IEEE Solid-States Circuits Magazine - Fall 2020 - 101
A Review
of Wafer Packing
and New Results
Examining optimal die placement
Wing-Kong Ng, Wing-Ting Tam, Annie Hin-Cheung Ko,
Wing-Shan Tam, and Chi-Wah Kok
T
his article reviews the waferpacking problem,
which combines
gross die per wafer
(GDW) estimation and its associated
optimal die-placement problems. It
has been reported in the literature
that there is limited set of possible
die-placement schemes under regular die placement; the mathematical
models used to compute GDW for
each regular die-placement scheme
are presented in this article. As a
result, optimal wafer packing (the
maximum number of GDWs) and its
associated die-placement scheme
can be obtained by comparing all
GDWs obtained from this limited
set of die placements. This article
further investigates a particular irDigital Object Identifier 10.1109/MSSC.2020.3021845
Date of current version: 18 November 2020
1943-0582/20©2020IEEE
regular die placement commonly
applied in devices fabricated in
expensive substrates to achieve a
higher GDW when compared to that
of regular die-placement schemes.
At the same time, a simple GDW approximation formula is presented
and shown to be able to obtain a
close approximation to the optimal
GDW within 5% accuracy, in general.
Furthermore, when the length of
the long side of the die to the effective radius of the wafer is smaller
than 1%, the estimation accuracy
will be almost certain to improve to
higher than 99% in most cases. Such
a simple GDW estimation equation
can be an effective tool to estimate
engineering and costs for application-specific IC businesses.
Estimating Die Cost
Wafer cost is the only cost figure
provided by the IC foundry. There-
fore, to determine the cost of an
IC, an estimation of the number of
GDWs is required. Using only the
GDW to estimate die cost has overly
simplified this engineering problem, where the yield loss and other
engineering factors involved in the
design and manufacturing cycles
would also affect the number of
good dies that can be eventually
fabricated [1]. As a result, a significant amount of research proposes
different figures of merit (FoMs) to
determine the efficiency of a particular die-placement scheme [2]. However, the presented FoM makes use
of simple GDW estimation instead of
the exact GDW computation with a
given die-placement scheme. There
are various GDW estimation formulas online, in textbooks, and reported in research papers [3]-[9]. These
formulas give substantially different estimation results; furthermore,
IEEE SOLID-STATE CIRCUITS MAGAZINE
FA L L 2 0 2 0
101
IEEE Solid-States Circuits Magazine - Fall 2020
Table of Contents for the Digital Edition of IEEE Solid-States Circuits Magazine - Fall 2020
Contents
IEEE Solid-States Circuits Magazine - Fall 2020 - Cover1
IEEE Solid-States Circuits Magazine - Fall 2020 - Cover2
IEEE Solid-States Circuits Magazine - Fall 2020 - Contents
IEEE Solid-States Circuits Magazine - Fall 2020 - 2
IEEE Solid-States Circuits Magazine - Fall 2020 - 3
IEEE Solid-States Circuits Magazine - Fall 2020 - 4
IEEE Solid-States Circuits Magazine - Fall 2020 - 5
IEEE Solid-States Circuits Magazine - Fall 2020 - 6
IEEE Solid-States Circuits Magazine - Fall 2020 - 7
IEEE Solid-States Circuits Magazine - Fall 2020 - 8
IEEE Solid-States Circuits Magazine - Fall 2020 - 9
IEEE Solid-States Circuits Magazine - Fall 2020 - 10
IEEE Solid-States Circuits Magazine - Fall 2020 - 11
IEEE Solid-States Circuits Magazine - Fall 2020 - 12
IEEE Solid-States Circuits Magazine - Fall 2020 - 13
IEEE Solid-States Circuits Magazine - Fall 2020 - 14
IEEE Solid-States Circuits Magazine - Fall 2020 - 15
IEEE Solid-States Circuits Magazine - Fall 2020 - 16
IEEE Solid-States Circuits Magazine - Fall 2020 - 17
IEEE Solid-States Circuits Magazine - Fall 2020 - 18
IEEE Solid-States Circuits Magazine - Fall 2020 - 19
IEEE Solid-States Circuits Magazine - Fall 2020 - 20
IEEE Solid-States Circuits Magazine - Fall 2020 - 21
IEEE Solid-States Circuits Magazine - Fall 2020 - 22
