Failure rate prediction of optical semiconductor devices

Microelectron. Reliab., Vol. 25, No. 3, pp. 525 540, 1985. Printed in Great Britain.

0026 2714/8553.00+ .00 © 1985 Pergamon Press Ltd.

FAILURE

RATE

PREDICTION

SEMICONDUCTOR H. Atsugi Ono

SUDO

Electrical

1839,

and

Y.

for

OPTICAL

NAKANO

Communication

Atsugi-shi,

(Received

OF

DEVICES

Laboratory,

Kanagawa,

publication

Japan

30

N.T.T.

243-O1

January

1985)

Abstract

The failure modes of optical classified

into wear-out

estimation methods

and random failures.

are also presented

lognormal

and exponential

life-test

data of InGaAsP/InP

examples,

statistical

mode.

This analysis

reliability

semiconductor

assurance

scale and conditions

The failure rate

Moreover,

DH LDs and Ge-APDs

analysis

are

for each mode using

distributions.

suggests

devices

based on the

as concrete

is carried out for the wear-out

some problems

of these devices. are statist~cally

underlying

Finally,

the high-

the testing

investigated

te confirm

the random failure rates ol 300 FITs for LDs and 3 FITs for Ge-APDs obeys

assuming

the temperature

the Arrhenius

dependency

of the failure rate

law.

1. Introduction

Semiconductor detectors

devices

such as long-wavelength

and ICs with high performance

indispensable

for practically

realizing

light transmission

systems.

important

problems

is the reliability

detectors

which were newly developed

since yielded

and reliability

are

long haul, high capacity

Above all, one of the urgent and of laser diodes and in recent years and have

some field data.

These devices must have high reliability, failure rate when applied undersea

laser diodes,

optical

to highly reliable

cable transmission 525

systems.

that is, a low systems

such as

For such systems

in

526

H. SUDO and Y. NAKANO

particular,

the reliability

the first N.T.T.

undersea

FITs respectively In general,

failures

transmission

semiconductor

life. (I)

devices have two failure modes: (2)

in which the device characteristics

or over a relatively

change

short period,

and (2) wear-out

in which the device characteristics

change slowly to

finally fall outside a tolerable failure modes of optical an inevitable reliability modes

for

system are 300 FITs and 3

for 25 years of service

(I) sudden failures instantly

targets of LDs and APDs available

range.

Conventionally,

devices have been assumed to be almost

part of system reliability

assurance

is necessary

random

technique

design.

However,

for random and wear-out

since early failures

are eliminated

a

failure through

the screening process. Primarily,

this paper reports

on the estimation methods

of

failure rates for each mode after the assumed failure modes of semiconductor

devices have been classified

wear-out modes. InGaAsP/InP

Secondly,

conventional

DH LDs and Ge-APDs

regard to the wear-out

3 FITs for Ge-APDs. statistically

to confirm these LD and Ge-APD values

of life-test

that the temperature

data on semiconductor

the Weibull

exponential

and lognormal

probability

density functions

various

assuming

respectively.

and the lognormal distributions

failure patterns.

devices:

the

distributions.

concern

distribution,

The

the failure

in the random and wear-out

The Weibull

the exponential

characterizing

law.

are usually used for the ststistical

exponential,

comprising

are

rate estimation methods

Three distributions

periods

are

scale and conditions

of the failure rate obeys the Arrhenius

2. Failure

treatment

treated with

are 300 FITs for LDs and

the testing

from the random failure viewpoint dependency

data for

such that some problems

requirements

Finally,

investigated

life-test

are statistically

failure mode,

clarified when reliability

into random and

failure

however,

one, exhibits wide applicability For LDs especially,

its degradation

failure

for

the distribution

is presently unknown,

such

Optical devices

that the lognormal

distribution

527

has most frequently been

used. (3)(4) This section demonstrates

the failure rate estimation

methods

distributions.

for lognormal

2-1. Wear-out

and exponential

failure mode

For the lognormal function,

f(t),

rate, ~(t),

distribution,

cumulative

failure function,

are expressed

f(t)

the probability

density

F(t),

and failure

as

exp ---~r~(in t/tm)2,

) ~ T~/

F(t) = ~ ( I

+ erf~ Ir in t/t m)

(I)

(2)

,

and

A(t) =
t is service

is standard

complementary by

A(t).

time in hours,

deviation,

error function,

yrs

if the distribution

and 300 FITs),

between

parameters,

25 years.

can be obtained

tm and O ,

these parameters

allows

failure

In contrast,

that the maximum

of the curves

domain where

in Fig.

the s m a l l e r O b e c o m e s .

for the assurance

from

are given.

for the constant,

at 25 years of service are plotted

The solid portions wear-out

in 109 devicehours.

of operation

that the shorter tm becomes,

smaller ~ t h e n

erfc is the

and the "FIT" unit is represented

One FIT is equal to one failure

relationships

means

tm is median life in hours,

erf is the error function,

The failure rate in t Eq.(3)

(3)

"1°9'

The

A (3, 30 I. This This

of a given failure rate.

in the figure indicate

the maximum

the

failure rate occurs at

the broken portions

of the curves indicate

failure rate occurred before 25 years of service

life and that the wear-out

failure period already passed.

