Self-consistent method for optimization of parameters of diode temperature sensors
In the framework of the diffusion transport model through an abrupt asymmetric p n-junction, the ideality factor of which is assumed to be equal to unity, and with the help of criteria commonly used to describe theoretically the semiconductor diode structures, the relations are obtained for estimati...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
1999
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| Цитувати: | Self-consistent method for optimization of parameters of diode temperature sensors / N.R. Kulish, Yu.M. Shwarts, V.L. Borblik, Ye.F. Venger, V.N. Sokolov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 1999. — Т. 2, № 2. — С. 15-27. — Бібліогр.: 24 назв. — англ. |
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irk-123456789-1191082017-06-05T03:03:26Z Self-consistent method for optimization of parameters of diode temperature sensors Kulish, N.R. Shwarts, Yu.M. Borblik, V.L. Venger, Ye.F. Sokolov, V.N. In the framework of the diffusion transport model through an abrupt asymmetric p n-junction, the ideality factor of which is assumed to be equal to unity, and with the help of criteria commonly used to describe theoretically the semiconductor diode structures, the relations are obtained for estimation of parameters of the diode temperature sensor. The set of these parameters provides either the maximum extent of a thermometric characteristic toward the higher temperature range, or maximum sensitivity of the diode temperature sensor. For Ge, Si, GaAs diode temperature sensors with n⁺p- and р⁺n- junctions the limits of thermometric characteristics were determined, together with temperature dependencies of sensitivity, static and dynamic resistance calculated for cases of the maximum length of the thermometric characteristic and of maximum sensitivity. It has been shown that experimentally measured characteristics of diode temperature sensors are within the ranges determined by the limiting characteristics. The ways of further improvement of diode temperature sensors are discussed. 1999 Article Self-consistent method for optimization of parameters of diode temperature sensors / N.R. Kulish, Yu.M. Shwarts, V.L. Borblik, Ye.F. Venger, V.N. Sokolov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 1999. — Т. 2, № 2. — С. 15-27. — Бібліогр.: 24 назв. — англ. 1560-8034 PACS 07.07.D http://dspace.nbuv.gov.ua/handle/123456789/119108 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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| description |
In the framework of the diffusion transport model through an abrupt asymmetric p n-junction, the ideality factor of which is assumed to be equal to unity, and with the help of criteria commonly used to describe theoretically the semiconductor diode structures, the relations are obtained for estimation of parameters of the diode temperature sensor. The set of these parameters provides either the maximum extent of a thermometric characteristic toward the higher temperature range, or maximum sensitivity of the diode temperature sensor. For Ge, Si, GaAs diode temperature sensors with n⁺p- and р⁺n- junctions the limits of thermometric characteristics were determined, together with temperature dependencies of sensitivity, static and dynamic resistance calculated for cases of the maximum length of the thermometric characteristic and of maximum sensitivity. It has been shown that experimentally measured characteristics of diode temperature sensors are within the ranges determined by the limiting characteristics. The ways of further improvement of diode temperature sensors are discussed. |
| format |
Article |
| author |
Kulish, N.R. Shwarts, Yu.M. Borblik, V.L. Venger, Ye.F. Sokolov, V.N. |
| spellingShingle |
Kulish, N.R. Shwarts, Yu.M. Borblik, V.L. Venger, Ye.F. Sokolov, V.N. Self-consistent method for optimization of parameters of diode temperature sensors Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Kulish, N.R. Shwarts, Yu.M. Borblik, V.L. Venger, Ye.F. Sokolov, V.N. |
| author_sort |
Kulish, N.R. |
| title |
Self-consistent method for optimization of parameters of diode temperature sensors |
| title_short |
Self-consistent method for optimization of parameters of diode temperature sensors |
| title_full |
Self-consistent method for optimization of parameters of diode temperature sensors |
| title_fullStr |
Self-consistent method for optimization of parameters of diode temperature sensors |
| title_full_unstemmed |
Self-consistent method for optimization of parameters of diode temperature sensors |
| title_sort |
self-consistent method for optimization of parameters of diode temperature sensors |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
1999 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/119108 |
| citation_txt |
Self-consistent method for optimization of parameters of diode temperature sensors / N.R. Kulish, Yu.M. Shwarts, V.L. Borblik, Ye.F. Venger, V.N. Sokolov // Semiconductor Physics Quantum Electronics & Optoelectronics. — 1999. — Т. 2, № 2. — С. 15-27. — Бібліогр.: 24 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT kulishnr selfconsistentmethodforoptimizationofparametersofdiodetemperaturesensors AT shwartsyum selfconsistentmethodforoptimizationofparametersofdiodetemperaturesensors AT borblikvl selfconsistentmethodforoptimizationofparametersofdiodetemperaturesensors AT vengeryef selfconsistentmethodforoptimizationofparametersofdiodetemperaturesensors AT sokolovvn selfconsistentmethodforoptimizationofparametersofdiodetemperaturesensors |
| first_indexed |
2025-07-08T15:14:17Z |
| last_indexed |
2025-07-08T15:14:17Z |
| _version_ |
1837092210652217344 |
| fulltext |
15© 1999, Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Semiconductor Physics, Quantum Electronics & Optoelectronics. 1999. V. 2, N 2. P. 15-27.
Introduction
The following main properties of diode temperature sensors
(DTS) are critical for a consumer: 1) range of measured tem-
peratures; 2) accuracy of temperature measurement; 3) sen-
sitivity; 4) magnitude of supply current. The values of spe-
cific characteristics as well as the interrelation between them
are determined by the set of electrophysical parameters of a
semiconductor (bandgap width, emitter and base doping
levels, concentration of deep centers) and by design param-
eters of the diode (n+p- or p+n-junction, p n - junction area
and depth, base length). Previously the effects of only some
of mentioned factors on the DTS characteristics were stud-
ied, namely: of the base doping level on sensitivity [1, 2]; of
the supply current on sensitivity and the range of measured
temperatures [2-4]; of the junction type (n+p or p+n) on the
thermometric characteristic (TMC) [2]. In these papers nei-
ther an optimization of main DTS characteristics was done,
nor a question about the possibility of such an optimization
was raised.
