### Demystifying Measurements

### from HBM and CDM ESD Testers

### (How to Solve ESD Problems by

### Thinking in Pictures)

### Tim Maloney

### Intel Corp.

### IEW Seminar

### Outline

Tim Maloney, Intel Corp. 2

•Quick review of math background

•Complex impedances, Laplace Transforms, s-domain •HBM as a 2-pole circuit

•Extracting RC and network from waveform •Measurement aside: Transformer effects •CDM as a 2-pole circuit

•Network from I_{pk}, Q_{fp}, Q_{total} and V_{0 }

•Spark rise time and scope response may add poles •Oscilloscope bandwidth limits and effects on waveforms

•Measurement aside: 2-pole oscilloscope model •Other ESD examples: CCDM, TLP

•Antenna response to CDM events •ESD chair antenna

•Appendices:

### Flow Chart of Outline

Tim Maloney, Intel Corp. 3

Math review

HBM 2009-11

Antennas 2011-13

Thermal 2013-15

IEC, Chairs

2015 TLP, CCDM

2012

CDM 2013-14

### Math Review

Tim Maloney, Intel Corp. 4

Double Exponential (e.g., HBM) F(s) f(t) Differentiate: s d/dt

Integrate: 1/s ∫ Unit step: 1/s

Impulse: 1 ↑

Laplace Transform and inverse:

### Gaussian Convolution

Tim Maloney, Intel Corp. 7

### ⇔

“flip and slide”*

) exp(

)

( _{2}

2

*f*

*t*
*t*

*f*

τ

− =

2 2

2

**g* *f* *g*

*f* τ τ

τ = +

Source: www.wolfram.com

### Convolution in Excel

Tim Maloney, Intel Corp. 8

Suppose you have two functions with identical time steps and want to convolve them—these could be, for example, a digital record of a scope trace and a calculated filter impulse response in the time domain.

Once you have the filter impulse response, there’s no reason to sweat FFTs, number of points in powers of 2 (don’t you hate that?), etc., you can install free “Excellaneous” VB macros, at

http://www.bowdoin.edu/~rdelevie/excellaneous/#downloads , into Excel and use one of several convolution macros.

Macrobundle12 is the latest, appearing as a Word file.

This is what was done for modeling oscilloscope response in a 2011 EOS/ESD paper,

### Flow Chart of Outline

Tim Maloney, Intel Corp. 9

Math review

HBM 2009-11

Antennas 2011-13

Thermal 2013-15

IEC, Chairs

2015 TLP, CCDM

2012

CDM 2013-14

**Two-pole HBM (or CDM) Network **

### ,

### 1

### )

### (

_{2}

### +

### +

### =

*RCs*

*LCs*

*Cs*

*s*

*Y*

### )

### (

### )

### (

### ),

### 1

### (

### )

### (

_{0}0

*a*

*s*

*s*

*aV*

*s*

*V*

*e*

*V*

*t*

*V*

*at*

### +

### =

### −

### =

−**C **

**L **

**R **

### So

### )

### )(

### )(

### (

### )

### (

0*c*

*s*

*b*

*s*

*a*

*s*

*abc*

*CV*

*s*

*I*

### +

### +

### +

### =

_{and }

*c*

*b*

*RC*

### =

### 1

### +

### 1

### (Vieta, 1579)

Slide 11

**Elmore Theorem (1948) **

### ∫

∞ −### =

0*dt*

*e*

*t*

*h*

*s*

*H*

**(**

**)**

**(**

**)**

*st*

### ∫

∞### ⋅

### ⋅

### ⋅

### +

### −

### +

### −

### =

0 3 3 2 2### 6

### 2

### 1

*st*

*s*

*t*

*s*

*t*

*dt*

*t*

*h*

**(**

**)[**

**]**

### ∑

∞_{∫}

=
∞
### −

### =

0_{0}

### 1

*k*

*k*

*k*

*k*

*dt*

*t*

*h*

*t*

*s*

*k*

**!**

**(**

**)**

**.**

**)**

**(**

### A waveform

*h(t)*

### transforms and expands in powers of t:

### 0

th_{ moment (k=0) is integral (total charge Q}

t

### for HBM)

**Waveform Moments **

### ∫

∞

### =

0

0

*I*

*t*

*dt*

*m*

**(**

**)**

### = charge Q

### = centroid (time)

### = Elmore Delay

### = 2

nd_{ moment }

### For a current function,

### I(s)=

*m*

_{0}### (

*1+m*

_{1}*s+m*

_{2}*s*

*2*

_{+…+m}

_{+…+m}

*n*

*s*

*n*

### )

### ∫

### ∫

∞ ∞### =

### −

0 0 1*dt*

*t*

*I*

*dt*

*t*

*tI*

*m*

**)**

**(**

**)**

**(**

### ∫

### ∫

∞ ∞### =

0 0 2 2### 2

*I*

*t*

*dt*

*dt*

*t*

*I*

*t*

*m*

**)**

**(**

**!**

**)**

**(**

Slide 13

**Simple extraction of any moment **

### Start with a network function (impulse response),

### N(s)=

*a*

_{0}*+a*

_{1}*s+a*

_{2}*s*

*2*

_{+…+a}

_{+…+a}

*n*

*s*

*n*

### Step response (HBM, CDM, TLP) is

### M(s)=

*a*

_{0}*/s+a*

_{1}*+a*

_{2}*s+…+a*

_{n}*s*

*n-1*

### DC offset (

*a*

_{0}*/s) *

### gives

*a*

_{0}*, *

### remove to

### get

### L(s)=

*a*

_{1}*+a*

_{2}*s+…+a*

_{n}*s*

*n-1*

### Now integrate to get

### K(s)=

*a*

_{1}*/s+a*

_{2}*+…+a*

_{n}*s*

*n-2*

### DC offset gives a

_{1}

### .

### Successive

### Integration*

Tim Maloney, Intel Corp. 14

) ) 2 ) (( ) ( 1 ( ) 2 1 )( 1 ( ) ( 2 2 2 0 2 2 2

0 ≈ − + + + − − − +_{}

+ + +

+

= *CV* *RC* *s* *RC* *LC* *RC* *s*

*s*
*s*
*LCs*
*RCs*
*CV*
*s*

*I* _{e}_{e}_{e}*e*

*e*
*e*
τ
τ
τ
τ
τ
τ

0.5 1.0 1.5 2.0

2 2 4 6 8

Expand I(s) around s=0, using

Now integrate, i.e., multiply by 1/s, to get charge Q(s):

) ) 2 ) (( ) ( 1 ( ) ( ) ( 2 2

0 − + + + − − − +

≈

= *RC* *RC* *LC* *RC* *s*

*s*
*CV*
*s*
*s*
*I*
*s*
*Q* *e*
*e*
*e*
*e*
τ
τ
τ
τ

This is primarily a step of height CV_{0 }, the total charge Q

0.5 1.0 1.5 2.0

2.5 Now suppose we normalize, remove the

step and integrate again…
current
charge
+
+
+
+
=
−
3
2
1
1
1
*x*
*x*
*x*
*x*

### Time Constant from Integration

Tim Maloney, Intel Corp. _{15 }

+ − − − + + + − ≈ − ) 2 ) (( ) ( 1 ) (

1 2 2

0
*e*
*e*
*e*
*e*
*RC*
*LC*
*RC*
*s*
*RC*
*s*
*CV*
*s*
*Q*
*s*
τ
τ
τ
τ

Again, suppose we normalize, remove the step and integrate again…

This is a (negative) step that measures
RC+τ_{e} (=A_{1}-A_{2}+A_{3} areas):

