Materials Science s a nd Applications, 2011, 2, 1601-1621
doi:10.4236/msa.2011.211214 Published Online November 2011 (http://www.SciRP.org/journal/msa)
1601
Predictive Modelling of Etching Process of
Machinable Glass Ceramics, Boron Nitride, and
Silicon Carbide
Huey Tze Ting1, Kha led A bou -El- Hos se in 2, Han Bing Chua3
1School of Engineering & Science, Curtin University of Technology, Sarawak, Malaysia; 2School of Engineering, Nelson Mandela
Metropolitan University, Port Elizabeth, South Africa; 3School of Engineering & Science, Curtin University of Technology, Sarawak,
Malaysia.
Received M ay 28 th, 2011 ; revised July 30th, 2011; accept ed October 24th, 2011.
ABSTRACT
The present paper discusses the development of the first and second order model for predicting the chemical etching
variables, namely, etching rate, surface roughness and accuracy of advanced ceramics. The first and second order
etching rate, surface roughness and accuracy equations were developed using the Response Surface Method (RSM).
The etching variables included etching temperature, etching duration, solution and solution concentration. The predic-
tive models’ analyses were supported with the aid of the statistical software package—Design Expert (DE 7). The ef-
fects of the individual etching variables and interaction between these variables were also investigated. The study
showed that predictive models successfully predicted the etching rate, surface roughness and accuracy readings re-
corded experimentally with 95% confident interval. The results obtained from the predictive models were also com-
pared with Multilayer Perceptron Artificial Neural Network (ANN). Chemical Etching variables predictive by ANN
were in good agreement with those with those obtained by RSM. This observation indicated the potential of ANN in
predicting chemical etching variables thus eliminating the need for exhaustive chemical etching in optimization.
Keywords: Chemical Etching, Machinable Glass Ceramic, Boron Nitride, Silicon Carbid e , RSM, ANN
1. Introduction
Advanced ceramic is categorized into oxides, non-oxides
and composite ceramics. It possesses great mechanical
properties, such as the capability to operate under high
temperature, high abrasion resistance, longer service life
and dimensional stability. Their versatility has been de-
monstrated in the development of aerospace and refract-
tory materials, and electrical, thermal, structural and me-
dical application [1].
Among advanced ceramics, machinable glass ceramics
(MGC) is one of the common materials in the industry.
MGC is polycrystalline material, produced with con-
trolled nucleation and crystallization. These materials are
unique because of their ability to be machined to precise
tolerances with a good surface finish. MGC possesses
low thermal conductivity and is highly recommended as
high temperature insulators. It shows excellent properties,
especially in semiconductor and electronics industries.
MGC is white in colour and it can be highly polished
without da maging its prope rties. This makes MGC a use-
ful in the manufacture of medical and optical devices
[2,3]. Silicon Carbide (SiC) is the most attractive mate-
rial in manufacturing devices used in high power and
high temperature applications. This arises from its high
thermal conductivity, high electric field breakdown volt-
age, and wide bandgap. SiC is also known as one of the
hardest materials among advanced ceramics and it is
widely used for tribological applications in extreme con-
ditions because of its unique properties, such as high
hardness, good corrosive resistance, and excellent che-
mical stability [4]. Another MGC material is boron ni-
tride (BN). BN consists of equal numbers of boron and
nitrogen atoms. B is isoelectrionic to similarly structured
carbon lattice and thus exists in various crystalline forms.
Its hardness is inferior only to diamond, but its thermal
and chemical stability is superior. Because of its excel-
lent thermal and chemica l stability, BN i s widely used in
the building o f high-temperature equi pment.

Predictive Modelling of Etching Process of Machinable Glass Ceramics, Boron Nitride, and Silicon Carbide
1602
Chemical etching (CHM) is the oldest non-traditional
machining method of removing selected surface areas by
immersing the work piece material into a chemical re-
agent. The removal process will continuously take place
even though the penetration rate of etching rate may be
very small and over-etching might happen during the
process. CHM was applied in 2500 B.C. to produce jew-
elry out of copper in the citric acid and replaced hand-
tool engraving process [5-7]. The development of CHM
has rapidly progressed after the Second World War when
North American Aviation started running mass produc-
tion using CHM on rocket materials. In the 20th century,
CHM was employed as a key process in the fabrication
of integrated circuits, bioMEMS, and microfluidid de-
vices [8-10]. CHM is well-known for its efficiency in
lightening surface weight, fabrication and the production
of dimensionally precise components [5,11]. In terms of
cost efficiency, CHM is economically acceptable among
other machining operations. With the minimum set up
procedure and equipment, CHM can be carried out easily.
On the other hand, CHM must be conducted in fume
hood or a place that is totally covered due to the usage of
chemical reagents and their hazardous effect towards
human health. The disposal of waste chemical reagents is
another problem encountered if CHM is chosen. How-
ever, CHM requires only a short necessary machining
time, hence resulting in low cost production and causing
no damage on mechanical properties.
Mask patterning is the most common method of fab-
riccation in CHM. Yet, this method is usually accompa-
nied with a few problems such as undercutting, mask
adhesive issues and their unstable resistivity to chemical
reagents. Thus, a new technology that is based on em-
ploying CHM after indentation has been introduced. This
technique has demonstrated its versatility and lower
production cost using basic facilities and manufacture,
simplicity of process with no material selectivity required
[12]. One of the key issues of this technology is its abil-
ity to increase and control the etching rate difference
between indented and non-indented areas. Saito et al
[13,14] were the first to develop this technique and prove
its feasibility for micro-machining and fabrication of
alumina-silicate glass. Nagai et al. [15] and Kang and
Youn [12] who fabricated micro-patterns on advanced
ceramics, found in this technique a substitute for the ap-
plication of masks.
Various studies have been reported on the machining
operations of advanced ceramics [16-24] such as deep
reactive-ion etching [25], powder blasting [26-28], laser
drilling [29-31], and conventional machining [32-34]. In
terms of the etching process, chemical etching is among
the most commonly used method compared to other ad-
vanced machining methods (laser beam machining, elec-
tron discharge machining and etch). Watanabe [35] ob-
tained a linear relationship between etching rate and
temperature while comparing wet etching and mechanic-
cal machining. Willia ms et al. [36] stated that not all ma-
terials were etched in all etchants due to time limitations.
This is probably caused by the limited chemical reaction.
Gaiseanu et al. [37] found that relationship between
etching duration and etching rate was significant in in-
fluencing the HF etching results of boron nitride. Minhao
et al. [38] performed their etching experiments on silicon
at a constant etching period and reported that the etching
rate obtained was surprisingly linear. They concluded
that a mino r cha nge of e tchi ng time had sl ightl y cha nged
the linear shape of etching rate to curvature. Olsen et al.
[39] also indicated that an increased in etching time
would decrease the bond strengths of alumino silicate in
HCl etching.
The present study will provide some important scien-
tific findings on CHM of advanced ceramics with solu-
tion of HCl, HBr and H3PO4. T his paper will also discuss
on various types of DoE and its application, identify ma-
terial machinability and highlight the relationship be-
tween etching rates, surface roughness and dimensional
accuracy, and present the predictive models by RSM and
ANN.
2. Design of Experiment (DoE)
In manufacturing processes, a few practical problems
related to the process parameters that determine the de-
sired product quality, optimization and maximizing of
manufacturing system performance often occur. In order
to attain a high quality process with suitable variables,
different statistical methodologies have been proposed to
simulate the various conditions encountered during ma-
terial processing and establish relationship between pa-
rameters and variables for a better system understanding
and control. By selecting a suitable experimental design
method, it is able to reduce the necessary number of ex-
perimental runs and filter out effects due to statistical
variations. A number of experimental design methods
have been developed for experimental planning and data
acquisition. The Design of Experimental (DoE) is well-
known in data analysis, process optimization and charac-
terization of complicated processes. With a relatively
small number of experimental runs, DoE is able to rea-
sonably establish the relationship between etching pa-
rameters and process performance. Many researchers
have design their experiment through DoE to filter out
the secondary factors.
DoE is combination of mathematical and statistical
techniques used to predict and analyze process behavior
in different conditions with relatively fewer, but essential
number of experiment tests [40]. The technique is cate-

