Degradations of semiconductor devices under pulsed heat overloading
The linear heat model of degradations of semiconductor devices under pulsed electric overloading has been constructed. Expressions for temporal dependencies of the temperature under different forms of pulse of current are obtained.
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| Published in: | Вопросы атомной науки и техники |
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| Date: | 2000 |
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| Format: | Article |
| Language: | English |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2000
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| Cite this: | Degradations of semiconductor devices under pulsed heat overloading / V.I. Chumakov // Вопросы атомной науки и техники. — 2000. — № 3. — С. 96-98. — Бібліогр.: 7 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860264930742108160 |
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| author | Chumakov, V.I. |
| author_facet | Chumakov, V.I. |
| citation_txt | Degradations of semiconductor devices under pulsed heat overloading / V.I. Chumakov // Вопросы атомной науки и техники. — 2000. — № 3. — С. 96-98. — Бібліогр.: 7 назв. — англ. |
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| container_title | Вопросы атомной науки и техники |
| description | The linear heat model of degradations of semiconductor devices under pulsed electric overloading has been constructed. Expressions for temporal dependencies of the temperature under different forms of pulse of current are obtained.
|
| first_indexed | 2025-12-07T18:59:33Z |
| format | Article |
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Problems of Atomic Science and Technology. 2000. N 3. Series: Plasma Physics (5). p. 96-98 96
UDC 621.382
DEGRADATIONS OF SEMICONDUCTOR DEVICES
UNDER PULSED HEAT OVERLOADING
V.I. Chumakov
Kharkov State technical university of radioelectronics,
61166, Kharkov, Lenin av.,14
The linear heat model of degradations of semicon-
ductor devices under pulsed electric overloading has
been constructed. Expressions for temporal dependen-
cies of the temperature under different forms of pulse of
current are obtained.
The thermal degradations are one of the general rea-
sons of refusal of radioelectronic equipment (REE) un-
der pulsed electrical overload. The special danger pre-
sent heat overloading of semiconductor devices, which
forms the element base of REE. For determination of
critical levels of energy, that lead to arising the thermal
damage, use linear heat model, adjusting the depend-
ency an threshold power of thermal damage on duration
of square-wave form pulse thermal overloading in the
manner of
Pï/S = B1 (Tï-Tí) t
-0,5 , (1)
where S - p-n junction area, pCTkB ρπ=1 - constant,
defined by thermal parameters of material, Tí, Tê - ini-
tial and final temperature of material accordingly [1].
As a degradation effect it is possible to understand any
phenomena, adjusting to change the semiconductor de-
vice characteristics at achievement of the temperature of
junction Tê. So, if as final temperature the melting tem-
perature of semiconductor is considered, then degrada-
tion effect reveals itself in the manner of junction pene-
tration and irreversible damage of semiconductor de-
vice. The value wB=B1(Tê-Tí) (W-B constant) character-
izes the susceptibility of semiconductor device of dif-
ferent types to thermal overloading.
To determine the temporal dependencies of semi-
conductor temperature under arbitrary pulse form of
electric overloading it is possible to get following ex-
pression by means of Dhuamel integral [2]
[ ]∫ ττ−
τ−
τ
ρ
+=
t
dtrH
td
d
P
pCíTtT
0
),(
)(
)(
1
)( , (2)
where ),( trH - transient response, representing the
reaction on electric overloading in form of unit-step
Heaviside function; jU and bR - parameters of
equivalent scheme of semiconductor sample (fig.1.);
)(tP - instantaneous power of electric overloading un-
der current flow )(ti :
bRtijUtitP )(2)()( += . (3)
Using (2), will get for overloading in the form of
square-wave pulse by height 0P
[ ]),(),(0)( τ−−+= trHtrHPíTtT , (4)
or for normalized temperature with account (1)
=τ
τ−τ−
τ=
−
−
= ∫
t
d
tPtd
d
P
íÒêT
íTtT
tf
0
)(0
1
)(
)(
)(
)(
∫ τ
τ−
τ=
t
d
t
P
BSw
0
1
)(
2
1
. (5)
Fig.1. The equivalent scheme of semiconductor sample.
[ ]nxpx , - depletion region; [ ]pxX ,1 and [ ]2, Xnx -
quasi-neutral regions of semiconductor; bR and jR -
accordingly resistance of quasi-neutral and depletion
regions; jU - p-n junction voltage.