0.5 1.0 1.5 2.0

0.2
0.4
0.6
0.8
1.0
1.2
A_{1 }
A_{2 }
A_{3 }
Q(t)/CV_{0 }
nsec

We now have C
from V_{0} and
integrating I(t) to
get Q. We get R
from the 2nd

integration if we can estimate

### About Successive Integration

Tim Maloney, Intel Corp. 16

0.5 1.0 1.5 2.0

2 2 4 6 8 nsec amps

Centroid, 267 psec

RC+τ_{e } is the centroid
(“balance point”) of the
original current waveform

Remove the time constant, continue the integration and you get an expression including inductance L. This can be repeated to the limits of measurement accuracy.

+ − − − + + + − ≈ − ) 2 ) (( ) ( 1 ) (

1 2 2

Slide 17

**Obtaining true RC time constant **

### RC=A/Q

_{t}

### , the Elmore Delay of the integrated HBM current

t t

### Q

### Q

### RC

### ∫

### ∫

∞

###

###

###

###

###

###

### −

### =

0 0*dt*

*d*

*τ*

*τ*

*h*

*t*

**)**

**(**

**Current Transformers for HBM Waveforms **

### )

### )(

### (

### )

### (

*b*

*s*

*a*

*s*

*s*

*s*

*T*

### +

### +

### =

### Transfer function:

### where

*a *

### = 1/

### τ

_{xf}

### (lo-freq cutoff)

*b *

### = 1/

### τ

_{hf}

### (hi-freq cutoff )

*s*

### =

### σ

### + j

### ω

### (complex frequency)

### Zero at

*s *

### = 0 guarantees

### eventual zero integral

Slide 19

**Tektronix CT1, CT2 Current Probes* **

*figures used with permission from Tektronix, Inc.