Predictive Modelling of Etching Process of Machinable Glass Ceramics, Boron Nitride, and Silicon Carbide 1603
gorized by the number and level of variables, objective
and characteristics of processing. Basically, there are
similar designs, where the statistical method is applied in
the ana lysis with ANOV A and o ther releva nt infor ma -
tion [40-42]. Table 1 shows the design se lection of DoE.
Response surface objective is used to perform optimiza-
tion of the processes, to troubleshoot problems and to
make processes more robust against external and non-
controllable influences.
Many research studies have shown that DoE approach
was able to eliminate secondary factors by reducing the
effect of the process period [42,43]. Pierlot et al. [44]
indicated the ability of DoE to determine the influences
of process variables on the responses and to estimate the
significance of the regression equation coefficients. They
also indicated the advantage of DoE in increasing the
data accuracy by filtering out the errors from the process.
Subramanian et al. [45] reported that DoE significantly
improved the etching result of niobium cavities by re-
ducing the number of testing and successfully reduced
thee parameter range. Chen et al. [46] applied the DoE
method to optimize etching process in commercial etch-
ers and the optimization result was in good agreement
with the experimental data.
2.1. 2k Factorial Design
The factorial design allows each complete test or rep-
lication of all the possible combinations of the levels of
the factors to be investigated. The 2k factorial design is a
screening method, a linear process and first level model.
By applying this method, each of the results is pre- ex-
amined and the range of the variables is determined. The
specialty of 2k factorial design is that its ANOVA con-
sists of a curvature term, which is used to the nature of
the process. If the curvature term is signifycant, the cor-
responding process will have t o proceed to the ne xt stage
(second order model). In contrast, the corresponding re-
sult will proceed to the first order model analysis. This is
because a significant curvature in ANOVA indicates the
relationship between variables exists and a higher level
of model should be used to study the related process, as
the 2k factorial design only capable of studying linear
process.
As a screening method, graphs produced by 2k facto-
rial design are used to determine the range of variables. If
the line positively increases, it means that the variables’
range might fall at a higher level, and vice versa. The
advantages of this method are that it is able to reduce the
number of experimental runs, the process period and in-
crease the cost effectiveness. Usi ng the 2 k factorial design
of experiment, a mathematical model (first-order) of etch-
ing rate, surface roughness and dimensional accuracy as
a function of etching temperature, etching duration, etch-
ing solution and solution concentration has been devel-
oped with a 95% confidence level. These model equations
have been used to develop contours of each result [47].
2.2. Response Surface Methodology (RSM)
RSM is a statistical tool used to analyse complicated
processes in which h a response of interest is influenced
by several factor [41]. The Central Composite design
(CCD), Box-Behnken design and 33 design are the most
common RSM design methods. Each of these is used in
different circumstances. CCD is mainly used in sequen-
tial experimentation, thus making it flexible for industria l
process development. It is widely used because of its
ability to be partitioned naturally into two subsets: the
first subset is used to estimate linear and two-factor in-
teraction effects; and, second, to estimate the curvature
effects of the process. Compared with other RSM designs,
CCD is more efficie nt and able to pro vide more informa-
tion with minimum number of experimental runs.
As mentioned previously, the range of each parameter
has been reduced through 2k factorial design. The pur-
pose of doing this is to reduce the time taken in deter-
mining the interaction of parameters and their relation-
ship. In this research, the input are etching temperature,
etching solution, etching duration, and etching concen-
tration. Their range is stated in Table 2 and a central
point is added to the process to determine the peak point
for each result. This is the purpose of employing CCD as
the statistical method in studying this pro cess. With three
numeric factors, one categoric factor and five central
points are added to DE7, the CCD is able to randomly
generate 40 experimental runs for the three set of results.
This is to minimize experimental errors ( such as change
of temperature during experiment) and to ensure consis-
tency in the result. Similar to other RSM method, p-value
is the main co nsideration used in selectin g the model and
determining the significant variable.
Table 1. The design selection gui deli ne [40].
Number of factors Comparati v e O bjec tive Screening Objective Response Surface Objective
1 1 factor completely randomized design- -
2 - 4 Randomized block design Full/Fractional factorial Central composite/Box-Behnken
5 or more Randomized block design Fractional factorial/Plackett-BurmanScreen first to reduce number of factors

