JP3685356B2 - Method for measuring dopant concentration of silicon wafer - Google Patents

Description

【００４０】
【表２】

【００４１】
【表３】

【００４２】
【表４】

【００４３】
【表５】

【００４４】
【表６】

【００４５】
【発明の効果】
本発明のシリコンウエハのドーパント濃度測定方法によれば、シリコンウエハに非接触でドーパント濃度を求めることができる。
【図面の簡単な説明】
【図１】アーヴィンカーブを示すグラフ。
【図２】波数と吸収係数の関係を示すグラフ。
【図３】実施例１におけるサンプル１の赤外吸収スペクトルを示すグラフ。
【図４】実施例１におけるサンプル２の赤外吸収スペクトルを示すグラフ。
【図５】実施例１におけるサンプル３の赤外吸収スペクトルを示すグラフ。
【図６】実施例１における吸収係数より求めたドーパント濃度と抵抗率より求めたドーパント濃度の相関図。
【図７】実施例２におけるサンプル４〜７の赤外吸収スペクトルを示すグラフ。
【図８】実施例２における吸収係数より求めたドーパント濃度と抵抗率より求めたドーパント濃度の相関図。[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a method for measuring the dopant concentration of a CZ silicon wafer in a non-contact manner.
[0002]
[Prior art]
Conventionally, the dopant concentration of a CZ silicon wafer is measured using a four-probe method.
[0003]
In the four-probe method, four needles are aligned on a straight line and brought into contact with the wafer, a direct current is passed from the two outer needles, and a potential difference generated between the two inner needles is measured. Then, the resistivity is calculated from the obtained potential difference, and the dopant concentration is obtained according to the Irvine curve.
[0004]
[Problems to be solved by the invention]
In the four-probe method, since the four needles are brought into contact with the wafer surface, there is a problem that the surface is easily damaged.
[0005]
In addition, there is a drawback that the measured value tends to vary depending on the contact state between the tip of the needle and the surface of the wafer. The average may be obtained by measuring a plurality of times, but in that case, the possibility of scratching increases accordingly.
[0006]
In view of the problems of such a four-probe method, an object of the present invention is to provide a dopant concentration measurement method capable of obtaining a dopant concentration without contact with a silicon wafer.
[0007]
[Means for Solving the Problems]
The present invention measures an infrared difference absorbance A between a sample silicon wafer having a thickness d containing a dopant and a reference silicon wafer having substantially the same thickness d and no dopant, and the formula α _e = A / log / d calculates carrier absorption coefficient alpha _e a (cm ^-1) by (loge = 0.4343), wherein [0008] the dispersion theory of carrier absorption coefficient alpha _e (cm ^-1)
[Expression 1]
In addition, the gist of the method is a silicon wafer dopant concentration measurement method for obtaining a dopant concentration N (cm ⁻³ ) based on an Irvin curve that gives a relationship between the dopant concentration N and the resistivity R.
[0009]
DETAILED DESCRIPTION OF THE INVENTION
The method for measuring the dopant concentration of a silicon wafer according to the present invention measures an infrared difference absorbance A between a sample silicon wafer having a thickness d containing a dopant and a reference silicon wafer having substantially the same thickness d and not containing a dopant. _{α e = a / loge / d} , (loge = 0.4343) calculated carrier absorption coefficient alpha _e a (cm ^-1) by, for formula (hereinafter this carrier absorption coefficient alpha _e (cm ^-1), herein Then, this formula is called the formula of dispersion theory)
[0010]
[Expression 1]
The dopant concentration N (cm ⁻³ ) is obtained based on an Irvin curve that gives the relationship between the dopant concentration N and the resistivity R.
[0011]
A conversion table (table) of absorption coefficient α _e (cm ⁻¹ ) versus resistivity R (Ωcm) based on the dispersion theory formula and Irvin curve regarding the carrier absorption coefficient α _e (cm ⁻¹ ) in advance. 1, Table 4), or a conversion table of absorption coefficient α _e (cm ⁻¹ ) vs. dopant concentration N (cm ⁻³ ) is prepared, and the dopant concentration N (cm ⁻³ ) is utilized using this conversion table. Can be requested.
[0012]
It is also possible to graph the conversion tables (Tables 1 and 4) and obtain the dopant concentration N (cm ⁻³ ) using this graph.
[0013]
In the method of the present invention, for example, the infrared difference absorbance A at a wave number of 650 / cm can be measured.
[0014]
In the method of the present invention, the dopant concentration of a boron-doped wafer having a resistivity of 0.1 to 16 Ωcm can be measured.
[0015]
In the method of the present invention, the dopant concentration of a phosphorus-doped wafer having a resistivity of 0.1 to 1.6 Ωcm can be measured. Outside these ranges, there is less correlation between the infrared absorbance value and the dopant concentration, and a one-to-one correspondence cannot be made accurately due to various factors such as measurement errors.
[0016]
【Example】
Irvin curve is also defined in ASTM F723-81, and gives a relationship between “resistivity R” and “dopant concentration (carrier concentration) N”. In general, the Irvine curve is used as a table and a graph, and the graph is shown in FIG.
[0017]
Further, according to the classical dispersion theory, the “carrier absorption coefficient α _e ”, “carrier concentration (dopant concentration) N”, and “electric conductivity δ ₀ (= 1 / R)” are There is a relationship of Formula 1.