IEEE Solid-States Circuits Magazine - Fall 2020 - 23
IEEE Solid-States Circuits Magazine - Fall 2020 - 24
IEEE Solid-States Circuits Magazine - Fall 2020 - 25
IEEE Solid-States Circuits Magazine - Fall 2020 - 26
IEEE Solid-States Circuits Magazine - Fall 2020 - 27
IEEE Solid-States Circuits Magazine - Fall 2020 - 28
IEEE Solid-States Circuits Magazine - Fall 2020 - 29
IEEE Solid-States Circuits Magazine - Fall 2020 - 30
IEEE Solid-States Circuits Magazine - Fall 2020 - 31
IEEE Solid-States Circuits Magazine - Fall 2020 - 32
IEEE Solid-States Circuits Magazine - Fall 2020 - 33
IEEE Solid-States Circuits Magazine - Fall 2020 - 34
IEEE Solid-States Circuits Magazine - Fall 2020 - 35
IEEE Solid-States Circuits Magazine - Fall 2020 - 36
IEEE Solid-States Circuits Magazine - Fall 2020 - 37
IEEE Solid-States Circuits Magazine - Fall 2020 - 38
IEEE Solid-States Circuits Magazine - Fall 2020 - 39
IEEE Solid-States Circuits Magazine - Fall 2020 - 40
IEEE Solid-States Circuits Magazine - Fall 2020 - 41
IEEE Solid-States Circuits Magazine - Fall 2020 - 42
IEEE Solid-States Circuits Magazine - Fall 2020 - 43
IEEE Solid-States Circuits Magazine - Fall 2020 - 44
IEEE Solid-States Circuits Magazine - Fall 2020 - 45
IEEE Solid-States Circuits Magazine - Fall 2020 - 46
IEEE Solid-States Circuits Magazine - Fall 2020 - 47
IEEE Solid-States Circuits Magazine - Fall 2020 - 48
IEEE Solid-States Circuits Magazine - Fall 2020 - 49
IEEE Solid-States Circuits Magazine - Fall 2020 - 50
IEEE Solid-States Circuits Magazine - Fall 2020 - 51
IEEE Solid-States Circuits Magazine - Fall 2020 - 52
IEEE Solid-States Circuits Magazine - Fall 2020 - 53
IEEE Solid-States Circuits Magazine - Fall 2020 - 54
IEEE Solid-States Circuits Magazine - Fall 2020 - 55
IEEE Solid-States Circuits Magazine - Fall 2020 - 56
IEEE Solid-States Circuits Magazine - Fall 2020 - 57
IEEE Solid-States Circuits Magazine - Fall 2020 - 58
IEEE Solid-States Circuits Magazine - Fall 2020 - 59
IEEE Solid-States Circuits Magazine - Fall 2020 - 60
IEEE Solid-States Circuits Magazine - Fall 2020 - 61
IEEE Solid-States Circuits Magazine - Fall 2020 - 62
IEEE Solid-States Circuits Magazine - Fall 2020 - 63
IEEE Solid-States Circuits Magazine - Fall 2020 - 64
IEEE Solid-States Circuits Magazine - Fall 2020 - 65
IEEE Solid-States Circuits Magazine - Fall 2020 - 66
IEEE Solid-States Circuits Magazine - Fall 2020 - 67
IEEE Solid-States Circuits Magazine - Fall 2020 - 68
IEEE Solid-States Circuits Magazine - Fall 2020 - 69
IEEE Solid-States Circuits Magazine - Fall 2020 - 70
IEEE Solid-States Circuits Magazine - Fall 2020 - 71
IEEE Solid-States Circuits Magazine - Fall 2020 - 72
IEEE Solid-States Circuits Magazine - Fall 2020 - 73
IEEE Solid-States Circuits Magazine - Fall 2020 - 74
IEEE Solid-States Circuits Magazine - Fall 2020 - 75
IEEE Solid-States Circuits Magazine - Fall 2020 - 76
IEEE Solid-States Circuits Magazine - Fall 2020 - 77
IEEE Solid-States Circuits Magazine - Fall 2020 - 78
IEEE Solid-States Circuits Magazine - Fall 2020 - 79
IEEE Solid-States Circuits Magazine - Fall 2020 - 80
IEEE Solid-States Circuits Magazine - Fall 2020 - 81
IEEE Solid-States Circuits Magazine - Fall 2020 - 82
IEEE Solid-States Circuits Magazine - Fall 2020 - 83
IEEE Solid-States Circuits Magazine - Fall 2020 - 84
IEEE Solid-States Circuits Magazine - Fall 2020 - 85
IEEE Solid-States Circuits Magazine - Fall 2020 - 86
IEEE Solid-States Circuits Magazine - Fall 2020 - 87
IEEE Solid-States Circuits Magazine - Fall 2020 - 88
IEEE Solid-States Circuits Magazine - Fall 2020 - 89
IEEE Solid-States Circuits Magazine - Fall 2020 - 90
IEEE Solid-States Circuits Magazine - Fall 2020 - 91
IEEE Solid-States Circuits Magazine - Fall 2020 - 92
IEEE Solid-States Circuits Magazine - Fall 2020 - 93
IEEE Solid-States Circuits Magazine - Fall 2020 - 94
IEEE Solid-States Circuits Magazine - Fall 2020 - 95
IEEE Solid-States Circuits Magazine - Fall 2020 - 96
IEEE Solid-States Circuits Magazine - Fall 2020 - 97
IEEE Solid-States Circuits Magazine - Fall 2020 - 98
IEEE Solid-States Circuits Magazine - Fall 2020 - 99