Predictive Modelling of Etching Process of Machinable Glass Ceramics, Boron Nitride, and Silicon Carbide
1604
Table 2. Parameter of chemical etching.
Variable/Parameter –1 0 +1
Etching temperature, ˚C 30 60 100
Etchi ng dura tion, mins 30 150 240
Sol utio n conce ntr a tion –1 0 +1
Etching solution (categoric variab le) HCl HBr H3PO4
2.3. Artificial Neural Network (ANN)
ANN is an emulation of biological neural system engi-
neering that presents different computational paradigm in
which the solution to a problem is learned from a set of
examples, just like the way human brain works [48].
ANN is an adaptive system, most often applied to non-
linear system that learns to perform a function from the
data. In ANN, the basic unit or building block of the
brain is the neuron [49]. ANN consists of several la yers,
name ly input la yer, hid den la yer and output la yer. T rain-
ing ANN includes supervised learning (self supervised),
unsupervised learning (system must develop its own rep-
resentation of the input stimuli) and reinforcement learn-
ing (system grades the action and adjusts its parameters).
After the training phase, ANN parameters are fixed and
the system is deployed to solve the problem on hand.
In ANN, multilayer perceptron (MLP) is used as su-
per vised ne twor k with b ack-p ro pagati on algo rithm a s the
trainer of the network. Input of this process are etching
temperature, etching duration, etching solution and solu-
tion concentration; and, output consists of etching rate,
surface roughness and etching ratio. During the training
process, corresponding error parameter is found for etch
of the training pattern. After determining the changed
weight, each training pattern is again fed to the network
to find the level of maximum error. This process is con-
tinued till the maximum error becomes less than the al-
lowable error specified by the user. Testing process is
always used to validate the training data [50]. MLP neu-
ral networks have become a popular technique for mod-
eling manufacturing processes , in addition to many other
applications. It has been theoretically proven that any
continuous mapping from an m-dimensional real space to
an n-dimensional real space can be approximated within
any given permissible distortion by the three-layered
feed-forward neural network with enough intermediate
units [50-53]. Advantages of MLP are it is effective in
modeling process mean and process variation simultane-
ously using one integrated MLP model. The MLP model
with a large number of hidden neurons can produce an
equivalent or smaller training error and generalization
error for the back propagation with momentum (BPM)
method [54].
3. Research Methodology
Materials that were investigated in this study include
MGC, SiC and BN. Each substrate was cut into 10 mm ×
10 mm × 10 mm dimension and cleaned with distilled
water for 10misn and dried in the oven for an hour. Nec-
essary measurements were taken before and after the
etching process. The experimental procedure was carried
out in three steps: cleaning, etching and neutralization.
The material surface was cleaned in the first step to en-
sure no contamination objects exists on the material sur-
face which might affect surface ro ughness d uring etc hing.
Then, the material was removed and cleaned with dis-
tilled water. Lastly, the material was baked in the over
for 60 minutes. The variables investigated in this study
are etching temperature, etching duration, etching solu-
tion and solution concentration (in Table 2). With 95%
level of confidence, this experimental study was con-
ducted and analyzed by CCD. Analysis of Variance
(ANOVA) was provided in CCD and, p-value was used
to study the significance of model. The parameters stud-
ied and the model’s lacks of fit were as indicated and
assessed respectively. Predictive empirical model on this
experimental model was also generated. Each of these
materials has undergone fifty-four runs of experiments
with four variables carried out inside the flat bottom flask
equipped with a condenser coil. All experiments were
randomly organized to make sure the observation was
independently distributed. Figure 1 shows the set up
condition of CHM of advanced ceramics.
Figure 1. Chemical etching set up.

Predictive Modelling of Etching Process of Machinable Glass Ceramics, Boron Nitride, and Silicon Carbide1605

All materials were produced by GoodFellow. Inc.
MGC used contains 46% SiO2, 16% Al2O3, 17% MgO,
10% K2O, 7% B2O3. SiC used was reaction bonded with
low porosity and very fine grain. BN exhibits a hexago-
nal structure and is sometimes known as white graphite,
due to its lubricity and anisotropic properties, heat resis-
tance, and high thermal conductivity. Their properties are
as shown in Table 3 .
Surfing roughness (nm)
surfing roughness before-surfing roughness after (1)


