substrate. The lattice mismatch can be defined as
[(dfilm – dsubstrate)/dsubstrate], where d is the lattice
spacing of the plane parallel to the substrate. Au
on Si has a lattice mismatch of –24.9%, which is
too high to produce epitaxial deposits. Therefore,
the epitaxy in the Au-Si system can be explained
by the formation of coincidence site lattices (CSLs),
in which four unit meshes of Au coincide with
three unit meshes of Si (20). These CSLs lower the
mismatch from –24.9% for a single unit cell to
+0.13% for the CSL (fig. S8). Similarly, the lattice
mismatch for ZnO on Au was minimized from
+12.7% to +0.16% for the CSL (fig. S9). The lattice
mismatch for Cu2O on Au is +4.7%, which is low
enough to produce cube-on-cube epitaxial films
with reasonable in-plane and out-of-plane strain
in the material (fig. S10).
High optical transmittance and low sheet resistance are imperative for Au foils to be used as
flexible and transparent substrates. Figure 4A
shows the photograph of a wafer-size Au foil with
a diameter of 50.8 mm. Figure 4B shows the optical transmittance of Au foils as a function of
thickness. All of the foils showed a maximum in
transmittance around 500 nm and the peaks
slightly red-shifted with an increase in thickness.
The sheet resistance, in terms of ohms per square,
for all of the foils (measured with a four-point
probe) increased along with transmittance as
the Au foil thickness decreased. A 7-nm-thick Au
foil showed the highest transmittance at 85%,
and the 28-nm-thick foil showed the lowest at
25%. The maximum transmittance (~500 nm) as
a function of thickness is in close agreement with
previous studies on evaporated gold thin films (25).
The endurance of the Au foils as a function of
sheet resistance was measured by subjecting
the foils to as many as 4000 bending cycles (Fig.
4C). Bending cycles for all of the foils were performed with a steel rod as a guide with a radius
of curvature of 3 mm. The sheet resistance of 28-,
16-, and 11-nm-thick Au foils increased by 4%,
6.3%, and 34%, respectively, after 4000 cycles of
To evaluate the flexibility and transmittance
of Au foils for light emission, we spin-coated
an OLED based on tris(bipyridyl)ruthenium(II)
(26, 27). The complex showed strong photoluminescence with an excitation wavelength of
455 nm and an emission of bright red-orange
color around 660 nm (26). The complex was dissolved in a 3% (w/v) polyvinyl alcohol solution,
spin-coated onto a 28-nm-thick Au foil, and dried
in air. An indium/gallium (InGa) eutectic was used
Fig. 4. Transmittance, sheet resistance, and flexibility of Au foils with
diode and OLED fabrication. (A)
Wafer-size Au foil with diameter of
50.8 mm and thickness of 28 nm.
(B) Transmittance and sheet
resistance of Au foils as a function
of thickness. (C) Sheet resistance of
Au foils with thicknesses of 11, 16,
and 28 nm as a function of bending
cycles with a bending curvature of
3 mm. (D) Current-voltage response
of Au foil/RuII(bpy)3/InGa junction,
showing rectifying behavior. Inset:
chemiluminescence of RuII(bpy)3BF4
OLED on flexible 28-nm-thick Au foil.
(E) Current-voltage response of Cu2O
diode on Au foil (epitaxial) and stainless steel (polycrystalline) substrates.
(F) Dark saturation current density
(Js) and diode quality factor (n) of
epitaxial and polycrystalline Cu2O diodes measured using log(J) versus V at forward bias.
Fig. 3. X-ray diffraction and pole figures to study the in-plane and out-of-plane orientation. (A) Out-of-plane orientation of electrodeposited Au(111) on Si(111). (B) Out-of-plane x-ray diffraction showing
satellite peaks (Laue oscillations) caused by constructive and destructive interference. (C) Out-of-plane
orientation of Au(111) foil, electrodeposited Cu2O on 30-min Au foil, and electrodeposited ZnO on 10-min
Au foil. (D to G) In-plane orientation was determined using (220) pole figure of Si(111) (D), (220) pole
figure of Au(111) foil (E), (220) pole figure of Cu2O(111) on Au(111) foil (F), and (102) pole figure of ZnO(002)
on Au(111) foil (G). The radial lines in the pole figure correspond to 30° increments of the tilt angle.