METHOD FOR CRYSTAL DRAWING A DOTED MONOCRYSTALLINE CRYSTAL FROM SILICON

Description

[0001] The invention relates to a method for growing a doped single crystal from silicon.

[0002] Crystal growth is an important preliminary step in the production of semiconductor devices. Semiconductor crystal growth methods have been improved to obtain single-crystal semiconductor blocks that can have, for example, a diameter of 200 mm to 300 mm and a length of more than two meters.

[0003] Components for controlling large currents (power components) require highly doped silicon crystals, which are further processed into the corresponding components.

[0004] One of the challenges in growing heavily doped silicon using the Czochralski method is to increase the maximum doping concentration or reduce the minimum resistance without reducing the yield of usable crystals. State of the art

[0005] DE 10 2019 210 254 A1 describes a method for growing a single crystal from silicon which has a specific resistance of no 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 probability of the occurrence of dislocations.

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

[0007] DE 10 2021 206 550 A1 describes a method for growing a single crystal with a very low resistance using a magnetic field.

[0008] Y. Mukaiyama et al., J. Cryst. Growth, 619 (2023), 127333, discloses a three-dimensional numerical simulation to predict constitutional undercooling during the growth of heavily B-doped Czochralski-Si single crystals taking into account B-transport in the melt and the segregation effect.

[0009] Y. Mukaiyama et al., J. Cryst. Growth, 532 (2020), 125433, disclose discontinuous simulations of the dynamics of intrinsic point defects considering the effects of thermal stress and dopant concentration in a large diameter silicon crystal grown using the Czochralski method.

[0010] The phenomenon of constitutional undercooling is not initially problematic at a relatively low doping level, which is generally used for growing semiconductor crystals.

[0011] However, during crystal growth from a heavily doped melt—where the dopants have a small equilibrium segregation coefficient, much less than one—constitutional undercooling can occur at the melt-crystal interface. This causes the rod to become displaced and unusable for the device manufacturing process.

[0012] A crystal-growing process can be modified in many different ways to produce crystals with moderate dopant levels. For example, crystal rotation, crucible rotation, magnetic field position and strength, and distances between various components can be adjusted, to name just a few.

[0013] If the dopant level is to be increased, i.e., the resistance in the crystal is to be further reduced, it turns out that many processes that can be easily produced with high resistance result in defects, i.e., they are rejects.

[0014] What these sections of the prior art have in common is that they do not present a targeted method for optimizing processes in this regard. Many expensive experiments would have to be undertaken, in which it is not clear a priori whether, firstly, the corresponding crystal meets the requirements, and secondly, whether the proposed process will produce suitable crystals with sufficient stability.

[0015] The object of this invention is therefore to provide a method that makes it possible to modify crystal growing processes in such a way that they have a high dopant level and at the same time meet the quality requirements while simultaneously reducing experimental effort.

[0016] This problem is solved by the methods described in the claims. Brief description of the figures

[0017] Figure 1 shows the factor f CSas a function of the specific resistance for the dopants phosphorus (P), arsenic (As) and antimony (Sb). Figure 2 shows the sum of the simulated parameter CS and an offset constant C Offset For example process A, the graph shows the process as a function of resistance (dashed curve). The limiting resistance at which the crystal can just barely be pulled is determined by varying the resistance until the curve is formed by the sum of the simulated parameters. CS at the triple point of the simulated crystal and the offset constant C Offset The value becomes zero. The dark-colored bar indicates the resistance range at which crystal pulling is futile. Realistically, there is a small transition range (light hatching) where crystal pulling is possible with a high risk, but is not recommended for economic reasons. Figure 3 shows the sum of the simulated parameter CS at the triple point of the respective crystal and an offset constant C Offset for four example processes (A "dashed" B "full", C "slash dot", D "slash-dot dot") each represented as a function of resistance.

[0018] The respective limiting resistances, at which a crystal can just barely be pulled, were symbolized by the downward-pointing arrows on the abscissa axis. Detailed description of the invention

[0019] As mentioned previously, the phenomenon of constitutional undercooling at the relatively low doping levels generally used for growing semiconductor crystals is not initially problematic. Only an increase in the desired dopant concentration can lead to constitutional undercooling and thus to a high probability of dislocations and ultimately to the total failure of the respective crystal.

[0020] The inventors have, among other things, successfully attempted to use a significantly modified computer simulation method to narrow down and solve the aforementioned problem.

[0021] The physical effect of constitutional undercooling is described, for example, in the dissertation by L. Stockmeier (ISBN 978-3-8396-1345-0, "Heavily n-type doped silicon and the dislocation formation during its growth by the Czochralski method").

