Computer implementation method for simulation of energy-filtered ion implantation (EFII) using an ion tunnel

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) a simulation area (g) within a substrate (26); defining (203) an ion tunnel (70) for receiving ions (10) directed from an ion beam source (5); implementing (204) the determined at least a portion of the energy filter (25), the ion beam source (5), the determined simulation area (g) within the substrate (26), and the defined ion tunnel (70) in a simulation environment; 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 the energy distribution in a doping depth profile (40) of the implemented substrate (26); and determining (206) a total simulation volume (S V and determining (206)

Description

Technical Field

[0001] Cross - reference to Related Applications This application claims the benefit and priority of Luxembourg Patent Application No. LU102559, filed on February 24, 2021. The entire disclosure of Luxembourg Patent Application No. LU102559 is incorporated herein by reference.

[0002] The present invention relates to a computer - implemented method for simulating energy - filtered ion implantation using ion tunnels.

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 a few nanometers to several tens of micrometers.

[0004] Ion implantation is a method for 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 a few 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] It is necessary to generate a depth profile having a depth distribution wider than the doping concentration peak or defect concentration peak obtainable 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 are known for generating a depth profile 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. 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 device 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 depending on 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 it 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 hand side is E1, the energy of the upper ion beam 10-1 will have substantially the same value E1 on the right hand side as well (there is only a small energy loss due to the stopping power of the film which 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 hand side is substantially absorbed by the energy filter 25, the energy of the lower ion beam 10-2 on the right hand 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 to a greater depth in the substrate material 30 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 hand 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 would be obtained if, for example, all the energies of the ions were considered geometrically equally and the materials of the energy filter and the substrate were the same. The Gaussian curve shows an approximate depth profile which has a maximum value at a depth d3 and no energy filter 25. It will be understood that the depth d3 is greater than the depth d2 since 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 lies in the energy dependence of the following stopping mechanisms. Ions with high kinetic energy preferentially lose their energy by so-called electronic stopping, i.e., by exciting 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 will 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 fine structure 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 thermo-mechanical 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 rise to 80% depending on the process conditions and the 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 that includes a silicon dioxide layer 22 having a thickness of, for example, 0.2 to 1 μm sandwiched between a single piece of material, such as 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 can be made from, for example, silicon, but can 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 an ion implantation process for a given ion current for 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 rather than 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 within x - y (in a plane perpendicular to the sheet plane) can be optionally provided. Further, 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. Further, 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 is 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 rotational setup, and a fixed setup for ion implantation for wafer processing is also possible, for example, as shown in Figure 2A.

[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, which generates 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-filtering structural 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 structural elements arranged side by side form an energy filter. The dimensions of the energy-filtering structural 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-filtering 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 the 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 the shape and material selection as well as lateral scattering, 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 from the substrate that is sufficiently large, 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 occurs. 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 through 7C show the 1-D (z-y integrated) doping depth profile 40 simulated with a filter dimension of 1000 μm×1000 μm as well as the 2-D profile in the x-y plane of the substrate 26. The upper plots in FIGS. 7A through 7C show the two-dimensional distribution of the doping concentration in the y-x plane. The corresponding lower representations in FIGS. 7A through 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 implantation 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, and 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 translationally symmetric in z. The implanted ions are aluminum, 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 of the doping along the y-axis 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 visible. 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 distance between the filter and the substrate 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, multiple 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 microstructure 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 that is "composed" of a large number of individual events. To form a typical distribution in the substrate by a statistical scattering process, a large number of single ions (usually 1×10 12 cm -2 ~1×1015cm -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 dimensioning of processes and products. To enable a reasonable simulation with sufficient statistics from the perspectives of time and cost, a method that significantly reduces the complexity and computational effort for simulation without sacrificing accuracy by taking into account different size ratios must thus be used.

[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 have to be subdivided into a fine grid in the nanometer range and simulated with a corresponding large number of events to resolve the relevant properties 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

[0039] An object of the present invention is to provide a method for enabling 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 processes and their effects within the substrate as accurately as possible without artifacts.

[0040] Implementing an ion implantation layout 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 region g of the total simulation volume S shown in FIG. 8 V is low. Due to the requirement for a high grid and event density in the simulation region, the total number of simulation events within the total simulation volume S V increases, and these can only be simulated with cost-intensive computing techniques and long simulation periods.

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

[0042] The object of the present invention is to provide a computer-implemented method that greatly improves the efficiency of Monte Carlo simulations of the energy-filtered implantation process, i.e., reduces the effort for model implementation, reduces the complexity of computer simulations, and ultimately shortens the calculation time or reduces the requirements for computer hardware performance. Regarding the geometric simulation model, the present invention improves the ratio of the simulation region 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 region g. As a result, the simulation time can be saved.