### 1 MHz

_{10 KHz }

**Current Probe Step Response **

### •

### For CT1,

### τ

_{xf}

### ≈

### 6.35

### µ

### sec

### •

### For CT2,

### τ

_{xf}

### > 100

### µ

### sec

### •

### This has considerable effect as “real” waveform transforms

### to measured waveform

### – Impulse response is derivative of step response

### – Convolution means eventual negative values measured

**V**

**t**

### τ

_{xf}**V**

**t**

### τ

_{xf}### step

### impulse

Slide 21

**HBM 0 **

### Ω

** Waveform, CT1 Convolution **

### ∫

∞

### −

### =

0

1

### (

*t*

### )

*HBM*

### (

### τ

### )

*CT*

### 1

### (

*t*

### τ

### )

*d*

### τ

*HBM*

_{CT}

_{imp}**HBM waveform, calculated**

0 1 2 3 4 5 6 7

0 100 200 300 400 500 600 700 800 900

**time, ns**
**c**
**u**
**rr**
**e**
**n**
**t,**
** a**
**rb**
** u**
**n**
**it**
**s**

**HBM and CT1 convolution**

-0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07

660 680 700 720 740 760 780

**time, ns**
**c**
**u**
**rr**
**e**
**n**
**t,**
** a**
**rb**
** u**
**n**
**it**
**s**
CT1 HBM
pure HBM

### Calculation shows zero crossing of measured waveform

Slide 22

**4-pole HBM model, with socket cap C**

_{2}

_{2}

**C**

_{hb}**C**

_{1}**R**

_{hb}**L**

_{1}**C**

_{2}**R**

_{1}### When R

_{1}

### = 500

### Ω

### ,

### ,

### 1

### )

### 1

### (

### )

### (

_{4}500 4 3 500 3 2 500 2 500 1 1 0 500

*s*

*b*

*s*

*b*

*s*

*b*

*s*

*b*

*s*

*C*

*R*

*C*

*V*

*s*

*I*

*hb*

*hb*

− − − −

### +

### +

### +

### +

### +

### =

*b*

_{1-500}

### =R

_{hb}

### (C

_{hb}

### +C

_{1}

### )+R

_{1}

### (C

_{hb}

### +C

_{2}

### ),

Slide 23

0 0.5 1 1.5 2 2.5 3 3.5

0 100 200 300 400 500

**time, nsec**

**Cu**

**rre**

**n**

**t,**

** A**

**4 kV 0**

### Ω

** HBM Waveform with CT1 **

### t

_{d}

### = 126 nsec

**decay constant t**

_{d}** is out of spec **

**CT2 removes droop and t**

_{d}** is in spec **

### 36.8% I

_{pk }

**Cu**

**rre**

**n**

**t,**

**Effects of Low-Frequency Cutoff **

**CT2 and CT1, 500 ohm**

-0.01 -0.005 0 0.005 0.01 0.015 0.02 0.025 0.03

760 780 800 820 840 860 880 900 920

**time, nsec**

**cu**

**rr**

**en**

**t,**

** A**

### CT1

_{CT2}

### CT2 provides a more accurate waveform tail

Slide 25

**0 **

### Ω

### and 500

### Ω

### HBM waveforms

### )

### C

### (C

### R

### C

### R

### C

### R

### b

### C

### R

2 hb

1 hb

hb 1

hb 500

1 500

hb hb

### +

### +

### =

### −

### =

### =

−

### τ

### τ

_{0}

**Socket Capacitance C**

_{2}

_{2}

**, from Waveforms **

*hb*

*C*

*R*

*C*

### =

### −

### −

500 0 500

2

### τ

### τ

**Tester**

**C**

_{hb}**, pF**

**R**

_{hb}**, k**

### Ω

### τ

_{0}**, nsec **

### τ

_{500}**, nsec **

**C**

_{2}**, pF**

### MK-4

### 114

### 1.412

### 161

### 225

**13.9 **

Zapmaster

512

### 101

### 1.445

### 146

### 222

**51 **

Zapmaster

Slide 27

**Designing for Reduced Socket Capacitance **

**C _{1}**

**C _{hb}**

**R _{hb}**

**Z _{0}**

**R _{1}**

**V _{0}**

**Z _{in}**

### Most tester “socket” cap is distributed, can benefit

### from high Z

_{0}

### Could raise Z

_{0}

### with ferrites…

2 1

2 1

2 0 2

1

### 1

### )

### 1

### (

### 1

### 1

*C*

*s*

*R*

*R*

*Z*

*sC*

*R*

*Z*

*Y*

*in*

*in*

### =

### ≈

### +

### −

### =

### +

### α

### α

### , reduces effective cap

2 1 0

*C*

*L*

Slide 28

**Using Distributed Resistance in Tester **

**α**

**C**

_{2}**Z _{0}’_{, R}**

**a**

**Y**

_{in}**R**

_{1}**R**

_{1}**R**

_{a}### Take some of

### R

_{hb }

### and

### distribute in-line

###

###

###

###

###

###

###

###

###

###

###

###

### +

### ′

### −

### +

### +

### +

### ≈

### )

### (

### 1

### 1

1 1 2 0 1 1 21

*R*

*R*

*R*

*Z*

*R*

*R*

*R*

*sC*

*R*

*R*

*Y*

*a*

*a*

*a*

*in*2 ' 0

*C*

*L*

*Z*

### =

*t*

### α

### , reduces effective cap

### For

### α

### <0.5, need

2 1 2

0 2

### 2

*Z*

*R*

*R*

_{a}### +

### ′

### >

### If R

_{1 }

### = 500

### Ω

### ,

Slide 29

**Additional Discussions in the Paper **

### •

### Expression for full loop HBM current I

_{full}

### (s) for 4-pole

### model

### •

### Expansion of H(s) transfer functions

### •

### Pole-zero sum rules

### – From Vieta, 1579

### – Use sum rule to calculate effect of inductance L

_{1}

### on 0

### Ω

### HBM waveform rise time

### •

### These and other concepts adopted from the signal

### integrity field

**HBM Paper Conclusions **

### •

### Current probe transformers examined

### – Tek CT2 is more agreeable for HBM time

### decay spec, little droop due to low-f cutoff

### • CT1 still ok for most spec-related measurements

### • CT2 is now called out in JS-001 HBM spec (2012)

### – Tek CT2 also works better for integrals,

### centroids needed for HBM circuit model

### elements (accurate asymptotic properties)

### •

### 4-pole HBM model with socket cap re-examined

### – Analysis: Time constants (centroids) of 0

### Ω

### and 500

### Ω

### waveforms readily yield socket cap

### value C

_{2}

Slide 31

**HBM Paper Conclusions, cont’d **

### •

### Synthesis: Design strategies for reducing tester C

_{2}

### – “Socket” cap is mostly distributed along line

### – Analytical model points to lower effective C

_{2}

### :

### • Effective line Z

_{0}

### can be raised

### – Ferrite loading

### • Part of R

_{hb}

### (e.g., 300 out of 1500

### Ω

### ) can be distributed

### along that line

### • Effective cap can thus be reduced by half or more

**More HBM Trickery (and pictures) **

### See Appendix II, IEW11 presentation

### •

### HBM double exp: What are the poles?

### •

### Short

### τ

### (a few nsec) from I(t) rise time

### •

### Long

### τ

### (about 150 nsec) from

### integrated current Q(t) rise time

### •

### Adjustments for 3-pole HBM

### Flow Chart of Outline

Tim Maloney, Intel Corp. 33

Math review

HBM 2009-11

Antennas 2011-13

Thermal 2013-15

IEC, Chairs

2015 TLP, CCDM

2012

CDM 2013-14

Slide 34

### CDM Tester simulates event

**Vf**

**Cg**
**300 M**Ω

**Cf**
**Cfrg**

**1 ohm disk **
**resistor here**
**dielectric to **

**field plate**

**top gnd **
**plane**

**.**
*****

+ +

+ =

**Cfrg****Cf**

**Cfrg****Cf**

**Cg****Cf**

**Cg****Cf****Vf**

**Q**_{imm}

**Immediate charge **
**packet is **

3 capacitors collapse to one equivalent “fast” cap

**Simplified CDM Network **

Slide 35

2

### 1

### )

### (

*LCs*

*RCs*

*Cs*

*s*

*Y*

### +

### +

### =

2 0

1 ) ( ) ( )

(

*LCs*
*RCs*

*CV*
*s*

*Y*
*s*
*V*
*s*

*I*

+ +

= =

**R**

**L**

**C**

**V(s) **

### ≈

**V**

_{0}**/s**

### •

### Examine step response of this network

### •

### R is spark resistance, ~25-30 ohms

**2-pole First Peak charge, Q**

_{fp}

_{fp}

### First half-cycle is what causes damage

2 4 6 8 10

0.1 0.1 0.2 0.3 0.4 0.5

2 4 6 8 10

0.2 0.4 0.6 0.8 1.0 1.2

Q_{fp }(area)

Q_{fp }(16% overshoot)

amps

nC

t, nsec

t, nsec
Example for D=0.5, RC_{0}=1 nsec, C_{0}V_{0}=1 nC:

### 1

### ),

### 1

### exp(

### 1

2 0 0### <

### −

### −

### +

### =

*D*

*D*

*D*

*V*

*C*

*Q*

_{fp}### π

) 1 ( )( 0 0 _{2}

*s*
*s*
*s*
*V*
*C*
*s*
*Q*
+
+
=
2
0
0
1
)
(
*s*
*s*
*V*
*C*
*s*
*I*
+
+
=

See Appendix A, esd13

0 0

### 2

*LC*

*RC*

*D*

### =

**2-pole I**

_{max}

_{max}

** = f(R**

_{eq}

_{eq}

**,D) **

Slide 37

### •

### For D>1

### •

### For D<1

### ))

### 1

### (

### tanh

### 1

### exp(

### 2

_{1}2

2 0 max

*D*

*D*

*D*

*D*

*D*

*R*

*V*

*I*

*eq*

### −

### −

### −

### =

−### ))

### 1

### (

### tan

### 1

### exp(

### 2

1 22 0 max

*D*

*D*

*D*

*D*

*D*

*R*

*V*

*I*

*eq*

### −

### −

### −

### =

−### Also maps to

### package size

### I

_{max}

### trend

### Lower C

_{0}

###

### lower

### D, lower I

_{max }0 0.2 0.4 0.6 0.8 1

0 1 2 3 4 5

**g**

**(D)**

**D -- Damping factor**

**I _{max}**

**= g(D) *V**

_{0}/R_{eq}### See Appendix B, esd13

0 0

**2-pole RLC calculation **

Q_{a }

Q_{fp }
V_{0 }
I_{max }

C_{0 }

L_{eq }
D

C_{max }

R_{eq }

### derived

### quantity

### measured

### quantity

0 0

### 2

*LC*

*RC*

*D*

### =

0 0

*V*

**Empirical Fit for C**

_{0 }

_{0 }

**vs. Target Size **

### •

### Metal targets (JEDEC, P4, P6) represent a worst

### case for equivalent capacitance of package area

### •

### Tester inductance and spark resistance give the

### rest of the circuit model

Slide 39 y = 0.6696x

0 5 10 15 20 25 30

0 10 20 30 40 50

**C**

**o**

**, p**

**F**

**Sqrt(Area), mm **

**Co vs. Target Size **

250V 500V

Linear (500V)

