Supplementary Information for ‘Electrowetting at a liquid
metal-semiconductor junction’
S. Arscott and M. Gaudet
Institut d’Electronique, de Microélectronique et de Nanotechnologie (IEMN), CNRS UMR8520, The University of
Lille, Cité Scientifique, Avenue Poincaré, 59652 Villeneuve d'Ascq, France.
A. Silicon wafers and their preparation.
Commercial, 3-inch diameter - 380 µm thick - (100) silicon wafers (Siltronix, France) were used for the
experiments having two doping types: p-type (resistivity ρ = 5-10 Ω cm) and n-type (ρ = 5-10 Ω cm).
The silicon wafers were cleaned and deoxidized using H2SO4/H2O2 (vol/vol = 3/1) and HF (50%) based
solutions. The mercury was degreased using acetone, isopropyl alcohol and deionized (DI) water – and
metallic contamination minimized using nitric acid followed by a DI water rinse.
Ohmic contacts were formed on the rear surface of the silicon wafers using ion implantation: Boron -1020
cm-3 – for the p-type wafers, and Phosphorous – 1020 cm-3 – for the n-type wafers). The fabrication and
the experiments were performed in a class ISO 5/7 cleanroom (T = 20°C±0.5°C; RH = 45%±2%).
B. Extraction of Schottky diode parameters.
The following equations are used to extract the Schottky diode parameters [2A]:
N 
EC  E F  kT ln  C 
 ND 
N 
E F  EV  kT ln  V 
 NA 
kT  A**T 2 

bn 
ln 
q  J S 
kT  A**T 2 

bp 
ln 
q  J S 
ND 


1
 

q r  0  d (1 / C 2 dV ) 
2
q r  0 N
C
2(V  Vbi 
kT
)
q
NC and NA are the effective density of states in the conduction and valence bands, k is Boltzmann’s
constant, T is the temperature, A** is the effective Richardson’s constant, Js is the current density
intercept at V = 0 from the I-V measurements. C is the capacitance (F m-2) of the Schottky junction in
reverse bias [2A] – the model given in Fig. 5.
The following constants were used, all taken from Ref. [2A]:
εr
11.9
-
[2A]
qφ0
0.3
eV
[2A]
Eg
1.12
eV
[2A]
Nc
2.82x1019
cm-3
[2A]
Nv
1.83x1019
cm-3
[2A]
A** n-type
112
A/cm2/K2
[2A]
A** p-type
32
A/cm2/K2
[2A]
qΔφ
<40
mV
[2A]
The following table gives a summary of the extracted parameters:
θsat
N(a)
Ds
(deg)
(deg)
cm-3
(m-2
n-type
141.3
139.1
5.22E+14
p-type
141.9
137.7
2.12E+15
θ
Vbi
Vbi
φb
φb
(Hg-Si)(b)
(Al-Si)(b)
(Hg-Si)(b)
(Al-Si)(b)
2.98x1015
1.10
1.06
0.82
0.78
3.48x1015
1.01
1.00
0.77
0.77
eV-1)(a)
C. Measurement details.
For the electrowetting experiments, a DC voltage [E3634A Power Supply (Agilent, USA)] was applied to
the mercury droplet via a metal probe. The reverse bias voltage was ramped (5 V s-1). The contact angle
data was gathered using a commercial Contact Angle Meter (GBX Scientific Instruments, France) contact angle hysteresis was negligible.
I-V measurements were performed using a 2612 System SourceMeter® (Keithley, USA). Small-signal C-V
measurements were carried out using a Precision Impedance Analyzer 4294A (Agilent, USA) using a bias
voltage of ±40 V. A full calibration (open circuit – load (200 Ω) – short circuit) was performed using a
P/N101-190 S/N33994 Impedance Standard Substrate (Cascade Microtech, USA) over the frequency
range (500 Hz – 1MHz) prior to the measurements.
Supplementary Figure. Detailed energy-band diagram of a metal n-type semiconductor
junction. Qsc is the space-charge density in the semiconductor, Qss equals the surface-state density
on the semiconductor, Vbi is the built-in voltage, qφbn corresponds to the barrier height, qφb0 is
the barrier height at zero electric field, φ0 corresponds to the energy level at the surface, qΔφ is
the Schottky barrier lowering.
D. Derivation and assumptions for Equation 2 in the manuscript.
Following the reasoning given in ref. [1A] - a modification of the contact angle can be interpreted using
the following equation where E is the stored energy (J/m2) in the capacitance:
cos  cos 0 
E

