1
Supp
orting
Information:
In Situ
Lithiation
-
Delithiation of Mechanically
Robust Cu
-
Si Core
-
shell Nanolattices
in a Scanning
Electron Microscope
Xiaoxing Xia
*
1
, Claudio V. Di Leo
2
, X. Wendy Gu
1,3
, Julia R. Greer
1
1
Division of Engineering and Applied Science, California Institute of Technology
, 1200 E.
California Blvd.
, Pasadena, CA 91125, United States
2
School of Aerospace Engineering, Georgia Institute of Technology
, 270 Ferst Drive
, Atlanta,
GA 30332, United Sta
tes
3
Department of Chemistry, University of California at Berkeley,
419 Latimer Hall, Berkeley,
CA 94720, United States
2
Experiment Section
The Cu
-
Si core
-
shell nanolattices were fabricated by first making 3D polymer templates via two
-
photon lithogra
phy in a positive resist (Microchem AZ4620), electroplating Cu into the openings
within this template, stripping the resist matrix, and then depositing a layer of a
-
Si onto the Cu
scaffold by plasma enhanced chemical vapor deposition (PECVD). The photoresi
st was spincoated
onto a 15nm Au
-
coated glass cover slip and cured at 110°C for 3min. Two
-
photon lithography
(Nanoscribe, GmbH) was used to write the octet lattice structure designed in MatLab using laser
powers in a range
of
0.
8
-
1.2mW and a writing speed
of
10μm/s. The patterned photoresist was
developed in a solution of AZ400k: DI water at 1: 4 ratio. Using the remaining photoresist matrix
as a 3D template, galvanostatic Cu electrodeposition was conducted in a three
-
electrode setup with
a Cu counter elect
rode and Ag/AgCl reference electrode. The electroplating bath was composed
of 100g/l CuSO
4
•5H
2
O, 200g/l H
2
SO
4
, and commercial Cu elec
troplating additives (5ml/l 205
M,
1ml/l 205KA, and 1ml/l 205KR, Electrochemical Products, Inc
). After electroplating, the
photoresist matrix was removed by soaking in 1
-
methyl
-
2
-
pyrrolidone, leaving the freestanding
Cu lattices on a Au thin film on a glass substrate.
The Cu lattices had a ~20% variation in beam
diameter for the range of lithograph
y laser power used in this work.
A layer of a
-
Si was then
deposited on the Cu lattice scaffold by PECVD at 200°C with 5% silane precursor gas at 250sccm
flow rate and 800mTorr pressure
for 30min
.
To analyze the microstructure of
the Cu core, Si shell and t
he Cu
-
Si
interface, we pr
epared a thin
lamella of the
Cu
-
Si
beam cross
-
section using a SEM/FIB Dualbeam (Nova 600, FEI) and
positioned
it
onto a TEM grid with a micromanipulator (Omniprobe).
The final thinning step of
the TEM sample was
completed
using 8ke
V Ga ion beam
at 42pA to minimize beam damage.
TEM analysis revealed the presence of a few, 20
-
30nm
-
sized voids located
at the
Cu
-
Si
interface
(Fig. 1f). Possible ion
beam
damage due to FIB was examined using the open source software
package SRIM
-
The Stopp
ing and Range of Ions in Solids
(
http://www.srim.org/
), which conduct
s
Monte Carlo simulation of
the trajectory of implanted ion and recoiling target atom with full
damage cascade
.
Fig. S1 shows the cross
-
sections of the interaction volume on Si and Cu tar
get
after 10000 8keV Ga ion bombardment, where
x
-
axis is
the
depth in the target sample and
y
-
axis
is
the
coordinate on the target surface
with Ga ion being implanted at y = 0. The red dots are those
collisions between the ion and target atoms in which the
target atoms are knocked from their lattice
sites. The green dots are collisions between recoiling target atoms and other target atoms.
The
width and the depth of the Ga interaction volume of the Si target are
both
~40nm (Fig. S1
-
a) and
those of the Cu ta
rget are ~20nm (Fig. S1
-
c). During FIB milling, the amount of damage on the
cross
-
sectional face in the lateral direction to the incident Ga beam is approximately half of the
interaction volume on each side of the TEM lamella.
