JP7582070B2 - Method for predicting thermal donor behavior in silicon wafer and method for manufacturing silicon wafer - Google Patents

Description

The present invention relates to a method for predicting thermal donor behavior in a silicon wafer and a method for manufacturing a silicon wafer.

Silicon wafers are widely used as semiconductor substrates in the fabrication of various semiconductor devices, such as RF (radio frequency) devices, MOS devices, DRAMs, and NAND flash memories. In the device process, which is the process of fabricating semiconductor devices using silicon wafers, various heat treatments such as oxidation and nitridation, plasma etching, and impurity diffusion are carried out.

The oxygen in a silicon wafer is normally electrically neutral, but when the silicon wafer undergoes a relatively low-temperature heat treatment below about 600°C (hereafter referred to as "low-temperature heat treatment"), it is known that several to a dozen oxygen atoms gather together to form oxygen clusters in the silicon crystal. These oxygen clusters are donors that emit electrons, and are called thermal donors. Thermal donors become electrically neutral when subjected to high-temperature heat treatment of about 650°C or higher, and such high-temperature heat treatment is called donor killer heat treatment (donor killer annealing).

The carrier concentration of the silicon wafer changes due to the generation of thermal donors, and as a result, the resistivity of the silicon wafer changes before and after the low-temperature heat treatment in the device process. For example, if the silicon wafer is a high-resistivity p-type wafer, it can be inverted to an n-type wafer depending on the amount of thermal donors generated.

Such changes in the resistivity of silicon wafers can have a significant effect on the device characteristics of semiconductor devices. Research has been conducted into the mechanism of thermal donor generation after low-temperature heat treatment of silicon single crystals, and various methods have been considered to accurately predict the thermal donor concentration in silicon wafers.

In Patent Document 1, the amount of carriers generated Δ[C] due to oxygen donors generated when a silicon single crystal is subjected to a low-temperature heat treatment is proposed to be expressed by the following formula A, which uses the oxygen concentration [Oi] in the silicon single crystal, the heat treatment temperature T, the heat treatment time t, and the diffusion coefficient D(T) of oxygen at the heat treatment temperature T.
Δ[C]=α[Oi]5×exp(-β・D(T)・[Oi]・t) ...(Formula A)
(In the above formula A, α and β are constants.)

According to Patent Document 1, the method is versatile and is capable of evaluating the amount of carriers generated in silicon single crystals with higher accuracy than conventional methods.

JP 2013-119486 A

However, predictions of thermal donor behavior have been limited to predictions of thermal donor behavior when heat treatment is performed for a long period of time, for example, several tens of hours, at low temperatures of less than about 600°C. Therefore, the formula (Formula A) disclosed in Patent Document 1 cannot explain the behavior of thermal donors when the heat treatment time is short.

The present invention aims to provide a method for predicting the amount of thermal donors generated and a manufacturing method that can be applied especially when the heat treatment time is short.

After examining the relationship between the heat treatment temperature, heat treatment time, and the amount of thermal donor generated under various conditions, the inventors found that there is a negative correlation between the heat treatment time and the heat treatment temperature at which the amount of thermal donor generated is maximum for that heat treatment time. They also found that this correlation can be used to accurately predict the behavior of thermal donor generation. The gist of the present invention, which was completed based on the above findings, is as follows.

<1> A method for predicting thermal donor behavior in a silicon wafer, comprising:
The relationship between the heat treatment time and the heat treatment temperature at which the amount of thermal donor generated is maximized during the heat treatment time is negatively correlated.
A method for predicting thermal donor behavior in silicon wafers.

<2> The negative correlation is expressed by the following formula (1):
[T _m ]=-at+b...(1)
(In formula (1), [T _m ] is the heat treatment temperature at which the amount of thermal donor generated is maximized, t is the heat treatment time, and a and b are non-negative constants.)
The method for predicting thermal donor behavior in a silicon wafer according to any one of <1>, wherein the thermal donor behavior is expressed by the following relational expression:

<3> The amount of the thermal donor generated is expressed by the following formula (2):
[T _D ]=A×[O _i ] ^B ×t ^C ×exp{-(T-T _m ) ² /(2T ₀ ² )} ...(2)
(In formula (2), [T _D ] is the amount of thermal donor generated, T is the heat treatment temperature, [O _i ] is the oxygen concentration, and T ₀ , A, B, and C are constants.)
The method for predicting thermal donor behavior in a silicon wafer according to <1> or <2>, wherein the thermal donor behavior is represented by the following relational expression:

<4> A method for predicting thermal donor behavior in a silicon wafer described in any one of <1> to <3>, wherein the heat treatment time is 10 hours or less.