[0022] The underlying mathematical model for the numerical modeling of this problem, together with suitable software, is described in the necessary details in Mukaiyama et al. [Y. Mukaiyama, V. Artemyev, K. Sueoka, J. Crystal Growth, 597 (2022) 126844, https: / / doi.org / 10.1016 / j.jcrysgro.2022.126844].

[0023] The inventors recognized that significant adjustments were necessary to achieve substantial improvements in yield. These significant adjustments are explained below.

[0024] A value C.S., which is calculated at the interface between the melt and the crystal, is defined as: CS = ∂ T ∂ n − f CS ∂ c ∂ n , where ∂ T ∂ n the partial derivative of temperature and ∂ c ∂ n represents the partial derivative of the concentration of the dopant along the normal on the interface between the crystal and the melt in the melt.

[0025] The factor f CS represents a function of the specific resistance and material properties of the dopant and can be determined using material data constants and the "density / resistance" diagram of the dopant ( SEMI standard MF723-0307, ​​2012 Practice for conversion between resistivity and dopant or carrier density for boron-doped, phosphorus-doped, and arsenic-doped silicon).

[0026] In Figure 1 is this factor f CS The specific resistance is represented as a function of different dopants such as phosphorus, arsenic, or antimony. It is easily possible to determine this factor for other dopants as well, and therefore the inventive process is not limited to these dopants.

[0027] The numerical differences in f CS Differences in the ionized fraction of the dopant and its segregation coefficients can be attributed to variations in the material properties of phosphorus (P), arsenic (As), and Sb as dopant materials.

[0028] The modified boundary conditions for heat transport and dopant transport for modeling are explained below.

[0029] For the 3D simulations performed, the temperature at the interface between the crystal and the melt was assumed to be constant.

[0030] The inventors have recognized that the boundary conditions for concentration (demixing boundary conditions) from Mukaiyama et al. [Y. Mukaiyama, V. Artemyev, K. Sueoka, J. Crystal Growth, 597 (2022) 126844,]] are valid for a positive crystallization rate. − ρ melt D melt ∂ c ∂ n = ρ crys V crys c melt 1 − k , c crys = kc melt

[0031] The inventors have further recognized that in the case of a negative crystallization rate (=melting), the following equation is preferably used as a replacement: − ρ melt D melt ∂ c ∂ n = ρ crys V crys c melt − c crys

[0032] Here, c is the mass concentration. ρ melt the density of the melt, D melts the diffusion coefficient of the dopant in the melt, c crythe concentration of dopants in the crystal and n the normal to the interface at the melting or growth front.

[0033] The parameter c cry is a value known from current calculations when the crystallization rate is positive and it is a function of the crystal length.

[0034] In the present invention, its value was approximated by the average dopant concentration in the crystal. It has been found that the exact values ​​of c cry They are not necessary for the calculation. Furthermore, they are difficult to implement in the software.

[0035] An experimental shape of the interface between the melt and the crystal can be determined by cutting a rectangular slice (a so-called "board") from a sample of the crystal using two longitudinal sections made along its center. This board can then be examined for resistance variations. The added dopant integrates irregularly into the crystal. Preferably, the dopant contains boron or phosphorus. This leads to a locally inhomogeneous resistance distribution of the silicon, which is called "striation." Although great efforts are made to avoid striation to prevent negative effects during the device manufacturing process, striation is nevertheless always measurable on the doped rod.Since the dopant is incorporated from the melt into the crystal along the melt / crystal interface, the original shape of the interface between crystal and melt can be determined in the form of growth lines by analyzing the measured resistance distribution.

[0036] For the simulation, unsteady 3D simulations are necessary, for which there are two ways to carry them out: Either the shape of the interface between crystal and melt is adjusted by adapting the Stefan boundary condition so that it corresponds to reality, or the shape of the interface is fixed, accepting that the Stefan condition is not necessarily fulfilled.

[0037] Both approaches can be unsuitable for calculations under certain conditions. In the first case, the interface may deviate from the experimental one, which affects the calculations of the flow and the species. In the second case, the calculated crystallization rate would be incorrect, and consequently, so would the species distribution at the interface, since it follows the demixing boundary conditions.

[0038] To avoid this difficulty, the inventors realized that the calculations must be performed using the calculated interface, and artificial heat sources must be introduced simultaneously to obtain both the prescribed interface shape and the correct crystallization rate.

[0039] This method is also advantageous because it allows fluctuations in the crystallization rate and the dopant species around the correct averaged values.

