Lecture 33 (CHE 323) Statistical Process Control (SPC)

this is chemical processes for micro and

nof Fabrication I'm Chris Mack and this

is lecture 33 semiconductor

manufacturing statistical process

control last time we looked at another

important aspect of semiconductor

manufacturing yield and we spent some

time on one of the two uh yield

detractors

defects today with our introduction very

very brief introduction to statistical

process control we're going to look at

the second detractor of yield uh

parametric yield

loss the process uh can be controlled uh

in in certain ways uh that we're going

to talk

about and we have various metrics that

we use to help us control this process

um but when it comes to process control

we generally think about the parametric

yield side that we're trying to control

we also need to control the defects but

that's kind of a separate category of of

control defect control when we talk

about process control we're generally

talking about controlling the

parametrics of our process what are the

parametrics things like film thicknesses

and um doping concentrations and feature

sizes and Edge depths Etc all the things

that we can measure and put a numerical

value on

it parametric yield loss comes from

these parametrics these parameters like

a film thickness um that is off-kilter

it's far enough away from its desired

value that it causes the device to not

function properly if we want parametric

yield to be

high there are two ways that we can do

it uh one is we design a process that

can tolerate high yields uh excuse me

that can tolerate large amounts of

process variation and still produce high

yields uh that's great if we have a

process that's insensitive to variation

in a certain process variable then we

don't have to worry so much about that

process variable the second thing is

once we have an accept unn acceptable

amount of process variation that we can

tolerate we need to make sure that we

control the process to stay with within

that acceptable

variation there are two tools that we

often use for process control actually

there's quite a few more than just these

two but there's only two we're going to

talk about statistical process control

and process capability metrics those are

the topics of today's lectures lecture

but another very important area of

process control is called APC advanced

process control it's basically a

feedback loop where we make measurements

uh of of parameters of Interest like uh

film thickness and then we use a

feedback loop to control the equipment

that performs that uh deposition for

example um to try to keep it in control

so it's a feedback based uh process

control mechanism fascinating topic

we're not going to be able to talk about

it in this class instead we're going to

focus on SBC and process capability

metrics what is PC it's a tool to detect

systematic process

excursions so we've got a variable and

it has some known statistical history it

tends towards this mean and this

standard deviation for example now if we

see uh some variation in that process

parameter that is unexpected based on

its history its known statistical

history we call that a process Excursion

and the SBC is a tool to identify when a

process Excursion

occurs for example here's the mean

nitride thickness versus Lot number so

we process a lot of Wafers say 25 Wafers

at the same time then we might take

three of those Wafers and measure the

nitride thickness and we might measure

the nitride thickness at Five Points on

the wafer and we'll average all of those

together and get a mean nitride

thickness value we might get a standard

deviation might get some other

parameters as well um but we're going to

focus just on that one parameter the

mean nitride thickness and then we plot

that mean as a function of Lot number

every day we process another lot or

maybe we process a dozen lots a day some

something like that but we we sequence

through lot numbers and we plot that

mean measured mean nitride thickness and

we get some variation of that mean

value and what we want to do is look

at this variation and

ask is this particular point a problem

is it just normal statistical

fluctuations or is it something else

going on maybe something happened to

this lot that's different than the other

Lots that's what SPC is all about the

SPC method goes like this we establish

an historical mean and standard

deviation for a variable under under

consideration now for example I said the

mean nitride thickness what I mean by

that is the mean measurement of one lot

the lot mean and then we'll plot that as

a function of lots and that in and of

itself will have a mean value in a

standard deviation so for example if we

look here uh this is the mean nitrate

thickness but this is the mean within

one lot we can also calculate Cal the

mean value of all these data points

which is the mean uh of all the lots and

then of course we can have a standard

deviation historically the standard

deviation of this Min nitrite thickness

um amongst all the

Lots this mean will follow a normal

distribution now we know that's true

because of the central limit theorem if

you haven't studied that or if you've

forgotten it from your statistics or

probab ility of course it's very very

important you might go back and look it

up basically says that if uh I sum up a

bunch of

variables then uh that sum will follow a

normal distribution even if the

individual variables do not so this mean

value we can track and know that it has

an approximately normal

distribution then we'll use a three

sigma probability as an indicator of a

problem now in other words suppose some