The aim of this paper is to develop the self-consistent
procedure for determination of electrophysical and design
parameters of DTS based on the given values of the range
of measured temperatures, the temperature measurement
accuracy and sensitivity. The paper consists of three sec-
tion. In the first section the general equations are given
establishing relations between diode electrophysical and
design parameters and DTS characteristics. It is shown that
two sets of parameter values can be distinguished, the first
one providing a maximally wide range of measured tempera-
tures, and the second one giving the maximum DTS sensi-
tivity. In the second section the self-consistent procedure
of determination of these parameters for Ge, Si and GaAs
DTS was carried out. In the third section the calculated tem-
perature dependencies of the voltage drop across n+p- and
ð+n-junctions, sensitivity, static and dynamic resistance of
Ge-, Si- and GaAs-based DTS are presented, corresponding
either to the maximum length of TMC or to maximum sensi-
tivity of DTS. The comparison has been made of calculated
and experimental DTS characteristics. In conclusion, the
ways of an improvement of diode temperature sensors are
briefly discussed.
PACS 07.07.D
Self-consistent method for optimization of parameters of
diode temperature sensors
N. R. Kulish, Yu. M. Shwarts, V. L. Borblik, Ye. F. Venger, V. N. Sokolov
Institute of Semiconductor Physics of NASU, 45, Prospect Nauki, 252028 Kiev, Ukraine.
Abstract. In the framework of the diffusion transport model through an abrupt asymmetric p n-junction,
the ideality factor of which is assumed to be equal to unity, and with the help of criteria commonly used
to describe theoretically the semiconductor diode structures, the relations are obtained for estimation of
parameters of the diode temperature sensor. The set of these parameters provides either the maximum
extent of a thermometric characteristic toward the higher temperature range, or maximum sensitivity of
the diode temperature sensor. For Ge, Si, GaAs diode temperature sensors with n+p- and ð+n- junctions
the limits of thermometric characteristics were determined, together with temperature dependencies of
sensitivity, static and dynamic resistance calculated for cases of the maximum length of the thermometric
characteristic and of maximum sensitivity. It has been shown that experimentally measured characteris-
tics of diode temperature sensors are within the ranges determined by the limiting characteristics. The
ways of further improvement of diode temperature sensors are discussed.
Keywords: temperature, sensor, ð+n- junction, ideality factor, thermometric characteristic,
sensitivity.
Paper received 01.12.98; revised manuscript received 03.06.99; accepted for publication 12.07.99.
N. R. Kulish et al.: Self-consistent method for optimization of parameters ...
16 SQO, 2(2), 1999
1. Relations connecting the electrophysical
and design parameters of the diode with
characteristics of the diode temperature sensor
In conducting the relations which establish the connection
between electrophysical and design characteristics of the
diode and characteristics of DTS the following criteria were
used: 1) the maximum value of temperature registered by
DTS is assumed to be below the temperature corresponding
to the transition to intrinsic conduction of the base and is
determined by the temperature when the voltage at pn-junc-
tion is equal to the thermal voltage; 2) the base doping level
has to be less than the value at which the effect of tunnel
processes on transport through pn-junction should be tak-
en into account; 3) the signal-to-noise ratio should be great-
er than unity.
The resulting relations will, naturally, depend on the
specific transport mechanism through pn-junction, i.e. on
the form of the temperature dependence of the current and
on the magnitude of the voltage drop across pn-junction. In
this paper the procedure of determination of the relation
linking the electrophysical and design parameters with DTS
characteristics is carried out using the model of the diffu-
sion transport mechanism for an abrupt asymmetric junc-
tion. During this procedure 1) the one-dimensional model
of pn-junction is used with heavily doped (in assumption of
fully ionized impurities and non-degenerated carriers) and
uniform p- and n-regions, the voltage drops at which are
negligibly low; 2) the voltage drop at Ohmic contacts is
neglected; 3) the width of the space charge region of pn-
junction is supposed to be significantly less than the major-
ity carriers diffusion length; 4) the injection level is sup-
posed to be low.
Under these conditions the dependence of the cur-
rent density J on the voltage drop U across pn-junction
has the form [5]
],1)/[exp( −= kTqUJJ s (1)
where Js is the diffusion saturation current density [6,7]
,]/()[/( 21
ibbbbs nLdthNLqDJ −= (2)
ni = (NcNv)1/2exp(-Eg/2kT) - is the intrinsic carrier con-
centration, Nc and Nv are effective densities of states in
the conduction and valence band, respectively, q is the
electron charge, k is the Boltsmann constant, Ò is tem-
perature, Lb =(Dbτb)1/2 and Db =µbkT/q are the diffu-
sion length and coefficient of diffusion of minority car-
riers, Nb, µb and τb are impurity concentration, mobility
and minority carrier lifetime in the base, respectively, d
is the base length, Eg is the width of the semiconductor
bandgap, the temperature dependence of which is deter-
mined by the equation [8]
)/()0()( 2 bTaTETE gg +−= , (3)
where Eg(0) is the bandgap width at absolute zero tempera-
ture, a and b are constants. In the case of p+n-junction,
Nb=ND, where ND is the donor concentration, τb=τp, µb =µp,
Db=Dp, Lb=Lp, and, in the case of n+p-junction, Nb=NA, where
NA is the acceptor concentration, τb=τn, µb=µn, Db=Dn,
Lb=Ln. Here the subscript n denotes the parameters related
to electrons, and subscript p is related to holes.
At a given value of the current density J, from (1) the
equation of the thermometric characteristic of the diode
temperature sensor follows
]1)/ln[()/()( += sJJqkTTU (4)
The intrinsic carrier concentration, and, the saturation
current density increase with increasing temperature. At
some temperature Ò=Tm the saturation current density Js
approaches to the operation current density J. In this case
the voltage drop U across the pn-junction becomes of the
order kT/q. Temperature Tm, corresponding to this condi-
tion, is the maximum (limiting) temperature which can be
measured with the diode thermometer from the voltage drop
across the pn-junction.
Assuming qU=kTm in (4) and considering, for defi-
niteness, n+p-junction, we obtain the transcendent equa-
tion for determination of the limiting temperature
Fig. 1. Simplified schemes of variants of pn-junction location in
respect to the base of the package: a) ideal, b) typical, c) preferrable.
1 � heavily doped substrate, 2 � base, 3 � pn-junction, 4 � emitter, 5
� base of the package.
a)
b)
c)
N. R. Kulish et al.: Self-consistent method for optimization of parameters ...
17SQO, 2(2), 1999
,
}]/)()(/[{)]([
])([)/2())(1(4
ln
/)(
2/12/1
2/1322/3
−
=
qTkTTdthTJN
kTTqhkTmme
kTE
T
mnmmnmnA
mmnmhe
mg
m
τµτ
µπ (5)
where me è mh are the effective masses of density of states
in conduction and valence bands, respectively.