Etchin r adio
=Etching rat e at non-indented areaEtching rate
atindented area
(2)
Etching rate rate was measured by measuring the
weight difference b efore and after etching and divided by
etching duration. The weight of each material was taken
in a close-up weight balancer (with a deviation of
±0.0001 g) and time taken with a digital watch. Surface
roughness was inspected closely with Atomic Force Mi-
croscope (AFM) with a deviation of ±1.5 nm. It is meas-
ured by the changes of surface rough ness before and after
etching (1), where the higher positive change (or lower
surface roughness after etching) was preferable. Etching
ratio is the measurement of dimensional accuracy as
shown in (2) and Figure 2 presents the measurement of
etching ratio taken before and after etching. The meas-
urement of the depth of the indented and non-indented
area (etching ratio) was completed by using a micrometer
(with a deviation of ±0.0001 m).
4. Results and Discussion
ANOVA and p-value were used to determine the ade-
quacy of the models developed by DoE. They were em-
ployed to estimate the lack of fit. With 95% of confident
interval, all experimental data were analyzed and results
Table 3. Properties of advanced ceramics).
Advanced ceramics MGC BN SiC
Resistance to concentrated acid Poor Fair Good
Resistance to alkal is Fair Fair Good
Compressive strength (MPa) 345 120 1500
Tensile modulus (GPa) 67 25 70
Density (gcm–3) 2.52 2.20 3.10
Coefficient of thermal
expansion (JK–1kg–1) 13 × 10–6 36 × 10–6 4.6 × 10–6
Specific heat (JK–1kg–1) 790 2000 1100
Thermal conductivity (Wm–1K–1) 1.5 50 200
Figure 2. Patterning accuracy.
that had less than 0.5 p-value were considered as signify-
cant. The lower the p-value is, the more critical the re-
spective variable. As mentioned earlier, each experiment-
tal design is going through the first order model. The
decision on whether to proceed to the second order
model or analyze current ANOVA data was made based
on the presence of curvature in the result. Once the cur-
vature was verified in the first order model, indicating
the experimental process was quadratic and a higher
level interaction between the parameters had occurred,
we then proceeded to the second order model where
CCD was used.
4.1. Fir st O rder Mo del
Table 4 shows the curvature’s p-value of ANOVA data
for etching rate, surface roughness and etching ratio. The
curvature’s p-value of less than 0.5 is considered signify-
cant indicating that a relationship between variables ex-
ists and therefore central points are needed to determine
the behaviour of the process. Table 5 shows the ANOVA
results for etching rate, surface roughness and etching
Table 4. Curvature p-value for first order model.
Material SolutionEtching
rate Surface roughness Dimensional accuracy
HCl 0.021 0.0400 0.0240
HBr 0.022 0.0400 0.0500 MGC
H3PO4 0.012 0.0292 0.0050
HCl 0.045 0.0059 0.0429
HBr 0.016 0.0400 0.0352 BN
H3PO4 0.046 0.0431 0.0400
HCl 0.019 0.0010 <0.0001
HBr <0.0001 0.0337 0.0255 SiC
H3PO4 0.047 0.0489 0.0178

Predictive Modelling of Etching Process of Machinable Glass Ceramics, Boron Nitride, and Silicon Carbide
1606
Table 5. ANO VA for RSM-second order model.
MGC
Material Etching ra te Surface
rough ness Etching ratio
Type 2FI 2FI 2FI
Model <0.0001 0.0168 0.0376
A-Temperature <0.0001 0.0299 0.0012
B-Duration 0.0192 0.4673 0.0152
C-Solution <0.0001 0.5510 0.2022
D-Concentration 0.5914 0.2273 0.3224
AB 0.0002 - 0.0154
AC 0.0089 - 0.0372
BC 0.0127 - -
Lack of fit 0.2354 0.9987 0.216
BN
Type 2FI CUBIC 2FI
Model 0.0002 0.0002 0.0044
A-Temperature 0.0274 0.0002 0.0863
B-Duration 0.6767 0.0998 0.0033
C-Solution <0.0001 0.0109 0.0907
D-Concentration 0.5411 0.2541 0.0112
AB 0.0645 - 0.0046
AC - 0.0118 -
BC - 0.0003 -
Lack of fit 0.0591 0.7238 0.3281
SiC
Type QUA QUA QUA
Model <0.0001 0.008 <0.0001
A-Temperature 0.0052 0.2111 <0.0001
B-Duration 0.5673 0.0051 0.0001
C-Solution 0.0433 0.0397 <0.0001
D-Concentration 0.2705 0.3203 0.0126
AB - - 0.0618
AC - 0.0071 -
BC <0.0001 - -
Lack of fit 0.9913 0.9513 0.8770
-Indicate insi gnificant value (p-value more th an 0. 5).
ratio with the second order model. It was found that all
material fitted well to CCD model with a p-value of less
than 0.5 and the p-value for lack of fit was more than 0.5.
The etching rate, surface roughness and dimensional
accuracy of MGC fitted well to the 2-factorial interaction
(2FI). Table 5 shows that etching rate of MGC matches
the 2FI model, while its surface roughness and etching
ratio show a 98.32% and 97.24% agreement respectively
with the 2F1 model. The etching temperature is found to
be the most important variable in CHM of MGC. Both
etching temperature and etching duration both affected
the etching rate of MGC while, the etching ratio was af-
fected significantly by etching duration. However, solu-
tion concentration did not show any effect in the MGC
etching process. The interaction between temperature and
etching duration and that of temperature and etching so-
lution showed significant effect on the etching rate and
etching ratio. Only the interaction between etching dura-
tion and solution affected the etching rate significantly.
The BN etching rate and etching ratio matched the 2FI
model with a near 100% confidence interval respectively
while, BN surface roughness matched the cubic model.
Etching temperature and etching solution were the most
significant parameters for etching rate and surface rough-
ness. The etching duration affected the results of etching
ratio significantly The interaction between etching tem-
perature and etching duration influenced the changes of
etching ratio with 99.54% confidence interval. The re-
sults further showed that the interactions between etching
solution and temperature with etching duration appeared
to influence the surface roughness.
The etching rate, surface roughness and etching ratio
of SiC matched well with the quadratic model, exhibiting
near-perfect agreements respectively. Each result showed
no lack of fit. For etching rate, etching temperature and
etching solution were found to be significant. The inter-
action between etching duration and etching solution was
also found to affect the etching rate. For surface rough-
ness, etching duration, etching solution and interaction
between etching temperature and etching duration have a
magnitude lower than 0.5 p-value. This means that these
factors significantly affect surface roughness. All factors
affected etching ratio, however, etching temperature and
etching solution exerted the most significance effect,
followed by etching duration and solution concentration.
4.2. Etching Rate
Etching temperature was found to have the most signify-
cant influence on etching rate of all materials tested.
Figure 3 shows the graph of etching rate versus etching
temperature for MGC, BN and SiC. The results showed
that etching rate was slower at the lower temperature
whereas, the rate of etching increased with increasing

Predictive Modelling of Etching Process of Machinable Glass Ceramics, Boron Nitride, and Silicon Carbide1607
(a)
(b)
(c)
Figure 3. (a) Graph of MGC etching rate vs etching tem-
perature; (b) Graph of BN etching rate vs etching tem-
perature; (c) Graph of SiC etching rate vs etching tem-
perature.
temperature. The peak of etching rate of MGC and BN
took place at the boiling point of the solution. For SiC,
etching rate reached its peak point at around 60˚C and
decreased above this temperature. These observations
agree with those found in [55]. Cai et al. found that etch-
ing rate of copper decreased after a certain tempera ture.
At high temperatures, dissolution of solution is more
active and more reaction occurs [56,57]. William et. al.
and Prudhomme et. al. reported a similar result and they
concluded that etching rate increased with dissolution of
solution, especially at high temperatures. Figure 4 is an
Arrhenius plot for MGC, BN and SiC in HBr solution.
The Arrhenius law states that the rate of chemical reac-
(a)
(b)
(c)
Figure 4. Arrhenius plot (a) MGC in HBr; (b) BN in HBr;
and (c) SiC in HBr.

