Ultra-thin free-standing single crystalline silicon membranes with strain
control
A. Shchepetov,
1
M. Prunnila,
1
F. Alzina,
2
L. Schneider,
2
J. Cuffe,
2,a)
H. Jiang,
3
E. I. Kauppinen,
3
C. M. Sotomayor Torres,
2,4
and J. Ahopelto
1,b)
1
VTT Technical Research Centre of Finland, P.O. Box 1000, FI-02044 VTT, Espoo, Finland
2
Catalan Institute of Nanotechnology, Campus de la UAB, 08193 Bellaterra (Barcelona), Spain
3
Nanomaterials Group, Department of Applied Physics and Center for New Materials,
Aalto University School of Science, P.O. Box 15100, FI-00076 Aalto, Finland
4
Catalan Institution for Research and Advanced Studies (ICREA), 08010 Barcelona, Spain
(Received 28 February 2013; accepted 2 May 2013; published online 17 May 2013)
We report on fabrication and characterization of ultra-thin suspended single crystalline flat silicon
membranes with thickness down to 6 nm. We have developed a method to control the strain in the
membranes by adding a strain compensating frame on the silicon membrane perimeter to avoid
buckling after the release. We show that by changing the properties of the frame the strain of the
membrane can be tuned in controlled manner. Consequently, both the mechanical properties and the
band structure can be engineered, and the resulting membranes provide a unique laboratory to study
low-dimensional electronic, photonic, and phononic phenomena.
V
C
2013 AIP Publishing LLC.
[http://dx.doi.org/10.1063/1.4807130]
Silicon has been the dominant material for microelec-
tronics since early 60s. It can be produced with very high
crystalline quality, extreme purity, and well controlled elec-
trical properties. Silicon on insulator (SOI) material has been
the cornerstone in the development of state-of-the art transis-
tors,
1
MEMS devices,
2
opto-mechanical structures,
3
pho-
tonic crystals,
4
even lithiated anodes for batteries,
5
etc.
Furthermore, thin free-standing SOI structures are ideal to
investigate basic physics phenomena in low dimensional
structures, such as thermal properties.
6–9
The most common
way to fabricate supported single crystalline Si membranes
is to release the top Si layer of a SOI wafer by etching from
the backside through the handle wafer and the buried oxide
(BOX) layer. However, to obtain very thin membranes, the
process usually requires thermal oxidation to thin down the
SOI film, followed by removal of the grown oxide. Thermal
processes tend to create compr essive stress in the SOI film,
10
leading to buckling of the membranes after release (see Fig.
1(a)). The buckling has been observed in numerous experi-
mental works [see, e.g., Refs. 11–13], and it can be detrimental
for device applications exploiting thin free-standing structures.
It also complicates experimental work, especially optical
measurements, because the angle of incidence of the laser
beam may not be well defined. More importantly, the strain,
and, consequently, the elasto-mechanical properties of the
membrane are unknown. Strain in a Si film can be adjusted,
for example, by growing silicon epitaxially on a SiGe buffer
14
or by depositing thick SiN layers on top and bottom of the Si
layer.
15
However, these approaches do not allow the fabrica-
tion of bare free-standing Si membranes with tunable strain.
In this Letter, we report on fabrication and characteriza-
tion of large area ultra-thin flat suspended single crystalline
Si membranes with controlled strain and thickness down to
6 nm. Our method involves insertion of a strain compensat-
ing Si
3
N
4
frame around the Si membrane perimeter, as
shown in Figs. 1(b) and 1(c). The Si
3
N
4
layer has small ten-
sile stress that creates a pulling force that flattens the Si
membrane–similarly as a drumhead is tuned. The magnitude
of the strain is related to the strain compensation ratio
R
c
¼ w
c
/w
m
, where w
m
is the width of the bare Si part of the
membrane and w
c
is the width of the area of the released
membrane covered with the Si
3
N
4
film. We show that this
approach not only removes the detrimental buckling but also
provides an elegant way to control the strain and, conse-
quently, the strain dependent properties such as the energy
band structure and elasto-mechanical properties of the lattice
without degrading the crystalline quality.
