Gas Flow Effects on Precision Solder Self-Alignment

Bingzhi Su, M. Gershovich, and Y. C. LeeDepartment of Mechanical Engineering

University of Colorado, Boulder, CO 80309

ABSTRACT

Self-aligning soldering technology is being developed for low cost, passive, precision

optical alignments. To avoid contamination problems, the solder reflow process must use

reacting or inert gas instead of chemical flux materials. Since the accuracy of these optical

alignments should reach the range of a few micrometers (µm), the gas flow may affect the

aligning process. Therefore, the effects of the gas flow on the self-aligning process must

be understood.

The experiments described show that gas flow effects do exist. The top plate, 8.4 mm

× 8.4 mm, can be moved by the gas flow by as much as 4.5 µm and 7.8 µm at gas flow

rates of 2.5 L/min and 5.0 L/min, respectively. The numerical analysis in this study models

the gas flow effects for a wide range of chip sizes, solder geometry, and gas flow

direction. In the numerical analysis, fluid computation and solder force calculation are

conducted to study the gas flow effects on chip displacement that is the distance away

from the well aligned position along the gas flow direction. The results show that the gas

flow effects are related to many factors including chip size, gas flow rate, solder height,

and flow direction. For a one-dimensional laser array, these effects are negligible because

the chip size is very small. However, for a chip larger than 5 mm × 5 mm, the effects

should be controlled for micron-level precision alignment.

INTRODUCTION

Soldering is a popular connection technology used for passive alignment of

optoelectronic packages. More and more optoelectronic assemblies are being soldered and

the processes have been reviewed by Basavanhally [1], and Tan and Lee [2]. These

processes can be broken into the following four categories: (1) solder the assembly with

no precision self-alignment [3,4], (2) solder and allow self-alignment with no mechanical

stops [3-10], (3) solder and allow self-alignment with one mechanical stop [11-13], and

(4) solder and allow self-alignment with two mechanical stops [14]. Self-aligning soldering

technology is widely used for optoelectronic packaging because of its low cost.

The principle of self-alignment during the soldering process is explained in Figure 1.

Figure 1(a) shows a chip tacked to the substrate with solder bumps at the corresponding

solder wetting pads or bump sites. During reflow, the molten solder spreads over the pads

and creates momentarily a shape with higher energy (see Figure 1(b)), which causes the

chip to move relative to the substrate until the solder joint attains the minimum total

energy for an accurate alignment(see Figure 1(c)). Sometimes, misaligned solder joint

profiles are preferred because they could be used to push one standoff against another for

the alignment [14].

Figure 1. The mechanism of self-alignment

chip

substrate

(a) initial alignment

(b) reflow

(c) final alignment

The aligning motion is affected by many design and manufacturing parameters [1,2].

The design parameters have been studied extensively by measurements and modeling

[12,15,16]; however, the effects of manufacturing parameters have not been reported in

detail. This study was initiated to understand and characterize manufacturing variables.

The first effect studied was the effect of gas flow on self-alignment.

To avoid contamination problems, fluxless solder reflow processes are usually

preferred for optoelectronic assemblies. Without chemical flux, a reacting gas must be

used to remove the solder’s surface oxide. Alternately, an inert gas can be used to prevent

oxidation of the solder that has been cleaned before assembly. In these situations, the flow

of gas may result in a viscous drag to pull the chip away from its desired position. In the

present study, the experiment demonstrates the gas flow effects, and the numerical

analysis studies the gas flow effects for a wide range of the parameters that can affect the

self-alignment such as chip size, gas flow rate, solder height, flow direction, etc..

