JPH1114470A - Method for analyzing interface stress of sample - Google Patents

Abstract

PROBLEM TO BE SOLVED: To quantitatively obtain a force per unit length and a force per unit area acting near an interface of a sample using a Raman spectral method. SOLUTION: The laser beam of single wave length emitted from a laser part 11 is made incident on a sample 17's interface through a lens system, the peak value of a Raman light reflected from the interface is detected with a detection part 15 through the lens system and a spectroscope 14, a deviation in wavelength of the peak value of the Raman light against the single wavelength of the incident light is calculated as a shift amount of the peak value of the Raman spectrum, and a stress distribution acting near the sample's interface is obtained with a computer 16 comprising a stress calculation part wherein a stress calculation equation is programmed based on a theory of linear elasticity which calculates a stress per unit length a unit area with the shift amount and a central position of the incident light as variable.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for analyzing interfacial stress of a sample, and more particularly to a method for analyzing interfacial stress of a semiconductor sample by Raman spectroscopy.

[0002]

2. Description of the Related Art Conventionally, Raman spectroscopy has been used as a method for quickly and non-destructively analyzing interface stress on various semiconductors. Therefore, the interface stress analysis method for semiconductor samples using Raman spectroscopy has been widely used. Have been doing. Therefore, interface stress analysis of a semiconductor sample using Raman spectroscopy is performed by a system combining a laser, an optical microscope, a high-performance CCD detector, a computer, and the like.

FIG. 6 is a diagram showing a waveform of Raman light with respect to incident light and a peak waveform of a measured Raman spectrum. FIG. 6A shows a waveform of the Raman light with respect to the incident light. In general, when a material surface is irradiated with light having a predetermined wavelength, a Raman spectrum is scattered in addition to the irradiated light. FIG. 6 (b)
Indicates the peak waveform of the measured Raman spectrum,
Usually, the measured Raman spectrum has a peak waveform close to the Lorentz function. To determine the peak position, Lorentz-type fitting is performed, and the shift amount Δω of the Raman spectrum is measured from the difference between the frequency of the peak value of the Raman light and the frequency (single wavelength) of the incident light.

[0004] The frequency of the peak value of the Raman spectrum varies depending on the substance, and is greatly affected by the stress (strain) acting on the substance. By utilizing this property, the stress of the material can be analyzed. In the conventional interface stress analysis method using Raman spectroscopy, the frequency of the peak value of the Raman spectrum detected near the interface of the semiconductor sample is the same as the peak value of the standard spectrum detected at the sample without stress or at the measurement point. The computer calculates how much it deviates from the position, and analyzes that the shift amount is proportional to the stress (strain). It is assumed that there is a uniform stress in the incident area where the laser beam is incident, and the stress is expressed as a function formula of shift amount (stress = f (Δω)).

[0005]

However, when measuring the stress at the interface of the electrode on which the semiconductor surface is formed, the strain is the largest at the end of the electrode, and the strain decreases as it goes inward. In the interfacial stress analysis method using Raman spectroscopy, it is based on the assumption that the strain is uniform in the incident area (in the light arrival area). Can not.

(I) Since the laser beam diameter is as large as about 1 μm, sufficient spatial resolution cannot be obtained in a region where a change in stress is large. (Ii) Since light penetrates into the sample, data averaged in the depth direction is detected. That is, since the diameter of the laser beam incident on the analysis area is finite, and the penetration length of the incident light is finite, the detected data is a weighted average value in the light arrival area, Actually, when there is a considerably changed stress distribution in the analysis region of the semiconductor sample and a large stress is applied at a portion such as the interface of the semiconductor, the stress obtained by assuming that there is a uniform stress is conventionally obtained. The values result in fairly small stress values. Also, depending on the material, averaging of data is performed over a wide area for substances with a large penetration depth of incident light. Particularly, accurate evaluation is required near the interface where the highest accuracy is required from the reliability of the semiconductor sample. There is a problem that can not be done.

The present invention has been made in view of the above circumstances. For example, the stress acting per unit length or per unit area in the vicinity of the interface of a semiconductor sample requiring high accuracy is determined by Raman spectroscopy and linear An object of the present invention is to provide a method for analyzing the interfacial stress of a sample, which can be quantitatively obtained by using a stress calculation formula based on the theory of elasticity.

