Transcript of thin films when

Micro and Nanostructures in Thin Films
Maria Cecilia Salvadori
Thin Films Laboratory, Institute of Physics,
University of São Paulo, Brazil
Synthesis and characterization of nanostructured thin films:
(I) Electrical resistivity of metal thin films, with thickness
between fraction of nanometer and 10 nm: measurements and
development of a new quantum model;
(II) Thermoelectric power of thin films, with thickness
smaller than the mean free path of conducting electrons, showing
considerable different behavior, when compared with thicker
films;
(III) Elastic Modulus of nanostructured thin films, with
thickness between 20 nm and 80 nm, observing a decrease, when
compared with the bulk material;
(IV) Hydrophobic or hydrophilic character of surfaces with
periodic microstructures fabricated on it.
I – Electrical resitivity of nanostructured thin films
Quantum effects are expected in electrical resistivity () of thin
films when:
(a) The film thickness (d) is smaller than the electronic mean
free path (l0)
(b) The energy-level quantization is enhanced in the direction
along the film thickness d, that can be estimated by the
 3n 
number of Fermi subbands, N  d  
 
be small.
1
3
which must
In the case of Pt and Au films, that we have studied, these 2
conditions were satisfied:
Conditions to apply the Quantum Formalism
Condition (a)
Condition (b)
Metal
d (nm)
l0(nm)
n (m-3)
N
Pt
1.3  d  11.7
~10
6.6 1028
5 < N < 47
Au
1.8  d  10.5
~50
5.9 1028
7 < N < 41
In the quantum model the calculation of the conductivity
( = 1/) as function of the film thickness d is done considering the
2 2 2

energy E   2 quantization of the conducting electrons in
2md
the direction along the film thickness d and using the Boltzmann
transport equation.
In this way, the conductivity generated by the surface is given
by:
e2
d5
6
 s (d ) 
 2 6 2 FS N ( N  1) (2 N  1)
N
k2

 
1
2
where
2m
k  2 E F - E 

2
are the wave numbers associated to the
quantization in the direction along the film
thickness d
and
Fs is a parameter that depends of the interaction between the
conducting electrons and the rough film surface.
To calculate Fs , we take into account the height fluctuations
d
z(x, y)    h(x, y)
2
of the film surface, which generate a scattering potential
2 2 2

E


 
U    h(x, y) 
h(x, y)
3
md
 d 
Then, the electrons scattering due to U is calculated by the
transition probability given by:


k U(x, y) k 
2
In the Fishman and Calecki works, the scattering depends of the
correlation distance () of the surface.
But to fit this model with experimental data, it is necessary to
have  ~ nm.
These parameter values have no physical meaning.
Indeed, we have measured the correlation distance for the
Pt and Au films, obtaining:
ξPt(d) ≈ 200 nm
e
ξAu(d) ≈ 40 nm.
In our model we calculated the electron scattering by the surface
taking into account an effective interaction range:
l s (d)  V // τ c