The final TEM sample is appro
ximate 80
-
100nm thick
but the total damage region is about 40nm thick
for Si and
about 20nm thick
for Cu
.
Therefore, we believe it is unlikely that the
20
-
30nm
-
sized voids
at the Cu
-
Si interface found
during
TEM analysis
were
caused by
FIB damage.
It is worth mentioning that SRIM doesn't take
into account any thermal effects, so the calculated ion damage is what would have happened at
0K. Implanting at room
-
temperature (300K) will cause most of the implantation damage to “self
-
anneal”. The target da
mage might disappear because at room temperature, the lattice atoms have
adequate energy to allow simple target damage to regrow back into its original crystalline form.
Furthermore, we used the Omniprobe to lift out a Cu beam before Si deposit
i
on and glue
d it
sideways on the substrate with Pt deposition in the SEM (with the major axis of the elliptical
beam
cross
-
section parallel to the substrate). An atomic force microscope (AFM) was used to measure
3
the root
-
mean
-
square roughness of
the
Cu surface to be 2
2nm.
We
believe it is possible that
the
Cu surfac
e roughness is what gave rise to
the voids at the Cu
-
Si interface during Si deposition.
Figure
S1.
SRIM simulation result
s
of 8keV Ga ion interaction volume in (a) Si and (c) Cu target and the
Ga ion trajectories in (b) Si and (d) Cu target
.
The volume of Cu and Si in the nanolattices was calculated using Solidworks, in which a model
of a Cu
-
Si core
-
shell octet unit cell was
created. The modeled Cu
-
Si beam has an elliptical cross
-
section (
0.9μm minor axis and 2μm major
) for the Cu core and a 250nm conformal coating of Si,
and the model takes into account the volume in lattice beams and at lattice nodes. The Si volume
in an 8
μm
unit cell is calculated to be 98
μm
3
, and the Cu volume is 122
μm
3
.
A custom
-
made lithiation setup was constructed by assembling a
n electrochemical
half
-
cell
with
a
Li
counter
electrode inside
the vacuum
chamber
of an
in
situ
SEM nanomechanical instrument
(Quanta 200 SEM, FEI and Nanomechanics, Inc.). The electrochemical cell was
connect
ed
to an
external potentiostat
. The glass substrate supporting the Cu
-
Si core
-
shell nanolattices was held
vertically on the side of a SEM sample holder. A
~
500μm
–
diameter pi
ece of Li was attached to a
W tip inside of a glovebox, transferred to the SEM in an Ar
-
filled container and then quickly
mounted onto the nanomechanical arm inside the SEM chamber with less than 10s exposure in air.
The
negative electrode of the
potentiostat was connected to the Li electrode via the W tip, and the
positive electrode of the potentiostat was connected to the Au film on the sample substrate. We
aligned the Li electrode to be positioned directly above the Cu
-
Si nanolattice in the SEM
image.
4
The Li electrode can be lowered to form a half
-
cell, in which either solid Li
2
O or 10wt% LiTFSI
in
P
14
TFSI
ionic liquid was used as the electrolyte. The lithiation rate
퐶
푟푎푡푒
is
the rate of discharge
defined by the m
ultiplicative inverse
of the
number of hours it takes to fully discharge an
electrochemical cell based on the theoretical capacity of Si (i.e. 0.25C indicates a full discharge in
4hr). Fig. S2
-
a and Fig. S2
-
b are close
-
up SEM images
of Cu
-
Si nanolattice beam before and after
lithiati
on with solid Li
2
O electrolyte
.
Figure
S2. SEM images of Cu
-
Si nanolattice beams before and after lithiation with solid
Li
2
O
electrolyte.
The volume expansion of each lithiated Cu
-
Si nanolattice was estimated by assuming a change in
the cross
-
sectional
area of the Si shell of the lattice, and by assuming that each beam does not
elongate in the axial direction (Fig. S
3
). The minor and major axis of the cross
-
section of the Cu
scaffold and the Cu
-
Si core
-
shell beam before and after lithiation were measured
from SEM images
for each nanolattice, and used in these calculations.