[0018]
[Expression 1]
In Equation 1, κ, m ^* , ε ₀ , and c are constants, and the mobility μ is expressed as “dopant concentration N” and “electrical conductivity δ ₀ ” according to the equation μ = 1 / (N · e · δ ₀ ). It is requested from.
[0019]
Accordingly, by measuring the “infrared difference absorbance A” and calculating the “carrier absorption coefficient α _e ” by the equation α _e = A / log / d, (log = 0.4343), the “resistivity R ", That is," dopant concentration (carrier concentration) N "can be obtained.
[0020]
At that time, the value of “resistivity R” is varied in various ways (“dopant concentration N” varies according to the Irvine curve), and a correspondence table of “resistivity R” vs. “carrier absorption coefficient α _e ” is prepared. And good.
[0021]
Table 1 is a correspondence table of “resistivity R” versus “carrier absorption coefficient α _e ” in the case of boron doping. However, vacuum dielectric constant ε ₀ = 8.854 × 10 ⁻¹² S ⁴ A ² / m ³ kg, Si relative dielectric constant ε = 11.68, electron charge e = 1.602 × 10 ⁻¹⁹ SA, carrier The effective mass of m ^{* was} 1.78 × 10 ⁻³¹ kg.
[0022]
Table 4 is a correspondence table of “resistivity R” versus “carrier absorption coefficient α _e ” in the case of phosphorus doping. However, vacuum dielectric constant ε ₀ = 8.85418 × 10 ⁻¹² S ⁴ A ² / m ³ kg, Si dielectric constant ε = 11.68, electron charge e = 1.60219 × 10 ⁻¹⁹ SA, carrier The effective mass of m ^* = 2.642 × 10 ⁻³¹ kg.
[0023]
As can be seen from Tables 1 and 4, the infrared absorption by carriers increases as the dopant concentration increases. Also, the lower the wave number, the stronger.
[0024]
Tables 1 and 4 are convenient if they are graphed.
[0025]
Also, instead of Table 1 and Table 4, the value of “Dopant Concentration N” is changed variously (“Resistivity R” also changes according to the Irvine curve), and “Dopant Concentration N” vs. “Carrier Absorption Coefficient α _e ” A correspondence table or graph may be created.
[0026]
The thickness of the wafer to be measured is about 600 μm to 2 mm, for example.
[0027]
As the wave number, 650 cm ⁻¹ with relatively small infrared absorption other than free carriers can be used.
[0028]
As shown in FIG. 2, in the vicinity of 650 cm ⁻¹ , the influence of silicon lattice vibration and the influence of carbon can be reduced. However, in that case, the level of carbon and other impurities (if present) must be the same for the reference and the sample. In addition, since the influence of the error due to the difference in thickness is large, attention is required.
[0029]
Of course, the wave number may be other than 650 cm ⁻¹ .
[0030]
Example 1
Three types of boron-doped silicon wafers with different resistivity (samples 1 to 3, thickness 2 mm) and non-doped reference silicon wafers (thickness 2 mm) are prepared, and normal incidence infrared absorption measurement is performed with an infrared spectrometer. The absorption coefficient of 650 cm ⁻¹ was determined.
[0031]
Table 2 shows the measured values of the differential absorbance of samples 1 to 3, the calculated value of the absorption coefficient, and the dopant concentration obtained from the calculated value based on Table 1. Moreover, in FIGS. 2-4, the infrared absorption spectrum of the samples 1-3 is shown.
[0032]
On the other hand, the resistivity of Samples 1 to 3 was measured by the 4-probe resistivity measurement method, and the dopant concentration was determined from the Irvine curve. The results are shown in Table 3.
[0033]
And the correlation of the dopant density | concentration investigated from the absorption coefficient and the dopant density | concentration calculated | required from the measured value of resistivity was calculated | required. FIG. 5 is a correlation diagram thereof. A very good correlation was obtained with R ² = 0.99.
[0034]
Example 2
Four types of phosphorus-doped silicon wafers (samples 4 to 7, thickness 2 mm) having different resistivity and non-doped reference silicon wafers (thickness 2 mm) are prepared, and absorption coefficient of wave number 650 cm ⁻¹ is obtained by an infrared spectrometer. Asked.
[0035]
Table 5 shows the measured values of the differential absorbance of samples 4 to 7, the calculated value of the absorption coefficient, and the dopant concentration obtained from the calculated value based on Table 4. FIG. 5 shows the measured infrared absorption spectrum.
[0036]
On the other hand, the resistivity of Samples 4 to 7 was measured by the 4-probe resistivity measurement method, and the dopant concentration was determined from the Irvine curve. The results are shown in Table 6.
[0037]
And the correlation of the dopant concentration calculated | required from the absorption coefficient and the dopant concentration calculated | required from the measured value of resistivity was investigated. FIG. 5 is a correlation diagram thereof. A very good correlation was obtained with R ² = 0.99.
[0038]
The dopant concentration obtained from the measured resistivity value is approximately 0.063 times + 3 × 10 ¹⁵ times the dopant concentration obtained from the absorption coefficient. Therefore, it is possible to convert both freely.
[0039]
[Table 1]