event occurs we can calculate the

probability that that event occurred

randomly based on this normal

distribution if the probability of the

event occurring randomly is less than

3% then chances are this is an error

some systematic deviation from what is

expected and not just normal V pattern

variation prob probabilistic

variation the point . 3% is based on the

three sigma probability 97 you know

99.7% of the time were within 3 Sigma of

the

mean so we'll use this uh 3 Sigma

probability um to indicate that

something is likely wrong now it's not a

guarantee that it's a a systematic error

but it's probable and the result is what

we call the Western Electric rules since

this was was developed by the Western

Electric Company some time ago the main

Western Electric rules are these and

there are some other ones that we're not

going to talk about but these are the

main ones it gives you a feel for what

these rules are all

about for example we say that if any

single point Falls outside of the plus

or minus 3 Sigma limits then we we we

say that the this Western Electric rule

has been

violated there's only A3 % probability

of that happening randomly so if it

happens there's a likelihood fairly High

likelihood that it's something besides

just random

variation another possibility eight

successive points are above the mean or

eight successive points are below the

mean either one of these events has a 4%

probability of

occurring and that's close enough to 3%

that we say if this happens the this

Western Electric rule has been violated

now what could cause this to happen well

a mean shift something happens in our

process and now uh the the mean value of

that parameter has shifted to a higher

level or to a lower level and I have a

new uh mean uh that will result in a lot

something like you know 8 sucessive

points being above or below the

mean Another Western elect rule if two

out of three successive points are

between 2 Sigma and 3 Sigma or between

minus 2 Sigma and minus 3 Sigma of the

mean then this rule is violated again

there's about a 3% probability of this

happening uh so if it does happen we say

it's uh an indicator that there might be

a problem and the last one that we'll

talk about four out of five successive

points are greater than one Sigma that

is between between 1 Sigma and 3 Sigma

of the mean or between minus 1 Sigma and

minus 3 Sigma there's about a 5%

probability that either one of these

might happen uh so it fits our general

rule of thumb of about 3% probability uh

events get flagged um as potential

problems how do we use these Western

Electric

rules these rules can detect both a

shift in the mean and some growth in the

variation of the parameter there's a few

more rules besides the one we've

mentioned but the ones I mentioned give

you a flavor for what's going on they're

the most important rules and then when a

rule is violated we sound the alarm now

it's not literally an alarm going off in

the Fab but uh essentially when that

happens um you get a page or you get a

text that says you need to come in and

look at this if you're the engineer in

char charge for example an alarm means

it needs to be investigated generally we

uh we do all of this data analysis and

checking the Western Electric rules in

an automated uh fashion with software

nobody's actually looking at the data um

except for software uh so the software

will automatically send an email or send

a text or something like that when a

rule has been violated and it's called

an alarm when you get an alarm you look

at it and try to decide is this a

problem is it a is it something that

might have uh happened in the Fab that

caused uh something to go wrong can I

find that cause and can I fix it

sometimes of course these alarms will be

false in fact about 3% of the time uh

these things will happen just due to

Pure Randomness so sometimes you'll have

some false alarms and and that's okay

that's the nature of the game but you

need to separate out what's a false

alarm from what's a real problem for

example you might find that the nitride

thickness um had a mean shift so eight

out of eight data points in a row were

above the mean and when you go and look

you might notice

that the point in time when the mean

shift occurred happened to be right

after you clean the tube of your CBD

furnace so maybe uh there was a problem

with the cleaning process and as a

result uh the nitride thickness is no

longer uh in Spec um maybe it was

because you changed some gas canisters

for the processed gases used in the

nitride uh CBD process something like

that so you look for a cause and then

try to address

it we also can use uh this these rules

as a measure of how well our processes

in control we measure something called

the average run length that is how many

number of points on average are there

between alarms if we're having alarms

all the time then we have something

wrong in our Fab if we have a fairly

large number of points between alarms on

average then things are looking good so

we can also use the average run length

as a way of looking at the Fab in

general and saying things are going well

or things are not going

well

here's an example of an SP spc's chart

so we've plotted the historical mean the

red line here and then we have a

historical value for Sigma and we plot

the plus 1 plus 2 + 3 -1 -2 -3 values

and sure enough this one data point that

we saw

before is greater than 3 Sigma away from

the mean and so we would flag it as an

alarm and we'd want to go look at what

might have caused that

um when it

happened uh we might search through this

data to look for other possible alarms

as well but I don't see any when I look