[0043] Therefore, there is a need to improve the computer-implemented 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 simulating energy-filtered ion implantation is provided. The method includes determining at least a part of an energy filter, determining a simulation region within a substrate, defining an ion tunnel for receiving ions from an ion beam source, implementing in a simulation environment the determined at least a part of the energy filter, the ion beam source, the determined simulation region within the substrate, and the determined ion tunnel, 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 substrate, and defining a total simulation volume S V The method further includes defining a total simulation volume S. Thus, the geometric dimensions of the filter model in the simulator are minimized by defining the ion tunnel, and thus the ratio of the total simulation volume in the substrate to the simulation region is optimized. The desired degree of lateral homogenization means that the average deviation of a profile parallel to the ion beam along the z or y direction, i.e., along the substrate surface, is less than 10% or 5% or 3%. Implementing the approximated geometric dimensions of the energy filter includes using an analytical mathematical description of the energy filter and / or using a mesh description. The advantage of the present invention results from the improvement of the ratio of the total simulation volume S V to the simulation region g, which enables a reduction of simulation events compared to conventional models while maintaining the same event density in the simulation region g. This has a positive effect on simulation time, hardware, resources, and energy consumption.

[0045] In one aspect of this method, at least a part of the filter unit cell of the energy filter is defined as at least a part of the energy filter. The filter unit cell is defined as a part of the energy filter that represents the entire energy and angular spectrum of a specific energy filter. A plurality of unit cells can be added to form an actual energy filter.

[0046] In one aspect of this method, the simulation environment is a Monte Carlo simulation environment.

[0047] In one aspect of this method, the dimensions in the z - y plane of the ion tunnel are defined such that ions reaching the first edge of the defined total simulation region are re - introduced at the other edge of the defined total simulation region.

[0048] In another aspect of this method, the ion tunnel is defined such that ions from the first edge of the defined total simulation region move in the y - z plane to the opposite edge of the defined total simulation region.

[0049] In another aspect of this method, at least a part of the energy filter is defined such that at least a part of the energy filter is at least half of the filter unit cell.

[0050] In one aspect of this method, the ion tunnel is defined such that the ion tunnel must have dimensions at least the same as the determined simulation region.

[0051] In another aspect of this method, the ion tunnel is defined such that the tunnel must have dimensions at least the same as the filter unit cell or a multiple of the filter unit cell.

[0052] In one aspect of this method, the required dimensions of the simulation region in the substrate are determined by the simulation task.

[0053] In one aspect of this method, the required dimensions of the simulation region within the substrate are determined by the dimensions of the masking structure on the substrate.

[0054] In one aspect of this method, the method further includes implementing approximate geometric dimensions of an energy filter and / or a support structure in a triangular shape, a pyramid shape, an inverted pyramid shape, or a freeform shape.

[0055] In one aspect of this method, the method further includes implementing approximate geometric dimensions of a filter unit cell composed of a plurality of basic elements having different shapes, different material compositions, or different layer structures.

[0056] In one aspect of this method, the method further includes tilting the energy filter.

[0057] In one aspect of this method, the method further includes mirroring the ion beam about an axis perpendicular to the ion beam by a mirror within the ion tunnel.

[0058] In one aspect of this method, the method further includes superimposing a plurality of simulations at different primary energies, ion types, or incident angles of the primary ions.

[0059] The present invention will now be described with reference to the drawings. It will be understood that the aspects described in the drawings and the aspects of the present invention 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 or more aspects of the present invention can be combined with the features of a different one or more aspects of the other aspects 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

[0060]

Figure 1

Figure 2A

Figure 2B

Figure 3A

Figure 3B

Figure 4A

Figure 4B

Figure 4C

Figure 4D

Figure 5A

Figure 5B

Figure 6A

Figure 6B

Figure 7

Figure 8

Figure 9

DETAILED DESCRIPTION OF THE INVENTION

[0061] FIG. 8 shows a static computer simulation model according to an aspect of the present invention for simulating a doping depth profile 40 in a simulation model that reduces the total simulation volume S V by implementing an ion tunnel 70, where the ions 10 at both edges of the ion tunnel 70 are mirrored with respect to the center of the x-axis in the y-z plane.

[0062] The task of simulating the dopant depth profile 40 includes two subtasks. The first subtask is to calculate the energy and angular distribution after the ions 10 pass through the energy filter 25, and the second subtask is to determine the effect of the ions 10 acting on the substrate 26 with this calculated energy and angular distribution.