[0008]

According to the present invention, a laser beam of a single wavelength emitted from a laser section is incident on an interface of a sample through a lens system, and the peak value of Raman light reflected from the interface is determined by the lens. Detected by the detection unit via the system and the spectroscope, the shift of the wave number of the peak value of the Raman light with respect to a single wavelength of the incident light is calculated as a shift amount of the peak value of the Raman spectrum, and the shift amount and the incident light Using a computer having a stress calculation unit in which a stress calculation formula for calculating stress per unit length or unit area using the center position as a variable based on linear elasticity theory is used to obtain a stress distribution acting near the interface of the sample. This is a method for analyzing the interfacial stress of a sample that is a feature. In the present invention, linear elasticity is a calculation method that shows all stress distributions in a material when a certain force is applied to a certain region of the material.

According to the present invention, the peak value of Raman light obtained from the vicinity of the interface of the sample on which the laser beam is incident is detected, and the computer is programmed with a stress calculation formula based on linear elasticity theory, thereby obtaining the incident light. The shift of the wave number of the peak value of the Raman light with respect to a single wavelength is calculated as the shift amount of the peak value of the Raman spectrum, and the calculated shift amount and the center position of the incident light per unit area acting on the vicinity of the sample interface or The stress per unit length can be calculated quantitatively.

It is preferable that the shift amount of the peak value of the Raman spectrum is calculated by at least a fitting process, a smoothing process, or both processes. The fitting process means that the Raman spectrum detected by the detection unit has noise on it, for example,
Since its peak waveform is similar to the Lorentz function,
This is a process of removing noise that does not match the Lorentz function and extracting its peak value. The smoothing process is a process of removing a noise by using data averaged at several points before and after the signal intensity at each wave number obtained by the measurement, and extracting a peak value thereof. According to the above processing, the accuracy of the shift amount of the peak value of the Raman spectrum is improved, so that the local stress at the interface of the sample can be obtained.

Preferably, the shift amount of the peak value of the Raman spectrum is calculated by a function of a distance from the interface and a fitting process based on at least two or more detection data detected near the interface. According to the above process, the accuracy of the shift amount of the peak value of the Raman spectrum is further improved, so that the local stress at the interface of the sample can be obtained.

[0012]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, the present invention will be described in detail based on an embodiment shown in the drawings. Note that the present invention is not limited by this.

FIG. 1 is a block diagram showing a sample interfacial stress analysis system using Raman spectroscopy according to one embodiment of the present invention. In FIG. 1, reference numeral 11 denotes a laser unit, which may be composed of, for example, an Ar gas laser or a He—Ne laser having a wavelength of 488 nm or 514.5 nm. Reference numeral 12 denotes a microscope, which includes a high NA objective lens 12a and a reflecting mirror 12
b, 12c. 13 is an XY stage with an accuracy of 0.01 μm for mounting the sample,
The position holding accuracy is maintained at ± 0.5 μm / 10H or less. Reference numeral 14 denotes a spectroscope (U-1000 double monochromator) for obtaining Raman spectroscopy. Reference numeral 15 denotes a detection unit, and PM
(Potomultiplier), MCD (Mutichannel Detecte)
r), it is preferable to be composed of a CCD (Charge Coupled Device).

Reference numeral 16 denotes a computer including a CPU, a ROM, a RAM, a keyboard, a display, and the like. The computer 16 calculates the shift between the wave number of the peak value of the Raman light detected by the detection unit 15 and the single wavelength of the incident light as the shift amount of the Raman spectrum peak value, and calculates the calculated shift amount. A stress calculation unit having a stress calculation formula for calculating stress as a variable and a data processing unit for processing data at high speed are provided. This stress calculation formula is created based on the theory of linear elasticity, and a program of the stress calculation formula is stored in the ROM of the computer in advance.

Reference numeral 17 denotes a sample of a semiconductor device mounted on the high-precision XY stage 13. For example, an electrode on a silicon substrate is formed on the sample 17, and the stress distribution near the electrode end is measured by Raman spectroscopy. A laser beam of a predetermined wavelength emitted from the laser unit 1 is incident on the interface at the electrode end of the sample 17 through the lens system of the microscope 2, and the peak value of the Raman light reflected from the interface and the peak value of the incident light are determined by the lens Detection is performed by the detection unit 5 via the system and the spectroscope 4. When the detected data is sent to the computer 6, the computer 6 inputs the detected data into a stress calculation formula programmed based on the theory of linear elasticity, and calculates the shift of the wave number of Raman spectroscopy with respect to a single wavelength of the incident light. Is calculated as the shift amount Δω of the peak value of the Raman spectrum, and the stress per unit length or unit area is calculated from the calculated shift amount Δω and the center position of the incident light.

