Discussion

Figure 4.16: Intersection between the isoline corresponding to the normalised intensity value and the experimental lattice parameter, respectively, of CdZnSSe layer (sample A).

isoline corresponding to the normalised intensity value experimentally obtained and the similar isoline for the experimental lattice parameter. In the same way are obtained also Fig. 4.15 and Fig. 4.16 made for sample A and B. The values for the normalised intensity and corresponding lattice parameters are shown in Table 4.2, followed by the determined Cd and S concentrations. As expected, the S concentration increases with the decrease of the spacer thickness, pointing out a strong intermixing at smaller spacer thickness. The values of the Cd concentrations are still small in comparison with the nominal ones.

Using these concentration values for the simulation of XRD diffraction patterns, a small shift of the calculated pattern is observed compared with the experimental scan.

This confirms the fact that, using this approach, the values obtained for the average lattice parameter of the superlattice are underestimated. However, a semiquantitative estimation of the Cd and S concentration in the quaternary CdZnSSe could be obtained.

4.4 Chemical composition of CdSe and ZnSSe layers This contains the local modulus of the beam g, given bya(g₀₀₂, r) =|A(g₀₀₂, r)|, and the local phase of the (002) beam, given by p(g₀₀₂, r). The condition for a good accuracy of the measured local modulus of the (002) beam requires a good signal-to-noise ratio, a small dependence on specimen thickness fluctuations and local variations of imaging parameters such as the defocus.

Looking at the dependence of the structure factor on the composition, as shown for Cd_xZn_1−xSe and ZnS_xSe_1−x in Fig. 2.6, it is obvious, for example, that this is negative for a Cd concentration x<0.4 and positive for x>0.4. Consequently, the same value for the modulus of the (002) beam corresponds to two different concentrations. To get rid of this ambiguity, the phase of the (002) beam has to be taken into account. This phase has a difference ofπ between the regions with x<0.4 and x<0.4. Therefore, it is desirable to know at least the sign s(g002, x) of the (002) beam. For clarity, the sign of a beam g in accordance with its structure factor is defined as:

s(g, x) := sign(F_S(g, x)) (4.3) The sign of the (002) beam for Cd_xZn_1−xSe is given by:

s(g₀₀₂, x) = (

−1 :x <0.4

+1 :x >0.4 (4.4)

Then, the local signed modulus of the beam g is defined as:

a_S(g, r) =s(g, x(r))· |F(g, r)| (4.5) In the conventional{002}DF imaging condition the modulus and the phase of the beam are not directly accessible. Actually the local intensity of the electron wave is recorded in the image plane. The Fourier transform of the image intensity (the diffractogram) can be used then for investigation. This means that the ambiguity of the modulus of the (002) reflection discussed in the previous section cannot be resolved.

Furthermore, a diffractogram reflection corresponds to a spatial frequency g_pwhich is not related to only one beam, but contains contributions from interferences of pairs of beams and, for sufficiently thin specimens, the undiffracted beam g = 0 has the largest amplitude. If we consider the{002} DF images shown in the previous section, only the (002) beam had passed through the objective lens, hence the corresponding diffractogram contains only a reflection at g = 0. The local amplitude of this beam J(g₀₀₀, r) = F(g₀₀₂, r)² is usually small. As a consequence, a measurement ofJ(g₀₀₀, r) obtained from a{002}DF image has a small signal-to-noise ratio.

Another disadvantage of using{002}DF images is the larger impact of inelastically scattered electrons. The objective lens posseses different focal lengths for inelastically scattered electrons and elastically scattered electrons. Therefore, inelastically scattered electrons cause a diffuse (incoherent) background intensity Iinel in the image. These a-dditional electrons can lead, for example, to a nonvanishing image intensity when the concentration is around 40 % for Cd and respectively 60% for S. The effect of inelastic scattering on the interpretation of the{002}DF images is readily estimated by assuming that I_inel is constant over each line scan. The normalised intensity shown in the {002}

DF images is given by:

I₀₀₂ = I_el+I_inel

I₀+I_inel (4.6)

where I_elis the intensity of elastically scattered electrons and I₀is the intensity of elasti-cally scattered electrons in the reference region where x = 0. In the absence of inelastic scattering, the normalised intensityI^∗ =Iel/I0 is obtained in simulations. SinceIel ≤I0

the observed normalised intensityI₀₀₂is smaller then the simulated oneI^∗. Therefore, the interpretation of the intensity distribution in DF (002) images leads to concentrations for Cd and S that are smaller then the real ones.

Since the background intensity is one of the big problems for the accuracy of the experimental normalised intensity, the limits of the chemical evaluation using (002) dark field imaging were recently analysed for the case of InGaAs/GaAs system [125].

Comparing the experimental data obtained from ternary InGaAs layers with diffe-rent In content with the simulations, the presence of the background intensity was iden-tified. The chemical contrasts are not distinguishable in a range of0.1< x < 0.2where the minimum of the intensity is reached. In this range the contribution of the (004) reflection and the diffuse scattering from amorphous material exceeds over the useful signal and the actual In concentration cannot be determined. The same procedure was applied to a certain extent for quaternary InGaAsN layers [126].

In principle, similar considerations can be made for the CdSe/ZnSSe system as well.

Since the simulations of the intensity reveal a minimum at nominal Cd concentrations of about 40%, it is expected that in a range of about 10 % around the minimun the concentration cannot be really distinguished. The nonvanishing measured intensity is interpreted as useful signal and results in a misestimation of the Cd concentration towards smaller or larger values. The two situations can be recognised by the presence of the characteristic change in contrast which is observed in DF images at concentrations larger then 40 %.

In the case of S in ZnSSe, the minimum calculated intensity occurs at around 60%. At the nominal values of 12 to 40 % S concentration in the spacer layers of the investigated samples, the useful signal has to be clearly predominant. Hence, the results obtained from the {220} DF images are in good agreement with the nominal S concentrations.

Therefore, the smaller value of the average lattice parameter of the superlattice shown by the comparison with HRXRD can be assigned to an underestimation of the Cd con-centration. This indicates that the Cd concentrations in the investigated samples can be in a range of 40±10% making the same assumption as in Ref. [126].

The chemical sensitivity of the (002) reflection can be further exploited to quantify the composition of the ternary compounds at higher resolution and better accuracy by using an electron interference pattern obtained from primary and chemically sensitive {002}beam. This approach has two advantages compared with the DF technique. First, the inelastically scattered electrons can be considered as incoherent and their effect is reduced. Secondly, the generation of the images with periodic contrast pattern enables an effective noise reduction by the Wiener-filtering technique. In the Fourier trans-formed images, the significant information is localised in the reflections, whereas the noise spreads over the whole area.

Employing the Compositional Evaluation by Lattice Fringe Analysis (CELFA) tech-nique [127], based on the evaluation of high resolution lattice fringe images obtained from the two beam interference a better accuracy of the determined Cd content can be expected in general. The method has been successfully applied for ternary materials [54, 120]. In the case of quaternary compounds the situation is still complicated by the fact that there are two variables. Moreover, to obtain a good high resolution image,

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