[0063] As seen in FIG. 8, the computer simulation model is simplified by using the ion tunnel 70. The method according to the present invention is provided, for example, to implement an energy filter ion implantation (EFII) process in a Monte Carlo environment.

[0064] As can be seen in Fig. 8, the narrower widths of the energy filter 25, the ion source 5, and the substrate 26 are defined as a total simulation S, rather than the overall filter width, for example, for the irradiation of a 6-inch (15.54 cm) wafer. v as a volume (see the dotted line in Fig. 8). To obtain correct simulation results, ions 10 that reach the (e.g., right) edge of the simulation region g are re-introduced on the left side. In this ion tunnel 70, these ions 10 thus move from one edge of the ion tunnel 70 to the opposite edge of the ion tunnel 70 in the y-z plane. As can be seen in Fig. 8, the distance (fs) 50 between the energy filter 25 and the substrate 26 must be selected such that the distance 50 meets the requirements described according to the application. These requirements are a desired degree of lateral homogenization, i.e., less than 10%, less than 5%, less than 3%, in most applications. However, there are applications where a dopant or implantation defect or depth profile of energy deposition that is location-dependent is desired, or a dopant or implantation defect or depth profile of energy deposition that is y-z position-dependent is desired. This can range from a complete structure transfer (in contact, see Fig. 6A) through any intermediate steps to complete homogenization, see Fig. 6B. For the EFII process, this distance 50 is the minimum distance leading to the desired degree of lateral homogenization of the energy distribution. The desired degree of lateral homogenization is that the average deviation of the profile parallel to the ion beam across the substrate surface, along the z or y direction, is less than 10% or 5% or 3%.

[0065] As can be seen in Fig. 8, due to the mirroring of the ions 10 in the ion tunnel 70 by the mirror 80, there is no loss of the characteristic energy spectrum of the energy filter 25 at the end of the ion tunnel 70 in the substrate 26 for the scattered ions 10 with large scattering angles outside the ion tunnel 70. Total simulation volume S V(Dotted line reference) results from the required dimensions of the simulation region g (dashed line reference) and from the dimensions of the energy filter 25 corresponding to at least half of the filter unit cell 30. The filter unit cell 30 is defined as a part of the energy filter 25 representing the entire energy and angular spectrum of a specific energy filter 25. A plurality of unit cells 30 are added to form the actual energy filter 25. The ion tunnel 70 must have at least the dimensions of the simulation region g, or at least the width of one (or half) of the filter unit cell 30. Furthermore, the ion tunnel 70 must also always be composed of an integer multiple of the minimum filter unit cell 30. The required dimensions of the simulation region g on the substrate 26 result from the simulated application, for example, in the case of implantation into the masking structure on the substrate 26. The dimensions of the masking structure will thus define the extent of the simulation region g.

[0066] In one example, implantation parameters of 12 MeV as the primary energy, a distance of 50 (fs) = 500 μm, dimensions of the common filter unit cell 30 of approximately 5 - 50 μm, and a simulation region g = 2 μm are used, and the total simulation volume S V The ratio of the simulation region g to S V ≈ 10 - 4%, where g is the simulation region and S V is the total simulation volume.

[0067] It will be understood that the present simulation is not limited to the triangular filter unit cell 30. Rather, pyramids, inverse pyramids, or more generally free-form structures or support structures can also be simulated using the computer-implemented method 200 of this document. It should be noted that more complex energy filters 25 can also be simulated using the method 200. For example, the filter unit cell 30 can be composed of a plurality of basic elements with different shapes, different material compositions, or different layer structures. It is also possible to tilt the energy filter 25 or mirror it about an axis perpendicular to the ion beam 10. Further, for example, the superposition of a plurality of simulations at different primary energies, ion types, or incident angles of the primary ions is also conceivable.

[0068] FIG. 9 shows a flowchart of the computer-implemented method 200 according to this description. The computer-implemented method 200 for the simulation of energy filter ion implantation (EFII) includes a step 201 of determining at least a part of the energy filter 25 as input parameters for a simulation model. At least a part of the energy filter 25 can be at least one filter unit cell 30, which is defined as a part of the energy filter 25 representing the entire energy and angular spectrum of a specific energy filter 25. A plurality of the filter unit cells 30 can be added to form the actual energy filter 25. Thus, the approximated geometric dimensions of at least a part of the energy filter 25 are determined in step 201. For example, the approximated geometric dimensions of the filter unit cell 30 of the energy filter 25 are implemented in step 201 in a simulation environment. However, the present invention is not limited thereto, and the approximated geometric dimensions of a plurality of filter unit cells 30 of the energy filter 25 can be implemented in step 201.

