Role of a Pb2+ stabilizer in the electroless nickel plating system: A theoretical exploration

Article abstract of DOI:10.1021/jp036070k

The electroless nickel plating process involves multiple chemical reactions that interrelate mutually in intricate ways and take place almost simultaneously. This work attempts to provide a theoretical template for understanding this complicated system from the role of heavy metal stabilizers. Pb²⁺ ion was selected for the study because it is the most effective species in this category. A theoretical expression of the nickel deposition rate is created by envisioning the Stern-Grahame electrical double layer presumably attached to the plating frontier (the inner Helmholtz plane) as a one-dimensional potential well and the electron transfer from the Fermi level of plating frontier to Ni²⁺ ions at the outer Helmholtz plane as the quantum tunneling effect. The deposition of P atoms is assumed to go through the oxidative-addition of hypophosphite (H₂PO₂ ^-) ions at Ni atoms on the plating frontier and on this basis its theoretical deposition rate is developed. Another adsorption state of H ₂PO₂^- on the surface Ni atoms is proposed to form by its two oxygen atoms, and the P(I) center supplies electrons to the plating frontier through these two oxygen bridges. Establishing the relationship between Pb²⁺-ion concentration and the Fermi level of the plating frontier (i.e., inside the solid Ni-P alloy deposition layer on the plating substrate) is an important step for deriving the nickel and element phosphorus deposition rates. The stabilizing effect of the lead ion is attributed to its participation as the neutral atom in the lattice of the Ni-P film at the plating frontier, which results in the ascension of Fermi energy. Thus, the oxidation of hypophosphite at the plating frontier is retarded, which in turn slows down the deposition of both Ni and P that needs electrons. The dependence of the deposition rates of Ni and P on concentrations of Pb ²⁺ ion was experimentally examined. It is found that the theoretical models predict well the experimental trends. The parameters designated in the theoretical model are determined through a self-consistent computation procedure.

Full text of DOI:10.1021/jp036070k

J. Phys. Chem. B 2004, 108, 10919-10929
10919
Role of a Pb2+ Stabilizer in the Electroless Nickel Plating System: A Theoretical
Exploration
X. Yin,†,‡ L. Hong,* and B-H. Chen‡
,†
Department of Chemical and Biomolecular Engineering, National UniVersity of Singapore, 10 Kent Ridge
Crescent, Singapore 119260, and Department of Chemical Engineering, National Cheng Kung UniVersity,
1
UniVersity Road, Tainan 70101, Taiwan
ReceiVed: July 17, 2003; In Final Form: February 3, 2004
The electroless nickel plating process involves multiple chemical reactions that interrelate mutually in intricate
ways and take place almost simultaneously. This work attempts to provide a theoretical template for
2
+
understanding this complicated system from the role of heavy metal stabilizers. Pb ion was selected for the
study because it is the most effective species in this category. A theoretical expression of the nickel deposition
rate is created by envisioning the Stern-Grahame electrical double layer presumably attached to the plating
frontier (the inner Helmholtz plane) as a one-dimensional potential well and the electron transfer from the
2
+
Fermi level of plating frontier to Ni ions at the outer Helmholtz plane as the quantum tunneling effect. The
-
deposition of P atoms is assumed to go through the oxidative-addition of hypophosphite (H
2 2
PO ) ions at Ni
atoms on the plating frontier and on this basis its theoretical deposition rate is developed. Another adsorption
-
state of H PO
2 2
on the surface Ni atoms is proposed to form by its two oxygen atoms, and the P(I) center
supplies electrons to the plating frontier through these two oxygen bridges. Establishing the relationship between
2+
Pb -ion concentration and the Fermi level of the plating frontier (i.e., inside the solid Ni-P alloy deposition
layer on the plating substrate) is an important step for deriving the nickel and element phosphorus deposition
rates. The stabilizing effect of the lead ion is attributed to its participation as the neutral atom in the lattice
of the Ni-P film at the plating frontier, which results in the ascension of Fermi energy. Thus, the oxidation
of hypophosphite at the plating frontier is retarded, which in turn slows down the deposition of both Ni and
P that needs electrons. The dependence of the deposition rates of Ni and P on concentrations of Pb2 ion was
experimentally examined. It is found that the theoretical models predict well the experimental trends. The
parameters designated in the theoretical model are determined through a self-consistent computation procedure.
+
1
. Introduction
EN-plating system, heavy metal ion stabilizers play a mysterious
role since only a trace amount of them is sufficient to fulfill
the function. More importantly it affects P% in the Ni-P
deposition film. Hence, how these types of stabilizers act to
intervene in the deposition rates of nickel and phosphorus
represents the core knowledge of the EN process.
Since the pioneering work by Brenner and Riddell in 1946,1
the electroless nickel (EN) plating technique, a solution reaction
of metal deposition, in which a chemical reducing agent is used
in place of external electric current, has achieved a broad
spectrum of industrial applications ranging from protective and
decorative coatings2,3 to its use as a diffusion barrier between
base metal and final gold overplate4,5 in the microelectronic
packaging industry. The acid EN plating bath is the most
frequently used system, in which the overall reaction is typically
expressed by two equations
The electroless plating surface of an object is often regarded
as self-catalytic because the Ni-P alloy film grows only at the
surface once the deposition is initiated. This process differs from
normal chemical reduction of metal ions in a water solution
where metal blacks are produced everywhere. In an EN bath,
-
although hypophosphite (H2PO2 ) is known as a reducing agent,
cat.
2+
-
2+
2
H PO + 2H O + Ni
8
it seldom reduces the coexisting Ni ion in a pure single phase
solution at plating temperature. However, the plating would take
place forthwith when a palladium metal grain is introduced into
the solution. This simple fact indicates that hypophosphite itself
2
2
2
+
-
3
Ni + 2H + 2H PO + H (1a)
2
2
-
-
-
2
H PO + 6H + 4H O f 2P + 5H + 8OH (1b)
2
2
2
2
2
+
is not the reductive species from which Ni can gain electrons
directly. Instead, the reductive species is generated through
However, the complicated nature of the reaction has yet to date
-
chemical adsorption of H2PO2 on the reactive surface metal
been fully understood,6
-11
in particular the stabilization mech-
1
2,13
(first Pd and then Ni) atoms.
These surface atoms possess
anism, which is an essential element in ensuring that the plating
system is free of propagation of colloidal Ni particles. In an
1
1
unsaturated-coordination environment compared to those located
in the bulk phase. It is supposed, therefore, that the EN plating
mechanism involves the following four key reaction steps:
(1) How does H2PO2- undergo cleavage on the plating
frontier?
*
To whom correspondence should be addressed. E-mail: chehongl@
nus.edu.sg. Fax: +65-6779-1936. Tel: +65-6874-5029.
†
National University of Singapore.
National Cheng Kung University.
‡
1
0.1021/jp036070k CCC: $27.50 © 2004 American Chemical Society
Published on Web 06/29/2004

10920 J. Phys. Chem. B, Vol. 108, No. 30, 2004
Yin et al.
TABLE 1: Substrates Used for EN Plating
substrates
brass
equipment
thickness
size
2
0.2 mm
∼ 1 µm
2.5 × 2 cm
2
Anelva, Japan model 43 N
1 × 1 cm
-
7
E-beam evaporated Al
base P e 5 × 10 Torr; V ) 3.7 to 4.1 kV
deposition temp. ) 25 °C ∼ 50 °C
2) How are elemental P and orthophosphate ion H2PO3-
TABLE 2: Pretreatment Procedures for the Al Substrates
(
produced?
step
immersion
soak clean
50 g/L NaOH etching
temperature/time
3) How do Ni2 ions gain electrons from the plating surface?
