DE102007001348B4 - Process and assembly for the preparation of crystalline moldings from melts in Czochralski arrangements - Google Patents

Abstract

The invention relates to a method and an arrangement for the production of crystalline shaped bodies from melts in Czochralski arrangements by manipulation of drawing speed and heat flow through the liquid / solid phase boundary. It is envisaged that the adjustment is carried out in two control circuits, wherein in a first control loop a desired pulling speed is determined and this is set in the process and in a second control loop a desired stroke rate is determined and fed to the process and a desired heat flow liquid / solid determined by the phase boundary and fed to the process, wherein for determining the target pulling rate, an actual molded body growth rate is measured or calculated from other measured variables and this is compared with a predetermined reference molding growth rate and wherein an actual Shape-body geometry parameter and an actual derivative of this shape-body geometry parameter after the mold body length is compared with a reference mold body geometry parameter and a reference derivative of the mold geometry parameter after the mold body length and for determining the desired heat flow through the Ph Asc limit liquid / fixed an actual stroke rate measured or calculated from other measured variables and this is compared with the target stroke rate. Furthermore, an arrangement is provided.

Description

The The invention relates to a method and an arrangement for Preparation of crystalline moldings from melts in Czochralski arrangements by manipulation of pulling speed and heat flow through the phase boundary liquid / solid.

Under A Czochralski arrangement is understood to mean a construction that consists of a crucible containing a melt and a pulling rod exists, over the from the crucible a shaped body is pulled upwards. From a technical point of view, the production is of semiconductor or oxide single crystals according to the so-called Czochralski technique undoubtedly the most important industrial application.

at Czochralski crystal growth is the most important industrial criterion for assessing success the yield. This term refers to both the usable Volume as well as the achieved properties of the crystal. In the first case, it is important to achieve the desired cylindrical shape with as possible low tolerances by controlling a so-called (molding) geometry parameter observed.

Of the Moldings geometry parameters (in the following geometry parameter) characterizes the cross section a crystalline shaped body: A crystalline shaped body with, for example, circular Cross section corresponds to the radius of a circle, with an elliptical cross section the root of the sum of the squares of the two semiaxes, at an equilateral hexagonal cross-section, for example, the radius of the surrounding Circle.

at Presence of only two locally concentrated control variables in one Process, as it is present with the manipulated variables heat flow through the phase boundary liquid / solid and pulling speed is the case, with a manipulated variable already for the Control of mold growth rate is used, it is necessary even complicated fabrics to describe with a geometry parameter.

• 1. Schwankungen der Meniskushöhe (Solche Schwankungen können zum einen ungewollter Natur sein oder sich zum anderen aus dem Referenz-Verlauf des Geometrieparameters ergeben.),
• 2. Veränderung der thermischen Verhältnisse während der Züchtung,
• 3. Absenkung des Schmelzlevels während des Prozesses,
• 4. konvektionsbedingte Temperaturschwankungen vor der Phasengrenze des wachsenden Kristalls.

The second industrial criterion, the achieved properties of the crystal to be grown, is multifactorial. On the one hand, it is important that the selected crystal form - or more generally the crystalline shaped body - of the (crystal) shoulder on the (crystal) cylinder to the end cone, as precisely as possible, which is also realized on the control of the geometry parameter. On the other hand, the crystal or molding growth rate is becoming increasingly important. Crystal defects such as inclusions, precipitates, sub-grain boundaries, dislocations, twins, polycrystalline envelopes, foreign and intrinsic point defects, etc. can be influenced or avoided in their concentration, frequency or occurrence by the targeted adjustment of the molding growth rate. Causes of the fluctuation of the actual molding growth rate - despite constant pulling speed - are z. In the following points:

• 1. Variations in the meniscus height (Such fluctuations may be unwanted in nature or result from the reference curve of the geometry parameter).
• 2. change in thermal conditions during breeding,
• 3. lowering of the melting level during the process,
• 4. Convection-related temperature fluctuations before the phase boundary of the growing crystal.

The from the outside given courses for certain System sizes - such as the geometry parameter or the molding growth rate referred to as reference trajectories. Thus the relevant actual sizes of the Reference trajectory must follow for certain Command values, for example for the Temperature in the melt or for the drawing speed - corresponding Setpoint profiles specified or calculated. The course of the reference trajectories for the is to be regulated sizes within the physical limits arbitrary.

The tracking solely the geometry parameter along a reference trajectory is in the Czochralski method usually on the Setting of setpoint curves for the Pulling rate and / or the heat flow through the phase boundary realized. The determination of these courses is time consuming and new perform, if changes were made in the construction of the plant. The parameters of usually used linear PID controller (PID = proportional-integral-derivative) are still during the process due to changing thermal conditions to change empirically found laws. Also these controller parameters have to time-consuming found by "trying" become.

Methods for the crystal growth of single crystals according to the Czochralski method are known in which the control of the crystal diameter and, in part, the growth rate of the mold body takes place via an adjustment of the drawing speed and / or the temperature.