Next, we studied the certainty which depends size used in life tests of point estimated

on the sample

distribution

parameters. (5) The upper and lower limits of the relative median life, sample

(tmp/tmh)I/Sh,

are plotted

in Fig.

size at the 60 and 90 % confidence

intervals

o f ~ / S h versus

2 as a function of levels.

The confidence

sample size are shown at the 60 and 90 %

528

H. SUDOand Y. NAKANO

30,,,"!

~3

300 i

//

/ 1I

2

i

o '°~

'°~

,d

MEDIAN

Fig.

I: Relationships deviation

,d

LIFE

,o"

,do

(HOURS)

between median

for the attainment

life and standard of failure rates of 3,

30 and 300 FITs at 25 years of service.

confidence

levels in Fig. 3. Here,

and standard deviation

t

mp

of the lognormal

distribution Figures

deviation

the larger is the sample size,

experimental

values of

from the perfect

lognormal

technique.

for each confidence the narrower

level that

are the confidence

5

•. .

E

-

\

~

°l

u. m ..j

,0%

1

Z

..--e--60 '1~-----------'---~'

/~

-<

/

./~

)0"/.

wO.5 W

_> I-.,<

,,-I, 0.1 0

10

20

30

40

50

SAMPLE

Fig.

60

70

80

90

100

SIZE

2: Upper and lower limits for relative median (tmp/tmh)I/Sh, Confidence

respectively.

life,

as a function of sample size.

level values

life

parameters,

obtained by the maximum likelihood 2 and 3 demonstrate

the median

population

and tmh and S h are the point-estimated median life and standard

andOare

are 60 and 90 %

Optical devices

5

529

I

0 Z

o

' k 90 °~

I.< > W

1

a

90 %

/

<0.5 Gi z <

I-LU > I'< 0~0.1

0

10

20

30

40

50

60

SAMPLE

Fig.

3: Upper and lower limits deviation,.~'/Sh, Confidence

80

fO

90

100

SIZE

for relative

standard

as a function of sample

size.

level values are 60 and 90 %

respectively.

intervals

of the relative median

values estimated uncertainty, requires

from small sample size exhibit

and in general,

deviation,

is the confidence

life. Considering

the confidence

i00 samples

limits of median

function exp(-~t).

interval

standard

of the relative

and S h = 1 as an example, deviation

at the 90 % confidence

are

level.

Random failure mode

In the random failure period, throughout

20 and 50. Figure 2

life and standard

about ~18 % andtl2 % respectively

2-2.

The

large

that the larger is a point-estimated

the wider

deviation.

it is sssumed that the life test

a sample size of at least between

also implies

median

life and standard

the device operating

the failure rate is constant

times since the failure density

is expressed by the exponential A point-estimated

distribution,

f(t) =

value of the failure rate in a fixed

time testing plan is given as

A=

r/t.N,

(4)

where r ~ N and r, N and t denote the number of failed devices,

530

H, SUDO and Y. NAKANO

sample size, and testing time respectively. failure

(MTTF)

The mean time to

is a reciprocal of the failure rate,

MTTF = 1 / ~

The confidence

that is,

(5)

.

limits of the random failure rate can be

estimated by multiplying

the point-estimated value by some factor

which is as a function of confidence

level and failed numbers. (6)

When one-sided and two-sided MTTF estimations testing plan are performed,

in the fixed time

the factor multiplied by its point-

estimated value can be plotted for various rs in Figs. a function of the confidence reciprocal

to each other,

level. As the MTTF and

4 and 5 as

~

are

the upper and lower MTTF limits

correspond to the lower and upper limits of ~

respectively.

102

7 Ix. II.,-

101

~• , 1 o o I,-I tU n"

-2

lO

0

10

20

30 40 50 60 70 80 CONFIDENCE LEVEL (%)

90 100

Fig. 4: Upper and lower limits for relative mean time to failure

(MTTF) as a function of confidence

level when

two-sided estimation of MTTF in a fixed time testing plan is performed. failures.

Parameter is the number of

Optical devices

531

102

I.I.