+
(
(
1
2
3
4
5
6
7
60 °C/5 min
4) How does the Pb2 ion affect the above reaction steps?
+
room temp./15 s
room temp./10 s
room temp./30 s
room temp./10 s
room temp./30 s
until dry
Theoretically, we propose that these questions be accessed
from the perspectives of coordination activation and interfacial
electron transfer. The first two reactions are believed to be driven
by coordination to surface Ni atoms for the formation of P(III)
and P(0) species, which requires electron transfer between
50 vol % HNO
1st zincation
50 vol % HNO
2nd zincation
3
etching
3
etching
drying by air jets
-
H2PO2 and Ni atoms, whereas the coordination provides low
phosphorus and nickel upon the Pb2 concentration in a plating
solution are proposed on the deduction basis. The experimental
deposition rates were employed to determine those parameters
that derived from fundamental assumptions in the models via a
self-consistent computation procedure.
+
activation energy pathways. Question 3 is essentially governed
by the Fermi energy of the plating frontier as it represents the
level with 0.5 probability of all electron states, and therefore, it
affects electron-transfer efficiency in the Stern-Grahame (S-
G) EDL. Question 4 is related to the re-location of the Fermi
level due to the presence of Pb in the lattice of the plating
frontier.
The S-G EDL attached to the plating frontier consists of
the inner Helmholtz plane (IHP) and the outer Helmholtz (OHP).
The space embraced between is also known as the Stern layer.
In this work, reduction of nickel ions within the EDL is deemed
as the electron tunneling effect to penetrate the energy barrier
including the effect of (i) the Fermi level of the Ni-P layer,
over which there are statistically 50% of electronic states
available for accommodation of electrons, and (ii) the potential
in the Stern layer. The basic concepts of interfacial tunneling
have been described in the book of Bockris and Khan. Besides
deposition of Ni atoms at the plating surface, it is inevitable
that a small portion of Ni atoms formed in the EDL is going to
migrate reversely, as the agglomeration form (tiny Ni particles),
into the plating solution through OHP. These tiny seeds possess
highly reactive surfaces and thus have capability of causing
decomposition of the plating solution through a quick prolifera-
tion process.11 Heavy metal cations, especially Pb , are known
as effective reagents1 to inhibit the propagation of Ni colloidal
particles. The heavy metal ions are generally thought to furnish
2
. Experimental Section
2.1. Substrates and Their Activation. Two kinds of
2
substrates, a brass sheet (2 × 2.5 cm , 0.2 mm thickness) and
2
an Al deposited silicon wafer (1 × 1 cm Al layer and thickness
) 1µm), were used in this work as the substrates for the EN
plating. The brass substrate was employed to investigate the
2
+
dual effects of a Pb stabilizer on the Ni plating rate and P
content in the deposited films since a larger size of it than that
of the Al/Si substrate can offer more reliable results by
measuring the mass gained with time. The Al-deposited silicon
wafer with smaller dimensions was used to examine the
composition of the deposited Ni-P films.
14
The EN plating cannot take place directly on an aluminum
substrate as there is an overlaying thin layer of oxides.18
A
double zincation process was used to remove the oxides and to
form a thin protective zinc layer (Table 1). Commercial soak
cleaner (PSC1139, Plaschem Singapore) and zincation solution
(PZB 1800, Plaschem Singapore) were used. The substrate was
thoroughly rinsed with DI water after every step of processing.
The brass substrate was first cleaned with the soak cleaner
in an ultrasonic bath (Elma, T1040H) for 10 min under room
temperature to remove contamination and followed by removing
surface oxides in a H2SO4 solution (10 vol %) for 2 min at
ambient temperature. Pure brass cannot be electrolessly plated
by nickel; thus, tiny Pd particles were introduced to the brass
surface as the seeds for initiating the catalytic reduction of Ni.
After being rinsed with DI water, the cleaned brass is activated
with an activation solution having ingredients as PdCl2 0.18
g/L, FeCl3 0.8 g/L, NiSO4 5 g/L, HAc 25 mL/L, D,L-malic acid
20 g/L, 69% HNO3 10 mL/L, and NaF 10 g/L, for 20s at room
temperature.
2.2. Electroless Nickel Plating. The EN solution used in this
work was formulated in-house (Table 2). The initial pH value
of the plating bath was adjusted by a dilute NaOH solution (5
wt %) to 5.0 ( 0.1. The pH value of the plating process was
monitored by a CyberScan pH 500 m (Eutech). The bath
temperature was controlled within 90 ( 1 °C through a TE-
10D thermoregulator (TECHNE) at atmospheric environment.
The plating was conducted by immersing one piece of the
substrate into a magnetically stirred EN solution (80 mL) in a
2+
5,16
1
7
a geometric block via adsorption on the plating frontier of Ni
seeds. However, this explanation is unsatisfactory due to two
experimental facts: (1) there is a rather large gap in Pb
concentration between the minimum and the critical levels, in
which the plating rate of Ni slows down, and (2) the content of
phosphorus in the Ni-P deposition film decreases with increas-
ing concentration of Pb . In this work, an alternative interpreta-
tion is proposed: Pb2 ions act by lowering the reductive
potential of the plating frontier after they are co-deposited into
the Ni lattice.
2
+
2+
+
In addition to preventing the EN bath from running away,
Pb2 ions also function to restrict the deposition of phosphorus
on the plating frontier regardless of the desired plating item or
colloidal Ni particles. As mentioned just now, the co-deposition
of Pb on the plating surface would raise its Fermi level, which
we found from the experiment to affect less the Ni deposition
rate than the phosphorus deposition rate. It is also interesting
to note that an EN plating process comprises virtually numerous
oscillation cycles in the deposition rates of both Ni and P despite
the fact that detection of the phenomenon experimentally is
relatively difficult, though not impossible. Two theoretical rate
expressions describing the dependence of deposition rates of
+
2
100 mL beaker for 20 min. The plating rate (R) (mg/cm h or
can be converted to mA/cm by the Faraday relationship) on
2

Pb2 Stabilizer in Electroless Nickel Plating System
+
J. Phys. Chem. B, Vol. 108, No. 30, 2004 10921
TABLE 3: Composition of Electroless Plating Bath
NiSO
NaH PO
NaAc
DL-malic acid
lactic acid (90%)
borax
4
‚6H
2
2
O
26 g/L
28 g/L
10 g/L
15 g/L
15 mL/l
6 g/L
2
‚H
2
O
Pb(Ac)
pH adjuster
2
variable
NaOH (0.2M) (pH 5)
the brass substrate was determined with the gravimetrical
method and then calculated according to the following formula:
(
M - M ) × 60
t
0
R )
(2)
A × t
s
where t is the plating duration (min), Mt (mg) is the mass of
the object plated for a length of time t, M0 (mg) is the the initial
2
weight of substrate, and As is the surface area of specimen (cm ).
The phosphorus deposition rate (RP) and the nickel deposition
rate (RNi) were calculated as follows:
RP ) R × P%
(3)
(4)
RNi ) R × (1 - P%)
where P% is the phosphorus content by mass in the Ni-P film.
.3. Composition of the Deposited Films. The phosphorus
2
Figure 1. Schematic illustration of the electric double layer likely to
be formed along the plating frontier in an EN plating system.
mass content (P%) of the deposited films on the brass was
determined using an energy dispersive X-ray (EDX) micro-area
analyzer (JEOL JSM-5600LV). The surface composition of
deposited EN films was examined using the X-ray photon
spectroscopy (XPS). The XPS was carried out on an instrument
(
1) H2PO2- anions are more strongly adsorbed on the catalytic
nickel surface via the H corner of the tetrahedron than other
-
-
phosphoroxy anions (H2PO3 , H2PO4 , etc.).