Item in EP 1 252 375 B1 is a method of controlling the growth of a silicon single crystal in which growth rate and diameter deviations can be minimized. Here, a method is described whereby unwanted deviations of the crystal diameter at a predetermined observation interval are empirically minimized by changing the pulling rate and the temperature of the heaters. This method makes it possible empirically to make a correction of deviations in the crystal diameter, which occur in the ongoing breeding process.

In DE 600 01 274 T2 describe a method and a device which affects the crystal diameter of a silicon single crystal specifically only by controlling the temperature. The method is characterized by the provision of a method and an apparatus which make it possible to set a desired crystal diameter by changing the temperature of the melt. A control and / or control of the pulling rate, which is usually used to change the crystal diameter, is here according to the invention just hidden.

Together is the aforementioned method that as manipulated variables the usual Parameters pulling speed and temperature are used and the setting of the drawing speed and / or the temperature in a procedure (control loop) takes place. It is not possible, the mold growth rate and the crystal diameter - or in general terms the shaped body geometry parameter - independent of each other predetermined reference curves to track.

In the publication "Indium Phosphide and Related Materials Conference Proceedings, 2006, International Conference at Princeton, NJ May 7, 2006, Piscataway, NJ, USA, IEEE, P. 144 " a control model indicated, with the crystal shape and pulling speed can be controlled.

In Scripture EP 1 252 375 B1 For example, a method for controlling the growth of a silicon single crystal to minimize growth rate and diameter deviations is described. The process is carried out according to known crystal growth control principles, namely diameter control and growth rate control.

The font EP 1 541 721 A1 discloses a method of producing silicon single crystals. Therein, a cascade control structure for controlling a single quantity, that of the crystal diameter, will be described.

Of the Invention is based on the object, a method and an arrangement for the preparation of crystalline moldings from melts in Czochralski arrangements by manipulating the pulling rate and the heat flow through the phase boundary liquid / solid to provide an improvement in the yield and the quality of the crystalline shaped body can be effected.

Besides that is It is an object of the invention, both the geometry parameter and the growth rate of the crystalline shaped body in limits given by the physical properties of the system independently to regulate each other, d. h., the progressions of the relevant actual values track corresponding reference trajectories.

The solution The object is achieved with the features of claim 1 and the features of claim 5.

advantageous Further developments of the invention are specified in the subclaims.

Thus, the inventive method for the production of crystalline moldings in Czochralski arrangements by manipulation of pulling rate and heat flow through the phase boundary liquid / solid, characterized in that the adjustment is carried out in two control loops, wherein in a first control loop determines a target pull rate and This is set in the process and determines a target stroke rate in a second control loop and supplied to the process and a desired heat flow through the liquid / solid phase boundary determined and this is set in the process, wherein for determining the target pulling rate, an actual molding. Growth rate is measured or computationally determined from other parameters and this is compared with a predetermined reference molding growth rate and wherein an actual molding geometry parameter and a Is-derivative of this shaped body geometry parameter after the molding length is compared with a reference molding geometry parameter and a reference derivative of the molding geometry parameter after the molding body length and measured to determine the desired heat flow through the phase boundary liquid / fixed an actual stroke rate or calculated from other measured variables and this is compared with the desired stroke rate.

The inventive arrangement for the production of crystalline shaped bodies from melts by manipulation of pulling speed and heat flow through the phase boundary liquid / solid is characterized in that the arrangement has two control circuits and a Czochralski plant, wherein the first loop a regulator, the second control loop comprises a first regulator and a second regulator, wherein in the first control loop a first input of the controller is an actual mold growth rate can be applied, at a second input of the first regulator, a reference molding growth rate can be applied and at an output of the controller, a target pulling speed is outputable and connected to a first input of the Czochralski plant is and in the second control circuit at a first input of the first Regulator an actual-shape geometry parameter and an actual derivative of the shaped body geometry parameter can be applied after the molding length is, at a second input of the first regulator, a reference mold geometry parameter and a Referenzableitung of the shaped body geometry parameter after the molding body length can be applied is and at an output of the first controller, a target Hubrate can be output is connected to a second input of the second regulator is, at a first input of the second regulator an actual stroke rate can be applied and at an output of the second controller, a desired heat flow through the phase boundary liquid / solid is dispensable and with a second entrance of the Czochralski plant connected is.

The inventive method refers to the Czochralski method for the growth of moldings Melting and melting solutions. Only with melting of elements one can strictly speaking of speak pure melts, because all melts of compounds due the existence of a - if no matter how small - stoichiometric deviation strictly speaking, melt solutions are.

Considered the effect of breeding from melting solutions, that would be Density of the melt due to onset of segregation processes time-dependent. One however, such influence is negligible with small stoichiometric deviations (<1%). For this reason, the term melt is also used for melting solutions.

to Determination of the target drawing speed becomes an actual molded body growth speed measured or arithmetically determined from other parameters and these with a predetermined reference molding growth rate compared.