Predictive Modelling of Etching Process of Machinable Glass Ceramics, Boron Nitride, and Silicon Carbide
1608
tion increases exponentially with the absolute tempera-
ture [58]. It is well-known that chemical etching proc-
esses are limited by either chemical etching reaction or
the transport of etchant molec ules by diffusio n. Diffusion
limiting processes are relatively insensitive to tempera-
ture at lower activation energies and are usually encoun-
tered at high concentration [59].
The Arrhenius law’s equation suggests that etching
rate increases as the temperature increases. Activation
energy, Eo is the minimum amount of energy needed to
activate molecules to a condition in which it is equally
likely that they will undergo chemical reaction. Table 6
listed the Eo of each material in different etching solu-
tions. A similar phenomenon has been observed and re-
ported by Vartuli et al. [60] in the case of advanced
ce-ramics wet etching, that is, that no etching was found
at an etching temperature of 75˚C; Tehrani and Imanian
[61] proved that high temperature greatly increased the
oxidizing power, which caused a rapid increase in the
etching rate; Makino et al. [24] found that all ceramic
materials’ tested etching rate was increased with in-
creasing etching temperature but less ideal etching be-
haviour was also common with more aggressive etching
rates [62,63].
The next significant factor is the type of etching solu-
tion. The selection of a suitable chemical solution is the
key to success. To effectivel y etch a material, we have to
make sure the material is compatible with the etching
solution for chemical reaction purposes [6]. Figure 5
Illustrates etching rate versus etching solution for MGC,
BN and SiC. It shows that the etching rate of MGC and
BN in HBr acid was higher compared to that of other
solutions; and, the etching rate of SiC in H3PO4 acid was
the highest. William et al. [36] summarized a list of che-
mical etching process for various materials, etching solu-
tions and variables. Their results showed that the etching
solution was the main priority to successfully machine
the materials. Simon et al. [64] tested four advanced ce-
ramics in different etchants and the materials were found
to exhibit different etching properties. Three materials
were well-etched in molten-salt and one was etched with
the electrolytic etching method.
Table 6. Ea value of Arr henius plot (kJ/mol).
HCl HBr H3PO4
BN 0.1132 0.6037 0.0013
MGC 0.4592 0.6685 0.1329
SiC 0.4978 0.7769 0.1548
(a)
(b)
(c)
Figure 5. (a) Graph of MGC etching rate vs etching solution;
(b) Graph of BN etching rate vs etching solution; (c) Graph
of SiC etching rate vs etching solution.

Predictive Modelling of Etching Process of Machinable Glass Ceramics, Boron Nitride, and Silicon Carbide1609
4.3. Surface Roughness
The quality of surface roughness after CHM is important,
especially in industry. In semi-conductor manufacturing,
excessive roughness destroys the integrity of very thin
layers, such as gate or tunnel oxide. In optics, surface
roughness causes light scattering, which can be good or
bad for the product. For high quality X-ray mirrors, sur-
face roughness is measured and must be minimized. For
diffusers, controlled surface roughness is important to
achieve the diffused scattering that is isotropic and
achromatic. In our current study, a smoother material
surface is required to produce products of high quality.
The surface roughness is judged before and after CHM.
So, the higher the positive changes of surface roughness,
the better the material surface it is.
As reported previously [12,14,16], poor surface rough-
ness was obtained with a prolonged etching duration
(over etching) and high temperatures. In this work, etch-
ing temperature was found to significantly influence the
surface roughness of MGC and BN. As shown in Figure
6, reduction of surface roughness for MGC, BN and SiC
was increased with etching temperature. Reduction of
surface roughness takes place mainly due to the chemical
reaction at the desired surface area [69,70]. This phe-
nomenon is similar to etching rate all materials where it
increases with rising etching temperature. For MGC and
BN (Figure 6(a) and Figure 6(b)), better surface rough-
ness is obtained at a higher temperature while the best
surface roughness of SiC was obtained at 80˚C. After this
temperature, SiC is over-etched and the surface rough-
ness increased. Images in Figure 7 show the respective
surface roughness examined by AFM at different tem-
peratures. The surface roughness of MGC improved with
temperature and its surface roughness decreased 30 nm
after etching at 65˚C and decreased 77.5 nm after etching
at 100˚C. Figure 8 shows the surface condition of BN
after etching in 7.5 Morality HBr for 75 mins. The sur-
face condition of BN improved up to 40˚C. A higher
temperature over-etched the BN surface and was no
longer feasible and useful. The best surface roughness
was obtained at 40˚C. Figure 9 shows SiC etched by 6 M
HBr for 180 mins. The changes of surface behavior were
similar to MGC, where better surface roughness was ob-
tained at a higher etching temperature. The best surface
roughness was obtained at 65˚C.
The selection of etching temperature influences the
surface finish. In manufacturing, they also tend to apply
the highest temperature to etch the substrate [11]. Choi et
al. [65] also concluded that etching temperature signify-
cantly influenced the degree of transformation of the
surface. Several researchers have found that the lower
surface roughness was obtained at the beginning of the
(a)
(b)
(c)
Figure 6. (a) Improv ement M GC of surface roughness with
etching temperature; (b) Improvement BN of surface rou-
ghness with etching temperature; (c) Improvement SiC of
surface roughness with etching temperature.