Figure S
3
. Illustration of Si volumetric expansion
calculation from the Si shell cross
-
sectional area
change.
Figure
S4. SEM image of the
in situ
half
-
cell
with ionic liquid electrolyte after the Cu
-
Si
nanolattice was fully immersed and the size of
the ionic liquid droplet was stabilized.
5
F
ig. S4
is a SEM image of the half
-
cell setup during the electrochemical characterization after the
Cu
-
Si nanolattice was fully submerged and the size of the ionic liquid droplet was
stabilized
.
Cyclical
voltammetry
was conducted between 0.01V and 2.5V at 2mV/s s
canning rate inside SEM
with the Cu
-
Si nanolattice and Li counter electrode using i
onic liquid electrolyte (Fig. S5
-
a). The
shape of the CV curve qualitatively agrees with that of Si lithiation but the anodic peaks were
found to be at 0.71V and 1.20V inste
ad of 0.
37V and 0.62V reported in Ref. 1
. We suspect the
observed overpotential is possibly due to
bad ion transport in the
ionic liquid electrolyte and
the
internal resistance of the
in situ
setup.
Figure
S5
. (a) Cyclic voltammogram for the
in situ
half
-
cell with the ionic liquid electrolyte at a voltage
scanning rate of 2mV/s. (b) Galvanostatic discharge voltage profile of the
in situ
half
-
cell with the ionic
liquid
ele
c
trolyte
at a discharge rate of
~
0.25C.
Fig. S5
-
b displays a representative disc
harge voltage profile during a galvanostatic discharge at
10nA (~0.25C) with a 0.07V cutoff voltage. Via the combined motion of the sample stage and the
nanomechanical arm, the
suspended ionic liquid droplet wa
s fine tuned to immerse the Cu
-
Si
nanolattice
structure with minimal contact between the substrate and the ionic liquid droplet in
order to reduce the influence of Si thin film surrounding the nanolattice on measured
electrochemical behavior. The area of the Si thin film on the substrate in contact w
ith the ionic
liquid also participated in the lithiation reaction and contributed to the total capacity. Therefore,
the gravimetric specific capacity is normalized by the mass of Si in the nanolattice plus a 750nm
-
thick Si thin film disk of 70
μm
in diamete
r.
Simulation Section
Details of the fully
-
coupled diffusion
-
deformation finite element model, including the constitutive
equations, boundary conditions and material parameter values, have bee
n previously report
ed in
Ref. 32
. To adopt the model into the
current system, the Cu core was
modeled as linear elastic with
a
Young’s modulus of 110
GPa and a
P
ois
s
on
’s
ratio of 0.34.
In Fig. 3a, the nodes on edge AC
were prescribed zero horizontal displacement and zero Li flux, the nodes on edge CE were
prescribed z
ero vertical displacement and zero flux. We prescribed a constant flux boundary
condition on edge AE, with a magnitude of
퐽
=
(
푉
/
퐴
)
∙
푐
푚푎푥
∙
퐶
푟푎푡푒
/
ℎ
where
푉
and
퐴
are the
volume and
surface
area
of the a
-
Si shell,
푐
푚푎푥
is the maximum molar concen
tration of Li in the
6
Li
-
Si alloy,
퐶
푟푎푡푒
is the rate of discharge, and
ℎ
= 3600s/hr is a unit conversion factor. Simulations
were run until a normalized concentration of
푐
푛표푟푚푎푙푖푧푒푑
=
푐
/
푐
푚푎푥
=
1
was reached in any
element of the mesh.
The s
imulations were performed under plane strain conditions because the
relatively high stiffness of the
Cu
, 110GPa, compared with that of the a
-
Si, 80GPa, effectively
suppresses the out
-
of
-
plane expansion of the a
-
Si shell.
In order to determine the effect
s
o
f using a plane
-
strain condition
,
we performed additional three
-
dimensional simulations. The simulations used only a single element in the out
-
of
-
plane direction
(see Fig. S6
)
,
which
we
shall refer to as the z
-
direction. The bottom surface
of this thin sheet
(not
visible in Fig.