### τ

** = R**

_{eq}

_{eq}

***C**

_{0}

_{0}

** is linear vs. C**

_{0}

_{0}

small target

large target

Leq=2.39±0.6nH

Leq=4.26±0.4nH

### •

### Dielectric thickness variation, 14-59 mils, several

### companies

### •

### Linear Req*C

_{0}

### happens repeatedly

### •

### JEDEC targets, no ferrites; note low inductance Leq

### •

### 20.6

### Ω

### slope, 26 psec offset

**More **

### τ

** = R**

_{eq}

_{eq}

***C**

_{0}

_{0}

** linearity **

Slide 41 y = 20.562x + 68.704

0 100 200 300 400 500 600

0 5 10 15 20 25

**ta**
**u**
**=**
**R**
**e**
**q**
***C**
**o**
**, p**
**s**
**e**
**c**
**Co, pF **
**Orion2, 250V **

Leq=10.33±1.49 nH

y = 27.798x + 8.8219

0 100 200 300 400 500 600 700 800

0 5 10 15 20 25 30

**ta**
**u**
**=**
**R**
**e**
**q**
***C**
**o**
**, p**
**s**
**e**
**c**
**Co, pF **
**Orion2, 500V **

Leq=12.03±2 nH

### •JEDEC tester with ferrite (higher Leq)

### •JEDEC coins plus P4, P6 targets

20.6 Ω, 68.7 psec offset

### τ

** = R**

_{eq}

_{eq}

***C**

_{0}

_{0}

** linearity for 7 metal targets **

y = 27.482x + 56.849

0 100 200 300 400 500 600 700 800

0 5 10 15 20 25 30

**ta**

**u**

**=**

**R**

**e**

**q**

***C**

**o**

**, p**

**s**

**e**

**c**

**Co, pF **

**JEDEC, 500V **

### •JEDEC tester with ferrite, 500V

### •27.5

### Ω

### , 56.8 psec offset

**Air Spark + 25 ohms **

Slide 43

**Leq=11.62**±**1.16 nH **

### •

### Terminate CDM2 test head with SMA tee, 50

### Ω

### in each branch

### •

### 50

### Ω

### termination and 50

### Ω

### scope channel; 25

### Ω

### instead of 1

### Ω

### •

### Test like regular CDM, with air spark in series

### •

### No ferrites but extra Leq seems due to 50 ohm mismatch at top

### of test head

### •

### Req = 48.9

### Ω

### ; 25

### Ω

### plus air spark

**Example of 2-pole RLC fit**

### •

### 500V, 25

### Ω

### + air spark, 4.57pF small target

### •

### I

_{max}

### and Q

_{fp }

### match are guaranteed by method

**2-pole RLC fit for large JEDEC target**

### •

### JEDEC tester with ferrite, 500V

### •

### RLC fit is 28.6

### Ω

### , 11.7 nH, 16.3 pF

Slide 45

-4 -2 0 2 4 6 8 10 12

0 1 2 3 4

**cu**

**rr**

**en**

**t, A**

**time, nsec**

**Large JEDEC target, 500V**

measured 2-pole fit

**What can we do so far? **

### •

### With these methods, we can readily:

### •

### Estimate equivalent cap C

_{0}

### from package size

### •

### Estimate R

_{eq}

### from slope-intercept of

### τ

### = R

_{eq}

### C

_{0 }

### as

### measured by metal targets

### •

### Estimate L

_{eq}

### for ferrite/no ferrite situation

### •

### Therefore, generate a complete set of worst-case

### CDM waveforms for a given product situation

### – Focus on I

_{max}

### and Q

_{fp }

### at test voltage V

_{0 }

**I**

_{max}

_{max}

** vs. Q**

_{fp}

_{fp}

**, 25 ohm + air spark **

Slide 47

sm

lg

P4 P6

### •Come close to green (JEDEC) point at intermediate voltage for

### each target, closest approach being a least squares fit

### •JEDEC legacy result expected when I

_{max}

### , Q

_{fp}

### match

### •Data and analysis for 50

### Ω

### and 25

### Ω

### CCDM/CDM2 could be even

### better. See III.5 of text, esd13 paper.

**RLC element trend: Compression of D **

### •

### Why is the damping factor D compressed into a

### mid-range for so many measurements?

Slide 48

(a)

0 0.2 0.4 0.6 0.8 1 1.2

0 2 4 6 8 10 12 14

**da**

**m**

**pi**

**ng**

** fa**

**ct**

**or**

**, D**

**Co, pF**

**D vs. Co, dielectric thickness variation**

(b)

0 0

### 2

*LC*

*RC*

*D*

### =

**Damping factor and EM field dissipation **

### •

### D=1/

### √

### 2 maximizes field energy burn rate of spark,

### thus minimizing the time integral, A

_{e }

### (=

### √

### 2)

### •

### With optimized D(t) it is possible to beat

### √

### 2…

Slide 49 0 0

### 2

*LC*

*RC*

*D*

### =

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70 1 2 3 4 5 6

**Po**

**w**

**er**

**time units**

**I²R vs. time**

D=0.5 D=0.707 D=1

### A

_{p}D=0.5 D=1 (a) 0 0.2 0.4 0.6 0.8 1 1.2

0 1 2 3 4 5

**fr**
**ac**
**tio**
**n o**
**f E**
**time units**

**Remaining Field Energy vs. t**

D=0.707

(b)

### A

_{e}

See Appendix C, esd13

0

*LC*

**Why you should read the Appendices **

### •

### Appendix A:

### First Peak Charge (Q

_{fp}

### )

### – Take generalized i(t) expression for RLC,

### integrate first cycle, find that Q

_{fp}

### /C

_{0}

### V

_{0}

### = f(D)

### •

### Appendix B:

### Peak Current (I

_{max}

### )

### – Differentiate i(t) to find that I

_{max}

### is V

_{0}

### /R

_{eq}

### times a

### unique monotonic function g(D)

### •

### Appendix C:

### Maximum Burn Rate of Field Energy

### – Find i

2_{(t)R}

eq

### =P(t), convert to P(s), find that field

### collapse time is

### τ

### =D+1/2D, min at D=1/

### √

### 2

**Conclusions **

### •

### RLC calculation scheme for CDM waveforms

### – Used 4 measured quantities, V

_{0}

### , Q

_{fp}

### , Q

_{a}

### , I

_{max }

### – Spreadsheet extraction of RLC

###

### D to fit all 4

### quantities precisely

### •

### Linear trends allow RLC prediction:

### – C

_{0}

### goes as

### √

### Area of target/package

### –

### τ

### = R

_{eq}

### *C

_{0 }

### vs. C

_{0}

### is linear (slope-intercept)

### • Fits JEDEC, air spark + 25

### Ω

### , ferrite-free tests

### •

### JEDEC legacy conditions (I

_{max}

### ,Q

_{fp}

### ) approximated

### – With air spark + 25

### Ω

### , possibly better with CCDM

### •

### Damping factor D stays near maximum burn rate

Tim Maloney, Intel Corp. 52

### Simplified CDM Network (again)

2

### 1

### )

### (

*LCs*

*RCs*

*Cs*

*s*

*Y*

### +

### +

### =

**Examine step response of this network **

**R is spark resistance, ~25-30 ohms **

V(s)=Vo/s

2 0

1 ) ( ) ( )