EXPERIMENTAL STUDY

Experimental system

The diagram of the experimental system is shown in Figure 2. The hot plate is made of

brass with a high thermal conductivity so that there is a uniform temperature distribution

over the plate. The gas flow is introduced from the gas inlet. The dimension of the test

vehicle is shown in Figure 3. The size of the chip is 8.4mm×8.4mm×1.27mm and the

diameter of the solder pads is 1.27mm. The solder used for the experiment is eutectic

solder (37/63 Pb/Sn) and its volume is controlled at 0.377±0.000002 µl by using the

solder balls from Alpha Metals Inc.. The chip weight is 100 dyne or 25 dyne/joint. In

order to precisely measure the micro-motion of the chip during reflow, a high-resolution,

non-contact sensor is needed. After reviewing different types of sensors, we chose a

displacement fiber-optic sensor 88TN1 from Philtec Inc. because of its low cost, high

accuracy, and compact size [17]. The details of the system can be found in [18].

Figure 2. The diagram of the experimental system

Figure 3. The assembly test vehicle

Φ 1.27 mm

8.4 mm

8.4 mm

1.27mm

-10123456789

10

0 1 2 3 4 5 6 7 8 9 10

Time (seconds)

Dis

plac

emen

t( µm

)

With gas flowWithout gas flow

Figure 4. Displacement of the chip with a gas flow rate of 2.5 L/min

-10123456789

10

0 1 2 3 4 5 6 7 8 9 10

Time (seconds)

Dis

plac

emen

t( µm

)

With gas flowWithout gas flow

Figure 5. Displacement of the chip with a gas flow rate of 5.0 L/min

The experimental results of gas flow effects

In the experiments, forming gas with a composition of 90% N2 and 10% H2 was used

during reflow. The temperature of the hot plate was set at 275oC. Figure 4 and Figure 5

show the chip moved away from the well-aligned position by 4.5 µm and 7.9 µm during

reflow at the gas flow rates of 2.5 L/min and 5.0 L/min, respectively. These results were

repeatable in the experiments[18]. This experimental study demonstrates that the gas flow

effects on self-alignments do exist, and should be carefully considered during reflow.

NUMERICAL STUDY

The experimental study demonstrates the presence of gas flow effects. However, the

measured quantitative results are specific to the cases studied; they can not be generally

applied to all possible cases. In fact, there are two important factors that can affect the

drag force acting on the chip: the fluid velocity near the chip and the surface area of the

chip. To extend the scope of the study, a numerical analysis is conducted to characterize

the gas flow effects on the chip over a wide range of chip sizes (from 1000 µm × 1000 µm

× 100 µm to 8000 µm × 8000 µm × 500 µm) with circular or rectangular solder pads. For

the analysis, first we conducted the fluid computations of the reflow chamber and obtained

the drag force acting on the chip, then we calculated the solder surface tension and

estimated the chip displacement.

In the fluid computation, the reflow chamber is simplified as two-dimensional. The

two-dimensional assumption is reasonable for the following three reasons: (a) the chip size

is very small compared to the reflow chamber; (b) the chip is located on the center line of

the bottom of the reflow chamber so that the flow field around the chip is parallel to and

symmetric about the center line, and (c) what is concerned in the simulation is the flow

field around the assembly other than that around the wall of the reflow chamber. The

results show that the error introduced by the simplification is negligible.

The forces acting on the chip during reflow are shown in Figure 6. The drag force

caused by the gas flow includes both a shear force and the pressure acting on the sides of

the chip. The restoring force is provided by the misaligned solder joint. The force balance

is:

Drag force + Restoring force = 0

In this study, the drag force is obtained by fluid computation. The displacement of the

chip is then determined from the shape of the solder joints that provide a restoring force to

balance the drag force.

Figure 6. Force balance on chip in the reflow chamber

Fluid Computation

The chamber geometry used in the calculation is shown in Figure 7. The dimensions

of the chamber used for calculation are very similar to the dimensions of the experimental

chamber. Gas flow rates of 2.5 L/min and 5.0 L/min were chosen for the study. It should

be noted that the gas flow rate used here is the equivalent value for a two-dimensional

chamber section which has the same volume as that of the three-dimensional reflow

chamber used in the experiment.

