Classifications

• • C—CHEMISTRY; METALLURGY
  • C30—CRYSTAL GROWTH
  • C30B—SINGLE-CRYSTAL GROWTH; UNIDIRECTIONAL SOLIDIFICATION OF EUTECTIC MATERIAL OR UNIDIRECTIONAL DEMIXING OF EUTECTOID MATERIAL; REFINING BY ZONE-MELTING OF MATERIAL; PRODUCTION OF A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; SINGLE CRYSTALS OR HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; AFTER-TREATMENT OF SINGLE CRYSTALS OR A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; APPARATUS THEREFOR
  • C30B15/00—Single-crystal growth by pulling from a melt, e.g. Czochralski method
  • C30B15/20—Controlling or regulating
  • C30B15/206—Controlling or regulating the thermal history of growing the ingot
• • C—CHEMISTRY; METALLURGY
  • C30—CRYSTAL GROWTH
  • C30B—SINGLE-CRYSTAL GROWTH; UNIDIRECTIONAL SOLIDIFICATION OF EUTECTIC MATERIAL OR UNIDIRECTIONAL DEMIXING OF EUTECTOID MATERIAL; REFINING BY ZONE-MELTING OF MATERIAL; PRODUCTION OF A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; SINGLE CRYSTALS OR HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; AFTER-TREATMENT OF SINGLE CRYSTALS OR A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; APPARATUS THEREFOR
  • C30B29/00—Single crystals or homogeneous polycrystalline material with defined structure characterised by the material or by their shape
  • C30B29/02—Elements
  • C30B29/06—Silicon
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N27/00—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means
  • G01N27/02—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating impedance
  • G01N27/04—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating impedance by investigating resistance
  • G01N27/041—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating impedance by investigating resistance of a solid body

Definitions

• the present invention relates to semi-conductor ingot crystallization processes and relates more particularly to a method or method for experimentally validating the thermal history of a semiconductor ingot obtained by simulation of a crystallization process.
• the high-efficiency photovoltaic cells are mostly made from chips from Czochralski monocrystalline silicon ingot (Cz). Although known for its high electronic performance, especially in terms of the life of charge carriers, silicon CZ is not free of defects and impurities. Oxygen is the main impurity of silicon CZ and is in the form of atoms in interstitial positions in the crystal lattice. Among the defects of silicon CZ, mention may be made of oxygen precipitates, oxygen vacancies and thermal donors. Thermal donors are agglomerates (oxygen based) that form at temperatures between 350 ° C and 550 ° C and affect the electrical properties of the material by creating free electrons.
• the ingot manufacturers use computer tools to simulate the Czochralski crystallization process. Thanks to these simulations, it is for example possible to know the temperature in each portion of the ingot at a given moment of crystallization, as well as its evolution during crystallization. This evolution, commonly called “thermal history”, has a great influence on the amount of defects formed during crystallization in the portion of the ingot considered.
• the thermal history of the ingot varies according to many parameters, such as the relative height (also referred to as the "solidified fraction") at which the relevant portion of the ingot is located, the geometry and materials of the parts that make up the crystallization furnace, the drawing speed of the ingot and the power delivered by the oven resistances.
• the thermal simulation of an ingot makes use of complex physical models. These models can lead to erroneous values of the thermal history if, for example, the calculation algorithm does not converge sufficiently or the definition of the mesh is too weak.
• Thermal donors are oxygen-based defects that form between 350 ° C and 500 ° C during crystallization and whose concentration is a marker of the thermal history of the ingot.
• the validation method according to the invention makes a comparison between theoretical and experimental values of the concentration of thermal donors, the theoretical value of the concentration of thermal donors being derived from the simulated thermal history.
• the validation method according to the invention does not require measurements in situ, ie inside the crystallization oven.
• the concentration of interstitial oxygen and the concentration of thermal donors can indeed be measured after the ingot has been removed from the furnace, and therefore much more simply than the temperature during the crystallization.
• the manufacture of the ingot is therefore not affected by the validation method according to the invention, which makes it possible to obtain results that are faithful to the crystallization process used.
• the calculation of the theoretical value of the concentration of thermal donors comprises the following operations:
• This method of calculation makes it possible to accurately determine the concentration of thermal donors formed during the crystallization process (between 350 ° C. and 550 ° C.), taking into account the exact temperature profile in the portion of the semiconductor ingot.