[0040]
[Table 2]

[0041]
[Table 3]

[0042]
[Table 4]

[0043]
[Table 5]

[0044]
[Table 6]

[0045]
【The invention's effect】
According to the dopant concentration measuring method for a silicon wafer of the present invention, the dopant concentration can be obtained without contact with the silicon wafer.
[Brief description of the drawings]
FIG. 1 is a graph showing an irvine curve.
FIG. 2 is a graph showing the relationship between wave number and absorption coefficient.
3 is a graph showing an infrared absorption spectrum of Sample 1 in Example 1. FIG.
4 is a graph showing an infrared absorption spectrum of Sample 2 in Example 1. FIG.
5 is a graph showing an infrared absorption spectrum of Sample 3 in Example 1. FIG.
6 is a correlation diagram between a dopant concentration obtained from an absorption coefficient and a dopant concentration obtained from resistivity in Example 1. FIG.
7 is a graph showing infrared absorption spectra of Samples 4 to 7 in Example 2. FIG.
8 is a correlation diagram between a dopant concentration obtained from an absorption coefficient and a dopant concentration obtained from resistivity in Example 2. FIG.

Claims (5)

Infrared-difference absorbance A of a sample silicon wafer having a thickness d containing a dopant and a reference silicon wafer having substantially the same thickness d and no dopant is measured, and the formula α _e = A / (d · log) , ( loge = calculated carrier absorption coefficient alpha _e a (cm ^-1) by 0.4343), the equation for the carrier absorption coefficient .alpha.e (cm ^-1)

And a silicon wafer dopant concentration measurement method for obtaining a dopant concentration N (cm ⁻³ ) based on an Irvin curve giving a relationship between the dopant concentration N and the resistivity R. Advance, based on the formula and Arvin curve of the dispersion theories carrier absorption coefficient ^{αe (cm -1) (Irvin curve} ), conversion chart of the absorption coefficient α _e (cm ^-1) versus resistivity R ([Omega] cm) (Table 1 , Table 4), or, the absorption coefficient α _e (cm ^-1) in advance to create a conversion table of pairs dopant concentration N (cm ^-3), by utilizing the conversion table dopant concentration N a (cm ^-3) 2. The method for measuring a dopant concentration of a silicon wafer according to claim 1, wherein the concentration is determined.   The method for measuring a dopant concentration of a silicon wafer according to claim 1, wherein the infrared difference absorbance A at a wave number of 650 / cm is measured.   The method for measuring a dopant concentration of a silicon wafer according to any one of claims 1 to 3, wherein the dopant concentration of a boron-doped wafer having a resistivity of 0.1 to 16 Ωcm is measured.   4. The method for measuring a dopant concentration of a silicon wafer according to claim 1, wherein the dopant concentration of a phosphorus-doped wafer having a resistivity of 0.1 to 1.6 Ωcm is measured.

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