The expression (5) allows enough simply to derive
formulas for temporal dependencies of semiconductor
sample temperature sample under arbitrary forms of
pulse of current with duration èτ [3]:
1. The square-wave pulse:
tbRIjUI
BSw
tf
+= 2
002
1
)( .
2. The triangular pulse:
+
τ
−−
τ
=
2/3
2
2/3
1
2/3
3
4
)( utt
uSBw
jUmI
tf
−
τ
+ 2/5
12
132/5
5
8
tt
ujU
bRmI
,
where 21 utt τ−=
3. Exponential pulse:
( ) ( )
BSw
tDbRItDjUI
tf
ττ+ττ
=
222
00
)( ,
where ∫−=
x
dvvexexD
0
)(
22
- Douson integral [2].
4. Sine-wave pulse:
97
{ +πθπθ−πθπθ
τ
)()cos()()sin()( SC
BSw
ujUmI
tf
[ ]
πθπθ−πθπθ−θ+ )()sin()()cos(
2
SC
jU
bRmI
,
where ut τ=θ ,
dt
x
t
t
xS ∫
π
=
0
sin
2
1
)( , dt
x
t
t
xC ∫
π
=
0
cos
2
1
)( - Fresnel
integrals.
The graphs of temporal dependencies of normalized
temperature for pulses of different form shown on fig.2.
For estimation of temporary features of heat process
in semiconductor value 2L
Tk
PC
T
ρ=τ , named thermal
relaxation time constant, is introduced. Here L - typical
size of energy-deposition region. Constant Tτ is con-
nected with constant W-B by expression
( ) TíTêT
L
Tk
Bw πτ−= . (6)
In linear model principle super-positions is kept, i.e.
each following pulse deliver an additional heating of the
element, and final temperature forms from separate por-
tions of energy, delivered by separate pulses. The de-
pendency of power, which required for realization heat
damage under action of pulse sequence, possible gets by
means of (2):
( ) ( ) ( )[ ]∑
=
θ−−τ+θ−−
=
N
i
irHuirHíTêT
SBw
ïP
1
)1(,)1(,
,(7)
where θ - pulse time cycle, N - number of pulses in the
sequence.
As it can be seen from (7), if the pause between
pulses has enough duration, so process a thermal con-
ductivity establishes uniform heat distribution in mate-
rial, and power of single pulse realize insignificant heat-
ing, then the stationary process is fixed in medium, and
heat degradations do not appear. But if each following
pulse provides the increase of background temperature,
that, eventually, as a result of actions of series N of
pulses a melting temperature of material is attained.
Temporary diagrams of heating process due to sequence
of square-wave pulses of power are shown in fig.3.
Each pulse with height P0 can be presented as the dif-
ference of Heaviside functions, acting at moments of
time θn and )( un τ+θ , where θ - pulse time cycle,.
...2,1,0=n "Negative power" corresponds to the semi-
conductor cooling down process during the pause be-
tween pulses in consequence of thermal conductivity
process.
If the temperature at moment of completion of pulse
reaches value of f1, then to starting of following pulse
remaining temperature corresponds to value )(θf .
Herewith for achievement of the temperature of melting
fn = 1 as a result of actions N pulses, it is necessary to
satisfy the condition 1=∆fN , where f∆ - increase of
the temperature during one cycle. When the temperature
of heating corresponds to value f2,, and in pause be-
tween pulses occurs cooling down process to starting
temperature, as a result the stationary process estab-
lished.
The expression (1) is got for adiabatic heating re-
gime of semiconductor under the action of short-pulse
overload. In linear model is expected that current flows
through section less, than real size of junction section
[1]. The threshold current value, which is sufficient for
heat overloading, may be calculated using estimation of
time tï that required for realization thermal overload,
which are got from (5)
1
0
1
)(
2
1
=τ
τ−
τ∫
ït
d
ït
P
BSw
; 0
)(
=
dt
ntdf
. (8)
From these expressions, using also (3), possible get
values of maximum current or average power of pulse,
under which occur the thermal degradation.
The examples of typical dependencies threshold cur-
rent of overloading on time of achievement maximal
temperature shown on fig.4 for exponential and triangu-
lar pulses. The numerical calculation shows that for
exponential current the damage approach in narrow
range of pulse duration 924,0/2653,0 <τ< ènt ; for
triangular current thermal degradation occur on trailing
edge of pulse 184,1/2 >τunt .
