JP3461793B2 - Crystal structure analysis method - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of analyzing a crystal structure of a semiconductor thin film or a multiple quantum well structure using X-ray diffraction.

[0002]

2. Description of the Related Art Broad peaks are often observed in the structure evaluation of epilayers using double crystal X-ray diffraction.
In such a case, it is an important subject for evaluation to clarify why broadening occurs and its cause. The conventional two-crystal X-ray diffraction evaluation technique has few effective means for obtaining a clear answer to such a problem, and a vague discussion is made as an analogy with other experimental results by changing the growth conditions. Was there.

On the other hand, in recent years, a reciprocal lattice mapping evaluation technique has been developed, and by measuring the direction of the spread in the reciprocal lattice space, it has become possible to distinguish between the peak spread due to the mosaic crystal and the peak spread due to the composition distribution. .

However, the reciprocal lattice mapping evaluation takes a long time to measure, it is difficult to evaluate a weak peak, and it is difficult to perform a more detailed analysis and study on the peak shape because the reciprocal lattice space is sparsely scanned. There are problems such as. In order to solve these problems, an analysis method capable of clarifying the broadening factor by directly analyzing the peak broadening shape obtained by double crystal X-ray diffraction has been desired.

Recently, the authors have proposed and reported, as an example of such an analysis method, a method for easily determining whether or not a peak is broadened by a mosaic crystal by considering the index (hkl) dependence. (K. Nakashima a
nd H. Sugiura, J .; Appl. Cryst
allgr. , 30, 1002-1007 (199
7)) However, the problem is that this method is applicable only to the case where the peak spread is due to the mosaic crystal and cannot be applied to the analysis when the peak spread is due to other factors.

Also, there have been almost no reports of such analysis methods for other factors. In particular, regarding the peak broadening due to the distribution of the composition, which is an important broadening factor, a method of directly and simply analyzing the peak broadening shape obtained by 2-crystal X-ray diffraction has not been known so far. Especially in the case of the composition distribution in the epitaxial layer containing strain, the effect of lattice relaxation may be considered in addition to the composition distribution, so the analysis was extremely difficult.

[0007]

When the crystal structure is evaluated by X-ray diffraction, whether or not the broadening shape of the measured peak is determined by reflecting the uneven distribution of the composition in the crystal. Provided is a crystal structure analysis method capable of easily determining a crystal structure.

[0008]

The structure analysis method of a crystal by X-ray diffraction according to the present invention is as follows: (1) Measurement steps Two or more (hkl) reflection profiles having different indices are taken from the Χ ray incident angle (θ). ) With a symmetrical reflection arrangement, and one point of the reference Χ ray incident angle (θ _ref ) in each (hkl) profile is selected, and the X-ray which is the horizontal axis of the profile is selected. With the incident angle as a new horizontal axis, the difference in the incident angle of the X-ray from the reference point Δθ _(hkl) : = θ−θ
_The process of converting to _ref .

(2) Profile conversion step Based on the difference in the diffraction angles, the lattice constant a corresponding to the reference point
₀ cube, inverse square of X-ray wavelength λ, inverse square of the reflection index h, and twice the Bragg angle θ _{B, (hkl)} of (hkl) reflection corresponding to the reference point. The difference ΔA _(hkl) having the dimension of the lattice constant obtained by multiplying the sine and the constant (−2) by the difference Δθ _(hkl) of the diffraction angles is calculated, and the horizontal axis of each (hkl) profile is calculated as by converting the difference Δθ of the diffraction angle _{(hk l)} to said difference ΔA _(hkl), the step to draw the re normalized horizontal axis (hkl) profile new. That is,

[0010]

[Formula 1]

[Equation 1] is calculated, and each (hkl) profile in which the horizontal axis is renormalized is newly drawn. (3) Analysis / judgment step The spread peaks observed in a series of the renormalized (hkl) profiles having different indices (hkl) obtained are the targets of analysis, and the spread shape of the spread analyzed peaks. And extracting the values of the difference ΔA _(hkl) of a plurality of points for each (hkl) profile, and the amount of each ΔA _{(hkl) of the} feature point calculated from the index (hkl) ( k ² + l ² ) / h ² and the step of producing a graph, and determining whether or not a series of plot points for each feature point are on a certain straight line in the graph The step of determining whether or not the peak broadening shape of the broadened peak is the peak broadening shape caused by the distribution of the composition.