2) Electrons can transfer from the hypophosphite to the
(
(
Kratos Axis His, Manchester, U.K.) equipped with the Al KR
corner of the tetrahedron via hydrogen atoms and be surrendered
to the nickel substrate.
X-ray source (at 1486.6 eV) by using the takeoff angle at 90°.
The pass energy is 40 eV for high-resolution scans.
(3) Electrons can also transfer from the substrate to adsorbed
hypophosphite.
3
. Structural Relevancy for Electron Transfer in the
The above assumptions could be modified by the following
two different pathways of chemisorption: (1) the oxidative
Stern-Grahame Layer
3
.1. Electron Transfer through Ni(0)-H2PO2- Coordina-
addition,22 by which the P-H bond of H2PO2- undergoes
tion Complexes Formed at the IHP. As proposed in the
Introduction, the Pb2 stabilizer affects the plating rate (R) and
phosphorus content (P%) in the deposition layer (Ni-P alloy)
via the electronic effect. The electron effect means the fluctua-
hemolytic cleavage on a Ni atom, and (2) the Ni-O bonding
model, in which hypophosphite anion lands at the IHP via its
oxygen ends (Figure 2). The oxidative addition produces P and
the surface hydrogen atoms, which needs to abstract three
electrons from the surface Ni atoms (eq 5). With respect to the
oxygen-landing model in association with the oxidation of
hypophosphite, oxygen has a stronger affinity and greater spatial
+
1
9-21
tion of electron flow density occurring in the S-G EDL
-
(
Figure 1), wherein the IHP is attached by anions (e.g., H2PO2 ,
-
2-
H2PO3 , and SO4 ) except water molecules and the OHP
2+
+
mainly by solvated cations (e.g., Ni , Na , etc.). On the basis
of this model, Ni2 ions pick up electrons and are converted to
metal atoms within the EDL. To describe the electron flow
density occurring in the S-G layer, a suitable theoretical method
is to treat the flow of electrons as the quantum mechanical
tunneling. Namely, the S-G layer can be presumed to be the
one-dimensional potential well. On the other hand, the phos-
phorus content is affected by the adsorption state of hypophos-
phite ions on the IHP of the S-G layer. With reference to the
accessibility than hydrogen to the surface Ni atoms. Moreover,
+
23-25
according to Taube’s theory,
the oxygen atom is more
proper than the hydrogen atom in functioning as the bridge for
electron transfer from phosphorus (I) to Ni. The products of
this pathway are orthorphosphite, electrons to the IHP and
protons discharged to the plating solution (eq 6)
-
-
+
H PO
+ 3e (Ni ) + 4H f
m
2
2
(ads)
Ni - 2H
+ Ni - P
+ 2H O (5)
1
2-13
m
(suf)
m
(suf)
2
adsorption model proposed by Smith and Sadakow,
a
clearer picture to describe it should be based on the concept of
the transition metal complex, i.e., hypophosphite ion as the
ligand and Ni atom as the central metal.22 The redox reaction
of hypophosphite can thus take place within the coordination
sphere rather than within the S-G layer. This is important to
differentiate the deposition of Ni atoms from the deposition of
P atoms as well as the generation of the orthophosphite ion.
-
-
-
+
H PO
+ H O f 2e (Ni ) + H PO
+ 2H (6)
2
2
(ads)
2
m
2
3
(aq)
2
+
-
Ni + 2e (Ni ) f (Ni )
(7)
m
m
where (Nim) represents the Ni atoms on the surface plating
frontier or at the IHP. It may note that these three equations
are proposed to describe the reactions happening on the surface
of “electrode”, and they do not represent elementary steps.
The key assumptions of the hydrogen landing model proposed
by Smith & Sadakkow1
2,13
are as follows:

10922 J. Phys. Chem. B, Vol. 108, No. 30, 2004
Yin et al.
charge carried by nickel ions to the total cationic charge at the
OHP. At an equilibrium of plating, k1 and k2 should vary
negligibly. Thus, the plane density of nickel ions at the OHP,
Ni
OHP
-2
n
(m ), has a linear relationship with the plane density of
P
hypophosphite anions at the IHP, n
:
IHP
Ni
OHP
P
IHP
n
) krn
(8)
where kr is a constant (kr ) k2/k1).
P
Furthermore, n , can be described as
IHP
P
IHP
P
B
n
) C V˜ N exp(-G /kT)
(9)
ads
ads
P
B
where C is the bulk concentration of hypophosphite anions in
the EN bath, V˜ is the molar volume of the solution, Nads denotes
the number of available adsorption sites for hypophosphite anion
per unit surface area on the IHP, k is the Boltzmann’s constant,
T stands for the absolute temperature, and Gads means the Gibbs
-
adsorption energy per adsorbate species (e.g., a H2PO2 anion).
It has been aware that the rate of adsorption of hypophosphite
is affected to a large extent by the thermodynamic work function
(Φ) that includes the vacuum work function of the solid
adsorbent in question and the effect due to the presence of
adsorbates on surface (Φ ) Φvacuo + b). The change in the
work function represents the collective effect of the individual
coordination adsorption sites as aforementioned, and therefore,
the free energy of adsorption has a linear relationship with the
3
1
work function. Applying this concept, we could presume that
the adsorption of H2PO2 at the IHP obeys the relationship as
follows when a change in the work function is incurred due to
the adsorption of stabilizer species at the IHP
Figure 2. Sketch to show the two different reaction pathways through
which hypophosphite ions are converted to orthophosphate and
phosphorus, respectively.
-
Various types of atomic clusters containing the Ni(0)-P(0)
bond have been known.26 From the viewpoint of coordination
0
ads
Gads + k Φ ) G + k Φ
(10)
G
G
0
chemistry, a phosphorus atom is a σ ligand that could cause an
22,26
0
ads
increase in electron density at the nickel atoms coordinated.
In eq 10, G is defined as the average Gibbs free energy of
It has been known that the negative charge density at the central
transition metal atom (or ion) of a complex is a favorable factor
to the oxidative addition of reactant molecules. Once a
phosphorus atom is deposited on the IHP, its adjacent nickel
atoms would show a higher preferentiality to the oxidative
addition of hypophosphite. This action will be therefore followed
by deposition of phosphorus (eq 5) at the neighborhood of this
site. However, this trend can be constrained by the oxidation
step that supplies electrons to the oxidative addition (eq 6). The
coordination chemistry points out that oxidative addition requires
the Ni atoms which have low coordination numbers (CN), which
happen at edges or corners, whereas the oxidation step does
not have such spatial preferentiality. The surface complexes are
formed upon adsorption of hypophosphite to the Ni atoms.
