Online proceedings - EDA Publishing Association

7-9 October 2009, Leuven, Belgium
of the silicon bench can greatly reduce package size and
interconnection length within components, which result in
reduction of parasitic capacitance and inductance in the
package suitable for high-speed applications. Meanwhile, the
SiOB provides exclusive advantages of high precisely optical
alignment for low insertion loss coupling from optical
components to fiber core, good thermal mismatch, excellent
thermal conductivity, and better resistor fabrication for
impedance matching of signal transmission. On the other
hand, SiOB still has its intrinsic shortcoming. Silicon
substrate is lossy material in the RF/microwave/millimeter
wave regimes. Electrical signals transmitted between on-chip
circuitries can easily leak into silicon substrate and be coupled
to generate substrate noise. Electrical losses of the signals
due to induced eddy current in the substrate also degrade the
quality of the performance of passive components in the
driving circuitry. In order to resolve this issue, a layer of 3µm
BCB (benzo-cyclo-butene) is utilized for passive fabrication
where the loss can be greatly reduced. Owing to high thermal
resistance characteristic of BCB, laser diode directly mounted
on the top of it would have inevitable working temperature
raise that could affect the laser performance.
Therefore, in this paper, the equivalent ETCM of SiOB
mounted with 160Gbp/s VCSELs will be developed by
considering the characteristics of device materials and
geometries. The presented model can not only reasonably
simplify the complicated configuration but also provide an
indication for system optimization.
II.
MODEL ANALYSIS
According to the essential meanings and emphases of
common π-circuit model, three main blocks, labeled heating
source, propagated resistance, and common base resistance,
are employed in the general electrothermal network π-model,
shown in Fig. 1, representing the thermal source, thermal flow
path, and the common base of thermal conducting system,
respectively. As mentioned by A. M. Darwish et al. that it is
appropriate to assign adiabatic surface between each heating
source and the next [2], the adopted dash-lines in the network
π-model represent an adiabatic surface enclosed each
presented blocks where the effective contact area can be
eventually well defined. Meanwhile, the impedance
parameters Z i , where i present 1, 2, 3, and 4, can be defined as
the thermal resistance of heating source itself, source-source,
nature or forced air convection, thermal capacitance, and
other specified boundary conditions, and so on. Boundary A
and B can be the ground level of the thermal flows, other
heating components of thermal conducting system with
specified thermal conditions, or interconnections between
different systems. It should be specially emphasized that
icons of the source of thermal flow and the block of heating
source represent the thermal generation and flow and main
heated component, respectively.
Fig. 3(a) and (b) show the modified electrothermal
π-network model and the associated equivalent ETCM of the
VCSELs on SiOB, respectively, where Z 1 and Z 2 , Z 3 , and Z 4
are thermal resistance of a VCSEL (R VCSEL ) itself, an infinite
thermal resistance due to the negligence of nature air
convention here, and thermal capacitance of SiOB (C SiOB ),
respectively. Boundary A and B are the adjacent R VCSEL of the
operating VCSEL and ground level for entire thermal
conducting system, respectively. It is noted that two
parameters, the source of thermal flow and Z 1 , are the
components of the heating source in the modified network
π-model since the VCSELs are main thermal flow generators
and also the heated components themselves in our case.
Additionally, the blocks of propagated resistances and
common base resistances are represented by parallel
connection of thermal resistance of gold (R Gold ), air (R Air ), and
BCB (R BCB ) and SiOB (R SiOB ), respectively.
Four switches adopted in the structure mean the VCSEL
can be single operated. According to Fourier’s conduction
law, R VCSEL , R Gold , R Air , and R BCB can be easily calculated as R i
=t i /k i A i , where i, t, k, and A are adopted material, thickness,
thermal conductivity, and contact area of the materials,
respectively. Then, C SiOB is equal to Q/∆T where Q and ∆T
represent dissipated power and temperature difference,
respectively. Parameter R SiOB , however, has complicated
thermal behavior due to its large volume and aspect ratio. It
can be calculated as follows [2]:
[ f ( g[ 2s]
1)
]
1 ⎛ V + ⎞ 1 ⎛ h( 2.
3t)
⎞
R SiOB
= ln⎜
+ ⎜ ⎟
[ ( [ ])] ⎟
ln , (1)
2π Wk ⎝ V f g L ⎠ 4π sk ⎝ h(s) ⎠
where
(a)
(b)
Fig. 3. (a)Scheme of the modified general electrothermal network π-model.
The source of thermal flow and Z 1 are the components of the heating source
due to the VCSELs are main heating generators themselves in our case.
(b)The equivalent electrothermal circuit model of the VCSELs on the SiOB,
where Z 1 and Z 2, Z 3, and Z 4 are thermal resistance of VCSEL (R VCSEL), an
infinite thermal resistance due to without nature air convention here, and
thermal capacitance of SiOB (C SiOB), respectively.
©EDA Publishing/THERMINIC 2009 9
ISBN: 978-2-35500-010-2