Determination of Mn and P concentration
in Ga_1-xMn_xAs_1-yP_y

L. Horák¹, V. Holý¹, V. Valeš¹, C. R. Staddon², P. Wadley², R. P. Campion²

¹ The Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University, Ke Karlovu 5, 121 16 Prague 2, Czech Republic

² School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK

horak@karlov.mff.cuni.cz

Gallium manganese arsenide phosphate is a modification of the intensively studied magnetic semiconductor GaMnAs. There is a hope that incorporation of phosphorus could increase Currie temperature due to the stronger interaction in tighter lattice. Influence of phosphorus on concentration of interstitial manganese is another unknown and important effect. These are reasons to improve commonly used method for concentration determination in technological laboratories.

The easiest x-ray approach to determine a concentration of Ga_1-xMn_xAs_1-yP_y quaternary is a comparison of measured lattice parameters with computed ones from Vegard’s law. For this purpose, the tabulated parameters for GaAs and GaP are used. MnAs and MnP is not natively zinc-blend structure, lattice parameters for MnAs(Z-B) and MnP(Z-B) are extrapolated from the x-ray measurements of ternaries with known content from the growth. One lattice parameter is given by two unknown values of concentrations; we have to measure only special series of samples to have the same number of measured parameters and unknown concentration, e.g. the series with the same concentration of P including one sample with no Mn content.

We present a method of concentration determination based on comparison of simulated and measured diffraction curves. For computation of simulated curve the structure factor is used, which is affected by element concentrations. The influence on the structure factor differs for substitutional and interstitial atoms. The dependence of the structure factor on expansion coefficients (relation between concentration and lattice parameter) is very weak. Those coefficients are not very known today and meaning of concentration used in experimental calibration curve is unclear; this is the main advantage of this approach.

The change of intensity with a different concentration can be observed for the so-called weak diffractions. These diffractions are very sensitive to Mn and P content, because contributions of Ga and As atoms to the structure factor have the opposite phase but the similar amplitude. This is demonstrated by Figure 1, which shows a simulated diffraction curve for three diffractions with varying phosphorus concentration from 0% to 30%. The curve for strong diffraction (004) differs only by the peak position, which corresponds to the different lattice parameter, whereas peak intensity is strongly dependent on the concentration in case of weak diffractions (002) and (006). Interesting fact can be derived from this plot; there is a specific concentration of phosphorus, which makes structure factor of GaAsP zero, and in this case, the pure Mn contribution to structure factor can be measured.

The substitutional manganese has very small effect on lattice parameter, which is not quantified yet. Figure 2 shows the shift of peak for (004) which is not sufficient to determine anything, but intensity of (002) diffraction changes rapidly while there is no significant shift.

There are two types of interstitial positions; manganese can be positioned inside of gallium (or arsenic) tetrahedron. Unfortunately, they compensate each other their effect on structure factor for weak diffraction and contribution is too small for strong diffraction. It is case of diamond lattice for the same occupancy where weak diffraction turns to forbidden. We can estimate only the difference of those occupancies from structure factor, the absolute values are surely included in lattice parameter, but we do not know expansion coefficients again.

The number of parameters increases with sensitivity to positions of atoms in the lattice. It is obvious that there is no extra information about lattice parameter for different diffractions, while structure factors differ. We should measure many diffractions to determine concentration properly, but our task was to develop method for rapid laboratory characterization of grown samples. For some instrumental reasons it is necessary to measure reciprocal space maps, not only line scans over substrate and layer peak. If we take into account, that intensity of weak diffraction is very low, those measurements are very time consuming. It is important to find fast method for standard laboratories with no main focus on x-ray and many samples to characterize. We measure only two diffractions (002) and (004), which takes at least 3 days. To solve problem of many parameters we use the control samples with the same phosphorus concentration and no manganese. The assumption of equal concentration is reasonable, control samples are grown anyway within the growing procedure.

The dynamic scattering theory is used to simulate diffraction curves. It is possible to determine concentrations, but there are still problems with numerical instability of optimizing algorithm. To get unique solution one has to use simply model such as homogeneous layer with some fixed parameters (e.g. concentration of As antisites). The aim of this work is to develop a reliable robust method for characterization in a technological laboratory. Latest progress and conclusions will be presented in the talk.

Figure 1 Simulated diffraction curves, concentration of phosphorus goes from 0 to 30%

Figure 2 Concentration of substitutional Mn goes from 0 to 10%

Figure 3 Difference of interstitial Mn concentration goes from 0 to 0.05