In the fabrication commercially available bonded
150 mm (100) SOI wafers are used. First, a 20 nm thick ther-
mal oxide is grown on the SOI wafer and the SOI film is trans-
ferred onto a new handle wafer with the 20 nm thick oxide
acting as a new buried oxide layer. The SOI film is thinned by
thermal oxidation and oxide stripping to desired thickness.
Then a 280 nm thick Si
3
N
4
film under tensile stress is depos-
ited by low pressure chemical vapor deposition (LPCVD) and
patterned by UV-lithography and plasma etching, followed by
deep etching from the backside through the wafer to release
the membranes. The Si
3
N
4
frame around the Si membrane
provides a pulling force and prevents buckling of the mem-
brane. This approach allows fabrication of flat free-standing
single crystalline membranes with size up to several square
millimeters and with thickness down to a few nanometers.
The fabricated membranes have a square shape with the edges
in h110i crystal direction. The crystalline quality of the mem-
branes was verified by high resolution transmission electron
microscopy (HRTEM). The images were taken directly from
the supported free-standing membranes without transferring
them onto a TEM grid to reveal the true condition of the
membranes. The surface profiles were measured by optical
profilometry and the strain by Raman spectroscopy.
a)
Present address: MIT, Room 7-034C, 77 Massachusetts Avenue, Cambridge,
Massachusetts 02139, USA.
b)
E-mail: Jouni.ahopelto@vtt.fi
0003-6951/2013/102(19)/192108/4/$30.00
V
C
2013 AIP Publishing LLC102, 192108-1
APPLIED PHYSICS LETTERS 102, 192108 (2013)
Downloaded 07 Jun 2013 to 158.109.1.11. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://apl.aip.org/about/rights_and_permissions
The total width of the suspended area w
s
ranges in
these samples from 700 to 1700 lm. The surface profiles of
37 nm thick membranes with and without the strain com-
pensation, measured by an optical profilometer, are shown
in Fig. 2(a). I n both cases the area of the free-standing bare
Si membrane is 1000 by 1000 lm
2
and R
c
¼ 0.35 for the
compensated m embrane. The amplitude of the undulation
of the non-compensated membrane is about 4 lmwhereas
the compensated film is completely flat. All the samples
with thickness ranging from 6 to 54 nm analyzed using
HRTEM showed no defects and had high crystalline qual-
ity, emphasizing that the thickness or the strain does not
affect the quality of the membrane. As an example a
lattice image of a 9 nm thick membrane and the correspond-
ingdiffractionpatternareshowninFigs.2(b) and 2(c).
The membrane has a strain compensation ratio R
c
¼ 1.3,
corresponding to tensile strain of about 1.2 10
3
as will
be shown below.
Raman spectroscopy is a convenient non-destructive
and extremely sensitive method to measure strain in the free-
standing membranes.
16
The shift of the LO phonon Dx
LO
peak at x
LO
¼ 520 cm
1
wavenumber reflects the strain in
the membrane. Assuming biaxial isotropic stress, the shift of
the peak can be translated into in-plane strain
jj
as
17
Dx
LO
¼
1
x
0
q p
c
12
c
11
jj
: (1)
Here c
jj
are the stiffness constants, which for Si are
c
11
¼ 1.66 10
11
and c
12
¼ 0.64 10
11
.
18
The parameters p
and q have values p ¼1:49x
2
0
and q ¼1:97x
2
0
.
19
Sets of 6, 27, and 54 nm thick membranes with different
compensation ratio R
c
were characterized by Raman spec-
troscopy. The measurements were carried out in ambient at
room temperature with excitation at 514.5 nm at different
power levels to exclude the effects of potential heating of the
membrane. The beam was focused to a 1 lm diameter spot
using a 50 objective lens. To illustrate the effect of the
compensation ratio R
c
and the thickness of the membrane on
the induced strain, LO phonon peaks measured from sets of
54 and 6 nm thick membranes with various R
c
of 0.8, 1.2,
and 3.5, together with a reference Si LO peak, are shown in
Fig. 3. The shift of the LO phonon peak to lower energy with
increasing compensati on ratio indicates increasing tensile
strain in the membranes. This is the strain tuning effect due
to the Si
3
N
4
frame, which can be represented in more quanti-
tative way by transferring the peak shift into strain using Eq.