The method according to the invention comprises the following steps:
In order to determine the desired pull rate, an actual mold body growth rate is first measured or computationally determined from other measured variables and compared with a predefinable reference mold body growth rate.

to Determination of the desired stroke rate as an intermediate variable becomes an actual shaped body geometry parameter and an actual derivative of this shaped body geometry parameter the molded body length with a reference shaped body geometry parameter, a reference derivative of the shaped body geometry parameter after the Molded body length compared and for determining the desired heat flow through the phase boundary liquid / solid becomes an actual stroke rate measured or arithmetically determined from other measurands and these with the Target stroke rate compared.

to Determination of the desired stroke rate initially becomes an actual shaped body geometry parameter and an actual derivative of this shaped body geometry parameter the molded body length measured or calculated from other parameters and with a predefinable reference shaped body geometry parameters and a reference derivative of this shaped body geometry parameter compared to the molded body length.

to Determination of the desired heat flow through the phase boundary liquid / solid then an actual stroke rate is determined and compared with the desired stroke rate.

und insbesondere linear ausgeführt nach Gleichung (c₁)

umgerechnet und diese in den Prozess eingestellt wird.A preferred embodiment of the method according to the invention is characterized in that in the first control loop the deviation of the actual molding growth rate from the predetermined Reference molding growth rate is detected and in the required for the correction of this deviation target pulling speed on the execution of a proportional-integral-derivative control in the controller 1.1 according to equation (c)

and in particular linearly carried out according to equation (c ₁ )

converted and this is set in the process.

v_p,soll

die Soll-Ziehgeschwindigkeit,

v_g

die Ist-Formkörper-Wachstumsgeschwindigkeit,

V_g,ref

die Referenz-Formkörper-Wachstumsgeschwindigkeit

φ

die Bezeichnung für die Funktion allgemeiner PID-Regler mit Wachstumsgeschwindigkeit als Eingang in Gleichung (c),

k_p1

der Koeffizient P-Anteil Regler 1.1,

k_i1

der Koeffizient I-Anteil Regler 1.1,

k_d1

der Koeffizient D-Anteil Regler 1.1,

v_p0

die Ist-Ziehgeschwindigkeit zum Einschaltzeitpunkt Regler 1.1,

t, τ

die Zeit.

In equations (c) and (c ₁ ) are included

v _{p, shall}

the target pull rate,

v _g

the actual molding growth rate,

V _{g, ref}

the reference mold growth rate

φ

the term for the function of general growth-rate PID controllers as input in equation (c),

k _p1

the coefficient P-share controller 1.1 .

k _i1

the coefficient I-part controller 1.1 .

k _d1

the coefficient D-part controller 1.1 .

v _p0

the actual pulling speed at the switch-on time controller 1.1 .

t, τ

the time.

und insbesondere linear ausgeführt nach der Gleichung (c₁)

und die Soll-Ziehgeschwindigkeit im Prozess eingestellt wird, wodurch der Formkörper-Geometrieparameter verändert wird.In this embodiment, the method comprises the following steps:
In a first control loop, the deviation of the actual molding growth rate from the reference molding growth rate is corrected. This is done by detecting the deviation and in the required for the correction of this deviation target pulling speed on the execution of a proportional-integral-derivative control in the controller 1.1 is converted according to equation (c)

and in particular carried out linearly according to the equation (c ₁ )

and adjusting the target pull rate in the process thereby changing the shaped body geometry parameter.

und insbesondere linear ausgeführt nach Gleichung (h₁)

ermittelt und dem Verfahren zugeführt wird.In a further embodiment of the method according to the invention, it is provided that in the second control loop the deviation of the actual shaped body geometry parameter and the actual derivative of the molded body geometry parameter is dependent on the mold body length of the predefinable reference molded body geometric parameter and the reference derivative of the molded body Geometry parameters are recorded according to the length and an intermediate variable, the nominal stroke rate according to equation (h)

and in particular linearly carried out according to equation (h ₁ )

determined and fed to the process.

v_z,soll

die Soll-Hubrate,

g

die Bezeichnung für die in Gleichung (d₂) definierte Funktion,

f

die Bezeichnung für die in Gleichung (d₁) definierte Funktion

r_i

der Ist-Formkörper-Geometrieparameter,

r ' / i

die Ist-Ableitung des Formkörper-Geometrieparameters nach der Formkörperlänge,

ξ

die Bezeichnung für die Funktion in Gleichung (h),

r ' / i,ref

die 2. Ableitung des Referenz-Formkörper-Geometrieparameters nach der Formkörperlänge,

r r / i,ref

die Referenz-Ableitung des Formkörper-Geometrieparameters nach der Formkörperlänge,

r_i,ref

die Referenz-Formkörper-Geometrieparameter

ε₀ und ε₁

Einstellparameter des Reglers 2.1.

