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SEMI M51-0303 © SEMI 2002, 2003 13 R1-1.3.6 On the othe r hand, too hi gh a stepping-up of the applied electric field stress, fo r example, 1.0 MV/cm or more, l eads to broadenin g of the dielectri c breakdown electric f…

SEMI M51-0303 © SEMI 2002, 2003 12

of MOS capacitors with an electrode area of S and a

defect density of ρ

is given by the following equation.

Y = 1 – F = exp(-ρ

R1-1.2.3 The failure fraction, F, is calculated using this

expression. Here, the necessary MOS capacitor

number, n, for the observation of one breakdown MOS

capacitor is assumed to be 1/F. Thus, this n was

calculated from the value of S and ρ

as shown in

Table R1-1.

Table R1-1 Necessary number for observation of

one breakdown MOS capacitor

1/F = Necessary number for observation of one breakdown

MOS capacitor

S (mm

) 1 5 10 20 50

= 10 cm

-2

11 3 2 1 1

= 1 cm

-2

101 21 11 6 3

= 0.1 cm

-2

1001 201 101 51 21

R1-1.2.4 In the same way, the yield probability, Y, and

necessary number, n, for observation of available MOS

capacitors was calculated as indicated in Table R1-2.

Table R1-2 Necessary number for observation of

available MOS capacitors

1/Y = Necessary number for observation of available MOS

capacitors

S (mm

) 1 5 10 20 50

= 10 cm

-2

1 2 3 7 148

= 1 cm

-2

1 1 1 1 2

= 0.1 cm

-2

1 1 1 1 1

R1-1.2.5 The number of needed MOS capacitors is

shown in Table R1-3 though both “1/F” and “1/Y” were

done to one or more. To observe ten MOS capacitors

or more respectively in an actual evaluation including

reproducibility, the number of MOS capacitors required

for the measurement will then be multiplied by ten and

reaches the value shown in Table R1-3 below.

Table R1-3 Necessary number of MOS capacitors

(in the case of

= 1 or 10)

S (mm

) 1 5 10 20 50

Confirmation of

breakdown (ρ

= 1)

101 21 11 6 3

Confirmation of alive

(ρ

= 10)

1 2 3 7 148

Necessary number

(large one in above)

101 21 11 7 148

×10 1010 210 110 70 1480

R1-1.2.5.2 In Table R1-3, the term confirmation of

breakdown (ρ

= 1) means the number of elements

necessary to confirm at least one breakdown in the case

of ρ

= 1, and the term of confirmation of alive

(ρ

= 10) means the number of elements necessary to

confirm at least one alive in the case of ρ

= 10.

R1-1.2.6 When a silicon wafer with a surface defect

density of 10/cm

is measured, if MOS capacitors with

an electrode area of 50 mm

are used, it breaks down.

Therefore, it is unsuitable for the comparative

evaluation of the defect distribution as in this test.

R1-1.2.7 To confirm that 10 MOS capacitors are

“alive” or “dead”, it is necessary to measure 70 MOS

capacitors with an electrode area of 20 mm

, or 110

MOS capacitors of 10 mm

, or 210 MOS capacitors of

5 mm

R1-1.2.8 When the defect density of a sample wafer is

0.1/cm

, we can confirm broken 10 MOS capacitors of

50 mm

by measurement of only 210 MOS capacitors.

For MOS capacitors of 1 mm

, it will be necessary to

measure about 10,000, and this is not realistic.

R1-1.3 Recommended Measurement Condition

R1-1.3.1 The electric field step, E

step

, and hold time,

hold

, used in this round robin are shown in Figure R1-2.

R1-1.3.2 In TZDB measurement, the voltage is

increased with each step. Then, the electric current is

measured after a constant hold time. This hold time is

usually initiated as a time period required for

measurement stabilization. It is possible that

measurement results are influenced by voltage

instability when the hold time is shorter than 100 ms.

R1-1.3.3 On the other hand, because too long a hold

time––that is, 800 ms or more––leads to a long total

measurement time, the influence of TDDB becomes

conspicuous in the high electrical field region, and it is

possible that the breakdown failure fraction of the MOS

capacitors increases.

R1-1.3.4 In Figure R1-2, the B-mode failure percents

are shown as a function of the hold time of the applied

electric field stress with a step height of 0.25 MV/cm.

A hold time from 100 ms to 800 ms did not have any

particular influence in the measurement results of this

round robin. Thus, we have proposed 200 ms as a

practicable recommended hold time.

R1-1.3.5 In this TZDB measurement, the applied

electric field was increased each step directly after the

current measurement. Too low a step height of the

applied electric field, ∆E––that is, 0.1 MV/cm or less––

leads to an unnecessarily long measurement time, and

the influence of TDDB becomes conspicuous in the

high electrical field region.

SEMI M51-0303 © SEMI 2002, 2003 13

R1-1.3.6 On the other hand, too high a stepping-up of

the applied electric field stress, for example, 1.0

MV/cm or more, leads to broadening of the dielectric

breakdown electric field. That is, the reliability of the

measurement result is decreased.

R1-1.3.7 In this round robin as shown in Figure R1-4,

the B-mode failure percent did not depend on the step

height of the applied electric field stress with a hold

time of 200 ms. An electric field step height of 0.1-0.5

MV/cm did not cause any problems in the measurement

results. Therefore, considering the above practical

factors, a step height range of 0.1–0.5 MV/cm, and

especially, 0.25 MV/cm are recommended.

TZDB(Step Voltage)

a) Group I: B, D, E b) Group II: A, F

step

(MV/cm)

0.1 0.25 0.5 1.0

100 I I - -

200 II I

, II II II

hold

(ms)

800 - I I -

(* E measured T

hold

= 400ms)

step

hold

Judgement Current:10

-5

Figure R1-2

Applied Gate Electric Field Stress Condition in TZDB and Measurement Group Division

0 0.2 0.4 0.6 0.8 1

100

hold

(s)

B-mode ratio (%)

Tox: 25 nm

S: 10 mm

High

Middle

Low

Figure R1-3

B-Mode Failure Percent vs. Hold Time of Applied Electric Field Stress with a Step Height of 0.25 MV/cm in

TZDB

0 0.2 0.4 0.6 0.8 1 1.2

100

ste

(MV/cm)

B-mode ratio (%)

Tox: 25 nm

S: 10 mm

High

Middle

Low

Figure R1-4

B-mode Failure Percent vs. Step Height of the Electric Field Stress with a Hold Time of 200 ms in TZDB

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