REVISED VERSION
LOW TEMPERATURE NBSI THIN FILM THERMOMETERS ON SILICON NITRIDE MEMBRANES
FOR BOLOMETER APPLICATIONS
Ph.Camus
1,2
2
2
2
, L.Bergé , L.Dumoulin , S.Marnieros , J.P.Torre
3
1
Institut d’Astrophysique Spatiale, Bat 121, 91405 Orsay Cedex (France) (with postdoctoral ESA fellowship)
CNRS/IN2P3-Centre de Spectrométrie Nucléaire et de Spectrométrie Moléculaire, Bat 108, 91405 Orsay
Cedex (France)
3
CNRS-Service d’Aéronomie, BP3, 91371 Verrières-le-Buisson Cedex (France)
2
Abstract
We report the design of amorphous NbSi thin film bolometer thermometers on Silicon Nitride membranes. Due
to the low thermal conductivity of Si3N4 , this material has several applications in millimeter wavelength
bolometers and microcalorimetry. Compared to NTD-Ge thermometers, similar sensitivities are obtained with a
2
50 times lesser volume. The smallest realized films have a rectangular surface (100 x 400 m ) and are 100nm
thick. Optimization of the thermometer shape, NbSi composition and electrical material contact is discussed. The
goal of this development is to manufacture a complete array of bolometers by photolithography techniques.
5
1. NbSi thermometric layer
NbxSi1-x alloys exhibit a metal-insulator transition
(MIT) at a composition which depends on the
manufacturing process. The films are deposited by
co-evaporation of pure Nb and Si under ultra high
-8
vacuum (<10 mBar) conditions and the MIT is
obtained for a composition of around x = 9%
[1,2,3].
The thermometers are designed to have an
impedance of 10M, optimized to a J-FET
amplifier. The alloy resistivity is primarily
dependent on the composition, but also on the
annealing temperature (100-150°C) [2]. This
property can be used to reduce the composition
scattering effect on resistance. Compositions below
9% Nb were used where the alloy behaves like an
Anderson insulator [1,2,3]. At low bias power, the
electrical behaviour can be adequately analysed
within the framework of MIT theories. Over a
limited temperature and composition range, the
resistivity is well described by a law =
n
0.exp(T0/T) , where 0 and n are slowly varying
with alloy composition. The sensitivity defined by
A0 = -dln/dlnT = n.ln(/0) depends only on the
resistivity. The correlation between A0 and the
resistivity obtained from several samples
composition between 7-8.5% and at 100-500mK is
in full agreement with previous measurements [3]
made on sapphire substrates (fig.1).
To optimize the thermometer shape, non-ohmic
effects must be considered. Numerous analyses of
previous experiments showed that the resistivity of
NbSi alloys can be described by an electron-phonon
5
decoupling model P = V.I = g.(T -Tph ) and a
first-order
electric
field model (E,T)
=
n
0.exp{T0/T.(1-qe.LLOC.E/2.kB.T)} [3], where is
the film volume, qe the electron charge, E the
electric field, kB Boltzmann’s constant and LLOC a
characteristic localization length. The electrical
field effect is classically described by (E,T) =
(0,T).exp(-qeLhE/kBT) [4][2], where Lh is a
characteristic length for the hopping process. At low
electrical field (E<<kBT/qe), the two lengths are
n
related by Lh=LLOC.n/2.(T0/T) .
2. Optimization
Due to the combined effect of the electron-phonon
coupling and the electrical field, there is an optimal
bias power value. Considering only the Johnson
noise contribution, the equivalent substrate
temperature noise is given by :
4k B  Tph
NET 
K / Hz
A2  PJ


A is the sensitivity of the resistivity relative to the
substrate temperature and PJ the bias power. A
simple calculation gives a model for the sensitivity
A for a given bias power in the case of constant bias
current :
REVISED VERSION
A 