At this time, the higher the measurement accuracy of the shift amount Δω of the peak value of the Raman spectrum and the center position of the incident light, the more the stress in the local region can be measured. XY
The stage 13 is driven and controlled by a computer and a high-precision motor.
, And sequentially measuring the shift amount Δω of the peak value of the Raman spectrum and the center position of the incident light, it is possible to measure the stress distribution according to the change in strain in the submicron region.

Embodiment 1 FIG. 2 is a schematic diagram showing a force per unit length acting on an interface of a sample in Embodiment 1. In FIG. 2, 1 indicates a GaAs substrate, and 2 indicates a Ga substrate.
A WN electrode formed on the As substrate 1 (for example, having a width of 50 μm)
m, tungsten nitride having a thickness of 0.3 μm). Reference numeral 3 denotes a force Sdy per unit length assuming that it acts on the interface of the end of the WN electrode extending in the {110} direction on the (001) GaAs substrate 1. S is the stress per unit length (N
/ M). Reference numeral 7 denotes an incident area of the laser beam incident on the interface with energy of hν, which is indicated by hatching. Here, h indicates Planck's constant, and ν indicates the frequency of the laser beam.

The shift of the wave number of the peak value of the Raman spectrum with respect to a single wavelength of the incident light is calculated as the shift amount Δω (cm ^-1 ) of the Raman spectrum from the following equations (1) to (7). . [Equation 1] to [Equation 7] are stored in the program of the stress calculation unit of the computer 16. A point P at which the force Sdy3 is away from the coordinates (x ₁ , y ₁ , z ₁ )
The equation of the displacement amount (du, dv, dw) to be made is, for example, A.
EHLove, `` A TREATISE ON THE MATHEMATICAL THEOR
Y OF ELASTICITY ”, p.243.

[0019]

(Equation 1)

In the equation (1), r ₁ indicates the distance from the point where the force acts to the point P. λ and μ indicate parameters specific to the substance, and Young's modulus E = μ (3λ + 2μ) / (λ +
μ) and Poisson's ratio = λ / (2 (λ + μ)). From this equation [Equation 1], the total displacement (u, v, w) that the whole WN electrode makes at point P is the other W
Taking into account the force (-Sdy) acting on the N electrode end, the following can be written.

[0021]

(Equation 2)

The length of the WN electrode 2 is assumed to be sufficiently long, and the integration range is from -∞ to ∞. Further, if (u, v, m) is differentiated by x, y, z from the definition of the distortion amount, the distortion amounts ε _xx (r), ε _yy (r), ε _zz (r), ε
_xy (r), ε _yz (r), ε _zx (r) are obtained as a function of coordinates.

[0023]

(Equation 3)

As shown in the incident area 7 in FIG. 2, the Raman spectrum detected by irradiating the strain distribution with the incident light is a weighted average value in the incident area in consideration of the beam diameter and the penetration length of the incident light. It is considered to be. When the incident light is located at a point x in a direction away from the end of the WN electrode, the weighted average value in the measurement area is ε _ij (x) (i, j = x, y, z). It can be calculated by the equation of [Equation 4].

[0025]

(Equation 4)

Here, α and α 'are the respective incident lights, the attenuation rate of the Raman spectroscopy in the substrate, and Sx is x which is the incident light.
The area in the y-plane and D (x | x ′, y) indicate the intensity distribution of the beam in Sx. When the incident light is a circle having a radius a and the intensity inside the circle is uniform, the expression of [Expression 4] can be simplified as the following expression of [Expression 5].

[0027]

(Equation 5)

If each bar ε _ij can be calculated, the shift amount Δω of the peak value of the Raman spectrum actually observed in the experiment
Is Physical Review B, 1972, Vol. 5, No. 2, p.
580-593 (F. Cerdeira et.al., Phys. Rev. B5580 (19
72)) (1, 1) of the three ω _{0 in} the expression (2),
The (2, 2) component is rewritten to ω _TO and the (3, 3) component is rewritten to ω _LO , which is calculated from the following equation (Equation 6).

[0029]

(Equation 6)

In the equation (6), p, q, and r are parameters connecting the strain and the spring constant. ωTO and ωLO indicate the frequencies of the TO and LO phonons when there is no distortion, respectively.
The subscripts x, y, and z of [Equation 6] correspond to [1] of the crystal.
00], [010], and [001]. In the analysis, the eigenvectors (100), (010),
It should be noted that the following Raman tensors correspond to (001).