[0012]

In the present invention, the measured peak spread shape is re-normalized by using the step of forming the difference amount having the dimension of the lattice constant of ΔA, and the characteristic points of the spread shape are extracted and their index is calculated. By analyzing the dependence graphically by the new plotting method, the origin of the shape of the peak spread is examined.

By these newly devised steps, it is simple and clear to solve the problem "whether the peak broadening shape is caused by the distribution of the composition" which cannot be analyzed by the conventional method. It became possible to give an answer to. In particular, the remarkable effect of this method is that it can be determined in the general case including lattice relaxation.

[0014]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS First, the principle and concrete procedure of the present invention will be briefly explained, and then concrete examples will be presented. The main flow of these steps is schematically shown in FIG.

A plurality of X-ray diffraction measurements are performed on the sample to be analyzed by changing the reflection index (hkl). (Hk
l) Reflection is measured by arranging the measurement sample while keeping the X-ray incident direction fixed (hkl) and arranging it so that the surface becomes a vertical plane (symmetrical reflection arrangement). (Cf. K. Nakashima,
J. Appl. Phys. , 72.1189 (199
2)) This gives a series of (hkl) X-ray diffraction profiles with the X-ray incident angle on the horizontal axis and the X-ray diffraction intensity on the vertical axis.

Next, one reference point (usually the substrate peak position) is determined from the obtained diffraction profile. At this time Δ
θ: = θ−θ _ref (where θ is the X-ray incident angle at an arbitrary point, θ _ref is the X-ray incident angle at the reference point), and the horizontal axis of the diffraction profile is the X-ray incident from the reference point. It is assumed that the angle difference is converted to Δθ (left in FIG. 1). Conventionally, this Δθ is used as the horizontal axis.

On the other hand, in the present invention, this conventional difference amount Δ
Difference amount ΔA _(hkl) introduced by the following formula instead of θ
Analyze using. In the case of (hkl) reflection profile, the difference amount ΔA _(hkl) is calculated from the conventional difference amount Δθ _(hkl).

[0018]

[Formula 2]

Is defined by Here, λ is the wavelength of the X-ray, and h is h in the reflection index (hkl). Also, a ₀
Is the lattice constant corresponding to the reference point (substrate), and θ _{B, (hkl)} is the Bragg angle in the case of (hkl) reflection (that is, of the reference layer having the lattice constant a ₀ ). It is important that this difference amount has a dimension of the lattice constant and is an amount representing the difference of the lattice constant from the reference lattice constant a ₀ (FIG. 1, central diagram).

Now, it is assumed that there is an X-ray peak or a peak spread due to the composition distribution. In this case, since the composition has a distribution, different composition layers have different lattice constants, and as a result, a distribution appears in the lattice constants. This distribution of lattice constants causes the peak broadening of X-ray peaks. In this case, the analysis becomes difficult especially in the general case where the lattice matching with the substrate is not assumed. That is, when the lattice matching with the substrate is maintained, the composition distribution is Δa _⊥
However, in the general case, Δa
_This is because it is necessary to consider two distributions, _⊥ and Δa _// (where Δa _⊥ is the lattice constant in the direction perpendicular to the substrate and Δa _// is the lattice constant in the direction parallel to the substrate).

However, the difference amount ΔA _(hkl) works effectively for the analysis of these two distributions. That is, the following relation holds for ΔA _(hkl) .

[0022]

[Formula 3]

Therefore, the spread shape of the X-ray peak when the horizontal axis is converted to ΔA _(hkl) is (k ² + l ² ) / h
By analyzing as a ^second function, information about .DELTA.a _⊥ and .DELTA.a _// 2 two distributions that are obtained. In order to do this simply, in this method, several characteristic positions found in the peak spread shape are selected, and these selected several characteristic points (point A and point B in FIG. 1) are respectively selected. It is investigated whether or not the exponential dependence of the above equation 2 is exhibited. Therefore, draw a graph in which the position ΔA _(hkl) of the feature point is plotted against (k ² + l ² ) / h ^{2 and see} if the plot points corresponding to each feature point lie on a straight line corresponding to equation 2 above. Check whether or not it is (right in FIG. 1).