101

I--

0 o I-.
10

Fig.

20

30 40 50 60 70 80 CONFIDENCE LEVEL (%)

90 100

5: Upper limit for relative mean time to failure (MTTF)

as a function of confidence

one-sided

estimation

plan is performed.

level when

of MTTF in a fixed time testing

Parameter

is the number of

failures.

3.

Statistical

treatment

This section describes

of life-test

the statistical

data for 1.3-~m buried heterostructure The treatment was conducted failure.

First,

data

treatment

(BH) lasers and Ge-APDs.

from the viewpoint

two characteristic

parameters,

standard deviation

are estimated by plotting

versus

of cumulative

the percent

temperatures Arrhenius

on lognormal

law expresses

of life test

of wear-out median

life and

the time to failure

failure at accelerated

graph paper.

the temperature

Next,

assuming

dependency

that the

of median

life, a failure rate at 25 years of service under the normal operating

condition

mentioned

in section 2-1.

3-1.

Semiconductor

A histogram

presented

lasers

of increased

total of 55 DC-PBH

gradual

for each is estimated using the method

drive current per 104 hours for a

lasers (7) operated with 5 mW/facet

in Fig. 6. (8) In this life test,

drive current

increase.

degradation will certainly

41 devices

The lasers showing

at 50 °C is exhibited a

such gradual

fail when the drive current reaches

532

H. SUDO and Y. NAKANO

50 °C , 5 mW/facet N=55

re Ld m =E

I0

Z

I

O -I0

i

V-,

I 0

~,R

I 7

I0

INCREASING RATE OF

,Ji, r 7 67.1

DRIVING CURRENT ( m A / k H )

Fig. 6: Histogram of increased

drive current per I04 hours

for 55 LDs operated with 5 mW/facet

the tolerable

limit.

at 50 °C.

This failure accords with that of wear-out.

One of the 55 devices

showed a rapid increase

in drive current

and failed after 6000 hours of aging. In calculating two assumptions

the laser life based on Fig.

were made.

First,

6, the following

the end of life was defined as

the time when the initial value of the drive current by 50 n~. Second, operating

the drive current

time even after 104 hours.

the lognormal cumulativ~ illustrated

projection

failures in Fig.

increases

linearly with the

Based on these assumptions,

of time to failure versus

for lasers

is increased

the percent

tested at 50 °C and 5 mW/facet

of is

7. The device which showed a rapid increase

of the drive current was excluded. From this chart,

the median

life and standard deviation

4.8xi05 hours and 1.04 are obtained respectively operated at 50 °C and 5 mW/facet. into Eq.(3)

Substituting

gives a point-estimated

25 years of service

Ta, differs

the derating

law is assumed

extrapolating

life,

tm(Ta)

these parameters

failure rate of 1700 FITs at

law when the aging

from the normal operating

To. If the Arrhenius median

for lasers

life.

Let us now consider temperature,

of

temperature,

to be capable of

tm, tm(T a) at T a is given as

= tm(To)ex p Ea/k(Ta-l-To-l),

(6)

Optical devices

/

99

90 A

//

80 70

oO 6 0

~ 30 hi

20

~>

IO

U

1

/ 104

i0 5

i0 6

OPERATING

Fig.

533

TIME

107

(HOURS)

7: Lognormal projection of time to failure versus % of cumulative

failures for LDs tested at 50 °C and 5

mW/facet. where Ea and k are activation

energy and Boltzmann's

constant.

The dependence of the degradation rate on temperature and/or current has not yet been specified and remains an urgent problem to be solved. The failure rate at 25 years of service under the I0 °C and 5 mW/facet

conditions

is plotted in Fig. 8 using Eqs.(3)

functions of standard deviation

and (6) as

for various Eas. Here, we adopt

the median life of 4.8~i05 hours at 50 °C and 5 mW/facet, assume that standard deviation failure rate decreases becomes

small,

and

is independent of temperature.

The

for any Ea as the standard deviation

and in particular,

decreases more rapidly for

standard deviations below a certain value for smaller Eas. To attain the required wear-out

failure rate,

standard deviation as

well as activation energy can be considered to be key parameters. Standard deviation must be below 0.2 to confirm a failure rate of 300 FITs,

for example,

at i0 °C and 5 mW/facet

energy of 0 eV. However, 7 into account, value below 0.2,

for an activation

taking the present value of 1.04 in Fig.

it would seem to be very difficult to attain a such that extremely strict conditions would be

imposed on the device screening procedure. standard deviation,

however,

relaxes

The restriction on

to 0.8 and 1.6 for the

activation energies of 0.2 and 0.4 eV respectively.