Governing equations and boundary conditions

For the two-dimensional flow field, the governing equations can be written as follows:

Continuity equation∂ ρ

∂∂ ρ

∂

( ) ( )U

xV

y+ = 0 (1)

Shear Force

Pressure

Restoring ForcePressure

Momentum equation∂ ρ

∂∂ ρ

∂∂∂

∂∂ µ ∂

∂∂

∂ µ ∂∂

∂∂ µ ∂

∂

( ) ( )UUx

VUy

px x

Ux y

Uy y

Vx

+ = − +

+

+

2 (2)

∂ ρ∂

∂ ρ∂

∂∂

∂∂ µ ∂

∂∂∂ µ ∂

∂∂

∂ µ ∂∂

( ) ( )UVx

VVy

py y

Vy x

Vx x

Uy

+ = − +

+

+

2 (3)

Energy equation

CpUTx

CpVTy x

kTx y

kTy

∂ ρ∂

∂ ρ∂

∂∂

∂∂

∂∂

∂∂

( ) ( )+ =

+

(4)

where U is the gas velocity in the x direction; V is the gas velocity in the y direction; T is

the temperature; ρ is the density; k is the thermal conductivity; µ is the viscosity; Cp is the

specific heat, and p is the pressure.

At the gas inlet boundary, the gas velocity profile is assumed to be uniform, with a

value calculated by the gas flow rate. The gas temperature is 300K. At the gas outlet

boundary, the velocity and temperature profiles are assumed to be fully developed:

∂∂ Ux

= 0 ,∂∂ Vx

= 0 , and ∂∂ Tx

= 0 . At the wall and the bottom of the chamber, U = 0,

V = 0, and T = 300 K. At the hot plate under the substrate, U = 0, V = 0, and T = 550 K.

Figure 7. The calculation domain in the fluid computation

x

y

3.81

cm

0.381cm

6.35cm

4.76cm

Substrate on a hot plate

Gas inlet

Gas outlet

0.50

8cm

Procedure for fluid computation

Given a flow rate, the above governing equations with the boundary conditions are

solved by using SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) method

[19]. Seven steps are carried out to solve the equations:

1. Assume the U, V, T distribution in the chamber.

2. Guess the pressure field P*.

3. Solve the momentum equation to obtain U* and V*.

4. Solve the P’ equation and update the pressure P= P* + P’.

5. Update the velocities U and V by velocity correction equations.

6. Solve the energy equations.

7. Repeat steps 2 to 6 until the convergence is reached.

In the model, an uneven grid is used. A typical grid number for the computation is 102

× 62. Also, in order to verify that this mesh is fine enough, a mesh of 202 × 82 is used to

calculate the drag force. The results differ by less than 2% for the two different meshes so

the drag force obtained from the fluid computation is not significantly mesh dependent.

After the problem converges, the drag force acting on the chip can be calculated by adding

the viscous force along the surface to the force due to pressure difference.

Solder surface tension calculation

In the solder surface tension calculation, the public domain software Surface Evolver

[20] was used. Numerically, Surface Evolver uses a gradient descent method on a space of

admissible surfaces to find the local minimum of the energy function. In the calculation, two

cases were studied, one is with circular solder pads, and the other is with rectangular solder

pads. The restoring force due to a single solder joint with a given misalignment can be

calculated.

For the cases studied, the gravitational potential energy of the solder joint can be

ignored since it is very small compared with the surface energy. Hence, the energy function

contains only two terms: the surface energy and the load due to the weight of the chip

component.

For a quasi-static self-aligning model, the restoring force and normal reaction force

generated by the solder during shape changes can be calculated [21] by

FEPS

S

H CONSTANT

==

∂∂

(5)

FEHN

S

P CONSTANT

==

∂∂

(6)

where FS and FN are restoring force and normal reaction force, respectively. P is the

misalignment level, H is the joint height, and ES is the local minimum surface energy of the

solder joint at P and H. The coefficient of surface tension of solder used in the study is

350 dyne/cm.

