JP5697413B2 - Silicon single crystal manufacturing method, silicon single crystal manufacturing apparatus, silicon single crystal resistivity distribution calculation method - Google Patents

Description

  The present invention relates to a silicon single crystal manufacturing method, a silicon single crystal manufacturing apparatus, and a silicon single crystal resistivity calculation method for manufacturing a silicon single crystal by an FZ method.

  According to the FZ (floating zone melting) method, a polycrystalline silicon material having high resistivity is partially heated to form a molten zone, and a dopant is supplied to the molten zone using a gas doping method. The molten zone is solidified to produce a silicon single crystal having a straight body portion having substantially the same diameter and a diameter expanding / contracting portion adjacent to the straight body portion and whose diameter is enlarged or reduced. The diameter expanding / contracting portion is a lower tapered portion that is adjacent to the lower portion of the straight body portion and has a diameter that decreases downward, or a tail portion that is adjacent to the upper portion of the straight body portion and has a diameter that decreases upward. According to the FZ method, the resistivity distribution in the longitudinal direction of the silicon single crystal is substantially the same in principle by solidifying the molten zone while supplying the dopant (dopant gas) to the molten zone under the same supply conditions ( It is said that a uniform silicon single crystal can be obtained.

  However, in a silicon single crystal manufactured by the FZ method, the resistivity distribution may not always be the same over the entire area in the longitudinal direction of the silicon single crystal. In order to improve this, for example, the following Patent Document 1 discloses a technique for controlling the amount of dopant supplied to the raw material silicon material in accordance with the change in the growth state of the silicon single crystal during the step of forming the straight body portion. Is disclosed.

JP 2009-221079 A

  However, even the technique described in Patent Document 1 has a problem in that the resistivity distribution in the longitudinal direction of the silicon single crystal may not be the same in the silicon single crystal manufactured by the FZ method. Therefore, it is desired to more reliably manufacture a silicon single crystal having substantially the same resistivity distribution in the longitudinal direction of the silicon single crystal.

  The present invention relates to a silicon single crystal manufacturing method, a silicon single crystal manufacturing apparatus, and a silicon single crystal that can more reliably manufacture a silicon single crystal having substantially the same resistivity distribution in the longitudinal direction of the silicon single crystal. It is an object of the present invention to provide a method for calculating the resistivity distribution of a silicon single crystal used for manufacturing.

  As a result of intensive studies to solve the above problems, the inventor has formed a straight body part while supplying a dopant to the melting zone corresponding to the straight body part, and a melting part corresponding to the diameter expansion / contraction part. It has been found that the cause of the problem is that the conditions for supplying the dopant to the molten zone are the same when the diameter expansion / contraction portion is formed while supplying the dopant to the belt. And when this inventor forms a straight body part, supplying a dopant to the fusion zone corresponding to a straight body part, a diameter expansion / contraction part is supplied, supplying a dopant to the fusion zone corresponding to a diameter expansion / contraction part. It was discovered that by changing the supply conditions of the dopant to the melting zone when forming, a silicon single crystal having substantially the same resistivity distribution in the longitudinal direction of the silicon single crystal can be more reliably produced. The present invention has been completed.

  In the method for producing a silicon single crystal according to the present invention, a raw material silicon material that is a raw material of a silicon single crystal is partially heated to form a molten zone, and the molten zone is solidified while supplying a dopant to the molten zone. A silicon single crystal manufacturing method by an FZ method for manufacturing a silicon single crystal having a straight body portion having substantially the same diameter and a diameter expanding / contracting portion adjacent to the straight body portion and having a diameter expanding or contracting. A straight body part forming step of forming the straight body part while supplying a dopant to the melt zone corresponding to the straight body part, and the diameter expanding / contracting part before and / or after the straight body part forming step. A diameter expanding / contracting portion forming step of forming the diameter expanding / contracting portion while supplying a dopant to the melt zone corresponding to the step of forming the straight body portion based on a predetermined change condition in the diameter expanding / contracting portion forming step. Do in the process And changes the supply conditions of the dopant in the diameter scaling unit forming process on Punt supply conditions.

  In addition, it is preferable to obtain a silicon single crystal in which the resistivity distribution in the longitudinal direction of the straight body portion is substantially the same over the entire region in the longitudinal direction of the straight body portion including a region adjacent to the diameter expanding / contracting portion. .

  Moreover, it is preferable that the supply conditions of the said dopant are the density | concentration of the dopant in the flow volume and / or dopant gas containing a dopant.

  The change condition is based on a resistivity distribution model calculated based on the dopant concentration Cm (x + Δx) in the melting zone before solidification and the dopant concentration C (x + Δx) in the silicon single crystal after solidification. It is preferable to set based on this.

凝固後のシリコン単結晶におけるドーパントの濃度Ｃ（ｘ＋Δｘ）を下記式（５）により算出する凝固後ドーパント濃度算出工程と、
Ｃ（ｘ＋Δｘ）＝ｋ_０Ｃｍ（ｘ＋Δｘ）・・・（５）
凝固後のシリコン単結晶におけるドーパントの濃度Ｃ（ｘ＋Δｘ）を微少量Δｘごとに順次算出することによりシリコン単結晶全体の抵抗率分布モデルを算出する抵抗率分布モデル算出工程と、を備えることが好ましい。 As a step of calculating the resistivity distribution model,
The position in the longitudinal direction of the silicon single crystal from the end opposite to the straight body portion in the diameter expansion / contraction portion is x, the width along the longitudinal direction of the silicon single crystal in the melting zone is w, and the position x When the volume of the silicon single crystal after solidification is Vc (x) as a function of, and the volume of the melting zone corresponding to the diameter expansion / contraction part is Vm (x) as a function of the position x, the position a melting zone volume calculating step of calculating a volume Vm (x) of the melting zone corresponding to the diameter expansion / contraction portion in x by the following formula (1);
Vm (x) = Vc (x + w) −Vc (x) (1)
When the time required for the silicon single crystal to grow at a growth rate v by a minute amount Δx is Δt = Δx / v and the amount of dopant supplied to the melting zone per unit time is G, the silicon single crystal A dopant supply amount calculating step for calculating the supply amount of the dopant supplied to the melting zone when only a small amount Δx grows by the following formula (2);
GΔt (2)
The dopant segregation coefficient is k ₀ , the dopant concentration in the melt zone before solidification is Cm (x) as a function of the position x, and the melt zone solidifies while a small amount of silicon single crystal is grown by Δx. When the amount of increase in the volume of the silicon single crystal is ΔVc, the amount of dopant incorporated into the silicon single crystal after solidification when the silicon single crystal grows by a small amount Δx is expressed by the following formula (3 ) Dopant uptake amount calculation step calculated by
k ₀ Cm (x) ΔVc (3)
When the volume of the melting zone corresponding to the diameter expansion / contraction portion is Vm (x + Δx) when the silicon single crystal grows from the position x by a minute amount Δx, the silicon single crystal is only a minute amount Δx from the position x. A dopant concentration calculation step before solidification in which the concentration Cm (x + Δx) of the dopant in the melting zone before solidification when growing is calculated by the following formula (4) based on the formulas (1) to (3);

A post-solidification dopant concentration calculating step of calculating a dopant concentration C (x + Δx) in the silicon single crystal after solidification by the following formula (5);
C (x + Δx) = k ₀ Cm (x + Δx) (5)
A resistivity distribution model calculating step of calculating a resistivity distribution model of the entire silicon single crystal by sequentially calculating the dopant concentration C (x + Δx) in the solidified silicon single crystal for each minute Δx. .