In equations (h) and (h ₁ ) are

v _{z, shall}

the nominal stroke rate,

G

the name for the function defined in equation (d ₂ ),

f

the name for the function defined in equation (d ₁ )

_i

the actual shaped body geometry parameter,

r '/ i

the actual derivative of the shaped body geometry parameter after the molded body length,

ξ

the name for the function in equation (h),

r '/ i, ref

the second derivative of the reference molded part geometry parameter after the molded part length,

rr / i, ref

the reference derivative of the shaped body geometry parameter after the molded body length,

r _{i, ref}

the reference mold geometry parameters

ε ₀ and ε ₁

Setting parameters of the controller 2.1 ,

In a second control loop, the deviation of the actual-shaped body geometry parameter and the actual derivative of the shaped body geometry parameter after the molding body length with the predetermined reference shaped body geometry parameter and the reference derivative of the shaped body geometry parameter the molded body length determined and first an intermediate size that Target stroke rate, determined and fed to the process.

wobei

und

sind. Hierin ist h_i die näherungsweise berechnete Meniskushöhe in Abhängigkeit vom Formkörper-Geometrieparameter r_i und dessen Ableitung r'i nach der Länge, beispielsweise

The determination of the target stroke rate is done as follows:
The setpoint for the stroke rate can be obtained from a mathematical model of the process. This can be noted as follows (equation (d)):

in which

and

are. Herein, h _{i is} the approximately calculated meniscus height as a function of the shaped body geometry parameter r _i and its derivative r ' i according to the length, for example

ρ_s

die Dichte des Kristalls

ρ_m

die Dichte der Schmelze

R_c

der Tiegelradius

α

die Laplacekonstante und

Θ₀

der Benetzungswinkel.

Denote here

ρ _s

the density of the crystal

ρ _m

the density of the melt

R _c

the crucible radius

α

the Laplace constant and

Θ ₀

the wetting angle.

und

sind die partiellen Ableitungen der Meniskushöhe nach dem Formkörper-Geometrieparameter r_i bzw. nach αi = arctan(r'i ).The expressions

and

are the partial derivatives of the meniscus height after the shaped body geometry parameter r _i or after α i = arctan (r ' i ) ,

critical On this model is that it's just the dynamic behavior of the molded body geometry parameter and its derivation after the molding length as an immediate reaction on the molding growth rate and describes the pulling rate.

The molded body growth rate v _g is the rate at which the length l of the molded body changes. Equation (a) describes this relationship: dl dt = v G (A)

The relationship between pull rate v _p and mold growth rate v _g is referred to as lift rate v _z (equation (b)):

A concrete modeling of the thermal relationships in the plant, the one considerable empirical adaptation due to numerous parameters and structural indeterminacy would not be required.

Now, the dynamic behavior of the error r _i - r _{i, ref} , ie the time profile of its deviation from the reference value r _{i, ref} , can be specified (equation (f)): r '' i - r '' i, ref + ε 1 (r ' i - r ' i, ref ) + ε 0 (r i - r i, ref ) = 0, ε 1 , ε 0 > 0 (f) or generally nonlinear: r '' i - ξ (r '' i, ref , r ' i - r ' i, ref , r i , r i, ref ) (f 1 ).

Since the quantities r _{i, ref} , the reference shaped body geometry parameter, as well as its first and second derivation after the molded body length, r ' i, ref and r '' i, ref , given and thus known and, furthermore, the actual shaped body geometry parameter r _i and its derivative r ' i are available from a measurement or a suitable reconstruction algorithm, it is possible to derive from equation (f) the course of r '' i which is required to follow the reference curve with just this error dynamics: r '' i = r '' i, ref - ε 1 (r ' i - r ' i, ref ) - ε 0 (r i - r i, ref ) (g). or in a nonlinear case r '' i = ξ (r '' i, ref , r ' i - r ' i, ref , r i - r i, ref ) (g 1 )

und insbesondere linear, Gleichung (h₁)

die dem Verfahren zugeführt wird.Substituted in equation (d) results as a setpoint for the manipulated variable v _z ,
(general case)

and in particular linear, equation (h ₁ )

which is fed to the process.

und insbesondere linear ausgeführt nach der Gleichung (i₁)

umgerechnet und diese im Prozess eingestellt wird.In a next refinement of the method according to the invention, it is provided that the deviation of the actual stroke rate from the nominal stroke rate is detected in the second control circuit and injected into a desired heat flow required to correct this deviation through the phase boundary liquid / solid via the execution of a proportional integral-derivative control in the regulator 2.2 according to the equation (i)

and in particular carried out linearly according to the equation (i ₁ )

converted and this is set in the process.

Q_soll

der Soll-Wärmestrom durch die Phasengrenze flüssig/fest,

Ψ

die Bezeichnung für die Funktion allgemeiner PID-Regler mit Hubrate als Eingang in Gleichung (i),

v_z,soll

die Soll-Hubrate,

v_z

die Ist-Hubrate,

t und τ

die Zeit,

Q₀

der Ist-Wärmestrom durch die Phasengrenze flüssig/fest zum Einschaltzeitpunkt Regler 2.2,

k_p2

der Koeffizient P-Anteil Regler 2.2,

k_i2

der Koeffizient I-Anteil Regler 2.2 und

k_d2

der Koeffizient D-Anteil Regler 2.2.

