A priori probabilistic model for the reliability of an "organised structure"
The basic possibility to create information model of the certain product (a semiconductor electronic device, or its element: p-n junction, quantum well, etc.) has been considered. Each product may be represented uniquely as a certain sequence of the Numbers set by technical requirements, drawings an...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2005
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| Cite this: | A priori probabilistic model for the reliability of an "organised structure" / E.A. Sal'kov, G.S. Svechnikov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2005. — Т. 8, № 3. — С. 100-105. — Бібліогр.: 7 назв. — англ. |
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| author | Sal'kov, E.A. Svechnikov, G.S. |
| author_facet | Sal'kov, E.A. Svechnikov, G.S. |
| citation_txt | A priori probabilistic model for the reliability of an "organised structure" / E.A. Sal'kov, G.S. Svechnikov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2005. — Т. 8, № 3. — С. 100-105. — Бібліогр.: 7 назв. — англ. |
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| description | The basic possibility to create information model of the certain product (a semiconductor electronic device, or its element: p-n junction, quantum well, etc.) has been considered. Each product may be represented uniquely as a certain sequence of the Numbers set by technical requirements, drawings and process charts. The set Number may be realised only with a certain probability, therefore, the Number (N) in the initial engineering data is set with a maximum deviation from a mean value, i.e., the tolerance ±ΔN. During operation or storage, such processes as wear or ageing destroy the product deforming the tolerance of the set sequence of numbers, what is accompanied by inevitable increase of entropy. Hence, each product is endowed with the information negentropy, which may be calculated and may serve as initial value when solving an adequate equation of production of the thermodynamic entropy. As a particular example, the simplified model has been considered: a semiconductor plate covered on each side with insulator, which degrades during storage. The equality of a square of the tolerance and the real Number dispersion determined by the probability with which the Number realises with the set tolerance was taken as the base approximation.
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 3. P. 100-105.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
100
A priori probabilistic model for the reliability
of an “organised structure”
E.A. Sal’kov, G.S. Svechnikov
V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine,
41, prospect Nauky, 03028 Kyiv, Ukraine
Abstract. The basic possibility to create information model of the certain product (a
semiconductor electronic device, or its element: p-n junction, quantum well, etc.) has
been considered. Each product may be represented uniquely as a certain sequence of the
Numbers set by technical requirements, drawings and process charts. The set Number
may be realised only with a certain probability, therefore, the Number (N) in the initial
engineering data is set with a maximum deviation from a mean value, i.e., the tolerance
±ΔN. During operation or storage, such processes as wear or ageing destroy the product
deforming the tolerance of the set sequence of numbers, what is accompanied by
inevitable increase of entropy. Hence, each product is endowed with the information
negentropy, which may be calculated and may serve as initial value when solving an
adequate equation of production of the thermodynamic entropy. As a particular example,
the simplified model has been considered: a semiconductor plate covered on each side
with insulator, which degrades during storage. The equality of a square of the tolerance
and the real Number dispersion determined by the probability with which the Number
realises with the set tolerance was taken as the base approximation.
Keywords: reliability of electronic devices.
Manuscript received 29.06.05; accepted for publication 25.10.05.
1. Introduction
For solving the reliability problem of a organised
structure (OS), two kinds of information are basically
used [1]: a priori formalised on the basis of priori
assumed probability distribution for realisation of those
or other OS properties, and a posteriori, based on the
empirical data received as a result of tests.
Any OS, i.e. a certain product, or a semiconductor
electronic device in a case in which we are interested, or
its element may be represented uniquely with a certain
sequence of Numbers set by technical requirements, OS
drawings and process charts, i.e. a sequence of
technological operations (TO) of its production [2].
At that, each Number may be realised only with a
certain probability, therefore, the Number is set in the
initial engineering data as its mean value (〈Number〉)
with a tolerance deviation ±ΔNumber.
It is presumed that produced OS is endowed with
information negative entropy – negentropy [3]. During
operation or storage, such processes as wear or ageing
destroy the OS with deforming, first of all, a tolerance of
the set sequence of numbers, what is accompanied by
inevitable increase of entropy.