(1). Fig. 4 shows the strain obtained from the measured LO
phonon peak shifts for the 6, 27, and 54 nm thick membranes
as a function of the compensation ratio R
c
. The behavior is
similar for all membranes: The strain increases rapidly for
small R
c
and then begins to saturate at larger R
c
, showing
that thicker membranes need more force to build up the
strain.
The strain has an effect on many properties of the
membranes, such as the mechanical resonance frequencies,
Q-value, and electronic band structure. Silicon has six
equivalent conduction band energy minima, and the biaxial
strain lifts the degeneracy of these valleys. The energy of the
two out-of-plane valleys decreases compared to the four
in-plane valleys, as shown in the inset to Fig. 4, leading to
changes in their relative population. The energy splitting
DE
c
between the in-plane and out-of-plane valleys of the
silicon conduction band can be written as
20
FIG. 2. (a) Surface profiles of 37 nm thick free-standing membranes meas-
ured with optical profilometer. Blue symbols: Surface profile of strain-
compensated membrane with w
s
¼ 1700 lm and w
m
1000 lm, i.e., R
c
¼ 0.35.
Red symbols: Non-compensated membrane with w
s
¼ w
m
¼ 1000 lm. The
missing points result from a too large incident angle for detection. The solid
line is a guide to the eye. In the insets lines show where the 3-dimensional
profilometer images of the membranes were taken from, (left) without strain
compensation and (right) strain compensated. (b) High resolution TEM
image of a 9 nm thick Si membrane with w
c
¼ 400 lm and w
m
¼ 300 lm,
i.e., the strain compensation ratio R
c
¼ 1.3. (c) Diffraction pattern of the
same membrane.
FIG. 1. (a) Optical micrograph of a 37 nm thick free-standing Si membrane
without strain compensation. (b) Optical micrographs of a strain compen-
sated 37 and 6 nm thick Si membranes. In (a) and (b) the total width of the
suspended membrane w
s
¼ 1000 lm and in (b) w
c
is 350 lm and w
m
300 lm,
i.e., R
c
¼ 1.2. (c) Schematics of the membrane structure. w
c
is the distance
from the edge of the membrane to the edge of the stress compensating Si
3
N
4
layer and w
m
is the width of the bare Si membrane. F denotes the pulling
force due to the Si
3
N
4
frame.
192108-2 Shchepetov et al. Appl. Phys. Lett. 102, 192108 (2013)
Downloaded 07 Jun 2013 to 158.109.1.11. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://apl.aip.org/about/rights_and_permissions
DE
c
¼ N
u
1 þ 2
c
12
c
11
e
jj
; (2)
where N
u
¼ 9.0 eV is the uniaxial deformation potential.
18
Here, as in Eq. (1), we have used biaxial isotropic stress and
zero stress boundary conditions for the bottom and top surfa-
ces of the membrane. The strain induced energy splitting is
shown in Fig. 4 in the right axis. At large R
c
the splitting is
of the order of the thermal energy at room temperature. This
splitting has an effect, for example, on carrier mobility
21
and
on thermal electron-phonon coupling
22
in the membrane.
The strain affects also the valence bands and the band gap
E
g
. There is no simple analytical formula for the energy shift
of valence bands. Fit to the simulation results of Ref. 23
gives the band gap change DE
g
19:15 e
jj
eV for small
strain. The change in the band gap as a function of R
c
is
plotted in the second right y-axis in Fig. 4. The maximum
DE
g
in the current membranes is 30 meV which can be
detected by absorption or photol uminescence measurements.
The LPCVD silicon nitride used in these experiments
for strain compensation has relatively low tensile stress of
about 300 MPa. By changing the growth parameters the
stress can be varied between 0 and 1000 MPa, providing a
mean to increase substantially the strain in the membranes
and, conseq uently, to tune the properties of the membranes.