[0031]

(Equation 7) In the equation of [Equation 7], k is a constant.

FIG. 3 is a graph showing the shift amount Δω of the peak value of the Raman spectrum calculated in the first embodiment. The shift amount of the peak value of the Raman spectrum shown in FIG. 3 is a result obtained by performing the calculations of [Equation 1] to [Equation 7] and fitting. Here, the incident beam diameter is 1
The analysis was performed with μm. The horizontal axis of the graph represents the distance (μ) measured from the center position of the incident light in the direction away from the end of the WN electrode.
m), the vertical axis represents the shift amount Δω (cm ⁻¹ ) of the peak value of the Raman spectrum with reference to the value at a point of 4 μm in the direction in which the center position of the incident light moves away from the end of the WN electrode.
The data of the peak value at each point is obtained by fitting with a Lorentz function.

Although it is possible to evaluate the stress S acting on the interface only from the data of one point, the optimum S was obtained from the data of five points by the least square method in order to further improve the accuracy. It should be noted that the electric field vectors of the incident light and the Raman light at the time of measurement are in the [100] and [010] directions, respectively, and the mode corresponding to the eigenvector (001) is observed. At a point about 0.5 μm away from the WN electrode, the calculation result showed that the bar ε _ZX was large, and it was considered that mode mixing had occurred, and that point was excluded from the fitting. At other measurement points bar ε _ZX is bar ε _XX ,
It was analyzed to ignore small enough in comparison with the bar ε _ZZ.
In this case, the expression of [Equation 6] is calculated as follows.

[0034]

(Equation 8) By solving [Equation 8] in reverse, it can be written into the equation of [Equation 9].

[0035]

(Equation 9)

The equations [Equation 8] to [Equation 9] are stored in the program of the stress calculation unit of the computer 16. [Delta] [omega] is determined by the above [Equation 1] to [Equation 7], and the center position (x) and [Delta] [omega] of the measured laser beam are calculated by [Equation 9]
To obtain the stress S to be obtained.
Here, fitting was performed using the formula of [Equation 9] to further increase the accuracy, and the stress S acting per unit length was obtained. From the result of this fitting, the stress S = 439 was applied to the GaAs substrate 1 in the annealed WN electrode.
(N / m) was found to be working. Similarly, in the case of a WN electrode without annealing, the stress S = 233 (N /
m) is working.

For example, even if the diameter of the incident light is 1 μm,
Since the accuracy of the shift amount between the center position of the incident light and the peak value of Raman spectroscopy is improved, it is possible to measure the stress according to the change in strain in the submicron region. Such local information at the interface can be obtained for the first time by the interface stress analysis method of the present invention.

[Embodiment 2] FIG. 4 is a schematic diagram showing a force per unit area acting on an interface of a sample in Embodiment 2. In FIG. 4, reference numeral 4 denotes a ZnSe substrate, and reference numeral 5 denotes a ZnSe substrate.
Au / Cr electrodes (for example, having a width of 5
00 μm and a film thickness of 0.20 / 0.05 μm). Numeral 6 denotes a force σdxdy per unit area acting on the interface of the Au / Cr electrode end extending in the {110} direction with respect to the ZnSe substrate 4 of the vector (001). σ indicates the stress per unit area (dyn / cm ² ). Reference numeral 7 denotes an incident area of the laser beam incident on the interface with energy of hν, which is indicated by hatching. Here, h indicates Planck's constant, and ν indicates the frequency of the laser beam.

Actually, the distance affected by the stress is at most about 10 μm. Here, a model in which a constant stress is applied from both ends of the electrode toward the inside of the electrode to 20 μm is used. The displacement amount (du, du, d) to be created at a point P which is separated by coordinates (x ₁ , y ₁ , z ₁ ) from the force σdxdy 6 shown in FIG.
dv, dw) is obtained by converting the force Sdy per unit length into the force σdx per unit area in the equation of [Equation 1] of the first embodiment.
dy.

[0040]

(Equation 10)

In the equation (10), r1 indicates the distance from the point on which the force acts to the point P, and λ and μ indicate parameters specific to the substance. The total displacement (u, v, w) generated by the entire electrode at an arbitrary point (x, y, z) is given by the following [Equation 11] considering that the stress applied to the other end of the electrode is + σdxdy. ].

