Corresponding author: Kirill D. Shcherbachev (shcherbachev.kirill@mail.ru)

The capabilities of X-ray diffuse scattering (

Among the problems faced by the technologies of semiconductor single crystals with preset properties that are determined mainly by the structural perfection and homogeneity of the crystals, there are important issues relating to the origins and properties of microdefects in their crystal lattice as well as microdefect study and nondestructive control methods. Hereinafter we will consider microdefects to be local violations of crystal lattice periodicity caused by clusters of point defects (intrinsic or impurity), dislocation loops or dispersed phase precipitates having submicron or micron sizes. All these violations are first type defects [

Below we will dwell upon more detailed aspects of the problem in question: capabilities of the

The theory of X-ray diffuse scattering

The

where

If the local displacements around the defects are small and _{dif}(

where _{H}_{0} is the unit cell volume. For example, a defect with a Coulomb type displacement field _{0})/^{2} has the power _{0}) which depends on the direction of the unit vector _{0} and its sign is similar to that of Δ_{i}_{i}

where _{mn}_{mn}_{i}_{i}_{i}_{1} differs from zero, for tetragonal symmetry π_{3} = 0 and for trigonal symmetry π_{2} = 0. In some cases, γ_{i}_{i}

During point defect association in the course of structural transformation caused by post-crystallization cooling and process heat treatments, the sizes of the strong distortion regions around defects increase. As a result, the range of ^{-2} is true (the Huang scattering region) is narrowed. For heavily distorted regions (_{0}(^{–1/2} range the asymptotic diffuse scattering cross-section expression takes on as follows [

here the function Ψ ~ 2 depends on the angle between the vectors

The components of the tensor _{nm}

where Ω_{mn}_{n}b_{m}_{m}b_{n}_{11} + _{12} + 2_{44}; _{ij}

The first term in brackets of Eq. (2) corresponds to Huang scattering which is symmetrical relative to the reciprocal lattice site (_{z}_{z}

The shape of the diffuse scattering iso-intensity contours is determined by the type of the defects and the symmetry of their displacement fields. The shape of the diffuse scattering iso-intensity curves allows one to determine the symmetry of the displacement field and choose between their possible configurations. It is sometimes sufficient to analyze the

Huang scattering region: scattering at weak elastic lattice distortions far from the defect centre. The distance r from the defect centre is far greater than its characteristic size R0. The intensity expression is I (q) ~ q-2. The tangent of the slope angle of the lg I (q) = f (lg q) dependence in this region is -2;

asymptotic diffuse scattering (ADS) region: scattering at relatively strong lattice distortions obeying the elastic continuum theory. In this case I (q) ~ q-4, which corresponds to a slope of -4 (in the same coordinates). The bending point q0, which marks the Huang to asymptotic scattering transition can be used for evaluating the defect’s power:

defect core scattering region. This is the region of small r ≤ R0 (Laue scattering) in which scattering is quite difficult for experimental measurement since at low defect concentrations and sufficiently large q > qT even Laue scattering is but a small part of the thermal diffuse scattering which decreases in the same coordinates with a slope of –2. This scattering can be used as the internal reference for defect concentration determination [14].

The expression of diffuse scattering at thermal oscillations [

where

A convenient expression was reported [_{def} of microdefects in the crystal from the ratio of the Huang and thermal diffuse scattering intensities:

where _{H}_{T} are the wave vectors for the angular deviations from the reciprocal lattice site where Huang or thermal diffuse scattering dominate.

This expression allows measuring the

The above

Huang scattering is efficient if all the microdefects have the same sign of power ^{-0.5} << _{0}^{-3}, where _{0} is the characteristic microdefect size [_{z}_{z}^{3}_{z}_{z}_{z}

where _{zi}_{z}^{3} = _{z}^{-0,5} << _{0}^{-3} is as follows [

for dislocation loops:

where _{L}

for defect clusters with the radius Rcl: ncl=43πQRcl.

