Method for pulling doped silicon single crystal

Abstract

The invention relates to a method for pulling a single crystal from a melt consisting of silicon and a dopant according to the Czochralski method, comprising the following steps in a given sequence: a) performing a time-dependent computer simulation of a predetermined crystal pulling process having a predetermined dopant concentration (C) in the melt, with the aim of obtaining a temperature gradient and a dopant gradient for each time increment t, wherein the two gradients are determined at the interface between the crystal and the melt in the normal direction of the melt interface, b) determining a maximum dopant concentration (Cmax) in the melt, and c) pulling up a single crystal having a dopant concentration less than the determined maximum dopant concentration (Cmax), characterized in that a parameter (CS) is calculated for each time increment t, which is determined by formula, wherein the parameter fCS is determined from the product of the average concentration (C) of the dopant in the melt, the density of the silicon melt, the Avgamde constant, the molar mass of the silicon and the slope of the liquidus, and then generating an average value of the values obtained for the parameter (CS) wherein only those values having the (CS) value less than zero are included, and determining the maximum dopant concentration (Cmax) by adapting the above defined dopant concentration (C) until the magnitude equals zero.

Description

TECHNICAL FIELD

[0001] The present invention relates to a method of pulling a doped silicon single crystal.

[0002] The growth of crystals is an important prerequisite for the production of semiconductor components. Semiconductor crystal growth methods have been improved in order to obtain single-crystalline semiconductor blocks which can have diameters of, for example, 200 mm to 300 mm and lengths of more than two meters.

[0003] Components for controlling large currents (power components) need to be further processed to provide the high-doped silicon crystals of the respective components.

[0004] One of the challenges in growing high-doped silicon by the Czochralski method (or called the pull-up method) is to increase the maximum dopant concentration or to reduce the minimum resistivity without reducing the yield of usable crystals. BACKGROUND

[0005] DE 10 2019 210 254 A1 describes a method of pulling a silicon single crystal having a specific resistivity of not more than 20 x 10 -3 ohm cm, wherein the first phase of the crystal growth process is optimized with the aim of reducing the likelihood of dislocations occurring.

[0006] EP 3 864 197 A1 relates to a method of controlling the concentration of a dopant in a melt with the aim of reducing the occurrence of dislocations.

[0007] DE 10 2021 206 550 A1 describes a method of pulling single crystals with very low resistivity using a magnetic field.

[0008] The phenomenon of constitutional supercooling is not a problem at first for the relatively low doping levels that are usually used for growing semiconductor crystals.

[0009] However, during the growth of crystals from a highly doped melt, in which the dopant has a small equilibrium segregation coefficient far less than 1, constitutional supercooling can occur in the melt at the interface between the melt and the crystal. This will have the effect that the rod is displaced and is no longer available for the component (manufacturing) process.

[0010] The method of pulling a crystal can be modified in a variety of ways in order to produce crystals with moderate dopant levels. For example, crystal rotation, crucible rotation, magnetic field position and strength, distance between different mounting components, to name a few.

[0011] If the dopant level is increased, i.e. the resistivity in the crystal is further reduced, it is found that many processes that can be implemented without difficulty at high resistivity will be affected by dislocations, i.e. produce waste.

[0012] The commonality of the cited prior art is that they do not show a specified method that can optimize the process for this effect. Many expensive experiments have to be carried out, where it is not clear from the outset whether the respective crystal meets the requirements and secondly whether the proposed process also provides a suitable crystal with sufficient stability. SUMMARY

[0013] It is therefore an object of the present application to provide a method that makes it possible to modify the crystal pulling (or crystal growth) process such that it has a high dopant level and at the same time meets the quality requirements, while at the same time reducing the complexity of the experiments.

[0014] This object is achieved by the method described in the claims. BRIEF DESCRIPTION OF DRAWINGS

[0015] Figure 1 The factor is shown as a function of the specific resistivity of the dopants phosphorus (P), arsenic (As) and antimony (Sb).

[0016] Figure 2 The simulated parameters at the triple point of the respective crystal of the example process A are shown as a sum of the simulated parameters as a function of the resistivity (dashed curve). The limit resistivity at which the crystal is still just pullable is determined by changing the resistivity until the curve of the simulated parameters as a sum of the offset constant becomes zero.

[0017] The dark bars drawn are intended to show the range of resistivities for which there is no prospect of successful crystal pulling. There is in fact a small transition region (with light hatching) in which the crystal pulling can be carried out at high risk, but is not advisable for economic reasons.

[0018] Figure 3 The simulated parameters as a sum of the offset constant are shown for each of the four example processes (A "dashed", B "solid", C "dot-dashed", D "double dot-dashed") at the triple point of the respective crystal, where each is shown as a function of the resistivity.