凝固後のシリコン単結晶におけるドーパントの濃度Ｃ（ｘ＋Δｘ）を下記式（５）により算出する凝固後ドーパント濃度算出部と、
Ｃ（ｘ＋Δｘ）＝ｋ_０Ｃｍ（ｘ＋Δｘ）・・・（５）
凝固後のシリコン単結晶におけるドーパントの濃度Ｃ（ｘ＋Δｘ）を微少量Δｘごとに順次算出することによりシリコン単結晶全体の抵抗率分布モデルを算出する抵抗率分布モデル算出部と、
前記ドーパント供給条件変更部における前記変更条件は、前記抵抗率分布モデル算出部により算出された前記抵抗率分布モデルに基づいて、前記直胴部に対応する前記溶融帯にドーパントを供給しながら前記直胴部を形成するときにおけるドーパントの供給条件に対して、前記直径拡縮部に対応する前記溶融帯にドーパントを供給しながら前記直径拡縮部を形成するときにおけるドーパントの供給条件を変更するように、設定されることを特徴とする。 In the silicon single crystal manufacturing apparatus of the present invention, a raw material silicon material that is a raw material of a silicon single crystal is partially heated to form a melt zone, and the melt zone is solidified while supplying a dopant to the melt zone, A silicon single crystal manufacturing apparatus by an FZ method for manufacturing a silicon single crystal having a straight body portion having substantially the same diameter and a diameter expanding / contracting portion that is adjacent to the straight body portion and whose diameter is enlarged or reduced. ,
A dopant supplier for supplying dopant to the melt zone;
A dopant supply condition changing unit for controlling the dopant supply unit to change the dopant supply condition based on a predetermined change condition;
The position in the longitudinal direction of the silicon single crystal from the end opposite to the straight body portion in the diameter expansion / contraction portion is x, the width along the longitudinal direction of the silicon single crystal in the melting zone is w, and the position x When the volume of the silicon single crystal after solidification is Vc (x) as a function of, and the volume of the melting zone corresponding to the diameter expansion / contraction part is Vm (x) as a function of the position x, the position a melting zone volume calculating part for calculating a volume Vm (x) of the melting zone corresponding to the diameter expansion / contraction part in x by the following equation (1);
Vm (x) = Vc (x + w) −Vc (x) (1)
When the time required for the silicon single crystal to grow at a growth rate v by a minute amount Δx is Δt = Δx / v and the amount of dopant supplied to the melting zone per unit time is G, the silicon single crystal A dopant supply amount calculation unit that calculates the supply amount of the dopant supplied to the melting zone when the crystal grows by a minute amount Δx by the following formula (2);
GΔt (2)
The dopant segregation coefficient is k ₀ , the dopant concentration in the melt zone before solidification is Cm (x) as a function of the position x, and the melt zone solidifies while a small amount of silicon single crystal is grown by Δx. When the amount of increase in the volume of the silicon single crystal is ΔVc, the amount of dopant incorporated into the silicon single crystal after solidification when the silicon single crystal grows by a small amount Δx is expressed by the following formula (3 ) A dopant uptake amount calculation unit calculated by
k ₀ Cm (x) ΔVc (3)
When the volume of the melting zone corresponding to the diameter expansion / contraction portion is Vm (x + Δx) when the silicon single crystal grows from the position x by a minute amount Δx, the silicon single crystal is only a minute amount Δx from the position x. A dopant concentration calculation unit before solidification that calculates the concentration Cm (x + Δx) of the dopant in the melting zone before solidification when growing by the following formula (4) based on the formulas (1) to (3);

A post-solidification dopant concentration calculation unit for calculating the concentration C (x + Δx) of the dopant in the silicon single crystal after solidification by the following formula (5);
C (x + Δx) = k ₀ Cm (x + Δx) (5)
A resistivity distribution model calculation unit that calculates a resistivity distribution model of the entire silicon single crystal by sequentially calculating the concentration C (x + Δx) of the dopant in the silicon single crystal after solidification for each minute Δx;
The changing condition in the dopant supply condition changing unit is based on the resistivity distribution model calculated by the resistivity distribution model calculating unit, while supplying the dopant to the melting zone corresponding to the straight body part, To change the supply condition of the dopant when forming the diameter expansion / contraction part while supplying the dopant to the melting zone corresponding to the diameter expansion / contraction part with respect to the supply condition of the dopant when forming the body part, It is characterized by being set.

凝固後のシリコン単結晶におけるドーパントの濃度Ｃ（ｘ＋Δｘ）を下記式（５）により算出する凝固後ドーパント濃度算出工程と、
Ｃ（ｘ＋Δｘ）＝ｋ_０Ｃｍ（ｘ＋Δｘ）・・・（５）
凝固後のシリコン単結晶におけるドーパントの濃度Ｃ（ｘ＋Δｘ）を微少量Δｘごとに順次算出することによりシリコン単結晶全体の抵抗率分布モデルを算出する抵抗率分布モデル算出工程と、を備えることを特徴とする。 The method for calculating the resistivity distribution of a silicon single crystal according to the present invention uses a FZ method to partially heat a raw material silicon material that is a raw material for a silicon single crystal to form a molten zone, and supply a dopant to the molten zone. However, when the molten zone is solidified to produce a silicon single crystal having a straight body portion having substantially the same diameter and a diameter expanding / contracting portion adjacent to the straight body portion and whose diameter is enlarged or reduced. A method for calculating a resistivity distribution of a silicon single crystal used,
The position in the longitudinal direction of the silicon single crystal from the end opposite to the straight body portion in the diameter expansion / contraction portion is x, the width along the longitudinal direction of the silicon single crystal in the melting zone is w, and the position x When the volume of the silicon single crystal after solidification is Vc (x) as a function of, and the volume of the melting zone corresponding to the diameter expansion / contraction part is Vm (x) as a function of the position x, the position a melting zone volume calculating step of calculating a volume Vm (x) of the melting zone corresponding to the diameter expansion / contraction portion in x by the following formula (1);
Vm (x) = Vc (x + w) −Vc (x) (1)
When the time required for the silicon single crystal to grow at a growth rate v by a minute amount Δx is Δt = Δx / v and the amount of dopant supplied to the melting zone per unit time is G, the silicon single crystal A dopant supply amount calculating step for calculating the supply amount of the dopant supplied to the melting zone when only a small amount Δx grows by the following formula (2);
GΔt (2)
The dopant segregation coefficient is k ₀ , the dopant concentration in the melt zone before solidification is Cm (x) as a function of the position x, and the melt zone solidifies while a small amount of silicon single crystal is grown by Δx. When the amount of increase in the volume of the silicon single crystal is ΔVc, the amount of dopant incorporated into the silicon single crystal after solidification when the silicon single crystal grows by a small amount Δx is expressed by the following formula (3 ) Dopant uptake amount calculation step calculated by
k ₀ Cm (x) ΔVc (3)
When the volume of the melting zone corresponding to the diameter expansion / contraction portion is Vm (x + Δx) when the silicon single crystal grows from the position x by a minute amount Δx, the silicon single crystal is only a minute amount Δx from the position x. A dopant concentration calculation step before solidification in which the concentration Cm (x + Δx) of the dopant in the melting zone before solidification when growing is calculated by the following formula (4) based on the formulas (1) to (3);

A post-solidification dopant concentration calculating step of calculating a dopant concentration C (x + Δx) in the silicon single crystal after solidification by the following formula (5);
C (x + Δx) = k ₀ Cm (x + Δx) (5)
A resistivity distribution model calculating step of calculating a resistivity distribution model of the entire silicon single crystal by sequentially calculating a dopant concentration C (x + Δx) in the silicon single crystal after solidification for each minute Δx. And

According to the present invention, it is possible to provide a silicon single crystal manufacturing method and a silicon single crystal manufacturing apparatus that can more reliably manufacture a silicon single crystal having substantially the same resistivity distribution in the longitudinal direction of the silicon single crystal. Can do.
In addition, according to the present invention, it is possible to provide a method for calculating the resistivity distribution of a silicon single crystal used when manufacturing a silicon single crystal.