It can be seen from (5) that Tm is shifted towards the
higher temperatures for semiconductors with the great-
er bandgap width Eg, and, for a specific semiconductor,
at higher operation current density and doping level. In
the short-base diodes (d<<Ln) temperature Òm does not
depend on τn and is lower for shorter base lengths d, and
in the long-base diodes (d>>Ln) it is independent of d
and is higher for greater τn. While calculating Òm one
should take into account that Eg, µn, τn are the tempera-
ture-dependent parameters, and NA, J and d do not de-
pend on Ò. The analysis of the influence of semiconduc-
tor parameters on the magnitude of Òm we will begin by
the study of the effect of doping impurity concentration
and of the current density.
Concentrations of donors ND and acceptors NA. The emit-
ter impurity concentration ND has an upper limit deter-
mined by the solubility limit, and that of the base impu-
rity concentration NA is determined either by an ava-
lanche breakdown of pn-junction, or by electron band-
to-band tunneling. Here the diode without band-to-band
tunneling is considered, therefore the upper limit of the
impurity concentration in the base NÀm is estimated from
the approximate relation between the avalanche break-
down voltage Ub and NAm [9]
4/3162/3 )10/(]1.1/)300([60 −≈ Amgb NKEU , (6)
where Eg (300 K) is the bandgap width at 300 Ê. If the values
of Eg (300 K) in eV and of NÀm in cm-3 are inserted into (6),
the value Ub in volts can be obtained. It follows from (6) that
the base doping level can be increased only if the avalanche
breakdown voltage Ub is reduced.
Operation current density. When the current is flowing
through pn-junction, the Joule heating takes place. As a
result, the temperature of pn-junction is higher by ∆Tí
than the temperature of the semiconductor substrate be-
ing in contact with ambient. In this case ∆Tí is connect-
ed with the thermal power density P/S by the relation
[10, 11]
,/ λSPlÒí =∆ (7)
where P=IU(Ò), I=JS is the operation current, λ(Ò) is
the coefficient of thermal conductivity, S is the pn-junc-
tion area (Fig. 1), from which the thermal diffusion to-
ward the sample surface occurs, l is the pn-junction depth
in respect to the outer surface of the chip. Actually, ∆Tí
is the systematic measuring error due to Joule heating
of pn-junction.
From (7) the expression for the upper limit of the opera-
tion current density it follows that
lTUTTJ ím )(/)(λ∆= . (8)
To find Jm the maximum values of U(T) and l and mini-
mum values of λ(T) and ∆Tí should be inserted into (8).
Then the systematic error due to overheating will not exceed
a given value ∆Tí for the whole range of the thermometric
characteristic.
Upper limit of temperature. According to (5) the temper-
ature Tm can be varied in a wide range depending on the
specific set of semiconductor parameters. In the consid-
ered transport model the upper limit of measured tem-
peratures should be less than the temperature Ti of tran-
sition to intrinsic conduction in the diode base [12]. We
will assume that, in the framework of the given model,
the greatest value of Tm is equal to the temperature Ti′ at
which the intrinsic charge carrier concentration is as small
as 10 % of the base acceptor concentration NÀ. This lim-
iting value of temperature Tm= Ti′ will then be determined
from the transcendent equation
( ) ( ) ( ) ( )[ ]///
v
/2 /exp1.0 iigiicA kTTETNTNN −= . (9)
If the values Tm= Ti′, J=Jm, NA=NÀm from (9), (8), (6) are
inserted into (5), then the equation (5) will define the relation
between other parameters: d, l, τn.
Sensitivity. According to (4) we find the sensitivity
α(Ò)=dU(Ò) /dT:
].
1
)(ln
)(ln
2
1
)(ln
)(ln
2
1
)(ln
)(ln
)/2(
/2
2
7
[
)(
)(
)(
dT
dE
kkT
E
Td
d
Td
d
Td
Ld
Ldsh
Ld
JJq
kJ
T
TU
T
ggn
n
n
n
s
−+−+
++
+
−=
τµ
α
(10)
For determination of parameters most affecting the mag-
nitude of α(Ò) far from the point Ò=Òm, we simplify (10) tak-
ing into account, that until qU>>kT, the relation J>>Js is
valid. The estimations show that the term Eg /kT dominates
in the brackets of (10). In these approximations the equation
(10) is reduced to the form
α µ π
τ
( ) ln
( ) ( / ) ( )
( / )
/ /
/
T
k
q
q kT kT h m m
JN th d L
n e h
A n n
= −
4 21 2 2 3 3 2
1 2 . (11)
It follows from (11) that α(Ò) does not depend on the
semiconductor bandgap width. Since |α|∼1/ln(JNA) an
increase of sensitivity should be observed at the lower
current density and doping impurity concentration in the
base, or, in other words, with decreasing the limiting tem-
perature Tm. In the short-base diodes the sensitivity (11)
does not depend on the minority carrier lifetime τn and
increases, in absolute magnitude, with reduction of the
base length d, and in the long-base diodes it increases
with reduction of τn and does not depend on the base
length.
To find α(Ò) at Ò=Òm the voltage U(Òm) in (10) is substi-
tuted by its value kTm /q, and J is determined from the fol-
N. R. Kulish et al.: Self-consistent method for optimization of parameters ...
18 SQO, 2(2), 1999
lowing relation
)()1( ms TJeJ −= , (12)
which follows from (4). As a result we get the approximate
expression
( ) .
)(1
m
mg
m qT
TE
e
e
T
−−=α (13)
According to (13) at the limiting point of TMC Ò=Tm the
sensitivity is fully determined by properties of material which
is used in a technical realization of DST.
Operation current and pn-junction area. According to
[8,13] thermal and shot noise dominate in the diode tem-
perature sensors. In the considered transport model the
mean-square value of the noise current <iN
2> is described
by the expression [8, 14]
ωBqIkTGi N )24(2 −>=< , (14)
where G=dI/dU=q(I+Is) /kT is the differential conductance,
Âω =1/2πτ is the bandwidth, τ is the minority carrier life-
time, ω is the circular frequency. In the right-hand side of
(14) the expression in parentheses determines the spectral
density of current fluctuations Si(ω) for low frequencies and
does not depend on the fluctuation frequency ω. In a small
vicinity of some point of the current-voltage characteristic
with the dynamic resistance r=dU/dI the spectral density of
current fluctuations Si(ω) is connected with the spectral
density of voltage fluctuations SU(ω) by the relation SU(ω)
= r2Si(ω). Then the mean-square value of the noise voltage
<UN
2> can be written as
.