By experimentally confirming that all of them are on a certain straight line, it can be easily determined that the spread shape of the peak to be analyzed is caused by the distribution of the composition. In this case, a remarkable feature of this analysis method is that it can be applied even in general cases in which lattice matching with the substrate is not assumed, including a state in which the lattice is relaxed.

FIG. 1 shows the flow of the analysis procedure. First the index
A plurality of X-ray diffraction measurements are performed by changing (hkl). Next measurement
The horizontal axis of each defined (hkl) profile is Δθ_(hkl)Or
From ΔA_{( hkl)}By converting to
Draw a new standardized profile. Got
It corresponds to the expanded peak in each profile that is the subject of analysis.
However, a point that characterizes the peak broadening shape (feature
Select multiple points. In Figure 1, the two peaks indicated by A and B are peaks.
Draw it assuming that it will be selected as the feature point of the spread shape.
It Position of selected feature point ΔA_(hkl)The value for each (hkl)
Each file is collected as analysis data and these are specified.
Value (k) determined from the number (hkl)²+1²) / H ²Function of
Then, the plotted graph is prepared.

In the obtained graph, it was confirmed that a series of plot points corresponding to the respective characteristic points were all on a certain straight line, so that the broadened peak of the analysis object was generated due to the distribution of the composition. I can conclude that there is. Moreover, if it does not ride on a certain straight line, it can be concluded that the peak spread of the analysis target is caused by another cause other than the composition distribution.

Specific examples of the present invention will be described below. First, as a first embodiment, an analysis example of the peak broadening caused by the composition distribution under the condition of lattice matching with the substrate will be shown. The sample used has a structure in which five In _1-x Ga _x As layers (thickness 1000 Å) having different compositions x are laminated and grown on an InP substrate.
The composition x is x = 0.41,0.42,0.43,0.4
It was set to 4, 0.45. This five-layer laminated structure was regarded as a structure having an artificially produced composition distribution, and was used for the experimental confirmation of the present invention.

FIG. 2 shows an X-ray diffraction profile obtained by measuring the same sample with a plurality of indices (hkl) changed and converting the horizontal axis into Δθ. In addition to the substrate peak, a multilayer peak from the In _1-x Ga _x As multilayer structure in which the peak shape spreads on a trapezoid is observed. In the profile of FIG. 2, the trapezoidal peak broadening shape changes disparately when the index (hkl) is changed, and no uniformity is seen. The analysis method of the present invention is applied to this trapezoidal multilayer peak.

FIG. 3 shows the results of applying the present invention to the peaks spread on the trapezoid of FIG. That is, FIG. 3 shows the result of collecting and arranging each renormalized (hkl) profile by converting the horizontal axis into the difference ΔA. It can be seen that the trapezoidal spread shape of each peak is in good agreement with the position and the spread width of the trapezoid even if the index (hkl) is changed.

That is, in this case, the obtained ΔA _(hkl) value data is (k ² + l ² ) /
It can be seen that it takes a constant value that does not depend on h ² . Therefore, even without plotting, it can be simply concluded that the spread shape on the trapezoid is due to the distribution of the composition only in FIG.

Next, as a second embodiment, an analysis example of the peak broadening caused by the composition distribution under general conditions including lattice relaxation with respect to the substrate will be shown. As the sample, an InGaAsP layer produced by selective growth on an InP substrate was used. The epilayer portion other than the selectively grown portion was removed by etching and the measurement was performed. This sample has a complicated composition distribution due to selective growth.

FIG. 4 shows the index (hkl) for the same sample.
Multiple measurements are changed, and the horizontal axis is Δθ. _(hkl)To ΔA_(hkl)
2 shows an X-ray diffraction profile converted into. In Fig. 4
There is also a trapezoidal peak, but in the case of Fig. 3
Unlike Fig. 4, when the index (hkl) is changed,
Both the placement and the spread width of the trapezoid change.

This indicates that the same sample contains lattice relaxation, and analysis in the general case is required. As the characteristic points of the spread shape, the upper and lower ends of the trapezoidal peak are taken at the positions indicated by the arrows in FIG. 4, and their ΔA
_The results of collecting _(hkl) value data and plotting them against (k ² + l ² ) / h ² are shown in FIG. It can be seen that the plot points at both the upper end and the lower end are on a straight line as shown in FIG. Therefore, it can be easily concluded that the trapezoidal peak in FIG. 4 is caused by the distribution of the composition. Therefore, it was confirmed from this example that the present invention functions very effectively.