(

*LCs*
*RCs*

*CV*
*s*

*Y*
*s*
*V*
*s*

*I*

+ +

Tim Maloney, Intel Corp. 53

### 2-pole CDM solutions

### •

### The poles are

### •

### where the damping factor, and

### •

### the characteristic frequency

### •

### Note only two independent variables for an

### RLC waveform profile

### •

### Thus the same waveform results with

### –

### L1=

### α

### L, C1=C/

### α

### , R1=

### α

### R,

### α

### >0

### –

### many ways to get the same profile

## [

2### 1

## ]

2 ,

1

### =

### −

*D*

### ±

*D*

### −

*P*

### ω

*LC*

*RC*

*D*

### 2

### =

*LC*

### 1

### =

### ω

54

### Definitions of CDM Tester Parameters

Tim Maloney, Intel Corp. d2-fplt

(effective)

±V

d1-fplt (probe)

upper gnd plate (Area=Afplt)

field plate

t-fplt

(dielectric thickness)

target dia

targ-th

probe radius = a

### L and C Model Parameters

Tim Maloney, Intel Corp. 55

Textbook references for C (e.g., Kaiser):

“Our” Bob Renninger for L, 1991 EOS/ESD:

d=d1, probe length

2a

### Measurements of Voltages on IC Leads

Slide 56

### • Device held by vacuum in a Discharge Test Fixture simulating

### an automated handler pick and place mechanism

### • Device held at a distance of 2.5 mm from ground

### • Device leads charged to a known voltage

### Discharge

### Test Fixture

### Discharge Target

### •

### Made with FR-4 double-sided PC board material

### •

### SMA connector on bottom

### •

### 50-ohm cable to LeCroy oscilloscope with 50-ohm input.

### •

### Current calculation based on 50 ohms

Slide 57

### Top

### Bottom

### Waveform Analysis

### •

### I

_{max}

### , Q

_{fp}

### , and Q

_{a}

### are calculated from

### oscilloscope data, while V

_{0}

### is the initial

### charging voltage

### •

### C

_{0}

### V

_{0}

### = fC

_{0}

### * V

_{0}

### /f where f = 1.5 for

### charging at 2.5 mm from ground

### •

### Previously described computation

### methods solve for R,L, and C

Slide 58

**Test fixture discharge for 500V, **
**64-pin device.**

Qa

Qfp

Vo

Imax

Co

Leq D

Cmax

Req

derived quantity measured quantity

*LC*

*RC*

*D*

### 2

### =

Time (500 psec/div) Pulse Height

2.27 Amps

### Blind Alleys and Dubious Ventures

### in CDM Modeling

Tim Maloney, Intel Corp. 59

•Method of Moments for fixture capacitance

•Parallel plate and fringing field estimates work well enough (but we’re glad MoM was done at least once) •Plasma physics modeling of spark

•Too many unknown quantities; may as well use linearized
models with R_{spark} and τ_{spark }

•1990s publications can help with the linearization •Field and ground plates are an open-circuited radial

transmission line but does it really have any ¼-wave effects? •Modeling hasn’t shown that the device feels much

•Maybe try a shorted package trace stub in conjunction… •Device could feel resonances that may not be

### CDM Summary

Tim Maloney, Intel Corp. 60

• CDM tester configuration and RLC equivalent • RLC circuit extraction from waveforms

• Exact matching of charge and peak current
• Remarkable result: RC = R_{0}C + τ_{0 }

• Describes how R varies with capacitance • Trends in damping factor D

• Estimating L and C from hardware properties

### Flow Chart of Outline

Tim Maloney, Intel Corp. 61

Math review

HBM 2009-11

Antennas 2011-13

Thermal 2013-15

IEC, Chairs

2015 TLP, CCDM

2012

CDM 2013-14

**The Problem **

### Same CDM pulse on fast and slow oscilloscopes

### Filter models needed for measurement channel

-4 -2 0 2 4 6 8 10

0 500 1000 1500 2000 2500

**c**

**u**

**rr**

**e**

**n**

**t,**

** A**

**m**

**p**

**s**

**time, psec**

**500V small JEDEC target**

8 GHz Tek scope

1 GHz Tek scope

**Use LTI* System Theory **

Slide 63

### *LTI=Linear, Time-Independent

### Generalized transfer function:

### Expansion in powers of s:

### Use to model voltage step and scope

*m>n *

Tim Maloney, Intel Corp. 64

Treats Gaussian, 1-pole, and 2-pole response functions:

2 2 D for 2 is ; 2 2 1 2 2 1 2 0 3 4 2 2 0

3 = − + ⋅ − + = π =

ω π

ω

*dB*

*dB* *D* *D* *D* *f*

*f*
2-pole bandwidth:
Gaussian bandwidth:
πτ
2
177
.
1
3*dB* =

*f* _{rise time }τ_{10-90%}_{=1.812}τ

### Bandwidth-Rise Time Product

Tim Maloney, Intel Corp. 65

for Gaussian and for 2-pole with 0.6<D<1. For pseudo-Gaussian, D=0.707.

3396 .

0 % 90 10

3*dB* ⋅

### τ

− ≅*f*

Convolved 10-90% rise times of Gaussian,

pseudo-Gaussian add in quadrature:

2 2 2

1 2

12

### τ

### τ

### τ

= +0 0

% 90 10

2 2D

RC ; 509 . 1 2

2 3396 . 0

ω ω

π

τ _{−} = ⋅ *RC* = *RC* = =

### Waveform Analysis

Tim Maloney, Intel Corp. 66

**C **

**L **

**R **

+
+
=
2
1
)
(
2
2
0
*s*

*s*

*s*

*V*

*s*

*V*

*e*

*e*τ τ Recall that

τ_{10-90%}=1.509τ_{e }for a
pseudo-Gaussian
)
2
1
)(
1
(
)
(
)
(
)
(
2
2
2
0
*s*
*s*
*LCs*
*RCs*
*CV*
*s*
*Y*
*s*
*V*
*s*
*I*
*e*
*e*
τ
τ +
+
+
+
=
=
Thus

Now has spark rise time. Add a scope filter (2 more poles, pseudo-Gaussian) if scope speed is an issue

### Waveform and Peak Current

Tim Maloney, Intel Corp. 67

Total charge Q(nC) for voltage V

84 psec rise time 3 GHz scope RLC series circuit

In Mathematica*, Ipeak can be extracted with a 1-line command:

For quadratic terms, *s* (σ+jω) in GHz and coefficients in nsec and nsec2

In this case, 60 mil diel thickness gives Ipk=5.495 amps and Q=0.8509 nC for 500V

*Mathematica is licensed software; some progress is possible with free I.L.T. app as cited in references.