<5> The method for predicting behavior of thermal donors in a silicon wafer according to any one of <1> to <4>, wherein the oxygen concentration of the silicon wafer is 1×10 ¹⁷ atoms/cm ³ or more and 7×10 ¹⁷ atoms/cm ³ or less (ASTM F121-1979).

<6> A method for evaluating a silicon wafer using the method for predicting thermal donor behavior of a silicon wafer according to any one of <1> to <5> above,
determining the amount of thermal donors generated in the silicon wafer after the heat treatment;
determining a predicted resistivity of the silicon wafer after the heat treatment based on the amount of thermal donor generated;
A method for evaluating a silicon wafer, comprising:

<7> A method for producing a silicon wafer, comprising:
determining heat treatment conditions in a device process performed on the silicon wafer;
A step of determining a predicted resistivity of the silicon wafer after a heat treatment according to a heat treatment condition in the device process by using the silicon wafer evaluation method according to the item 6.
designing a target value of the oxygen concentration or resistivity of the silicon wafer before being subjected to the device process based on the predicted resistivity;
A method for producing a silicon wafer, comprising:

The present invention provides a method for predicting the amount of thermal donor generated and a manufacturing method that can be applied even when the heat treatment time is short.

1 is a graph showing a plot of thermal donor concentration when a silicon wafer having an oxygen concentration [ _Oi ] of 6× ¹⁰ atoms/ ^cm3 is subjected to heat treatment at 430° C. or higher and 530° C. or lower for 30 minutes or longer and 300 minutes or shorter, and a relationship between the heat treatment temperature and heat treatment time at which the amount of thermal donor generated is maximized. 1 is a graph showing a plot of thermal donor concentration when a silicon wafer having an oxygen concentration [ _Oi ] of 4 x ¹⁰¹⁷ atoms/ ^cm3 is subjected to heat treatment at 430°C or higher and 530°C or lower for 30 minutes or longer and 300 minutes or shorter, and showing the relationship between the heat treatment temperature and heat treatment time at which the amount of thermal donor generated is maximized. 1 is a plot showing the relationship between the heat treatment temperature and the heat treatment time at which the amount of thermal donor generated is maximized in Experiments 1 and 2, and a graph showing the reproducibility based on predicted values using calculation formula (1). 1 is a graph showing the reproducibility of the amount of thermal donor generated based on the predicted value using calculation formula (2) in experiment 1. 13 is a graph showing the reproducibility of the amount of thermal donor generated based on the predicted value using calculation formula (2) in experiment 2. 1 is a graph confirming the reproducibility of the amount of thermal donor generated based on the predicted value using the conventional technology (Formula A) in a comparative example.

Before describing the embodiments, the inventors will explain the experiments that led to the present invention. In order to confirm the reproducibility of the method for predicting thermal donor behavior in silicon wafers, the inventors confirmed experimental values of the amount of thermal donors generated when low-temperature heat treatment was performed for a short period of time. The experimental values were obtained as follows.

(Experiment 1)
An n-type silicon single crystal ingot with a diameter of 300 mm and a surface orientation of (100) was grown by the CZ method. The single crystal silicon ingot was sliced into silicon wafers, and the oxygen concentration was measured by Fourier transform infrared spectroscopy. The silicon wafer used in Experiment 1 had an oxygen concentration of 6×10 ¹⁷ atoms/cm ³ (ASTM F121-1979, the same applies to oxygen concentration hereinafter). In order to eliminate thermal donors generated during the crystal growth of the silicon wafer, a donor killer treatment was performed in advance for 30 minutes in a nitrogen atmosphere at 650° C.

Then, low-temperature short-time heat treatment was performed in a nitrogen atmosphere at 430°C, 450°C, 470°C, 490°C, 510°C, and 530°C for 30 minutes, 60 minutes, 120 minutes, and 300 minutes at each heat treatment temperature to generate thermal donors in the silicon wafer.