Hence, it is rational to propose that the oxidative addition and
the oxidation of hypophosphite take place at the IHP simulta-
neously but at different locations. This mutually promoting
deposition mechanism could well account for the laminated Ni/P
structure and nonhomogeneous P distribution in the Ni-P
adsorption for the landing of a hypophosphite anion onto the
IHP in the absence of stabilizers, Φ0 is the corresponding work
function of the Ni deposition film, and kG is a proportional
constant describing the influence of work function on the
adsorption tendency of H2PO2 . Combining eqs 9 and 10, the
adsorption plane density of hypophosphite anion at the IHP can
be related to the work function of the plating frontier
-
P
IHP
P0
IHP
n
) n exp[k (Φ - Φ )/kT]
(11a)
G
0
in which
P0
IHP
P
B
0
ads
n
) C V˜ N exp[-G /kT]
(11b)
ads
P0
IHP
n
is the plane density arrived at equilibrium in a system
Ni
where nil stabilizer is present. Similarly, n
can be also
OHP
linked with eq 11a by applying eq 8
Ni
OHP
P0
n
) krn exp[k (Φ - Φ )/kT]
IHP G 0
deposition layer (Figure 3), which have been found experimen-
Ni0
tally.2
7,28
The content and distribution of P(0) in the Ni/P
) n
exp[k (Φ - Φ )/kT]
OHP G 0
(12)
deposition layer are known to affect the corrosion resistance of
the layer.
Ni
OHP
is the number of hydrated Ni2+ ions per unit area
where n
3
.2. Relation of Adsorption at EDL and the Work
at the OHP.
2
+
Function of Ni Deposition Film. According to Grahame’s
theory,2 the potential decreases linearly from the IHP to the
OHP, whereas it decreases almost exponentially in the diffuse
layer. We can assume that k1 is the ratio of charge of the
hypophosphite anion to the total negative charge (from other
types of coexisting anions) at the IHP, and k2 is the ratio of
3.3. Diffusion of Free Pb Ions toward the OHP. As
aforementioned, Ni ions are reduced at the OHP, and the
required electrons come from the plating frontier through the
S-G layer (tunneling effect). Most of the nickel atoms (or
colloids) formed at the OHP deposit on the substrate. However,
a handful of them are to diffuse outward into the bulk solution
9,30
2+

Pb2 Stabilizer in Electroless Nickel Plating System
+
J. Phys. Chem. B, Vol. 108, No. 30, 2004 10923
Figure 3. Schematic illustration of the periodical change of the phosphorus rich region.
OHP can be written as
app
D
D
Pb
OHP
Pb
B
Ni Ni
C
) C - k
C
≈
Pb/Ni
OHP
app
Pb
Pb
B
Pb-C
Pb
B
Pb-C
B
C - C
(C > C
) (13a)
(13b)
B
Pb
OHP
) 0 (CB e C PB b-C
)
Pb
C
app
app
where DNi and DPb are the apparent diffusivities of nickel
particles and lead ions, respectively, resulting from the ap-
proximation of the mass conservation law
2
2
∂
c
t
∂ c
app∂ c
)
D
+ r ≈ D
2
2
∂
∂
x
∂x
where r is the term denoting generation or consumption by the
reaction. Furthermore, the steady-state assumption leads to
2
Ni
2
Pb
Ni
Pb
app∂ C
app∂ C
app∂C
app∂C
D
) DPb
) 0 or kPb/Ni
2
D
) DPb
Ni
Ni
2
∂
x
∂x
13c)
∂
x
∂x
(
where kPb/Ni is the corresponding flux ratio of lead ions to tiny
Pb
Pb
OHP
nickel particles, CB and C
are the concentrations of the
lead ions in the bulk of solution and at the OHP, respectively,
Ni
OHP
C
is the concentration of Ni colloidal particles at the OHP,
Pb-C
and CB
is the critical bulk concentration of lead ion, over
Figure 4. (a) Schematic illustration of the diffusion directions of Ni-P
2
+
which the lead ion concentration influences both the plating
colloids and Pb ; (b) The concentration profiles for the diffusion of
colloidal nickel particles diffusion from the OHP to the bulk of solution
rate and phosphorus content at the desired plating surface. In
Ni
2
+
and the diffusion Pb from bulk phase to the OHP.
the integration of eq 13c to obtain eq 13a, C ) 0 means no
B
2+
unstabilized (by the adsorption of Pb ) nickel colloidal particles
are present in the bulk of plating solution.
through the diffuse layer.11 The Pb2+ ions in the bulk of the
solution will set down quickly on these Ni colloidal particles
as they have a much larger and hence reactive specific surface
area than the plating object. It may be note that, besides the
desired plating surface, the individual Ni colloidal particle also
has an EDL. Hence, there is a flux of Pb2 from the bulk of the
3
.4. Effect of a Stabilizer on the Work Function of Ni
Colloidal Particles. In EN plating baths, substantially low
2+
concentrations of the heavy metal ion stabilizer, such as Pb
(
2+
in ppm level), are normally used. It is unlikely that Pb ions
+
inhibit the propagation of Ni colloidal particles through the
action of spatial blocking, namely, by forming an obstructing
layer on Ni particles. Being identified as an effective stabilizer,
the lead ion must play a catalytic role in the deactivation of Ni
particles. From the viewpoint of physics, the work function of
Ni colloidal particles (substrate) would be very sensitive to
2
+
solution toward the OHP in response to the decrease of Pb
concentration hereabout (Figure 4). Assume this process will
quickly reach the steady state, which means that the flux of the
Ni colloidal particles diffusing outward from the OHP (of the
2
+
plating surface) has a linear relationship with the inward Pb
+
2
diffusion flux from the solution body. In the case that the Pb
2+
adsorption of Pb on them. The change in the thermodynamic
Pb
concentration in the bulk (C ) is greater than its critical value
work function of the substrate, ∆Φ ) Φ - Φ , is found to be
B
0
Pb-C
B
+2
(C
), Pb can diffuse to the OHP of the desired plating
proportional to the number N and the dipole moment p of
3
2,33
surface, and the concentration in (very close proximity to) the
adsorbed species

10924 J. Phys. Chem. B, Vol. 108, No. 30, 2004
Yin et al.
∆
Φ ) - 4πpN
(14a)
The negative sign in eq 14a means that the work function of
pure nickel (∼ 4.9 eV) is decreased by the adsorbed Pb, whose
work function is about 4.25 eV. Heavy metal cations have larger
ionic radii and can be more easily adsorbed on the surface of
Ni particles through electrochemical displacement
2
+
2+
34
(
Ni ) + nPb f (Pb ) + nNi , E° ) 0.1319 V (14b)
n n
As the concentration of lead ions is substantially low, it can be
assumed that there is a simple and approximate relationship
Pb
OHP
between N and C
Pb
OHP
N ) a(C
)
(15)
where a is the constant signifying the fraction of those Ni surface
sites on an individual Ni particle at which the displacement of
Ni with Pb2+ ions can carry out. These Ni sites must have low
coordination numbers. The work function (Φ) of the substrate
Figure 5. Schematic illustration of the electron tunneling process from
nickel surface to the dehydrated Ni2 ions at the OHP.
+
2+
can now be linked with the concentration of Pb ion in an EN
effect is that electrons over the plating frontier are easier to
give up relative to the pristine Ni-P lattice. As discussed above,
the resulting IHP can promote the oxidative addition of
hypophosite (the cathodic process) from the viewpoint of
electronic factor. However, it inhibits the oxidation of hypo-
phosphite (the anodic process). Therefore, the deposition rates
of both Ni and P are to be pulled down with tightening up of
the electron supply channel.