Fig.2. The dependencies of the temperature for different
pulse forms: square-wave - 1, exponential - 2, sine-
wave - 3, and triangular - 4
98
Fig.3. The temporary diagrams of semiconductor heating by sequence of pulses.
Fig.4. Dependency of threshold current of thermal damage on time of heating toe maximum temperature (the trian-
gular pulse of current - line; the exponential current - dot [2]).
The localization of current results the effect of heat
localization, that forms the base of nonlinear model of
thermal breakdown of semiconductor [4,5]. In this case
nonlinear equation of thermal conductivity results to
sharpening regime, for which are executed the condition
∞→)(tf , under 0tt → , i.e. during finite time gap
possible achievement of infinite temperature in local
areas of medium. In [4] is shown that one of the general
reasons of arising the sharpening regime is uniformly
distribution of starting temperature of sample, increas-
ing in consequence of semiconductor conductivity rising
advance of its thermal conductivity under current flow-
ing and Joules heating of semiconductor. Besides, in
extrinsic semiconductor possible determination of non-
uniform bulk resistance, that results the effect of current
filament already on initial stage of shaping thermal
structure [6,7].
As a result of analysis of processes semiconductor
elements heating the temporary dependencies of the
temperature of sample under pulsed current loading are
got. It allows to define the critical regimes of operation
REE and take into account them under defining of rea-
sons of refusals and studies of questions to electromag-
netic compatibility.
References:
1. Wunsch D.S., Bell R.R. IEEE Trans. on Nuclear. Sci.
1968. NS.15, No.6. P.244-259.
2. Dwyer V.M., Franklin A.J., Campbell D.S. IEEE
Trans. on Electron Dev. 1990, ED.37, Nî.11, pp.2381-
2387.
3. Simulation of radioelectronic devices thermal failures
/ V.I. Chumakov // Radioelektronika i informatika
,1992, N 2, p.31-37.
4. Virchenko Yu.P., Vodyanitskii À.À., Kovtun G.P.
Preprint, Kharkov: KhIFT, 1992, 32 p. (in Russian).
5. Galaktionov V.À., Kurdyumov S.P., Posashkov S.À.,
Samarskii À.À. In : Mathematic modeling. Processes in
nonlinear medium. Moskow: Nauka, 1986, p.142-182
(in Russian).
6. Blakemore J. Solid-state physics.-Moskov: Mir.-
1988.-608 ñ (in Russian).
7. Carroll J. Microwave generator on hot electrons.
Moskow: Mir, 1972.-382 ñ (in Russian).
|
| id | nasplib_isofts_kiev_ua-123456789-82375 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T18:59:33Z |
| publishDate | 2000 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Chumakov, V.I. 2015-05-29T07:28:09Z 2015-05-29T07:28:09Z 2000 Degradations of semiconductor devices under pulsed heat overloading / V.I. Chumakov // Вопросы атомной науки и техники. — 2000. — № 3. — С. 96-98. — Бібліогр.: 7 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/82375 621.382 The linear heat model of degradations of semiconductor devices under pulsed electric overloading has been constructed. Expressions for temporal dependencies of the temperature under different forms of pulse of current are obtained. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Рlasma Dynamics and Plasma-Wall Interaction Degradations of semiconductor devices under pulsed heat overloading Article published earlier |
| spellingShingle | Degradations of semiconductor devices under pulsed heat overloading Chumakov, V.I. Рlasma Dynamics and Plasma-Wall Interaction |
| title | Degradations of semiconductor devices under pulsed heat overloading |
| title_full | Degradations of semiconductor devices under pulsed heat overloading |
| title_fullStr | Degradations of semiconductor devices under pulsed heat overloading |
| title_full_unstemmed | Degradations of semiconductor devices under pulsed heat overloading |
| title_short | Degradations of semiconductor devices under pulsed heat overloading |
| title_sort | degradations of semiconductor devices under pulsed heat overloading |
| topic | Рlasma Dynamics and Plasma-Wall Interaction |
| topic_facet | Рlasma Dynamics and Plasma-Wall Interaction |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/82375 |
| work_keys_str_mv | AT chumakovvi degradationsofsemiconductordevicesunderpulsedheatoverloading |