The outputs of the model are the solder surface shapes and the surface tension forces

(restoring force and normal reaction force), while the inputs are pad geometry (circular or

rectangular, etc.), pad size, solder volume, joint height, misalignment level, and surface

tension coefficient. The model user should also set the convergence criteria. For this

study, the convergence criteria are set to be:

(a)At each mesh level, the calculation converges when the energy difference between two

adjoining iterations is smaller than 1.0×10-10 (dyne⋅cm)

(b)The mesh size is refined until the energy difference between two successive mesh

densities is smaller than 1.0×10-8 (dyne⋅cm)

The energy level calculated is on the order of 10-4 (dyne⋅cm).

Unlike the solder joint with the circular pads, the misalignment direction for a solder

joint with the rectangular pads is very important. Typically, there may be two

misalignment directions. One is along the long side of the rectangular pad, and the other is

along the short side. The study calculates the restoring forces corresponding to the two

different misalignment directions. For a given flow rate, the displacement of the chip is the

misalignment that corresponds to the restoring force that balances the gas drag force.

Results of numerical studies will be presented and discussed.

RESULTS AND DISCUSSION

Before conducting extensive numerical simulations, the model was verified using the

experimental results. Table 1 lists the modeling and experimental results. The modeled

chip size of 8.4mm×8.4mm×1.27mm is the same as that used in the experiment reported

earlier.

At the gas flow rate of 2.5 L/min, the chip displacement in the experiment is 4.5 µm

while the calculated displacement is 4.2 µm; At the gas flow rate of 5.0 L/min, these two

displacements are also close to each other. These results verify the accuracy of the model

and confirm that the two-dimensional fluid computation is suitable to study the gas flow

effects in the three-dimensional reflow chamber. Different simulations were then carried

out to characterize the effects.

Table 1. The chip displacement with the size of 8.4mm×8.4mm×1.27mm and 4 solder joints

Gas flow rate(L/min) Calculated displacement(µm) Measured displacement (µm)2.5 4.2 4.55.0 8.3 7.8

Drag force acting on the chip

Figure 8 shows the drag force acting on the chip for a series of chip sizes at the gas

flow rates of 2.5 L/min and 5.0 L/min, respectively. The reason that the unit of the

horizontal axis uses mm2 rather than mm is that the drag force is nearly linear in relation to

the chip surface area. As shown in the Figure, the drag force increases with increasing

chip area and increasing gas flow rate. In addition, the effect of the chip thickness is also

important. The cross section of the 500 µm thick chip is much larger than that of the 100

µm chip and results in a large pressure drop.

0

1

2

3

4

5

0 10 20 30 40 50 60 70

Chip area: long side x short side (mm2)

Dra

g fo

rce

actin

g on

chi

p(dy

ne)

Chip thickness:100µm, flow rate 5.0 L/minChip thickness:500µm, flow rate:5.0 L/minChip thickness:100µm, flow rate:2.5 L/minChip thickness:500µm, flow rate:2.5 L/min

Figure 8. Predicted drag force acting on the chip

Restoring force caused by misaligned solder

Figure 9 shows the restoring force acting on the chip for different misalignments for

the case listed in Table 2. The solder pads are circular with a diameter of 200 µm. The

solder volume is 2.356×106 µm3. As shown in the Figure, the restoring force increases

with increasing misalignment.

