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Chip Scale Review May • June • 2018


A closer look into sub-micron die placement: Cpk and Cmk

By David R. Halk

[ASM AMICRA Microtechnologies GmbH]

lacement accuracy is one of the

most critical process parameters

to obtain and to maintain in the

photonics assembly industry. For a well-

informed buyer and user of die bonding

equipment, it is important to be familiar

with the terms Cpk and Cmk and their

significance, especially when selecting an

automated tool for a bonding process that

requires sub-micron placement accuracy.

Die bonding, or die attach, is an essential

part of the assembly process, where

electronic components, in their rawest form

(semiconductor die), are picked and placed

onto a substrate medium held temporarily

in place by a semi-liquid material (epoxy or

solder). In other words, die bonding plays a

major role in the “level one” assembly process.

The die must be positioned accurately in a

repeatable position to establish interconnect

with the package substrate.

As interconnect dimensions are getting

smaller and smaller, die bonders’ placement

accuracy and repeatability are forced to

obey ever tighter limits, pushing placement

requirements to sub-micron levels. In some

cases, the die attach machine must bond the

die held in place during the heating process.

The engine of a photonic integrated circuit

(PIC) is based on light generated by a laser.

Here the die attach machine is required to

bond the laser, typically using an in situ AuSn

eutectic bonding process. The goal is to direct

the emitted light into the PIC’s waveguide,

which is a very small opening etched into the

silicon sub-mount or substrate.

Definition and significance of Cmk

and Cpk

The objective of this article is to show how

Cmk data is used in selecting a die bonder that

requires sub-micron placement accuracy, with

the following considerations:

• How is Cpk/Cmk calculated and what

are the constituents of Cpk?

• How does Cpk apply to first-pass yield

and PPM?

• How can the photonics assembler apply

Cpk to critical processes?

Cmk, or machine capability index, is an

effective measure to quantify a die bonder’s

placement capabilities. To

understand the importance of

Cmk, we will first cover the

more popular process capability

indices, Cp and Cpk, which

serve as useful tools in gaining

insight on how to improve

first-pass yield throughout the

assembly line.

Cpk, or process capability,

compares the upper and lower

specification limits (USL,

LSL) to the output deviation of

a process. This comparison is

made by forming the ratio of

the required process specification or limits to

the measured process values, as indicated by

standard deviation, or sigma [1].

Cpk, therefore, is a capability index that

assesses how close the measured process

mean (average) is to the specification limits

(USL, LSL). If the process is under control

and the distribution of the measured data

is well within the specification limits, the

difference between USL and mean (or the

difference between LSL and mean) should be

>3 sigma, or 3 standard deviations. If Cpk is

>1, the process mean is sufficiently far from

the specification limit [1].

Calculation of Cp and Cpk [2]

USL - Xmean

Cpk (upper) = -------------------------

3 * Sigma

Xmean - LSL

Cpk (lower) = ------------------------

3 * Sigma


Cpk = min (Cpk upper, Cpk lower)

USL = upper specification limit

LSL = lower specification limit

X = mean (average)

σ (sigma) = standard deviation (Std)

The theoretically achievable repeatability

of a die bonder is difficult to measure or

estimate. There are several factors that must

be considered, such as: the sub-pixel grey-

level vision system, the vision alignment

algorithm, linear encoder quadrature,

optical resolution, etc.

Figures 1a



show these values and their interrelations as

a Cpk diagram.

Popular example of managing Cpk

To get an idea how Cpk influences a

specific industrial process such as photonics

placement, let’s take a look at a familiar daily

routine such as navigating a car though a

narrow garage door as shown in

Figure 2


The garage opening illustrates, or defines,

the specification limits of a process and the

position of the parked car represents the

output of the process. If the width of the car

is just a bit narrower than the opening, you

better park it right in the middle (which is the

center of the specification) if you want to get

all of the car into the garage. If the car is wider

than the opening, it does not matter if you

have it centered, it won’t fit anyway. If the car

is 2X narrower than the opening (six sigma

process), it doesn’t matter if you park it exactly

centered. It will fit and you have plenty of

room on either side.

What the above discussion illustrates is that

if you operate a process that is in full control

and shows little variation, you should be able

to meet customer requirements (i.e., to park

the car easily within the garage). Cpk indicates

the relationship between the size of the car, the


Figure 1:

Cpk diagrams where a) Cpk = 1; and b) Cpk = 2.