IEEE Solid-States Circuits Magazine - Fall 2020 - 100
IEEE Solid-States Circuits Magazine - Fall 2020 - 101
IEEE Solid-States Circuits Magazine - Fall 2020 - 102
IEEE Solid-States Circuits Magazine - Fall 2020 - 103
IEEE Solid-States Circuits Magazine - Fall 2020 - 104
IEEE Solid-States Circuits Magazine - Fall 2020 - 105
IEEE Solid-States Circuits Magazine - Fall 2020 - 106
IEEE Solid-States Circuits Magazine - Fall 2020 - 107
IEEE Solid-States Circuits Magazine - Fall 2020 - 108
IEEE Solid-States Circuits Magazine - Fall 2020 - 109
IEEE Solid-States Circuits Magazine - Fall 2020 - 110
IEEE Solid-States Circuits Magazine - Fall 2020 - 111
IEEE Solid-States Circuits Magazine - Fall 2020 - 112
IEEE Solid-States Circuits Magazine - Fall 2020 - 113
IEEE Solid-States Circuits Magazine - Fall 2020 - 114
IEEE Solid-States Circuits Magazine - Fall 2020 - 115
IEEE Solid-States Circuits Magazine - Fall 2020 - 116
IEEE Solid-States Circuits Magazine - Fall 2020 - 117
IEEE Solid-States Circuits Magazine - Fall 2020 - 118
IEEE Solid-States Circuits Magazine - Fall 2020 - 119
IEEE Solid-States Circuits Magazine - Fall 2020 - 120
IEEE Solid-States Circuits Magazine - Fall 2020 - 121
IEEE Solid-States Circuits Magazine - Fall 2020 - 122
IEEE Solid-States Circuits Magazine - Fall 2020 - 123
IEEE Solid-States Circuits Magazine - Fall 2020 - 124
IEEE Solid-States Circuits Magazine - Fall 2020 - 125
IEEE Solid-States Circuits Magazine - Fall 2020 - 126
IEEE Solid-States Circuits Magazine - Fall 2020 - 127
IEEE Solid-States Circuits Magazine - Fall 2020 - 128
IEEE Solid-States Circuits Magazine - Fall 2020 - Cover3
IEEE Solid-States Circuits Magazine - Fall 2020 - Cover4
https://www.nxtbook.com/nxtbooks/ieee/mssc_fall2023
https://www.nxtbook.com/nxtbooks/ieee/mssc_summer2023
https://www.nxtbook.com/nxtbooks/ieee/mssc_spring2023
https://www.nxtbook.com/nxtbooks/ieee/mssc_winter2023
https://www.nxtbook.com/nxtbooks/ieee/mssc_fall2022
https://www.nxtbook.com/nxtbooks/ieee/mssc_summer2022
https://www.nxtbook.com/nxtbooks/ieee/mssc_spring2022
https://www.nxtbook.com/nxtbooks/ieee/mssc_winter2022
https://www.nxtbook.com/nxtbooks/ieee/mssc_fall2021
https://www.nxtbook.com/nxtbooks/ieee/mssc_summer2021
https://www.nxtbook.com/nxtbooks/ieee/mssc_spring2021
https://www.nxtbook.com/nxtbooks/ieee/mssc_winter2021
https://www.nxtbook.com/nxtbooks/ieee/mssc_fall2020
https://www.nxtbook.com/nxtbooks/ieee/mssc_summer2020
https://www.nxtbook.com/nxtbooks/ieee/mssc_spring2020
https://www.nxtbook.com/nxtbooks/ieee/mssc_winter2020
https://www.nxtbook.com/nxtbooks/ieee/mssc_fall2019
https://www.nxtbook.com/nxtbooks/ieee/mssc_summer2019
https://www.nxtbook.com/nxtbooks/ieee/mssc_2019summer
https://www.nxtbook.com/nxtbooks/ieee/mssc_2019winter
https://www.nxtbook.com/nxtbooks/ieee/mssc_2018fall
https://www.nxtbook.com/nxtbooks/ieee/mssc_2018summer
https://www.nxtbook.com/nxtbooks/ieee/mssc_2018spring
https://www.nxtbook.com/nxtbooks/ieee/mssc_2018winter
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_winter2017
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_fall2017
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_summer2017
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_spring2017
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_winter2016
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_fall2016
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_summer2016
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_spring2016
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_winter2015
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_fall2015
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_summer2015
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_spring2015
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_winter2014
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_fall2014
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_summer2014
https://www.nxtbook.com/nxtbooks/ieee/solidstatecircuits_spring2014
https://www.nxtbookmedia.com