Predictive Modelling of Etching Process of Machinable Glass Ceramics, Boron Nitride, and Silicon Carbide
1610
2.00 um 5.00×5.00 um
2.00 um 5.00×5.00 um
(a) (b)
2.00 um 5.00×5.00 um
2.00 um 5.0 0×5.00 um
(c) (d)
2.00 um 5.00×5.00 um
2.00 um 5.00×5.00 um
(e) (f)
Figure 7. AFM images of MGC. (a)-(b) respective surface
roughness before and after 180 minsetching in 19˚C HBr
solution; (c)-(d) surface roughness before and after (180
min) etching in 65˚C HBr solution; (e)-(f) respective surface
roughness before and after (180 min) etching in 100˚C HB r
solution.
process and increased after certain etching temperatures.
Jardiel et al. found that increasing the temperature to
50˚C improved etching and better surface roughness was
observed [66]. Platelets show sharp boundaries instead of
rounded ones observed in the thermally etched samples.
Choi et al [68] and Cakir et al. [70] noticed the trend of
surface roughness changed with etching temperature.
Poor surface roughness is obtained at higher etching
temperatures [65,67]. They found that all the treated sur-
faces were rougher than that of the untreated surface [11].
As the temperature increased near to boiling point,
roughness values increased to about 15 um Ry due to
preferential etching of the grain boundary areas [24].
The etching process relied on the reaction between
anion of etching solution with the material composition.
2.00 um5.00×5.00 um
2.00 um 5.00×5.00 um
(a) (b)
2.00 um5.00×5.00 um
2.00 um 5.00×5.00 um
(c) (d)
2.00 um5.00×5.00 um
2.00 um 5.00×5.00 um
(e) (f)
Figure 8. AFM images of BN in 7.5M HBr for 75min (a)
19˚C before etching and (b) 19˚C after etching; (c) 65˚C
before etching and (d) 65˚C after etching; (e) 100˚C before
etching and (f) 100˚C after etching.
If they are chemically matched, this process will start at
the faster rate. This could be the reason why etching so-
lution appears as the dominant factor in chemical etching
of BN and SiC. Figure 10 shows a graph of surface
rough ness ver sus etchi ng soluti on of MGC, B N and SiC.
However, etching solution has only 44.9%-influence on
the chemical etching of MGC shown in Figure 10(a).
The changes of surface roughness with respect to etching
solution are relatively small. HBr gave the least changes
of surface roughness in chemical etching of BN and SiC.
Figures 11-13 show the AFM images of MGC, BN and
SiC with different etching solutions. We have demon-
strated that the type of etching solution used will have
influence on the properties of the surface roughenss of
the materials. In a typical test, the surface roughness was
accessed after etching in 65˚C for 120 minutes. MGC

Predictive Modelling of Etching Process of Machinable Glass Ceramics, Boron Nitride, and Silicon Carbide1611
2.00 um 5.00×5.00 um
5.00×5.00 um
2.00 um
(a) (b)
2.00 um 5.00×5.00 um
2.00 um 5.00×5.00 um
(c) (d)
2.00 um 5.00×5.00 um
2.00 um 5.00×5.00 um
(e) (f)
Figure 9. AFM images of SiC in 6M HBr for 180 min (a)
19˚C before etching and (b) 19˚C after etching; (c) 65˚C
before etching and (d) 65˚C after etching; (e) 100oC before
etching and (f) 100˚C after etching.
obtained better surface roughness in H3PO4 solutio n, than
HCl followed by HBr with the least e ffect. Ho wever, for
BN and SiC, better surface roughness was achieved with
HBr solution. The nature of the material microstructure
that existed might cause the different trend of surface
roughness properties observed in MGC, BN and SiC [11].
With the same type of etching solution and other inde-
pendent variables, the only difference between these ma-
terials is their microstructure and composition. Williams
et al. summarized that the degree of roughening probably
depends on the microstructure and thus varies with the
method of material preparation [36]. Prudhomme et al.
[17] also observed that roughness of the same material is
different when treated with two different etching solu-
tions.
In regard to the effect of etching duration the changes
of surface roughness were less crucial in for MGC and
(a)
(b)
(c)
Figure 10. Surface roughness vs etching solution (a) MGC,
(b) BN and (c) SiC.

Predictive Modelling of Etching Process of Machinable Glass Ceramics, Boron Nitride, and Silicon Carbide
1612
2.00 um 5.00 ×5 .0 0 u
m
(a)
2.00 u
m
5.00×5.00 u
m
(b)
2.00 u
m
5.00×5.00 um
(c)
Figure 11. AFM images of MGC at 65˚C for 120 min in 0
level etching solution (a) 10 M HCl, 6 M HBr and 12 M
H3PO4.
2.00 u
m
5.00×5.00 um
(a)
2.00 u
m
5.00×5.00 um
(b)
2.00 u
m
5.00×5.00 um
(c)
Figure 12. AFM images of BN at 65˚C for 120 min in 0 level
etching solution (a) 10 M HCl, 6 M HBr and 12 M H3PO4.