Before to begin creation of offered model for the a
priori reliability estimation, we want to define a point of
issue in terms of the theory of probability. Let us agree
that we do not reconstruct existing developed methods of
a priori reliability estimation (APR) or a posteriori
reliability estimation (APO) [1, 2].
The idea of the offered method is based on the
following probabilistic hypothesis [3]. If all geometrical,
physical and chemical, qualitative, etc. digital OS
characteristics determined by Numbers with indication
of tolerance ±ΔN on drawings or documents are mixed
in a random manner, we shall receive an unorganised
system with the maximum information entropy. By
making inverse procedure and returning all numerical
characteristics to their places on the drawing in a random
manner, we shall receive an OS featuring the
negentropy. The latter may be calculated, if we postulate
the following positions:
1) A strictly defined sequence of numbers set by
drawings and process charts is an information OS model
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 3. P. 100-105.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
101
endowed with the appropriate negentropy as we said
above.
2) Each Number from the sequence is set with the
maximum deviation from its mean value 〈N〉, i.e. the
t o l e r a n c e ±ΔN. During OS production, the
Number and the tolerance are realised with a certain
probability P(J).
3) The dispersion of each Number equal to 〈[Δ(N)]2〉
may be expressed through the tolerance determined by a
designer and implemented by a technologist. The basic
assumption is as follows: the tolerance is set as ±ΔN and,
hence, it may be expressed approximately (at least,
formally) through dispersion of Number as:
〈[Δ(Number)]2〉1/2 = ±ΔN. (1.1)
4) Technological operation is defined by a set of
conditions R [1, 4] on the realisation of which an event
A occurs, i.e. realization of 〈N〉 within of the tolerance
±ΔN. There exists a probability distribution for
realisation of each allowable deviation, i.e. the tolerance
established for the given technological operation.
5) The complete probability that the OS will be
produced according to the deviations from their mean
value given on drawings (±ΔN) can be calculated by the
Bayes a priori estimation method [1]. The full Bayes
conditional probability determines the probabilistic
space where the characteristics set by the design exist
under the accepted OS production technique.
In order to calculate negentropy, we shall use a
known Bayes formula [4] for the conditional probability
P(A / B) of an event A (the next TO, the probability
P(A)) under the condition that an event B occurred (the
previous TO, the probability P(B)):
( ) ( )
( )BP
ABPBAP = . (1.2)
P(AB) = P(A) P(B) is the probability that two
independent events realize, i.e. TOs which are inde-
pendent on each other in themselves. The operation B
can be considered as an event which may be realised,
and only with one of n incompatible events (TOi) A1,
A2, ..., Ai, ..., An. In such case, the formula for full
probability TO B will be
( ) ( ) ( )i
n
i
i B/APAPBP ⋅= ∑
=1
. (1.3)
In our case, the complete conditional probability of
realisation TO Ai, i.e.
( ) ( ) ( )
( ) ( )i
n
i
i
ii
i
B/APAP
B/APAP
/BAP
⋅
⋅
=
∑
=1
, (1.4)
allows to estimate quantitatively the negentropy TO Ai,
which is “expend” in operation process, returning the OS
to a chaotic “initial” condition (deterioration).
The negentropy value corresponding to the
probability (1.4) may be used as an initial condition for
quantitative solution of the entropy production equation
[5] which reflects the evolution of separate OS
characteristics due to OS operation or during its storage
(that is, in practice, ageing).
2. Thermodynamic entropy and its balance equation
For a case of semiconductor technologies (growth,
doping, p-n junction formation, structures, etc.), is
necessary to use the thermodynamic approach to
determination of the entropy and its production (for
example, ageing).
The entropy production in the thermodynamics [5-7]
is associated with the presence of spatial heterogeneity
in the distribution of temperature, partial chemical
potentials μi and convective speed U0. In this case, the
spatial heterogeneity of the chemical potential is caused
by spatial heterogeneity for the concentration of
components Ci and/or temperature.
