Thin film microcalorimeter
from 1.5 to 800 K
,
for heat capacity
measurements
D. W. Denlinger, E. N. Abarra, Kimberly Allen, P. W. Rooney, M. T. Messer,
S. K. Watson, and F. Hellman
Department of Physics, University of California at San Diego, La Jolla, CaIifomia 92093
(Received 18 November 1993; accepted for publication
13 January 1994)
A new microcalorimeter for measuring heat capacity of thin films in the range 1.5-800 K is
described. Semiconductor processing techniques are used to create a device with an amorphous
silicon nitride membrane as the sample substrate, a Pt thin film resistor for temperatures greater
than 40 K, and either a thin film amorphous Nb-Si or a novel boron-doped polycrystalline
silicon thermometer for lower temperatures. The addenda of the device, including substrate, is
4X 10m6 J/K at room temperature and 2~ 10e9 J/K at 4.3 K, approximately two orders of
magnitude less than any existing calorimeter used for measuring thin films. The device is capable
of measuring the heat capacity of thin film samples as small as a few micrograms.
I
I
I. INTRODUCTION
Many materials of current fundamental or technological interest can only be made, or are primarily made, in
thin flhn form. Examples include multilayers, many amorphous materials, and ultrathin films of reduced dimensionality. In the study of these materials, measurement of the
specific heat can provide information on the electron and
phonon densities of states, magnetic interactions, and
structural or electronic phase transitions. Specific heat
measurements can also discriminate between superconducting transitions which are characteristic of bulk properties or of a minority second phase. Magnetic ordering
can be detected in zero applied magnetic field. Specific heat
measurements of thin films have, however, been limited to
relatively thick films at low temperatures. We describe here
the development of a microcalorimeter capable of measuring the thermodynamic properties of thin films between 1.5
and 800 K.
As technology has progressed, so has the ability to
fabricate calorimeters capable of measuring smaller masses
over a wider temperature range (a good review of small
sample calorimetry is given by Stewart’). Commercially
available differential scanning calorimeters are currently
capable of measuring samples as small as a few mg from 77
K to well above room temperature. Differential scanning
calorimetry is primarily used for measuring the heat capacity of bulk samples but thin film samples can also be
measured if enough material can be prepared and if the
film can be removed from the substrate, which would otherwise overwhelm the small sample signal. This is usually a
difficult task, almost inevitably exposing the sample to air
and limiting the types of samples and substrates which can
be used.
All techniques for measuring thin film samples face
two fundamental problems. First, the substrate, thermometer, and heater used for the measurement all possess significant heat capacity which must be subtracted from the
total measured heat capacity. Second, for most experiments, it is impossible to make the thermal link small
enough to permit an adiabatic measurement of the heat
946
Rev. Sci. Instrum.
65 (4), April 1994
capacity, as is usually done for bulk samples, due to the
need for electrical leads.
The first problem is addressed by using thin film heaters and thermometers. At low temperatures, thin insulating substrates with high Debye temperatures (e.g., sapphire) may be used; this technique has been used by Kenny
and Richards,2 for example, to allow measurements of
monolayers of He. It is not, however, useful above about
100 K, where even a high Debye temperature material
begins to have an appreciable heat capacity since the substrate is inevitably many times the thickness of the thin
film sample.
The second problem has been addressed through various measurement techniques. In 1968 Sullivan and Seidel’
developed an ac method capable of measuring bulk samples of 100 mg at low temperatures (down to 1.4 K). In
1972 Bachmann et aL4 reported on a calorimeter which
used a relaxation method to measure bulk samples as small
as 1 mg from 1 to 35 K. About the same time, Greene
et tiL5 developed an apparatus which measured thick films
at low temperatures. Specific heat measurement over a
wide temperature range (4-380 K) for bulk samples (>20
mg) was achieved in 1980 by Griffing and Shivashankar’j
who employed a GaAsP light emitting diode (LED) as the
temperature sensor. A very small sample calorimeter was
developed by Graebner7 in 1989 in which bulk samples as
small as a few micrograms are mounted directly on a
Chromel-Constantan
thermocouple; a similar technique
has been used by Geer et al.* to measure specific heat of
self-supporting single layers of liquid crystals in which a
thermocouple can be embedded. This technique permits
measurements of extremely small samples in particular
cases but does not eliminate the substrate problem for thin
films. Earlier work on thin film calorimeters had been done
by Early, Hellman, Marshall, and Geballe’ in 1981 using
doped epitaxial Si thermometers on a sapphire substrate
(and a relaxation method patterned after Bachmann et ai. )
to measure samples smaller than 1 mg at low temperatures.
