JP2940271B2 - Crystal dislocation density measurement 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 for measuring the dislocation density of a crystal by X-ray topography.

[0002]

2. Description of the Related Art Conventionally, as a method of measuring the dislocation density of a crystal, a method of forming an etch pit by etching and then obtaining it from the density of the etch pit (J. Phys. C6 40 (19
79) 151)) and a method of obtaining the density from dislocation observation by a transmission electron microscope (TEM). Although dislocation evaluation using an X-ray topograph is also performed, there is no disclosure of a method for evaluating the dislocation density from an X-ray topographic image.

[0003]

Both the etching method and the TEM method are destructive tests. Therefore, the crystal after measurement cannot be used for another purpose.
In addition, the etching method cannot be performed without an appropriate etchant for forming an etch pit. Even if there is an appropriate etchant, since the etchant usually forms an etch pit only on a surface in a specific direction, it is necessary to polish the surface before etching. For this reason, the measurement of dislocation density by etching requires a lot of trouble and time. The method using a TEM also requires a lot of trouble and time for sample preparation. Further, since the observable region is very narrow, only a small region of a crystal having a high dislocation density can be measured.
The present invention has been made in view of such conventional circumstances, and an object of the present invention is to provide a method for measuring the dislocation density of a crystal in which the dislocation density can be measured non-destructively and easily over a wide range.

[0004]

In order to achieve the above object, a method for measuring the dislocation density of a crystal according to the present invention comprises:
This is a method for measuring the dislocation density of a crystal by a transmission X-ray topograph of the crystal, wherein the sum of the lengths of the dislocation lines is L, and the volume of the diffraction region from which L is obtained is V, the dislocation density D of the crystal
D is determined by DD = 2L / πV. Also, the present invention is a method for measuring the dislocation density of a crystal by a reflection X-ray topograph of a thin film crystal, wherein the number of dislocation lines in a certain direction i per unit length is smaller of _Ni , the film thickness or the X-ray penetration depth. Is t, the dislocation density DD of the thin film crystal is determined by DD = 2 (N ₁ + N ₂ + N ₃ +...) / Πt.

[0005]

(1) According to the method of the present invention, when calculating the dislocation density from an X-ray topograph, assuming that the dislocation is a straight line and its direction is isotropic, What is necessary is to divide the length by the volume of the diffraction area and add 2 / π. FIG. 2 is an explanatory diagram of the dislocation density calculation method. The angle 3 between the normal to the crystal surface 1 and the dislocation line 2 is defined as θ. here,
Assuming that the dislocation density per unit solid angle is a, the dislocation density within the range of the solid angle dΩ on the crystal surface 1 in FIG. 2 is a · cos θ · dΩ. By integrating this over the entire hemisphere, the dislocation density DD can be calculated as in the following equation (1).

[0006]

(Equation 1) Next, let the thickness 4 of the crystal be t. Assuming that a projection length 5 of a dislocation line photographed by a transmission X-ray topograph on the crystal surface is 1, it is represented by t · tan θ. At this time, the length L of the dislocation line photographed by the X-ray topograph per unit area
₁ is calculated as in the following equation (2).

[0007]

(Equation 2) Here, assuming that the area for measuring the length of the dislocation line is S and the sum of the lengths of the dislocation lines is L, the following equation (3) is obtained. L = SL ₁ = π ² atS / 2 = π ² aV / It becomes 2. Here, V is the volume of the diffraction region obtained by summing the lengths of dislocation lines. Therefore, the dislocation density is represented by the following equation (4) by the total length L of the dislocation lines of the X-ray topograph. DD = 2L / πV

(2) In a reflection X-ray topography of a thin film crystal which has been grown on a substrate, dislocations are usually observed only in a limited direction. This is because dislocations exist along a specific slip surface, and dislocation lines are observed only in the direction of the line of intersection between the slip surface and the surface of the thin film crystal. For example, in the case of zinc blende type crystal, since the slip plane of dislocation is {111} plane, the surface of the thin film crystal is {11}.
Dislocations are observed only in three directions on the {1} plane and its neighboring planes, and only in two directions on the {100} plane. Here, assuming that the number of dislocation lines in one direction per unit length is N, there are N dislocation lines of unit length per unit area.
Therefore, the sum of the lengths of dislocation lines per unit area is equal to N. Therefore, if total the number per unit length of the dislocation lines in all directions, the value is the sum L ₁ length of dislocation lines per unit area. Equation (1) and Equation (2)
Since the dislocation density DD is 2L ₁ / πt, the dislocation density in a certain direction i is represented by the following equation (5), where N _i is the dislocation linear density. DD = 2 (N ₁ + N ₂ + N ₃ +...) / Πt where t is the thickness of the diffraction region. When the penetration depth of the X-ray is smaller than the thickness of the epi layer, the value is t. The X-ray penetration depth is defined as the depth at which the intensity of the X-ray becomes 1 / e, and is the reciprocal of the absorption coefficient μ of the sample with respect to the X-ray. It is expressed as in equation (6) (reference [1]: X
International Tables for X-ray Crys
tallography (1959) 157, The KYNOCH Press)).