[0019] The respective limit resistivity at which the crystal is still just pullable is marked by an arrow pointing downwards on the abscissa. DETAILED DESCRIPTION

[0020] As already mentioned, the phenomenon of constitutional supercooling is not a problem at first at the relatively low doping levels that are usually used for growing semiconductor crystals. Only when the desired dopant concentration is increased can constitutional supercooling and thus a high probability of dislocations and thus a complete failure of the respective crystal result.

[0021] Among other efforts, the inventors have successfully tried to limit and solve the problem using a significantly modified computer simulation method.

[0022] The physical effect of component undercooling is described, for example, in the thesis of L. Stockmeier (ISBN 978-3-8396-1345-0, “Heavy n-type doped silicon and dislocation formation during its growth by the Czochralski method”).

[0023] The underlying mathematical model of the numerical modeling of the problem and the necessary details of the appropriate software are described in the work of Mukaiyama et al. [Mukaiyama, V. Artemyel, K. Sueoka, J. Crystal Growth, 597 (2022) 126844, https: / / doi.org / 10.1016 / j.jcrysgro.2022. 126844].

[0024] The inventors have recognized that significant modifications (or adjustments) are needed to achieve a significant increase in yield. These significant modifications are set out below.

[0025] The value CS calculated at the interface between the melt and the crystal is defined here as: ， where denotes the partial derivative of the temperature, and denotes the partial derivative of the dopant concentration along the normal to the interface between the crystal and the melt.

[0026] The factor is a function of the specific resistivity of the dopant and material properties and can be determined with the aid of material data constants of the dopant and the “density / resistivity” chart (SEMI Standard MF723-0307, 2012, Practice for Conversion Between Resistivity and Doping or Carrier Density for Boron-Doped, Phosphorus-Doped, and Arsenic-Doped Silicon).

[0027] Figure 1 This factor is shown as a function of the specific resistivity of different dopants such as phosphorus, arsenic or antimony. The factor can also be easily determined for other dopants, and thus the method of the invention is not limited to these dopants.

[0028] The numerical differences of for different dopants can be attributed to differences in the ionization fraction and the segregation coefficient of the dopant. Material properties can explain the differences of phosphorus (P), arsenic (As) and Sb as dopants.

[0029] The following sets out modified boundary conditions for modeling the transport of heat and dopants.

[0030] For the 3D simulation carried out, it was assumed that the temperature at the interface between the crystal and the melt is constant.

[0031] The inventors found that the concentration boundary condition (segregation boundary condition) from Mukaiyama et al. [Mukaiyama, V. Artemyel, K. Sueoka, J. Crystal Growth, 597 (2022) 126844] is valid for positive crystallization rates.

[0032] The inventors also found that in the case of negative crystallization rates (= melting), this equation should preferably be replaced by the following equation: In this equation, c is the mass concentration, is the density of the melt, is the diffusion coefficient of the dopant in the melt, is the concentration of the dopant in the crystal, and n is the normal to the interface at the melt or growth front.

[0033] The parameters are known from the current calculation when the crystallization rate is positive and are a function of the crystal length.

[0034] In the present invention, their values are obtained approximately from the average dopant concentration in the crystal. It has been found that the exact values of are not required for the calculation. Furthermore, it is difficult to implement them in software.

[0035] The experimental form of the interface between the melt and the crystal can be determined by cutting a rectangular piece (so-called platelet) from the crystal block to be examined by means of two longitudinal sections along the center of the crystal block. This platelet can then be examined for changes in the resistivity. The added dopant is incorporated into the crystal in a random (or irregular) manner. The dopant preferably comprises boron or phosphorus. This leads to a locally inhomogeneous resistivity distribution of the silicon, the so-called "striations". Despite the great efforts taken to avoid striations in order to be subjected to no adverse effects in the component process, striations in the doping rod are always measurable. Since the dopant is incorporated from the melt into the crystal along the melt / crystal interface, the original shape of the interface between the crystal and the melt in the form of growth striations can be determined by means of an analysis of the measured resistivity distribution.

[0036] The simulation requires an unstable 3D simulation, and there are two means of implementing them: Alternatively, the shape of the interface between the crystal and the melt can be adjusted by adapting the Stefan boundary conditions to make them correspond to reality, or the shape of the interface can be fixed, thus accepting situations where the Stefan conditions are not necessarily satisfied.

[0037] Both methods may not be suitable for calculations under specific conditions. In the first case, the interface may differ from the experimental interface, affecting the calculation of flow and (substance) species. In the second case, the calculated crystallization rate will be incorrect, and therefore the species distribution at the interface will also be incorrect, as it follows segregation boundary conditions.

