This document discusses a new method for synthesizing nano-porous or nano-wire silicon using silver electroless deposition and metal-assisted etching. It establishes models to explain the heterogeneous nucleation of silver nanoparticles, their growth, and diffusion of silicon ions. An experiment is designed where silver nanoparticles are deposited on silicon wafers through controlled variations of factors like HF and AgNO3 concentrations and deposition time. After coating with a thin copper film, metal-assisted etching is used to create the nanostructures, with etching time as a variable. The document analyzes the nucleation process and establishes equations to model the influence of temperature, supersaturation, surface energy, and contact angle on the heterogeneous nucleation rate of silver nanoparticles.

1. Nano-porous or nano-wire Si by electroless Ag
nanoparticle deposition and metal-assisted etching
Yang He (10400425) MT602 advisor: Prof. Woo Lee
Abstract
This article presents a new Ag electroless deposition method to synthesize the nano-porous or
nano-wire Si by metal assistant etching. Ag heterogeneous nucleation model, Ag nuclei growth
model and Si4+ ions diffusion model were established to discuss the size control of the nano-
structure. In addition, the binding energy and electrostaticfield of (100) (110) and (111) Si surface
layer attached by Ag atoms was calculated via first principle density functional theory (DFT)
method. After classified discussion and solving the ordinary differential equations deriving from
the mathematical models, an experiment was designed to obtain the nano-pores or nano-wires
silicon material.
1. Introduction
As the continuing depletion of fossil fuel, a state-of-art technology is desperately needed to
facilitate the development of modern economy. Hence the environment-friendly and practical
solar energy draws a tremendous attention [1]. The most significant material as promising
building blocks is silicon wafer. Nonetheless, the cost of solar grade silicon is roughly $25~40/kg
making the whole photovoltaic (PV) device enormously costly [2]. The efficiency of the
photovoltaic cell is inverse proportion to its impurity level. So the purification process of the
Silicon ingredient is necessaryin the PV industry. In fact the metallurgicalgrade siliconis as cheap
as approximately 3 dollars. But the conversion of metallurgical grade into solar grade enlarge the
expenditure about three times. Currently, nano-technique makes an immense difference in
nearly every field of the world, such as opto-electronics, integrated-electronics and energy
storage etc. Nano-structure materials also can be feasible means to solve the chief barrier to
wide-range PV application.[3-5] The principle ideato modify the conventional metallurgicalgrade
silicon is that size-effect of the nano-material can keenly affect the physical properties. In this
case, the solar cell produced from nano-structured silicon wafer can be less sensitive to the
quantity of impurity. In Sivakov, V et al.’s theoretical research [5], the electrical performance of
SC and Si based solar cells with perpendicular nano-wires array are invulnerable to the
purification of Si wafer. If the Silicon nano-pores and nano-wires materials can be successfully
synthesized, the cost of solar cell can be highly reduced. Additionally, the manufacture period of
singleproduct can be considerably falldue to neglecting the time-consuming purification process.
After that academicproposition, severalgroups experimentally tested the verification of this idea
[6-9].
Controllable nano-structure of Si, such as nano-pores and naon-wires turn into a required
technique to accomplish the application of metallurgical grade silicon. There are many well-
documented approaches to make produce Si nano-structures, for instance reactive ion etching
(RIE), vapor-liquid-solid (VLS) growth, electrochemical etching etc. Although all of them provide
a practical way to control the size and morphology of the Si wafer, the availability of these

