Growth and characterization of Ge1

©Sociedad Mexicana de Ciencia de Superficies y de Vacío
Superficies y Vacío 17(4), 10-14 diciembre de 2004
Growth and characterization of Ge1-xSnx alloys grown on Ge(001) and
GaAs(001)
H. Pérez Ladrón de Guevara
Instituto Tecnológico de San Luis Potosí
Avenida Tecnológico S/N Km. 1 carretera a Rio Verde, C. P. 78437, San Luis Potosí, S.L.P.,Mex.
A. G. Rodríguez, H. Navarro-Contreras, M. A. Vidal
Instituto de Investigación en Comunicación Óptica (IICO), Universidad Autónoma de San Luis Potosí
Avenida Karakorum 1470, Lomas 4ta sección, C.P. 78210, San Luis Potosí, S.L.P.,Mex.
Single crystal Ge1-xSnx alloys were grown on Ge(001) and GaAs(001) substrates using a RF magnetron
Sputtering. HRXRD and Raman spectroscopy were used to determine the Sn concentration of the alloys,
HRXRD also shows that alloys with Sn<0.04 are pseudomorphic. Optical properties of the alloys were
analysed in order to determinate the band gap transitions.
Keywords:
∆ω-=∆θ-∆τ are defined for these planes. Then we
obtain the relations
1. Introduction
One of the most fascinating ideas in modern
semiconductor physics represents the realization of
direct energy-gap material based fully on group IV
elements Single crystal Ge1-xSnx alloys have
interesting optical and electrical properties. These
alloys have been reported to transform from
indirect to direct fundamental band gap for x larger
than 0.12.[1] Because of this property they open the
possibility to develop totally based group IV
optelectronic infrared materials systems. The Ge1xSnx alloys exhibit the first direct band gap tunable
from 0.614 > EDG > 0.346 eV for x = 0.06 to 0.15,
[1,2] but it is expected that at higher Sn (∼0.4)
concentrations the EDG decreases to 0 eV [3]. In
addition, Ge1-xSnx would be expected to exhibit
high carrier mobility because of a lower effective
mass than that of the Ge and the lack of polar
optical scattering [3,4] inherent to III-V materials.
Thus this relatively new semiconductor alloy is the
only known example of a direct band gap
semiconductor among the compounds which can be
formed from column IV elements.
In this work we report the structural, Raman, and
optical characterization of Ge1-xSnx alloys obtained
by RF magnetron sputtering grown on two different
substrates Ge(100) and GaAs(100) with Sn
concentration up to 14%.
∆θ =
∆τ =
cos τ s
a⊥ = as
cos τ l
sen τ s
all = a s
sen τ l
∆ω + + ∆ω −
2
+
∆ω − ∆ω −
2
sen θ s
cos τ s
sen θ s
= as
sen θ l
cos(τ s + ∆τ ) sen (θ s + ∆θ )
sen θ s
sen τ s
sen θ s
= as
sen θ l
sen(τ s + ∆τ ) sen(θ s + ∆θ )
These relations are obtained from Braggs’s law
and trigonometric expressions. In these expressions
the elastic constants of the film are not necessary.
The values of ∆ω+ and ∆ω- are obtained from
HRXRD measurements. They are defined as the
separation between the maximums of the diffraction
peeks in the Rocking Curves (figure 2) in the
asimetric planes (in this case ∆ω+ and ∆ω- are the
separation in the planes (-1-15) and (115)
respectively).
The lattice parameters of the alloys, the Sn
concentration and the relaxation of the films were
found using the Macrander´s relations and assuming
the Vegard´s law. It’s found that the alloys with low
Sn concentration x<0.04 have pseudomorphic
characteristics, since the in-plane lattice parameters
in both Ge1-xSnx grown on Ge and GaAs have the
same value of the substrate lattice parameter (figure
3).
The thickness of the Ge1-xSnx alloys that presents
pseudomorphical characteristics were compared
with several critical thickness models [6-9] (figure
2. Experimental Procedure and analysis.
In the HRXRD analysis we used the Expressions
of Macrander[5] defined for asymmetrical
diffraction planes (figure 1) where ∆ω+=∆θ+∆τ and
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©Sociedad Mexicana de Ciencia de Superficies y de Vacío
Superficies y Vacío 17(4), 10-14 diciembre de 2004
τs
θs-τs
4). It was found that the only model in agreement
with our results is the People and Bean model [9],
this model was proposed for the Ge1-xSix alloy. This
is a group IV alloy like Ge1-xSnx alloy and we
believe that this is the reason for the agreement in
the results.