S6
) is
constrained to have zero displacement in the z
-
direction, while all of the nodes
on the top surface with normal in the z
-
direction are constrained to have the same displacement in
the z
-
direction. That is, the
top surface is constrained to remain flat and all nodes must move in
unison in the z
-
direction. This type of boundary condition is equivalent to modeling a long rod
where any manner of end conditions (in this case
the nodes of the nanolattice) is
neglecte
d.
Figure S
6
. Comparison between a 3D simulation and a plane
-
strain simulation of the beam cross
-
section.
Figur
e S6
shows
contours of normalized concentration (top) and out
-
of
-
plane stress
휎
푧푧
(bottom)
for a 3D simulation (left) compared to a plane
-
strain simulation (right). As shown through these
simulations, there is little effect in performing a plane strain simulation against a 3D simulation of
7
the form considered here. The reason for this is that the Cu core is relatively stiff compared to the
a
-
Si shell and hence there is little out
-
of
-
plane displacement in the 3D simulations when the surface
is constrained to remain flat. Of course, if one is to consider the entire
nanolattice
structure in a
3D simulation, the results, even at the center of on
e segment of the
nanolattice
, will be affected by
the presence of the nodes.
In order to determine if fracture will occur in the a
-
S
i shell during lithiation or de
lithiation we use
the fractu
re energy measu
rements of Pharr et al. (
Ref. 35
)
. Since the
maximum tensile stress in the
a
-
Si shell duri
ng lithiation and de
lithiat
i
on cycles occur at low
Li
concentrations, we employ
ed
the
fracture toughness of
Γ
=
6
.
9
퐽
/
푚
2
which was measured experimentally by Pharr
et al.
at low Li
conce
n
trations
(Ref. 35
)
. Since
we do not have good knowledge of the pre
-
existing flaws in the a
-
S
i shell,
following Xiao et al.
(Re
f. 34) and Pharr et al. (Ref. 35
)
, we assume
d
that there is a through
crack in the a
-
Si shell with length equal to initial thickness of the a
-
Si shell give
n by
ℎ
푓
=
0
.
25
휇푚
.
The energy release rate
퐺
for a fully cracked film may be expressed a
s
퐺
=
푔
(
훼
,
훽
)
휎
2
ℎ
푓
퐸
̅
푓
(1)
where
푔
(
훼
,
훽
)
is a function of the Dundurs parameters,
훼
and
훽
, which are defined by
훼
=
퐸
̅
푓
−
퐸
̅
푠
퐸
̅
푓
+
퐸
̅
푠
,
훽
=
휇
푓
(
1
−
2
휈
푠
)
−
휇
푠
(
1
−
2
휈
푓
)
2
휇
푓
(
1
−
휈
푠
)
+
2
휇
푠
(
1
−
휈
푓
)
where
퐸
̅
=
퐸
/
(
1
−
휈
2
)
is the plane
-
strain modulus, and
휇
=
퐸
/
(
2
(
1
+
휈
)
)
is the shear modulus
(Ref
. 36
)
. For the a
-
Si shell,
a Young’s
modulus
퐸
푆푖
=
80
퐺푃푎
and
a
P
ois
s
on
’s
ratio
푣
푆푖
=
0
.
22
where used, and for Cu, a Young’s modulus
퐸
퐶푢
=
110
퐺푃푎
and a
P
ois
s
on
’s
ratio
푣
퐶푢
=
0
.
34
was
used. Using our calculated values of
훼
and
훽
,
the tabulated values for
푔
(
훼
,
훽
)
found in Beuth (Ref.
36
)
were used to find
푔
=
1
.
28
for our system. Finally, e
quating the energy release rate
퐺
with the
experimentally measured fracture energy
Γ
,
we
are able to
solve for
휎
푐
=
1
.
35
퐺푃푎
.
Alternatively, we may compute the critical flaw size
ℎ
푐
for fracture to occur in a th
in film through
ℎ
푐
=
2
휋
퐺
퐸
̅
푓
휎
2
(2)
by
equating
퐺
=
훤
and using the maximum principal stress
휎
=
0
.