+ + + + + + = ) 1 )( 0028 . 075 . 1 )( 0016 . 056 . 1 ( )

( _{2} 0 _{2} _{2}

*LCs*
*RCs*
*s*
*s*
*s*
*s*
*CV*
*t*

### 1-Whoa! What did he just do with

### that I(t) function?

Tim Maloney, Intel Corp. 68

Introduce 84 psec spark rise time:

3 GHz scope response:

0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 1.0 nsec

0.2 0.4 0.6 0.8 1.0
2
4
6
8
1.0 nsec
Scope modeling:
https://sites.google.com/site/esdpubs/
documents/esd11.pdf
+
+
⇒
+
+
⇒
2
0
2
0
0
2
0
2
0
0
0
2
1
2
1
ω
ω
ω
ω
*s*
*s*
*s*
*V*
*s*
*s*
*D*
*s*
*V*
*s*
*V*
2
0
2
0
2
1
1
ω
ω
*s*
*s*+
+

**Gaussian Convolution **

Slide 69

### Resulting Width:

### Bessel-Thomson filtering CDM RLC

Tim Maloney, Intel 70
Using FFPA book values L=6 nH, C_{sm}=5 pF, C_{lg}=15.76 pF,

Calculated ratio R_{lg}=0.9, R_{sm}=0.75.
Curve is nearly insensitive to D when D<1

Measured ratio R_{lg}=0.899, R_{sm}=0.74 (5 or 6 samples)
J-lg

J-sm

Ratio=Ipk_{1GHz}/Ipk_{8GHz }

JEDEC CDM targets

noted

Presented at Sept 2013 CDM

### TDMR version of esd13 (CDM models)

Tim Maloney, Intel Corp. 71 convolved

(a)

next slide

### CDM I

_{max}

### multiplier for D

### ≈

### 0.707

Tim Maloney, Intel Corp. 72 (b)

Good estimate of peak current change

given scope bandwidth and FWHM, using 2-pole

pseudo-Gaussian scope model

### Further notes on CDM waveform

### xforms

### FWHM adds in quadrature, as with rise time formula

### from Gaussian math in 1999 M-S paper:

### •

### FWHM of f

_{0}

### =1 GHz is 507 psec; scale from there

### •

### Q

_{fp}

### (first peak charge) not affected much; often <1%

### •

### If FWHM > 1/f nsec, Imax multiplier

### ≈

### 1, no correction

### •

### Our CDM committee’s Orion2 data fits pretty well

### •

### Large target correction for 1 GHz is 10-13%

### •

### Small target should use 2-3 GHz scope & correct

### •

### Small target is at least 40% low for 1 GHz

### 4-pole Bessel-Thomson scope filter

Tim Maloney, Intel Corp. 74

### )

### 1

### )(

### 2

### 1

### )(

### 2

### 1

### (

### )

### (

2 2 02 2 02 2 2 01 2 01 1 0*LCs*

*RCs*

*s*

*s*

*D*

*s*

*s*

*D*

*CV*

*s*

*I*

### +

### +

### +

### +

### +

### +

### =

### ω

### ω

### ω

### ω

For f_{3dB}=1 GHz,

ω_{01}=10.07439 GHz
D_{1}=0.620703

ω_{02}=8.9862 GHz
D_{2}=0.957974

Scalable to any f_{3dB}!

### Flow Chart of Outline

Tim Maloney, Intel Corp. 75

Math review

HBM 2009-11

Antennas 2011-13

Thermal 2013-15

IEC, Chairs

2015 TLP, CCDM

2012

CDM 2013-14

### TLP s-domain Model

Tim Maloney, Intel Corp.

R_{d }

Z_{0}, τ

V_{0}/s
Z_{in} of an open-circuited

transmission line of

impedance Z_{0}, transit time

τ, is Z_{0} coth(τs)

Wave series with time step 2τ, round-trip transit time Simple square pulse if reflection coefficient = 0:

### [

### ]

2 0_{0}

2
0
0
0
0 _{,}_{ }
)
1
(
1
)
(
)
coth(
)
(
*Z*
*R*
*Z*
*R*
*e*
*e*
*R*
*Z*
*s*
*V*
*s*
*Z*
*R*
*s*
*V*
*s*
*I*
*d*
*d*
*s*
*s*
*d*
*d* +
−
=
−
−
+
=
+

= −_{−}

### ρ

### ρ

### τ

ττ

### [

### ]

*k*

*k*
*d*
*k*
*t*
*u*
*k*
*t*
*u*
*Z*
*R*
*V*
*t*

*I*

### ∑

τ τ ρ### CCDM in the s-domain

Tim Maloney, Intel Corp. 77

Z_{0 }

Z_{0}, τ

V_{0}/s

Z_{L }
CCDM Z_{L} is (nearly)

sL +1/sC but could
be anything for this
general expression.
)
sinh(
)
cosh(
)
sinh(
)
cosh(
)
(
)
sinh(
)
cosh(
)
sinh(
)
cosh(
1
1
)
( 0
0
0
0
0
0
0
*s*
*s*
*s*
*Z*
*Z*
*s*
*Z*
*Z*
*s*
*V*
*s*
*Z*
*s*
*Z*
*s*
*Z*
*s*
*Z*
*Z*
*s*
*V*
*s*
*I*
*L*
*L*
*L*

*L* τ τ

τ
τ
τ
τ
τ
τ +
+
⋅
+
=
+
+
+
⋅
=
*s*
*L*
*L*
*e*
*Z*
*Z*
*s*
*V*
*s*
*sZ*
*V*
*s*
*s*
*s*
*s*
*Z*
*Z*
*s*
*V*
*s*
*sZ*
*V* _{τ}
τ
τ
τ
τ
τ
τ
2
0
0
0
0
0
0
0
0
)
(
1
)
coth(
1
)
sinh(
)
cosh(
)
sinh(
)
cosh(
)
(
1
)
coth(

1 _{⋅} −

+ + + ⋅ = + − ⋅ + + + ⋅ =

### CCDM 2-pole Model

Tim Maloney, Intel Corp. 78

### C

### V(s)

### ≈

### Vo/s

### L

### Z

_{0 }

•The transmission line impedance Z_{0} replaces the spark
resistance, aside from relay spark

•Z_{0}=50 ohms is higher than usual air spark R, resulting
in lower Ipeak for given V_{0}, but stability is good