• the calculation of the theoretical value of the concentration of thermal donors is carried out by iterations and comprises, for each time step, the following operations:
• the content A [DT] n of thermal donors formed during said time step DT n is calculated using the following relation:
• a [DT] n AT n * a * Di ⁇ T * [O,] 4 * m ⁇ T n Y 2
• a is a constant
• Tn the temperature associated with said time step DT h
• Di (Tn) the diffusion coefficient oxygen at the temperature Tn
• m (T n ) the concentration of free electrons at the temperature Tn.
• the thermal history in the portion of the semiconductor ingot is advantageously described by means of two polynomials of the second degree.
• Steps a) to d) of the validation method according to the invention can be performed for different portions distributed along the semiconductor ingot, in order to verify the thermal simulation of the whole of the ingot, and not only of a portion.
• These different portions preferably include the upper end, called the head, and the lower end, called tail, of the semiconductor ingot. They are advantageously in a number greater than or equal to 5.
• FIG. 1 represents steps S1 to S4 of a method for validating a thermal history according to the invention.
• FIG. 2 shows an example of a thermal history of a portion of semiconductor ingot, obtained by simulation of the ingot crystallisation process, as well as the results of the step of adjusting this thermal history by two polynomial functions. .
• thermal history is used to describe the evolution of the temperature of a portion of a semiconductor ingot during the crystallization of the ingot.
• a portion preferably corresponds to a slice of the semiconductor ingot oriented perpendicularly to the longitudinal axis (or pulling axis) of the ingot and whose thickness may be variable according to its position in the ingot.
• the position of a portion or slice of the ingot is referred to as “relative height” and is generally expressed as a percentage of the total height of the ingot.
• Each of the portions of the ingot has a specific thermal history, which can be calculated by simulation of the crystallization process. All these thermal histories make it possible to reconstitute the evolution of the temperature field in the semiconductor ingot.
• the validation method described below makes it possible to know whether the calculation of the thermal history for at least a portion of the semiconductor ingot is accurate and, if necessary, to know its degree of precision. With this information, it is then possible to optimize the crystallization process by relying on thermal simulations, to refine the physical model used during these simulations to improve the accuracy of the calculation of the thermal history or, in the case of a manifestly erroneous thermal history, to profoundly modify the physical model or even change model.
• the semiconductor ingot is, for example, a monocrystalline silicon ingot obtained by the Czochralski crystallization process (also known as CZ silicon).
• the validation method firstly comprises a step S1 for measuring the interstitial oxygen concentration [Oi] in the portion of the ingot whose thermal history is to be validated.
• the measurement of the interstitial oxygen concentration [Oi] can be carried out at one point, for example by Fourier transform infrared spectroscopy (FTIR) on a thick wafer (typically between 1 mm and 2 mm thick) taken from the portion of the ingot and whose surface has been polished.
• FTIR Fourier transform infrared spectroscopy
• the interstitial oxygen concentration [Oi] is measured on the entire ingot, that is to say without prior cutting of platelets.
• the concentration [Oi] can be measured at the scale of the ingot by an infrared spectroscopy technique commonly called "Whole-rod FTIR".
• This technique derived from Fourier Transform Infrared Spectroscopy (FTIR), involves exposing the portion of the ingot to an infrared beam. The absorption of the infrared beam by the portion of the ingot makes it possible to determine an interstitial oxygen concentration averaged over the diameter of the ingot.
• the initial electrical resistivity is first measured in the ingot portion to determine acceptor and / or donor dopant concentrations.
• the ingot is then annealed in order to create new thermal donors, different from those formed during crystallization.
• the temperature of this annealing is preferably constant and between 350 ° C and 550 ° C.
• the electrical resistivity after annealing is measured in the same area of the ingot. From this second resistivity value and the dopant concentrations, it is possible to calculate the concentration of thermal donors formed by the annealing.
• the concentration of interstitial oxygen [Oi] in the portion of the ingot is determined from the concentration of newly created thermal donors and the duration of the annealing between 350 ° C and 550 ° C, for example by means of an abacus .
• This last technique is precise and particularly simple to implement. It is advantageous even when it is applied to a plate taken from the ingot because, unlike the FTIR technique, it does not require the polishing of the wafer and is not limited in terms of thickness.
• the validation method of FIG. 1 then comprises a step S2 making it possible to determine a theoretical value [DT] th of the concentration of thermal donors formed in the portion of the ingot during the crystallization.
• This theoretical value [DT] th is calculated from the thermal history of the portion of the ingot and from the interstitial oxygen concentration [Oi] measured in step S1, using a mathematical model which describes the kinetics of formation of thermal donors.
• the calculation of the thermal donor concentration [DT] th consists of the following operations.