Pb
B
plating solution (C ) by combining eqs 14a and 15
Pb
Φ ) Φ - 4πpa(C
)
OHP
(16a)
0
Here Φ0 is the work function of clean Ni-P layer (without
carrying Pb). On the other hand, to figure out the change of
Pb
B
work function in the desired plating surface when C
>
Pb-C
C
, we just need to plug eq 13a into 16a. Therefore, the
B
3.5. Nickel Deposition. The electroless plating system is often
explained as being driven by an auto-catalytic surface because
work function of the desired plating surface can be linked with
the concentration of Pb2 (C ) in plating solution
+
Pb
B
2+
the reduction of Ni at OHP has the certain relationship with
11
the adsorption of hydrogen atoms at the plating frontier. The
surface Ni-H species will have two destinies, being released
either as protons or as hydrogen molecules. An EN plating
process is always accompanied by the release of hydrogen
bubbles and a decrease in the pH value. A tenable explanation
for this is that the adsorbed hydrogen atoms can undergo
coupling to form hydrogen gas or depart as protons after
Pb
B
Pb-C
B
Φ ) Φ - 4πpa(C - C
)
(16b)
0
At this point, the relationship of the work function and the Fermi
energy (Ef) becomes essential. According to the theoretical
35
model described by Eisberg and Resnick , there is an abrupt
leap of the potential energy of an electron (V0) in a metal at the
boundary from bulk to environment, representing the depth of
the potential well from the lowest energy state to the state of
electron being far outside the metal. It is also understandable
that most energetic electrons in the metal are in the state having
an energy interval Φ0 below the top of the potential well (V0 >
2+
transferring electrons to Ni ions through the IHP.
With respect to the transfer of electrons from the plating
2+
frontier to the Ni ion within the S-G layer, it is assumed to
be an electron tunneling process (Figure 5), which can be
described using a rectangular potential energy barrier expressed
Φ0). Thus, the relationship between the work function Φ0 (or
36
as
0
f
Φ) and Fermi energy E (or Ef) can be expressed as
U(x) ) 0, x < 0 in region I
0
f
V ) Φ + E ≈ Φ + E
(16c)
0
0
f
U(x) ) U , 0 < x < L in region II
0
in which Φ and Ef are the thermodynamic work function and
Fermi energy, respectively, and the subscript or superscript “0”
represent under the condition without the co-deposited stabilizer
Pb.
The above approximation equal sign implies that, if the
concentration of co-deposited Pb atoms in the Ni-P lattice of
the plating surface is considerably low, the influence incurred
on V0 can be ignored. Hence, the following expression can be
obtained from eqs 16b and 16c
U(x) ) 0, x > L in region III
where L and U0 represent the width and the height of the
potential barrier, respectively. U0 as illustrated in Figure 5
includes the contribution of all electronic states (or energy levels)
to the tunneling process, despite the fact that electrons from
the states of E > Ef (labeled by the solid rectangle) have a much
higher probability to penetrate through the barrier. The height
14
of potential barrier U0 was estimated to be ∼14.8 eV, in which
the Fermi level of Ni-P (∼10 eV) can be obtained from the
universal equation given in the book of Eisverg and Resnick,35
and the relationship between U0 and the thermodynamic work
function Φ is V0 ) Φ + Ef ) U0 + b, where b reflects the
influence of adsorption on the work function. The adsorption
of negative charges on the plating surface, e.g., hypophosphite,
creates a repulsive action to the entrance of electrons into the
0
f
Pb
B
Pb-C
E ) E + 4πpa(C - C
)
(16d)
f
B
0
f
Pb
Pb-C
where Ef ) E if C < CB
.
B
On the basis of eqs 16a and 16d, it can be concluded that
participation of Pb(0) into the Ni-P lattice of both Ni colloidal
particles and the desired plating surface causes a decrease in
the work function and an increase in the Fermi energy. The

Pb2 Stabilizer in Electroless Nickel Plating System
+
J. Phys. Chem. B, Vol. 108, No. 30, 2004 10925
solution. For this, the work function is related to the interfacial
potential, in which the adsorption free energy takes the main
part.
Using the WKB (after Wentzel, Kramers, and Brillouin)
approximation,3
7-39
the tunneling probability of the state with
a energy level E, W(E), can be expressed by
4
πL
h
W(E) ) exp -
2m(U - E)
(17)
x
0
{
}
where m is the static mass of electron, U0 ) 14.8 eV, h is the
F f
Figure 6. Independent of K value on the Fermi energy (E ).
Planck’s constant, and the barrier width L is chosen as 5 ×
-
10
1
0
m. For the cathodic reaction, if the interfacial electron
filled or not, is given by per unit volume,42 where m is the static
mass of electron and p ) h/2π
transfer is the rate determining step, the most generic expression
of the current density is given by the form39
3
/2
E
8
mπ
1 2m
1/2
F(E) )
x
2mE )
(21)
3
2
(
2
)
ic ∝ e0 ∫ ∫C(x)G(x,E)W(x,E)f(E)F(E) dE dx (18a)
h
2π p
where e0 is the charge of an electron, C(x) is a one-dimensional
Submitting eq 17 and 19-21 into eq 18c, the current density,
iC, can be expressed as
2+
concentration of the acceptor (Ni ) within the Stern layer at
distance x from the plating frontier, G(x,E) is the probability of
finding the acceptor possessing potential energy E at distance
x from the plating frontier, W(x,E) is the probability of electrons
Ni
0 OHP
i ) K δ F(E,Ef)
(22a)
C
2
+
migrating from an energy level E in the plating frontier to Ni
in which F(E,Ef) is a function of the Fermi energy (Ef) and the
energy level (E) of interest
ion within the S-G layer, f(E) is the Fermi-Dirac distribution
of occupied electron states with an energy level E in the metal
electrode, and F(E) is the density of electronic state with an
energy level E in the cathode (the Ni plating frontier). Since it
is rational to assume, according to the tunneling effect, that most
of the dehydrated nickel ions gain electrons at the OHP of the
desired plating surface, the G(x,E) and W(x, E) functions in the
integral can thus be reduced to be ones with a single variable
E. Consequently, the above double integral becomes
âE 4πL
exp
-
2m(U - E)
]x
E
x
0
[
(
)
kT
h
F(E,E ) )
∫
dE
(22b)
f
E - Ef
1
+ exp(
)
kT
whereas K0 can be expressed as
3
/2
e0
âEg
2m
i ∝ e (
∫
C(x)|x ) L dx)(
∫
G(E)W(E)f(E)F(E) dE)
K ) λ
G(E ) exp -
(22c)
c
0
0
2
(
2
)
g
(
)
kT
2
π p
(
18b)
2+
From eqs 12 and 16b, we obtain
The integration of the C(x) term yields the plane density of Ni
at the OHP that is expressed by δOHP
Ni
Ni
OHP
n
n
4π pakG
Pb
B
)
exp[k (Φ - Φ )/kT] ) exp -
(C -
Ni
OHP
Ni0
OHP
G
0
[
kT
i ) λe δ
∫
G(E)W(E)f(E)F(E) dE
(18c)
c
0
Pb-C
B
λ is introduced here as a proportional constant. According to
the Boltzmann’s distribution, the energy-level distribution of
the acceptor, G(E), in solution is given as14
C
) (23)
]
Substituting the value of barrier height (U0 ) 14.8 eV), barrier
-
10
width (L ) 5 × 10 m), the symmetry factor (â ) 0.5), and
the EN plating temperature (T ) 363 K) into eq 22b and
integrating the equation over the range 0< E < U0, it becomes
G(E) ) G(E ) exp[â(E - E )/kT]
(19)
g
g
where Eg is the ground-state energy of the acceptor (Ni2+ ion).