The resistivity of the silicon wafers subjected to each heat treatment was measured according to the resistivity measurement method using the four-probe method specified in JIS H 0602:1995. The carrier concentration was calculated from the Irvin curve based on the resistivity measurement results and the resistivity measurement results before the low-temperature heat treatment. Furthermore, the difference in carrier concentration before and after the low-temperature heat treatment that generates thermal donors was taken as the amount of thermal donors generated. The relationship between the heat treatment temperature and the amount of thermal donors generated for each condition was plotted in Figure 1. Furthermore, the point at which the amount of thermal donors generated is maximized for each heat treatment time plot in Figure 1 is also shown, along with a virtual line assumed by the inventors.

(Experiment 2)
Except for changing the oxygen concentration of silicon wafers to 4× ¹⁰ atoms/ ^cm , the heat treatment temperature and the amount of thermal donor generated for each condition were plotted in the same manner as in Experiment 1, and are shown in Figure 2. In addition, for each heat treatment time plot in Figure 2, the point at which the amount of thermal donor generated is maximum and a virtual line assumed by the inventors are also shown.

Conventionally, it was believed that the amount of thermal donor generated was maximum at a heat treatment temperature of 450°C, regardless of the length of the heat treatment time. However, the inventors found from the results of Experiments 1 and 2 that there is a negative correlation between the heat treatment time and the heat treatment temperature at which the amount of thermal donor generated is maximum (i.e., the peak temperature in Figure 1 or Figure 2). The "negative correlation" here means that the shorter the heat treatment time, the higher the heat treatment temperature at which the amount of thermal donor generated is maximum during that heat treatment time. If the relationship between the heat treatment time and the heat treatment temperature at which the amount of thermal donor generated is maximum during that heat treatment time is known, it is possible to predict the heat treatment temperature at which the amount of thermal donor generated is maximum when the heat treatment time is changed. As described later, it becomes possible to predict the relationship between the amount of thermal donor generated and the heat treatment temperature under any heat treatment condition, particularly in the case of short-term low-temperature heat treatment.

Next, he came up with the idea that the negative correlation could be expressed as a linear relationship.
[T _m ]=-at+b...(1)
The following relational expression was predicted. In formula (1), [T _m ] is the heat treatment temperature at which the amount of thermal donor generation is maximized, t is the heat treatment time, and a and b are non-negative constants. It is useful from the viewpoint of ease of calculation that the relationship between the heat treatment time and the heat treatment temperature at which the amount of thermal donor generation is maximized during the heat treatment time is expressed as a linear function having a negative correlation. The coefficients of this predicted formula were appropriately set to match the experimental values, and the relationship shown in FIG. 3 was confirmed. In the plot showing the relationship between the heat treatment temperature at which the amount of thermal donor generation is maximized and the heat treatment time, it was confirmed that the extrapolation of the line segment expressed by the above formula had good reproducibility. It was also found that this relationship can be applied in the same way regardless of the oxygen concentration of the silicon wafer to which the heat treatment is applied. Here, in Experiments 1 and 2, the value of a was 0.11. However, the specific value of a was obtained from the above experimental results, and for example, a is determined in the range of 0.05 to 0.15 depending on the experimental results. Similarly, the value of the constant b was 493 in Experiments 1 and 2, but is determined depending on the experimental results from a range of, for example, 450 to 550.

Next, he came up with the idea that the amount of thermal donor generated experimentally could be expressed by a relational equation including a Gaussian function,
[T _D ]=A×[O _i ] ^B ×t ^C ×exp{-(T-T _m ) ² /(2T ₀ ² )} ...(2)
The following relational expression was predicted. In formula (2), [T _D ] is the amount of thermal donor generation, T is the heat treatment temperature, [O _i ] is the oxygen concentration, and T ₀ , A, B, and C are constants. Here, T ₀ corresponds to the standard deviation in a normal distribution represented by a Gaussian function. From this formula, the amount of thermal donor generation in a silicon wafer with an arbitrary oxygen concentration and heat treatment conditions can be predicted using T _m obtained from formula (1) obtained above. The results of appropriately setting coefficients to match this prediction formula to experimental values are shown in Figures 4 and 5. It can be confirmed that the predicted value of the amount of thermal donor generation using the calculation formula has good reproducibility. Here, in experiments 1 and 2, the value of constant A was 1.1 x 10 ^8. However, the value of constant A was obtained from the above experimental results, and for example, the value of constant A is determined according to the experimental results from a range of 0.5 x 10 ⁸ to 1.5 x 10 ⁸ . Similarly, the value of constant B was 4 in Experiments 1 and 2, but the value of constant B is determined, for example, from a range of 3 to 5 inclusive, depending on the experimental results. Similarly, the value of constant C was 0.85 in Experiments 1 and 2, but the value of constant C is determined, for example, from a range of 0.50 to 1.30 inclusive, depending on the experimental results. Similarly, the value of constant _T0 was 30 in Experiments 1 and 2, but the value of constant _T0 is determined, for example, from a range of 10 to 50 inclusive, depending on the experimental results.

