with different shapes, different material compositions, or different layer structures.

[0068] After the first process step, in the next step, the relevant characteristics of the ion beam characteristics (energy and angle, y-z coordinate dependence of the energy and angle of the ions) acting on the simulation region g due to the filter characteristics and the characteristics of the primary ions are calculated for all of the selected basic elements 25a-1, 25a-2, …, 25a-n. The method 300 according to the present invention is not limited to a triangular energy filter 25. Rather, a pyramidal, inverse pyramidal, or more generally a free-form structure for the energy filter 25 can also be simulated using the method 300. For example, the energy filter 25 or the filter unit cell 30 can be composed of a plurality of basic elements 25a-1, 25a-2, …, 25a-n having different shapes, different material compositions, or different layer structures. It is also possible to tilt the energy filter 25 or to mirror it about an axis perpendicular to the ion beam 10.

[0069] As shown in FIG. 14, after the first process step, the method 300 for the simulation of energy filter ion implantation (EFII) includes, as a second process step, a step 304 of determining a virtual ion beam source 5 based on the determined energy angle spectrum, and a step of determining a desired degree of lateral (y-z coordinate) homogenization of the energy and angle distribution of the ions of at least one selected basic element 25a-1, 25a-2, 25a-3, …, 25a-n for one EFII. In a further aspect, the energy angle distribution of a single energy filter 25 is determined, and the energy filter 25 may be a "simple" basic cell as shown in FIG. 10 or a "complex" basic cell as shown in FIG. 12. The determination of the energy angle distribution can be performed by a plurality of steps using different methods. Simulation methods (simulation of one or more basic elements), analytical methods, as well as experimentally obtained results or combinations of such methods are conceivable.

[0070] Method 300 for the simulation of energy filter ion implantation (EFII) also includes, as a second process step, step 305 of simulating the implantation effect within the simulation region g in substrate 26. In the next step, a virtual ion beam source 5 with certain energy angle characteristics is defined, which is composed of the ion beam characteristics of the basic elements 25a-1, 25a-2, 25a-3, …, 25a-n selected in the first process step of method 300. Thus, this composite virtual ion beam source 5 exactly corresponds to (or approximates) the ion beam characteristics (energy and angular distribution) of the entire energy filter 25 to be simulated. As shown in FIGS. 13A and 13B, this virtual ion source 5, also called the EFIIS source 5, is used to simulate the implantation effects (defect generation, doping profile, masking effect) in the target substrate 26 (simulation region g) under investigation.

[0071] Therefore, for each new filter shape, selection of a new filter material, new layer composition of the energy filter 25, new primary ions, new primary ion energy, new primary ion implantation angle (i.e., distribution), a new virtual ion beam source 5, i.e., the EFIIS source 5, is defined. The ion beam source 5, i.e., the EFIIS source 5, can be used to simulate and analyze the effects of ion implantation on any substrate 26. The ion beam source 5, i.e., the EFIIS source 5, and the basic elements 25a-1, 25a-2, 25a-3, …, 25a-n of the underlying energy filter 25 can also be stored in a database (not shown) in the first process step of method 300. Furthermore, it is possible to continuously improve the virtual ion beam source 5, i.e., the EFIIS source 5, by matching the simulation results with the experimental results.

[0072] As shown in FIG. 14, method 300 further includes that the implantation effect is one of defect generation, doping profile, and masking effect. Method 300 further includes that for a new filter shape, selection of a new filter material, a new layer composition of the energy filter 25, a new primary ion, a new primary ion energy, and a new primary ion implantation angle, a new virtual ion beam source 5 is determined. Method 300 further includes step 306 of storing at least one basic element 25a-1, 25a-2, 25a-3, ..., 25a-n in a database (not shown). Method 300 further includes step 307 of storing the virtual ion beam source 5 in a database (not shown).

[0073] A further important advantage results from varying the shape parameters within the simulation region to systematically investigate the simulation region g. This is shown, for example, in FIGS. 15A to 15C, which show a typical simulation investigation when varying the masking thickness on the substrate 26. The purpose of this investigation is to determine the required masking thickness, geometric shape, material composition, and layout, and to use Monte Carlo simulations to investigate / optimize the 3D dopant profile in the substrate for a fixed energy filter 25 and fixed primary ion characteristics, i.e., for a given ion beam source, i.e., the EFIIS source. By separating the first process step and the second process step according to method 300 and certain EFII parameters, it is necessary to execute the first process step only once and the second process step for each change in the masking thickness. This saving of process steps for each follow-up investigation of the second process step is reflected in a saving of simulation time. A library solution can also be considered in which the ion beam characteristics are stored together with the parameters defined for the follow-up simulations in Monte Carlo simulations. The optimization of these simulations has a positive effect on simulation time, hardware, resources, and energy consumption.

[0074] As shown in FIG. 14, method 300 further includes step 308 of parametrically analyzing masking structure 70 on substrate 26 to detect the geometric shape, material composition, and layout of the masking thickness, as well as to investigate / optimize the 3D dopant profile within the substrate, as shown in FIGS. 15A through 15C. As shown in FIG. 14, method 300 further includes that the analysis 308 of masking structure 70 on substrate 26 is performed by using Monte Carlo simulation.