[0069] Furthermore, method 200 includes step 202 of determining a simulation region g within substrate 26 as a further input parameter for the simulation model. For example, the simulation region g within substrate 26 is a laid-out structure. Furthermore, method 200 includes step 203 of defining an ion tunnel 70 for receiving ions 10 from ion beam source 5. The defining step 203 includes the step of defining the ion tunnel 70 in the z-y plane for receiving ions 10 from the ion beam source 5. Accordingly, the width of the ion tunnel 70 is defined and the energy filter 25 and the ion tunnel 70 are implemented. The ion tunnel 70 is defined by application, for example, by a specific layout structure (i.e., the simulation region g) and the minimum range of the filter unit cell 30, and is adapted to emit at least the entire angular and energy spectrum.

[0070] The region of the ion tunnel 70 in the z-y plane must be decomposable into an integer multiple of the filter unit cell 30. Accordingly, method 200 includes step 204 of implementing at least a determined portion of the energy filter 25, the ion beam source 5, the determined simulation region g within substrate 26, and the defined ion tunnel 70 in a simulation environment. In the implementing step 204, the approximated geometric dimensions of the energy filter 25, the ion beam source 5, the substrate 26, the simulation region g, and the ion tunnel 70 are implemented in the simulation environment. The input parameters for the simulation model are thereby defined and implemented. After defining and implementing the input parameters for the simulation model, method 200 includes step 205 of determining a minimum distance 50 between the energy filter 25 and the substrate 26 to enable a desired degree of lateral homogenization of the energy distribution in the doping depth profile of the substrate 26. The minimum distance 50 between the energy filter 25 and the substrate 26 is determined by at least one of experiments, regression simulations (trying multiple distances), or mathematical calculations.

[0071] In the determination step 205 of the minimum distance 50, for example, the minimum filter unit cell 30, i.e., the minimum part of the energy filter 25 representing the complete energy and angle spectrum, is implemented in the simulator to simulate the angular distribution. In the determination step 205 of the minimum distance 50, in another example, a plurality of filter unit cells 30 are implemented in the simulator to simulate at the first estimated distance. Then the results are analyzed for the desired degree of lateral homogenization, and the distance is repeatedly changed until the homogenization criterion is met (for example, the average deviation between profiles is less than 5%). Alternatively, in the determination step 205 of the minimum distance 50, for example, data from experiments or a database can be used. The method 200 is not limited to the specific order / sequence of steps 201, 202, 203, 204, and 205.

[0072] The method 200 further includes a step 206 of determining the total simulation volume S V The determining step 206 includes determining the total simulation volume S by determining a narrower width of the energy filter (25), a narrower width of the ion beam source (5), and a narrower width of the substrate (26). Thus, the method 200 is executed such that first the minimum energy filter size (for example, the filter unit cell 30) is determined in step 201, and at the same time the simulation region g is determined in step 202. Thereafter, after the implementation of the input parameters, the size of the ion tunnel 70 is determined in step 204. Independently of steps 201, 202, 203, and 204, the minimum distance 50 is determined in step 205. Then, as a result of combining the minimum energy filter size, the simulation region g, the ion tunnel 70, and the minimum distance 50, a simulation of energy filter ion implantation (EFII) occurs. By determining the ion tunnel 70, the geometric dimensions of the filter model in the simulator are minimized, and thus the ratio of the total simulation volume S V in the substrate 26 to the simulation region g is optimized. V

[0073] The desired degree of lateral homogenization means that, along the z or y direction, i.e., the average deviation of the profile parallel to the ion beam 10 across the substrate surface of the substrate 26 is less than 10% or 5% or 3%. The advantage of the present invention results from the fact that the ratio of the total simulation volume S V to the simulation region g is improved, which enables a reduction in simulation events compared to the conventional model while maintaining the same event density in the simulation region g. This has a positive effect on the simulation time, hardware, resources, and energy consumption. The method 200 further includes a step 207 of performing a simulation.

[0074] The simulation environment can be, for example, a Monte Carlo simulation environment. The ion tunnel 70 is defined such that ions 10 reaching the first edge of the determined total simulation volume S V are reintroduced at the other edge of the determined total simulation volume S V The ion tunnel 70 is defined such that ions 10 from the first edge of the determined total simulation volume S V move in the y - z plane to the opposite edge of the determined total simulation volume S V The narrower width of the energy filter 25 is defined such that the narrower width of the energy filter 25 is at least half of the filter unit cell 30. The ion tunnel 70 is defined such that the ion tunnel 70 must have at least the same dimensions as the determined simulation region g. The required dimensions of the simulation region g of the method 200 within the substrate 26 are determined by the simulation task. The required dimensions of the simulation region g within the substrate 26 are determined, for example, by the dimensions of the masking structure 26a on the substrate 26.