In the above formulas (1) and (2), the heat treatment time is not particularly limited, but in order to obtain better reproducibility with experimental values, the heat treatment time is preferably 10 hours or less, and more preferably 5 hours or less. Previous thermal donor behavior prediction methods did not show good reproducibility between predicted values and experimental values in the case of short heat treatment times of 10 hours or less, and the present invention is the first to make it possible to predict the amount of thermal donor generated in short heat treatment times.

In the above formulas (1) and (2), the oxygen concentration of the silicon wafer is not particularly limited, but in order to obtain better reproducibility with experimental values, the oxygen concentration of the silicon wafer is preferably 1×10 ¹⁷ atoms/cm ³ or more and 7×10 ¹⁷ atoms/cm ³ or less (ASTM F121-1979), and more preferably 2×10 ¹⁷ atoms/cm ³ or more and 6×10 ¹⁷ atoms/cm ³ or less.

The silicon wafers used in this experiment can be made by slicing single crystal silicon ingots grown by the Czochralski method (CZ method) or the floating zone melting method (FZ method) with a wire saw or the like. Compared to the FZ method, silicon wafers formed by the CZ method have a higher oxygen concentration and are more susceptible to changes in resistivity due to thermal donor generation. Therefore, it is preferable to use the prediction method according to this embodiment for CZ wafers. The conductivity type of the silicon wafer can be either p-type or n-type.

(Silicon Wafer Evaluation Method)
Also, the silicon wafer can be evaluated using the embodiment of the thermal donor behavior prediction method for the silicon wafer described above. First, a step of determining the amount of thermal donor generation in the silicon wafer generated after heat treatment under predetermined conditions is performed according to the embodiment of the thermal donor behavior prediction method for the silicon wafer described above. As the predetermined conditions, it is preferable to use the heat treatment history to which the silicon wafer is subjected in the device process. Note that, when a high-temperature heat treatment equivalent to a donor killer heat treatment is included, only the heat treatment history after the high-temperature heat treatment may be used. Then, a step of determining a predicted resistivity of the silicon wafer after heat treatment under the predetermined conditions is performed based on the determined amount of thermal donor generation. Note that the resistivity can be determined from the amount of thermal donor generation generated by using an Irvin curve. This silicon wafer evaluation method allows highly accurate evaluation of whether the resistivity of the silicon wafer when subjected to heat treatment under predetermined conditions satisfies a predetermined standard.

(Silicon Wafer Manufacturing Method)
Furthermore, it is also preferable to manufacture a silicon wafer using the above evaluation method. First, a step of grasping the heat treatment conditions in the device process applied to the silicon wafer is performed. If a high-temperature heat treatment equivalent to a donor killer heat treatment is included, it is sufficient to grasp the presence or absence of the high-temperature heat treatment and the heat treatment conditions after the high-temperature heat treatment, and if the high-temperature heat treatment is not included, it is preferable to grasp all the heat history. Then, a step of obtaining a predicted resistivity of the silicon wafer after the heat treatment according to the heat treatment conditions in the device process is performed using the above-mentioned silicon wafer evaluation method. Next, a step of designing a target value of the oxygen concentration or resistivity of the silicon wafer before being subjected to the device process is performed based on the obtained predicted resistivity, and the silicon wafer is manufactured according to this design. If a silicon wafer manufactured by this silicon wafer manufacturing method is used, the silicon wafer is obtained by considering the change in resistivity of the silicon wafer after the above-mentioned device process, so that the adverse effect on the device characteristics due to the generation of thermal donors can be suppressed.

