Download Your Paper`s Title Starts Here:

Modeling of physical and chemical processes of anodic bonding
technology
Pshchelko N.S., Sevryugina M.P.
National University of Mineral Resources "The University of Mines", 199106, Saint-Petersburg,
Russia
[email protected]
Keywords: Physical and mathematical modeling, technological processes, anodic bonding,
electric field, connection of materials, charge accumulation
Abstract. Modeling ideas of physical and chemical processes when using an anodic bonding for
materials connection are developed. The kinetics of a charge accumulation in an electrode region in
a dielectric is considered. The thickness of a charge layer, electric fields strength and value of the
ponderomotive pressure providing connection of materials are calculated. It is shown that the
necessary ponderomotive pressure resulting in a dielectric-to-conductor seal is normally about ten
MPa and the time required is about ten minutes.
Intorduction
Implementation of advanced technologies is associated actually not only with development of the
new materials possessing required set of properties, but also with a problem of their connection –
pastings, welding and other ways of continuous or temporary fixing. In particular, the special
interest is represented by a problem of manufacturing a unit made of metals, other conducting
materials, including semiconductors, with dielectrics. Examples of conducting materials are copper,
aluminum, alloys, silicon, and examples dielectrics – ceramics of various structure, polycrystalline
glass, sapphire etc. Many of these materials are nonplastic, insoluble in each other, have high
temperature of melting. Usually applied ways of connection (for example, welding by melting,
contact welding, diffusive welding) not always can break a barrier of incompatibility of metals and
semiconductors with nonmetallic materials and ensure high-quality connections of many of them.
Therefore development of theoretical ideas of possibilities of nonconventional ways of fixing of
materials (constant or temporary) represent an obvious interest.
In this work modeling ideas of physical and chemical processes when using an anodic bonding for
materials connection are offered. Importance of their development is obvious, since the received
results will allow to choose reasonably parameters of a technological mode of manufacturing
dielectric-to-conductor seals.
Theoretical aspects
Interaction of objects, for example, solid bodies, resulting in their fastening to each other caused
by electric voltage applied across these objects is called as electric adhesion. Electric adhesion
grows out of an electrostatic (ponderomotive) attraction of electrified bodies in the case when
charges of different signs appear to be divided by a dielectric gap between contacting surfaces or a
thin layer of one of the fastened objects, grown poor by carriers of a charge and having therefore the
increased resistance adjoining an interface of a contact. The most part of the applied voltage
therefore falls on this narrow layer. In this way big electrostatic fields and forces arise leading to
formation of strong connection, remaining perfect after shutdown of electric voltage at the expense
of diffusive and electrochemical superficial processes between connected bodies. Dielectric-toconductor seal manufactured in such a way can be named as uncontrollable electroadhesive contact
(UEAC).
In a number of our works earlier a theoretical bases of manufacturing of electroadhesive "gluing
together" [1,2], and some possibilities of their practical use [3,4] were considered. In particular, it
was showed that durability of electroadhesive connections of ionic dielectric to metal appears at
level of durability of the similar connections received by diffusive welding. It was also shown that
on the basis of use of electric adhesion (anodic bonding technology) adhesion of films put on
substrates both after and in the course of their drawing can be considerably increased.
However, at calculation of magnitude of ponderomotive pressure arising in the course of
electroadhesive connection steady state mode was considered only, i.e. in our previous works it was
considered that connected details are subjected to electric field for a very long time. Actually,
necessary time of endurance was defined only experimentally. Therefore the purpose of this work is
calculation of transients at electroadhesive junction of ionic dielectrics with conductors
(semiconductors) when an electric voltage is applied on a contact. Calculation of a value of
response time of this process will allow to choose reasonably time of the junction formation and to
increase quality of manufactured "gluing together".
The major role at UEAC formation is played by migratory (interlayer) polarization of dielectric:
under the influence of forces of electric field free charges in dielectric move from anode to the
corresponding electrode (cathode). In case of ionic dielectric free carriers of a charge are usually
positive ions therefore at when the voltage is applied across the contact they will start to move
(migrate) to the cathode. Thus the place occupied by a positive ion before the voltage was applied
(anode region in dielectric), the, will obtain a noncompensated charge of vacancy. Since the typical
ionic dielectric used for manufacturing of UEAC is alkaline glass, further consideration will be
carried out, for definiteness, on an example of this dielectric.
In a migratory polarization process of development negative charges of vacancies will collect in
a thin layer of some thickness of xm, fig. 1
Fig. 1. Model for calculation of transients ina
system “conductor - ion dielectric” at their
junction by anodic bonding technology. 1metal; 2-the air gap caused by a roughness of
contacting surfaces; 3-a layer of localization
of a volume vacancy charge in dielectric; 4the
layer
of
dielectric
without
noncompensated charges.
If the air gap is not ionized (i.e. its conductivity is negligibly small - γ1=0), and, therefore,
compensations of a charge of vacancies does not occur, at accumulation of a negative charge in xm
results finally to same value of the charge as on the cathode. So the strength of electric field Е3 in
dielectric becomes equal to zero and migration of ions will stop. Thus, all applied voltage U0
appears to be distributed between very thin air gap d1 and a layer xm of also small (as it will be
shown below) thickness.
On the basis of Ampere's citcuital law, Gauss' law of flux and Kirchhoff's 2-nd law the following
system of the equations can be written down:
dE3
dE1

