Kein Folientitel

1
Matching of Primitive Devices for Analog and
Mixed Signal Applications MOS-AK meeting, 21
Oct. 2002 Guenter Lau, Process
Characterization, X-FAB Group
2
Table of Contents

• Matching - Mismatch, Reasons lead to Mismatch
• Mismatch Variance Model, Hardware Software
  Tools
• MOS Transistor Matching
• Resistor ( Contact) Matching
• Bipolar Transistor Matching
• Capacitor Matching
• Plans for the Future

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Mismatch - Matching
Definition Differences between identically
designed components for analog devices are
commonly associated with terms matching or
mismatch. Types of mismatching The mismatch
can have stochastic and systematic reasons.
4
Mismatch - Matching
Stochastic mismatch The stochastic mismatch
caused by time-independent random variations in
physical quantities is generally treated to be
normally distributed and described by its
standard deviation (s). Systematic
mismatch When the average (µ) of the observed
distribution is not zero, the term systematic
mismatch is used.
5
Local Parameter Variations

• random local variations in doping concentration
• built-in charges, local mobility fluctuations
• oxide granularity
• grain boundary distribution, doping fluctuations
  in poly gate
• random dimensional variations (oxide thickness,
  polysilicon thickness, effective line width)
• white noise mismatch-generating process
  
• stochastic mismatch

6
Global Parameter Variations

• equipment induced non-uniformity's
• spatial (non random) variation across the wafer
  
• (e.g. gate oxide thickness, polysilicon
  line-width) due to temperature gradients
  and /or
• etch- and deposition rate variations
• additional stochastic mismatch (distance D)
• systematic mismatch (mean µ ? 0).

7
Systematic Mismatch

• Sources of systematic mismatch
• asymmetry in placement of the device (different
  neighbored elements)
• different device orientation (rotated, mirrored)
• metal coverage effects (over one of
• the matched components)
• (de-)biasing of (one of) the matched
• components due to voltage drops in
• the device connections

8
Systematic Mismatch

• Sources of systematic mismatch
• temperature differences due to non-uniform die
  heating (local dissipation)
• stress non-uniformity's related to physical die
  (crystal) edges
• stress non-uniformity's caused by packaging

Measurements show that the systematic mismatch of
not carefully designed pairs can reach
considerable values and multiple exceed the
stochastic mismatch.
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Mismatch caused by measurement system

• Measurements performed quite near the resolution
  of the measurement system.
• The limited reproducibility and accuracy of the
  test system and asymmetry with respect to the
  probe card can influence the matching results
  
• stochastic and / or systematic mismatch.
• Not the absolute accuracy of the parameters but
  there differences are important

10
Mismatch caused by measurement system

• To improve the measurement capability cmk,
• multiple measurements (5 - 20 times) were
  performed.
• The standard deviation of multiple
  measurements of one parameter (P) range from
  0.01 to 0.04 ( to 0.4 for extrapolated
  parameters.)

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Mismatch Variance Model

• The stochastic matching is defined as the
  standard deviation of the
• normal distribution of N (Ngt100)
• absolute differences ?P (P1-P2), or
  (e.g. for Vt)
• relative differences ?P/P 200(P1-P2)/(P1P2)
  , (e.g. for Id, R)
• A²p A²p A²p
• ?² (P1- P2) ---------- ---------- or
  --------
• 2 W1L1 2 W2L2
  WL
• were Ap is a process-dependent fitting
  constants
• (Pelgroms law)

1s
12
Long Distance Matching

• ?² (P1- P2) S²p D²12 , were Sp is a
  process-dependent fitting constants
• Investigation however show that the long distance
  mismatch does not
• necessarily show a linear increase with distance.
• parameter variations are more complicated.
• additional effects depending on reticle position

Example of parameter distribution across the wafer
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Equipment

• Test Equipment
• Parametric Test System Keithley S450
• Prober Electroglass EG2001
• Keithley Probe Card Adapter (Ceramic Probes)
• Standardized Test Program

• Data Storage and Analysis
• Data Base (analogue to Parametric Test Data)
• Wafer Map with calculation of ?P or ?P/P
• Statistical Data Analysis (SDA) --gt ? (?P/P)