2. methods do not guarantee an industry scale manufacture. Recently, metal-assisted chemical
etching draw an incremental attention. The reason why metal-assisted etching becomes a hot
research area is apparently recognized from various report [6-9,10-21]. Metal-assisted etching
does not have any ‘device threshold’ to overcome. It is cheap and easy and the productivity of
large scale synthesis is substantial. The main procedures of the synthesis can be implemented
on abasicchemicallab with a normal hood. Metal-assistedetching alsoshows its ability to govern
the configuration of the surface of Si wafer. For example, cross section shape[10-12] (Figure 1),
radius of wires or pores [12], the distribution and surface density of nano-wires or pores [12][13
(Figure 2), length [11,12,14,15] (Figure 4) and orientation[16] (Figure 3), the surface to volume
ratio[14,15]. The area of etching is not limited to a device-defined region as long as the dish is
sufficient big to contain the Si wafer and etchant. Moreover, the crystallinity of the nano-
structure Si is high [14,17]. That means Si’s the former property as a semiconductor can be
maintained after etching. Therefore, the metal assistedetchcan be apromising means to provide
the cheap but reliable metallurgical grade silicon in PV industry.
Figure 1. a. Ag particle, b. Au particle, c. Pt
particle. [10]
Figure 2. Si nano-structure etched by different
thickness of Ag film (5nm, 10nm and 20nm).
[13]
Figure 3. a. Ag particles with large separate
distance, b. Ag particles change the deriction
during etching. [16]
Figure 4. Nano-arrays using nanosphere
lithograpy method. [15]

3. It is obvious that the deposition of the noble metal is incredibly important to control the metal-
assisted etch method. As for the metal type, Pd, Pt, Ag and Au are the most common used noble
metals. The methods to deposit the metal is vary, such as focused ion beam deposition, electrode
deposition, electroless deposition, thermal evaporation, sputtering, electron beam evaporation,
and spin-coating of particles etc. In fact, since the position of deposited noble nano-particles is
extremely essential to define the Si’s sub-structure, the methods to ‘put’ metal particles to the
‘right’ place become a vital part of the deposition. There are three common used ways to control
the arrangement of noble metal particles: 1. Nanosphere lithography method (Figure 4) [15], 2.
AAO mask method [18], 3. Interference lithography method [13,14,19]. But these methods have
complicated requisites. For example, the recipe of photoresist, the laser interference facility and
the time control of bake time are inevitably thought over in an interference lithography method.
Thus a convenient method is valuable to substitute those involved methods. In this paper, a
simple electroless deposition method is elucidated and the research about it is proposed. The
mechanism of this method is fully illustrated to interpret the setting of experimental parameters.
2. Research plan
2.1 Experiment design
There are five procedures in my designed experiment:
 Preparation of silicon wafer: I choose the single crystalline P-type Si wafer, for example
boron-doped Si as the substrate. The surface Miler Index of wafer is (110). After careful
surface polishing, wafers are cut into roughly 1.5*1.5 cm2 square pieces. Each small samples
are washed with water and acetone. All of them are stored in ultra-clean condition to avoid
the surface contamination of dust in atmosphere.
 Ag nano-particle deposition: Six different molarity ratios of HF and AgNO3 aqueous mixtures
are prepared, i.e.
Number HF (M) AgNO3 (M)
1. 0.05 5e-4
2. 0.15 5e-4
3. 0.25 5e-4
4. 0.35 5e-4
5. 0.15 1e-3
6. 0.15 1e-4
Table 1.
Samples are pre-cleaned in 1 wt% HF to remove the surface native oxides. Then they are
immersed into the metallization solution mixtures for a series of delicately designed time. The
time control and the bath temperature are carried out to find out the optimal Ag nano-particle
deposition. The control group of immersion time and bath temperature is:

4. Number Time (min) Temperature (K)
1. 0.1 343
2. 0.5 343
3. 1.0 343
4. 2.0 343
5. 0.5 298
6. 0.5 318
7. 0.5 363
Table 2.
 Cu thin film deposition: All of samples are dried and put into the vacuum chamber to have
the Cusputtering using Argon plasma.A very thin filmof Cuwill be deposited above the whole
surface of the wafer.
 Metal-assisted etching: The aqueous mixture comprising of HF solution (40%), H2O2(35%),
and ultra-clean water is prepared. Then the mixture is poured onto an open Teflon
crystallizing dish.Samples are put in the dish and etched in the mixture in astatictemperature
oven (323K) for different time (0.5 hour, 1 hour and 2 hours).
 Wash: After etching, samples are cleaned with de-ionized water and the Ag and Cu particles
are washed away by concentrated nitric acid. Then the Si oxide is removed using a buffered
HF solution.
Note that the most important procedures above are 1. Ag nano-particle deposition, 2. Cu thin
film deposition and 3. Metal-assisted etching. The mechanism of nucleation, growth and
diffusion will be discussed in detail. All the experimental parameters are elaborately set
according to the analysis.
2.2 Discuses of experimental procedures
2.2.1 Ag nano-particle electroless heterogeneous nucleation
The mechanism of Cu electroless deposition on Si wafer was depicted by Morigana et al [20].
Peng et al. also explained how the pits are produced through the deposition[21]. But only a
summarization of the interpretation of the phenomena is offered by the previous study. The
nucleation process in this experiment is demonstrated as follow.
The surface area of Silicon wafer has the galvanic displacement reaction. The cathode and
anode are shown on Figure 5.
The possible anodic reaction is:
𝑆𝑖 + 4𝐻𝐹2
−
→ 𝑆𝑖𝐹6
2−
+ 2𝐻𝐹 + 𝐻2 + 2𝑒−
𝑆𝑖 + 2𝐻2 𝑂 → 𝑆𝑖𝑂2 + 4𝐻+
+ 4𝑒−
𝑆𝑖𝑂2 + 2𝐻𝐹2
−
+ 2𝐻𝐹 → 𝑆𝑖𝐹6
2−
+ 2𝐻2 𝑂
The possible cathodic reaction is:

5. 𝐴𝑔+
+ 𝑒−
→ 𝐴𝑔
2𝐻+
+ 2𝑒−
→ 𝐻2
Figure 5. Schematic of Ag heterogeneous nucleation
The Ag+ ions in solution will absorb electrons from Silicon due to the electronegativity difference.
So there are a number of free cluster of Ag atoms at the surface of Si. LaMer mechanism can be
used to describe this nucleation process of three steps[22]. As shown on Figure 6, (I) a rapid
increase of Ag cluster at the surface of Si wafer, (II) when the concentration approach the critical
concentration, the rate of nucleation will have a nearly ‘infinite’ grow, which turns to reduce the
concentration of free Ag cluster, (III) the concentration of Ag cluster will tend be steady, if we
need to create new nuclei, there must be another source to supply extra Ag cluster, like
increasing the concentration of AgNO3 solution and improving the reaction rate simultaneously.
Figure 6. three steps of LaMer nucleation process. [22] Figure 7. Free energy diagram [23]
The mathematical model can be used to discuss the heterogeneous nucleation of Ag nano-
particles. First we treat the Ag particle is spherical and has homogeneous nucleation, then the
modification can be added to the model to make it in heterogeneous case[23]. The Free energy
of an Ag cluster G have two component: the bulk crystal energy Gv and the surface energy
Gs, and is defined by:

6. ∆𝐺 = 4𝜋𝑟2
𝛾 +
4
3
𝜋𝑟3
∆𝐺𝑣 (1)
 is the surface tension, Gv can be expressed as:
∆𝐺𝑣 =
−𝑘 𝐵 𝑇𝐼𝑛(𝑆)
𝑉
(2)
Where kB is the Boltzmann’s constant, S is the supersaturation of the solution, T is temperature
and V is the molar volume.
From Figure 7, the surface energy is always positive and the bulk energy is always negative, so a
peak of total free energy canbe find. If the radius of Ag cluster is biggerthan a certain value given
by equ (3) (critical radius) related that free energy peak given by equ (4) (critical Gibbs energy),
the Ag cluster can grow spontaneously, and it is called ‘nuclei’.
𝑟𝑐𝑟𝑖𝑡 =
−2𝛾
∆𝐺𝑣
=
2𝛾𝑣
𝑘 𝐵 𝑇𝐼𝑛𝑆
(3)
∆𝐺 𝑐𝑟𝑖𝑡 = ∆𝐺 𝑐𝑟𝑖𝑡
ℎ𝑜𝑚𝑜
=
4
3
𝜋𝛾 𝑐 𝑐𝑟𝑖𝑡
2
(4)
In this research, a uniform distribution of nano-pores or naon-wires are wanted. Thus the
nucleation of Ag particle is very vital to control the nano-structure. So the rate of nucleation is
required to be controlled. Here a rate of homogeneous nucleation in an Arrhenius form can be
expressed as:
𝑑𝑁
𝑑𝑡
= 𝐴𝑒𝑥𝑝(−
∆𝐺𝑐𝑟𝑖𝑡
𝑘 𝐵 𝑇
) = 𝐴𝑒𝑥𝑝(
16𝜋 𝛾3
𝑉2
3𝑘 𝐵
3
𝑇3( 𝐼𝑛( 𝑆))
2) (5)
The Ag particles would adhere to the silicon surface to have the heterogeneous nucleation
forming a cup-shape nuclei with a spherical contact angle  shown on Figure5. A factor 
dependent  can be applied to convert the equ (5) into a rate of heterogeneous nucleation.
𝜙 =
(2+cos 𝜃)(1−𝑐𝑜𝑠𝜃 )2
4
(6)
ϕΔ𝐺 𝑐𝑟𝑖𝑡
ℎ𝑜𝑚𝑜
= Δ𝐺 𝑐𝑟𝑖𝑡
ℎ𝑒𝑡𝑒𝑟𝑜
(7)
Put equ(6) and equ (7) into equ(5):
𝑑𝑁
𝑑𝑡
= 𝐴𝑒𝑥𝑝(
4𝜋𝛾3
𝑣2
(2+𝑐𝑜𝑠𝜃)(1−𝑐𝑜𝑠𝜃)2
3𝑘 𝑩
3
𝑇3( 𝐼𝑛𝑆)2 ) (8)
It is clear that the rate of heterogeneous nucleation is governed by supersaturation S, surface
free energy , temperature T and contact angle . In order to find out the influence of these
factors, I calculate the rate with treating one parameter as variable and others are constant.

7. Initially, I set 𝛾=0.1 J/m2, V=1.0283e-5, =pi/6, T=298 K and S=2. Then those parameters are
varying in a proper range to provide the plots (Figure 8.a-d).
Figure 8. Plot of heterogeneous nucleation with different parameters as variables: a.Temperature,b.
Supersatrutation, c. contact angle and d. surface energy.
Figure 8 illustrate that, the variation of temperature of supersatruration does not have an
influence on the rate of nucleation when temperature approaching 280K and supersatruration
approaching 1. In contrast, surface energy of Ag cluster and contact angle has an obvious impact
of that rate. However, only an increase of several ten times can significantly contribute to the
enhancement of nucleation rate. The increase of surface energy at that level is unpractical. As
for contact angle, the diverse orientations of the Si wafer can lead to different distortion of
interfacial area, thus, offering a different contact angle. From Figure 8.c we can know that, a
smaller contact angle can give a higher nucleation rate. That means if the Si wafer can ‘wet’ Ag
clusters, Ag atoms can be easily absorbed and form nuclei.
2.2.2 Si surface orientation and the binding energy
Here I establish three models of Si wafer’s common crystal plane: (100), (110) and (111) using
Materials Studio. Single layer of Ag atoms are attached on the top layer of Si wafer demonstrated

8. on Figure 9. a-c. Then I use an ab initio method, i.e. density function theory (DFT), to optimize
the geometry and calculatethe binding energy and electrostatic field.All model’s K mesh is 3*3*1.
a b c
Figure 9 Si surface with miller plane a.(100), b.(110), c.(111). The yellow atom is silicon and the blue
one is attached Ag atom.
a b c
Figure 10 Electrostatic field contour of a. (100), b.(110), c.(111) plane.
Surface Binding energy (eV) (kcal/mol)
(100) -14.57742 -335.247
(110) -20.25122 -467.013
(111) -9.98549 -236.275
Table 3. Binding energy of Si layer and attached Ag atom
The result are listed on table 3 illustrating that the (110) plane has the highest binding energy.
That mean (110) plane can match Ag atoms better than (100) and (111) plane. Due to the low
distortion, the contact angle on this small corresponding to fast heterogeneous nucleation rate.
It also explains why I choose (110) plane wafer to do experiment. In addition, I plot the
electrostatic field contour on Figure 10. It is apparent that (110) plane structure has extensive
electrostatic field. Thus free Ag+ ions in the solution can be captured by coulomb’s force
increasing the redox reaction rate on the silicon surface. Thus step (II) on figure 6 can be
elongated because of the improvement of supply of free Ag cluster.

