Supporting materials
Influence of Alkyl Chain Length on Phosphate
Self-Assembled Monolayers
Doris M. Spori, Nagaiyanallur V. Venkataraman, Samuele G. P. Tosatti, Firat
Durmaz, Nicholas D. Spencer*, Stefan Zürcher.
Laboratory for Surface Science and Technology, Department of Materials, ETH
Zurich, Wolfgang-Pauli-Str. 10, CH-8093 Zurich, Switzerland
[email protected], [email protected],
[email protected], [email protected],
[email protected], [email protected]
1. Layer model and parameters for WVASE data fitting
Layer description
Alkylphosphate
SAM
used layer model
Cauchy[5]
titanium dioxide
TiO2_mat
natural silicon oxide
silicon
SiO2_mat
Si_jell
fitting parameters
d
An = 1.45
Bn=0.01
Cn=0.00
d, n, k before
adsorption, after
adsorption fixed
none
none
layer thickness
measured
10-20 nm
2.3 nm
1 mm (Substrate)
2. XPS Three-layer model for the calculation of the thickness calibration
curves:
Three-layer model. Data from an XPS experiment are usually specified as atomic
concentrations, calculated using an equation of the form.
XA =
IA /RA
I j /R j
(1)
j
where XA is the atomic composition of element A in a sample containing j
components, IA is the measured spectral intensity for element A and RA is the relative
sensitivity factor for element A. However, these numbers are only strictly correct for
homogeneous samples. For non-homogeneous samples in the z-direction one needs a
method to calculate the effectively emitted electrons, after being attenuated by all the
overlayers. This depends on the structure of the sample as well as the attenuation
length of the electrons in each layer. To do so, we use the method described by Smith
and Livesey [1], who use a modified approach developed originally by Paynter [2] but
re-expressed in terms of atomic concentration, given by the forward transform
equation 2
N
N
n j,iT j ( ,i) /
X j( ) =
i= 0
T j ( ,i)
i= 0
N
n y,iT j ( ,i) /
y
(2)
N
i= 0
T j ( ,i)
i= 0
with the transition function Tj( ,i) (equation 3) for element j in the ith layer with
layer thickness ti, attenuation length factors
j,i
T j ( ,i) = exp( t i /
and emission angle
j,i
cos ) (3)
Using this approach, the theoretical XPS results can be calculated for any n-layer
model. In this article, we have used this formalism for the calculation of calibration
curves, where everything remains constant except the thickness of the alkyl layer (see
Figure 1). These curves were then used to measure the effective thickness of the
SAMs as a function of alkyl chain length. A difficulty with this approach is that the
correct attenuation length factors
j,i
need to be known. Since it is very difficult or
impossible to measure them directly, we have to rely on an empirical approach. The
semi-empirical equation CS2 developed by Cumpson and Seah uses
j,i
values that
have been calculated for 27 elements by accurate Monte-Carlo calculations and then
fits a semi- empirical function to this data depending only on the lattice parameter a,
the average atomic number Zav in a layer and the kinetic energy E of the electron [3].
j,i
= 0.316a 3 / 2
Z
0.45
E
+ 4 [nm]
[ln(E /27) + 3]
(CS2, 4)
Our three-layer model consists of a first layer of alkyl chains tilted 30° from the
surface normal, which is expected for an ordered layer [4]. This leads to a lattice
parameter a of 0.11 nm and an average atomic number Zav of 2.66 (CH2 groups). The
second layer contains the phosphate heads with a calculated dimension of 0.35 nm for
a and a Zav of 8 (calculated for 0.5 eq of H2O resp. OH per PO4). The third layer is the
substrate TiO2. For this layer, Zav is 12.67 and a was calculated according to equation
5, with the average atomic mass µ equal to 26.62 g/mol, the density
TiO2
equal to
4.24 *103 kg/m3 and the Avogadro constant NA.
a = 10
µ
8
1/ 3
N Av
(5)
The values used for each layer and the corresponding calculated
j,i
are printed in
table 2 and the calculated calibration curves with the measured data points in Figure 1
for the case of the data acquired with the SAGE 100. The data acquired with the
PHI5700 instrument are shown in the main text of this publication. It can be seen that
for all data points corresponding to one SAM, a thickness d can be found, yielding an
almost perfect fit. This is true for data acquired on both instruments and emission
angles ((PHI 5700 45°; SAGE 100 90°).
Table 2. Parameters used for the calculation of the calibration curves (3-Layer Model)
Layer 1
H(CH2)n chains Layer 2
30° tilted
PO4 (H2O)0.5
kg/m3
Layer 3
TiO2
4240
Lattice parameter a [nm]
0.11
0.35
atomic mass µ
0.22
26.62
Average atomic number Zav
2.67
Kinetic Energy
1
8.00
2
12.67
3
O1s PO4
956
1.34
5.43
2.31
O1s TiO2
956
1.34
5.43
2.31
Ti2p
1027
1.41
5.74
2.44
C1s
1202
1.60
6.47
2.74
P2p
1353
1.76
7.08
3.00
Atomic %
Layer 1
Atomic %
Layer 2
Atomic %
Layer 3
% O1s PO4(OH)0.5
0
81.80
0
% O1s TiO2
0
0
66.67
% Ti2p
0
0
33.33
% C1s
100.00
0
0
% P2p
0
18.20
0
Figure 1: Calculated calibration curves for alkyl phosphate SAMs on TiO2 for 90°
emission angle, as used on the SAGE 100. Measured values for C10, C11, C12, C13,
C14, C15 and C18 are also depicted in the figure.
Literature:
(1) Smith, G. C.; Livesey, A. K. Surface And Interface Analysis 1992, 19,
175-180.
(2) Paynter, R. W. Surface And Interface Analysis 1981, 3, 186-187.
(3) Cumpson, P. J.; Seah, M. P. Surface And Interface Analysis 1997, 25,
430-446.
(4) Zwahlen, M.; Tosatti, S.; Textor, M.; Hahner, G. Langmuir 2002, 18,
3957-3962.
(5)
(2001)
A Short Course in Ellipsometry, version 3.335, J. A. Woollam Co., Inc.