)(
2)(
2
2
2
s
s
n
N
II
II
q
kT
U
+
+
>=<
τπ (15)
To find the systematic error ∆TN due to the pn-junction
noise we use the relation
)( NN UTT =∆α , (16)
where ><≡ 2
NN UU . Inserting the expression (15) for
<UN
2> into (16) we come to the relation which permit
estimation of the minimum operation current value re-
sulting in a given error ∆ÒN
,4121
2
1
00
0min
++−=
I
I
I
I
II ss
(17)
where
2
2
0
)(
)(
Nn Tq
kT
I
∆
≡
ατπ . (18)
For currents I>Imin the systematic error of the tempera-
ture measurement related to the noise will be less than ∆TN.
At 4Is/I0<<1 it follows from (17) that Imin=I0.
The minimum value of the area Smin of pn-junction can
be easily found from the known values of the current densi-
ty Jm (8) and current Imin (17)
mJIS /minmin = . (19)
The maximum values of the pn-junction area Smax and of
the current Imax we will determine from the following techno-
logical restrictions. Manufacture of semiconductor devices
has the tendency to minimization of the device size which is
provided by its fabrication technology. The minimum size of
a chip is determined by the technique of wafer sawing and is
500õ500õ400 µm3 [15]. With account of sides of the crystal
deteriorated by sawing, the pn-junction area reduces to the
values Smax=300õ300 µm2. Then the maximum value of oper-
ation current is
maxmax mJSI = . (20)
Resistance of thermodiode. The static resistance R(I) of a
thermodiode in the considered model is identified with
the magnitude
,1ln)(
+==
sI
I
qI
kT
I
U
IR (21)
where Is=JsS, and U and Js are determined by equations (4)
and (2), respectively.
The dynamic resistance r(I) is equal to
.
)(
)(
sIIq
kT
dI
dU
Ir
+
== (22)
2. Limiting parameters of diode
temperature sensors
It follows from the above analysis that at some set of elec-
trophysical and design parameters of the diode the maxi-
mum length of TMC is realized, and another set provides the
maximum sensitivity of DTS. The procedure of their determi-
nation should be carried out using the self-consistent tech-
nique, since the parameters entering into these sets are in-
terconnected. It is of interest to compare the values of these
parameters for specific semiconductor materials, based on
which the sensors with abrupt asymmetric pn-junction,
where diffusion transport mechanism is realized, are fabri-
cated. Below the numerical estimations of parameters are
carried out for DTS fabricated from Ge, Si, and GaAs. The
choice of these structures is explained by the fact that an
industrial technology of diode manufacture based on these
materials is well developed [15, 16].
The semiconductor constants necessary for the calcula-
tion are presented in Table 1. In calculations it is taken into
account that in the case of full ionization of impurity atoms
the minority carrier lifetime is independent of temperature
[10]. For the calculation of the temperature dependence of
mobility the relations used are presented in Table 2. The
total mobility was calculated using the Matissen rule with
account of charge carrier scattering at ionized impurities and
at acoustic (in the case of Ge, Si) or optical (in the case of
N. R. Kulish et al.: Self-consistent method for optimization of parameters ...
19SQO, 2(2), 1999
GaAs) phonons.
2.1. The set of parameters providing the maximum
length of TMC
To achieve the maximum length of TMC towards a higher
temperature range, the base region should be doped to the
maximum possible level when the influence of the tunnel
processes on transport can still be neglected. This situa-
tion occurs when Ub>6Eg/q, i.e. when the breakdown is due
to the avalanche multiplication only [8]. Therefore, for esti-
mation of NAm (Table 3) in (6) the value Ub=6Eg(300 Ê)/q
should be used [8]. It should be noted that Ub does not
depend on the type of conductivity of the base [9], there-
fore, for n- and p-types of conductivity the equation (6)
gives the same values of the doping impurity concentration
(Table 3). The emitter doping impurity concentration was
assumed to be equal to the limit concentration of solubility
of impurities commonly used in the diode fabrication tech-
nology [15, 16]. To find the temperature Òm=Òi′, correspond-
ing to the maximally possible length of TMC, one should
insert into (9) the known values of NA=NAm (Table 3) and of
semiconductor constants (Table 1), and also to take into
account the dependencies of Eg and of the product NcNv on
temperature. The calculated values of Òm= Òi′ are presented
in Table 3.
Since the operation current density, base length, pn-junc-
tion depth and minority carrier lifetime in the base are interre-
lated (see (5)), then for determination of the optimized (corre-
sponding to the maximum length of TMC) values of these
parameters we will carry out the following procedure. Let us
take into account that in (8) the thermal conductivity coeffi-
cient λ (Fig. 2) and the voltage drop U across the pn-junc-
tion are functions of temperature. At a fixed value of ∆ÒH
and l one should insert into (8) the maximum value of the
voltage drop at pn-junction U=Umax and the minimum value
Table 1. Constants of semiconductors used in calculations of limiting parameters of diode temperature sensors.
Parameter Ge Si GaAs
E
g
(T=0), eV 0.7412 [10] 1.1557 [10] 1.5216 [10]
à, eV/Ê 4.774.10-4 [8] 4.73.10-4 [8] 5.405.10-4 [8]
b, K 235 [8] 636 [8] 204 [8]
m
e
/m
o
0.56 [10] 1.08 [10] 0.068 [10]
m
h
/m
o
0.35 [10] 0.56 [10] 0.49 [10]
Table 2. Equations used in calculation of carrier mobility.
*Mobility due to phonon scattering µL and scattering at ionized impurity atoms µI.