where, V  V  V , VF 
3π 2 n
m
2
//
2
F
and τ c  d
2
z

1
3
Vz
Therefore
V //
 π 
l s (d)  
d 

Vz
3n
1
3
 3n 
ν  π 

2
3

d 
   1
ν

2
1
2
,
πν
VZ 
md
In our model:
(a) h(x,y) = n hn sen(2r/n), where r is the position vector
modulus in the (x,y) plane
(b) The wavelengths n  Dn, where Dn are the film grains sizes
(c) n are given by n = n F
In this way, Fs is given by:
Fs(g,ls) = g(d) ls(d)
Where the grain form factor g(d) is given by:
1
g(d) 
kF
n hn /Δ
2
(λF /λn )2
In the case of metals, where N >> 1, the total film resistivity
ρ(d) = ρbulk + ρs(d)
is given by
C Δ(d)2 g(d) l s (d)
ρ(d)
1
ρbulk
d 2 ( 1 - 0,15 /d)
where C is a constant that depends of the material, in this
case: CPt = 6.261x103 nm-2 e CAu = 28.072x103 nm-2,
Δ(d) is the roughness measured,
g(d) was obtained through the grain sizes measurement
ls(d) was calculated as previously described.
With this model, the Pt and Au resitivities were calculated,
for films thickness between 1 e 10 nm, showing excellent
agreement with the experimental data.
- M.C. Salvadori, A.R. Vaz, R.J.C. Farias, M. Cattani, Surface Review and Letters 11, 223 – 227 (2004).
- M.C. Salvadori, A. R.Vaz, R. J. C. Farias, M. Cattani, Journal of Metastable and Nanocrystalline Materials 20-21, 775 (2004).
- M. Cattani, M.C. Salvadori, Surface Review and Letters 11, 463-467 (2004).
- M. Cattani, M.C. Salvadori, Surface Review and Letters 11, 283 - 290 (2004).
- M. Cattani, M.C. Salvadori, J.M. Filardo Bassalo, Surface Review and Letters 12, 221-226 (2005).
-M. Cattani, A.R. Vaz, R.S. Wiederkehr, F.S. Teixeira, M.C. Salvadori, I.G. Brown, Surface Review and Letters 14, 87 - 91 (2007).
- M. Cattani, M.C. Salvadori, F.S. Teixeira, R.S. Wiederkehr, I.G. Brown, Surface Review and Letters 14, 345 – 356 (2007).
Based on these results, we proposed that a surface
morphological anisotropy
could induce anisotropy in the film resistivity.
In order to estimate the metric scale necessary to observe this
effect, we have calculated the film resistivity considering
a surface h(x,y) with different morphologies
along de directions x and y.
The geometry used for this estimate was:
That is a surface defined by a sinusoidal profile in the x-direction:
z  h sin( 2 x / L) ,
where h is the amplitude of the sinusoidal profile and L the
morphological wavelength.
A granular profile was assumed in the y-direction instead of a flat
profile, as nanostructured thin films usually are when formed by
filtered vacuum arc plasma deposition.
In this calculation gold was taken as the film material and the
average thickness was 5 nm.
The anisotropic factor ρx/ρy can be as high as 30, but for L < 6 nm.
We have investigated an alternative approach for creating an
anisotropic surface morphology.
The substrate was a glass microscope slide scratched in one direction
with ¼ μm diamond powder dispersed in water.
AFM image
The results show that resistivity anisotropy ratio ρx(d)/ρy(d) is greater
than unity and varies with thickness.
These results indicate a significant resistivity anisotropy that is a
consequence of the film morphological anisotropy
M.C. Salvadori, M. Cattani, F.S. Teixeira, R.S. Wiederkehr, I.G. Brown. Journal of Vacuum Science & Technology A 25, 330333 (2007).
(II) - Thermoelectric power in very thin film
When the film thickness becomes comparable to the mean
free path of the charge carriers
d  l0
all transport processes are expected to exhibit size effects.
For thin films of pure metal, with thickness d >> l, it is known that
T
ΔS F  Φ B  Φ F  9,2x10
ξ
3
 lU( 1  p) 
(μV/K)


d

where
ΦF and ΦB are the thermopowers of a thin-film and a thick-film of
the metal with respect to a thick standard film, respectively,
T the temperature,
ξ the Fermi energy,
 lnl(E) 
U 
E = electron energy,


ln
E

 E ξ
p the scattering coefficient.
The linear behavior of ΔSF as a function of 1/d have been
experimentally observed for d >> l.
In our work we measured Pt thermopowers for d ≤ l.
We have measured ΔSF for Pt using thermocouple Pt/Au,
with very thin Pt films
2.2 < d < 24.5 nm
(note that lPt ~ 10 nm )
and thick Au film (140 nm) as reference.
Our experimental results showed that ,
for thickness less than about 20 nm,
the thermopower ΔSF does not vary linearly with 1/d .
Experimental procedure:
- A number of thick Au films
were deposited on ordinary glass
microscope slides;
- Thin Pt films of different
thicknesses were deposited on
each sample;
- The voltage, generated on the hot junction, were measured as
function of the temperature, obtaining a linear graphic;
- The thermopowers (ΦF) were defined by the slope of these
linear graphics;
- The bulk thermopower (ΦB) was obtained using a thick Pt
film (~160 nm >> l ~ 10 nm), with the same procedure.
Our experimental results showed that ,
for d ≤ l ~ 10 nm (2.2 < d < 24.5 nm),
the thermopower ΔSF = (ΦB - ΦF) X 1/d is not linear.
SF (mV/K )
4
3
2
1
0
0,0
0,1
0,2
0,3
-1
0,4
0,5
1/d (nm )
The doted curve shows the linear behavior, typical for d >> l,
extrapolated to the region d << l.
M.C. Salvadori, A.R. Vaz, F.S. Teixeira, M. Cattani and I. G. Brown – “Thermoelectric effect in very thin film Pt/Au
thermocouples”. Applied Physics Letters 88, 133106-1 - 3 (2006).
ρ(d)/ρB = 1+ 6.5/d + 140/d 9
where semiclassical effects are
present in the term 6.5/d and
the quantum effects are
present in the term 140/d 9.
6
5
SF (V/K )
To explain this nonlinearity, we
have used our previous results
of resistivity for thin Pt films
(d < 10 nm):
4
3
2
1
0
0,0
0,1
0,2
0,3
0,4
0,5
-1
1/d (nm )
The nonlinear curve was calculated using the relation ρ(d)/ρB,
given above, with a quantum formalism and the Boltzmann
transport equations.
M. Cattani, M.C. Salvadori, A.R. Vaz, F.S. Teixeira, I.G. Brown – “Thermoelectric power in very thin films Pt/Au
thermocouples: quantum size effects”. Journal of Applied Physics 100, 114905-1 - 4 (2006).
(III) – Elastic modulus of nanostructured thin films
In this work we obtained the elastic modulus of thin films,
deposited on vibrating beams,
measuring the resonance frequencies.
The resonance frequencies for vibrating beams is given by:
2
E1
1.03
t
2
 