(Example)
It was confirmed that the above-mentioned formulas (1) and (2) could well reproduce the plotted values of oxygen concentration in the experimental results described above (see Figs. 3 to 5). The constants in formulas (1) and (2) were subjected to regression analysis, and the following values were adopted as the constants in formulas (1) and (2).
a = 0.11
b=493
_T0 =30
A = 1.1 x ¹⁰⁸
B=4
C=0.85

Comparative Example
The experimental values described above with reference to FIG. 1 were compared with the calculation results of the following formula A disclosed in Patent Document 1 (JP 2013-119486 A).
Δ[C]=α[Oi]5×exp(-β・D(T)・[Oi]・t) ...(Formula A)
(In the above formula A, α and β are constants.)
The results are shown in Figure 6. The values of the constants α and β were set to α = 1 x ^10-76 and β = 1 x ^10-5 , respectively. Comparing the experimental values with the calculated values, it was found that the calculation method of Patent Document 1 cannot reproduce the behavior of thermal donor generation in such an extremely short-time low-temperature heat treatment.

The following was found from the examples and comparative examples. In other words, by grasping the relationship between the heat treatment time and the heat treatment temperature at which the amount of thermal donor generated during that heat treatment time is maximized in Experiments 1 and 2 and obtaining formula (1), it became possible to predict the heat treatment temperature at which the amount of thermal donor generated during a short, low-temperature heat treatment is maximized. The inventors confirmed that by predicting the amount of thermal donor generated using formula (2), which includes formula (1), the amount of thermal donor generated can be accurately reproduced even under conditions of an extremely short, low-temperature heat treatment.

An object of the present invention is to provide a method for predicting the amount of thermal donors generated and a manufacturing method that can be applied even when the heat treatment time is short.

Claims (5)

A method for predicting thermal donor behavior in a silicon wafer, comprising the steps of:
The oxygen concentration of the silicon wafer is 4×10 ¹⁷ atoms/cm ³ or more and 6×10 ¹⁷ atoms/cm ³ or less (ASTM F121-1979),
Using the fact that the relationship between the heat treatment time and the heat treatment temperature at which the amount of thermal donor generated during the heat treatment time is a negative correlation ,
The heat treatment is performed in a nitrogen atmosphere, the heat treatment temperature is 430° C. or higher and 530° C. or lower, and the heat treatment time is 5 hours or less.
A method for predicting thermal donor behavior in silicon wafers. The negative correlation is expressed by the following formula (1):
[Tm]=-at+b...(1)
(In formula (1), [Tm] is the heat treatment temperature at which the amount of thermal donor generated is maximized, t is the heat treatment time, and a and b are non-negative constants.)
2. The method for predicting thermal donor behavior in a silicon wafer according to claim 1, wherein the thermal donor behavior is expressed by the following relational expression: The amount of the thermal donor generated is expressed by the following formula (2):
[T _D ]=A×[O _i ] ^B ×t ^C ×exp{-(T-T _m ) ² /(2T ₀ ² )} ...(2)
(In formula (2), [ _TD ] is the amount of thermal donor generated, T is the heat treatment temperature, [ _Oi ] is the oxygen concentration, and _T0 , A, B, and ^C are constants, the value of constant A being determined within a range of 0.5x108 ^to 1.5x108 , the value of constant B being determined within a range of 3 to 5, the value of constant C being determined within a range of 0.50 to 1.30, and the value of constant T0 _being determined within a range of 10 to 50. )
3. The method for predicting thermal donor behavior in a silicon wafer according to claim 1, wherein the thermal donor behavior is expressed by the following relational expression: A method for evaluating a silicon wafer using the method for predicting thermal donor behavior of a silicon wafer according to any one of claims 1 to 3 , comprising the steps of:
determining the amount of thermal donors generated in the silicon wafer after the heat treatment;
determining a predicted resistivity of the silicon wafer after the heat treatment based on the amount of thermal donor generated;
A method for evaluating a silicon wafer, comprising: A method for manufacturing a silicon wafer, comprising the steps of:
determining heat treatment conditions in a device process performed on the silicon wafer;
A step of determining a predicted resistivity of the silicon wafer after a heat treatment according to a heat treatment condition in the device process by using the silicon wafer evaluation method according to claim 4 ;
designing a target value of the oxygen concentration or resistivity of the silicon wafer before being subjected to the device process based on the predicted resistivity;
A method for producing a silicon wafer, comprising:

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