In the most common form, the equation of the
entropy balance S may be written through the density of
the entropy flow JS, entropy production per a unit of
volume σS and the sum of mass density of a component
system ρ = ∑ni as
( )
SSdiv
t
S σ
∂
ρ∂
+−=
⋅ J . (2.1)
As J = ρU0 is a convective flow, the full entropy
flow JS develops from the convective entropy flow
ρ ⋅ s ⋅ U0 and an additional flow having another physical
origin JS
′ = JS − sJ. From (2.1), in view of that
J
t
div−=
∂
∂ρ , we get:
Ssdiv σρ +′−=
∂
∂
⋅ J
t
S . (2.2)
This equation is applicable to a case of diffusion in
gases: local violation of chaos (equilibrium state), for
example, due to the increase of density of particles and
change of their speeds, will become gradually more
homogeneous both in a configuration space and space of
speeds. It is also applicable for consideration of ageing
of local formations in semiconductor structures.
For solving a specific problem, it is necessary to
develop mathematical (probabilistic) model for gene-
ration process of OS defects caused by tests/operation,
i.e. the specific mechanism of the entropy production.
Such specific mechanism can be simulated using the
same Bayes methods of statistical evaluation [1].
The complex OS model demands to determine weak
parts in practice. Theoretical estimations should be
carried out for these weak parts with subsequent
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 3. P. 100-105.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
102
“summation” of such estimations by a principle of
simple model. E.g., for the analysis of Eq. (2.2) under
the conditions of local (we mean a part of the OS) quasi-
equilibrium, it is possible to use thermodynamic
correlations. For example, it is valid for a homogeneous
system:
PdvdTds += ε ,
where s, ε, v are specific values for the entropy, energy
and volume, respectively, referred to a mass unit of the
system. Of course, the time variant of this equation will
be simply
dt
dvP
dt
d
dt
dsT +=
ε . (2.3)
In order to put Eq. (2.2) to a form comparable with
(2.3), we will use a known identity [7]
grad0 ⋅+
∂
= U
dtdt
d .
Then, for any physical value F, we will receive [7]:
( ) ( )0div UF
t
F
dt
dF
⋅⋅+
∂
⋅∂
= ρρρ . (2.4)
At this stage, we receive a general scheme for
theoretical estimations of OS characteristic stability
under a known initial negentropy value.
By similar further specifications (in particular, by
designating the relative density of a component system
as Ci = ρI / ρ), we shall generate the equation for entropy
production in an n-component system
.
1
1 t
C
T
t
v
T
P
tTt
S
i
n
i
i
∂
∂
⋅⋅−
−
∂
∂
⋅⋅+
∂
∂
⋅⋅=
∂
∂
⋅
∑
=
ρμ
ρερρ
(2.5)
The basic initial phenomenological equations are written
above. The latter also supposes a solution under a known
initial entropy value, negentropy S0 in our case,
approaches to finding of which are schematically stated
in equations (2.1) − (2.5).
3. Elementary model
The considered elementary model is as follows: plate is
cut off from the semiconductor, two planes covered with
an insulating layer. The form and parameters of the
model are shown in Fig. 1.
TO1: The plate is cut out the semiconductor. We
suppose that the probability to obtain the thickness x
within the tolerance ±Δx is determined by a Gaussian
distribution P(x); we also accept that the thickness
dispersion 〈(Δx)2〉 ≈ (±Δx)2. Then, if the mean value of
the plate thickness is 〈x〉, we will get for P(x):
Fig. 1. The form and parameters of the model.
( ) ( )
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
Δ±⋅
−
−⋅
Δ±⋅
= 2
2
)(2
exp
2)(2
1
x
xx
x
xP
π
. (3.1)
TO2: One side of the plate is covered with an
insulating layer (below, an index 2 refers to the TO’s
number). The mean thickness of the insulating layer is
〈d〉, and the dispersion is 〈(Δd)2〉, that is, it is equal to
square of the tolerance. The total thickness of two layers
y = d + x with a dispersion 〈(Δy)2〉 is defined by the
conditional probability that TO1 having the probability
(3.1) is made within the tolerance ±Δx, and TO2 is made
within the tolerance ±Δd. Then
( )
.
)(2
exp
)(2
1)/(
2
2
2
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
Δ±⋅
−−
−×
×
Δ±⋅
=
d
dxy
d
xyP
π
(3.2)
From (3.1), (3.2), the full conditional probability P(y)
for realisation of “plate A + layer В” may be written as
( ) ( )
[ ]
( )
.