It is a side view which shows typically the silicon single crystal manufacturing apparatus 1 of this embodiment. It is a block diagram which shows the function structure of the control apparatus 8 in the silicon single crystal manufacturing apparatus 1 shown in FIG. 2 is a schematic diagram showing a width w along a longitudinal direction of a silicon single crystal 10 in a melting zone 11. FIG. It is a flowchart which shows one Embodiment of the calculation method of the resistivity distribution of the silicon single crystal of this invention. It is a flowchart which shows one Embodiment of the manufacturing method of the silicon single crystal of this invention. It is a graph which shows the analytical solution of the resistivity distribution of a silicon single crystal. It is a graph which shows the measurement data of the resistivity distribution of the conventional silicon single crystal. It is a graph which shows the relationship between an analytical solution and the model of this invention. It is a graph which shows the relationship between the case where the gas flow rate in a taper is not adjusted with an analytical solution and the model of this invention, and the gas flow rate in a taper is increased by 15% in the model of this invention. It is a graph which shows the relationship between the length of a lower taper part / tail part and the increase / decrease rate with respect to the flow volume of a straight body part for every ratio of the growth rate of a lower taper part / tail part and the growth rate of a straight body part. 4 is a graph showing measured data of resistivity distribution of a silicon single crystal in Example 1. 6 is a graph showing measured data of resistivity distribution of a silicon single crystal in Example 2. 5 is a graph showing measured data of resistivity distribution of a silicon single crystal in Comparative Example 1. 10 is a graph showing measured data of resistivity distribution of a silicon single crystal in Comparative Example 2.

  Hereinafter, an embodiment of a silicon single crystal manufacturing apparatus of the present invention will be described with reference to the drawings. In the silicon single crystal manufacturing apparatus 1 of the present embodiment, the silicon single crystal manufacturing method and the silicon single crystal resistivity distribution calculation method of the present invention are used.

  FIG. 1 is a side view schematically showing a silicon single crystal manufacturing apparatus 1 of the present embodiment. As shown in FIG. 1, the silicon single crystal manufacturing apparatus 1 partially heats a raw material silicon material 9 that is a raw material of a silicon single crystal 10 to form a melt zone 11 and supply a dopant to the melt zone 11. This is a silicon single crystal manufacturing apparatus based on the FZ method for manufacturing a silicon single crystal 10 by solidifying a molten zone 11.

  The silicon single crystal 10 has a straight body portion 10a having substantially the same diameter, and diameter expanding / contracting portions 10b and 10c that are adjacent to the straight body portion 10a and whose diameter is enlarged or reduced. “The diameters are substantially the same” means that they are the same to the extent that they can be handled as a straight body. The diameter expanding / contracting portion includes a lower tapered portion (top portion) 10b adjacent to the lower portion of the straight body portion 10a and having a diameter decreasing downward, and a tail adjacent to the upper portion of the straight body portion 10a and having a diameter decreasing upward. Part 10c. In other words, the lower taper portion 10b is a portion whose diameter increases upward from the seed crystal 12 (described later).

  As shown in FIG. 1, a silicon single crystal manufacturing apparatus 1 includes a reaction furnace 2, a raw material holder 3, an induction heating coil 4, a seed crystal holder 5, a single crystal weight holder 6, and a dopant supply unit. The gas dope apparatus 7 and the control apparatus 8 are provided.

  The reaction furnace 2 contains a raw material holder 3, an induction heating coil 4, a seed crystal holder 5, a single crystal weight holder 6, a raw material silicon material 9, a silicon single crystal 10, a melting zone 11 and a seed crystal 12, and FZ A silicon single crystal is grown by the method.

  The raw material holder 3 is a member that is accommodated in the reaction furnace 2 and holds the upper end portion of the raw material silicon material 9 that is a raw material of the silicon single crystal 10. The raw material holder 3 is attached to the upper shaft 21 located immediately above it. The upper shaft 21 is configured to be rotatable and configured to be movable in the vertical direction.

  The induction heating coil 4 is accommodated in the reaction furnace 2. The induction heating coil 4 partially heats the raw silicon material 9 to form a melting zone 11, and solidifies the melting zone 11 to grow a silicon single crystal 10. The induction heating coil 4 is a ring-shaped member that is formed mainly of copper and surrounds the outer periphery of the raw material silicon material 9.

The seed crystal holder 5 is a member that holds and fixes the seed crystal 12 and the silicon single crystal 10 formed on the seed crystal 12. The seed crystal holder 5 is attached to the lower shaft 22 located immediately below the seed crystal holder 5. The lower shaft 22 is configured to be rotatable and configured to be movable in the vertical direction.
The single crystal weight holder 6 is a member that holds the lower tapered portion 10 b in the grown silicon single crystal 10. The single crystal weight holder 6 receives most of the weight of the silicon single crystal 10 so that the weight of the silicon single crystal 10 is hardly applied to the seed crystal 12.

  The gas doping device 7 functions as a dopant supply unit that supplies a dopant gas containing a dopant to the melting zone 11. The gas dope device 7 includes a gas cylinder 71, a flow rate control valve 72, and a dope gas nozzle 73.

  The control device 8 includes a CPU (Central Processing Unit), a storage device (none of which are shown), and the like, and controls the flow rate of the dopant gas supplied from the gas cylinder 71 by controlling the flow rate control valve 72 of the gas doping device 7. I do.

The gas cylinder 71 contains a dopant gas in a high pressure state.
The flow rate control valve 72 opens and closes the valve according to the control of the dopant supply condition changing unit 112 (described later) of the control device 8 and controls the flow rate of the dopant gas supplied to the melting zone 11.
The dope gas nozzle 73 is disposed in the vicinity of the induction heating coil 4 and supplies the dopant gas whose flow rate is controlled by the flow rate control valve 72 to the melting zone 11. By supplying the dopant gas to the melting zone 11 by the dope gas nozzle 73, the dopant is taken into the melting zone 11, that is, the silicon single crystal 10.

  In such a silicon single crystal manufacturing apparatus 1, the melting zone 11 is formed by heating the lower end portion of the raw silicon material 9 by the induction heating coil 4. Then, the silicon single crystal manufacturing apparatus 1 rotates the raw material silicon material 9 and the silicon single crystal 10 in the axial direction of the upper shaft 21 and the lower shaft 22 after the fusion zone 11 is fused to the seed crystal 12. Thus, the silicon single crystal 10 is grown from the melting zone 11.

Next, a description about the details of the control unit 8. FIG. 2 is a block diagram showing a functional configuration of the control device 8 in the silicon single crystal manufacturing apparatus 1 shown in FIG. FIG. 3 is a schematic diagram showing the width w along the longitudinal direction of the silicon single crystal 10 in the melting zone 11.
The control device 8 controls the flow rate control valve 72 of the gas dope device 7. The control device 8 includes a control calculation unit 81, a control output unit (Programmable Logic Controller) 82, and a flow rate control unit (Mass Flow Controller) 83.

  The control calculation unit 81 is configured by a general-purpose computer including a CPU (Central Processing Unit) and a storage device such as a hard disk. The control calculation unit 81 calculates the flow rate of the dopant gas controlled by the flow rate control valve 72 and supplied to the melting zone 11, and outputs a signal related to the flow rate to the control output unit 82.

  The control calculation unit 81 includes a melting zone volume calculation unit 101, a dopant supply amount calculation unit 102, a dopant uptake amount calculation unit 103, a pre-solidification dopant concentration calculation unit 104, a post-solidification dopant concentration calculation unit 105, and a resistivity. A distribution model calculation unit 106, a position calculation unit 111, and a dopant supply condition change unit 112 are provided.