In the equations (i) and (i ₁ )

Q _should

the desired heat flow through the phase boundary liquid / solid,

Ψ

the term for the function of general stroke rate PID controllers as input in equation (i),

v _{z, shall}

the nominal stroke rate,

v _z

the actual stroke rate,

t and τ

the time,

Q ₀

the actual heat flow through the phase boundary liquid / fixed to the switch-on time controller 2.2 .

k _p2

the coefficient P-share controller 2.2 .

k _i2

the coefficient I-part controller 2.2 and

k _d2

the coefficient D-part controller 2.2 ,

und insbesondere linear ausgeführt nach Gleichung (i₁)

umgerechnet wird und diese im Prozess eingestellt wird, wodurch der Formkörper-Geometrieparameter verändert wird.In this further method step in the second control loop, the deviation of the actual stroke rate v _z from the previously calculated setpoint stroke rate is corrected. This is done by detecting this deviation and converting it into a desired heat flow through the liquid / solid phase boundary necessary for correcting the deviation via the execution of a proportional-integral-derivative control in the controller 2.2 according to the equation (i)

and in particular carried out linearly according to equation (i ₁ )

is converted and adjusted in the process, whereby the molding geometry parameter is changed.

The The present method expands and improves the previous methods for the preparation of crystalline moldings by the Czochralski method by manipulating the pulling rate and the heat flow through the phase boundary liquid / solid, By manipulating these parameters in two independent and separate control circuits can be made.

To the idea according to the invention the method provides a control concept according to which by manipulation the pulling speed on the one hand and the heat flow through the phase boundary liquid / solid on the other hand, the molding growth rate on the one hand and the shaped body geometry parameter on the other hand, two independently predetermined reference curves be tracked can.

A In the process to be determined intermediate size, the stroke rate as the ratio of Pulling rate to molding growth rate and the derivative of a characterizing the cross-sectional area of the shaped body Moldings geometry parameter after the molding body length in addition to the system size shaped body geometry parameter first included in the regulatory and control process.

The Using the stroke rate as a controlled variable is another advantage of the procedure, since it does not have to determine whether the pulling speed or the molding growth rate The changes in the molded body geometry parameter cause. As described, this intermediate size can be derived from a mathematical Model of the process, so there is no need for empirical Adaptation of parameters. This model in turn has the advantage that there are only hydro-mechanical-geometric relationships of the Crystal growth describes, but not the complicated thermal relationships in the breeding plant, such as heat flows, convection etc. Thus, the model is relatively accurate and can be used for control purposes. The dynamic properties of the control are thus very good adjusted the dynamic behavior of the process. This is for others Procedures that are exclusive to controllers with empirically set parameters, not the case. The model-based controller in the second control loop continues to bring the advantage that it is no longer necessary, the controller parameters while of the process to change empirically to meet the changing to adapt to physical conditions of the process.

According to the method of the invention, the control concept makes it possible to vary the molding growth rate by manipulating the drawing speed in two process sequences in a first process sequence, and the desired molding geometry in the second process sequence to realize liquid / solid parameters by manipulating the heat flow through the phase boundary.

The inventive method can be used in all process variants of the Czochralski technique become. These are z. The conventional Czochralski process, the liquid encapsulated Czochralski method (LEC method), the Vapor Pressure Controlled Vapor Pressure Controlled Czochralski Method (VCZ Method), Fusion and solution breeding, High and low pressure method, breeding of materials related to in the breeding plant occurring electromagnetic spectrum from opaque to transparent behavior, etc.

in the The following will be with reference to an embodiment of the invention for the breeding of a 2 inch indium phosphide (InP) crystal with reference to the accompanying drawings explained in more detail. These Type of crystals grow with a circular cross-section. The molded body geometry parameter is in this case the crystal radius.

It demonstrate

1 a schematic section of a Czochralski plant and a schematic hint of control loops,

2 a schematic longitudinal section of a drawn according to the Czochralski crystalline molding,

3 the flow chart and the arrangement of the control circuits,

4 the exemplary courses of actual shaped body geometry parameters and reference shaped body geometry parameters as a function of time in the cultivation of an InP single crystal,

5 the exemplary courses of actual mold growth rate and reference mold growth rate as a function of time in the growth of an InP single crystal,

6 the exemplary course of the target pulling rate as a function of time in the cultivation of an InP single crystal using the described control,

7 the exemplary course of the setpoints and actual values of the stroke rate as a function of time in the cultivation of InP single crystals and

8th the exemplary course of the target heater temperature as a function of time in the cultivation of InP single crystals using the scheme described.

As in 1 schematically illustrated, the basic structure of a working according to the Czochralski principle breeding plant consists of a crucible 21 in the temperature field of one or more heaters 22 is arranged.