H. SUDO and Y. NAKANO

534

~ 10 4 uJ 0

OeV 10

. . . . . . r

. . . . . . .

~ 55_---

. . . .

u)

0.~ . ~

o)10 2 rr

/

tu

>-

~101 1-

10 0 uJ :::) .j

t

-1

~10

1

2

3

4

STANDARD DEVIATION

Fig. 8: Failure rate at 25 years of service under the conditions

of I0 °C and 5 mW/facet

standard deviation

as functions

for various Eas. Median

of

life of

4.8~I05 hours at 50 °C and 5 mW/facet.

The upper and lower limits of median

life,

standard

deviation

and failure rate for LDs at 25 years of service at a 90 % confidence

level are summarized

estimated using Eq.(3) standard

deviatior

in Table i. These values were

and Figs.

life and

of 4.8xi05 hours and 1.04 obtained

were used as the point-estimated mW/facet

2 and 3. A median

conditions.

from Fig.

7

values under the 50 °C and 5

The extrapolation

was accomplished with the Arrhenius

of median

life to ]0 °C

law assuming an activation

energy of 0.4 eV.

Table I. Upper and lower limits of the distribution parameters (tm,(~) and failure rates for LDs at a 90 % confidence level tm(h) (50 °C,5 mw/10

°C,5 mW)

O

)',,( F I T~)

at I0 °C,5 mW

Upper limit

5.6x105/4.3x106

1.23

166

Point estimation

4.8x105/3.6x106

1.04

47

Lower limit

3.8x105/2.9x106

0.89

8

Optical devices

Consequently, degradation

are important

and the activation

for the achievement

for the wear-out

3-2.

of devices with low

rates and their dispersions

specification reliability

both the selection

535

energy

of high

failure mode of LDs.

The Ge-APD

The p+n planar Ge-APD was used in the life tests. diameter of the photosensitive p-electrode

region was I00 ~m,

The

and both the

and bonding wire were AI. A preliminary

high-temperature

aging with no bias was carried out at the three

levels of 200, 260 and 295 °C. Ten samples were alloted at each level.

The dominant wear-out

abnormal breakdown Failure

failure mode of Ge-APD represents

due to the penetration

of AI into Ge.

an

(9)

is defined as the time when an abnormal breakdown

takes

place. The time to failure versus is plotted standard

in Fig.

deviation

the percent of cumulative

9 on lognormal

graph paper. Median

obtained under the conditions

failure

life and

of 260 and 295

°C are 4.7~I03 hours and 0.55 and 3.4~I02 hours and 0.8 respectively.

No failure was observed within

200 °C. The tentative Arrhenius

/

90

260=C/

27

A

80 co 70 tu Iz 6 0

v

/

50

.[

40

30 tu 2 0

i0z STORAGE TIME

I0

9: Lognormal

/

/

i '°I Fig.

time at

plot of median lives at 260 and

99

3

the testing

projection

cumulative MR 25:3-I

and 295 °C.

failures

/

I(

10 4

(HOURS)

of time to failure versus for Ge-APDs

tested at 260

% of

536

H. SUDO and Y. NAKANO

295 °C yields an activation

energy of about 1.96 eV. This value

is large compared with 0.9 eV of AI-Si alloys reported by J.R. Black. (I0) Even if a median

life of 4~I03 hours and a standard

deviation of i at 260 °C and an activation conservatively practical

assumed,

the extrapolated

failure rate at the

use temperature would be neglegibly

below i FIT. Here again, independent

4.

energy of 1 eV are

the standard

small,

deviation was assumed

to be

of temperature.

Considerations

for random failure

This section describes from the viewpoint

the reliability

of random failure.

assurance

three assumptions. requirements

philosophy

The investigation

follows was made on the basis of the experimental The first assumption

which

results and

is that the reliability

for LDs and APDs are 300 FITs and 3 FITs

respectively.

The second is that the application

temperature

I0 °C. The third is that the failure rate temperature obeys the Arrhenius The activation

energy versus

dependency

sample size for confirming

(LDs) at I0 °C is calculated

the number of failures umdel The elevated

is

law.

one-sided 60 % upper failure rate of 3 FITs FITs

that is, far

temperatures

in Fig.

(Ge-APDs)

the

and 300

i0. The parameter

is

the fixed time testing of 104 hours.

for Ge-APDs

and LDs are 150 and 50 °C

respectively.

With LDs, assuming one failure for 104 hours,

approximately

300 samples

even without

derating are sufficient

to

confirm the random failure rate of 300 FITs. As for Ge-APDs,

the extremely

low failure rate of 3 FITs

could not be confirmed by life tests at the I0 °C application temperature.