The melting zone volume calculation unit 101 calculates the volume Vm (x) of the melting zone 11 corresponding to the lower taper portion 10b at the position x in the longitudinal direction of the silicon single crystal 10 by the following formula (1). The “melt zone 11 corresponding to the lower taper portion 10b” refers to the melt zone 11 that becomes the lower taper portion 10b after solidification.
Vm (x) = Vc (x + w) −Vc (x) (1)

  In Formula (1), the position in the longitudinal direction of the silicon single crystal 10 from the end (lower end) opposite to the straight body 10a in the lower tapered portion 10b is defined as x (see FIG. 3). The width along the longitudinal direction of the silicon single crystal 10 in the melting zone 11 is defined as w (see FIG. 3). As a function of the position x, the volume of the silicon single crystal 10 after solidification is defined as Vc (x). As a function of the position x, the volume of the melting zone 11 corresponding to the lower taper portion 10b is defined as Vm (x).

The dopant supply amount calculation unit 102 calculates the supply amount of the dopant supplied to the melting zone 11 when the silicon single crystal 10 grows by a minute amount Δx by the following formula (2).
GΔt (2)
In equation (2), the time required for the silicon single crystal 10 to grow by a minute amount Δx at the growth rate v is Δt = Δx / v. Let G be the amount of dopant supplied to the melt zone 11 per unit time.

The dopant incorporation amount calculation unit 103 calculates the incorporation amount of the dopant incorporated into the solidified silicon single crystal 10 when the silicon single crystal 10 grows by a minute amount Δx by the following formula (3).
k ₀ Cm (x) ΔVc (3)
In formula (3), the segregation coefficient of the dopant is k ₀ . As a function of the position x, the dopant concentration in the melting zone 11 before solidification is Cm (x). Let ΔVc be the amount of increase in the volume of the silicon single crystal 10 that is increased by the solidification of the melting zone 11 while the silicon single crystal 10 grows by a small amount Δx.

式（４）において、シリコン単結晶１０が位置ｘから微少量Δｘだけ成長する際における下部テーパ部１０ｂに対応する溶融帯１１の体積をＶｍ（ｘ＋Δｘ）とする。 The pre-solidification dopant concentration calculation unit 104 calculates the dopant concentration Cm (x + Δx) in the melt zone 11 before solidification when the silicon single crystal 10 grows from the position x by a minute amount Δx, using the above formulas (1) to (3). Based on the above, it is calculated by the following formula (4).

In Equation (4), the volume of the melting zone 11 corresponding to the lower taper portion 10b when the silicon single crystal 10 grows from the position x by a minute amount Δx is Vm (x + Δx).

The post-solidification dopant concentration calculation unit 105 calculates the concentration C (x + Δx) of the dopant in the silicon single crystal 10 after solidification by the following equation (5).
C (x + Δx) = k ₀ Cm (x + Δx) (5)

  The resistivity distribution model calculation unit 106 calculates the resistivity distribution model of the entire silicon single crystal 10 by sequentially calculating the dopant concentration C (x + Δx) in the solidified silicon single crystal 10 for each minute amount Δx. That is, the resistivity distribution model is calculated based on the dopant concentration Cm (x + Δx) in the melting zone 11 before solidification and the dopant concentration C (x + Δx) in the silicon single crystal 10 after solidification. The resistivity distribution model can also be referred to as an approximate dopant concentration (resistivity) distribution of the entire crystal.

  The position calculation unit 111 determines which position in the raw material silicon material 9 is currently melted based on the position in the longitudinal direction (vertical direction) of the raw material silicon material 9 with respect to the induction heating coil 4, that is, the melting zone 11. Calculate and obtain where the position is. The position of the raw material silicon material 9 is acquired from a controller (not shown) of the apparatus main body.

  The dopant supply condition changing unit 112 controls the flow rate control valve 72 of the gas doping apparatus 7 so as to change the dopant supply condition based on a predetermined change condition. Based on the resistivity distribution model calculated by the resistivity distribution model calculating unit 106, the change condition is a dopant when the straight body portion 10a is formed while supplying the dopant to the melting zone 11 corresponding to the straight body portion 10a. The supply condition of the dopant when the lower taper portion 10b is formed while supplying the dopant to the melting zone 11 corresponding to the lower taper portion 10b is set.

The change condition is, for example, as in Example 1 to be described later, “Dopant gas supplied to the melting zone 11 corresponding to the straight body portion 10a with the flow rate of the dopant gas supplied to the melting zone 11 corresponding to the lower taper portion 10b” It is 13.8% higher than the flow rate. Further, as in Example 2 to be described later, “the flow rate of the dopant gas supplied to the melting zone 11 corresponding to the tail portion 10c is set to 40% higher than the flow rate of the dopant gas supplied to the melting zone 11 corresponding to the straight body portion 10a. % Reduction ”.
Also, the dopant supply condition changing unit 112 restores the changed supply condition of the dopant (for example, the flow rate is changed from the state of 13.8% increase or 40% decrease to the original flow rate).
The dopant supply condition changing unit 112 outputs a signal related to the change condition for changing the dopant supply condition to the control output unit 82.

The control output unit 82 generates a signal related to the flow rate based on the signal related to the change condition output from the dopant supply condition change unit 112, and outputs the signal to the flow rate control unit 83.
The flow control unit 83 controls the opening degree of the flow control valve 72 based on a signal related to the flow output from the control output unit 82.

  Next, a method for calculating the resistivity distribution of the silicon single crystal according to the present embodiment will be described with reference to FIG. The calculation method of the resistivity distribution of the silicon single crystal of the present embodiment includes a melt zone volume calculation unit 101, a dopant supply amount calculation unit 102, a dopant incorporation amount calculation unit 103, a pre-solidification dopant concentration calculation unit 104 in the control calculation unit 81, This is performed by the post-solidification dopant concentration calculation unit 105 and the resistivity distribution model calculation unit 106.

  FIG. 4 is a flowchart showing an embodiment of a method for calculating a resistivity distribution of a silicon single crystal according to the present invention. As shown in FIG. 4, the calculation method of the resistivity distribution of the silicon single crystal of the present embodiment includes a melting zone volume calculation step S1, a dopant supply amount calculation step S2, a dopant uptake amount calculation step S3, and a pre-solidification dopant. A concentration calculation step S4, a post-solidification dopant concentration calculation step S5, and a resistivity distribution model calculation step S6 are provided.

(S1) Melting Zone Volume Calculation Step The melting zone volume calculation unit 101 calculates the volume Vm (x) of the melting zone 11 corresponding to the lower taper portion 10b at the position x in the longitudinal direction of the silicon single crystal 10 according to the above equation (1). calculate.

(S2) Dopant supply amount calculation step The dopant supply amount calculation unit 102 calculates the supply amount of the dopant supplied to the melting zone 11 when the silicon single crystal 10 grows by a minute amount Δx by the above formula (2).

(S3) Dopant Uptake Amount Calculation Step The dopant uptake amount calculation unit 103 calculates the amount of dopant uptake taken into the solidified silicon single crystal 10 when the silicon single crystal 10 grows by a minute amount Δx. Calculated by

(S4) Pre-solidification dopant concentration calculation step The pre-solidification dopant concentration calculation unit 104 calculates the dopant concentration Cm (x + Δx) in the melt zone 11 before solidification when the silicon single crystal 10 grows from the position x by a minute amount Δx, Based on the equations (1) to (3), the calculation is made by the equation (4).

(S5) Post-solidification dopant concentration calculation step The post-solidification dopant concentration calculation unit 105 calculates the concentration C (x + Δx) of the dopant in the silicon single crystal 10 after solidification by the above equation (5).

(S6) Resistivity distribution model calculation step The resistivity distribution model calculation unit 106 sequentially calculates the dopant concentration C (x + Δx) in the solidified silicon single crystal 10 for each minute amount Δx, so that the silicon single crystal 10 as a whole is calculated. Calculate resistivity distribution model.