The second ionization energy of Ni can be used to approximate
the ground state of Ni2 ion. The factor â is the symmetry factor
F(E ) ) KF E exp[(16E - 5.1 14.8 - E )] (24a)
f
x
f
f
x
f
+
(
0 < â < 1) describing the geometry of the lowest unoccupied
x
E exp[(16E - 5.1
x
14.8 - E)]
2
+
orbitals of Ni , which are the d orbitals having symmetry with
1
+ exp[32(E - E )]
f
1
4.8
respect to the center, so the â value is chosen as 0.5. At a
K )
∫
dE (24b)
F
0
temperature T above absolute zero, the Fermi-Dirac distribu-
E exp[(16E - 5.1 14.8 - E )]
x
f
f
x
f
tion4
0-43
for the expectation of occupancy of a state with energy
E in the metal electrode is
The exponential term in eq 24a is purposely inserted in order
to obtain a constant value when E ) Ef. The value KF calculated
1
1.5
is equal to 0.0987 (eV ) and independent of the Fermi energy
f(E) )
(20)
E - Ef
(
(Ef; Figure 6). Furthermore, it is appropriate to presume that
1
+ exp
)
electrons taking part in the tunneling process should have energy
kT
4
3
states above the Fermi level of substrate being considered.
Thus, eq 24a expressed by Ef can be taken as the energy
threshold to calculate electron current density within the Stern
layer
where Ef is known as the Fermi energy (of the Ni-P deposition
layer in this particular case) and k is the Boltzmann constant.
The density of states F(E) at the energy level E, whether it is

10926 J. Phys. Chem. B, Vol. 108, No. 30, 2004
Yin et al.
In eq 27f, the maximum value of â is one. As for kG, we have
the relation from eq 10
F(E ) ) 0.0987 E exp[(16E - 5.1 14.8 - E )]
(25)
f
x
f
f
x
f
Therefore, the electric current density iC within the Stern layer
would be
o
ads
Gads - G
kG )
Φ - Φ
0
Ni0
OHP
i ) K n
E exp (16E - 5.1 14.8 - E ) -
C
0
x
f
[
f
x
f
From the normal adsorption heat, the numerator term can be
estimated to have a magnitude of about 0.1 eV/molecule; and
from the difference of vacuum work functions of Ni metal (4.9
eV) and Pb metal (4.25 eV), the denominator term falls in the
range of about 0.1-0.01 eV as the Pb content in Ni is very
4
πk pa
G
Pb
B
Pb-C
B
(
C - C
) (26)
]
kT
As far as the electron transfer between the two Helmholtz planes
-
1
-2
low. Therefore, k > â. On the basis of this estimation, it is
is concerned, nickel deposition rate RNi(mg h cm ) depends
on iC. Theoretically, this process could be also described by
Faraday’s law of electrolysis
G
0
clear that RNi < R .
Ni
3.6. Phosphorus Deposition. According to eq 5 proposed,
the deposition of phosphorus process is believed to experience
the three elementary steps (Figure 2): (1) landing of hypophos-
phite anion through its hydrogen corners, (2) oxidative addition
of it to surface nickel atoms, and (3) abstraction of the two
oxygen poles from the adsorbed P atom. The oxidative-addition
step could be considered as the rate determining step as it
involves the transfer of three electrons and breaking up of the
two P-H bonds. Thus, the P deposition rate can be written as
RNi ) Rk i
e C
(27a)
where ke is the electrochemical equivalent for the reduction Ni2+
2e ) Ni; and R is proportional constant and its value depends
on plating loading as well as the percentage of nickel colloidal
particles in the total Ni-P deposits at the moment t.
The nickel plating rate RNi (eq 27a) becomes
+
4
πk pa
P
IHP
P
IHP
G
R ) k′τn
) kPn
(28a)
RNi ) kNi E exp (16E - 5.1 14.8 - E ) -
P
p
x
f
[
f
x
f
kT
where kp′ is the rate constant of oxidative-addition step; and τ
is the percentage of those surface Ni sites that are unsaturated
with coordination and allow the oxidative-addition to take place.
With substitution of the eq 11a, eq 28a becomes
Pb
B
Pb-C
B
(
C - C
) (27b)
]
Ni0
OHP
where kNi ) RkeKn
.
Pb
Pb-C
2+
For CB eCB , as aforementioned, no Pb ions enter the
OHP of the desired plating surface under this condition.
Equation 27b is thus shortened as
P0
R ) k n exp[k (Φ - Φ )/kT]
(28b)
P
P
IHP
G
0
With further including eq 16b, the eq 28b can be expressed as
0
Ni
0
f
0
f
0
f
R ) k E exp(16E - 5.1 14.8 - E ) (27c)
Ni
x
x
P0
IHP
Pb
B
Pb-C
B
R ) k n exp[-k 4πpa(C - C
)/kT] (28c)
P
P
G
0
Ni
The term R is the nickel deposition rate without interference
Pb
2
+
of Pb stabilizer. This concept will be elaborated in section 4.
The electron flow rate within the Stern layer is mainly affected
by both the Fermi level of the Ni-P deposition layer and the
concentration of nickel ion at the OHP. Equations 27b,c offer
an interpretation for the catalytic deactivation effect of the Pb
ion. If we take the ratio RNi/RNi
0
P
0
IHP
R ) k n
(28d)
P
0
2+
Here the term R is the phosphorus deposition rate in the
P
2
+
0
absence of Pb at the OHP of the desired plating surface.
Equation 28c shows that the phosphorus deposition rate is to
decrease with an increase in the concentration of lead ion.
RNi
0
Ef
â
kT
4πL 2m
x
0
f
0
f
)
exp(
(E - E ) exp
( U - E -
f
)
(
x
0
0
h
R
x
Ef
4. Experimental Results and Discussion
Ni
4πk Pa
G
Pb
Pb-C
4.1. Critical Stabilizer Concentration. In an EN plating
U - E ) exp -
(C - C
) (27d)
x
0
f
)
(
B
B
)
system, there is usually a critical Pb(Ac)2 concentration (
kT
Pb-C
B
C
), below which the deposition rate and the composition
-
1
where â/kT ) 16 eV , U0 ) 14.8 eV, [4πLx(2m)]/h ) 5.1
of Ni-P film on the desired plating surface are not affected.
-
0.5
eV
.
2+
Pb ions can only diffuse to the OHP of Ni colloidal particles
The equation can be approximated as
and accept electrons from the Ni particles because they possess
much more reactive surface than the plating surface. For a given
RNi
0
Ef
â
kT
4πk Pa
G
2+
plating-bath, decreasing of Pb concentration depends on two
0
f
Pb
≈
exp(
(E - E ) exp -
(C -
f
)
(
B
0
variables: (1) the plating loading (PL), which is defined as a
ratio of the plating surface area to the volume of plating solution,
and (2) the plating time. Figure 7 shows a negligible effect of
kT
R
x
Ef
Ni
Pb-C
C
) (27e)
B
)
2+
Pb on both Ni plating rate and phosphorus content of the
0
f
Pb
Pb-C
deposit on the plating surface (the brass substrate with PL )
Combining it with eq 16d, i.e., Ef ) E + 4πPa(C - C
one obtains
),
B
B
Pb
B
2
1
.67 dm /L). Hence the concentration points C tested are
considered below the critical level. In this respect, the basic
Pb-C
relationship is that CB
increases with increasing PL because
RNi
0
Ef
4πPa
kT
Pb
B
Pb-C
Ni
≈
exp
(â - k )(C - C
)
(27f)
the Ni colloids concentration C
(stated by eq 13a) and a higher level of Pb concentration is
will rise with increasing PL
G
B
)
OHP
0
(
R
x
Ef
2+
Ni

Pb2 Stabilizer in Electroless Nickel Plating System
+
J. Phys. Chem. B, Vol. 108, No. 30, 2004 10927
2
Figure 7. Effects of Pb(Ac) concentration (below the critical
concentration) on (a) the Ni plating rate and (b) the phosphorus content.
hence requested to prevent fast reproduction of Ni colloidal
particles. In other words, for a given EN bath, the plating will
cease shortly if the desired plating surface area is substantially
smaller than the designed size.
