J. Vac. Sci. Technol. B 25„3…, May/Jun 2007

1. Optical properties of molecular-beam-epitaxy-grown InGaMnAs thin films
F. C. Peirisa͒ and J. I. Hungerford
Department of Physics, Kenyon College, Gambier, Ohio 43022
O. Maksimov and N. Samarth
Department of Physics and Materials Research Institute, Pennsylvania State University, University Park,
Pennsylvania 16802
͑Received 6 November 2006; accepted 26 March 2007; published 31 May 2007͒
The authors have determined the dielectric functions of a series of molecular-beam-epitaxy-grown
͑In0.5Ga0.5͒1−xMnxAs thin films deposited on InP substrates. Two variable angle spectroscopic
ellipsometers, covering both the IR and the UV range ͑0.2– 30 ␮m͒, were used to obtain optical
spectra for each of the samples. Using a standard inversion technique, the experimental data were
modeled to obtain the dielectric function for each of the quaternary samples. By using a parametric
semiconductor model, they deduced the critical point parameters corresponding to the electronic
transitions 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 Mn
concentration, the E1 critical point shows a redshift with respect to the Mn concentration. © 2007
American Vacuum Society. ͓DOI: 10.1116/1.2734161͔
I. INTRODUCTION Besides providing useful information such as the index of
Ga1−xMnxAs and In1−yMnyAs are two interesting ternary refraction and the absorption coefficient, the complex dielec-
systems manifesting both semiconductor and magnetic prop- tric function ͑⑀ = ⑀1 + i⑀2͒ of a semiconductor provides infor-
erties and belong to a class of materials known as diluted mation about the electronic structure of the lattice.14,15 The ⑀1
magnetic semiconductors.1–3 A large volume of work points and ⑀2 spectra can be used to determine the electronic tran-
to the fact that the ferromagnetic interaction can be aug- sitions in the Brillouin zone ͑i.e., E0, E1, E1 + ⌬1, E2͒, pro-
mented by increasing the Mn concentration, which in turn viding information on the band structure of the semiconduc-
would increase the Curie temperature of these systems.4 tor system. Although there are several methods available to
However, in Ga1−xMnxAs, the incorporation of Mn into the determine ⑀, spectroscopic ellipsometry is one of the more
GaAs lattice has an upper limit because of the constraints efficient methods, as it does not require one to perform a
involved in the solubility of Mn in GaAs and in In1−yMnyAs Kramers-Kronig transformation.16
system; although one can incorporate high concentrations of In this present study we have therefore used spectroscopic
Mn ͑around 20%͒, other parameters that govern the ferro- ellipsometry to investigate ⑀ for a series of
magnetic interaction ͑i.e., lighter hole mass and weaker Mn- ͑InyGa1−y͒1−xMnxAs thin films grown on InP substrates. Us-
hole exchange͒ tend to overcompensate the advantages ing a parametric semiconductor model to represent ⑀ ob-
gained by higher Mn concentrations in the alloy.5 It is con- tained from ellipsometry, we determined the critical point
ceivable therefore that some of the deficiencies involved in structure for each of these thin films. Our results show the
Ga1−xMnxAs and In1−yMnyAs systems can be rectified by functionality of E0 and E1 critical points as a function of the
marrying these systems to form the quaternary Mn concentration for the ͑InyGa1−y͒1−xMnxAs system.
͑InyGa1−y͒1−xMnxAs.6–8 This system has the distinct advan-
tage of large tunability, in terms of both lattice parameter and II. EXPERIMENTAL DETAILS
band gap, and also offers a variety of other benefits such as The ͑InyGa1−y͒1−xMnxAs samples were grown by low-
the flexibility of varying the magnetic anisotropy and the temperature molecular beam epitaxy ͑MBE͒ on semi-
easy magnetization axis.9 Most of the research performed to insulating InP ͑100͒ substrates. An Applied EPI 930 MBE
understand the interesting characteristics of the quaternary system equipped with In, Ga, Mn, and As effusion cells was
system has been limited mainly to magnetic properties, using used to perform the growth. Initially, the substrates were
techniques such as magnetometry, magnetoresistance, super- deoxidized ͑ϳ480 ° C͒, and a 100 nm thick In0.5Ga0.5As
conducting quantum interference device, and magnetic circu- buffer was deposited. The substrate temperature was then
lar dichroism. However, studies pertaining to optical proper- lowered to 300 ° C before depositing the quaternary layer.
ties of magnetic semiconductor systems can also furnish Reflection high energy electron diffraction ͑RHEED͒ was
insights into the origin of their ferromagnetic properties, es- used to monitor the quality of the specimens, which showed
pecially in terms of their band structure dynamics.10–13 Pres- a nice streaky pattern indicative of smooth two-dimensional
ently, however, there is a scarcity of such studies with re- growth. In all, a total of four samples were grown for this
spect to ͑InyGa1−y͒1−xMnxAs. study with y = 0.5, and 0 ഛ x ഛ 0.079. The other details re-
lated to the experimental growth procedures are published
a͒
Electronic mail: peirisf@kenyon.edu previously.8
1087 J. Vac. Sci. Technol. B 25„3…, May/Jun 2007 1071-1023/2007/25„3…/1087/3/$23.00 ©2007 American Vacuum Society 1087