  Next, the manufacturing method of the silicon single crystal of this embodiment will be described with reference to FIG. The method for manufacturing a silicon single crystal according to the present embodiment is performed using the silicon single crystal manufacturing apparatus 1 according to the embodiment.

FIG. 5 is a flowchart showing an embodiment of the method for producing a silicon single crystal of the present invention. As shown in FIG. 5, the method for manufacturing a silicon single crystal of the present embodiment includes a lower tapered portion forming step S21 in as a diameter of about scaling unit formed Engineering, a straight body forming process S22, the tail portion forming reaction process S23 And comprising.

(S21) Lower taper portion forming step S21
Lower taper part formation process S21 is a process of forming lower taper part 10b, supplying a dopant to fusion zone 11 corresponding to lower taper part 10b. In the lower tapered portion forming step S21, the dopant supply conditions in the lower tapered portion forming step S21 are changed with respect to the dopant supplying conditions in the straight body forming step S22 based on predetermined changing conditions. Specifically, in the lower taper portion forming step S21, the dopant supply condition changing unit 112 controls the flow rate control valve 72 of the gas doping apparatus 7 so as to change the dopant supply condition based on a predetermined change condition. . For example, the dopant supply condition changing unit 112 may state that “the flow rate of the dopant gas supplied to the melting zone 11 corresponding to the lower taper portion 10b is 13 more than the flow rate of the dopant gas supplied to the melting zone 11 corresponding to the straight body portion 10a. The flow control valve 72 of the gas dope apparatus 7 is controlled so as to increase .8% ”.

(S22) Straight body part forming step S22
The straight body portion forming step S22 is a step performed after the lower tapered portion forming step S21, and is a step of forming the straight body portion 10a while supplying a dopant to the melting zone 11 corresponding to the straight body portion 10a. For example, the dopant supply condition changing unit 112 “corresponds to the straight body portion 10a from the flow rate (13.8% increase) of the dopant gas supplied to the melting zone 11 corresponding to the lower taper portion 10b. The flow rate control valve 72 of the gas dope apparatus 7 is controlled so as to be the same as the flow rate of the dopant gas supplied to the melting zone 11 (original flow rate).

(S23) Tail portion forming step S23
The tail portion forming step S23 is a step performed after the straight body portion forming step S22, and is a step of forming the tail portion 10c while supplying the dopant to the melting zone 11 corresponding to the tail portion 10c.

  Next, when forming the straight body portion 10a while supplying the dopant to the melt zone 11 corresponding to the straight body portion 10a, the lower taper portion 10b while supplying the dopant to the melt zone corresponding to the lower taper portion 10b. When forming the silicon single crystal, it is possible to more reliably manufacture a silicon single crystal having substantially the same resistivity distribution in the longitudinal direction of the silicon single crystal 10 by changing the supply condition of the dopant to the melting zone 11. We will explain the background of the findings.

  FIG. 6 is a graph showing an analytical solution of resistivity distribution of a silicon single crystal. FIG. 7 is a graph showing measured data of resistivity distribution of a conventional silicon single crystal. FIG. 8 is a graph showing the relationship between the analytical solution and the model of the present invention. FIG. 9 is a graph showing the relationship between the analytical solution and the case where the gas flow rate during the taper is not adjusted in the model of the present invention and the case where the gas flow rate during the taper is increased by 15% in the model of the present invention. FIG. 10 is a graph showing the relationship between the length of the lower taper portion / tail portion and the rate of increase / decrease with respect to the flow rate of the straight body portion for each ratio of the growth rate of the lower taper portion / tail portion and the growth rate of the straight body portion. is there.

If a certain amount of dopant is supplied per unit time during the growth of a silicon single crystal produced by the FZ method, as shown in FIG. 6, after the crystal length exceeds a certain value, the dopant in the crystal The concentration (that is, resistivity distribution) is substantially the same. In FIG. 6, “standardized resistivity” is obtained by dividing the overall distribution by the target resistivity in the straight body portion so that the value in the straight body portion is 1.
For example, if phosphorus (P) has a segregation coefficient of 0.35, the resistivity distribution becomes constant (substantially the same) after the crystal length becomes about 400 mm (see the one-dot chain line shown in FIG. 6). ). However, this result shown in FIG. 6 is derived from an analytical solution that always treats the diameter of the material and the diameter of the crystal as the same.

When a silicon single crystal is actually grown by the FZ method, the dopant gas starts to be supplied from the lower taper portion in which the diameter (volume increase rate) changes (expands).
The lower taper portion was predicted to deviate from the resistivity distribution shown in FIG. 6, but the flow rate suitable for the straight body portion having a large volume from the lower taper portion stage (stage where the crystal length is 20 mm). If the dopant gas is supplied, the concentration of the dopant in the straight body portion is considered to be within the prescribed range. For example, in a crystal having a large diameter such as a diameter of 150 mm or 200 mm, the length of the lower taper portion becomes longer, so that the influence of the lower taper portion is considered to be negligible.

However, in practice, as shown in FIG. 7, the resistivity is the target value between the lower end of the straight body part (position where the crystal length is 500 mm) and about 100 mm (position where the crystal length is about 600 mm). A phenomenon that is higher than that (shown by a thick broken line in FIG. 6) was observed. In FIG. 7 , the white circle plots show the measured values of resistivity for four crystals. Assuming that the resistivity tolerance range is about ± 5% of the target value (that is, the normalized resistivity is about 0.95 to 1.05), the resistance is about 100 mm from the lower end of the straight body portion. It can be seen that most of the measured values of the rate are out of the acceptable range.

  In the model in which the diameters of the crystals shown in FIG. 6 are substantially the same, the resistivity should settle down (stabilize) if the crystal growth progresses by about 400 mm, but actually the behavior is different. Yes. The reason is that, in the lower taper part where the crystal diameter (volume increase rate) changes, the dopant incorporation is different from the dopant incorporation in the straight body part, and this difference is the lower taper part in the straight body part. This is presumably because it affects the dopant concentration (that is, resistivity) in the region adjacent to the portion.

式（６）において、結晶のドーパントの濃度をＣ（ｘ）とする。素材のドーパントの濃度をＣ_０とする。ドーパントごとの偏析係数をｋ_０とする。シリコン単結晶の長手方向の位置をｘとする。溶融帯の幅をｗとする。なお、位置ｘは、直胴部１０ａにおける下端部を０とした座標値として設定されている。 When the material and the crystal do not change with the same diameter, the material and the crystal can be handled as one dimension in which only the length changes. Therefore, the dopant concentration C (x) is an analytical solution represented by the well-known equation (6) below. Can be represented.

In the formula (6), the concentration of dopant bets crystals C (x). The concentration of the dopant material to _{C 0.} The segregation coefficient of each dopant and k _0. Let x be the position in the longitudinal direction of the silicon single crystal. Let the width of the melting zone be w. The position x is set as a coordinate value with the lower end portion of the straight body portion 10a being 0.

The graph shown in FIG. 6 shows the analytical solution shown in Equation (6) converted into resistivity. If the change in the volume (diameter) of the crystal is taken into consideration, it is necessary to expand the dimension of the model, so that it cannot be solved analytically. The present inventor has found that this is the reason why the behavior of the dopant concentration distribution in the lower tapered portion has been unknown so far.
On the other hand, the present inventor tried to numerically solve the behavior of the dopant concentration distribution in the lower taper portion, and derived the above-described resistivity distribution model.

In addition, it was verified as shown in FIG. 8 that there is no defect in the resistivity distribution model. That is, using the resistivity distribution model, a situation where there is an analytical solution shown in FIG. 6 (a situation where there is no change in diameter) was calculated. Here, the width w of the melting zone is set to 40 mm, and the segregation coefficient k ₀ = 0.35 (phosphorus). The analytical solution indicated by the solid line and the resistivity distribution model indicated by the white circle plot agree very well, and it can be confirmed that there is no defect in the resistivity distribution model.