To elaborate the Pb2 concentration effect on the composition
of the plating surface, XPS characterization was employed to
examine the Ni-P films developed on the Al-coated silicon
+
-
2
2
wafer. In this experiment, the PL value of 1.25 × 10 dm
-1
L
and 20 min of plating time were employed. The samples
were thoroughly washed. The phosphorus content on the
examined surface underwent a dramatic change in the concen-
Pb
tration range of CB from 10 to 15 ppm. The P2p peaks of
0
elemental P at 129-130 eV appear on the plated surface only
Pb
when CB is below 10 ppm (Figure 8a). Correspondingly, Pb
Pb
species is found to emerge on the XPS spectrum when CB is
greater than 10 ppm (Figure 8b). It may note hereby that the
Pb-C
Pb
critical value CB
differs from the CB at which Pb could be
Figure 8. XPS of the three elements in the deposition films (on Al/Si
observed by XPS. The critical value must be far below the
concentration that gives rise to XPS Pb peaks. The appearance
of Pb(II) species on the XPS spectrum is due to oxidation of
surface lead atoms since the samples were not stored in inert
atmosphere after purification.
substrate) prepared by using different Pb(Ac)
2
concentrations.
Pb
Pb-C
large [CB - CB ]value can be caused by two ways: (1) for
2+
a given PL but using a higher concentration of Pb or (2) for
a given concentration of Pb but reducing PL dramatically.
2
+
Pb
On the other hand, with using CB ) 15 ppm, the two Ni2p
4.2. Dependence of Deposition Rates RNi and RP on the
0
Pb
B
peaks at 852 and 869 eV representing Ni species disappeared
Stabilizer Concentration C . The reliance of the phosphorus
from its XPS spectrum (Figure 8c) despite the fact that an initial
deposition rate on the Pb(Ac)2 concentration has been investi-
gated by using the brass substrate (PL ) 1.67 dm /L, Figure
-
2
-1
2
plating rate of about 12 mg cm
h
(or equivalent to11 mA/
2
cm ) was still obtained. Instead, lead species was identified on
the same surface (Figure 8a). This phenomenon shows the Pb-
induced deactivation process, which is virtually self-promoted.
9), on which two concentration ranges symbolized by the
different rates can be identified. The P deposition rate slips very
slightly in the low concentration range (0∼10 ppm) but
perceptibly in the higher concentration range. In the low
stabilizer concentration range, both the nickel deposition rate (
Pb
Pb-C
It means that in the case of a larger [CB - CB ]value the
electrochemical displacement reaction (eq 14b) will gradually
overtake the deposition of Ni and consume the surface Ni atoms
and eventually form a Pb deposition layer as long as the different
0
Ni
-2 -1
2
R ) 12.23 mg cm
h
or equivalent to 11.22 mA/cm ) and
0
-2
-1
phosphorus deposition rate (R ) 1.24 mg cm
equivalent to 0.478 mA/cm ) are nearly constant (Figure 7).
h
or
P
Pb
Pb-C
2
in concentration [CB - CB ]exists. As aforementioned, a

10928 J. Phys. Chem. B, Vol. 108, No. 30, 2004
Yin et al.
0
f
Figure 10. The relationship between 4πpa and E .
2
Figure 9. Influences of the Pb(Ac) concentration on the deposition
rate of (a) phosphorus and (b) of nickel on brass substrate.
Combing eq 28c with eq 28d, the dependence of phosphorus
deposition rate on Pb2+ concentration can be expressed as
Figure 11. Change of the total plating rate (R) with the lead ion
concentration (C
S
)
4
πk pa
0
P
G
Pb
B
Pb-C
R ) R exp -
(C - C
)
(29a)
P
[
B
]
kT
Since the difference between U0 and Ef is much larger than the
0
f
difference between Ef and E , the term exp[-5.1x(14.8 - Ef)]
0
f
can be approximated with exp[-5.1x(14.8 - E )]. Substitut-
ing eq 16d into eq 27e, the nickel deposition rate can be written
as
0
Ni
R
0
f
Pb
B
Pb-C
R )
E + 4πpa(C - C
) exp 16 × 4πpa -
Ni
x
B
[
(
0
Ef
x
4
πk pa
Figure 12. Change of phosphorus content (P%) of the Ni-P films on
the lead ion concentration (C ).
G
Pb
Pb-C
B
(
C - C
) (29b)
S
)
B
]
kT
substituting the values of [(4πkGpa)/(kT)] and C PB b-C into eq
9b and fitting it with experimental data of nickel deposition
In Eqs 29a and 29b, there are four physical terms whose values
need to be determined
2
0
f
rate, the values of 4πpa and E were determined (Figure 9b).
Fixing the value of E and fitting the model with experimental
0
f
4
πk pa
G
0
f
Pb-C
B
,
4πpa, E , and C
data, Figure 10 shows the relationship of the term 4πpa with
kT
0
E . It is obvious that under a small energy level (less than 0.5
f
eV) the initial Fermi energy value affects the simulation value
Fitting these two theoretical models with the experimental data
was employed to figure out the above parameters. A Z value is
thus defined, as eq 30a, through minimizing the discrepancy
4
πpa significantly. In contrast, if the initial Fermi energy level
larger than 1 eV, the value of 4πpa is nearly a constant (i.e.,
exp
exp
0.0009 eV/ppm). Using the above simulation values, k can be
G
between the rates from experiments defined as RNi and RP
worked out to have a value near 2.4. That is, kG > â, which
supports the estimation obtained using eq 27f.
and from the above two equations. The Z value is minimized
by using the Nelder-Mead method,4
4-45
and the minimization
It is not an easy task to obtain the true initial Fermi energy
level due to several reasons: namely, (1) the compositional
nonuniformity of the deposited Ni-P film, (2) the effect of co-
deposited phosphorus, and (3) the aqueous solution instead of
vacuum as the reaction medium. Inspite of this, the initial Fermi
energy value is not absolutely necessary in the simulation as
long as the modeling value worked out is not very small. In
vacuo, the Fermi energy level of pure nickel is over 10 eV.46
Therefore, we let the value of 4πpa be 0.0009 eV/ppm (Figure
9b).
was conducted by using MATLAB 5.3 with a tolerance value
-
4
of 1 × 10
N
exp 2
Z ) (R - R
)
(30a)
∑
i)1
Fitting eq 29a with experimental data of phosphorus deposition
-
1
rate at T ) 363 K, the values of [(4πkGpa)/(kT)] (0.07 ppm )
Pb-C
and CB
(12.73 ppm) were obtained (Figure 9a). Further

Pb2 Stabilizer in Electroless Nickel Plating System
+
J. Phys. Chem. B, Vol. 108, No. 30, 2004 10929
References and Notes
It is also worth mentioning that both the phosphorus and
Pb
nickel deposition could still occur until CB ) 30∼35 ppm
(1) Brenner, A.; Riddell, G. J. Res. Natl. Bur. Stand. 1946, 37, 31.
(2) Ting, C. H.; Paunovic, M.; Pai, P. L.; Chin, G. J. Electrochem.
Soc. 1989, 136, 462.
2
-1
when the brass substrate was plated (PL ) 1.67 dm L , Figure
1
1). On the contrary, the phosphorus and nickel deposition cease
(3) Dubin, V. M. J. Electrochem. Soc. 1992, 139, 633.