Semiconductor Type of
conduc-
tivity
µL
* ,
cm2/V s
µ I
* ,
cm2/V s
Ge
n 7
66,1
109,4
T
Ln
⋅=µ
)/103,81ln(
104,11
3/228
5,117
NTN
T
In
⋅⋅+
⋅⋅=µ
p
33,2
91005,1
T
Lp
⋅=µ
)/103,81ln(
102,14
3/228
5,117
NTN
T
Ip
⋅⋅+
⋅⋅=µ
Si
n 9
6,2
1058,3
T
Ln
⋅=µ
)/105,41ln(
107,4
3/228
5,117
NTN
T
In
⋅⋅+
⋅⋅=µ
p
3,2
81040,2
T
Lp
⋅=µ
)/105,41ln(
108,5
3/228
5,117
NTN
T
Ip
⋅⋅+
⋅⋅=µ
GaAs
n 5
5,0
1058,1
T
Ln
⋅=µ
)/104,51ln(
107,20
3/228
5,117
NTN
T
In
⋅⋅+
⋅⋅=µ
p
5,0
31062,9
T
Lp
⋅=µ
)/104,51ln(
102,8
3/228
5,117
NTN
T
Ip
⋅⋅+
⋅⋅=µ
N. R. Kulish et al.: Self-consistent method for optimization of parameters ...
20 SQO, 2(2), 1999
of thermal conductivity coefficient λ=λmin (at Ò≤Tm). In this
case at any temperature registered by the diode sensor in
the considered temperature range the Joule heating will not
exceed ∆ÒÍ. If, for estimation of Jm, we assume that
Umax=Eg(Tm)/q, then, with account of above arguments,
(8) is converted to the form
,
)(
min
mg
H
m
ÒlE
qT
J
λ∆
= (23)
and the equation (4) is written as follows
.1
)(
ln)(
+=
TJ
J
q
kT
TU
s
m
(24)
The equation (24) describes the parametric set of
TMC crossing the point (U(Tm), Tm) in the plane (U,T).
In this set every individual characteristic is determined
by its own number of parameters ∆TH, d, l, τn. It is most
easy to establish connection between these parameters
in the limiting point Ò = Òm. Suppose that the current
density in (5) is equal to Jm determined according to (23).
Then instead of (5) we can write
,
)(
coth
)(0
mnmn
H TL
d
TL
l
TT ∆=∆ (25)
where
.
)()()()1(
min
2
0
A
mgmimmn
Nq
TETnkTTe
T
λ
µ−
=∆ (26)
For the case d = l (see Fig. 1a) in Fig. 3 the dependencies are
shown of the temperature measurement systematic error ∆TH
on the ratio d/Ln(Òm) calculated according to (25) for Ge-, Si-
and GaAs-based diode temperature sensors. It can be seen
in Fig. 3 that with decreasing ratio d/Ln(Òm) the reduction of
∆TH is observed with gradual approaching to the limiting
value ∆T0. Values ∆T0 calculated from (26) for Ge-, Si- and
GaAs-based diode temperature sensors are presented in
Table 3.
It follows from (25) that at d≠l in the short-base diodes
(d<<Ln) ∆TH= (l/d) ∆T0. It is clear that for a fixed value l/d
Fig. 2. Temperature dependence of thermal conductivity λ(Ò) Ge
[8,17], Si [8,17], GaAs [8, 18] .
1 10 100 1000
0,1
1
10
100
λ
,
W
/c
m
K
T, K
Ge
GaAs
Si
Table 3. Limiting parameters of temperature sensors with the maximum length of thermometric characteristic
Parameter Ge Si GaAs
Ub, W 4.45 6.93 9.13
ND, NA, ñm-3 1.35⋅1017 1.90⋅1017 2.25⋅1017
Tm, Ê 484 703 995
λ(Tm), W/ñm⋅Ê 0.30 0.50 0.15
∆T0, Ê (d=l=3µ) 6⋅10-2 1⋅10-2 4⋅10-1
Jmî , À/ñm2 85.35 17.00 186.00
Imax, À 7.68⋅10-2 1.53⋅10-2 1.67⋅10-1
Smax, ñm2 9⋅10-4 9⋅10-4 9⋅10-4
α(T=Tm), V/Ê -6.8⋅10-4 -8.0⋅10-4 -6.0⋅10-4
n+p-junction
τn, s 5.3⋅10-9 2.1⋅10-8 1.3⋅10-9
Imin, À 1.4⋅10-5 1.4⋅10-4 5.2⋅10-6
Smin, ñm2 1.7⋅10-7 8.0⋅10-6 2.8⋅10-8
p+n- junction
τp, s 4.5⋅10-10 4.0⋅10-9 2.4⋅10-11
Imin, À 1.7⋅10-4 7.4⋅10-4 2.8⋅10-4
Smin, ñm2 2.0⋅10-6 4.3⋅10-4 1.5⋅10-6
N. R. Kulish et al.: Self-consistent method for optimization of parameters ...
21SQO, 2(2), 1999
Fig. 3. Dependence of the systematic error ∆TH of temperature
measurement by Ge, Si, GaAs diode sensor on the base length d,
normalized by the diffusion length Ln of minority charge carriers.
Calculation was performed for Ò = Òm. Dashed line indicates the value
d/Ln= 1.
10
-2
10
-1
10
0
10
-2
10
-1
10
0
Si
G e
G aAs
d/L
n
∆T
h
,
K
there is a range of d/Ln(Òm) variation, within which ∆TH
varies slightly (Fig. 3). It should be noted that ∆TH is less
than ∆Tî, if l/d<1. Inserting into (23) the value ∆TH from
(25) we get the current density Jm for the short-base diode
as follows
.
)()()1( 2
dN
TnkTTe
JJ
A
mimmn
mom
µ−
≡= (27)
It follows from (27), with account of (9), that in the short-
base diodes the increase of NA and decrease of d result
in an increase of Jm. Values Jm= Jmî calculated from
(27) using data of Tables 1-3 are presented in Table 3.
Similarly it follows from (25) that in the long-base
diodes (d>>Ln(Òm)) ∆TH =∆T0 (l/Ln(Òm)). If, in this case
also l=d (Fig. 1a), then ∆TH =∆T0 (d/Ln(Òm)). The cur-
rent density Jm in the long-base diodes can be calculated
using the relation
)),(/( mnmom TLdJJ = (28)
where Jmo is calculated from (27). It follows from (28) that in
the long-base diodes the characteristic current density Jm
is independent of the base length d, if just this magnitude
determines the distance from the pn-junction to the cooling
surface (Fig. 1a).
The above relations make it possible to give follow-
ing recommendations regarding the choice of chip de-
sign and pn-junction parameters for DTS. The metal-
lurgic boundary of the pn-junction in diode structures fab-
ricated using diffusion and/or ion-implantation techniques
used to be situated at a depth ranging from 0.3 to 15 µm in
respect to the crystal face [15, 16]. To reduce the effect of
the surface on the transport current through the pn-junc-
tion it is usually situated at a depth of 2-3 µm. To reduce the
effect of bondage of the semiconductor chip to the basis of
the package on the transport current in diode structures, pn-
junction is usually situated in the top part of the chip (Fig.
1b). From the viewpoint of using the diode structure as the
temperature sensor such a construction of the chip is the
least reasonable, because in this case l is much longer than d,
which, according to (25) results in the greater temperature mea-
surement systematic error ∆TÍ due to Joule heating of the pn-
junction.