[0075] Method 200 further includes implementing an approximated geometric dimension of an energy filter 25 having a triangular shape, a pyramid shape, an inverse pyramid shape, or a free form. The step of implementing the approximated geometric dimension of the energy filter includes using an analytical mathematical description of the energy filter and / or using a mesh description. Method 200 further includes implementing an approximated geometric dimension of a filter unit cell 30 composed of a plurality of elements having different shapes, different material compositions, or different layer structures. Method 200 further includes tilting the energy filter 25 with respect to the ion beam 10. Method 200 further includes mirroring the ion beam 10 about an axis perpendicular to the ion beam 10 by a mirror 80 within the ion tunnel 70.

[0076] Method 200 further includes overlaying a plurality of simulations at different primary energies, ion types, or incident angles of the primary ions.

Explanation of Reference Numerals

[0077] 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 26 Substrate 30 Filter unit cell 40 Doping depth profile 50 (fs) Distance 60 Composite filter 70 Ion tunnel 80 Mirror 100 Ion implantation system 200 Computer-implemented method

Claims

1. A computer-implemented method (200) for simulation of energy filter ion implantation (EFII), comprising: Determining (201) at least a portion of an energy filter (25); Determining (202) a simulation region (g) within a substrate (26); Defining (203) an ion tunnel (70) for receiving ions (10) directed from an ion beam source (5); Implementing (204) the determined at least a portion of the energy filter (25), the ion beam source (5), the determined simulation region (g) within the substrate (26), and the defined ion tunnel (70) in a simulation environment; 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 the energy distribution in the doping depth profile (40) of the implemented substrate (26); Step (206) of determining the total simulation volume (S Ｖ ), and a method (200) including the same.

2. The method (200) according to claim 1, wherein at least one filter unit cell (30) of the energy filter (25) is defined as the at least a portion of the energy filter (25).

3. The method (200) according to claim 1, wherein the simulation environment is a Monte Carlo simulation environment.

4. The ion tunnel (70) is such that the ion (10) that has reached a first edge of the defined total simulation volume (S Ｖ ) is reintroduced at the other edge of the defined total simulation volume (S Ｖ ), the method (200) according to claim 1.

5. The ion tunnel (70) is such that the ion (10) from a first edge of the defined total simulation volume (S Ｖ ) moves in the y-z plane to an edge on the opposite side of the defined total simulation volume (S Ｖ ), and the y-z plane is parallel to the surface of the substrate (26), the method (200) according to claim 1.

6. The method (200) according to claim 2, wherein the at least a portion of the energy filter (25) is defined such that the at least a portion of the energy filter (25) is at least half of the width of the filter unit cell (30), the width of the filter unit cell (30) being measured in a direction parallel to the y-z plane, and the y-z plane being parallel to the surface of the substrate (26).

7. The method (200) according to claim 1, wherein the ion tunnel (70) is defined to have at least the same dimensions as the determined simulation region (g).

8. The method (200) according to claim 2, wherein the ion tunnel (70) is defined to have dimensions at least as large as the filter unit cell (30) or a multiple of the filter unit cell (30).

9. The method (200) according to claim 1, wherein the required dimensions of the simulation region (g) in the substrate (26) are determined by a simulation task.

10. The method (200) according to claim 9, wherein the required dimensions of the simulation region (g) in the substrate (26) are determined by the dimensions of a masking structure (26a) on the substrate (26).

11. The method (200) according to claim 1, further comprising implementing approximated geometric dimensions of an energy filter (25) having a triangular, pyramidal, inverse pyramidal, or freeform shape.

12. The method (200) according to claim 1, further comprising implementing approximated geometric dimensions of a filter unit cell (30) composed of a plurality of basic elements having different shapes, different material compositions, or different layer structures.

13. The method (200) according to claim 1, further comprising tilting the energy filter (25).

14. The method (200) according to claim 1, further comprising mirroring the ion beam (10) about an axis perpendicular to the ion beam by a mirror (80) in the ion tunnel (70), wherein the ion beam (10) is mirrored in a direction parallel to the y - z plane, and the y - z plane is parallel to the surface of the substrate (26).

15. The method (200) according to claim 1, further comprising superimposing a plurality of simulations at different primary energies, ion types, or incident angles of primary ions.

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