 0 1 dt   0 2 dt   3 E3

x

 0 2 E2   0 1 E1   dx

0

xm

 0 2 E3   0 1 E1  dx


0

xm

U 0  E1d1  E2 dx  E 3 (d 2  xm )


0

(1)
Here E1, E2, E3 –electric fields strengths in an air gap, in a layer of localization of a
noncompensated charge and in the main part of dielectric without noncompensated charges.,
respectively; t - time counted from the moment of the voltage U0 turning on , γ3 - specific
conductivity of dielectric; specific conductivity of an air gap and a layer of localization of
noncompensated charge are considered equal to zero since specific conductivity of air is negligible
in comparison with γ3 (at used temperatures of about 4000C), and all free positive ions (in glass
these are ions Na+, K+, etc.) are removed from a layer xm. Legitimacy of the last assumption is
provided by the value of . quartz glass (i.e. glass without ions of Na+, K+, etc.) conductivity which
is approximately 7 orders less than that of, for example, a windowpane; ρ – volume charge density
of migrating ions of conductivity; depending on total concentration of ions of this type п0 in the
glass; ε1 and ε2 - relative dielectric permittivity of an air gap and dielectric (glass), ε0 – an electric
constant. Dielectric permittivity of a glass layer with a thickness of xm from which conductivity ions
are removed, can differ from that of other part of a glass. However, even at removal from this area
of all ions of alkaline metals dielectric permittivity according to help data does not change
significantly.
The decision of system (1) leads to the expression showing that thickness xm of area of
localization of a volume charge changes depending on time as follows:
b

2


 4ac  b 1  e  b  4ac t 

 ,
xm (t ) 
2
 b  b  4ac  b 2  4ac t 

2 a 1 
e
 b  b 2  4ac



2
(2)
where

 1 3
a 
2 0 2 ( 1d 2   2 d1 )


 3 d1
b 
 0 ( 1d 2   2 d1 )


 1 3U 0
c 
 ( 1d 2   2 d1 )

(3)
From (2) and (3) follows that xm(t) – the sublinear curve leaving the beginning of coordinates,
aspiring to value
 d 
2 2
2 1
2 0 12 2U 0

xm 
(4)
1
with time constant
0 
  2 d1
1
b  4ac
2

 0 ( 1d 2   2 d1 )
3 d 
2
1
2 0 12U 0
.
(5)
 2
The received value  0 corresponds to characteristic time of migration of ions of conductivity
under the influence of electric field in xm layer in thickness. Taking into account that these ions
really are not free, and "jump out" of places of the fixing with with a frequency which the is less,
than more energy of activation of the ions, full value of a time constant of transient in the case
under consideration will become [5]
W
(6)
   0 exp( ) ,
kT
where W - energy of activation of migrating ions, k – Boltzmann constant, T – thermodynamic
temperature. Thus, taking into account the specified frequency factor and on the basis of (2) and (6),
we conclude that dynamics of thickness of xmf(t) of area of localization of a volume pre-anode
charge in ionic dielectric when manufacturing UEAC with it is described by expression
t 

b 2  4ac  b 1  exp(  ) 
 

x mf (t ) 
.
(7)
2
 b  b  4ac

t
2 a 1 
exp(  ) 
 b  b 2  4ac
 

Formulas (5) and (6) allow to define full value of a time constant of development of migratory
polarization when receiving UEAC and by that to choose reasonably time of endurance of UEAC
under electric voltage.
Similar to xmf (t) the strength of electric field of E1, in an air gap will change:
x 

xm  d 2  m 
 2U 0
2 

E1 (t ) 