The minimum value of ∆TÍ is realized in the con-
struction of the short-base diode sensor shown in Fig.1c.
If the thin emitter layer, with thickness less than the base
length, is present in this construction, ∆TÍ can be less
than ∆T0. The systematic error of the temperature mea-
surement by the diode sensor, the construction of which
is presented in Fig.1c, will be significantly less than the
systematic error of the temperature measurement by the
sensor shown in Fig. 1b. Thus, in the specific technical
realization of the diode temperature sensor the prefer-
ence should be given to the short-base diode structures
with reverse mounting of the chip on the package basis.
For these structures at d=Ln(Òm) the connection between
the base length and the minority carrier lifetime in the
base is determined by the relation
.
)(
)(
q
TkT
TLd nmnm
mn
τµ
== (29)
According to Fig. 3, ∆TÍ slightly depends on the ratio
d/Ln up to the value d/Ln=1. Note that the typical pn-
junction depth d=(2-3) µm. Assuming, for the definite-
ness, d=Ln(Òm)=3 µm, from (29) we calculate the minor-
ity carrier lifetime (Table 3).
To find the value of sensitivity (Table 3) at the point
T=Tm we will use the relation (13). The minimum value
of the operation current is found from (17). First, insert-
ing into (18) T=Tm, τn and α(Tm) from Table 3 we calcu-
late I0, and also the value ∆TN, assuming ∆TN=∆TH. Then
we express Is via I(I=Imin) using (12). Then we insert the
values of Is and I0 into (17) and solve the obtained equa-
tion in respect to Imin (Table 3).
To estimate Smin and Imax we will use the equations
(19) and (20) and the parameters from Table 3.
Thus, the calculation carried out in the section 2.1
permits to determine the set of parameter values provid-
ing the achievement of the maximum extent of the TMC
into the higher temperature region. For Ge-, Si- and
GaAs-based DTS with asymmetric n+p- or p+n-junction
these parameters are presented in Table 3.
2.2. Set of parameters providing the maximum sen-
sitivity of diode temperature sensors
From a number of similar DTS the sensors with the maximum
sensitivity are preferable. Let us investigate the behaviour
of α(Ò) at variation of temperature and parameters of the
H
N. R. Kulish et al.: Self-consistent method for optimization of parameters ...
22 SQO, 2(2), 1999
structure.
At the upper boundary of the temperature range cov-
ered by the thermometric characteristic (4), α(Òm) is deter-
mined by the equation (13). At temperatures Ò<Òm the sensi-
tivity α(Ò) is higher than α(Òm) and slightly depends on
temperature, except the relatively narrow transition region
in the vicinity of Òm, where it falls down to its limiting value
(13). In the plateau region, i.e. out of the mentioned transi-
tion region, the value α is determined by the equation (11).
At τn>>d2/(kTµn/q) ≡ τD the situation of the short-base
diode is realized (d<<Ln) when
−=
dIN
kTmmhkTS
q
k
T
A
nhe µπ
α
2/332 )()/2(4
ln)( . (30)
Thus, in the case of the short-base diode, sensitivity of the
sensor is independent of τn unless the characteristic minor-
ity carrier lifetime in the base is essentially longer than the
characteristic time τD of carrier diffusion to the Ohmic con-
tact where the surface recombination rate is infinite.
With reduction of τn (at τn<<τD) another limiting case of
the long-base diode (d>>Ln) is realized for which sensitivi-
ty α(Ò) is obtained from (30) by substitution of d by Ln
α
µ π
τ
( ) ln
( ) ( / ) ( )/ /
/T
k
q
S q kT kT h m m
IN
n e h
A n
= −
4 21 2 2 3 3 2
1 2 . (31)
With account of restrictions imposed on the base resis-
tance we find the criterion of validity of the equation
(31) at the increasing base length in the form
Ln<<d<<db≡ qµpNASR(I), where R(I) is the resistance of
the pn-junction (db has the sense of the length of the base
with the resistance comparable with that of the pn-junction
resistance).
According to (30), (31), higher sensitivity is provided
at the larger pn-junction area S, lower current I, concen-
tration NA and shorter base length d (for the short-base
diodes) or minority carrier lifetime τn in the base (for the
long-base diodes).
In calculation of α(Ò) we will assume that the maxi-
mum value of the pn-junction area (S=Smax) (Table 4) is
limited from above by the technology of wafer sawing
into chips of minimum possible size (see section 2.1).
The minority carrier lifetime in the base of diodes fab-
ricated on Czochralski-grown Ge, Si and GaAs single
crystals is about 10-8 s [15, 16, 19]. By reduction of con-
centration of oxygen precipitates it can be increased to
10-5 s [7, 19], and by heavy doping with impurities gener-
ating deep centres it is possible to reduce it to few pico-
seconds [20-22]. With increasing the doping concentra-
tion of deep impurities NI >1017 cm-3 (corresponding to
the minority carrier lifetime τn≈10-9 s) the reduction of
τn in Ge, Si [23] and GaAs [22] is accompanied with the
reduction of the charge carrier mobility. At high con-
centrations NI of charged deep centres the mobility
µn≈µI∼NI
-1 and lifetime τn∼NI
-1. Therefore, in the short-
base diodes an increase of the deep centre concentration
results in reduction of α(Ò) (30) due to mobility reduction,
and in the long-base diodes the value of α(Ò) (31) should
not vary significantly, because its reduction due to a de-
crease of τn is compensated by the respective mobility re-
duction. Below, in calculation of α(Ò), it is assumed that the
average minority carrier lifetime τn=τp=10-9 s (Table 4), which
corresponds to Ln> d=1 µm (Table 4).
Table 4. Limiting parameters of the temperature sensors with the maximum sensitivity.