Predictive Modelling of Etching Process of Machinable Glass Ceramics, Boron Nitride, and Silicon Carbide1613
2.00 u
m
5.00×5.00 um
(a)
2.00 um 5.00×5.00 um
(b)
2.00 um 5.00×5. 00 um
(c)
Figure 13. AFM images of SiC at 65˚C for 120 min in 0 level
etching solution (a) 10 M HCl, 6 M HBr and 12 M H3PO4.
BN as shown in Figures 14(a) and 14(b) compared to
14(c). Etching duration has a marked influence on sur-
face roughness in chemical etching of SiC. This is shown
clearly in Figure 14(c) where surface roughness dra-
matically increases with increasing etching duration. The
changes of surface roughness were slow in the beginning
probably due to material dissolution that resulted in re-
duction of chemical reaction. Prudhomme et al. [57] and
Cakir et al. [11,67] reported similar results. Better sur-
face roughness was found at higher etching duration.
Improvement in the surface state occurred when the sol-
ute was dissolved in the etching solution at a longer
etching period, which increases the energy gap for gen-
erating etch figure and reduces the damage of material’s
surface. Baranova and Dorosinskii [68] found that as the
duration of etching increased, insoluble reaction products
started forming and eroded the surface thus causing the
samples to be no longer suitable for further study. Etch-
ing time is important while longer etching period pro-
duced a constant etching process in the case of alumin-
ium etching, because dissolution of chemical solution
was not completed at the beginning of the process. After
this period, the etching process was observed to be more
stable [67].
4.4. Effect of Indentation
Industrial patterning involves designing and producing a
desirable pattern on the material surface. Method of
nano-patterning includes dry and wet mask patterning.
The selection of mask for patterning in CHM is an issue
due to the difficulties associated with the quality of the
mask and increasing demand for multi-kind and small-
quantity production in a market. In overcoming these
difficulties, a new technology has been introduced to
replace mask patterning by micro-indentation. This tech-
nique enhanced versatility and provided lower cost for
initial facilities and manufacture, simplicity of process
and material selectivity [12,13,69-71]. Typically, 5N
load (P = 500 Nm–2) is applied on the material surface
where patterning is required and then followed by etch-
ing process. By applying the load onto the desired area, it
is thought to enhance the bonding of the material struc-
ture and delay the chemical reaction happens at the in-
dented area At the end of the process, measurement is
taken at indented area and non-indented area [36]. The
indented area will become convex after etching. The
etching ratio comprising the relative etching rate between
that of non-indented area and indented area was then
compared. Patterning is successfully created when etch-
ing rate at non-indented area is higher than etching rate at
indented area. The higher the etching ratio is the better
the feasibility of the patterning process. One of the key
points of this technology is inducing an etching rate

Predictive Modelling of Etching Process of Machinable Glass Ceramics, Boron Nitride, and Silicon Carbide
1614
(a)
(b)
(c)
Figure 14. Improvement of surface roughness vs etching
duration in HBr solution (a) MGC; (b) BN and (c) SiC.
change arising from the indentation [13].
Patterning is successfully created when etching rate at
non-indented area is higher than etching rate at indented
area. A convex is built when e above phenomena takes
place. One of the most significant factors is the material
properties, which resulted from the production method
and subsequent processing. The convex is created by
applying a load onto the desired spot. By applying the
load onto this area, it is enhancing the bonding of the
material structure and delaying the chemical reaction
happening at the indented area [36]. A higher etching
ratio is preferred where higher etching rate occurred at
the non-indented area and lower etching rate at the in-
dented area.
The etching duration was found to be the most signify-
cant variable in etching ratio and Figure 15 shows a plot
etching rate of indented and non-indented area for MGC,
BN and SiC so l utio n. I t sho ws t hat t he highe st d iffe re nce
between indented and non-indented area occurs mostly at
200 min. This observation is consistent with the etching
rate results shown in Table 4, where etching rate is in-
creased with etching duration. The reduction of etching
rate at the longer etching duration is possibly due to the
insoluble deposit formed at the indented area [13]. A
peak etching ratio is found in the etching of BN at 90
min (Figure 16(a)). Etching rate at non-indented area
was found to be higher compared to etching rate at in-
dented area, especially at high temperature. This also
indicates that etching depth is dependent on time, where
one would expect a square root of time dependence for
etching depth and a much lower activation energy [72].
Cakir et al. observed that etching ratio of non-indented
to indented area increased with etching process. Similar
phenomena are observed in many research works [12,13,
69-71]. Nagai et al. [15] successfully conducted experi-
ments on macro-size patterning and chemical etching,
which led to the formation of well-ordered patterns of
surface crystal steps. Youn and Kang [12] fabricated Py-
rex glass by micro-indentation with HF etching. Saito et
al. [13,69,70] proved the feasibility of micro-machining
process in fabricating glass ceramic in HF etching. These
research works showed that patterning on the glass ce-
ramic surface becomes possible due to etching rate dif-
ference between indented and non-indented area. One of
the key challenges of this technology is to increase and
control etching rate difference between indented and
non-indented area.
With less than 0.05 p-value, solution concentration is
the main factor that is able to influence the etching ratio
of MGC, BN and SiC. Figure 17 shows the graph of
etching ratio vs solution concentration. Overall, etching
ratio is decreased with etching duration. A peak etching
ratio is found in the etching of BN, which is around

Predictive Modelling of Etching Process of Machinable Glass Ceramics, Boron Nitride, and Silicon Carbide1615
(a)
(b)
(c)
Figure 15. Etching rate of indented area and non-indented
area vs etching duration (HCl solution) (a) MGC; (b) BN
and (c) SiC.
–0.50 or 6 M HBr. This implied that higher etching rate
difference between non-indented and indented area could
be obtained in lower solution concentration. The result
sugge sts t hat, i n hi gher sol uti on co ncentr at ion r egio n, th e
(a)
(b)
(c)
Figure 16. Etching ratio vs etching duration (HCl solution)
(a) MGC; (b) BN and (c) SiC.

Predictive Modelling of Etching Process of Machinable Glass Ceramics, Boron Nitride, and Silicon Carbide
1616
(a)
(b)
(c)
Figure 17 . Etching ratio vs sol u tion conc entratio n (a) M GC;
(b) BN and (c) SiC.
leaching reaction scarcely occurred even at non-indented
area, resulting in a decrease of etching rate ratio. The
etching reaction of the material and the leaching reaction
are considered to be competitive reaction. When the
leaching precedes the etching reaction, the etching rate
would be increased. Saito et al. found etching ratio for
glass ceramic was obtained at lower pH region [13,69].
They also suggested that etching ratio can be controlled
by solution concentration. Saito et al. [70] also reported
that not only alkali and alkali earth metal oxide, but also
alumina in alumina silicate glass was leached out in HF
acid.
4.5. Predic tive Mod el s
Predictive models generated by RSM are presented in (3)
to (11), where t is etching duration, T is etching tem-
perature, c is solution concentration. These are empirical
models and can be applied in the industry for mass pro-
duction.
For MGC, etching rate (ER)
H3PO4
ER0.000257 0.00000430.0000012
0.00013 0.0000015
0.0000225 exp2
Tt
cTc
c