(2 ) 2 l 4 1
where t is the beam thickness
ℓ the beam length
E1 the elastic modulus of the material
ρ1 the material density
When we coat the beam with a thin film with
thickness , we modify its resonance frequency (νc):
2
12.36
t
 c2 
(2π ) 2 l 4
E1 ( w t / 12)  E2  [( w  2δ ) (1/2   / t   2 / 2 t 2 )  t / 6]
1 t w  2  2 ( w  t  2 )
where
w is the beam width
E1 the beam elastic modulus
1 the beam density
E2 the film elastic modulus
2 the film density
Measuring the resonance frequency shift, allows us
to determine the elastic modulus of the film (E2).
AFM probes were used as vibrating beams
Monocrystaline Si
AFM cantilever
Typical dimensions:
- length (ℓ): ~ 130 m
- width (w): ~ 40 m
- thickness (t): ~ 5 m
The thin films were deposited by Filtered Vacuum Arc.
A rotating holder has been used to uniformly coat the cantilever.
Experimental procedure:
- Determination of the resonance frequency of the original
cantilever
- Consecutive coatings of the cantilever, with thin films,
increase gradually the thickness
- Resonance frequencies are measured for each step of the film
deposition
The elastic modulus E2 of the film was calculated
through a best fit of the theoretical frequencies ratio (νc/ νu)
with the experimental results
 c2 1wt  12( E2 / E1 ) [( w  2 )(1/ 2   / t   2 / 2t 2 )  t / 6]

2
1tw  2  2 ( w  t  2 )
u
Typical graphic
Results
Film
Material
DLC
Bulk
Elastic Modulus
(GPa)
-
Measured
Elastic Modulus
(GPa)
616
Shift
%
-
Pt
158
140
12
Au
78.9
69.1
12
Pd
124
115
7
- M.C. Salvadori, I.G. Brown, A.R. Vaz, L.L. Melo, M. Cattani. Physical Review B 67, 153404-1 - 4 (2003).
- M.C. Salvadori, A.R. Vaz, L.L. Melo, M. Cattani. Surface Review and Letters 10, 571 - 575 (2003).
-M.C. Salvadori, M.C. Fritz, C. Carraro, R. Maboudian, O.R. Monteiro, I.G. Brown. Diamond and Related Materials 10,
2190-2194 (2001).
-- A.R. Vaz, M.C. Salvadori, M. Cattani. Journal of Metastable and Nanocrystalline Materials 20-21, 758 – 762 (2004).
Results Interpretation
- Grains with crystalline structure (D) and with bulk elastic
modulus
- Grain boundaries composed by disordered structures (d) and
with elastic modulus lower than the bulk
For nanocrystalline material, the
grain boundaries contribute
significantly for the film
proprieties, decreasing the elastic
modulus of the film.
(IV) - Hydrophobic character of surfaces with
periodic microstructures fabricated on it
Introducing micro or nanostructures on a surface, the
wettability of the surface can be considerable changed.
In this work we have fabricated
periodic microstructures on surfaces.
The originality of the work is related to the metric scale.
Experimental procedure:
- Periodic microstructures were fabricated on SU-8 epoxy deposited
on silicon surfaces.
- The technique used was electron beam lithography.
- The pattern was the same for all samples and consisted in
squares regularly spaced.
- Three samples were prepared with different structure periodicities:
200 μm , 20 μm and 2 μm.
- A reference sample was prepared with a continuous surface of
SU-8 (without structures).
The contact angle measurements were:
85º for the sample with periodicity of 200 μm,
90º for the sample with periodicity of 20 μm,
105º for the sample with periodicity of 2 μm
and
90º for the reference sample
With this result, we can observe that, decreasing the structure
dimensions, the contact angle increased.
Summary
Experimental results were presented on synthesis and
characterization of nanostructured thin films.
Emphasis was done in:
resistivity,
thermoelectric power,
elastic modulus
and
hydrophobic properties.
Acknowledgements:
This work was supported by the Brazilian sponsors:
FAPESP and by the CNPq.