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

[0041] Four cases were selected as examples for the calculations.

[0042] The first two cases originate from two different processes for 200 mm crystal diameters: one for arsenic (Process A) and the other for red phosphorus (Process B). The two subsequent processes are both arsenic-doped and have a crystal diameter of 300 mm; these are referred to as Process C and Process D. The difference between Processes C and D lies in the use of different crystal-pulling devices and pulling speeds, along with different crystal and crucible rotations.

[0043] The inventors determined that the statistically averaged lowest possible resistances for the 200 mm processes are 0.9 x 10⁻³ Ω cm for process A and 1.7 x 10⁻³ Ω cm for process B. For the 300 mm processes, these resistances are 1.75 x 10⁻³ Ω cm (process C) and 2.1 x 10⁻³ Ω cm (process D).

[0044] All these experimental values ​​apply to a specific position in the crystal, and the calculation cases were selected according to this one corresponding position.

[0045] It should be noted that the resistance values ​​determined represent average values ​​from many real experiments and that the results of each experiment vary from process to process, and some experiments may be unsuccessful, e.g., due to dislocations.

[0046] The specific causal relationship between the occurrence of dislocations and the level of dopant concentration is not yet known.

[0047] Nevertheless, the inventive process offers a means to at least prevent the problem.

[0048] The inventors assume that CS could be related to these experimental results.

[0049] The parameter CS defined above can be calculated using the tiller criterion as follows: CS V = G L V − 1 − k ⋅ C 0 ⋅ − m l k ⋅ D L where C 0 - Concentration in the melt, k - Segregation coefficient, DL - Diffusion coefficient in the melt, V - Crystallization rate, GL - Temperature gradient in the melt and ml - slope of the liquidus line is.

[0050] The parameter GL This can be taken, for example, from the corresponding 2D simulations.

[0051] According to the theory, whenever the condition CS < 0 is met, constitutional hypocooling would occur and the correspondingly drawn rod would become unusable.

[0052] However, this turned out to be incorrect. This means that a simple analysis using the well-known "Tiller criterion" is not possible and therefore unusable.

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

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

[0055] In the simulations, it is preferred that the distance of the nearest control volume to the interface between the crystal and the melt is a maximum of 0.125 mm.

[0056] The complete numerical grids in the aforementioned examples varied from approximately 3 million control volumes to 3.8 million control volumes.

[0057] The 3D simulations yield the instantaneous distribution of CS values ​​at each position on the interface between the crystal and the melt. These points are located on the crystal, which rotates above the melt.

[0058] For further calculations, CS values ​​calculated at points equidistant from the center of the crystal's interface surface were averaged.

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

[0060] When examining the determined CS values ​​at different radii, the inventors noticed that the smaller values ​​seemed to occur more frequently in the region of the triple point, while in the center of the crystal, the CS values ​​were either not negative or significantly less frequent. This would suggest that the constitutional undercooling originates at the triple point.

[0061] However, experimental findings by Mukaiyama et al. [Y. Mukaiyama, V. Artemyev, K. Sueoka, J. Crystal Growth, 597 (2022) 126844.] show, in contrast, that the consequences of constitutional undercooling tend to begin in the center of the crystal.

[0062] Despite this apparent contradiction, the inventors continued to apply their results and arrived at a method that uses simulation to predict the possible suitability of a crystal-pulling process for low resistance.

[0063] This method makes it possible to modify crystal growing parameters so that crystals with lower resistances can be grown without loss.

[0064] The inventive process for growing a monocrystalline crystal from a melt and a dopant according to the Czochralski process comprises the following steps: (a) performing a time-dependent computer simulation of a predefined crystal-pulling process with a predefined dopant concentration C in the melt, with the aim of determining a temperature gradient ∂ for each time step t. T / ∂ n , and a gradient of the dopant ∂ c / ∂ n to obtain, (b) determining both gradients at the interface between crystal and melt in the direction of the normal of the interface to the melt, (c) determining a maximum dopant concentration Cmax in the melt, and (c) growing a single crystal with a dopant concentration less than the determined maximum dopant concentration Cmax.

[0065] The inventive method also includes the calculation of a quantity CS, which is determined for each time step t by the following formula: CS = ∂ T / ∂ n − f CS ∂ c / ∂ n where the parameter f CS is determined by the product of the average concentration 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.

[0066] A time average CS is then calculated from the obtained CS values, whereby only those CS values ​​less than zero contribute. The time average can be calculated using the formula CS ¯ = 1 T 1 − T 0 ∫ T 0 T 1 CS τ dτ , ∀ CS τ < 0 , where T 0 and T 1 represent the absolute time start and end points.