)(2)(2
exp
)()(2
1
/()
22
2
22
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
Δ±⋅+Δ±⋅
−−
−×
×
Δ±+Δ±⋅
=
=⋅⋅= ∫
+∞
∞−
yx
dxy
yx
dxxyPxPyP
π
(3.3)
ТО3: The plate is covered with an insulating layer
from an opposite side (index 3). The mean thickness of
the insulating layer is 〈d〉, and the dispersion is
〈(Δd)2〉 = (±Δd2)2. The total thickness of the plate and
two layers z = x + d + d with the dispersion
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 3. P. 100-105.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
103
〈(Δz)2〉 = (±Δx)2 + 2(Δd)2 is defined by the conditional
probability (i.e., under condition that the concrete value
x = x + d according to (3.3) realises)
( )
( )
( )( )
( ) ⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
Δ±⋅
−+−
−×
×
Δ±⋅
=
2
2
2
2
exp
2
1/
d
ddxz
d
yzP
π
(3.4)
of the event that TO1 is made within the tolerance ±Δx
and TO2 within the tolerance ±Δd2, has the same
probability distribution as ТО1.
By analogy to (3.1), the full probability P(z)
considering (3.3) and (3.4) is equal to
( ) ( ) ( )
( ) ( )
[ ]
( )
[ ]
.
)(2)(2
2
exp
)(2)(2
1
/
,,,
22
2
22
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
Δ±+Δ±⋅
−−
−×
×
Δ±+Δ±⋅
=
=⋅⋅∫=
⋅∫=∫ ∫ ⋅⋅=
∞+
∞−
+∞
∞−
+∞
∞−
+∞
∞−
yx
dxz
yx
dyyzPyP
dyzyPdydxzyxPzP
π
(3.5)
So, at presence of distribution function for a random
variable P(X), it is possible to define the ensemble
entropy (negentropy) of random variables as [3]
( ) ( ) dXXPXPS ⋅⋅−= ∫
+∞
∞−
ln .
In particular, under the Gaussian distribution (3.1)
( )
( )
( )[ ] xconst SSx
exe
dX
x
XX
x
x
XX
x
S
Δ±
∞+
∞−
+=Δ±+
+⋅=⎥⎦
⎤
⎢⎣
⎡ Δ+⋅=
=
⎟⎟
⎟
⎟
⎠
⎞
⎜⎜
⎜
⎜
⎝
⎛
Δ⋅
−
−
Δ⋅
×
×∫
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
Δ⋅
−
−⋅
Δ⋅
−=
212
212
2
2
2
2
2
2
ln
2lnln2ln
22
1ln
2
exp
2
1
ππ
π
π
Here, we received an example of the scheme for
definition of the initial negentropy value
S0 = Sconst + S±Δx under the Gaussian distribution for the
probability that an event consisting in realisation of size
〈x〉 ± Δx occurs considering that 〈(Δx)2〉 ≈ (±Δx)2.
4. The entropy of ensemble as a whole. Degradation.
As a result of manufacturing of the plate and covering of
both sides with a dielectric, we received a structure of
total thickness z = x + 2d with the probability
distribution defined as (3.5). The entropy of this
ensemble is
( ) ( )
.)(2)(2ln
ln
22 dxe
dzzPzPS
Δ±⋅+Δ±⋅⋅=
=⋅⋅−= ∫
+∞
∞−
π
(4.1)
Let's assume now that the characteristic
d0 = d2 + d3 = 2d degrades, for example, decreases with
time according to the law ( )tf
d
td 0)( = , where f(t) is a
growing function of time, and f(0) = 1. The mean value
of the ensemble degrades in the same way.
Considering (3.1), the probability distribution for the
realisation of the thickness x within the tolerance ±Δ, i.e.
P(d(t)), will also change as
( )( )
( )
( )
( ) ( ).
;
2
exp
2
1
222
2
2
00
2
tfd
dd
d
tdP
t
t
⋅Δ±=
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⋅
−
−×
×
Δ±⋅
=
σ
σ
π
(4.2)
According to the above, the entropy of ensemble
changes in time
( ) ( ) ( ) .ln0ln
lnln
0
000
tfSStf
SSS t
++=+
++=+= σσ
In this case, S(0) is a required initial entropy value
for a part of the whole ensemble (only for dielectric
layers).