  Next, the relationship between the analytical solution and the resistivity distribution model when there is a change in diameter will be described with reference to FIG. In FIG. 9, the resistivity distribution derived by the analytical solution that does not take into account the change in volume is indicated by a one-dot chain line. In addition, when the dopant supply conditions are not changed (the flow rate is not adjusted), the resistivity distribution derived by the resistivity distribution model is indicated by a solid line. In addition, the resistivity distribution derived by the resistivity distribution model when the dopant gas flow rate is changed to 15% increase is indicated by a broken line. The shape of the lower taper portion was virtually a triangular pyramid with a height of 500 mm, and the growth rate of the lower taper portion was assumed to be 1.25 times the growth rate of the straight body portion.

  As shown by a one-dot chain line, a solid line, and a broken line in FIG. 9, immediately after the start of supply of the dopant (dopant gas), the resistivity rapidly decreases, but gradually increases as the volume of the molten zone increases. Under this condition, since the growth rate of the lower taper portion is faster than the growth rate of the straight body portion, the volume of the molten zone increases rapidly with respect to the supply amount of the dopant gas, and exceeds the target value of resistivity ( Overshoot). As is clear from this result, the resistivity distribution derived by the resistivity distribution model is completely different from the analytical solution that does not consider the change in volume.

In the analytical solution indicated by the one-dot chain line, the expression of overshoot is not shown. On the other hand, in the resistivity distribution derived by the resistivity distribution model in the case where the dopant supply conditions are not changed as indicated by the solid line, the occurrence of overshoot is shown.
That is, when the dopant supply conditions are not changed, the resistivity is between the lower end portion of the straight body portion (position where the crystal length is 500 mm) and about 200 mm (where the crystal length is about 700 mm). This is higher than the target value (normalized resistivity is 1) and is outside the acceptable range standard (about 0.95 to 1.05).
On the other hand, in the resistivity distribution derived from the resistivity distribution model when the flow rate of the dopant gas is changed to 15% increase, which is indicated by a broken line in FIG. The resistivity almost coincides with the target value over the entire area in the longitudinal direction of the straight body part from the position where the crystal length is 500 mm, and does not deviate from the acceptable range.

  From these considerations, when forming the straight body portion while supplying the dopant to the melt zone corresponding to the straight body portion, and when forming the diameter expansion portion while supplying the dopant to the melt zone corresponding to the diameter expansion portion By changing the dopant supply conditions, it is possible to obtain a silicon single crystal having substantially the same resistivity distribution in the longitudinal direction of the straight body, and the dopant supply conditions based on the resistivity distribution model. It can be seen that this effect can be obtained more reliably by making appropriate changes. As a result of examining this model in detail, when it is assumed that the shape of the lower taper portion or tail portion is a triangular pyramid, the optimum value of the increase / decrease rate (change amount) of the dopant supply condition is the lower taper portion or tail portion. It was found that it was determined by the length of the portion and the growth rate ratio between the lower tapered portion or the tail portion and the straight body portion. This optimal value distribution is shown in FIG.

According to the silicon single crystal manufacturing apparatus 1, the silicon single crystal manufacturing method, and the silicon single crystal resistivity distribution calculating method according to the present embodiment, for example, the following effects can be obtained.
In the method for manufacturing a silicon single crystal according to the present embodiment, in the lower taper portion forming step S21, the lower taper portion forming step S21 is performed with respect to the dopant supply conditions in the straight body portion forming step S22 based on predetermined change conditions. The dopant supply conditions are changed (for example, the dopant gas flow rate is increased by 15%). Therefore, by appropriately setting the change condition, in the region adjacent to the lower taper portion 10b in the straight body portion 10a, over the entire area in the longitudinal direction of the straight body portion 10a including the region adjacent to the lower taper portion 10b, A silicon single crystal having substantially the same resistivity distribution in the longitudinal direction of the straight body portion 10a can be obtained.

  In the method for producing a silicon single crystal according to the present embodiment, the changing conditions are the dopant concentration Cm (x + Δx) in the melting zone before solidification and the dopant concentration C (x + Δx) in the silicon single crystal after solidification. Are set on the basis of a resistivity distribution model calculated based on. Therefore, it is possible to easily set an appropriate change condition.

  Moreover, according to the method for calculating the resistivity distribution of the silicon single crystal of the present embodiment, the resistivity distribution model can be easily calculated.

The embodiments of the silicon single crystal manufacturing apparatus, the silicon single crystal manufacturing method, and the silicon single crystal resistivity distribution calculating method of the present invention have been described above. However, the present invention is not limited to the above-described embodiments. Absent.
In the above-described embodiment, the supply condition of the dopant is the flow rate of the dopant gas containing the dopant, but is not limited thereto. For example, the supply condition of the dopant may be the concentration of the dopant in the dopant gas, or may be both the flow rate of the dopant gas containing the dopant and the concentration of the dopant in the dopant gas.
In the above-described embodiment, the supply condition of the dopant is changed between the lower taper portion 10b and the straight body portion 10a as the diameter expanding / contracting portion, but is not limited thereto. The supply condition of the dopant may be changed between the tail portion 10c as the diameter expanding / contracting portion and the straight body portion 10a. That is, the description regarding the lower taper part 10b mentioned above can be applied also to the tail part 10c.

  EXAMPLES Hereinafter, although an Example demonstrates this invention further in detail, this invention is not limited to these. FIG. 11 is a graph showing measured data of the resistivity distribution of the silicon single crystal in Example 1. FIG. 12 is a graph showing measured data of resistivity distribution of a silicon single crystal in Example 2. FIG. 13 is a graph showing measured data of resistivity distribution of a silicon single crystal in Comparative Example 1. FIG. 14 is a graph showing measured data of resistivity distribution of a silicon single crystal in Comparative Example 2.

[Example 1]
Example 1 is an example in which a silicon single crystal having a diameter of a straight body part of 205 mm is manufactured by the FZ method. In Example 1, based on the resistivity distribution model, the lower taper portion corresponds to the flow rate of the dopant gas when the straight body portion is formed while supplying the dopant to the melting zone corresponding to the straight body portion. The flow rate of the dopant gas when the lower taper portion is formed while supplying the dopant to the melting zone is changed to 13.8% increase. This change condition of “13.8% increase” was mainly set by the shape of the lower taper portion, the ratio of the growth rate of the lower taper portion and the straight body portion, and the like.

This will be described in more detail with reference to FIG. In FIG. 11, the white circle plots show the measured values of resistivity for three crystals when the flow rate of the dopant gas is changed to 13.8% increase. Similarly to FIG. 9, also in FIG. 11, the resistivity distribution derived by the resistivity distribution model when the dopant supply conditions are not changed is shown by a solid line. In addition, the resistivity distribution derived by the resistivity distribution model when the dopant gas flow rate is changed to 13.8% increase is indicated by a broken line.
11 and 13, the position of the lower end portion of the straight body portion was “crystal length = 0 mm”.

By the FZ method, _three silicon single crystals having a diameter of 205 mm were manufactured while flowing PH ₃ gas as a dopant gas so that the normalized resistivity in the straight body portion was 1.
Here, when the calculation was performed using the resistivity distribution model in consideration of the growth rate of the lower taper portion and the shape of the lower taper portion (particularly the length of the lower taper portion), the melting zone corresponding to the straight body portion was calculated. In the lower taper portion, the dopant gas flow rate is increased by 13.8% with respect to the dopant gas flow rate to the lower end portion of the straight body portion (adjacent to the lower taper portion and the straight body portion starts. It was estimated that the resistivity distribution can be flattened from (part). Accordingly, the flow rate of the dopant gas was set to “13.8% increase”.