XFAB data analysis software
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WaferMap / SDA
Statistics Outlying-Selection Median /- 3
Interquartil Quote ... Outlying-Selection passed
Name Units Average St.Dev. N
Quote Min. Max. MVT_1 mV
0.16953 1.48003 889 99.9 -5.4821
4.8228 MVT_2 mV 0.07453 2.16834 869
97.6 -6.4926 6.5396 MVT_3 mV 0.11699
1.92374 889 99.9 -7.0498 6.7733
MVT_4 mV 0.09273 2.80148 888 99.8
-8.3014 9.7794 MVT_5 mV 0.20074
1.75966 867 97.4 -6.8681 7.218 MVT_6
mV 0.09481 2.30383 853 95.8
-7.8423 7.3454
µ
s
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MOS Transistor Matching

• L / W variations
• Identical electrical connections
• Dummy structures, Protection Devices
• Measurement of
• Vt Slope with extrapolation method
• Id _at_ Vg-Vt-0.2 ... 6V, Vd5V (14 points)

s(?Vt) AVt / sqrt (LW) mV
s(?Sl/Sl) ASl / sqrt (LW)
s(?Id/Id) AId / sqrt (LW)
with AIdf(Vg-Vt)
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MOS Transistor Matching
Vt mismatch (in mV)
s(DVt) 1.76mV
s(DVt) 2.17mV
s(DVt) 2.80mV
lt------- increasing transistor area
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MOS Transistor Matching
s(?Vt) mV
1 / sqrt (LW) 1/µm
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MOS Transistor Matching
60
s(?ID/ID)
VG - VT V
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MOS Transistor Matching
s(?ID/ID)
1 / sqrt (LW) 1/µm
20
MOS Transistor Matching
AID µm
VG - VT V
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MOS Transistor Matching

• The Vt and the Slope mismatch calculations show
  some limitations (especially for large devices)
  due to the limited resolution of the extrapolated
  method ? new method necessary.
• The direct measured drain currents give more
  reliable results.
• The drain current mismatch not only depends on
  the transistor area but also strongly depends on
  the operating conditions.

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MOS Transistor Matching

• Near the threshold voltage the Id mismatch
  drastically increases and shows an saturation
  in the sub-threshold region.
• The mismatch behavior quit good follow the simple
  1/sqrt(LW) law, only short and narrow (lt 0.8 µm)
  transistors sometimes show an poorer matching
  when predicted (additional L and W effects).

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MOS Transistor Matching
Offset (?ID/ID)
VG - VT V
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Resistor Matching
s(?R/R)
1 / sqrt (LW) 1/µm
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Contact Matching
delta Rcont Ohm
Iforce 1mA/µm²
Contact size 1.2x1.2µm²
Contact size 2.0x2.0µm²
Rcont 5 ... 30 ... 53 Ohm
Rcont 1 ... 9 ... 16 Ohm
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Bipolar Transistor Matching
1,00E-02
10
CX08
hfe is divided by 20
1,00E-03
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Matching VERTN1
1,00E-04
8
(fixed layout)
1,00E-05
7
1,00E-06
6
Ib, Ic in A
1,00E-07
5
s(DIb/Ib), s(DIc/Ic) in , s(D vbe) in mV

Ib1
1,00E-08
4
Ib2
Ic1
Ic2
1,00E-09
3
sigma(delta Ib/Ib)
sigma(delta Ic/Ic)
hfe1/20
1,00E-10
2
hfe2/20
sigma(delta vbe)
1,00E-11
1
1,00E-12
0
0,400
0,425
0,450
0,475
0,500
0,525
0,550
0,575
0,600
0,625
0,650
0,675
0,700
0,725
0,750
0,775
0,800
0,825
0,850
0,875
vbe in V
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Bipolar Transistor Matching
XB06 NPN with poly emitter
Vbe mismatch XB06 poly emitter npn
s(?Vbe) AVbe / sqrt
(LW) mV s(?lb/lb) AIb / sqrt (LW)
s(?Ic/Ic) AIc / sqrt
(LW)
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Capacitor Matching
?C/C 200 (S1-S2) / (S1S2) , with Sx
Cx / C1C2Cpar s(?C/C) AC / sqrt
(LW)
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Matching Analysis - Basic Principle
The deal with matching measurements and the
following data analysis seems to be sometimes
very mysterious and gives a lot of riddles.
Thats why
Only the natural views made before the subtle
comes, and always first of all try whether
somewhat quite simply and naturally can be
explained.
G.Chr. Lichtenberg
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Plans for the Future

• Improve the test programs / - routines to get
  more precise results and speed up the data
  collection, measurement of necessary modeling
  parameters

• Create (better) conditions for using mismatch
  data in design environment
• Buy a commercial product (AnalogXpert)?
• Model development
• Simulator Implementation (Monte Carlo)
  --gt (different behavior for area dependence)