In the crucible 21 At the beginning of the process, polycrystalline indium phosphide is added. Subsequently, the material is heated until it has melted. The crucible 21 then contains the melt 23 , The temperature at the heater of the plant 6 is at the beginning of the process about 1288 ° C, cf. 8th , About a about its longitudinal axis, possibly rotating, pulling rod 24 , becomes a seed crystal 25 to the melt 23 moved up. After its contact with the melt 23 it applies, the temperature of the heater 22 as well as the pulling speed v _{p of} the pulling rod, which is referred to as the pulling speed 24 so choose that a crystalline shaped body 30 of high structural quality and well-defined shape. The molded body geometry parameter 27 and other system sizes should be tracked corresponding reference trajectories. For this purpose, the temperature of the heater in the first hour of the process, before switching the described control, reduced to about 1275 ° C, such as 8th can be seen. The drawing speed is increased in the same time to a value of about 10 mm / h, cf. 6 , Between crystalline shaped body 30 and melt 23 a so-called meniscus forms 26 from whose height 31 sensitive from the molding geometry parameter 27 , its derivative 28 after the molding body length 29 and other influencing factors. The speed with which the length l 29 of the molding 30 is denoted as the molding growth rate v _g described in equation (a): dl dt = v G (A)

The relationship between pull rate v _p and mold growth rate v _g is referred to as lift rate v _z (equation (b)):

Usually, a crystalline molded body drawn by the Czochralski method has a characteristic cylindrical shape schematically shown in FIG 2 : After growing on the seed crystal 25 For procedural reasons, it may be necessary to use the molded part geometry parameter 27 First, to rejuvenate, leaving a thin neck 42 expresses. Subsequently, the shaped body geometry parameter 27 forming the so-called shoulder or the starting cone 43 brought to a certain value and held this value as long as possible constant. This area is called a cylinder 44 designated. This is also in the course of the shaped body geometry parameter in 4 Recognize: The molded geometry parameter increases from 2.5 mm to 27.5 mm in the first 4 hours of the process, then it is kept approximately constant. For separating crystalline shaped body 30 and melt 23 becomes the shaped body geometry parameter 27 last reduced again, see 4 , The course of the actual value of the shaped body geometry parameter is drawn through in this figure, the dotted of the reference value plotted.

The goal is now, as described, to obtain an optimal yield. This is done by controlling the mold geometry parameter and the growth rate in two control loops 1 and 2 , In 3 are the flowchart and the arrangement of the control loops 1 and 2 shown. Continues 4 the course of the controlled shape-body geometry parameter and 5 the course of the controlled molding growth rate.

The following process steps take place in the control circuits:
After switching on the control from a process time of approx. 1 hour (see 4 to 7 ) is in the control loop 1 in a regulator 1.1 over an entrance 3 an actual molded body growth rate v _g as a measured variable from a Czochralski plant 6 fed or entered. The course of the measured variable v _g is in 5 solid applied. About an entrance 4 becomes a predetermined reference molding growth rate v _{g, ref} in the controller 1.1 entered. The course of this size is in 5 Dotted applied. The regulator 1.1 Now, the values of the actual molding growth rate v _g and the reference molding growth rate v _{g, ref are available} for data processing.

hier mit k_p1 = 0,2, k_i1 = –0,35 min^–1, k_d1 = 0 min.About the execution of a proportional-integral-derivative control in the controller 1.1 is a required to correct the deviation of actual molding growth rate v _g and reference molding growth rate v _{g, ref} desired pulling rate v _{p, should be} determined according to equation (c ₁ ):

here with k _p1 = 0.2, k _i1 = -0.35 min ^-1 , k _d1 = 0 min.

This is done in such a way that the mentioned input values are compared with each other. If these values deviate, a correction is made. This is done by determining a value compensating for the deviation for the desired pulling speed v _{p, soll} . From an exit 5 of the regulator 1.1 Then, the determined target pull speed v _{p, should be} to Czochralski plant 6 over an entrance 6a led the Czochralski plant and so set in the process. This has the consequence that the molding growth rate changes and so the reference curve can be tracked. The one from the regulator 1.1 calculated course of the pulling speed is in 6 shown. 5 shows how, starting from a process duration of about 5 hours, the reference value, the course of which is shown dotted, was temporarily increased for the molding growth rate. The actual molding growth rate, whose course is represented by a solid curve, can be tracked to this reference curve.

In the second loop 2 takes place independently of the control loop 1 the control of the shaped body geometry parameter and its derivation after the molded body length. This is done in the control loop 2 first a regulator 2.1 the actual shaped body geometry parameter r _i (shown in FIG 4 , solid line) and its derivative after the molding body length r ' i over an entrance 7 as a measure of the Czochralski plant 6 fed or entered.

About an entrance 8th of the regulator 2.1 is the reference shape geometry parameter r _{i, ref} (shown in _FIG 4 dotted line), the reference derivative of the molded body geometry parameter after the molded body length r ' i, ref and the second derivative r '' i ref of the reference molded body geometry parameter is entered after the molded body length.

The regulator 2.1 Now the values for the actual shaped body geometry parameter r _i and its derivative according to the molded body length are available r ' i and the reference shaped body geometry parameter r _{i, ref} and its first and second derivative after the molded body length r ' i, ref and r '' i, ref for further data processing.

wird zunächst eine Zwischengröße – eine Soll-Hubrate v_z,soll – ermittelt nach Gleichung (h₁):

hier mit ε₁ = ε₀ = –400 m^–1.About a mathematical model, described in equations (d),

First, an intermediate variable - a desired stroke rate v _{z, soll} - determined according to equation (h ₁ ):

here with ε ₁ = ε ₀ = -400 m ^-1 .