 


(3)
HBr
ER0.00004 0.00000090.0000007
0.000130.00000150.000023 exp2
Tt
cTcc
 
  (4)
HCI
ER0.000047 0.00000060.000059
0.00000150.0000225 exp2
Tc
Tc c
 
 (5)
For MGC, improvement of surface roughness (SR)
H3PO4
SR69.95 0.8030.09511.9
0.0047 0.00410.395
Td
TtTc tc
 
 
c
Tc
c
c
c
c
(6)
HBr
SR74 0.7590.28689.80.405
0.0047 0.395
Ttc
Tt tc
 
 (7)
HCI
SR5.005 0.3230.235119.22
0.0047 0.4050.395
Tt
Tt Tctc
 
 (8)
For MGC, etching ratio (R)
H3PO4
R1.91 0.0420.0231.40
0.00026 0.0230.0057
Tt
Tt Tctc
 

(9)
HBr
R0.0042 0.0170.0290.68
0.00026 0.0230.0057
Tt
Tt Tctc
  
 (10)
HCI
R2.16 0.0420.0270.85
0.00026 0.0230.0057
Tt
Tt Tctc
 

(11)
5. Comparison between ANN and RSM
After determining ANN p rogramme and RSM predictive
model, the two techniques were then compared. This is

Predictive Modelling of Etching Process of Machinable Glass Ceramics, Boron Nitride, and Silicon Carbide1617
presented in Figure 18 (etching rate), Figure 19 (surface
roughness) and Figure 20 (etching ratio). It is clear that
the two groups of values are close to each other. The
error percentage of RSM and ANN techniques is rela-
tively small (0.01%) and can be neglected.
Results obtained by CCD’s predictive model clearly
showed its advantages depicted in Figures 18(b), 18(c),
(a)
(b)
(c)
Figure 18. Predictive etching rate by DOE and ANN com-
pared to experimental result (a) MGC; (b) BN and (c) SiC.
(a)
(b)
(c)
Figure 19. Predictive improvement of surface roughness by
DOE and ANN compared to experimental result (a) MGC,
(b) BN and (c) SiC.
19(c), 20(b) and 20(c). Results of CCD pr edictive model
in these figures are close to the experimental results. The
difference of CCD predictive results and experimental
results was less than 5%. Overall, both techniques used
were in good agreement with the experimental result.
With less than 10% error, it is revealed that CCD predict-
tive model performs better.

Predictive Modelling of Etching Process of Machinable Glass Ceramics, Boron Nitride, and Silicon Carbide
1618
(a)
(b)
(c)
Figure 20. Predictive etching ratio by DOE and ANN com-
pared to experimental result (a) MGC; (b) BN and (c) SiC.
6. Optimization
Table 7 shows the optimization for each material. As a
result, HBr based etch recipe provides the fastest yet
controllable results in the etching of MGC. The optimum
of HBr based etch recipe happened at 100˚C, with dura-
tion of 30 mins and 8.5 Molarity of HBr, where etch rate
is 0.0011 g/min, surface improvement, 80.879 nm and
etching ratio, 3.277.
Table 7. Optimization of etching rate, surface roughness
and etchi ng ratio.
MGC
Desirability 0.586 0.392 0.240
Solution HBr HCl H3PO4
Temperature (˚C) 100 100 100
Duration (min) 30 30 109
Concentration (Molarity) 8.5 10.5 9.5
Etching rate (g/min) 0.001 0.001 0.0003
Surface rou ghness
(improvement ) (u/min) 80.79 81.82 87.23
BN
Desirability 0.5624 0.3367 0.2425
Solution HBr HCl H3PO4
Temperature (˚C) 40 100 25
Duration (min) 62 128 137
Concentration (Molarity) 6.0 9.5 9.5
Etching rate (g/min) 0.0003 0.005 0.0002
Surface rou ghness
(improvement ) (u/min) <0.001 <0.001 <0.001
Etching ratio 3.153 0.533 1.45
SiC
Desirability 0.954 0.525 0.419
Solution HBr H3PO4 HCl
Temperature (˚C) 75 100 74
Duration (min) 240 172 240
Concentration (Molarity) 8.5 9.5 10.5
Etching rate (g/min) 0.001 0.012 0.0003
Surface rou ghness
(improvement ) (u/min) 128.71 34.17 62.786
Etching ratio 10.00 2.12 8.59
7. Conclusions
In summary, we have successfully conducted CHM on
MGC, BN and SiC. The results supported the feasibility
of wet chemical micro-patterning of advanced ceramics
for micro-devices applications. Direct patterning is suc-
cessfully introduced to meet the increasingly vocal de-
mand for multi-kind and small quantity production. In
this leading-edge of research involving the use of micro-
and nanotechnology, more flexible patterning techniques
are desired. The following concluding remarks can be
drawn.

Predictive Modelling of Etching Process of Machinable Glass Ceramics, Boron Nitride, and Silicon Carbide1619
1) CCD as a technique for design of experiment pro-
vides useful statistically results in analyzing the chemical
etching process of advanced ceramics.
2) Use of ANN in predicting the etching results were
found to be effective. These results were in good agree-
ment with those predicted by RSM. One of the disadvan-
tages is that more time is needed in looking for the suit-
able transfer function.
3) The relationships between etching rate, surface
roughness and etching ratio with etching temperature,
etching duration, etching solution and solution concen-
tration were successfull y established.
4) The optimum chemical etching process was carried
out with the optimization technique provided by DE 7.
The etching rate and improvement of surface quality
achieved is 0.0011 g/min, 80.789 nm respectively and the
etching ratio is 3.277.
8. Acknowledgements
The authors would like to acknowledge the support given
by Ministry of Science, Technology and Innovation (Ma-
laysia) MOSTI, and Curtin University-Sara wak Malaysia.
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