For the whole (z = x + 2d) ensemble, the entropy is
equal to:
.)()()(ln 22
0 tfdxSS ⋅Δ±+Δ±+=
Let's accept now that allowable (critical) values for
thickness of dielectric layers are equal to dcr. Then, with
change in time of d(t), distribution of probabilities
changes, of course, with the entropy; in such case,
failure of the whole ensemble is possible.
Graphically, this situation is depicted in Fig. 2 where
distributions of probability P[d(t)] are shown when the
film of the set thickness d0 degrades under the
exponential law up to the critical value of dcr.
There also exists the possibility to estimate the
number of failures of the above structure in a time
interval from t up to t + Δt. The number of working
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 3. P. 100-105.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
104
structures at the moment t is: ( )( ) dtdp
d
∂⋅∫
∞
cr
, and at the
moment t +Δt their number is ( )( ) dttdp
d
∂∂ ⋅+∫
∞
cr
.
The difference between these values is a number of
failures γ(t) within the interval t ÷ t + Δt:
( ) ( )( ) ( )( )
( ) ( )
( ) .
1
cr
crcr
crcr
tttf
ttfddp
t
d
d
ttdpd
d
tdpt
=
∂∂
⋅⋅=
=
Δ
⋅
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⋅∫
∞
+−⋅∫
∞
= ∂∂∂γ
Let's illustrate this, as above, with an example of the
degradation law exponential in time ( ) ( )ttf αexp= .
Then
( )
( ) ( )
;ln1
;exp;
cr
0
cr
cr0cr
d
d
t
tdd
tf
ttf
⋅=
−⋅==
∂∂
α
αα
hence,
( ) ( )
( ) ( )⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⋅
−
−⋅
⋅
⋅
=
=⋅⋅=
cr
2
0cr
cr
2
cr
crcr
2
exp
2 t
dd
t
d
ddpt
σσπ
α
αγ
where
( ) ( )
( )[ ] .exp
2exp
2
cr
0
0
2
cr0
cr
2
cr
2
⎥
⎦
⎤
⎢
⎣
⎡
⋅=⋅=
=⋅=
d
d
t
tt o
σασ
ασσ
Fig. 2. Probability distribution P[d(t)] for a case: film of the set
thickness d01 = 8 μm with the dispersion of 5 μm (curve d01)
degrades under the exponential law ( )t
d
td
⋅
=
αexp
)( 0 ,
reaching the value of d02 = 75 μm with the dispersion of 10 μm
(curve d02). The critical value of thickness of the film:
dcr = 70 μm.
Simple transformations result in:
( ) ( )
( )
.
2
exp
2
2
exp
2
2
0
cr
2
0
2
0cr
2
0
0
2
cr
2
cr
02
0
2
0cr
cr
0
0
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
⋅
⋅
−
−⋅
⋅
⋅
=
=
⎟
⎟
⎟
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎜
⎜
⎜
⎝
⎛
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⋅
−
−⋅
⋅⋅⋅
⋅
=
d
dddd
d
d
d
dd
d
d
kpd
t
σσπ
α
σπσ
α
γ
The probability of non-failure operation is expressed
by γ(t) as
( ) ( )( )
( )
.
2
exp
2
expexp
2
0
cr
2
0
2
0cr
2
00
2
cr
⎟
⎟
⎟
⎠
⎞
⎟⎟
⎟
⎠
⎞
⎜⎜
⎜
⎝
⎛
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⋅
⋅
−
−×
⎜⎜
⎜
⎝
⎛
×
⋅⋅
⋅−=−=
d
ddd
d
dtttF
σ
σπ
αγ
5. Conclusions
1. If real tolerances lose, during storage or operation,
connection with the set tolerances, the OS may not meet
to the technical requirements of reliability.
2. We consider indisputable that the OS (semi-
conductor device) may be represented uniquely with a
certain sequence of the Numbers which includes specific
characteristics of this OS. The elaborated produced OS
should be endowed with a certain information negative
entropy.