[0038] To avoid this difficulty, the inventors have recognized the need to utilize the interface of computation and simultaneously introduce an artificial heat source in order to obtain both a defined interface shape and the correct crystallization rate.

[0039] Therefore, this method is also advantageous because it allows for fluctuations in crystallization rate and dopant type around the correct average value.

[0040] This method can be implemented, for example, by using a modified version of the CGSim software from STR (https: / / str-soft.com).

[0041] As an example of the calculation, four cases have been selected.

[0042] The first two cases come from two different processes with crystal diameters of 200 mm for arsenic (Process A) and red phosphorus (Process B). The other two processes, both doped with arsenic and having crystal diameters of 300 mm, are referred to below as Process C and Process D. The difference between Process C and Process D lies in the use of different crystal pulling apparatus and different pulling speeds, as well as different crystal and crucible rotations.

[0043] The inventors have discovered that, for a 200 mm process, the statistically averaged lowest possible resistivity for process A is 0.9 × 10⁻⁶. -3 ohm cm, and for process B it is 1.7×10 -3 ohm cm. For a 300 mm process, these resistivities are 1.75 × 10⁻⁶. -3 ohm cm (process C) and 2.1×10 -3 ohm cm (process D).

[0044] All these experimental values ​​apply to specific locations within the crystal, and the calculations have been selected based on the corresponding location.

[0045] It should be noted that the determined resistivity values ​​are averages from many real experiments, and the results of each experiment are subject to different deviations (or dispersions) between different processes, and some experiments are unsuccessful, for example, due to dislocations.

[0046] To date, the specific causal relationship between dislocation occurrence and dopant concentration levels is unknown.

[0047] However, the method of the present invention provides at least a means to avoid this problem.

[0048] The inventors hypothesized that CS might be related to these experimental results.

[0049] The parameter CS defined above can be calculated using the Tiller standard as follows: in - Concentration in the melt, k - Segregation coefficient - Diffusion coefficient in the melt, V - Crystallization rate -Temperature gradient in the melt and m l - The slope of the liquidus line.

[0050] Here, parameters can be adopted, for example, from the corresponding 2D simulation. .

[0051] According to the theory, whenever the condition CS<0 is met, component supercooling always occurs, and the corresponding pulled rod will become unusable.

[0052] However, this was found to be the case. In other words, simple analysis using the known Thiele criteria is not feasible and therefore unavailable.

[0053] The inventors concluded that further measures were needed.

[0054] The inventors recognized that the numerical grids used in all 3D simulations must adequately resolve the concentration interface.

[0055] In the simulation, preferably, the closest control volume is no more than 0.125 mm away from the interface between the crystal and the melt.

[0056] In the example, the complete numerical grid varies from approximately 3 million control volumes to 3.8 million control volumes.

[0057] The results obtained from the 3D simulation are the current distribution of CS values ​​at each location on the interface between the crystal and the melt. These points are located on the rotating crystal above the melt.

[0058] For further calculations, the CS values ​​calculated at points equidistant from the center of the interface region with the crystal are averaged.

[0059] This yields a radial distribution of CS values ​​as a function of time.

[0060] In their analysis of the CS values ​​determined at different radii, the inventors noted that smaller values ​​were clearly more likely to occur in the triple point region, and that the CS values ​​in the middle of the crystal were relatively less likely to be in the negative region, or significantly less frequent. This would imply that the component undercooling has a starting point at the triple point.

[0061] However, experiments by Mukaiyama et al. [Mukaiyama, V. Artemyel, K. Sueoka, J. Crystal Growth, 597 (2022) 126844] showed by comparison that the consequence of supercooling of the components is that it is more likely to begin at the center of the crystal.

[0062] Despite this apparent discrepancy, the inventors continued to apply their results and arrived at a method that uses simulation to predict the potential applicability of crystal pulling processes (or procedures) for low resistivity.

[0063] This method allows for the modification of crystal pulling parameters, enabling the lossless pulling of crystals with relatively low resistivity.

[0064] The method of pulling single crystals from melt and dopant using the Chuklaski method of the present invention includes the following steps: (a) Perform a time-dependent computer simulation of a predetermined crystal pulling process (or procedure) in the melt with a predetermined dopant concentration C, with the aim of obtaining the temperature gradient for each time increment t. and dopant gradient The two gradients mentioned above are determined at the interface between the crystal and the melt along the normal direction of the melt interface. (b) Determine the maximum dopant concentration C in the melt. max ,as well as (c) The concentration of the pull-out dopant is less than the determined maximum dopant concentration C. max Single crystal.