The thinnest memb ranes fabricated here are 6 nm thick, cor-
responding roughly to 20 atomic layers. The membranes are
still very robust and preserve their crystallinity surprisingly
well, even under the tensile strain. Thermal oxidation is an
extremely well controlled process, and the interface between
silicon and the thermal oxide is very sharp, of the order of
one atomic layer. We expect that free-standing membranes
of thickness of 1–2 nm can be realized, having only a few
atomic layers remaining. In these membranes reconstruction
of the lattice will probably begin to play a role and the theo-
retically predicted effects in very small crystalline struc-
tures
24
can be investigated experimentally. The role of the
native oxide is not clear yet regarding the properties of the
thinnest membranes. Native silicon oxide is eventually
formed on silicon surfaces in ambient conditions. The thick-
ness of the oxide layer is of the order of 1 nm but the volume
is about twice of the consumed silicon, leading to inhomoge-
neous thickn ess of the oxide film and, potentially, local
straining of the underlying lattice. Furthermore, the pre-
sumed reconstruction of the lattice may alter the physical
properties and chemical activity of silicon.
In summary, we report a method to fabricate free-
standing Si membranes with thickness ranging down to sub-
10 nm and the strain accurately controlled. The strain enables
manipulation of the band structure of Si, permitting engineer-
ing of, e.g., electron-phonon and phonon-phonon coupling in
a 2-dimensional system, and investigation of the properties of
low dimensional systems by optical means due to the large-
area of the flat membranes. The fabricated membranes are ro-
bust and realization of even thinner membranes with high
strain using the demonstrated approach is envisaged.
The authors acknowledge the financial support from the
FP7 projects NANOFUNCTION (Grant No. 257375) and
NANOPOWER (Grant No. ICT-2010-256959). L.S., J.C.,
F.A., and C.M.S.T. acknowledge the support of the Spanish
projects nanoTHERM (Grant No. CSD2010-0044) and
ACPHIN (FIS200 9-10150). M.P. and A.S. acknowledge
funding from the Academy of Finland (Grant No. 252598).
1
J.-P. Colinge, Silicon-on-Insulator Technology: Materials to VLSI, 2nd ed.
(Kluwer Academic Publishers, Boston/Dordrecht/London, 1997).
2
J. T. M. van Beek and R. Puers, J. Micromech. Microeng. 22, 013001
(2012).
3
M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter,
Nature (London) 462, 78–82 (2009).
4
E. Dulkeith, S. J. McNab, and Y. A. Vlasov, Phys. Rev. B 72, 115102
(2005).
5
C. Yu, X. Li, T. Ma, J. Rong, R. Zhang, J. Shaffer, Y. An, Q. Liu, B. Wei,
and H. Jiang, Adv. Energy Mater. 2, 68–73 (2012).
6
A. Balandin and K. L. Wang, Phys. Rev. B 58, 1544–1549 (1998).
7
M. Schmotz, P. Bookjans, E. Scheer, and P. Leiderer, Rev. Sci. Instrum.
81, 114903 (2010).
FIG. 3. LO peaks measured by Raman scattering from 6 and 54 nm thick
free-standing Si membranes with the strain compensation ratio R
c
of 0.8,
1.2, and 3.5. The bottom curve is a reference spectrum measured from the
bulk part of the Si wafer, defining the reference peak position x
LO
¼ x
0
in
Eq. (1). Solid lines correspond to best fits with Lorentzian function.
FIG. 4. Strain as a function of strain compensation ratio R
c
(left y-axis) in Si
membranes with thickness of 6 nm, 27 nm, and 54 nm. First right y-axis:
Corresponding energy splitting DE
c
between the in-plane and out-of-plane
conduction band minima in Si. Second right y-axis: Change of the band gap
energy DE
g
. The splitting of the out-of-plane [001] and in-plane [100]/[010]
conduction band minima and the energy band gap are shown schematically
in the inset. The dashed curves are guides for the eye, and the error bar is the
same for all data points.