[0075] As shown in FIG. 16, in the energy-angle distribution of EFII of Al ions with an initial energy (E) of 12 MeV and typical filter dimensions, the maximum scattering angle α is about 70°.

Explanation of Symbols

[0076] 5 Ion beam source 10 Ion beam 20 Ion implantation device 21 Silicon layer 22 Silicon dioxide layer 23 Bulk silicon 24 Wafer wheel 25 Energy filter 25a Energy filter element 26 Substrate 30 Filter unit cell 40 Doping depth profile 50 Distance 60 Composite filter 70 Masking structure 100 Ion implantation system 200, 300 Computer-implemented method g Simulation region l Width

Claims

1. A computer-implemented method (200) for simulation of energy-filtered ion implantation (EFII), comprising: determining (201) at least a part of an energy filter (25); determining (202) at least a part of an ion beam source (5); determining (203) a simulation region (g) within a substrate (26); implementing (204) the determined at least a part of the energy filter (25), the determined at least a part of the ion beam source (5), and the determined simulation region (g) within the substrate (26); determining (205) a minimum distance (50) between the implemented at least a part of the energy filter (25) and the implemented substrate (26) to enable a desired degree of lateral homogenization of an energy distribution in a doping depth profile (40) of the implemented substrate (26); determining (206) a maximum predicted scattering angle (α) of the energy filter (25) by simulating an energy-angle spectrum for the energy filter (25); Step (207) of determining the total simulation volume (S Ｖ ), and a method (200) including the same.

2. The method (200) according to claim 1, wherein the minimum distance (50) between the energy filter (25) and the substrate (26) is between 100 μm and 1000 μm in a simulation of an EFII process of Al ions at a primary kinetic energy of 12 MeV.

3. The method (200) according to claim 1, wherein the energy filter (25) is composed of single filter unit cells (30), the single filter unit cells (30) are composed of a plurality of basic elements of different shapes, different material compositions or different layer structures, and an overall width of the energy filter (25) according to the determined maximum predicted scattering angle (α) is a number of the single filter unit cells (30) arranged adjacent to each other.

4. The method (200) according to claim 1, wherein the simulated region (g) analyzed within the substrate (26) is between 1 μm and 500 μm when viewed perpendicular to the ion beam (10) in any direction.

5. A computer-implemented method (300) for simulation of energy-filtered ion implantation (EFII), comprising: Approximating an energy filter (25) in at least one basic element (25-1, 25-2, 25-3, …, 25-n) (step 301); Selecting at least one of the at least one basic element (25-1, 25-2, 25-3, …, 25-n) to enable assembly of a desired shape and material composition of the simulated energy filter (25) from the selected basic element (25-1, 25-2, 25-3, …, 25-n) (step 302); Determining an energy angle spectrum for the selected at least one basic element (25-1, 25-2, 25-3, …, 25-n) (step 303); Determining a virtual ion beam source (5) based on the determined energy angle spectrum of the selected at least one basic element (25-1, 25-2, 25-3, …, 25-n) (step 304); Simulating implantation effects in a simulation region (g) within a substrate (26) (step 305), a method (300).

6. The method (300) according to claim 5, wherein the at least one basic element (25-1, 25-2, 25-3, …, 25-n) is at least part of at least one energy filter element (25a), a filter unit cell (30) of the energy filter (25), or one of a set of discrete energy filters (25).

7. The method (300) according to claim 5, wherein the energy filter (25) is triangular, pyramidal, inverse pyramidal, or freeform.

8. The method (300) according to claim 6, wherein the filter unit cell (30) of the energy filter (25) is composed of a plurality of basic elements of different shapes, different material compositions, or different layer structures.

9. The method (300) according to claim 5, wherein the implantation effect includes at least one of defect generation, doping profile, and masking effect.

10. A new filter shape, selection of a new filter material, a new layer composition of the energy filter (25), a new primary ion, a new primary ion energy, a new primary ion implantation angle, and a new virtual ion beam source (5) are determined, the method (300) according to claim 5.

11. The method (300) according to claim 5, further comprising the step (306) of storing the at least one basic element (25-1, 25-2, 25-3, …, 25-n) in a database.

12. The method (300) according to claim 5, further comprising the step (307) of storing the virtual ion beam source (5) in a database.

13. The method (300) according to claim 5, further comprising the step (308) of parametrically analyzing a masking structure (70) on the substrate (26) in order to optimize a masking thickness, a material composition and a masking layout, and in order to optimize a 3D dopant profile in the substrate.

14. The step (308) of analyzing the masking structure (70) on the substrate (26) in order to optimize the masking thickness, the material composition and the masking layout, and in order to optimize the 3D dopant profile in the substrate, uses Monte Carlo simulation, the method (300) according to claim 13.

15. A computer program comprising instructions which, when executed by a computer, cause the computer to execute the method according to any one of claims 1 to 14.

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