  In the melting zone corresponding to the lower taper portion (up to the lower end of the straight body portion), the dopant gas is supplied to the melting zone at an increase of 13.8% with respect to the flow rate of the dopant gas in the melting zone corresponding to the straight body portion, Immediately after reaching the lower end of the straight body, the flow rate of the dopant gas was returned. As a result, as shown in FIG. 11, the resistivity distribution of the three crystals became flat over the entire area of the straight body, and no defective portion was generated.

[Example 2]
Example 2 is an example in which a silicon single crystal having a diameter of the straight body portion of 155 mm is manufactured by the FZ method. In Example 2, based on the resistivity distribution model, the melt corresponding to the tail portion is formed with respect to the flow rate of the dopant gas when the straight body portion is formed while supplying the dopant to the melt zone corresponding to the straight body portion. The dopant gas flow rate when the tail portion is formed while supplying the dopant to the belt is changed to 40%. The change condition of “40% reduction” was set mainly by the shape of the tail part, the ratio of the growth rate of the tail part and the straight body part, and the like.

This will be described in more detail with reference to FIG. In FIG. 12, the white circle plots show the measured values of resistivity for three crystals when the flow rate of the dopant gas is changed to 40% reduction. Similarly to FIG. 9, also in FIG. 12, the resistivity distribution derived by the resistivity distribution model when the dopant supply conditions are not changed is indicated by a solid line. In addition, the resistivity distribution derived by the resistivity distribution model when the dopant gas flow rate is changed to 40% reduction is indicated by a broken line.
12 and 14, the position of the upper end portion of the straight body portion was “crystal length = 0 mm”.

By the FZ method, _three silicon single crystals having a diameter of 155 mm were manufactured while flowing PH ₃ gas as a dopant gas so that the normalized resistivity in the straight body portion was 1. After obtaining the straight body portion of the target length, the diameter was reduced to create a tail portion having a length of 140 mm.
Here, when the calculation was performed using the resistivity distribution model in consideration of the growth rate of the tail portion and the shape of the tail portion (particularly the length of the tail portion), the dopant to the molten zone corresponding to the straight body portion was calculated. By reducing the dopant gas flow rate by 40% in the tail portion relative to the gas flow rate, the resistivity distribution is increased to the upper end portion of the straight barrel portion (the portion adjacent to the tail portion and ending the straight barrel portion). It was estimated that it could be flat. Accordingly, the flow rate of the dopant gas was set to “40% reduction”.

  Immediately after reaching the melt zone corresponding to the tail portion (up to the upper end of the straight barrel portion) from the melt zone corresponding to the straight barrel portion, the flow rate of the dopant gas in the melt zone corresponding to the straight barrel portion is 40%. The dopant gas was supplied to the melting zone. As a result, as shown in FIG. 12, the resistivity distribution of the three crystals became flat over the entire area of the straight body, and no defective portion was generated.

[Comparative Example 1]
From the melting zone corresponding to the lower taper portion to the melting zone corresponding to the straight body portion, under the same conditions as the melting zone corresponding to the straight body portion in Example 1 (without changing the flow rate of the dopant gas), the dopant Gas was fed to the melting zone. The other conditions are the same as in the example.
In FIG. 13, the white circle plots show the measured values of resistivity for three crystals when the flow rate of the dopant gas is not changed. Similarly to FIG. 11, also in FIG. 13, the resistivity distribution derived by the resistivity distribution model when the dopant supply conditions are not changed is shown by a solid line.
When the resistivity of this crystal was measured by the four-probe method, a portion where the resistivity was higher than the target value (normalized resistivity was 1) was formed from the lower end of the straight body portion to a position of about 200 mm. In particular, in the first 100 mm portion, the deviation from the target value was large, and it became a defective part and could not be used as a product.

[Comparative Example 2]
From the melting zone corresponding to the tail portion to the melting zone corresponding to the straight body portion, under the same conditions as the melting zone corresponding to the straight body portion in Example 2 (without changing the flow rate of the dopant gas), the dopant gas Was fed to the melting zone. The other conditions are the same as in the example.
In FIG. 14, the white circle plots show the measured values of the resistivity for three crystals when the flow rate of the dopant gas is not changed. Similarly to FIG. 12, also in FIG. 14, the resistivity distribution derived by the resistivity distribution model when the dopant supply conditions are not changed is indicated by a solid line.
When the resistivity of this crystal was measured by a four-probe method, it deviated from the target value of resistivity (standardized resistivity is 1) from the upper end (0 mm) of the straight body part to a position of about 40 mm downward. However, the maximum was about 20%, which was a defective part and could not be used as a product.

DESCRIPTION OF SYMBOLS 1 Silicon single crystal production apparatus 2 Reactor 3 Raw material holder 4 Induction heating coil 5 Seed crystal holder 6 Single crystal weight holder 7 Gas dope apparatus (dopant supply part)
8 Controller 9 Raw material silicon material 10 Silicon single crystal 10a Straight body portion 10b Lower taper portion (diameter expansion / contraction portion)
10c Tail part (diameter expansion / contraction part)
DESCRIPTION OF SYMBOLS 11 Melt zone 12 Seed crystal 101 Melt zone volume calculation part 102 Dopant supply amount calculation part 103 Dopant intake amount calculation part 104 Pre-solidification dopant concentration calculation part 105 Post-solidification dopant density calculation part 106 Resistivity distribution model calculation part 111 Position calculation part 112 Dopant supply condition change section

Claims (4)

A straight cylinder whose diameter is substantially the same by partially heating a raw material silicon material which is a raw material of a silicon single crystal to form a molten zone and solidifying the molten zone while supplying a dopant to the molten zone A silicon single crystal by an FZ method for manufacturing a silicon single crystal having a portion and a diameter expanding / contracting portion adjacent to the straight body portion and having a diameter expanding or contracting, and a region adjacent to the diameter expanding / contracting portion A method for producing a silicon single crystal that obtains a silicon single crystal having substantially the same resistivity distribution in the longitudinal direction of the straight body part over the entire longitudinal direction of the straight body part ,
A straight body part forming step of forming the straight body part while supplying a dopant to the melt zone corresponding to the straight body part;
Before and / or after the straight body portion forming step, and a diameter expanding / contracting portion forming step of forming the diameter expanding / contracting portion while supplying a dopant to the melting zone corresponding to the diameter expanding / contracting portion, and
In the diameter expanding / contracting part forming step, based on a predetermined changing condition, the dopant supply condition in the diameter expanding / contracting part forming step is changed with respect to the dopant supplying condition in the straight body forming step ,
The change condition is based on a resistivity distribution model calculated based on the dopant concentration Cm (x + Δx) in the melting zone before solidification and the dopant concentration C (x + Δx) in the silicon single crystal after solidification. , Set,
As a step of calculating the resistivity distribution model,
The position in the longitudinal direction of the silicon single crystal from the end opposite to the straight body portion in the diameter expansion / contraction portion is x, the width along the longitudinal direction of the silicon single crystal in the melting zone is w, and the position x When the volume of the silicon single crystal after solidification is Vc (x) as a function of, and the volume of the melting zone corresponding to the diameter expansion / contraction part is Vm (x) as a function of the position x, the position a melting zone volume calculating step of calculating a volume Vm (x) of the melting zone corresponding to the diameter expansion / contraction portion in x by the following formula (1);
Vm (x) = Vc (x + w) −Vc (x) (1)
When the time required for the silicon single crystal to grow at a growth rate v by a minute amount Δx is Δt = Δx / v and the amount of dopant supplied to the melting zone per unit time is G, the silicon single crystal A dopant supply amount calculating step for calculating the supply amount of the dopant supplied to the melting zone when only a small amount Δx grows by the following formula (2);
GΔt (2)
The dopant segregation coefficient is k ₀ , the dopant concentration in the melt zone before solidification is Cm (x) as a function of the position x, and the melt zone solidifies while a small amount of silicon single crystal is grown by Δx. When the amount of increase in the volume of the silicon single crystal is ΔVc, the amount of dopant incorporated into the silicon single crystal after solidification when the silicon single crystal grows by a small amount Δx is expressed by the following formula (3 ) Dopant uptake amount calculation step calculated by
k ₀ Cm (x) ΔVc (3)
When the volume of the melting zone corresponding to the diameter expansion / contraction portion is Vm (x + Δx) when the silicon single crystal grows from the position x by a minute amount Δx, the silicon single crystal is only a minute amount Δx from the position x. A dopant concentration calculation step before solidification in which the concentration Cm (x + Δx) of the dopant in the melting zone before solidification when growing is calculated by the following formula (4) based on the formulas (1) to (3);