9. 2.2.3 Ag nano-particle growth
The growth of Ag nano-particle is basedon two factor: the redox reaction on surfaceand the free
Ag clusters’ diffusion [24]. Here I build a mathematic model to discuss the possible situations
about growth. The schematic illustration of diffusion layer structure near the surface of Ag nano-
particles are shown on Figure 11. D is the distance from the Ag particle surface to the bulk
solution whose concentration Cb is stable, Cr is the concentration at the surface of Ag nano-
particle and C0 is the solubility of Ag particles.
Figure 11. Environment near surface of Ag nano-particle.
If surface reaction is the restrict factor, the growth rate can be written as:
𝑑𝑟
𝑑𝑡
= 𝑟𝑘( 𝐶 𝑏 − 𝐶𝑖) (9)
In the same way, if the diffusion of Ag to the surface, the growth rate can be expressed as:
𝑑𝑟
𝑑𝑡
= 𝐷 𝐵
𝐶 𝑏−𝐶𝑖
𝐷−𝑟
(10)
Where k is the reaction rate and DB is the diffusion coefficient.
When the growth is governed by both mechanisms, the increase rate of particle with time can
give equ (11):
𝑑𝑟
𝑑𝑡
=
𝐷 𝐵 𝑘( 𝐶 𝑏−𝐶𝑖) 𝑟
𝑟𝑘( 𝐷−𝑟)+𝐷 𝐵
(11)
Ordinary differential equ (9), equ(10) and equ(11) can be solved in my Simulink model and the
solutions are plot on Figure 12 a-b. Note that assume that the concentration of bulk solution is
steady. The log(r) is linearly with time when the limit factor is reaction rate, while r is gradually

10. steady when growth is restricted by diffusion. Interestingly, the diffusion have a much more
significant influence on the growth rate. The particle can grow to a very large size in a short time
when the diffusion of Ag atoms is sufficientas shown on Figure 12.a. The diffusion is not adequate
in the case of Figure 12.b, the radius of Ag particle will be limited to a relatively small size no
matter how long the particle growth. If the diffusion rate is comparable to the reaction rate given
by Figure 12.c, the growth is governed by the reaction rate during the first period of time, while
the growth is fully limited by the insufficient diffusion later. Those information above is very
valuable in my designed experiment to control the distribution and size of the Ag particle.
2.2.4 Metal assisted etching, electronicand mass transfer
The Ag nano-particles formed on the former procedure can create pits on the place where they
are deposited. A number of reports have discussed the mechanism [10-12, 14-19, 21, 25]. They
think it is because of the strong electronegative activity of Ag nuclei absorbing the electrons from
matrix of the Si wafer. Simultaneously, the anodic reaction cause the etching of Si, therefore, Ag
particles can sink directly into the matrix of Si. That is also the reason why the surface nano-
structure of Si can form. Holes on the Si matrix can be ejected for the oxidation and dissolution
of the surface Si contacted with Ag particles.This scenario occurs because the Si oxidation energy
Figure 12. Radius of Ag nano-particle
during growth. The growth is limited
by a. reaction, b. diffusion and c.
neither reaction nor diffusion.
a. b.
c.

