semi合集-English.pdf - 第5445页
SEMI M60-0305 © SEMI 2005 13 11.5 Weibull Distribution 11.5.1 To convert cumulative percent to W eibull format (s ometimes referred to as “smallest extreme value probability distributio n III”), use the following equatio…
SEMI M60-0305 © SEMI 2005 12
11 Calculations
11.1 Current and Current Density
11.1.1 To calculate current(I) from current density(J), multiply the current density by the area of gate area(S) as
follows:
Symbolically:
I = J × S (1)
Example: Given a current density(J) of 1µA/cm
2
and a gate area(S) of 10 mm
2
, the current would be 100nA.
Similarly, compute current density(J, [A/cm
2
]) from measured current(I, [A]) and area (S, [cm
2
]) using.
J = I / S [A/cm
2
] (2)
11.2 Voltage and Electric Field Strength
11.2.1 To calculate voltage(V) from an electric field(E), multiply the electric field strength by the gate oxide
thickness(T
ox
) as follows:
Symbolically:
V = E × T
ox
(3)
where:
T
ox
= Gate oxide thickness, cm.
Example: Given an electric field(E) of 15 MV/cm and a gate oxide thickness(T
ox
) of 25nm, the voltage would be
37.5 V.
Similarly, compute electric field (E, [MV/cm]) from measured voltage(V, [V]) and gate oxide thickness(T
ox
, [cm])
using.
E = V / T
ox
[MV/cm] (4)
11.3 Oxide Voltage
11.3.1 Neglect the flatband voltage shift. The flatband voltage shift is due to gate-substrate work function
difference[
ms
] and oxide fixed charge[Q
f
]. Although it is better to consider this flatband voltage shift, its influence
on the oxide film thickness in the range recommended in this test method is small.
11.4 Calculation of Defect Density
11.4.1 Calculate the defect density using the following equation based on the Poisson distribution assumption of the
dielectric breakdown defects (see Standard EIA/JEDEC 35):
ox
= ln (1 F) / S (5)
Here
ox
= Defect density (defects/cm
2
) ,
F = Failure fraction for each oxide breakdown mode ,
and S = Capacitor gate area (cm
2
).
Example: Given a total of 100 MOS capacitors tested, with 30 accidental-mode-failed capacitors and a gate area of
10 mm
2
, the defect density would be as follows:
ox
= ln ( 1 ( 30 / 100 ) ) / 0.1
= 3.6 defects/cm
2
(6)
SEMI M60-0305 © SEMI 2005 13
11.5 Weibull Distribution
11.5.1 To convert cumulative percent to Weibull format (sometimes referred to as “smallest extreme value
probability distribution III”), use the following equation:
ln ( ln ( 1 F ) ) (7)
11.6 Where ln is the natural log operator and F is a percent of the cumulative failures. Care shall be taken so that F
is never exactly 1 since this will be in an undefined situation.
12 Report
12.1 Report the following for each wafer, as appropriate for the test conditions and as agreed upon by the parties to
the test.
12.1.1 Test Description
12.1.2 Date
12.1.3 Time
12.1.4 Operator
12.1.5 Measurement system ID
12.1.6 Sample lot ID
12.1.7 Wafer ID
12.1.8 Average oxide thickness
12.1.9 Gate area (cm
2
)
12.1.10 Gate material
12.1.11 Oxidation parameters
12.1.12 Type of wafer (Ex: n or p)
12.1.13 Applied stress parameters
12.1.14 Test temperature
12.1.15 Process comment
12.1.16 Capacitor ID such as adress
12.1.17 V-T characteristic data
12.1.18 Breakdown time
12.1.19 Weibull plot of Q
bd
12.1.20 Average, median and maximum Q
bd
12.1.21 Breakdown mode yield
12.1.22 Breakdown mode map or Tbd / Q
bd
map
12.1.23 Result of calculated defect density
SEMI M60-0305 © SEMI 2005 14
RELATED INFORMATION 1
OUTLINE OF ROUND ROBIN
NOTICE: This related information is not an official part of SEMI M60 and was derived from the GOI Task Force.
This round robin was conducted among Shin-Etsu Handotai Co., Ltd., Komatsu Electronic Metals Co., Ltd.,
Toshiba Ceramics Co., Ltd., Sumitomo Mitsubishi Silicon Corporation and MEMC Japan Ltd.
R1-1 MOS Structure
R1-1.1 Gate Oxide Thickness
R1-1.1.1 In this round robin, we evaluated the constant current TDDB (TDDB) of MOS capacitors with a gate
oxide film thickness of 25 nm on mirror-polished, p-type, CZ silicon wafers. In the TDDB evaluation, a negative
constant current was applied, and T
bd
was measured.
R1-2 Correlation between TZDB and TDDB
R1-2.1 Correlation Between TZDB and TDDB
R1-2.1.1 A correlation between TZDB and TDDB is shown in Figure RI-1. This result is based on round robin.
This figure is shown by defect densities of the TZDB and TDDB measurements. The defect densities of TDDB are
generally higher than those of TZDB. This result is shown that the sensitivity to dielectric breakdown defect of
TDDB measurement is higher than that of TZDB measurement.
R1-3 Classification of Breakdown mode
R1-3.1 In Figure RI-2, a typical cumulative failure fraction is shown as a function of charge injected before
breakdown. Such a plot is called the TDDB Weibull plot. In the Weibull plot of the TDDB result, the breakdown
events are categorized into the following three modes.
R1-3.2 A-A Mode — Initial Breakdown Failure
R1-3.2.1 Integrity of the oxide films in this mode is very low. There are COPs or oxygen precipitates other than
particles, alkaline and metallic contamination at the Si surface of the MOS capacitors in this category. Classification
of this mode with the following A-B mode is performed at a small amount of injected charge, Q
a
, as illustrated in
Fig RI-2. For example, the classification charge, Q
a
, was 0.01C/cm
2
in this round robin. This failure is caused by
defects generated during formation of the gate oxide such as pinholes and also by crystal defects such as COPs.
That is, this failure corresponds to the A mode and partial B mode failure of TZDB.
R1-3.3 A-B Mode — Intermediate Breakdown Failure
R1-3.3.1 This failure occurs in the intermediate time range from initial breakdown failure to wearout breakdown.
This failure is caused by extrinsic defects. This failure corresponds to the B mode and partial C-mode failure of
TZDB.
R1-3.4 W Mode — Wearout Breakdown
R1-3.4.1 This breakdown is also called intrinsic breakdown or wearout breakdown, and related to the intrinsic
lifetime of oxide films. The failure fraction steeply increases as shown in Figure R1-2. The measurement of this
breakdown should be performed carefully because the result depends on measurement conditions.
R1-3.4.2 Classification of the accidental and wearout modes, that is, the A-B and W modes, is far from easy
because the W mode gradually shifts toward the A-B mode as shown in Figures R1-3, R1-5 and R1-6. It is
statistically supported that the Weibull plot is straight in the W mode region. The regression straight line has the
correlation coefficient higher than 0.9 with the experimental data. When the A-B mode breakdown events are added
to the breakdown data, a correlation coefficient of the data and its straight line approximation decreases. This
characteristic to determine the classification of the accidental and wearout modes can be used. In this round robin,
the classification of the injected charge density, Q
w
, was determined as follows. A regression straight line in the
injected charge density range of higher than Q
w
was obtained by the least square method. The recommended
correlation coefficient is higher than 0.95. Q
w
is 2C/cm
2
in Figure R1-4. In a different manner, the cross point of
two regression straight lines in the A-B and W mode breakdown ranges was read as Q
w
.