A post-solidification dopant concentration calculating step of calculating a dopant concentration C (x + Δx) in the silicon single crystal after solidification by the following formula (5);
C (x + Δx) = k ₀ Cm (x + Δx) (5)
A resistivity distribution model calculating step of calculating a resistivity distribution model of the entire silicon single crystal by sequentially calculating the concentration C (x + Δx) of the dopant in the silicon single crystal after solidification for each minute Δx;
A method for producing a silicon single crystal, comprising: 2. The method for producing a silicon single crystal according to claim 1, wherein the supply condition of the dopant is a flow rate of a dopant gas containing a dopant and / or a concentration of the dopant in the dopant gas. A straight cylinder whose diameter is substantially the same by partially heating a raw material silicon material which is a raw material of a silicon single crystal to form a molten zone and solidifying the molten zone while supplying a dopant to the molten zone And a silicon single crystal manufacturing apparatus using the FZ method for manufacturing a silicon single crystal having a diameter expanding / contracting part adjacent to the straight body part and having a diameter expanding or decreasing , including a region adjacent to the diameter expanding / contracting part A silicon single crystal manufacturing apparatus for obtaining a silicon single crystal having substantially the same resistivity distribution in the longitudinal direction of the straight body portion over the entire length direction of the straight body portion ,
A dopant supplier for supplying dopant to the melt zone;
A dopant supply condition changing unit for controlling the dopant supply unit to change the dopant supply condition based on a predetermined change condition;
The position in the longitudinal direction of the silicon single crystal from the end opposite to the straight body portion in the diameter expansion / contraction portion is x, the width along the longitudinal direction of the silicon single crystal in the melting zone is w, and the position x When the volume of the silicon single crystal after solidification is Vc (x) as a function of, and the volume of the melting zone corresponding to the diameter expansion / contraction part is Vm (x) as a function of the position x, the position a melting zone volume calculating part for calculating a volume Vm (x) of the melting zone corresponding to the diameter expansion / contraction part in x by the following equation (1);
Vm (x) = Vc (x + w) −Vc (x) (1)
When the time required for the silicon single crystal to grow at a growth rate v by a minute amount Δx is Δt = Δx / v and the amount of dopant supplied to the melting zone per unit time is G, the silicon single crystal A dopant supply amount calculation unit that calculates the supply amount of the dopant supplied to the melting zone when the crystal grows by a minute amount Δx by the following formula (2);
GΔt (2)
The dopant segregation coefficient is k ₀ , the dopant concentration in the melt zone before solidification is Cm (x) as a function of the position x, and the melt zone solidifies while a small amount of silicon single crystal is grown by Δx. When the amount of increase in the volume of the silicon single crystal is ΔVc, the amount of dopant incorporated into the silicon single crystal after solidification when the silicon single crystal grows by a small amount Δx is expressed by the following formula (3 ) A dopant uptake amount calculation unit calculated by
k ₀ Cm (x) ΔVc (3)
When the volume of the melting zone corresponding to the diameter expansion / contraction portion is Vm (x + Δx) when the silicon single crystal grows from the position x by a minute amount Δx, the silicon single crystal is only a minute amount Δx from the position x. A dopant concentration calculation unit before solidification that calculates the concentration Cm (x + Δx) of the dopant in the melting zone before solidification when growing by the following formula (4) based on the formulas (1) to (3);

A post-solidification dopant concentration calculation unit for calculating the concentration C (x + Δx) of the dopant in the silicon single crystal after solidification by the following formula (5);
C (x + Δx) = k ₀ Cm (x + Δx) (5)
A resistivity distribution model calculation unit that calculates a resistivity distribution model of the entire silicon single crystal by sequentially calculating the concentration C (x + Δx) of the dopant in the silicon single crystal after solidification for each minute Δx;
The changing condition in the dopant supply condition changing unit is based on the resistivity distribution model calculated by the resistivity distribution model calculating unit, while supplying the dopant to the melting zone corresponding to the straight body part, To change the supply condition of the dopant when forming the diameter expansion / contraction part while supplying the dopant to the melting zone corresponding to the diameter expansion / contraction part with respect to the supply condition of the dopant when forming the body part, A silicon single crystal manufacturing apparatus characterized by being set. By the FZ method, a raw material silicon material that is a raw material for a silicon single crystal is partially heated to form a melt zone, and the melt zone is solidified while supplying a dopant to the melt zone, so that the diameter is substantially the same. Is a method of calculating the resistivity distribution of a silicon single crystal that is used when manufacturing a silicon single crystal having a straight body portion and a diameter expanding / contracting portion that is adjacent to the straight body portion and whose diameter is enlarged or reduced , The resistance of a silicon single crystal that obtains a silicon single crystal having substantially the same resistivity distribution in the longitudinal direction of the straight body portion over the entire length direction of the straight body portion including a region adjacent to the diameter expanding / contracting portion A rate distribution calculation method ,
The position in the longitudinal direction of the silicon single crystal from the end opposite to the straight body portion in the diameter expansion / contraction portion is x, the width along the longitudinal direction of the silicon single crystal in the melting zone is w, and the position x When the volume of the silicon single crystal after solidification is Vc (x) as a function of, and the volume of the melting zone corresponding to the diameter expansion / contraction part is Vm (x) as a function of the position x, the position a melting zone volume calculating step of calculating a volume Vm (x) of the melting zone corresponding to the diameter expansion / contraction portion in x by the following formula (1);
Vm (x) = Vc (x + w) −Vc (x) (1)
When the time required for the silicon single crystal to grow at a growth rate v by a minute amount Δx is Δt = Δx / v and the amount of dopant supplied to the melting zone per unit time is G, the silicon single crystal A dopant supply amount calculating step for calculating the supply amount of the dopant supplied to the melting zone when only a small amount Δx grows by the following formula (2);
GΔt (2)
The dopant segregation coefficient is k ₀ , the dopant concentration in the melt zone before solidification is Cm (x) as a function of the position x, and the melt zone solidifies while a small amount of silicon single crystal is grown by Δx. When the amount of increase in the volume of the silicon single crystal is ΔVc, the amount of dopant incorporated into the silicon single crystal after solidification when the silicon single crystal grows by a small amount Δx is expressed by the following formula (3 ) Dopant uptake amount calculation step calculated by
k ₀ Cm (x) ΔVc (3)
When the volume of the melting zone corresponding to the diameter expansion / contraction portion is Vm (x + Δx) when the silicon single crystal grows from the position x by a minute amount Δx, the silicon single crystal is only a minute amount Δx from the position x. A dopant concentration calculation step before solidification in which the concentration Cm (x + Δx) of the dopant in the melting zone before solidification when growing is calculated by the following formula (4) based on the formulas (1) to (3);

A post-solidification dopant concentration calculating step of calculating a dopant concentration C (x + Δx) in the silicon single crystal after solidification by the following formula (5);
C (x + Δx) = k ₀ Cm (x + Δx) (5)
A resistivity distribution model calculating step of calculating a resistivity distribution model of the entire silicon single crystal by sequentially calculating a dopant concentration C (x + Δx) in the silicon single crystal after solidification for each minute Δx. A calculation method of resistivity distribution of a silicon single crystal.

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