[0034]

When the crystal structure is evaluated by X-ray diffraction,
It is important to easily determine the controlling factors of the peak spread shape to be measured, but one of the issues for this is "whether the peak spread shape is caused by the composition distribution or not. In the past, we could not analyze this problem.

However, as a result of the present invention, a deterministic (that is, preliminary information is not required and trial-and-error process is not included) analysis using a graph is performed to easily and clearly solve this problem. It became possible to give an answer. In particular, the present invention has a remarkable effect that it can be applied even in the general case where the lattice matching with the substrate is not assumed, including the state in which the lattice is relaxed.

[Brief description of drawings]

FIG. 1 is a flowchart schematically showing a procedure of evaluation analysis of the present invention.

FIG. 2 is an index (hk) for an InGaAs multilayer structure sample.
A plurality of X-ray diffraction profiles measured by changing l).

FIG. 3 is an example in which the analysis method of the present invention is applied to a peak spread on the trapezoid of FIG. The result of collecting and arranging each (hkl) profile in which the horizontal axis is converted to the difference ΔA.

FIG. 4 is an X-ray diffraction profile obtained by measuring a selected growth sample by changing a plurality of indices (hkl) and converting the horizontal axis from the difference Δθ to the difference ΔA. As the characteristic points that characterize the peak spread shape, the upper end point and the lower end point indicated by arrows are taken and used for the analysis of FIG.

FIG. 5 is an example in which the analysis method of the present invention is applied to a selective growth sample. ΔA corresponding to the upper and lower points in FIG.
_(hkl) value data collected and plotted against the ^{(k 2 + l 2) /} h 2 Fig.

─────────────────────────────────────────────────── ─── Continuation of the front page (56) References JP 2000-88775 (JP, A) JP 11-183408 (JP, A) JP 10-213554 (JP, A) JP 2001-228103 ( (58) Fields surveyed (Int.Cl. ⁷ , DB name) G01N 23/00-23/227 H01L 21/66 JISC file (JOIS)

Claims (2)

(57) [Claims] 1. Two or more (hk having different indices)
l) a step of measuring the reflection profile with a symmetrical reflection arrangement with respect to the α-ray incident angle (θ), and one point of the reference α-ray incident angle (θ _ref ) in each (hkl) profile. A step of selecting and converting the X-ray incident angle, which is the horizontal axis of the profile, into a difference Δθ _(hkl) : = θ−θ _ref of the X-ray incident angle from the reference point as a new horizontal axis; Based on the difference in the line incident angle, the cube of the lattice constant a ₀ corresponding to the reference point, the inverse square of the wavelength λ of the X-ray, the reflection index h
Squared, the sine of twice the Bragg angle θ _{B, (hkl)} of the (hkl) reflection corresponding to the reference point, and a constant (−2) to the difference Δθ _{(hkl in the} X-ray incident angle _{. )} New difference with the dimension of the lattice constant obtained by multiplying Is calculated, and the horizontal axis of each (hkl) profile is converted from the difference Δθ _{(hkl )} of the X-ray incident angle to the new difference ΔA _(hkl) to renormalize the horizontal axis (hkl). A step of newly drawing a profile, and the broadened peaks observed in a series of the renormalized (hkl) profiles obtained with different obtained indexes (hkl) are the targets of analysis, and the broadening of the broadened peaks to be analyzed. The difference ΔA between a plurality of points (feature points) that characterize the shape
_The step of extracting the value of (hkl) for each (hkl) profile, and each ΔA _(hkl) value of the feature point with respect to the quantity (k ² + l ² ) / h ² calculated from the index (hkl) The process of preparing the plotted graph and determining whether or not the series of plotted points for each feature point on the graph are on a straight line, respectively, the peak broadening shape of the broadened peak to be analyzed is the composition. A method for analyzing a crystal structure using X-ray diffraction, which comprises a step of determining whether or not the shape is a peak broadening shape caused by the distribution. 2. The crystal structure analyzing method according to claim 1, wherein an upper end, a lower end, and a center of the peak spread shape are selected as the points that characterize the spread shape of the spread peak.