### Flow Chart of Outline

Tim Maloney, Intel Corp. 79

Math review

HBM 2009-11

Antennas 2011-13

Thermal 2013-15

IEC, Chairs

2015 TLP, CCDM

2012

CDM 2013-14

**Objectives (from esd12 & related pubs) **

### •

### Assembly factory

*in situ *

### static event monitoring

### • Need for 3-D chip assembly with hi-speed I/O

### •

### Antenna and detector arrangement in factory

### • Create CDM events at will using CDMES (event

### simulator) with antenna and detector

### •

### Detector calibrated with a “standard” pulse

### • Artificial, reproducible antenna-like pulse

### •

### Present theory of

**Outline **

### •

### CDM as a 2-pole circuit

### • Add spark rise time, map to time domain

### •

### CDM as a source of dipole radiation

### • Detect with monopole antenna

### • s-domain expressions for everything

### •

### Measured antenna signal, agrees with theory

### •

### Artificial antenna signals with “monocycle” pulser

### • Theory and experiment, compared favorably

### • Calibration of MiniPulse detector with monocycle

### pulser

**Simplified CDM Network **

### •

**Examine step response of this network **

### •

**R is spark resistance, ~25-60 ohms **

**V(s)=Vo/s **

### C

### L

**CDM dipole radiation, monopole **

**antenna **

Slide 83

### Experimental arrangement of CDM electric dipole

### initial source

**p**

### and 6 mm coaxial antenna.

### to 50

### Ω

### scope

**p**

### 15 cm

**150 cm monopole antenna **

•- - - - - -

Charge plate

### Coax to 50 ohm scope

Ground plate

**CDM Event Simulator (CDMES) **

### CDM pulse generator. Charge plate probe hits

### pedestal and dipole collapses, with current pulse and

### dipole radiation.

10 Meg

### +V

+++++ +++++ - - - - - -

**Simco-Ion CDMES Model **

### 7” long. Voltage cable and signal coax cable shown.

10 Meg

Charge plate

Coax to 50 ohm scope +V

Ground plate

-Slide 87

**Electric Dipole “equatorial” field **

sinθ=1 at equator

### In the s-domain,

s=σ+jω

### But we know that

### So

### Solve in time domain with inverse Laplace Transform;

### pole-zero expansion in natural frequencies

s=σ+jω

**Calculated current and field **

Slide 89

### Calculated CDM current pulse,

### 1 nsec full scale.

### E-field pulse E

_{θ}

### at 15 cm from CDM

### current source; 1 nsec full scale.

**Antenna Transfer Function **

### From Ref. 10, esd12

### (2007 Trans. EMC)

**Transfer function in terms of initial **

**dipole source p **

Slide 91

### Calculated antenna response to E-field,15

### cm from CDM source, 1.5 nsec full scale

**Adjust the current function slightly… **

Slide 93

### Measured current (top) and antenna response (bottom) to

### E-field at 15 cm, using artificial CDM source; 2 nsec/division

-100V pulse -0.496 A

max

125 mV =Vp-p -166.4 pC

antenna, 15 cm current

1.664 pF

### Antenna problem—ESD effects in chairs

Tim Maloney, Intel Corp. 94

Math review

HBM 2009-11

Antennas 2011-13

Thermal 2013-15

IEC, Chairs

2015 TLP, CCDM

2012

CDM 2013-14

### Recent Vermillion-Smith paper*

95

500mV/div, 20 ns/div, 50 Ω antenna termination Antenna is 15 cm long. Suppose it is #18AWG wire.

With concepts in this presentation, you can estimate the initial static field (in kV/cm) at the antenna. The

field then collapses over the time scale shown. You can also prove that the “radiation” is quasi-static, with

very little signal due to 𝑝̇ and 𝑝̈.

### ESD Publications

Tim Maloney, Intel Corp. 96

Download most from TJM ESD publications page:

https://sites.google.com/site/esdpubs/documents

**HBM: **

https://sites.google.com/site/esdpubs/documents/esd09.pdf https://sites.google.com/site/esdpubs/documents/esd10.pdf

https://sites.google.com/site/esdpubs/documents/MR13.pdf (nearly the same as esd10)

plus TJM, IEW 2011 (unpublished)

**CDM: **

https://sites.google.com/site/esdpubs/documents/esd13.pdf

https://sites.google.com/site/esdpubs/documents/tdmr14.pdf (augmented esd13) https://sites.google.com/site/esdpubs/documents/esd14.pdf (with Arnie Steinman)

https://sites.google.com/site/esdpubs/documents/Ipk-engnrg-2.xlsx (CDM tester modeling program, Excel file)

B. Atwood, et al., “Effect of Large Device Capacitance on FICDM Peak Current”, 5A.1, 2007 EOS/ESD Symposium, pp. 273-282.

**Oscilloscope filter models: **

https://sites.google.com/site/esdpubs/documents/esd11.pdf

**Antennas: **

https://sites.google.com/site/esdpubs/documents/pulsdipole11-emc.pdf https://sites.google.com/site/esdpubs/documents/esd12.pdf

https://sites.google.com/site/esdpubs/documents/emc13-proof.pdf (augmented esd12)

### Publications, cont’d

Tim Maloney, Intel Corp. 97

**Thermal, s-domain: **

https://sites.google.com/site/esdpubs/documents/irps13.pdf

plus Industry Council EOS Whitepaper section (not yet published)

**TLP, CCDM, s-domain: **

2012 TJM Seattle ESDA Tutorial (unpublished)

Pre-work for 2012 Seattle Tutorial (with RLC net practice):

https://sites.google.com/site/esdpubs/documents/prework-tjm1.pdf

**IEC, s-domain: **

TJM Abstract, 2015 EOS/ESD Symposium:

### Other References

Tim Maloney, Intel Corp. 98

• Free online inverse Laplace Transform applet:

http://www.eecircle.com/applets/007/ILaplace.html • Free “Excellaneous” VB macros for Excel, at

http://www.bowdoin.edu/~rdelevie/excellaneous/#downloads

• Rise time-bandwidth, quad addition, pseudo-Gaussians, etc.: C. Mittermayer and A. Steininger, “…Dynamic Errors for Rise Time Measurement with an Oscilloscope”, IEEE Trans. Instrumentation and Measurement", Vol. 48, pp. 1103-1107, December 1999.

• 1998 Lucent paper: R.E. Carey and L.F. DeChiaro, “…Physical Design Parameters in FICDM ESD Simulators …", 1998 EOS/ESD Symposium Proceedings, pp. 40-53.

•Y. Ismail, et al., “Equivalent Elmore Delay for RLC Trees”, ACM DAC, 1999.

•K. Verhaege, et al., “Analysis of HBM ESD Testers…”, EOS/ESD Symposium Proc., 1993, pp. 129-137.

### Appendix I—Metal heating, thermal effects,

### temp waveforms—from IRPS13

Tim Maloney, Intel Corp. 99

Math review

HBM 2009-11

Antennas 2011-13

Thermal 2013-15

IEC, Chairs

2015 TLP, CCDM

2012

CDM 2013-14

### Metal Self-Heating Test Pattern

100

M5

*t*
*V*
*RC*
*x*

*V*

∂ ∂ =

∂ ∂

2 2

heat flow for 1-D heat slab:

*Cp*
*sK*
*Z _{th}*

ρ

1

=

s=σ+jω

*K*
*Cp*
*s*

*th*

ρ

γ = _{Electrical: } _{Thermal: }

Volts ⇒ °C, temperature (usually a ∆T from room T) Amps ⇒ Watts

Coulombs ⇒ Joules

Ohms ⇒_{ thermal impedance }°_{C/W }

Farads ⇒ Joules/°C

1 µm2_{ metal cross section; electrical current through M5 }

K=thermal conductivity Cp=heat capacity

ρ=mass density

### Wires Embedded in ILD Oxide

101

M5

w_{m}+g

…… ……

w_{m}

t_{ox} hm

C_{metal}

Z_{01}, γ_{ox}tox

ZL Z02, γoxg/2

P(t)

Pattern C as shown

Pattern D is wider, g_{D}=2g_{C }

Thermal circuit model:

Note open circuit b.c. Thermal Ohm’s Law:

### Thermal Feedback Model

102

### +

### Z(s)

### α

### T(t)P

_{0}

### (t)

### P

_{0}

### (t)

### P(s)Z(s)=T(s)

### α

_{= metal tempco}

### T = temp (“voltage”)

### P

_{0}

### = I

2_{R}

0

### in (“current”)

### ))

### (

### 1

### (

### )

### (

*t*

*R*

_{0}

*T*

*t*

*R*

### =

### +

### α

α = metal tempco=0.0025/°C for Cumetal resistance ) ( * )] ( ) ( [ ) ( * ) ( )