• the thermal history of the portion of the ingot represented graphically by a curve of the temperature T as a function of the crystallization time t, is described analytically using one or more empirical expressions.
• This first operation called “adjustment” (or “fit” in English), consists in determining at least one function T (t) whose curve reproduces the thermal history (i.e. the temperature profile) simulated.
• Empirical expressions describing or representing the thermal history are advantageously chosen from polynomials of degree n (n being a nonzero natural integer), because the polynomial functions allow a precise adjustment of the thermal history curves of a semiconductor ingot.
• the thermal history curve comprises a high number of points, for example between 300 and 600 points distributed over a wide temperature range (typically 1400 ° C. at 200 ° C) of which at least 20 points in the temperature range 350 ° C-550 ° C.
• FIG. 2 shows by way of example the thermal history of a portion of a CZ silicon ingot located at a relative height of 1%.
• This thermal history example was obtained by simulation of the Czochralski crystallization process, using the simulation tool ANSYS ® Fluent ® . It makes it possible to distinguish two successive phases of the Czochralski process: the phase of solidification of the ingot and the cooling phase of the ingot.
• the end of the solidification phase is marked by the removal of the ingot from the molten silicon bath.
• the beginning of the cooling phase is marked by a faster decrease in temperature.
• the use of two second-degree polynomials makes it possible to limit the time and the calculation means necessary for the adjustment operation and is particularly suitable for this type of two-part thermal history.
• the second operation of the calculation of the theoretical value [DTjth is a discretization of the thermal history in no time Atn successive. This discretization can be performed, for example using a spreadsheet, associating with each time step Atn a temperature value Tn calculated using the empirical expression determined during the previous operation.
• the duration of the time steps Atn is chosen mainly according to the length of the ingot and the drawing speed during the crystallization process. It is preferably less than 10 min, for example equal at 1 min.
• each calculation of the temperature Tn is carried out with the empirical expression associated with the time step D ⁇ considered.
• the first polynomial (corresponding to the solidification phase) is used for the 35 * 60 / Atn (min) first time steps and the second polynomial is used for all subsequent time steps.
• a content (ie concentration) D [ ⁇ T] h is calculated in thermal donors formed during the time step D ⁇ .
• the content D [ ⁇ T] h in thermal donors is preferably calculated using the following relation:
• a [DT] n AT n * a * Di ⁇ T * [O,] 4 * pi ⁇ T h ) ⁇ 2 (1)
• a is a constant
• Tn is the temperature associated with the time step DT h
• Di (T n ) the diffusion coefficient of oxygen at the temperature T n
• m (T n ) the free electron concentration at the temperature T n .
• This relation (1) is taken from an article entitled "Unified model for training kinetics of oxygen thermal donors in Silicon", K. Wada, Physical Review B, Vol.30, N.10, pp. 5885-5895, 1984], which describes a model for calculating the kinetics of formation of thermal donors in CZ silicon at a constant temperature, for example 450 ° C.
• This document also provides the values of the parameters of the relation (1) or the formulas for calculating them, with the exception of the effective mass of the holes. The latter is according to the literature equal to 0.81 for silicon.
• the discretization in no time makes possible the use of the model of Wada, because it provides a constant temperature Tn for each step of time.
• the content D [ ⁇ T] h in thermal donors can be calculated for all the time steps of the simulated thermal history, for example from 1414 ° C to ambient temperature (ie 25 ° C), but the contribution of temperatures outside the range 350 ° C-550 ° C on the formation of thermal donors is negligible.
• the theoretical value [DT] th of the concentration of thermal donors is calculated from the contents A [DT] n in thermal donors formed during the different time steps.
• step S2 the sum of all the calculated A [DT] n contents constitutes the theoretical value [DT] th of the concentration of thermal donors formed during the crystallization:
• the concentration of thermal donors in the ingot at a given temperature can not exceed a maximum [DT] max concentration of thermal donors.
• concentration of thermal donors in silicon CZ which depends on the temperature.
• step S2 the theoretical value calculation [DT] th of the concentration of thermal donors is carried out by iterations, taking into account at each iteration of the maximum concentration [DT] max of thermal donors.
• This variant of calculation provides more precision on the calculation of the theoretical value [DT] th of the concentration of thermal donors.
• the Wada model is not the only model describing the formation kinetics of thermal donors and making it possible to calculate the theoretical value [DT] th of the concentration of thermal donors formed during the crystallization. Mention may especially be made of the model of Y. J. Lee et al., Described in the article ["Simulation of the kinetics of oxygen complex in crystalline Silicon", Physical Review B, Vol.66, 165221, 2002].