Parameter Ge Si GaAs
ND, NÀ, ñm-3 1.0⋅1014 1.0⋅1014 1.0⋅1014
τn=τp, s 1.0⋅10-9 1.0⋅10-9 1.0⋅10-9
Smax, ñm2 9⋅10-4 9 10-4 9 10-4
n+p- junction
Tm, K 260 390 513
∆T (T=Tm), mK 36.5 89.7 53.2
α(T=300 K), mW/K 1.74 2.72 2.36
J, mA/ñm2 9.6 3.0 17.8
I, µA 8.6 2.7 16.0
p+n- junction
Tm, K 262 394 526
∆T (T=Tm), mK 45.5 111.3 129.0
α(T=300 K), mW/K 1.76 2.67 2.26
J, mA/ñm2 6.3 2.0 3.3
I, µA 5.7 1.8 3.0
N. R. Kulish et al.: Self-consistent method for optimization of parameters ...
23SQO, 2(2), 1999
DTS, are presented in Table 4. The above self-consistent
procedure enabled to calculate the apparent dependence of
the doping impurity concentration NAî in the base on Òm
(Fig.5, bold lines), and to determine also the set of parame-
ters J, d/Ln, τn, NÀî, providing the highest sensitivity of the
sensor. In particular, inserting into (11) values of these pa-
rameters and the magnitude µn for temperature 300 K, we
find the dependence of sensitivity α(Ò=300 Ê) on the impu-
rity concentration NAî (Fig. 5, thin lines). It can be seen in
Fig. 5 that with increasing NAî the extent of TMC increases
and sensitivity of DTS decreases.
3. Limiting characteristics of diode temperature
sensors
Tables 3 and 4 contain the set of parameters, insertion of
which into equations presented in sections 1 and 2 makes
it possible to find the limiting characteristics of Ge, Si,
GaAs DTS: the temperature dependencies of the voltage
drop across the pn-junction (TMC) (Fig. 6), sensitivity
(Fig. 7), static (Fig. 8) and dynamic (Fig. 9) resistances
for n+p and p+n-junction-type diode temperature sensors.
In figures 6-9 numerals denote the characteristics mea-
sured experimentally; letter r denotes the characteristics
calculated using the parameter set providing the maximum
length of TMC (Table 3); 1 indicate those calculated using a
set providing maximum sensitivity (Table 4). Thin solid line
in the Fig.6 shows the temperature dependence of the ther-
mal voltage UT=kT/q. Curves denoted by letter r and l de-
termine the boundaries within which the characteristics of
DTS can vary during variation of electrophysical and design
parameters of the diode. From comparison of data presented
in figures 6a-9a and figures 6b-9b one can see that a change
of base conductivity from p-type to n-type has no marked
effect on the position of these boundaries. It follows from
figures 6-9 that experimentally measured characteristics of
Further increase of sensitivity (see (30), (31)) can be pro-
vided by the reduction of the current I and of doping impu-
rity concentration NA in the base. It should be mentioned,
however, that the range of variation of NA is limited from
above by the concentration corresponding to the case when
the effect of tunnel processes on transport in the diode
structure can still be neglected, and is limited from below by
the concentration of uncontrollable impurities in the semi-
conductor, the value of which for Ge, Si and GaAs is taken
to be equal to 1014 cm-3 (Table 4) [15, 16].
Since the base resistance increases with reduction of
NA, then the process of temperature measurement can
be affected, in addition to systematic errors due to Joule
heating of pn-junction ∆ÒH (see (25)) and the presence
of noise ∆ÒN (see (16), (15)), by the systematic error
∆ÒR, appearing as a result of an increase of the base
resistance
),(/),( AAbR NTINTRT α=∆ , (32 )
where the base resistance Rb(Ò,NA)=(d/qµpNAS)[1+
+(µp/µn-1)(Ln/d)th(d/Ln)] [6].
Because in the considered model the effect of the base
resistance on TMC and sensitivity is neglected, then the
magnitude of α(Ò) entering into (32) and (16) is deter-
mined from the variation of the voltage drop across the
pn-junction. The total systematic error is equal to the
sum of the above mentioned components. It follows from
(5) and (27), (28), that the decrease of NA results in re-
duction of the limiting temperature Òm, which becomes
less than Òi′, of the current density Jm and, according to
(7), of ∆TH. Therefore, in the further analysis it is suffi-
cient to restrict ourselves by the total error
.RN TTT ∆+∆=∆ (33)
Let us insert the values d=1µm and τn,p, Smax from Table
4, and the current density from (12) into (4) and (33). In this
case both the equation of thermometric characteristic (4)
and the equation of systematic error (33) becomes the two-
parameter ones, depending on Òm and NÀ. At a fixed value
of temperature Òm, the dependence ∆Ò on NÀ, resulting
from (33) has the minimum ∆Òmin=∆Ò(NÀî) at some value
of doping impurity concentration NÀ=NAî (Fig. 4). The con-
centration NÀ=NÀî, corresponding to ∆Ò=∆Òmin, is then
taken as a required doping impurity concentration which
will be used for the calculation of TMC of the diode sensor
from the mentioned set of thermometric characteristics
+
−
= 1
),(
),()1(
ln)(
Aos
Aoms
NTJ
NTJe
q
kT
TU . (34)
At a given temperature Tm (Tm<Ti′) we calculate NÀî(Tm)
and then determine the current density J from (12) and the
operation current from the relation I=JSmàõ. These parame-
ters, calculated for minimum acceptable concentration of dop-
ing impurity in the base NÀî=1014 cm-3 for Ge, Si and GaAs
Fig. 4. Dependence of the systematic error ∆T (1), due to both noise
(2), and the base resistance (3), on the impurity concentration in the
base. Tm = 300 Ê.
0
13
10
14
10
15
3
2
1
N A0
∆Tm in
N A, cm
-3
0.30
0.25
0.20
0.15
0.10
0.05
0
∆T
, K
1
N. R. Kulish et al.: Self-consistent method for optimization of parameters ...
24 SQO, 2(2), 1999
Fig. 5. Dependencies on the impurity concentration NAo in the base of n+p (a) è p+n (b) DTS of sensitivity at T=300 K (thin lines) and of
temperature Tm (bold lines), determined by the aggregate of parameters providing the minimum error of temperature measurement calculated
from the equation (33).
10
14
10
15
10
16
10
17
10
1
300
400
500
600
700
800
Si
Ge
. . . .
___
- - -
GaAs
n
+
p
2
2
3
10
14
10
15
10
16
10
17
300
400
500
600
700
800
. . .
___
- - -
Si
Ge
GaAs
m
p
+
n
0 200 400 600 800 1000
GaAs
Si
Ge
. . .
___
- - -
n
+
p
l
l
l
r
r
r
2
1
0 200 400 600 800 1000
GaAs
Si
Ge
. . .