at

it SBC charts are ubiquitous in the

world of semiconductor manufacturing as

I said it's almost all automated

measurements are made and the the data

automatically goes to a computer system

called a manufacturing execution system

or Mees software uh that collects the

data generates the charts uh you can

look at them online anytime you want and

then if there is an alarm it will

automatically send out emails or texts

to people to let them

know now another important uh metric

that we use is something called process

capability s SPC charts show how the

process is doing compared to his

historical Behavior that's very valuable

because if something changes you want to

know but that's not all we want to know

we would also like to know how the

process is behaving compared to the

specifications for the process what is

the spec what is the uh specification we

usually say spec um of a parameter so

example nitrite thickness we'll have a

spec on the mean and the allowed

variation of the nitride thickness where

does this spec come from well this spec

is based on the idea that if we keep the

parameter within the limits mean plus or

minus some

range then we're pretty sure our yield

is going to be high and the performance

of the device the performance of the

chip will not be affected because of

this variation in the

parameter we get these specs based on a

combination of experience and modeling

so we have modeling of how uh the

entire process will behave

modeling how the device will behave as a

function of of process parameters and we

can have a model that might tell us how

variations in the nitride thickness for

a particular step might affect the

overall performance or we might just

have some experience that says it needs

to be like

this um based on that we'll put together

uh process specifications and we'll ask

how does this long-term statistical

Behavior the historical statistical

behavior of a process compare

to what our specs are for that process

that's a very different question than

what SPC is designed to answer and we

use a metric called the process

capability index to answer that question

so our specs are defined by two

parameters the upper spec limit USL and

the lower spec limit

LSL and the difference between these is

the range of the parameter value that is

acceptable then we compare that range of

acceptable values to the historical Fab

performance so Sigma would be the

standard deviation of the actual

variable in the Fab so 6 Sigma would be

a plus and minus 3 Sigma range of that V

variable and then we'll look at the

compare we'll compare with this ratio

the upper spec limit minus lower spec

limit range of the the needed value

compared to the actual performance Six

Sigma that ratio is called C subp

the process capability

index higher CP means a more capable

process that means our uh performance

fits well within the spec limit

range H but there's a problem this

metric will not detect a mean shift and

it's only looking at the standard

deviation not at the mean of of the Fab

data so we going to we're going to

modify C subp

to

include mean variations and our new

metric will be called

CPK and that's how we pronounce it

that's what we always say what's the CPK

of the process for example CPK is

nothing more than this process

capability index C of P multiplied by 1

minus K and K is a term to to answer the

question has the mean drifted away from

the target value for that so this mean

here is the historical data from the Fab

and the target is the spec the actual

value we're trying to get for the mean

and then uh the ratio of of this

variation to 3 Sigma which is half of

the upper spec limit minus lower spec

limit is what K actually means so we

modify CP to include the possibility of

a mean

drift and the result is uh a new metric

CPK that includes both the variation and

the mean of the historical

data if CPK is bigger than one we have a

process with the possibility of success

CPK is less than one we will have yield

failure because of this um parameter

right obviously there's a CPK for every

process parameter that we monitor so a

CPK for nitrite thickness uh CPK for uh

dopent concentration a CPK for um uh

Junction depth for example everything

that we might measure in the Fab will

have a CPK value and if the CPK is less

than one that means that parameter is

negatively impacting the yield in my

fab so we want it it has to be greater

than one minimum requirement if it's

bigger than 1.5 it's good we've got a

good process and if it's bigger than two

we say the process is great this is

often called a Six Sigma quality and in

in the world of

manufacturing uh you can advertise that

you have a Six Sigma process if your CPK

is bigger than two on all the parameters

of course what it might mean is that

your specs are too loose uh and maybe

you could design better chips if you

were willing to use tighter specs uh so

that's another possibility if your CPK

is bigger than two but generally the

higher the CPK the

better so what have we learned in this

second of two lectures on the topic of

semiconductor

manufacturing well you should be able to

quickly answer these three questions

what is the guiding principle of

SPC what are the Western Electric

rules

what do you do when there is an SBC

alarm actually I apologize there's more

than three questions here I I forgot um

what is the difference between CP and

CPK and finally what constitutes a

mediocre good or a great capability in

my

manufacturing well that's our very brief

disc discussion of semiconductor

manufacturing next time we'll go back to

unit

processes and start talking about etch

till then