Optical properties of molecular-beam-epitaxy-grown InGaMnAs thin filmsF. C. Peirisa� and J. I. HungerfordDepartment of Physics, Kenyon College, Gambier, Ohio 43022

O. Maksimov and N. SamarthDepartment of Physics and Materials Research Institute, Pennsylvania State University, University Park,Pennsylvania 16802

�Received 6 November 2006; accepted 26 March 2007; published 31 May 2007�

The authors have determined the dielectric functions of a series of molecular-beam-epitaxy-grown�In0.5Ga0.5�1−xMnxAs thin films deposited on InP substrates. Two variable angle spectroscopicellipsometers, covering both the IR and the UV range �0.2–30 �m�, were used to obtain opticalspectra for each of the samples. Using a standard inversion technique, the experimental data weremodeled to obtain the dielectric function for each of the quaternary samples. By using a parametricsemiconductor model, they deduced the critical point parameters corresponding to the electronictransitions in the Brillouin zone. Their analysis indicates that in this particular quaternary system,while the critical point associated with the fundamental gap, E0, blueshifts as a function of Mnconcentration, the E1 critical point shows a redshift with respect to the Mn concentration. © 2007

American Vacuum Society. �DOI: 10.1116/1.2734161�

I. INTRODUCTIONGa1−xMnxAs and In1−yMnyAs are two interesting ternary

systems manifesting both semiconductor and magnetic prop-erties and belong to a class of materials known as dilutedmagnetic semiconductors.1–3 A large volume of work pointsto the fact that the ferromagnetic interaction can be aug-mented by increasing the Mn concentration, which in turnwould increase the Curie temperature of these systems.4

However, in Ga1−xMnxAs, the incorporation of Mn into theGaAs lattice has an upper limit because of the constraintsinvolved in the solubility of Mn in GaAs and in In1−yMnyAssystem; although one can incorporate high concentrations ofMn �around 20%�, other parameters that govern the ferro-magnetic interaction �i.e., lighter hole mass and weaker Mn-hole exchange� tend to overcompensate the advantagesgained by higher Mn concentrations in the alloy.5 It is con-ceivable therefore that some of the deficiencies involved inGa1−xMnxAs and In1−yMnyAs systems can be rectified bymarrying these systems to form the quaternary�InyGa1−y�1−xMnxAs.6–8 This system has the distinct advan-tage of large tunability, in terms of both lattice parameter andband gap, and also offers a variety of other benefits such asthe flexibility of varying the magnetic anisotropy and theeasy magnetization axis.9 Most of the research performed tounderstand the interesting characteristics of the quaternarysystem has been limited mainly to magnetic properties, usingtechniques such as magnetometry, magnetoresistance, super-conducting quantum interference device, and magnetic circu-lar dichroism. However, studies pertaining to optical proper-ties of magnetic semiconductor systems can also furnishinsights into the origin of their ferromagnetic properties, es-pecially in terms of their band structure dynamics.10–13 Pres-ently, however, there is a scarcity of such studies with re-spect to �InyGa1−y�1−xMnxAs.

a�

Electronic mail: peirisf@kenyon.edu

1087 J. Vac. Sci. Technol. B 25„3…, May/Jun 2007 1071-1023/2007

Besides providing useful information such as the index ofrefraction and the absorption coefficient, the complex dielec-tric function ��=�1+ i�2� of a semiconductor provides infor-mation about the electronic structure of the lattice.14,15 The �1

and �2 spectra can be used to determine the electronic tran-sitions in the Brillouin zone �i.e., E0, E1, E1+�1, E2�, pro-viding information on the band structure of the semiconduc-tor system. Although there are several methods available todetermine �, spectroscopic ellipsometry is one of the moreefficient methods, as it does not require one to perform aKramers-Kronig transformation.16

In this present study we have therefore used spectroscopicellipsometry to investigate � for a series of�InyGa1−y�1−xMnxAs thin films grown on InP substrates. Us-ing a parametric semiconductor model to represent � ob-tained from ellipsometry, we determined the critical pointstructure for each of these thin films. Our results show thefunctionality of E0 and E1 critical points as a function of theMn concentration for the �InyGa1−y�1−xMnxAs system.

II. EXPERIMENTAL DETAILS

The �InyGa1−y�1−xMnxAs samples were grown by low-temperature molecular beam epitaxy �MBE� on semi-insulating InP �100� substrates. An Applied EPI 930 MBEsystem equipped with In, Ga, Mn, and As effusion cells wasused to perform the growth. Initially, the substrates weredeoxidized ��480 °C�, and a 100 nm thick In0.5Ga0.5Asbuffer was deposited. The substrate temperature was thenlowered to 300 °C before depositing the quaternary layer.Reflection high energy electron diffraction �RHEED� wasused to monitor the quality of the specimens, which showeda nice streaky pattern indicative of smooth two-dimensionalgrowth. In all, a total of four samples were grown for thisstudy with y=0.5, and 0�x�0.079. The other details re-lated to the experimental growth procedures are published

8

previously.