In other words,

30,000

samples would have to be

life-tested

under the practical

no failures

to meet this 3-FIT requirement

is obviously very difficult tests. However,

use conditions

to conduct

if the activation

relative required

for 104 hours with

without

derating.

such large-scale

It

life

energy is 0.3 or 0.5 eV, the

sample sizes at the elevated

°C are then reduced to 500 or 30 respectively.

temperature

of 150

Optical devices

537

10 s IT ( G e - A P D ) 7a= 150"C U.I IJJ -I

~<10 2 r/)

FIT (LD) Ta= 5 0 ° C

10 ~

10' 0

1.5

0.5 ACTIVATION

Fig.

10: Arrhenius

ENERGY

lines representing

sample size to assure 3 FITs (LD) at a 60 % confidence

2

(eV)

activation (Ge-APD)

energy versus

and 300 FITs

level under the 10 °C use

condition.

Parameter

is the number of failures

104 hours.

Test temperatures

for

are 150 °C (Ge-APD)

and

50 °C (LD). Consequently,

as far as random failure

failure rate acceleration

minimizing

the sample size to be tested. high temperature

temperature

range where

service

standard

100 devices definition

failure,

a

and random failure rates

temperatures

the median

are presented

the standard deviation

of temperature.

in Fig.

life of 5,103 hours and the

of 1 at 260 °C and the activation

eV are used. Additionally, be independent

since

failure must be chosen.

the wear-out

failures,

deviation

However,

for

the random failure rate considerably

life at various

ii. For wear-out

In this case, a

is preferable

invokes wear-out

that of the wear-out

For this purpose, versus

conditions.

which is as high as possible

excessively

exceeds

the

factor must be clarified by confirming

the failure rate under accelerated temperature

is concerned,

On the other hand,

energy of 1

is assumed to one failure

in

for a 104-hour period at 150 °C is assumed to be the for random failure.

assumed for random failure.

The activation

Provided

energy of 0.4 eV is

that the activation

energy

is more than 0.4 eV, a random failure rate below 3 FITs will be attained

at I0 *C.

Using an activation random failures

energy of i and 0.4 eV for wear-out

respectively,

the test temperature

and

must be below

538

H. SUDOand Y. NAKANO

260Oc 200Oc

200°C i ,,, I--

103

1

i

175Oc

f

f

f

175Oc

o°0

" 10 2 LLI

u.

150 ° C..._.....--------~

1¢ I~ 0

f

10O00

20000

SERVICE LIFE (HOURS)

Fig.

Ii: Temperature dependency of wear-out and random failure rates versus wear-out

service life. A family of curves for the

failure rate is calculated using median life

of 5~i03 hours and standard deviation of 1 at 260 °C and the activation energy of i eV. Straight lines for the random failure rate assume one failure in i00 devices fo~ 104 hours at 150 °C and the activation energy of 0.4 eV.

200 °C to insure that random failure is more prominent of wear-out within the testing tame of i0,000 hours.

than that

It is proper

that the samples should be allotted to two or three test temperatures ranging from 150 to 200 °C.

5.

Conclusion

The failure modes of optical semiconductor devices were classified into wear-out and random failures,

and the estimation

method for failure rates was investigated applying the lognormal and exponential distributions

respectively.

Based on the life

test data of InGaAsP11nP DH LDs and Ge-APDs as concrete examples, a statistical analysis was conducted with regard to the wear-out failure mode. The following results were clarified:

Taking the present

median life of LDs at 50 °C and 5 mW into account, necessary

it is

to select devices with low degradation rates and

dispersions.

Paralleling

this,

the precise acceleration

factor

Optical devices

539

relative to the application temperature also needs to be evaluated. On the other hand, from the preliminary life-test results, a low failure rate below several FITs should be expected for Ge-APDs. As far as random failure is concerned, a requirement of 300 FITs for LDs could be confirmed by a life test for 104 hours with no failures using 300 devices at the very least without derating. As for Ge-APDs,

30,000 devices must be life-tested for 104 hours

with no failures under practical conditions to meet 3 FITs. Under such circumstances,

the confirmation of the failure rates at the

aging temperatures is indispensable to the evaluation of the random failure rate acceleration factor. Also for this purpose, a method to determine the testing scale and condition has been statistically investigated.

Acknowledgments

The authors wish to thank Tadashi Matsumoto for his continuous encouragement throughout this work and Genzo lwane and Kenichiro Takahei for their helpful discussions.

They also wish

to thank Mitsuo Fukuda and Osamu Fujita for their valuable comments.

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H. SUDO and Y. NAKANO

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