2. 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 using
the lattice parameters obtained by x-ray diffraction experi-
ments and comparing them to previously calibrated samples.
The thickness of the quaternary film was estimated from
RHEED oscillations and verified by x-ray reflectivity and
ellipsometry. Ellipsometric spectra were obtained using two
ellipsometers; 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 given
sample, once the spectra were taken separately in each of
these 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 incident
angles.
III. RESULTS AND DISCUSSION FIG. 1. Real part ͑⑀1͒ of the complex dielectric function of four different
Spectroscopic ellipsometry generally measures two pa- samples of ͑In0.5Ga0.5͒1−xMnxAs.
rameters, ⌿ and ⌬, at each wavelength that are related to the
ratio of reflection coefficients by
nonzero values for ⑀2͒ seems to blueshift as a function of the
Rp Mn concentration. In order to fully recognize the dependence
␳= = tan͑⌿͒ei⌬ ,
Rs of the critical point energies with respect to the Mn concen-
where R p is the complex reflection coefficient for light po- tration of the quaternary system, ⑀ for each sample was rep-
larized parallel to the plane of incidence, and Rs is the coef- resented using a parametric semiconductor model.19 In this
ficient for light polarized perpendicular to the plane of inci- method, ⑀ is expressed as a summation of energy-bounded,
dence. One must note that both ⌿ and ⌬ obtained from Gaussian-broadened continuous functions, accounting for
ellipsometry depend on the optical properties of the entire absorption effects that occur outside the model region.
structure, and since the technique is an inverse problem, a The ⑀ for all of the films were modeled according to the
suitable model has to be formulated to arrive at a reliable above stated scheme. This allowed us to determine two of
solution.17,18 the critical points associated with the electronic transition in
The ͑In0.5Ga0.5͒1−xMnx samples used in this study were the ͑In0.5Ga0.5͒1−xMnxAs quaternary system. In Fig. 3, E0 and
represented by a four layer model ͑i.e., InP substrate, E1 critical point energies are plotted as a function of Mn
In0.5Ga0.5As buffer, quaternary layer, and a surface oxide concentration. It is important to note that since the excitonic
layer͒. Using the sample in which the quaternary layer was effects dominate near the E1 critical point, the measurement
absent, ⑀ 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 For
the samples with the quaternary alloy, the thicknesses and ⑀
of the ͑In0.5Ga0.5͒1−xMnx layer were adjusted to match the
experimental 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 the
fundamental E0 band gap͒ as well as the thicknesses of the
quaternary 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 layer
thickness and the transparent region optical properties were
determined, the next step was to simulate the above band gap
optical properties of this layer.15
The components of the complex dielectric function, ⑀1
and ⑀2, determined from the above procedure are plotted in
Figs. 1 and 2, respectively. In both figures, ⑀ of In0.5Ga0.5As
is shown as solid lines. As is evident from both Fig. 1 and 2,
the incorporation of Mn into the lattice alters ⑀, particularly FIG. 2. Imaginary part ͑⑀2͒ of the complex dielectric function of four differ-
as noted in Fig. 2, the onset of the initial absorption ͑i.e., ent samples of ͑In0.5Ga0.5͒1−xMnxAs.
J. Vac. Sci. Technol. B, Vol. 25, No. 3, May/Jun 2007

3. 1089 Peiris et al.: Optical properties of molecular-beam-epitaxy-grown InGaMnAs 1089
these dielectric functions were represented by a parametric
semiconductor model which accounts for absorption effects
outside the model region. Our analysis indicates that in
͑In0.5Ga0.5͒1−xMnxAs, while the critical point associated with
the fundamental gap, E0, blueshifts as a function of Mn con-
centration, the E1 critical point shows a redshift with respect
to the Mn concentration.
ACKNOWLEDGMENTS
The work at Kenyon was supported by grants from Re-
search Cooperation ͑CC-6027͒, American Chemical Society
͑PRF-41803B͒, and National Science Foundation ͑DMR-
0521147͒. The work at Penn State was supported by the Na-
tional Science Foundation.
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JVST B - Microelectronics and Nanometer Structures