Table 2 The parameter for the solder calculation of the case with circular padchip

size(mm3)number of

solder joint onchip

Solder paddiameter(µm )

soldervolume(µm3)

Solder height(µm )

8×8×0.5 6 200 2.356×106 68

0

1

2

3

4

5

6

0 1 2 3 4 5

Misalignment of the chip (µm)

Res

torin

g fo

rce

(dyn

e)

Figure 9. The predicted restoring force acting on the chip bythe solder with circular pad

Figure 10 shows the restoring force at different displacements for the four cases listed

in Table 3. The four cases are for the chip with rectangular pads. The chip weight and pad

size are the same in all four cases. The main differences among them are the solder height

and misalignment direction. The results show that misalignment direction and solder height

are important factors in self-aligning soldering. The force corresponding to the 10 µm

solder height is much larger than that corresponding to the 75 µm solder height. For

example, cases 3 and 4 show that the force changes from 40 to 7 dyne for a misalignment of

3 µm when the height is increased from 10 to 75 µm. Such a force reduction is significant, and

will influence the gas flow effects to be simulated. The restoring force is larger when the

misalignment direction is along the short side than when it is along the long side. Figure 11

Table 3. The parameter for the solder calculation of the 4typical cases with rectangular pad

case chip size(mm3)

solder padsize(µm2)

misalignment direction solder height(µm)

solder jointnumber

1 8×8×0.5 300×100 along long side of pad 75 62 8×8×0.5 300×100 along long side of pad 10 63 8×8×0.5 300×100 along short side of pad 75 64 8×8×0.5 300×100 along short side of pad 10 6

explains this result. In this Figure, S and L are the length of the short and long sides of

the rectangular pad, respectively. H is the solder height. Because the solder volume is

constant, the change of H corresponding to the misalignment is very small and H can be

considered as constant. When the solder is moved by θ along the long side of the pad, the

change of the solder surface area can be roughly estimated as

∆AL =2S(H/cosθ)-2SH=2SH(1/cosθ -1) (7)

Similarly, when the solder is moved along the short side of the pad, the change of the

solder surface area can be roughly estimated as

∆AS =2L(H/cosθ)-2LH=2LH(1/cosθ -1) (8)

Because L>S, it is clear that ∆AS is larger than ∆AL. Hence, for a solder joint with

rectangular pads, the restoring force along the short side is larger than that along the long

side.

0

10

20

30

40

50

60

70

80

0 1 2 3 4 5 6

Misalignment of chip (µm)

Res

torin

g Fo

rce

(dyn

e)

Case 4

Case 2Case 3

Case 1

Figure 10. Predicted restoring force for the solder joint with rectangular pads

Figure 11. The misaligned solder joint with rectangular pads

Displacement of chip

With the drag and restoring force calculation, the chip displacement under different

flow conditions can be estimated. Figure 12 shows the predicted displacement of a chip

with 6 solder joints and circular pads. The pad diameter is 200 µm and the solder height is

around 65 µm. The displacement increases with increasing gas flow rate and chip size. For

the chip size of 5 mm × 5 mm, the displacement can be as large as 2.4 µm. As observed in

Figure 8, the chip thickness also affects the displacement. A thick chip is displaced more

by the flow due to the large drag. Figures 13-15 show the predicted chip displacement for

the cases with rectangular pads. The displacements are affected by solder height (10 µm

and 75 µm) and flow directions (along the long or the short side of the rectangular pad).

θ

S

H

L

As may be seen by comparing Figures 14 and 15, when the solder height is larger, the

displacement is larger. This is due to the higher joint having a smaller restoring force.

Comparing Figures 13 and 14, when the flow direction is along the short side of the

rectangular pad, the chip displacement is smaller. The restoring force with the flow

0.0

1.0

2.0

3.0

4.0

5.0

6.0

0 10 20 30 40 50 60 70

Chip area: long side x short side (mm2)

Dis

plac

emen

t of c

hip

( µm

)

Chip thickness:500µm, flow rate:5.0 L/minChip thickness:100µm, flow rate:2.5 L/min

Chip thickness:100µm, flow rate:5.0 L/min

Chip thickness:500µm, flow rate:2.5 L/min

Figure 12. Displacement of chips with 6 solder jointsCircular pad, solder height around 65 µm, and pad diameter 200µm

0.0

0.1

0.2

0.3

0.4

0.5

0 10 20 30 40 50 60 70

Chip area: long side x short side (mm2)