Raman spectroscopy was used to confirm the
existence of the Ge1-xSnx alloys and as another way
to determinate the Sn concentration according to the
linear relation ∆ωGeSn = ω0 – 76.8cm-1 [10] ¨ for the
Raman shift of the peak of Germanium from ω0 =
301.0 cm-1 (figure 5). It was found that the Sn
concentration predicted by the Raman shift of the
alloys is very near to the Sn concentration
determinate by HRXRD as shown in figure 6. This
results probes that Raman spectroscopy is another
way to determine the Sn concentration of the alloys.
The optical properties of the alloys were analysed
using a FT-IR interferometer for measuring the
transmittance of the Ge1-xSnx alloys. Transmittance
measurements were performed for this alloys
(figure 7) and hence the absorption coefficient
were obtained for each sample (figure 8). The
energy bandgap transition values were obtained by
fitting the absorption edge with a model that
includes the direct, indirect transitions and the
Urbach’s tail energy. Also the critical points of the
transmittance and the absorption coefficient, the
parabolic approximations and the differentiates of
this curves were considered.
The determination of the change between indirect
to direct band gap is not easy for Sn concentrations
0.6 < x < 0.13 due to the proximities of the gaps
sometimes only a transition value is observed.
However it’s possible to separate the gap values in
alloys with higher Sn concentration. The
experimental results obtained are not in agreement
with the Tight-Binding model [3] or the PseudoPotential model [11] previously proposed. The data
obtained are very nearly to the Potential of
Deformation theory [12] results published recently
and corroborated by FT-IR [1,2] and spectroscopic
ellipsometry [13], these results are shown in figure
9.
Although the change from indirect to direct band
gap is expected by Potential of Deformation
Theory around Sn = 10%, we only observe
experimentally this change to Sn = 14%.
τL
θL+τL
θL-τL
θs+τs
∆τ
dL
-
aS
ll
aS
θs
θs
ds
aS
aS
Figure 1. Diagram of a X-Ray
diffraction on
asymmetrical planes.as is the substrate lattice parameter,
aL┴ and aLll are the in-growth and in-plane latitice
parameters of the layer respectivaly, θs, θL, τs and τL are
the bragg´s angles and the tilt angle of the plane of the
substrate and layer respectivaly.
SnxGe1-x/Ge/Ge(001)
0
Tg= 170 C
x = 0.02
(004)
x = 0.04
x = 0.09
Intensity (a. u.)
x = 0.10
x = 0.14
SnxGe1-x/Ge/GaAs(001)
0
Tg= 150 C
(004)
x = 0.01
x = 0.06
x = 0.08
x = 0.09
31.5
32.0
32.5
33.0
Conclusions
In conclusion, we have shown that it is possible
to grow crystalline layers of Ge1-xSnx on Ge and
GaAs substrates, with Sn concentration up to x =
0.14. Coherent Ge1-xSnx layers (x < 0.04) can be
grown on Ge substrates according to People and
Bean critical thickness model and therefore have
ω/2θ (degrees)
Figure 2. HRXRD rocking curves on the (004) plane of
Ge1-xSnx alloys grown on Ge(100) and GaAs(100)
substrates. The curves show the precense of epitaxial
Ge1-xSnx layers. The Sn concentration is also shown for
each curve.
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©Sociedad Mexicana de Ciencia de Superficies y de Vacío
Superficies y Vacío 17(4), 10-14 diciembre de 2004
5.760
GeSn/Ge/Ge(100)
SnxGe1-x/Ge/Ge(100)
-1
Ge (301 cm )
5.700
o
a⊥
T=170 C
a⎟⎟
P=5x10 mbar
-2
GeSn128 (Sn 2%)
abulk alloy GeSn
abulk alloy Ge
5.670
Intensity (A.U.)
lattice parameter (Å)
5.730
5.640
5.760
SnxGe1-x/Ge/GaAs(100)
5.730
GeSn127 (Sn 14%)
GeSn126 (Sn 13%)
5.700
5.670
5.640
0.00
abulk alloy GaAs
0.02
0.04
0.06
0.08
0.10
GeSn125 (Sn 10%)
0.12
0.14
Sn concentration x
250
260
270
280
290
300
310
320
-1
Phonon Frecuency (cm )
Figure 3. The a⊥ (in-growth), a⎜⎢ (in-plane) and a0 (bulk)
lattice parameters of the Ge1-xSnx alloys are shown as
function of Sn concentration.