[0067] Averaging over 30 minutes of physical time or more is preferred.

[0068] The mean CS value is therefore a function of the radius and the concentration of the dopant C in the melt. Furthermore, it is now independent of time.

[0069] For the subsequent procedure, the mean value CS at a radial position of the crystal is selected. Preferably, the CS at the triple point of the crystal is used, i.e., at the nominal radius of the crystal.

[0070] Determining a maximum dopant concentration Cmax is achieved by adjusting the dopant concentration Cmax until the magnitude of CS is zero, preferably until the magnitude of CSmax is zero. C Offset is equal to zero, where the constant C Offset preferably determined experimentally. Determining the constant C Offset

[0071] Will the constant C Offset By pre-setting to zero, a lower limit for the dopant C max is obtained, below which it is always possible to grow a crystal without yield loss.

[0072] In some cases, however, this lower limit may appear too conservative, meaning that crystal growth with a dopant concentration is still possible above this limit.

[0073] For such cases, a C Offset preferably determined using experimental data as follows.

[0074] For a crystal-growing process, an empirical limit is determined, for example, by growing one or more crystals while successively increasing the dopant concentration until the crystal reproducibly exhibits dislocations. This empirical limit determined in this way is used to define the constant C Offset to obtain.

[0075] This constant obtained in this way C OffsetThis method can now be used, for example, to compare many different crystal-growing processes and select the one with the potential to avoid dopant-induced dislocations. The advantage of this method is that no further expensive experiments are required.

[0076] Particularly preferred for determining the constant are C Offset Several different processes of a process class were tested, with an averaged constant for each process class. C Offset is determined by arithmetically averaging the individual values.

[0077] The inventors recognized the potential benefits of defining process classes by grouping processes with similar characteristics into a single class. These characteristics include, for example, the nominal diameter of the crystal being pulled or the use of a magnetic field during crystal pulling. A particularly preferred method is to define a process class based on crystals with the same nominal diameter.

[0078] Figure 2 shows, as an example, the sum of the simulated parameter CS and an offset constant C Offset for an example process A The graph is shown as a function of resistance (dashed curve). The limiting resistance at which the crystal can just barely be pulled is determined by varying the resistance until the curve is formed by the sum of the simulated parameters. CS at the triple point of the simulated crystal and the offset constant C Offset It will be zero.

[0079] The dark-shaded bar indicates the resistance range at which crystal pulling is futile. Realistically, there is a small transition zone (light hatching) where crystal pulling is possible but risky, and therefore not recommended for economic reasons.

[0080] Figure 3 shows the sum of the simulated parameter CS at the triple point of the respective crystal and an offset constant C Offset for four example processes (A "dashed" B "full", C "slash dot", D "slash-dot dot") each represented as a function of resistance.

[0081] The respective limiting resistances, at which a crystal can just barely be pulled, were symbolized by the downward-pointing arrows on the abscissa axis.

Claims

1. A method of crystal pulling of a monocrystalline crystal from a melt composed of silicon and a dopant according to Czochralski, comprising the following steps in the sequence given: (a) performing a time-dependent computer simulation of a predefined crystal pulling process with a predefined dopant concentration C in the melt, with the aim of obtaining a temperature gradient ∂T / ∂n, and a gradient of the dopant ∂c / ∂n for each time increment t, where the two gradients are ascertained at the interface between crystal and melt in the normal direction of the interface to the melt, (b) ascertaining a maximum dopant concentration Cmax in the melt and (c) pulling a single crystal with a dopant concentration less than the ascertained maximum dopant concentration Cmax wherein, a parameter CS is calculated for each time increment t, which is determined via the formula CS = ∂ T / ∂ n − f CS ∂ c / ∂ n , where the parameter fCS is determined by the product of the average concentration of the dopant C in the melt, the density of the silicon melt, Avogadro's constant, the molar mass of silicon and the slope of the liquidus line, and then an average CS of the values obtained for the parameter CS is formed, where a contribution is made only by those values having a CS value of less than zero, and a maximum dopant concentration Cmax is ascertained by fitting the above-defined dopant concentration C to the magnitude of CS = zero.

2. The process as claimed in claim 1, wherein the parameter CS is ascertained at the triple point of the crystal.

3. The process as claimed in claim 1 or 2, wherein a maximum dopant concentration Cmax is ascertained by the fitting of the above-defined dopant concentration C until the magnitude of CS - COffset = zero, where, COffset is ascertained empirically by pulling one or more crystals, while gradually increasing the dopant concentration until the crystal reproducibly has dislocations.