Nano-porous or nano-wire Si by electroless Ag nanoparticle deposition and metal-assisted etching Yang He (10400425) MT602 advisor: Prof. Woo Lee

AbstractThis 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 electrostatic field 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 necessary in the PV industry. In fact the metallurgical grade silicon is 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 idea to modify the conventional metallurgical grade 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 single product can be considerably fall due to neglecting the time-consuming purification process. After that academic proposition, several groups 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 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 a basic chemical lab with a normal hood. Metal-assisted etching also shows 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 assisted etch can be a promising 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]

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 plan2.1 Experiment designThere 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-42. 0.15 5e-43. 0.25 5e-44. 0.35 5e-45. 0.15 1e-36. 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:

Number Time (min) Temperature (K)1. 0.1 3432. 0.5 3433. 1.0 3434. 2.0 3435. 0.5 2986. 0.5 3187. 0.5 363

Table 2.

Cu thin film deposition: All of samples are dried and put into the vacuum chamber to have the Cu sputtering using Argon plasma. A very thin film of Cu will 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 a static temperature 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 nucleationThe 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+4 H F2−¿→SiF6

2−¿+2 HF+H 2+2e−¿¿¿¿

Si+2H 2O→SiO2+4 H+¿+4e−¿ ¿¿

SiO2+2H F2−¿+2HF→Si F 6

2−¿+2 H 2O ¿¿

The possible cathodic reaction is:

Ag+¿+e−¿→Ag¿¿

2 H+¿+2e−¿ →H 2¿ ¿

Figure 5. Schematic of Ag heterogeneous nucleationThe 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:

∆G=4 π r2 γ+ 43π r3∆Gv (1)

is the surface tension, Gv can be expressed as:

∆G v=−kBTIn(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 can be find. If the radius of Ag cluster is bigger than 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=−2 γ∆Gv

= 2 γvk BTInS

(3)

∆Gcrit=∆Gcrithomo=4

3πγ ccrit

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:

dNdt

=Aexp(−∆Gcrit

kBT )=Aexp( 16π γ 3V 2

3kB3 T 3 (¿ (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+cosθ)(1−cosθ)2

4 (6)

ϕ ΔGcrithomo=ΔG crit

hetero (7)

Put equ(6) and equ (7) into equ(5):

dNdt

=Aexp( 4 π γ 3 v2(2+cosθ)(1−cosθ)2

3k B3 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. 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 on Figure 9. a-c. Then I use an ab initio method, i.e. density function theory (DFT), to optimize the geometry and calculate the binding energy and electrostatic field. All model’s K mesh is 3*3*1.

a b cFigure 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.

2.2.3 Ag nano-particle growth

The growth of Ag nano-particle is based on two factor: the redox reaction on surface and 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:

drdt=rk (Cb−C i ) (9)

In the same way, if the diffusion of Ag to the surface, the growth rate can be expressed as:

drdt

=DB

Cb−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):

drdt

=DBk (Cb−C i )rrk (D−r )+DB

(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 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 sufficient as 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.

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.

2.2.4 Metal assisted etching, electronic and 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 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 will be 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.

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]

c.

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. Si diffusion is an essential problem 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) Si 4+

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 Si 4+

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

C s−C0

r (12)

J2=D b

C s−C0

r+d (13)

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 Db(C s−C0)Db r+D s(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 Db(C s−C0)Db r+Ds(r+d )

tA=

D sDb(C s−C0) t2 π d2(D¿¿br+Ds(r+d))¿

(15)

Thus the depth of the nano-pores or the length of the nano-wires can be controlled.

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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