GeSn/Ge/GaAs(100)
-1
-1
-1
GaAs TO(268 cm ) GaAs LO(292 cm ) Ge(301 cm )
10000
GeSn141 (Sn 8%)
Frank and Van der Merwe [6]
Geometrical [7]
Matthews and Blakeslee [8]
People and Bean [9]
pseudomorphic layers
8000
6000
GeSn142 (Sn 8%)
Intensity (A.U.)
critical thickness
hc(Å)
Ge1-xSnx/Ge/Ge(100)
4000
2000
0
0.00
0.02
0.04
0.06
0.08
GeSn144 (Sn 7%)
GeSn145 (Sn 6%)
GeSn146 (Sn 9%)
0.10
Sn concentration x
GeSn147 (Sn 7%)
Figure 4. The thickness of the pseudomorphical Ge1-xSnx
layers is compare with several critical thickness models
reported everywere. [6-9]
GeSn148 (Sn 7%)
250
260
270
280
290
300
310
320
-1
Phonon Frecuency (cm )
Figure 5. Raman measurements of the Ge1-xSnx alloys
grown on Ge(100) and GaAs(100) substrates. The doted
lines indicate the positions of the LO and TO modes of
Ge and GaAs. The Sn concentration of the alloys is also
shown.
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©Sociedad Mexicana de Ciencia de Superficies y de Vacío
Superficies y Vacío 17(4), 10-14 diciembre de 2004
300
Ge1-XSnX/Ge/Ge(100)
299
Ge1-XSnX/Ge/GaAs(100)
298
297
148.41316
296
295
294
Absorption Coefficient (α)
-1
Raman Shift (cm )
301
293
292
291
290
289
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Sn Concentration (%) by HRXRD
Figure 6. Raman shift of the Ge1-xSnx alloys compare
with the Sn concentration determined by HRXRD. The
solid line is the Raman shift ∆ωGeSn = ω0 – 76.8cm-1 [10]
reported for Ge1-xSnx alloys.
EIndirect
Sn=0.14
EDirect
Ge
GeSn/Ge/Ge(100)
0.10
54.59815
Ge
Sn=0.14
0.09
0.2
0.3
0.4
0.08
0.07
0.6
0.7
0.8
0.9
Figure 8. Absorption coefficient obtained from the
transmittance measurements of the Ge0.86Sn0.14 alloy. The
determined direct and indirect band gap transitions of the
alloy are shown.
Sn=0.10
Transmittance
0.5
Energy (eV)
0.06
0.05
Sn=0.13
0.8
EcΓ Thigth-Binding
0.04
0.03
Energy (eV)
0.7
Sn=0.09
0.02
0.01
Sn=0.02
0.6
0.5
0.4
0.00
0.2
0.3
0.4
0.5
0.6
0.7
0.3
0.8
Energy (eV)
Ec L Thigth-Binding
0.00
Direct Gap/Ge
Indirect Gap/Ge
Direct Gap/GaAs
Indirect Gap/GaAs
Direct Gap (M. R. Bauer et al.[9])
Direct Gap (Atwater et al.[1,2])
Indirect Gap (Atwater et al.[1,2])
0.02
0.04
0.06
0.08
Ec L Pot. of Def.
EcΓ Pot. of Def.
0.10
0.12
0.14
Sn concentration by HRXRD
Figure 7. Transmittance measurements of the Ge1-xSnx
alloys grown on Ge(100) substrates. The Sn concentration
of th e alloys is shown for each curve.
Figure 9. Experimentally energy Band Gap values of the
Ge1-xSnx alloys compared with the predicted by the
Potential of Deformation Theory. The Sn concentration
values in the graph were determined by HRXRD.
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©Sociedad Mexicana de Ciencia de Superficies y de Vacío
Superficies y Vacío 17(4), 10-14 diciembre de 2004
[6] F. C. Frank and J. H. Van der Merwe, Proc. Roy.
Soc. (London) A 198 (1949) 216; J. H. Van der Merwe, J.
Appl. Phys. Lett. 34 (1963) 117; J. H. Van der Merwe, In
Single Cristal Films (Pergamon, New York, 1964) p. 139.
[7] D. J. Dunstan, S. Young and R. H. Dixon, J. Appl.
Phys 70 (6), 15 september 1991.
[8] J. W. Matthews and A. E. Blakeslee, J. Of Crystal
Growth, 27 (1974) p. 124.
[9] R. People and J. C. Bean , Appl. Phys. Lett. 47 (3)
August 1985.
[10] M. Rojas-López, H. Navarro and J. Greene, J. Of
Appl. Phys. 84, 2219 (1998).
[11] K. A. Mäder, A. Baldereschi, Solid State
Communications, 69, 12 (1989).
[12] J. Barden, W. Shockley, Phys. Rev. 80,72 (1950).
[13] M. Bauer, J. Tolle, C. Bungay, Solid Styate
Communications, 127, 355 (2003).
epilayers that are totally dislocations free. The Ge1xSnx alloys presents a tunable band gap. The values
of the Direct and Indirect band gaps are very similar
to the values predicted by the Potential of
Deformation Theory. A direct transition is
experimentally observed for alloys with Sn
concentration up to 0.14.
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