Thus, the

On the other hand, a change in the lattice parameter caused by point defects in the crystal is also related to the double-force tensor components. For example, in cubic crystals [

where Δ_{ij}_{11} = _{22} = _{33} and π_{1} = 3_{11}^{2}, whence

where

Equations (11) and (12) give the relaxation volume for one point defect which can be evaluated from the respective change in the lattice parameter:

where Δ

where _{i}_{v}

Thus, precision lattice parameter measurements allow evaluating the differential point defect concentration if the relaxation volumes are known. The symmetrical part of Huang scattering does not depend on the defect power sign, and the intensities of the radiation scattered from defects with opposite power signs are superimposed. However, at somewhat greater

Thus, precision lattice parameter and diffuse scattering measurements are complementary methods allowing one to analyze structural changes in the state of point defects at early stages of solid solution decomposition in semiconductors. We will demonstrate this below with some examples.

Early precipitation stages in Si(O) solid solution containing (7–8) ∙ 10^{17} cm^{-3} oxygen in silicon was studied [

^{3}^{5} compounds (e.g. 100 Frenkel pairs per one neutron remained after GaAs irradiation in the same reactor). However, the vacancy and interstitial type defects remaining in InSb agglomerated into vacancy and interstitial type microdefects. Fig. _{z}_{z}_{diff}(^{3} = _{z}^{16} cm^{-2}. The _{z}_{z}

_{z}_{t}, cm^{–2}: (^{16} cm^{–2}; (^{17} cm^{–2}; (^{18} cm^{–2}.

(_{z}^{18} cm-^{2} fluence (_{0} = 4·10^{14} cm-^{3}, _{fn}^{18} cm-^{2}; (_{0} =5·10^{13} cm-^{3}, _{fn}^{17} cm-^{2}; (_{0} = 1.7·10^{15} cm-^{3}, _{sn}^{17} cm-^{2}.

An interesting example demonstrating the efficiency of combined lattice parameter and _{2}Te_{3} complexes which do not form microdefects as suggested by the low diffuse scattering intensity). A similar observation was made later using the same methods for GaP single crystals that were also doped with a 6B subgroup element (sulfur). InP neutron irradiation decreased the lattice parameter over the entire Te concentration range. This decrease was for the first time revealed for InP and for single crystals irradiated with different neutron fluencies (Fig. _{In} (phosphorus in indium position) form in the crystal in a sufficient quantity to decrease the lattice parameter in the presence of Frenkel defects which increase the lattice parameter. The crystals were heat-treated [^{18} cm^{-3}. However, the change in the

InP lattice parameter as a function of major carrier concentration (^{19} cm^{–2} fluence (thermal and rapid neutron fluence ratio is 1).

InP lattice parameter as a function of rapid neutron fluence for crystals with different initial impurity content ^{–3}: (^{18} ; (^{16}; (^{16} ; (^{17} ; (^{16} ; (^{17}; (^{18}.

(^{19} cm^{–2}; (^{17} cm^{–2}; (^{19} cm^{–2}: (_{ann} = 200 °C; (

We consider another typical application example of the methods. Post-growth cooling of nonstoichiometric GaAs and GaP crystals with significant quantities of excess cations caused precipitation of excess Ga resulting in the formation of interstitial Ga (Ga_{i}_{i}_{i}^{18} cm^{-3} phosphorus vacancies. It can be seen from Fig. _{z}_{x}

Typical

Fig. _{x}_{x}

_{x}

Thus, analysis of the

We consider another interesting _{0} can be evaluated from the vector _{0} corresponding to the knee point in the

,

where

The other method is based on analysis of the dependence. Fig. _{z}_{z}_{z}^{-4} mm^{3}, and so their radius was estimated to be ~0.5 mm. This estimate agrees with the loop radius assessed from the _{0} value. (The respective figure is not shown for brevity.) The diffuse scattering pattern for the other region was completely different. The diffuse scattering intensity (the amplitude and period of the oscillation peaks) suggests that the number and sizes of the loops decreased. At the same time, intense scattering arose at _{z}

_{z}^{18} cm^{–3}) near the [[333]] site: (

Analysis of the results showed that the

For the GaP and InP examples, a structural microdefect formation mechanism was revealed associated with the interaction of defects forming during the decomposition and residual intrinsic defects.

The mechanism of sulfur polytropy in gallium phosphide was observed for the first time.

Study of the evolution of diffuse scattering iso-intensity contours in GaP, GaAs(Si) and Si(O) allows tracing the evolution of microdefects from matrix-coherent ones to microdefects with smeared coherency resulting from microdefect growth.

^{III}

^{V}compounds. Pt 1.