Dis

plac

emen

t of c

hip

( µm

)

Chip thickness:500µm, flow rate:5.0 L/minChip thickness:100µm, flow rate:2.5 L/min

Chip thickness:100µm, flow rate:5.0 L/min

Chip thickness:500µm, flow rate:2.5 L/min

Figure 13. Displacement of chip with 6 solder jointsRectangular pad, pad size 3 mm × 1 mm, solder height 10µm,

and flow direction: along short side of pad

direction along this side is larger than that with the flow direction along the long side. For

the chip size of 5 mm × 5 mm, the displacement of the chip can be as large as 3.2 µm

when the solder height is 75 µm and the flow direction is along the long side of the pad.

From the results shown in these Figures, it is clear that the gas flow effects are strongly

dependent on the flow rates, flow direction, and chip configuration. It may be negligible in

one case, but it can be important in another case. For a typical small laser array with

dimensions of 100 µm × 300 µm × 100 µm, the displacement is very small (less than 1µm)

in all the cases studied. However, the displacement can be as large as 3.2 µm for a chip

size of 5 mm × 5mm × 0.5 mm. In summary, the results demonstrate the following: (a) the

displacement of the chip increases with increasing chip size and increasing gas flow rate;

(b) the displacement can be reduced with the use of short solder joints; (c) the flow

direction is important when the pads are rectangular.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 10 20 30 40 50 60 70

Chip area: long side x short side (mm2)

Dis

plac

emen

t of c

hip

( µm

)

Chip thickness:500µm, flow rate:5.0 L/minChip thickness:100µm, flow rate:2.5 L/min

Chip thickness:100µm, flow rate:5.0 L/min

Chip thickness:500µm, flow rate:2.5 L/min

Figure 14. Displacement of chip with 6 solder jointsRectangular pad, pad size 3 mm × 1 mm, solder height 10µm, flow direction: alonglong side of pad

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

0 10 20 30 40 50 60 70

Chip area: long side x short side (mm2)

Dis

plac

emen

t of c

hip

( µm

)

Chip thickness:500µm, flow rate:5.0 L/minChip thickness:100µm, flow rate:2.5 L/min

Chip thickness:100µm, flow rate:5.0 L/min

Chip thickness:500µm, flow rate:2.5 L/min

Figure 15. Displacement of chip with 6 solder jointsRectangular pad, pad size 3 mm × 1 mm, solder height 75µm, flow direction:along long side of pad

CONCLUSION

This study has reported the gas flow effects on self-alignment associated with fluxless

soldering. At the present time, most optoelectronic devices, e.g. 1-D laser arrays or

receivers, are very small, and these effects are negligible. However, larger devices are

being assembled [22,23]. Roughly speaking, for any device larger than 5 mm× 5 mm, the

gas flow effects should be considered. The gas flow effects are related to gas flow rate,

chip size, solder shape, flow direction, and the number of solder joints. The effects can be

controlled by carefully considering these factors. The study obtains the following

conclusions:

(1) Gas flow effects may cause large displacements for a chip larger than 5 mm × 5 mm.

For example the displacement can be 3.2 µm with a flow rate of 5 L/min.

(2) The chip displacement increases with increasing gas flow rate.

(3) Chip size is a very important factor to the gas flow effects. The displacement is nearly

linearly proportional to the chip surface area.

(4) Chip thickness is another important factor. Thick chips have a large displacement due

to the large pressure induced drag.

(5) The restoring force is dependent on the solder height. The restoring force increases

with decreasing solder height. As a result, the displacement caused by the flow effects can

be reduced substantially by the use of short solder joints.

(6) For the solder joints with rectangular pads, the flow direction is important. The effect

of the flow directed along the short side is small because the solder’s restoring force is

large in this direction.

ACKNOWLEDGMENT

This study is supported by the National Science Foundation (Grant #MIP9058409).

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