3. If tolerances of the Numbers determining the
design and technological OS contents may be connected,
to some approximation, with the dispersions of
appropriate probabilistic distributions as
(dispersion)1/2≅±(tolerance), it is natural to use the Bayes
formula to determine the full conditional probability that
the OS is made according to the requirements to its
initial characteristics.
4. Hence, it is also possible to calculate the initial
value of the information entropy in order to solve the
negentropy production equation on a basis of the
physical, chemical and other data on the properties of
various OS parts (structures).
5. Critical negentropy values which changes in time
may be reasonably included into the technical
requirements list as the data for calculation of a priori
quantitative reliability characteristics of the device.
An extremely simplified model considered above
demands very complex calculations. The real device is
even more complex, but this circumstance may not
discredit the approach itself to the solution of the a priori
reliability forecasting problem on the basis of tolerances.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 3. P. 100-105.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
105
It is known from practice that the standard failure of the
device of any complexity is caused by failure of the so-
called weak parts, but not failure the device as a whole. In
this connection, the method offered here may be applied
to weak parts, essentially facilitating data processing with
the use of the appropriate PC programs.
In summary, we want to emphasise the main thesis
prompting to develop the proposed approach to APR: if
APR and APO results are close for the given OS, the
further improvement of this OS has to be charged to
designers, not technologists.
References
1. V.P. Savchuk, Bayes methods for statistic estimation.
Nauka, Moscow (1989).
2. A.A. Chernishov, Reliability of semiconductor devi-
ces and integrated circuits. Radio i Svyaz’, Moscow
(1988).
3. A.M. Yaglom, I.M. Yaglom, Probability and infor-
mation. Nauka, Moscow (1973).
4. B.V. Gnedenko, Theory of probability. Nauka, Mos-
cow (1969).
5. U.L. Klimontovich, Statistical physics. Nauka, Mos-
cow (1982).
6. V.L. Vorobiev, Principles of thermodynamic diag-
nostics and reliability of microelectronic devices.
Nauka, Moscow (1989).
7. K.P. Gurov, The phenomenological thermodynamics
of irreversible processes. Nauka, Moscow (1978).
|
| id | nasplib_isofts_kiev_ua-123456789-120977 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2025-11-24T14:55:13Z |
| publishDate | 2005 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Sal'kov, E.A. Svechnikov, G.S. 2017-06-13T11:44:35Z 2017-06-13T11:44:35Z 2005 A priori probabilistic model for the reliability of an "organised structure" / E.A. Sal'kov, G.S. Svechnikov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2005. — Т. 8, № 3. — С. 100-105. — Бібліогр.: 7 назв. — англ. 1560-8034 https://nasplib.isofts.kiev.ua/handle/123456789/120977 The basic possibility to create information model of the certain product (a semiconductor electronic device, or its element: p-n junction, quantum well, etc.) has been considered. Each product may be represented uniquely as a certain sequence of the Numbers set by technical requirements, drawings and process charts. The set Number may be realised only with a certain probability, therefore, the Number (N) in the initial engineering data is set with a maximum deviation from a mean value, i.e., the tolerance ±ΔN. During operation or storage, such processes as wear or ageing destroy the product deforming the tolerance of the set sequence of numbers, what is accompanied by inevitable increase of entropy. Hence, each product is endowed with the information negentropy, which may be calculated and may serve as initial value when solving an adequate equation of production of the thermodynamic entropy. As a particular example, the simplified model has been considered: a semiconductor plate covered on each side with insulator, which degrades during storage. The equality of a square of the tolerance and the real Number dispersion determined by the probability with which the Number realises with the set tolerance was taken as the base approximation. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics A priori probabilistic model for the reliability of an "organised structure" Article published earlier |
| spellingShingle | A priori probabilistic model for the reliability of an "organised structure" Sal'kov, E.A. Svechnikov, G.S. |
| title | A priori probabilistic model for the reliability of an "organised structure" |
| title_full | A priori probabilistic model for the reliability of an "organised structure" |
| title_fullStr | A priori probabilistic model for the reliability of an "organised structure" |
| title_full_unstemmed | A priori probabilistic model for the reliability of an "organised structure" |
| title_short | A priori probabilistic model for the reliability of an "organised structure" |
| title_sort | priori probabilistic model for the reliability of an "organised structure" |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/120977 |
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