Pb
at CB ) 10-15 ppm when Al/Si substrate was plated (PL )
(4) Lee, C. Y.; Lin, K. L. Thin Solid Films 1994, 249, 201.
(5) Nicewarner, E. Microelectron. Reliab. 1999, 39, 113.
(6) Abrantes, L. M.; Correia, J. P. J. Electrochem. Soc. 1994, 141,
-
2
2
-1
1
.25 × 10 dm L , Figure 8). This difference is consistent
Pb-C
with the previous conclusion that CB
varies with PL levels.
2
3
356.
7) Van den Meerakker, J. E. A. M. J. Appl. Electrochem. 1981, 11,
(
95.
Substituting the simulation parameters into eqs 29a and 29b,
the total plating rate, R, and the phosphorus content of the
deposited films, P%, can be expressed as follows:
(8) Mallory, G. O., Hajdu, J. B., Eds.; Electroless Plating: Funda-
mentals And Applications; American Electroplaters and Surface Finishers
Society: Orlando, FL, 1990.
(
9) Han, K. P.; Fang, J. L. J. Appl. Electrochem. 1996, 26, 1273.
(10) Kim, D. H.; Aoki, K.; Takano, O. J. Electrochem. Soc. 1995, 142,
3763.
(11) Yin, X.; Hong, L.; Chen, B.-H.; Ko, T.-M. J. Colloid Interface
Sci. 2003, 262, 89.
Pb
Pb
B
R ) 14.33 3 + 0.0009CB exp(-0.0556C ) +
x
Pb
B
3
.02 exp(-0.07C ) (30b)
(
12) Smith, S. F. Metal Finishing 1979, 77, 60.
(13) Sadakow, G. A.; Gorbunowa, K. M. Electrochimica 1980, 16, 230.
14) Bockris, J. O. M., Khan, S. U. M., Eds.; Quantum Electrochemistry;
Plenum Press: New York, 1979.
15) van der Putten, A. M. T.; de Bakker, J. W. G. J. Electrochem. Soc.
993, 140, 2229.
16) Zhang, S.; De Baets, J.; Vereeken, M.; Veraet, A.; Van Calster, A.
100%
P% )
(30c)
(
Pb
B
Pb
1
+ 4.75 3 + 0.0009C exp(0.0144C )
x
B
(
1
(
Figures 11 and 12 show both the experimental data and
simulation results. From the above theoretical model and
corresponding simulation, the reason for how the lead ions can
decrease both the plating rate of Ni and the phosphorus content
is now better understood. In comparison with the decrease in
phosphorus deposition rate, the deposition rate of nickel is less
affected by the presence of lead in the IHP. This is because a
relatively high Fermi level will promote the electron tunneling
probability W(Ef) and will be, therefore, facilitating reduction
2
+
of Ni ions at the OHP.
(
(
24) Taube, H.; Myers, H. J. Am. Chem. Soc. 1954, 76, 2103.
25) Richardson, D. E.; Taube, H. Coord. Chem. ReV. 1984, 60, 107.
Conclusions
(26) Lukehart, C. M.; Milne, S. B.; Stock, S. R.; Wittig, J. E. Trends
Inorg. Chem. 1996, 4, 9.
(
27) Schenzel, H. G.; Kreye, H. Plating Surf. Finishing 1990, 77 (10),
In this paper, the structure of the Stern-Grahame electrical
double layer (EDL) and the electronic tunneling theory of the
quantum mechanics were applied for explaining the electroless
nickel (EN) plating mechanism. The EDL of the substrate
consists of the inner Helmholtz plane (IHP) and the outer
5
0.
(
28) Zhang, Y. Z.; Sun, K.; Wu, Y. Y.; Zhang, J. W.; Yao, M. J. Mater.
Sci. Technol. 1996, 12, 342.
29) Hunter, R. J. Foundations of Colloid Science; Oxford University
Press: New York, 1987; Vol. 1, Chapter 6.
30) Behrens, S. H.; Borkovec, M. J. Phys. Chem. B. 1999, 103, 2918.
(
(
-
Helmholtz (OHP). On the IHP, the H2PO2 anions adsorb onto
(31) Masel, R. I. Principles of Adsorption and Reaction on Solid
Surfaces; Wiley: New York, 1996.
the substrate surface and donate electrons to the substrate
(32) Kiejna, A., Wojciechowski, K. F., Eds.; Metal Surface Electron
-
(
(
oxidation of H2PO2 ) or accept electrons from the substrate
Physics; Elsevier Science: New York, 1996.
(33) H o¨ lzl, J.; Schulte, F. K.; Wagner, H. Solid Surface Physics. In
Springer Tracts in Modern Physics; Springer-Verlag: New York, 1979; p
-
reduction of H2PO2 ) to form deposited elemental phosphorus.
Electrons tunneled from the plating frontier to the OHP and
combined with nickel ions to form nickel atoms. A handful of
Ni atoms produced at the OHP may diffuse into the bulk solution
in the form of colloidal particles, which is the source of
instability of the EN bath. To inhibit the propagation of Ni
particles that undertakes through the same mechanism, a critical
2
9.
(
34) Lange’s Handbook of Chemistry; McGraw-Hill: New York, 1992.
(35) Eisberg, R.; Resnick, R. Quantum Physics of Atoms, Molecules,
Solids, Nuclei, and Particles; John Wiley & Sons: New York, 1985.
(
(
36) Gasiorowicz, S. Quantum Physics; Wiley: New York, 1974.
37) Herbert, K. Quantum Mechanics for Engineering, Materials Science,
and Applied Physics; Prentice-Hall: Englewood Cliffs, NJ, 1994.
(38) Anton, Z. C. NonrelatiVistic Quantum Mechanics; The Benjamin/
Cummings: Menlo Park, CA, 1985.
concentration of Pb2 must be maintained in the solution. The
+
2
+
plating rate will be sacrificed should the concentration of Pb
(
39) Sakurai, J. J.; San, F. T. Modern Quantum Mechanics; Addison-
be higher than this level. Lead ion plays its role through
displacement reaction with Ni atoms. Two mathematical models
have been developed to explain the dependence of Ni plating
rate and phosphorus content of a Ni-P deposit layer on the
Pb concentration. According to the models, lead atoms
embedded in the Ni-P lattice can reduce work function of the
plating frontier, thus clogging up the oxidation of hypophosphite.
Consequently, both Ni plating rate and phosphorus content of
the deposited film are reduced. With fitting the mathematic
models with experimental data, the numerical values obtained
could also arrive at the same conclusion.
Wesley Pub. Co.: Reading, MA, 1994.
(40) Gerald, B. Solid State Physics; Academic Press: Orlando, FL, 1985.
(
41) Appleby, A. J. In ComprehensiVe Treatise of Electrochemistry
Kinetics and Mechanisms of Electrode Processes; Conway, B. E., Bockris,
J. O’ M., Yeager, E., Khan, S. U. M., White, R. E., Eds.; Plenum Press:
New York, 1983; Vol. 7, p 173.
2+
(
42) Blakemore, J. S. Solid State Physics; Saunders: Philadelphia, PA,
974.
43) Forster, R. J.; Loughman, P.; Keyes, T. E. J. Am. Chem. Soc. 2000,
122, 11948.
1
(
(
(
(
44) Mazur, U.; Hipps, K. W.; J. Phys. Chem. B 1999, 103, 9721.
45) Nelder, J. A.; Mead, R. Computer J. 1964, 7, 308.
46) Kittel, C. Introduction to Solid State Physics; Wiley: New York,
1996.