(*t* *P*_{0} *t* *Z* *t* *T* *t* *P*_{0} *t* *Z* *t*

*T* = +

### α

### [

### ]

) ( ) ( * ) ( ) ( 1 ) ( * ) ( ) ( 0 0*t*

*T*

*t*

*Z*

*t*

*P*

*t*

*T*

*t*

*Z*

*t*

*P*

*t*

*T*α − =

or =

### ∫

− ⇔*t*
*s*
*Z*
*s*
*P*
*d*
*Z*
*t*
*P*
*t*
*Z*
*t*
*P*
0
0
0

0( )* ( ) ( τ) (τ) τ ( ) ( )

For “current"

source
P_{0}(t):

mixer

thermal Ohm’s Law

### General Feedback Network

103

### +

### Z(s)

### FB(t)

### P

_{0}

### (t)

### Convolve

### P(t)*Z(t)=T(t)

### T(t)

Z(s)⇔Z(t)

For TLP:

### (

### )

20
0
2
0
0
0
50
)
(
+
=
=
*R*
*R*
*V*
*P*
*t*
*P*
−
+
+
+
= 1
50
)
(
1
)
(
1
)
( _{2}
0
0
0
*R*
*t*
*T*
*R*
*t*
*T*
*P*
*t*
*FB*
α
α

•Because of source resistance Z_{s}=50Ω, TLP introduces negative

feedback, and when R(t)>50 Ω, it becomes net negative

•Current source produces

positive feedback

•Voltage source produces

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0 50 100 150 200 250 300

**Amp**
**lit**
**ud**
**e **
**nsec **
exp fit
FEM data
118
.
0
432
.
0
142
.
0
)

(*t* = *e*−*t*/2.88 + *e*−*t*/71.4 +
*Z*

### Z(t) from Finite Element Modeling

differentiate and normalize

### Step response gives

### thermal

### impulse response

### Z(t)

104 0 100 200 300 400 500 600 700 800

0 200 400 600 800 1000

**de**
**lta**
**-T,**
** d**
**eg**
** C**
**nsec**

**FEM raw data**

8.44W step, M6 8.44W, M6-M7-M8

105

0 o_{C }

430 o_{C }

Close-up of metal after 200 nsec

### FEM results

M4 M5 M6

### Transmission Line Pulsing (TLP)

### •

### Transmission line pulsing generates brief, high current (several ampere)

### pulses; same current/time scale as ESD

### Setup:

### •

### Equivalent circuit

**50 ohms**
**Device**

**Scope**

**L**

**V**
**10 Meg**

**(R _{device}<50 **Ω

**):**

**50 ohms**

**Device**

**Scope**

**I _{device}=(V-V_{device})/50 **

** t _{pulse} = 2L/c, c=20 cm/nsec **

Apply to metal lines and use Cu tempco (α=0.0025) for *in-situ* T measurement

### TLP data

107
A_{C }

calculated from FB(t)

*C*
*e*

*t*

*T*( ) ≈ 440(1− −*t*/58)

measured 0 2 4 6 8 10 12 14

0 50 100 150 200 250

**W**

**atts**

**nsec**

**TLP Power, M5-C-60V**

Apwr

measured

### Pattern C, 60V

)
47
1
(
09
.
4
39
.
8
)
(
*s*
*s*
*W*
*s*
*W*
*s*
*P*
+
+
=
)
58
1
(
440
)
(
*s*
*s*
*C*
*s*
*T*
+
=

### Thermal Impedance

108 2 0 0 2 0 0 ) 50 (*R*

*R*

*V*

*P*+

= _{for TLP}

2
0
1
2
1
0
2
1
1
1
1
2
1
2
1
)
)
(
(
1
)
1
)(
(
)
(
*s*
*C*
*C*
*R*
*R*
*s*
*C*
*R*
*R*
*C*
*R*
*s*
*C*
*R*
*R*
*R*
*R*
*s*
*Z*
+
+
+
+
+
+
=

•Z(s) from slide 10 has 2 poles and 1 zero; 5-element RC network
•For TLP, temp should flatten out at P_{final}(R_{1}+R_{2}) = P_{final}Z_{0} = T_{final }

P(t) ⇔ P(s) C_{0 }

C_{1 }

R_{1 }
R_{2 }

### C

_{0}

### = 1.1 nJ/

### °

### C (metal + oxide)

### R

_{2}

### = 32.7

### °

### C/W (oxide)

### C

_{1 }

### = 20 nJ/

### °

### C

### R

_{1}

### = 2.52

### °

### C/W

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.91

0 50 100 150 200

**Am**

**pl**

**itu**

**de**

**nsec**

**Z(t) from TLP data (°C/nJ)**

) 00718 . 0 0185 . 0 ( 26 . 35 )

(*t* *e* *t*/31.6 *e* *t*/58

*Z* = − + −

109 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

0 5 10 15 20

**Am**

**pl**

**itu**

**de**

**nsec**

**Z(t) at short times**

Dt model TLP data

*Dt* model _{adiabatic}

**Thermal Impulse Response **

)
58
1
)(
6
.
31
1
(
47
1
26
.
35
)
(
*s*
*s*
*s*
*s*
*Z*
+
+
+
=

from °C/W

thermal sheath for
short time:
*Dt*
……
……
)
(
)
(
*s*
*P*
*s*
*T*
=

**TLP on Patterns C and D, 60V, 1 **

### µ

_{m}

_{m}

**2**

_{cross-section }

_{cross-section }

110

### Pattern C width = X

### T

_{final}

### = 440

### °

### C (“volts”)

### Z

_{0C}

### = 35.26

### °

### C/W (“ohms”)

### P

_{0}

### = 8.24W, P

_{final}

### =12.16W

### A

_{C}

### (normalized) = 58 nsec

-100 0 100 200 300 400 500

0 50 100 150 200

**de**
**lta**
**-T,**
** d**
**eg**
** C**
**nsec**
**M5-C-60V**
A_{C }

### Pattern D width = 1.48X (g

_{D}

### =2g

_{C}

### )

### T

_{final}

### = 225

### °

### C (“volts”)

### Z

_{0D}

### = 23.2

### °

### C/W (“ohms”)

### P

_{0}

### = 8.24W, P

_{final}

### =10.99W

### A

_{D}

### (normalized) = 46 nsec

-50 0 50 100 150 200 250 300 350

0 50 100 150 200

**de**
**lta**
**-T,**
** d**
**eg**
** C**
**nsec**
**M5-D-60V**
A_{D }

α= 0.0025

g_{C} ….

### Thermal Circuit Elements

111

P(t) ⇔ P(s) C_{0}

C_{1}

R_{1}
R_{2}

**Pattern TLP Volts ** **C _{0 }**

**R**

_{2 }**R**

_{1 }**C**

_{1 }**T**

_{final }C 60 1.1 nF 32.7Ω 2.52Ω 20 nF 440 °C C 70 1.09 nF 33.9Ω 2.84Ω 21.7 nF 645 °C D 60 1.53 nF 21.9Ω 1.33Ω 29.5 nF 225 °C

from TLP data