[0009]

(Equation 3) However, n: number of atoms in the unit cell, V _c: volume of the unit cell [rho: density, i: atoms for distinguishing suffix A: atomic weight, N _A: Avogadro's number of each atom (μ / ρ) _i is It is given in table form in [1]. When the film thickness is smaller than the X-ray penetration depth, the value of the film thickness is set to t. However, in this case, it is assumed that the dislocation density on the substrate side is sufficiently smaller than that of the epi layer. This is based on the fact that many of the dislocations occur at the interface with the substrate and are introduced into the epilayer.

[0010]

Embodiments of the present invention will be described below. (1) A transmission X-ray topograph of a CdZnTe crystal having a thickness of 1 mm was taken. The plane orientation of the crystal is {211}, the reflection plane is {111}, and the X-ray is AgKα. 0.2 × 0.
When the total length of dislocation lines was measured for a 2 mm region, it was 4.9 mm. By substituting this value for L in equation (4), the dislocation density DD was calculated as DD = 2 × 0.49 / 4 × 10 ⁻⁵ π, which was calculated to be 7.8 × 10 ³ cm ⁻² . The same measurement was performed on the whole crystal to obtain the distribution of the dislocation density of the crystal.

(2) FIG. 1 is a reflection X-ray topographic image of the epi layer when the above-mentioned CdZnTe crystal is used as a substrate and a HgCdTe crystal is grown thereon by a molecular beam epitaxy method. The epi film thickness is 11.27 μm, the reflection surface is {440}, and CuKα. In FIG. 1, the line shown in black is a dislocation line. Three {1} on {211}
Dislocation lines are seen in three directions crossing the 11 ° plane. In FIG. 1, the number of dislocation lines in three directions per cm is 223 / cm, 213 / cm, and 154 / cm, respectively. By the way, the penetration depth of X-rays in HgCdTe was calculated to be 5.4 μm by substituting the value of (μ / ρ) _i in the document [1] into equation (5). Therefore, the dislocation density DD was DD = 2 (223 + 213 + 154) /5.4×10 ⁻⁴ π, and was calculated to be 7.0 × 10 ⁵ cm ⁻² . The same measurement was performed on the entire thin film crystal to obtain a distribution of dislocation density of the crystal. These values were in good agreement with the dislocation density determined from the etch pits.

[0012]

As described above, according to the method of the present invention, the dislocation density can be easily and nondestructively measured over a wide range by an X-ray topograph.

[Brief description of the drawings]

FIG. 1 shows HgCdTe on a CdZnTe substrate.
X showing a reflected X-ray topographic image of the epi layer grown at 7 μm
It is a line photograph.

FIG. 2 is an explanatory diagram of a dislocation density calculation method.

[Explanation of symbols]

 Reference Signs List 1 crystal surface 2 dislocation line 3 angle between normal and dislocation line of crystal surface 4 crystal thickness 5 projection length of dislocation line to crystal surface

Claims (2)

(57) [Claims] 1. A method for measuring the dislocation density of a crystal by means of a transmission X-ray topograph of the crystal, wherein the sum of the lengths of the dislocation lines is L and the volume of the diffraction region from which L is obtained is V, A method for measuring the dislocation density of a crystal, wherein the dislocation density DD is determined by the following formula: DD = 2L / πV. 2. A method for measuring dislocation density of a thin film crystal by reflection X-ray topography, wherein the number of dislocation lines in a certain direction i per unit length is represented by N _i , film thickness or X-ray penetration depth. Where t is the smaller value of the dislocation density, the dislocation density DD of the thin film crystal is determined by the following formula: DD = 2 (N ₁ + N ₂ + N ₃ +...) / Πt .