Attempts have been made” to use semiconductor pro-
0034-6746/94/65(4)/946/14/66.60
@ 1994 American
Institute
of Physics
cessing technology to fabricate devices with thin film leads
and submicron thick substrates in order to reduce the addenda contribution below that of previous devices which
use relatively massive wires and sample platforms, but the
delicate substrates proved to be an insurmountable problem. Recent advances in membrane technology have made
it possible to fabricate strong, thin silicon nitride membranes which form thesample platform for our microcalorimeters. We use a 180 nm amorphous Si-N membrane
together with thin film metal leads and thin film thermometers to create a calorimeter with two orders of magnitude
less addenda than existing thin film calorimeters. The low
thermal conductivity of the Si-N provides the necessary
thermal isolation of the sample from its environment. Our
total addenda heat capacity (including substrate) is approximately 4~ low6 J/K at room temperature and drops
to below 1 X10-” J/K below 2 K. This enables us to
measure, for example, Al samples with mass as small as 3
pg. Our devices use a thin film Pt thermometer and either
thin film amorphous Nb-Si or boron-doped polycrystalline
silicon thermometers which, together, cover the range
from 1.5 to 800 K. All materials used in the construction of
the microcalorimeters are metallurgically stable over the
temperature range of interest and exhibit good thermal
cycling. The upper temperature limit is set at present by
the use of Au in the leads which becomes mobile at approximately 800-900 K, replacement of the Au with a different material would likely allow the devices to be useful
to close to 1200 K, the processing temperature of the nitride and polycrystalline silicon.
We use the relaxation technique described by Bachmann et al. However, the microcalorimeters could easily
be used with other techniques such as the ac method” or
the sweep method.4’11
In Sec. II we describe the apparatus, focusing in particular on the fabrication of the microcalorimeters, the development of the doped polycrystalline silicon lowtemperature thermometer, the device mounting, and the
electronics. In Sec. III we discuss the thermal relaxation
method for measuring specific heat and give details of our
experimental method, and in Sec. IV we show results.
II. APPARATUS
A. Microcalorimeter
construction
The processing steps to prepare the microcalorimeters
and samples are shown in Fig. 1. We start with a (lOO)oriented Si wafer which provides a relatively high-thermalconductivity “frame” to anchor to the copper block used
for the specific heat measurements. A thin ( 180 run) amorphous silicon nitride layer is deposited on both sides of the
wafer using a Si-rich low-stress low pressure chemical vapor deposition (LPCVD) process developed by Sekimoto
et al. I2 and refined at the Berkeley Microfabrication
Laboratory.13 The Si-N layer on the back of the wafer is
used as a mask to deilne a 0.5 X 0.5 cm2 square area at the
center of the device within which the Si is etched away in
KOH. The nitride on the front side becomes a 0.5 cm
square membrane at the center of a 1 cm square Si frame
Rev. Sci. Instrum.,
Vol. 65, No. 4, April 1994
[Figs. 1 (a) and 1 (b)]. We make the devices on 2 in. wafers
and are able to fit nine devices on a wafer. The rest of the
processing is done on the membrane, necessitating careful
handling.
We use platinum for the high-temperature thermometer (40-800 K) and for the sample heater. Pt is sputtered
on the membrane with a 3 nm Ti binding layer and wet
etched to make the pattern shown in Fig. 1 (c). The thermometers are measured by an ac bridge technique described below which uses a thermometer on the sample and
a matching thermometer on the Si frame as two arms of a
resistance bridge. The thickness and path lengths are chosen to give a room temperature resistance of approximately
1200 n for all three resistors (sample and matching thermometers and heater). Our Pt films have a resistivity of
about 23 psi cm, which is quite high due to a large residual
resistivity po. l4 This does not seriously affect the sensitivity
of the bridge since’dp/dT is independent of po; the value
of p, and hence R, only enters as $( fi) due to the need
to limit 12R self-heating (see Ref. 15).
The next processing step is to fabricate the electrical
leads connecting the heater and thermometers (both the Pt
thermometer and the Nb-Si low-temperature thermometers described below) on the membrane to the Si frame [see
Fig. 1 (d)]. There are several design requirements: the leads
should have small electrical resistances ( < 1% of the
heater and thermometer resistance), they should have a
relatively low thermal conductance to keep the sample
thermally isolated, and the thermal conductivity should be
a weakly varying, preferably linear, function of temperature. We have chosen an alloy of Au-Pd (93 at. % Au)
which meets these criteria.16,‘7 It is metallurgically stable
up to at least 500 “C! and has no phase transitions in the
temperature range of interest.‘* The alloy is coevaporated
onto the membrane from a single thermal evaporation
boati using a 3 nm Ti binding layer. This bilayer is photolithographically patterned and wet etched to provide
both the leads and the contact pads on the Si frame [see
Fig. 1 (d)]. The high percentage of gold facilitates the subsequent bonding of electrical leads from the cryostat to the
contact pads on the Si frame.