___
- - -
p
+
n
l
l
l
r
r
r5
4
3
Fig. 6. Thermometric characteristics of Ge, Si, GaAs diode sensors with abrupt asymmetric n+p (a) è p+n (b) junctions. Legends in the figure:
r - calculation using the parameter set providing the maximum length of TMC; l - calculation using the parameter set providing the maximum
sensitivity of DTS; experimentally measured characteristics are denoted as: 1 - our data for the silicon temperature sensor (I=10 µÀ,
NA=2×1017 cm-3), 2 - data of [13] for the silicon temperature sensor (I=10 µÀ), 3 - data of [2] for germanium temperature sensor (I=10 µÀ,
NA=(1-2) ×1017 cm-3), 4 - data of [1] for the silicon temperature sensor (I=10 µÀ, NA=1.6×1017 cm-3), 5 - data of [2] for GaAs temperature
sensor (I=10 µÀ, NA=9×1017 cm-3).
a b
a b
1.5
1.0
0.5
0
2.6
2.2
1.8
1.4
1.0
T, K T, K
T m
, K
NAo, cm-3
NAo, cm-3
T m
, K
αααα α ,
m
V
/K
αααα α,
m
V
/K
3.0
2.5
2.0
1.5
1.0
8
U
, V
U
, V
2.0
1.5
1.0
0.5
0
N. R. Kulish et al.: Self-consistent method for optimization of parameters ...
25SQO, 2(2), 1999
Fig. 7. Temperature dependencies of sensitivity exhibited by Ge, Si, GaAs diode sensors with abrupt asymmetric n+p (a) è p+n (b) junctions.
Legends in the figure: r � calculation using the parameter set providing the maximum length of TMC; l � calculation using the parameter set
providing the maximum sensitivity of DTS; experimentally measured characteristics are denoted as: 1 � our data for the silicon temperature
sensor (I = 10 µÀ, NA= 2×1017 cm-3), 2 � data of [13] for the silicon temperature sensor (I = 10 µÀ).
Fig. 8. Temperature dependencies of static resistance of Ge, Si, GaAs DTS with abrupt asymmetric n+p (a) è p+n (b) junctions. Legends in the
figure: r � calculation using the parameter set providing the maximum length of TMC; l � calculation using the parameter set providing the
maximum sensitivity of DTS: 1 � our data for the silicon temperature sensor (I = 10 µÀ, NA = = 2×1017 cm-3).
0 200 400 600 800 1000
10
3
10
4
10
5
l
l
l
r
r
r
n
+
p
GaAs
Si
Ge
. . .
___
- - -
1
R
,
O
m
0 200 400 600 800 1000
10
2
10
3
10
4
10
5
r
r
r
l
l
l p
+
n
GaAs
Si
Ge
. . .
___
- - -
R
,
O
m
Ge and Si DTS lie within the mentioned boundaries. TMC of
GaAs diode temperature sensor (Fig. 6b, curve 5), however,
is located near the left boundary of the range (near the curve
l in Fig. 6b). The impurity concentration in the base of this
diode (ND=9×1017 cm-3) is much higher than the concentra-
tion (ND=2,25×1017 cm-3) used in calculation of the right
boundary of the range. In the case of the diffusion-con-
trolled transport current the experimental TMC should be
situated near the right boundary (near the curve r in the Fig.
6b). Its location near the left boundary indicates that other
transport mechanisms dominate in this sensor.
Let us note that the magnitude of sensitivity α(Ò = 300Ê)
in Fig. 5 was calculated using the simplified equation (11),
and the value of α indicated in Figure 7 was evaluated from
the general equation (10). Comparison of these data has
shown that the sensitivity evaluation using the simplified
equation (11) gives the underestimated by 10-15 % value.
a b
a b
0 200 400 600 800 1000
G aAs
Si
G e
. . .
___
- - -
n+p
l
l l
r
r r
1
2
200 400 600 800 1000
p+n
G aAs
S i
G e
. . . .
___
- - -
l
l l
r
r r
T, K T, K
T, K T, K
-1
-2
-3
-1.0
-1.5
-2.0
-2.5
-3.0
-3.5
αααα α,
m
V
/K
N. R. Kulish et al.: Self-consistent method for optimization of parameters ...
26 SQO, 2(2), 1999
200 400 600 800 1000
10
2
10
3
10
4
p
+
n
GaAs
Si
Ge
. . .
___
- - -
r
r
r
l
l
l
r,
O
m
Fig. 9. Temperature dependencies of dynamic resistance of Ge, Si, GaAs DTS with abrupt asymmetric n+p (a) è p+n (b) junctions. Legends in
the figure: r � calculation using the parameter set providing the maximum length of TMC; l - calculation using the parameter set providing the
maximum sensitivity of DTS: 1 � our data for the silicon temperature sensor (I = 10 µÀ, NA = = 2×1017 cm-3).
0 200 400 600 800 1000
10
2
10
3
10
4
n
+
p
GaAs
Si
Ge
. . .
___
- - -
r
r
r
l
l l1
r,
O
m
a b
Conclusion
Using the diffusion transport model through an asym-
metric pn-junction the equations were obtained, for the
first time, connecting the length of TMC and sensitivity
of the diode temperature sensor with the operation cur-
rent, semiconductor parameters (minority carrier life-
time and mobility, doping impurity concentration in the
base) and parameters of the diode structure (pn-junc-
tion area, its depth in respect to the surface contacting
with the package, base length). These relations were ob-
tained using a set of fundamental criteria, some of which
were formulated for the first time.
The self-consistent consideration of the obtained re-
lations permits to determine the full sets of thermodiode
parameter providing required or fixed properties of the
thermodiode temperature sensor in the range of validity
of the chosen model. In particular, it is shown that fab-
rication of DTS possessing simultaneously the maximum
possible temperature extent of TMC and the highest sen-
sitivity is not possible. The change of parameters lead-
ing to the increase of sensitivity always results in shorten-
ing of the TMC length and vice versa.
It is found that for the thermometric applications the use of
short-base thermodiodes is preferable since in this case both
sensitivity and the TMC extent to the high-temperature range
is independent of the minority carrier lifetime, which is the
least technologically controllable diode parameter.
The effect of the pn-junction location in the chip in re-
spect to the surface being in a contact with a package base
on the temperature measurement systematic error due to
pn-junction Joule heating is analysed. It is found that in the
conventional technique of the chip mounting (pn-junction
is at the maximum distance from the surface contacting with
the package base) this error is maximum. Its lowest value is
expected if the pn-junction is situated at the minimum dis-
tance from the package base, and this distance is shorter
than the base length.
The intervals of TMC and sensitivity are determined
within which the Ge-, Si- and GaAs-based DTS can be
realized. From the comparison of calculated and exper-
imental characteristics TMC and temperature dependen-
cies of sensitivity it follows that none of experimentally
realized DST could provide the limiting TMC length or
the maximum possible sensitivity.
This work was carried out in the frames of the STCU
Project No. 477.
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