[0065] The method of the present invention also includes a calculation parameter CS for each time increment t, which is determined by the following formula: Where parameters It is determined by the product of the average concentration of dopant in the melt, the density of the silicon melt, Avogadro's constant, the molar mass of silicon, and the slope of the liquidus line.

[0066] Subsequently, a time-based average is generated from the obtained CS values. Only CS values ​​less than zero are included. The time-based average can be calculated using the following formula: T0 and T1 constitute the absolute start time and end point.

[0067] It is preferable to use an average value based on 30 minutes of physical time or a longer period.

[0068] average value Therefore, it is a function of the radius and the dopant concentration C in the melt. Furthermore, it is now independent of time.

[0069] To continue this method, an average value is selected at a radial location in the crystal. The preferred method here is to use the crystal at its triple point. That is, at the nominal radius of the crystal .

[0070] By adapting (or adjusting) the dopant concentration C until The value of the quantity is zero, preferably until... The value of C is zero to determine the maximum dopant concentration. max , where constant Preferably, it is determined through experiments.

[0071] constant The determination If constant If the value is predetermined to be zero, then dopant C is obtained. max The lower limit is below which crystals can be pulled without loss of yield under any circumstances.

[0072] In some cases, the lower limit may seem too conservative; however, this means that crystal pulling is possible even with dopant concentrations higher than that limit.

[0073] In such cases, Preferably, it is determined using the following experimental data.

[0074] For example, an empirical limit for the crystal pulling process is determined by pulling one or more crystals and gradually increasing the dopant concentration until the crystal reproducibly exhibits dislocations. This empirical limit, determined in this way, is used to obtain constants. .

[0075] The constant obtained from this can then be used. This allows for comparison of many different crystal pulling processes and selection of a process with the potential to avoid generating any dopant-related dislocations. The advantage of this method is that it eliminates the need for any further, costly experiments.

[0076] More preferably, by testing multiple different processes within a process category, and by determining the average constant for each process category. (where the individual values ​​are arithmetically averaged) to determine the constant. .

[0077] The inventors have recognized that process categories can be defined by combining processes with the same process characteristics to give a process category. These characteristics are, for example, the nominal diameter of the crystal to be pulled or the use of a magnetic field in crystal pulling. Process categories are more preferably defined by processes having the same nominal crystal diameter.

[0078] Figure 2 The simulation parameters of example process A are shown. With offset constant An example of the summation is shown as a function of resistivity (dashed curve). The resistivity is varied until the simulation parameters at the triple point of the simulated crystal are obtained. Offset constant The curve of the sum becomes zero to determine the limiting resistivity at which the crystal is still just pullable.

[0079] The dark bars are intended to indicate resistivity ranges where there is no prospect of successful crystal pulling.

[0080] The dark bars are intended to show resistivity ranges where successful crystal pulling is not feasible. There are actually small transition regions (shown by light shading) where crystal pulling could be performed at a high risk, but is not advisable for economic reasons.

[0081] Figure 3 The simulated parameters at the triple point of the corresponding crystals for four example processes (A "dashed line", B "solid line", C "dotted line", D "double-dotted line") are shown. With offset constant The sum of these is shown as a function of resistivity.

[0082] The corresponding limiting resistivity at which the crystal is still just about to be pulled is marked by a downward-pointing arrow on the horizontal axis.

Claims

1. A method of pulling a single crystal crystal from a melt consisting of silicon and a dopant according to the Czochralski method, comprising the following steps in a given order: (a) performing a time-dependent computer simulation of a predetermined crystal pulling process having a predetermined dopant concentration C in the melt, with the aim of obtaining for each time increment t a temperature gradient and a dopant gradient wherein the two gradients are determined at the interface between the crystal and the melt in the direction of the normal to the melt interface, (b) determining the maximum dopant concentration C in the melt max and (c) pulling the single crystal with a dopant concentration less than the determined maximum dopant concentration C max of the single crystal, wherein the parameter CS is calculated for each time increment t via the formula is determined, wherein the parameter f CS is determined by the product of the average concentration C of the dopant in the melt, the density of the silicon melt, the Avogadro constant, the molar mass of silicon and the slope of the liquidus line, An average of the values obtained for the parameter CS is then generated where only those values with a CS value less than zero are counted, and by adapting the dopant concentration C defined above to determining the maximum dopant concentration C max .

2. The method of claim 1, wherein determining said parameter at the triple point of the crystal .

3. The method of claim 1 or 2, wherein By adapting the dopant concentration C defined above until the magnitude = zero to determine the maximum dopant concentration C max where determined empirically by pulling one or more crystals and simultaneously gradually increasing the dopant concentration until the crystal reproducibly has dislocations.

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