71
퐺푃푎
measured during our
lithiation simulations, as well as the afo
rementioned material prop
erties (see Xiao et al. (Ref. 34
)
and Graetz et al.
(Ref. 42
)
)
. The calculation
yields a critical
fla
w size of
ℎ
푐
~
700
푛푚
,
which is
greater than the thickness of the a
-
Si shell prior to lithiation
and after lithiation
.
Given the stress profile obtained from FEA simulation, a simple Griffith model was adopted to
estimate the Cu
-
Si interfacial delam
ination condition under normal and shear stresses. Suppose an
internal crack of length 2a pre
-
exists at the Cu
-
Si interface possibly due to Si deposition flaw, the
energy release rate G is a function of mode I and mode II stress intensity factor
퐺
=
1
퐸
∗
(
퐾
퐼
2
+
퐾
퐼퐼
2
)
(3
)
8
where the effective elastic modulus
퐸
∗
=
2
(
1
퐸
̅
퐶푢
+
1
퐸
̅
푆푖
)
−
1
. As determine
d by Suo and Hutchinson
(Ref. 37
and
38
), for most bi
-
layer materials with reasonably small modulus mismatch, the
complex stress intensity factor can be approximated
as
퐾
퐼
+
푖
퐾
퐼퐼
=
(
휎
22
+
푖
휎
12
)
√
2
휋푎
(4
)
The fracture energy of the Cu
-
Si interface has been measured to be
Γ
=
7
.
9
퐽
/
푚
2
by Maranc
hi at
al. (Ref. 39). According to Irwin (Ref. 40
) and Griffit
h (Ref. 41
), the crack will propagate only if
the energy release rate G is greater than the fracture energy
Γ
. Using the maximum normal stress
휎
푚푎푥
=
0
.
74
퐺푃푎
and maximum shear stress
휏
푚푎푥
=
0
.
27
퐺푃푎
from the simulation results at 1C,
the critical crack leng
th for delamination of the Cu
-
Si interface is
푎
푐
=
203
푛푚
.
We also performed a simulation including both lithiation and delithiation steps at 1C. The
delithiation step began as soon as any element in the body reached a normalized concentration of
one
, an
d proceeded until any point in the body reached a concen
tration of 1%. Similar to Fig. 3c
and 3
d, Fig. S7
shows the interfacial normal stress and shear stress at the Cu
-
Si interface. For the
normal stress (left) we note that the interfacial stresses during
delithiation are mainly compressive,
and hence would not be expected to cause delamination. For the shear stress (right), we noted that
the magnitude of the maximum interfacial shear stress during delithiation is lower than that during
lithiation. Hence,
delithiation is
not
likely
to
lead to failure at the Cu
-
Si interface.
Figure S
7
.
Distribution profile of the
maximum
interfacial
(a)
normal
and (b)
shear
stress during lithiation
and delithiation calculated by finite element modelling.
However,
during de
lithiation
,
the maximum principal stress
was shown to be tensile
on the
exterior
free
surface of the Si shell. Fig. S8
shows contours of maximum principal stress at the s
tart, middle,
and end of the de
lithiation step. As shown in
Fig. S8
, this str
ess can reach a level of
휎
=
1
.
70
퐺푃푎
at low concentrations. This value is greater than the critical stress
휎
푐
=
1
.
35
퐺푃푎
computed in our earlier analysis, hence it is possible that fracture can occur in the a
-
Si shell during
deliathion. The critical fl
aw size
ℎ
푐
which would cause such failure can be computed using the
value of the maxmimum principal stress
휎
=
1
.
70
퐺푃푎
and the eq. (2) and is equal to
ℎ
푐
=
127
푛푚
. It is possible
but quite unlikely
that such a flaw is present in a
-
Si as it is roughly hal
f the
thickness of the original a
-
Si shell prior to lithiation.
We did not observe
such prominent flaws in
9
the TEM samples
, and no surface cracks were observed during
in situ
SEM delithiation
experiments at a delithiation rate of ~0.25C.
Figure S8
.
Contours
of the maximum principal stress
of
the
a
-
Si shell
in the beginning, middle and final
stage of delithiation.