.
(8)
 1 d 2   2 d 1  0 ( 1 d 2   2 d )
The greatest interest is represented, of course, by the established values of thickness of a layer of
localization of a volume charge of xmf(t) and strengths of the pulling fields E1 and E2. These values
of the specified magnitude define the value of developed ponderomotive pressure when
manufacturing UEAC. Calculations show that for achievement of ponderomotive pressure
1
necessary for "pasting" (tens MPas )[1,2] in an air gap p1   0  1 E12 and in points of the actual
2
1
contact p ô .ê .   0  2 E 22 , respectively in typical cases time of an order of ten minutes is required
2
that well corresponds to known experimental data.
At the same time, at practical use of anodic bonding technologies knowledge of reasonable value
of endurance time of UEAC is necessary as well.


Practical findings
Some results of calculations on the basis of the obtained expressions and with use of the
technique presented in [2], are given in fig. 2, 3 and 4. In calculations, according to [2], mechanical
properties of connected materials, and also consideration that ponderomotive pressure acts both in
an air gap, and in points of the actual contact on the corresponding share of the nominal connected
area were taken into account. It can be made by means of factor p0 . Numerical value
of p0 corresponds to the value of an average pressure over connected area at which 63 % of the
nominal area appear in the actual contact.
Fig. 2. The kinetics a of volume charge area localization xmf in a glass at various values of
the voltage applied. d2=2 mm; d1=1 µm; 1 =1;  2 = 4.5; p0 = 10 MPa; Т=600К;
W= 1.4  10 19 J;  3  1,89  10 7 (  m) 1 ; п0 = 1028 m-3.
Fig. 3. Dependence of an air gap electric field strength vs time and the voltage applied in a
glass. d2=2 mm; d1=1 µm; 1 =1;  2 = 4.5; p0 =10 MPa; Т=600К; W= 1.4  10 19 J;
 3  1,89  10 7 (  m) 1 ; п0 = 1028m-3.
Fig. 4. Dependence of ponderomotive pressure on time and temperature at the conductor –
ionic dielectric UEAC formation. d2=2 mm; d1=1 µm; 1 =1;  2 = 4.5; p0 = 10 MPa; U0 = 400
V; W= 1.4  10 19 J;  3  1,89  10 7 (  m) 1 ; п0 = 1028 m-3.
Conclusions
The given examples show that the necessary ponderomotive pressure resulting in a dielectric-toconductor UEAC seal is normally about ten MPa. The time required is about ten minutes at a
temperature about 600 K and the voltage applied of 400 V. More exact figures can be defined in
each case on the basis of the expressions obtained in this work. Theoretical results are in good
correspondence with experimental data.
References
[1]
[2]
[3]
[4]
[5]
V. S. Nagorny, N. S. Pshchelko, Theoretical bases of increase of adhesion of conductor layers
to dielectric substrates, Scientific and technical sheets to SPBGPU. Series: «Informatics,
telecommunications, management». 4 (82) (2009) 217-221.
N. S. Pshchelko, T.V.Stoyanova, Influence of a roughness of surfaces of electroadhesive
contact on its power characteristics, Non-ferrous metals. 5 (2008) 51-57.
V.S.Nagorny, N. S. Pshchelko, Pilot study of ways of increase of adhesion of carrying-out
particles to dielectric substrates, Scientific and technical sheets to SPBGPU. Series:
«Informatics, telecommunications, management». 3 (80) (2009) 185-190.
V. A. Moshnikov, I. E. Gracheva, M. G. Anchkov, N. S. Pshchelko, K. L. Levin,
Investigating properties of gas-sensitive nanocomposites obtained via hierarchical selfassembly, Smart Nanocomposites. 2 (2), 165-179.
P. T. Oreshkin, A. Ya. Scrap, M. V. Zubkov, S. V. Patrin, Long-term relaxation of
nonequilibrium conductivity in superficial and barrier structures of semiconductors, FTP. 18
(8) (1984) 1503-1505.