After determining the intermediate size, a further process step takes place:
About an exit 9 of the regulator 2.1 is the target stroke rate v _{z, should be} output and via an input 10 a controller 2.2 fed. About an entrance 10a of the regulator 2.2 is the actual stroke rate v _z as a measure of the Czochralski plant 6 entered. The regulator 2.2 Now, the values of the nominal stroke rate v _{z, soll} and the actual stroke rate v _{z are available} for further data processing. The curves of the setpoint and actual values of the stroke rate are in 7 shown. The course of the setpoints of the stroke rate are in 7 dotted, which represented the actual values drawn through.

hier mit k_p2 = –3 K, k_i2 = –0,3 K/min, k_d2 = 0 K min.About the execution of a proportional-integral-derivative control in the controller 2.2 the required heat flow, here represented by the temperature T _soll at the heater, is determined by the liquid / solid phase boundary to correct the deviation from actual stroke rate v _z and target stroke rate v _z, according to equation (i ₁ ):

here with k _p2 = -3 K, k _i2 = -0.3 K / min, k _d2 = 0 K min.

This happens in such a way that the values are first compared with each other. If the values deviate, a correction is made. This happens because a value compensating the deviation for the desired heat flow T _{soll is} determined by the liquid / solid phase boundary.

About an exit 11 the determined target heat flow T _soll through the phase boundary liquid / solid to Czochralski plant 6 over an entrance 6b guided and adjusted in the process, whereby a change of the shaped body geometry parameter r _{i is} effected. The course of the heat flow representing the heat flow through the phase boundary heating temperature 8th played. A look at 4 shows that the desired course of the shaped body geometry parameter can be maintained.

1

loop 1

2

loop 2

1.1

regulator 1

2.1

regulator 2

2.2

regulator 3

3

entrance the actual molding growth rate

4

entrance the reference molding growth rate

5

Target pull rate output

6

Czochralski-conditioning

6a

Target pull speed input

6b

entrance the desired heat flow through the phase boundary liquid / solid

7

entrance of the actual shaped body geometry parameter and input of the actual derivative of the molded body geometry parameter after the molded body length

8th

entrance of the reference mold geometry parameter and input of the reference derivative of the molded body geometry parameter after the molded body length

9

output the desired stroke rate

10

entrance the desired stroke rate

10a

entrance the actual stroke rate

11

output the desired heat flow through the phase boundary liquid / solid

21

crucible

22

stoker

23

melt

24

pull rod

25

seed crystal

26

meniscus

27

Moldings geometry parameters

28

derivation of the molded body geometry parameter after the length

29

Moldings Length / Length

30

crystalline moldings

31

Height of the meniscus

42

thin neck

43

start cone

44

cylinder

45

cone

h _i

meniscus height

v _g

Is moldings growth rate

v _{g, ref}

Reference moldings growth rate

v _p

Actual drawing speed

v _{p, shall}

Target pull rate

v _p0

Actual pulling speed at the switch-on time controller 1.1

v _z

Actual stroke rate

^v z, shall

Target stroke rate

_i

Is moldings geometry parameters

r _{i, ref}

Reference-shaped body geometry parameters

r '/ i

Actual derivation of the molded body geometry parameter after the molding body length

r '/ i, ref

Reference derivative the shaped body geometry parameter, after the molding body length

r '' / i

Second Derivation of the actual shaped body geometry parameter after the molding body length

r '' / i, ref

Second Derivation of the reference shaped body geometry parameter after the molding body length

l

Moldings Length / Length

Q

Actual heat flow through the phase boundary liquid / solid

Q ₀

Actual heat flow through the phase boundary liquid / solid at switch-on time controller 2.2

Q _should

Target heat flow through the phase boundary liquid / solid

T

the the actual heat flow through the phase boundary liquid / solid representing Temperature T at the heater

T ₀

the actual heat flow through the phase boundary liquid / solid representing temperature at the heater for switch-on time controller 2.2

T _shall

the the desired heat flow through the phase boundary liquid / solid representing Target temperature at the heater.

φ

description for the Function of general PID controller with growth rate as Entry in equation (c) Name for the function more general PID controller with stroke rate as input in equation (i)

G

Designation for the function defined in equation (d ₂ ) Designation for the function in equation (h)

f

Name for the function defined in equation (d ₁ )

k _p1

Coefficient P-share controller 1.1

k _i1

Coefficient I-part controller 1.1

k _d1

Coefficient D-share controller 1.1

k _p2

Coefficient P-share controller 2.2

k _i2

Coefficient I-part controller 2.2

k _d2

Coefficient D-share controller 2.2

ε ₀

Adjustment parameter controller 2.1

ε ₁

Adjustment parameter controller 2.1

t

Time

τ

Time

Claims (5)