11. level is far below the valence band of Si (Figure 13) [26]. The excessive holes can transport to a
lower hole area [25, 27] . If the rate of hole consumption is smaller than the rate of hole injection
at the interface area, the sidewalls of the Si substrate may be etched forming a cone shape
structure. So in my experiment, a thin film willbe deposited on the surface of Si wafer. Cu’s Fermi
level is slightly higher than Si’s valence band. Besides that, Cu’s electronegativity is lower than Si.
That means Cu can capture excessive holes on the off-Ag side preventing the etching of the
sidewall.
The whole processes involved in Ag metal assisted chemical etching can be displayed on Figure
15. Nadine Geyer et al. suppose a model to explain the mass transport of Si during metal assisted
etching [28]. However they only describe the possibility of Si diffusion manners without any
mathematical analysis.Sidiffusion is an essentialproblem to control the depth of the nano-pores
or nano-wires. Thus I originate the mathematical model here and give the solution of different
situation. There are two ways of the Si diffusion illustrated on Figure 16: (1) Si4+ dissolves in the
Ag crystal and diffuse through the thickness of Ag nano-particle and (2) Si4+ diffuse along the
interface (d+r) of the Ag particle and Si wafer. Assume that the Si4+ concentration on the bulk
solution is steady and the reaction rate of Si is unvaried. Diffusion of situation (1) and (2) can be
expressed by equ (12) and equ (13) respectively:
𝐽1 = 𝐷 𝑠
𝐶𝑠−𝐶0
𝑟
(12)
𝐽2 = 𝐷 𝑏
𝐶𝑠−𝐶0
𝑟+𝑑
(13)
Figure 13. a. Bands in a Si wafer and standard
potential of metal oxidants; b. Bands in a Si
wafer and standard H2O2/H2O potential. [26]
Figure 14. Diffusion of holes in
the Si substrate. [27]

12. Where Ds and Db are the diffusion coefficient on crystal and in interface respectively. Cs is the
Si4+ concentration of the bulk solution and C0 is the concentration of at the contacted surface.
Note that Ds << Db since the interface can be the high-diffusivity path. However, the length of
two means of diffusion is different. Generally, d >> r. But Section 2.2.1, 2.2.2 and 2.2.3 in this
paper have fully discussed how to control the dimensional parameter r and d. So that gives us an
ability to further control the depth of nano-pores or length of nano-wires. Combining two equs
we can obtain:
𝐽3 =
𝐷𝑠 𝐷 𝑏 (𝐶𝑠−𝐶0)
𝐷 𝑏 𝑟+𝐷𝑠 (𝑟+𝑑)
(14)
I calculate the flux with varying (d/r) ratios shown on Figure 17. When d is relatively small, the
diffusion is governed by method (2) and it also can give a high efficiency of diffusion. In contrast,
the efficacy will gradually decrease with the increase of (d/r) rate and keep stable eventually.
Because the depth can be given by:
𝐿 =
𝐷𝑠 𝐷 𝑏(𝐶𝑠−𝐶0)
𝐷 𝑏 𝑟+𝐷𝑠(𝑟+𝑑)
𝑡
𝐴
=
𝐷𝑠 𝐷 𝑏(𝐶𝑠−𝐶0 )𝑡
2𝜋𝑑2 (𝐷 𝑏 𝑟+𝐷𝑠 (𝑟+𝑑))
(15)
Thus the depth of the nano-pores or the length of the nano-wires can be controlled.
Figure 15. Processes in metal assisted
etching
Figure 16. Diffusion Model of Si metal
assisted etching

13. Figure 17. Flux percentage VS (d/t) ratio
3. Conclusion and Anticipated impact
The mathematical models of Ag heterogeneous nucleation, Ag nuclei growth, Si surface with
Ag monolayer DFT calculation and the Si4+ mass transport are all developed by myself.
According to the theoretical analysis, I design my experiment. By controlling parameters I
discussed above, the size and configuration of Si nano-pores or nano-wires material can be
theoretically defined. In addition, I introduce the Cu thin film deposition which are expected
to protect the sidewall from etching. As far as I know, this electroless controllable method is
not reported by others. Using this method, Si nano-pores or nano-wires material can cheaply
and easily synthesized.

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