192108-3 Shchepetov et al. Appl. Phys. Lett. 102, 192108 (2013)
Downloaded 07 Jun 2013 to 158.109.1.11. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://apl.aip.org/about/rights_and_permissions
8
J. Groenen, F. Poinsotte, A. Zwick, C. M. Sotomayor Torres, M. Prunnila,
and J. Ahopelto, Phys. Rev. B 77, 045420 (2008).
9
J. Cuffe, E. Chavez, A. Shchepetov, P.-O. Chapuis, E. H. El Boudouti, F.
Alzina, T. Kehoe, J. Gomis-Bresco, D. Dudek, Y. Pennec, B. Djafari-
Rouhani, M. Prunnila, J. Ahopelto, and C. M. Sotomayor Torres, Nano
Lett. 12, 3569–3573 (2012).
10
T. Iida, T. Itoh, D. Noguchi, and Y. Takano, J. Appl. Phys. 87, 675–681
(2000).
11
J. A. Rogers, M. G. Lagally, and R. G. Nuzzo, Nature (London) 477,
45–53 (2011).
12
P. E. Allain, X. Le Roux, F. Parrain, and A. Bosseboeuf, J. Micromech.
Microeng. 23, 015014 (2013).
13
C. M. Sotomayor Torres, A. Zwick, F. Poinsotte, J. Groenen, M. Prunnila,
J. Ahopelto, A. Mlayah, and V. Paillard, Phys. Status Solidi C 1,
2609–2612 (2004).
14
M. M. Roberts, L. J. Klein, D. E. Sav age, K. A. Lin ker, M. Friesen, G.
Celler, M. A. Eriksson , and M. G. Lagally, Nat. Mater. 5, 388–393
(2006).
15
D. Wang, H. Nakashima, J. Morioka, and T. Kitamura, Appl. Phys. Lett.
91, 241918 (2007).
16
J. Camassel, L. A. Falkovsky, and N. Planes, Phys. Rev. B 63, 035309
(2000).
17
I. De Wolf, Semicond. Sci. Technol. 11, 139 (1996).
18
Properties of Crystalline Silicon, edited by R. Hull (INSPEC: The
Institution of Electric Engineers, London, 1999).
19
M. Chandrasekhar, J. B. Renucci, and M. Cardona, Phys. Rev. B 17,
1623–1633 (1978).
20
C. Herring and E. Vogt, Phys. Rev. 101, 944–961 (1956).
21
E. Ungersboeck, S. Dhar, G. Karlowatz, V. Sverdlov, H. Kosina, and S.
Selberherr, IEEE Trans. Electron Devices 54, 2183–2190 (2007).
22
J. T. Muhonen, M. J. Prest, M. Prunnila, D. Gunnarsson, V. A. Shah, A.
Dobbie, M. Myronov, R. J. H. Morris, T. E. Whall, E. H. C. Parker, and D.
R. Leadley, Appl. Phys. Lett. 98, 182103 (2011).
23
S. Richard, G. Aniel, and F. Fishman, J. Appl. Phys. 94, 1795–1799
(2003).
24
D. Donadio and G. Galli, Phys. Rev. Lett. 102, 195901 (2009).
192108-4 Shchepetov et al. Appl. Phys. Lett. 102, 192108 (2013)
Downloaded 07 Jun 2013 to 158.109.1.11. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://apl.aip.org/about/rights_and_permissions
![FIG. 4. Strain as a function of strain compensation ratio Rc (left y-axis) in Si membranes with thickness of 6 nm, 27 nm, and 54 nm. First right y-axis: Corresponding energy splitting DEc between the in-plane and out-of-plane conduction band minima in Si. Second right y-axis: Change of the band gap energy DEg. The splitting of the out-of-plane [001] and in-plane [100]/[010] conduction band minima and the energy band gap are shown schematically in the inset. The dashed curves are guides for the eye, and the error bar is the same for all data points.](/figures/fig-4-strain-as-a-function-of-strain-compensation-ratio-rc-24gknd5e.webp)