Process for the preparation of crystalline moldings from melts in Czochralski arrangements by manipulation of pulling rate and heat flow through the phase boundary liquid / solid, characterized in that the adjustment is carried out in two control loops, wherein in a first control loop a target drawing speed is determined and this in the Process is set and in a second control loop a target stroke rate is determined and fed to the process and a desired heat flow through the liquid / solid phase boundary determined and fed to the process, wherein for determining the target pulling rate measured an actual molding growth rate or is calculated from other measured variables and this is compared with a predetermined reference molding growth rate and wherein for determining the target stroke rate as an intermediate size an actual molded body geometry parameter and an actual derivative of this shaped body geometry ieparameters is compared with the shape of a molded body with a reference shape geometry parameter and a reference derivative of the shaped body geometry parameter after the molding length and measured to determine the desired heat flow through the phase boundary liquid / fixed an actual stroke rate or computationally determined from other parameters and this is compared with the nominal stroke rate. A method according to claim 1, characterized in that in the first control loop the deviation of the actual molding growth rate from the predetermined reference molding growth rate is detected and in the required for the correction of this deviation target pulling rate on the execution of a proportional-integral-derivative Control in the controller 1.1 according to equation (c)

and in particular linearly carried out according to equation (c ₁ )

where v _{p, is} the target pull rate, v _{g is} the actual mold growth rate, v _{g, ref is} the reference mold growth rate φ designation for the function of general PID controller with growth rate Input in equation (c), k _p1 the coefficient P-share controller 1.1 , k _{i1 is} the coefficient I component controller 1.1 , k _{d1 is} the coefficient D proportion controller 1.1 , v _{p0 is} the actual pulling speed at the switch-on time controller 1.1 , t, τ are the time. A method according to claim 1 or 2, characterized in that in the second control loop the deviation of the actual shaped body geometry parameter and the actual derivative of the shaped body geometry parameter according to the molded body length of the predetermined reference molded body geometry parameter and the reference derivative of the molded body Geometry parameters are recorded according to the length and an intermediate variable, the nominal stroke rate according to equation (h)

and in particular linearly carried out according to equation (h ₁ )

where v _{z, is} the nominal stroke rate, g is the designation for the function defined in equation (d ₂ ), f is the designation for the function defined in equation (d ₁ ), r _{i is} the actual moldings geometry parameters, r ' i the actual derivative of the shaped body geometry parameter after the molded body length, the designation for function in equation (h), r '' i, ref the second derivative of the reference molded part geometry parameter after the molded part length, r ' i, ref the reference derivative of the shaped body geometry parameter after the molded body length, r _{i, ref} the reference molded body geometry parameters ε ₀ and ε ₁ setting parameters of the controller 2.1 where the function in equation (d ₁ )

where h _{i is} the approximately calculated meniscus height as a function of the shaped body geometry parameter r _i and its derivative r ' i is the length and the function in equation (d ₂ )

where ρ _{s is} the density of the crystal, ρ _{m is} the density of the melt, R _{c is} the crucible radius, α is the Laplace constant and Θ _{0 is} the wetting angle. Method according to one of claims 1 to 3, characterized in that in the second control loop, the deviation of the actual stroke rate is detected by the desired stroke rate and in a required for correcting this deviation desired heat flow through the liquid phase / fixed on the execution of a proportional-integral-derivative control in the controller 2.2 according to the equation (i)

and in particular carried out linearly according to the equation (i ₁ )

is converted and set in the process, where Q _is the target heat flow through the phase boundary liquid / fixed, Ψ the name for the function of general PID controller with stroke rate as input in equation (i), v _{z, is} the target stroke rate , v _{z is} the actual stroke rate, t and τ is the time, Q _{0 is} the actual heat flow through the phase boundary liquid / fixed to the switch-on time controller 2.2 , k _{p2 is} the coefficient P-share controller 2.2 , k _{i2 is} the coefficient I-part controller 2.2 and k _{d2 is} the coefficient D component controller 2.2 are. Arrangement for the production of crystalline moldings from melts by manipulation of drawing speed and heat flow through the liquid / solid phase boundary, characterized in that the arrangement comprises two control circuits ( 1 ) and ( 2 ) and a Czochralski plant ( 6 ), wherein, the first control loop ( 1 ) a controller ( 1.1 ), the second control circuit comprises a first controller ( 2.1 ) and a second controller ( 2.2 ), wherein in the first control loop ( 1 ) at a first entrance ( 3 ) of the controller ( 1.1 ) an actual molding growth rate can be applied to a second input ( 4 ) of the first controller ( 1.1 ) a reference molding growth rate can be applied and at an exit ( 5 ) of the controller ( 1.1 ) a desired pulling speed can be output and with a first input ( 6a ) of the Czochralski plant ( 6 ) and in the second control loop ( 2 ) at a first entrance ( 7 ) of the first controller ( 2.1 ) an actual shaped body geometry parameter and an actual derivation of the shaped body geometry parameter can be applied, at a second input ( 8th ) of the first controller ( 2.1 ) a reference shaped body geometry parameter and a reference derivative of the shaped body geometry parameter can be applied after the molded body length and at an output ( 9 ) of the first controller ( 2.1 ) a desired stroke rate can be output and with a second input ( 10 ) of the second controller ( 2.2 ) is connected to a first input ( 10a ) of the second controller ( 2.2 ) an actual stroke rate can be applied and at an output ( 11 ) of the second controller ( 2.2 ) a desired heat flow through the phase boundary liquid / fixed can be output and with a second input ( 6b ) of the Czochralski plant ( 6 ) connected is.