• [Ok] corresponds to the concentration of thermal donors of the family k (0 ⁇ k ⁇ 16) and whose time derivative is written:
• the Wada model tends to overestimate the formation kinetics of thermal donors compared to other more accurate models.
• the contents A [DT] n of thermal donors calculated in step S2 are advantageously multiplied by a reducing coefficient, for example of 0.75. This weighting of the contents A [DT] n greatly improves the accuracy of the calculation of the theoretical value [DT] th.
• the interstitial oxygen concentration [Oi] is measured by FTIR or its ingot scale variant at step S1 of the method, it is preferable to choose the same standard of measurement as that used in the thermal donor training model selected. Otherwise, a weighting coefficient is advantageously applied to the measurement of the interstitial oxygen concentration [Oi] before it is used as input to the Wada model. For example, if the measurement technique obeys the FTIR standard recommended by SEMI with a calibration coefficient of 6.28 ppma.cm, the measured value of the interstitial oxygen concentration [Oi] is multiplied by 5.5 / 6, 28, because the Wada model uses a calibration coefficient of about 5.5 ppma.cm. If the Lee model (calibration coefficient of 6.28 ppma.cm) is used and the interstitial oxygen concentration [Oi] is measured with the FTIR SEMI standard, no weighting coefficient is used.
• Step S3 of the validation method consists in determining an experimental value [DT] ex P of the concentration of thermal donors formed during the crystallization of the ingot.
• the experimental value [DT] ex P of the concentration of thermal donors can be obtained from the variation of resistivity or the variation of the concentration of charge carriers, caused by annealing at high temperature (> 600 ° C). This annealing at high temperature (typically 30 minutes at 650 ° C.) makes it possible to destroy the thermal donors formed during the crystallization of the ingot.
• the electrical resistivity can be measured (before and after destruction annealing) by the four point method, the Van der Pauw method, or derived from the eddy current measurement. This measurement technique is described in detail in patent FR 3009380, the content of which is incorporated by reference.
• the charge carrier concentration can be measured by Hall effect or deduced from CV measurements.
• the ingot is preferably doped so as to have an initial resistivity (ie after crystallization and before any heat treatment) greater than 1 ⁇ .cm, so that the variation of resistivity before-after annealing of destruction of the thermal donors is detectable with precision.
• Step S3 can be implemented after step S1 even when the patent technique FR2964459 and FR3009380 is used to measure the interstitial oxygen concentration [Oi]. In this case, it suffices to consider the initial electrical resistivity (or charge carrier concentration) of the ingot. Step S3 can also be carried out before step S1, in which case there are no more heat donors when annealing between 350 ° C and 550 ° C.
• the validation method is not limited to any order of the steps S1 and S3.
• the patent FR3009380 gives more details on the ways of articulating the step S1 of measuring the interstitial oxygen concentration [Oi] and the step S3 of measuring the concentration of thermal donors [DT] ex P.
• Steps S1 and S3 can be performed by the same equipment, for example the “OxyMap” equipment marketed by the company "AET Solar Tech”.
• step S4 of FIG. 1 the theoretical value [DT] th and the experimental value [DT] ex P of the concentration of thermal donors are compared. If the theoretical value [DT] th is close to the experimental value [DT] ex, typically between 0.7 * [DT] ex and 1, 3 * [DT] ex, the thermal history of the ingot portion is considered valid. If, on the contrary, the theoretical value [DT] th is far from the experimental value [DT] ex P , typically> 1, 3 * [DT] ex P , or ⁇ 0.7 * [DT] ex, then the thermal history of the ingot portion is not validated.
• the validation method described above is faster and easier to implement than the method of the invention. prior art.
• the results obtained are also faithful to the crystallization process employed, the Czochralski process in this example, since the validation method does not interfere with the crystallization of the ingot.
• the steps S1 to S4 of Figure 2 are performed for different portions distributed along the ingot (along the longitudinal axis of the ingot) to verify the validity of the thermal simulation in its entirety.
• the thermal simulation is considered to be right after the thermal history of each of the selected portions has been validated in step S4 of the method.
• the different portions of the ingot are preferably in a number greater than or equal to 5. They advantageously include the high end and the low end, respectively called “head” and “tail”, because their respective thermal histories are very different.
• the interstitial oxygen concentration [Oi] and the concentration of thermal donors [DT] ex are preferably measured at the same place in the different portions, for example on one edge or at the center of the slices coming from the ingot.

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• 2017
  • 2017-12-15 FR FR1762282A patent/FR3075379B1/fr active Active
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