(1)
1. For Electrowetting-on-dielectric (EWOD) - (C does not vary with V):
Q ( v )  Cv
V
(2)
V
CV 2
E   Q(v )dv   Cvdv 
K
2
0
0
(3)
The stored energy E = 0 at V = 0 thus the constant of integration K = 0. Thus by using Equation 1 we
obtain the well-known Young-Lippmann equation for EWOD:
cos  cos 0 
1
CV 2
2
(4)
C has units of F/m2. The second term of the RHS of Equation 4 is unitless i.e. [J/m2]/[J/m2].
2. For electrowetting at reverse bias Schottky barrier (C varies with V):
Considering the case of an n-type semiconductor, from ref. [2A] we have:

kT 
Qsc ( v )  2q r  0 N D  Bn  Vn   

q


Qss   qDs E g  q0  qBn  q 
(5)
(6)
where Qsc is the space-charge density in the semiconductor, q is the electric charge, εr and ε0 are the
dielectric constant of the semiconductor and relative permittivity of free space, ND is the doping density
in the semiconductor, φBn is the barrier height of the metal-semiconductor barrier, Vn is difference
between the bottom of the conduction band and the Fermi level, Δφ is the image force barrier lowering,
k is Boltzmann’s constant, T is the temperature, Qss is the surface-state charge density on the
semiconductor, Ds is the acceptor surface state density (states/m2/eV); Eg is the band gap (Ec-Ev), φ0 is
the energy level at the semiconductor surface.
At 300 K the Schottky barrier lowering Δφ is a function of voltage but is <40 mV for Silicon [2A] and can
be neglected in a first approximation. The thermal voltage kT/q = 25.8 mV at 300K and can also be
neglected. However, the energy level at the surface φ0 is of the order of 0.3±0.36 eV for silicon [2A].
In general Ds and Qss are not constant when the voltage is varied [3A] – however, in a first approximation
we consider this to be the case here.
If we consider electrowetting at 300K and neglect the Schottky barrier lowering Equations 5 and 6 can
thus be rewritten in the following form:
Qsc (v )  2q r 0 N D Vbi  v 
(7)
Qss   qDs E g  q0  qBn 
(8)
Where Vbi is the built-in voltage of the diode and v is the applied voltage.
Thus the voltage dependent charge Q(v) of an n-type Schottky diode can be approximated by and
written as:
Q(v )  2q r 0 N D Vbi  v   qDs E g  q0  qBn 
(9)
Applying Equation 3 we have:
E   2q r 0 N D Vbi  v   qDs E g  q0  qBn dv
V
0
(10)
E2
2q r  0 N D Vbi  V  2  qDs E g  q0  qBn V  K
3
3
(11)
We assume that the constant of integration K = 0 and E (J/m2) = ⅔(2qεrε0ND)1/2Vbi3/2 at V = 0. Using
Equation 1 we can thus write a modified Young-Lippmann equation for an approximation of
electrowetting on an n-type semiconductor as:
cos  cos 0 
2 2q r  0 N D
3
Vbi  V  2  qDs E g  q0  qBn V
3

(12)
From Equations 7, 8 and 12 and if we consider V>>Vbi then can write:
cos  cos 0 
2
QHF   V
3
(13)
Where:
   qDs E g  q0  qBn 
(14)
QHF can be obtained from the high frequency C-V measurements by integrating the measured highfrequency capacitance CHF with respect to voltage and injected into Equation 13.
Supplementary References
[1A] F. Mugele and J.-C Baret, Electrowetting from basics to applications. J. Phys. Condensed Matter. 17,
R705 (2005).
[2A] S. M. Sze, Physics of Semiconductor Devices - 3rd Edition (Wiley-Interscience, New Jersey, 2007).
[3A] D. Vu, S. Arscott, E.Peytavit, R. Ramdani, E. Gil, Y. André, S. Bansropun, B. Gérard, , A. C. H. Rowe
and D. Paget, Photoassisted tunneling from free-standing GaAs thin films into metallic surfaces. Phys.
Rev. B 82, 115331 (2010).