A

 T ph 1 5  A   
Tph

where

PJ
2k T  E
;  B
5
5gT ph
qe L LOC
A  A0 
1  2
A0  1   1 n
There is a strong influence of the electrical field on
sensitivity. The main parameter available to
optimize the film is the ratio of the electrodes length
(a) to the interelectrode distance (l). The thickness
(e) has the same influence as the electrodes length.
To avoid a 2D hopping process, the thickness must
be maintained well above the hopping length
(e>>Lh, i.e. 10-20nm). Table 1 lists the ideal
performances of different geometries and
temperatures.
As confirmed by parametric studies for a 10M
film, there is a flat optimum for a/l between 1 to 10
if e = 100nm. An increase of a/l, or thickness, is
favorable at low temperature (100mK). The optimal
5
bias power increases from PJ/gT = 0.08 at 100
mK to 0.20 at 300mK and the effective sensitivity
under polarization is 2.5-3.0.
Heat capacity is an important parameter in
millimeter wavelength bolometer applications
where NTD-Ge thermometers yield the best results.
Compared to NbSi layers, their performance is
limited by the same variable-range hopping
conduction process and non-ohmic effects [4]. A
common value for the electron-phonon coupling in
6
3
NTD-Ge at 100mK is 10-20W/K cm , while around
5
3
100W/K cm in NbSi. The volume required for the
same optimal bias power with a NbSi layer is 100
times less at 100mK. NbSi has a rather constant
-6
3
specific heat (20.10 J/K/cm ) between 100-300mK,
attributed to Nb nuclear moments and NbSi
localized magnetic moments [2]. A common
-6
estimation for NTD-Ge heat capacity is 10 .T
3
J/K/cm [4], leading to approximately the same heat
capacity for a given power. The main difference is
the volume required, which is precisely why NbSi is
well adapted to thin film thermometric layers.
3. Thermometers construction and
results
Rotation of the supporting system during coevaporation assured a spatial homogeneity. Gold
electrodes of 100-150nm thickness have been used
to fit the thermal link to the specific need in
bolometers applications. Nb superconducting
electrodes were also used to achieve the highest
thermal insulation. Two thermometers were
2
simultaneously evaporated, one 100 x 400m (M-
Type) at the center of a 4 or 5mm square Si3N4
2
membrane (100nm thick), and one 400 x 1700m
(F-Type) on the supporting Si frame. Gold wires
were used for electrical contacts and thermalization
of the frame with the cryostat.
A DC method was used to determine the thermal
response under low bias power (P < 0.1pW) in the
required temperature range. Due to the high thermal
coupling, the V(I) response of thermometers
deposited on the frame were used to fit the g and
LLOC parameters. The results, ranging between 805
3
200 W/K /cm and 3-15 nm, are in good agreement
with previous measurements made with sapphire
substrates [3].
From V(I) responses of thermometers deposited on
the membrane, an estimation of the local phonon
temperature is obtained. Except for the lowest
temperatures (100-150mK), non-ohmic effects are
dominated by the thermal link between the center of
the membrane and the frame. The latter is supposed
to be at the cryostat temperature. The influence of
the electrode material was investigated with 4mm
square membranes. The thermal conductance
defined by dP/dT (P is the bias power and T the
phonon temperature at the center of the membrane)
is given in fig.2 for various samples. With gold
electrodes, the thermal conductance is dominated by
a metallic conduction-type (dlnP/dlnT ≈ 2). The
gold
contribution
behaviour
is
roughly
proportionnal to the electrode thickness (100150nm). Niobium electrodes were used to estimate
the amorphous membrane contribution. The
estimated contribution of phonon conduction in
superconducting electrodes is negligible (<1%). A
comparison is given for two membranes sizes (4
and 5mm). The membrane conductance is compared
to a theoretical estimate based on a thermal
-5 1,98
conductivity k = 14.5.10 .T W/cm/K [5] (fig.2).
The temperature dependence and the influence of
the membrane size are not explained by this
diffusive model. The conductance is significatively
higher at 300mK (800pW/K for a 5mm membrane).
A millimeter wavelength bolometer made on such a
membrane would be limited by phonon noise and
adapted for medium background power (~100pW)
at 300mK, which is adequate for selected groundbased applications.
Acknowledgements : This work has been
partially funded under
ERBFMRXCT980167.
EEC contract TMR-
4. References
1.
Dumoulin, L & al, Progress in low temperature
thin film thermometers, Nucl. Instr. Meth. In
Phys. Res. A NIMA7386 (1995)
REVISED VERSION
2.
Marnieros, S & al, Low Temperature Specific
Heat of NbSi Anderson Insulator measured by
Cryogenic Bolometry, Phy. B 259-261, 826
(1999)
3. Marnieros, S, PhD Thesis, Université paris-Sud
France (1998)
4. Kenny T.W., & al, Bias-induced nonlinearities
in the dc I-V characteristics of neutrontransmutation-doped germanium at liquid 4He
temperatures, Phy. Rev. B., 39, N°12 (1989)
l
e
a/l
nm

M-Type
100
300
4
M-Type
100
100
4
F-Type
400
300
4 .25
F-Type
400
100
4.25
5.
6.
Leivo, M.M., Pekola, J.P., Thermal
characteristics of silicon nitride membranes at
sub-Kelvin temperatures, Appl. Phy. Let., 72,
N°11 (1998)
Holmes, W., Gildemeister, J.M., Richards,
P.L., Measurements of thermal transport in low
stress silicon nitride films, Appl. Phy. Let., 72,
N°18 (1998)
T
mK
A
NET
nK/Hz1/2
P bias
pW
P/Pd
%
100
300
100
300
3.08
2.41
3.08
2.39
92
44
22
11
0.69
130
11.7
2200
7.2
17
7.2
17
e=100nm, g=80W/K5/cm3, LLOC=10nm, R=10M, Pd=g..T5
Table 1 : Ideal performance of thermometric layer under optimal bias power
Figure 1 : Correlation between the sensitivity under low bias power and the resistivity
Composition vary between 7-8.5% Nb; the film geometry is 100mX400mX100nm; the line is obtained from
measurements made on sapphire substrates (A0=n.ln(/0), 0=5.10-4.m and n=0.65 [3]).
5E-9
Au 15 0
nm
Au 10 0
nm
4E-9
g 3E-9
(
W
/
2E-9
K
)
Nb 1 0 0
nm
Nb 1 0 0
nm
1E-9
0E+0
0 ,10
0 ,20
0 ,30
T (K)
0 ,40
0 ,50
REVISED VERSION
Figure 2 : Thermal conductance between the thermometer and the outer frame
The open symbols have been obtained on 4x4mm2 membranes, full one on 5x5mm2. Electrodes material and
thickness is indicated, electrodes width is 0,1mm. The dashed line is a theoretical estimation of the thermal
conductance of 5x5mm2 membranes (see text).