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1088 Peiris et al.: Optical properties of molecular-beam-epitaxy-grown InGaMnAs 1088

While the Mn concentrations were obtained using elec-tron probe microanalysis and x-ray photoelectron spectros-copy, the In and Ga concentrations were determined usingthe lattice parameters obtained by x-ray diffraction experi-ments and comparing them to previously calibrated samples.The thickness of the quaternary film was estimated fromRHEED oscillations and verified by x-ray reflectivity andellipsometry. Ellipsometric spectra were obtained using twoellipsometers; a rotating analyzer ellipsometer operating be-tween 200 and 1800 nm and a rotating compensator ellip-someter operating between 2 and 30 �m. For a givensample, once the spectra were taken separately in each ofthese instruments, they were merged together for the analy-sis. Additionally, for each sample, room temperature ellipso-metric data were obtained for at least two different incidentangles.

III. RESULTS AND DISCUSSION

Spectroscopic ellipsometry generally measures two pa-rameters, � and �, at each wavelength that are related to theratio of reflection coefficients by

� =Rp

Rs= tan���ei�,

where Rp is the complex reflection coefficient for light po-larized parallel to the plane of incidence, and Rs is the coef-ficient for light polarized perpendicular to the plane of inci-dence. One must note that both � and � obtained fromellipsometry depend on the optical properties of the entirestructure, and since the technique is an inverse problem, asuitable model has to be formulated to arrive at a reliablesolution.17,18

The �In0.5Ga0.5�1−xMnx samples used in this study wererepresented by a four layer model �i.e., InP substrate,In0.5Ga0.5As buffer, quaternary layer, and a surface oxidelayer�. Using the sample in which the quaternary layer wasabsent, � of the In0.5Ga0.5As buffer layer was first deter-mined. The results obtained for the buffer layer were consis-tent with the literature values for this particular alloy.19 Forthe samples with the quaternary alloy, the thicknesses and �of the �In0.5Ga0.5�1−xMnx layer were adjusted to match theexperimental data. This was achieved in two steps. First,focusing only on the � and � spectra obtained in the trans-parent region, � in the transparent region �i.e., below thefundamental E0 band gap� as well as the thicknesses of thequaternary system were determined. The thicknesses ob-tained from this method fell within 10% of the values re-corded by RHEED and x-ray reflectivity. After the layerthickness and the transparent region optical properties weredetermined, the next step was to simulate the above band gapoptical properties of this layer.15

The components of the complex dielectric function, �1

and �2, determined from the above procedure are plotted inFigs. 1 and 2, respectively. In both figures, � of In0.5Ga0.5Asis shown as solid lines. As is evident from both Fig. 1 and 2,the incorporation of Mn into the lattice alters �, particularly

as noted in Fig. 2, the onset of the initial absorption �i.e.,

J. Vac. Sci. Technol. B, Vol. 25, No. 3, May/Jun 2007

nonzero values for �2� seems to blueshift as a function of theMn concentration. In order to fully recognize the dependenceof the critical point energies with respect to the Mn concen-tration of the quaternary system, � for each sample was rep-resented using a parametric semiconductor model.19 In thismethod, � is expressed as a summation of energy-bounded,Gaussian-broadened continuous functions, accounting forabsorption effects that occur outside the model region.

The � for all of the films were modeled according to theabove stated scheme. This allowed us to determine two ofthe critical points associated with the electronic transition inthe �In0.5Ga0.5�1−xMnxAs quaternary system. In Fig. 3, E0 andE1 critical point energies are plotted as a function of Mnconcentration. It is important to note that since the excitoniceffects dominate near the E1 critical point, the measurement

FIG. 1. Real part ��1� of the complex dielectric function of four differentsamples of �In0.5Ga0.5�1−xMnxAs.

FIG. 2. Imaginary part ��2� of the complex dielectric function of four differ-

ent samples of �In0.5Ga0.5�1−xMnxAs.

1089 Peiris et al.: Optical properties of molecular-beam-epitaxy-grown InGaMnAs 1089

represents the critical point energy minus the binding energy�R1�.15 It is evident that the fundamental band gap, repre-sented by E0 critical point, clearly blueshifts as a function ofthe Mn concentration. The redshift we see for E1 is typical inseveral diluted magnetic systems �see, for example, resultsfor Cd1−xMnxTe,14 Zn1−xMnxSe,10 and Zn1−xMnxTe �Ref. 11�.The reason for the redshift in these ternary systems can beexplained in terms of the repulsive interactions between theMn d levels and the L-point band states. It is conceivable thatthe �In0.5Ga0.5�1−xMnxAs quaternary system may have a simi-lar effect which dictates the redshift in E1. However, theband structure calculations that would verify this phenom-enon are beyond the scope of this article.

IV. CONCLUSION

Using spectroscopic ellipsometry, we have investigatedthe optical properties of a series of �In0.5Ga0.5�1−xMnxAs thinfilms grown on InP substrates. The spectra obtained by ellip-sometry enabled us to determine the dielectric functions foreach of the samples explored in this study. Subsequently,

FIG. 3. Energy of the transition points E0 �squares� and E1−R1 �triangles�are plotted as a function of Mn concentration.

JVST B - Microelectronics and Nanometer Structures

these dielectric functions were represented by a parametricsemiconductor model which accounts for absorption effectsoutside the model region. Our analysis indicates that in�In0.5Ga0.5�1−xMnxAs, while the critical point associated withthe fundamental gap, E0, blueshifts as a function of Mn con-centration, the E1 critical point shows a redshift with respectto the Mn concentration.

ACKNOWLEDGMENTSThe work at Kenyon was supported by grants from Re-

search Cooperation �CC-6027�, American Chemical Society�PRF-41803B�, and National Science Foundation �DMR-0521147�. The work at Penn State was supported by the Na-tional Science Foundation.

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