[0042]

[Equation 11]

Here, A ₁ and A ₂ indicate regions where the stress shown in FIG. 4 acts. The electric field vectors of the incident light and the Raman light at the time of measurement are [100] and [010], respectively, as in the first embodiment.
It should be noted that the direction is observed and the mode corresponding to the eigenvector (001) is observed. By following exactly the same procedure as in the first embodiment, an equation similar to [Equation 9] is finally obtained.

[0044]

(Equation 12)

The shift amount Δω of the Raman spectrum obtained by the experiment is substituted into the equation of [Equation 12], and the absolute value of the stress initially assumed is σ = 3.35 × 10 ⁹ (dyn / c
m ² ). However, in the second embodiment, the shift amount Δω of the peak value of the Raman spectrum at each measurement point is obtained by fitting with a Lorentz function. As the shift amount Δω substituted in [Equation 12], a value at a point in a direction away from the electrode end of 3 μm was used. On the other hand, when the same sample was evaluated by the conventional method, the ZnSe substrate was transparent to the incident light, and information was obtained even from a deep region where the strain was relaxed. ⁹ (dyn / cm ² ), which is considerably underestimated.

As in the first embodiment, the second embodiment also
By improving the accuracy of the shift amount between the center position of the incident light and the peak value of the Raman spectrum, the local stress value σ acting on the interface can be obtained quantitatively. Therefore, the assumed stress distribution or force distribution is analyzed by using the strain distribution obtained by linear elasticity theory and considering the effect of the spatial spread of the incident light at each measurement point and the effect of penetration into the inside of the object. be able to.

FIG. 5 is a comparison diagram between the stress distribution obtained by the interface stress analysis of the present invention and the stress distribution obtained by the conventional interface stress analysis. FIG. 5A shows a stress distribution at the interface at the electrode end measured by the interfacial stress analysis of the present invention. As shown in FIG. 5A, it is possible to measure a stress corresponding to a change in strain in a laser beam incident region. FIG. 5B shows a stress distribution at the interface at the electrode end measured by the conventional interface stress analysis. As shown in FIG. 5B, even if there is a change in the distortion in the laser beam incident area, it is measured as an average stress.

[0048]

According to the present invention, the stress acting per unit length or per unit area in the vicinity of the interface of a semiconductor sample requiring high precision is determined by using a Raman spectroscopy and a stress calculation formula based on linear elasticity theory. Can be obtained quantitatively.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a sample interfacial stress analysis system using Raman spectroscopy according to one embodiment of the present invention.

FIG. 2 is a schematic diagram showing a force per unit length acting on an interface of a sample in Example 1.

FIG. 3 is a graph showing a shift amount of a peak position of a Raman spectrum calculated in Example 1.

FIG. 4 is a schematic diagram showing a force per unit area acting on an interface of a sample in Example 2.

FIG. 5 is a comparison diagram between a stress distribution obtained by the interfacial stress analysis of the present invention and a stress distribution obtained by the conventional interfacial stress analysis.

FIG. 6 is a diagram showing a waveform of Raman light with respect to incident light and a peak waveform of a measured Raman spectrum.

[Explanation of symbols]

 Reference Signs List 1 GaAs substrate 2 WN electrode 3 Force Sdy 4 ZnSe substrate 5 Au / Cr electrode 6 Force σdxdy 7 Incident area 11 Laser unit 12 Microscope 13 XY stage 14 Spectroscope 15 Detector 16 Computer 17 Sample

Claims (3)

[Claims] 1. A laser beam of a single wavelength emitted from a laser unit is incident on an interface of a sample via a lens system, and a peak value of Raman light reflected from the interface is detected via the lens system and a spectroscope. Part, the shift of the wave number of the peak value of the Raman light with respect to a single wavelength of the incident light is calculated as the shift amount of the peak value of the Raman spectrum, and the shift amount and the central position of the incident light as variables are unit lengths. Stress analysis applied to the vicinity of the interface of a sample by a computer having a stress calculation unit programmed based on linear elasticity with a stress calculation formula for calculating the stress per unit area or per unit area. Method. 2. The method according to claim 1, wherein the shift amount of the peak value of the Raman spectrum is calculated by at least a fitting process, a smoothing process, or both. 3. The shift amount of the peak value of the Raman spectrum is calculated by a function of a distance from an interface based on at least two detection data detected near the interface of the sample and a fitting process. The method for analyzing interfacial stress of a sample according to claim 1.