At lower temperatures, a more sensitive thermometer
than the Pt is needed, and, because of the demands for
large dR/dT, no single thermometer is adequate over the
entire low-temperature range desired (1.5-40 K). Therefore we use two thermometers of identical composition
with different geometries, giving resistances that differ by
about a factor of 10, a technique developed by Early.”
In order to keep the effective sensitivity of the device
thermometers constant with temperature, they need to
have a resistivity which depends on temperature as Te2.15
Amorphous Nb-Si is known to go through the metalinsulator transition at approximately 12 at. % Nb.” On
the insulating side of this transition the resistivity is thermally activated, while (barely) on the metallic side it is
proportional to T- 1’2. 21 By choosing a composition between, the desired dependence can be approximately
reached. Figure 2 shows the temperature dependence of a
Thin film calorimeter
947
U
Silicon
q
Si-N
1 cm
(e)
-T
.25 cm
(f)
0
Silicon
q
Si-N
E
Platinum
u
Nb-Si
E3 Sample
(9)
FIG. 1. Microcalorimeter at various stages of fabrication. (a)-(b) (lOO)oriented silicon wafer with 180 nm low-stress amorphous Si-N is etched
in KOH to leave a free-standing membrane 0.5 x0.5 cm2 supported by a
Si frame 1 X 1 cm’. (c) Pt is sputtered and patterned to form a hightemperature sample thermometer, matching thermometer, and a heater.
(d) Au-Pd leads and contacts on the frame are prepared by thermal
evaporation and photohthographic patterning. (e) Nb-Si is codeposited
by electron beam coevaporation; this is patterned into low-temperature
thermometers using a copper lift-off technique. (f) The 0.25 x0.25 cm”
sample is deposited through a shadow mask onto the back side of the
membrane. (g) Profile of finished device showing the shadow mask in
place (not to scale: typical film thicknesses are 100-500 nm and the
shadow mask is approximately 25 pm from the membrane).
Nb-Si thermometer containing approximately 10 at. %
Nb, which we have found to be ideal.
This material is prepared by electron beam coevaporation on the amorphous nitride membrane by using a copper
946
Rev. Sci. Instrum.,
Vol. 65, No. 4, April 1994
lift-off technique to form two pairs of strips as shown in
Fig. 1 (e). The higher-temperature thermometer has a
longer, narrower path than the lower-temperature thermometer. We use a sample thermometer and a matching
Thin film calorimeter
1.4 I
5.
&
.G
-4
-2
e
B. Polycrystallinb
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
A
A
0.0
'
'
0
'
'
20
'
A
'
'
A
'
40
Temperature
A
'
'
1
p
60
'
'
+
80
(K)
FIG. 2. Resistivity of coevaporated Nb-Si with approximately 10 at. %
Nb. Inset shows resistivity vs l/T*, the desired temperature dependence
(see Ref. 15).
thermometer on the Si frame as was done with the Pt
thermometers. We have found that we can use a substrate
temperature of at least 200 “C for this deposition, allowing
us to thermally cycle the completed devices up to at least
this temperature (for sample preparation, for example)
with no degradation of properties on returning to low
temperatures.22 Ifit is necessary to cycle the devices to still
higher temperatures, we use the polycrystalline silicon
thermometers which are described in the next section. It is
important to note that our measurement technique (the
relaxation method, to be described below) does not depend
on the thermometers maintaining any sort of calibration on
thermal cycling, only that they maintain the necessary sensitivity to temperature.
The last step is to deposit the sample at the center of
the back side of the membrane which electrically insulates
it from the thermometers. We have successfully made samples of a wide variety of materials by sputtering and evaporation. The 0.25 cmX0.25 cm sample can be patterned
photolithographically by spinning a layer of photoresist on
the sample at the bottom of the etch pit and focusing the
projection aligner down at this level. Alternatively, we
have developed Si evaporation masks [see Fig. 1 (f)] which
fit inside the membrane cavity and define the sample area.
Semiconductor processing techniques allow us to create
masks with clean square edges, and by using Si for the
mask, the sides of the mask automatically have the same
55” slope of the etch pit which is inherent in the anisotropic
KOH etching process of ( lOO)-oriented Si wafers. Use of a
shadow mask is essential if the devices are to be used for in
situ sample preparation and measurements.
The robustness of the devices may be of concern for
some applications, but we find they stand up to routine
careful handling and have even been successfully transported by mail.
Rev. Sci. Instrum.,
Vol. 65, No. 4, April 1994
silicon thermometers
We have developed a new boron-doped polycrystalline
silicon (polysilicon) low-temperature thermometer which
is metallurgically stable up to at least 1100 K, making it
ideal if we wish to make low-temperature specific heat
measurements on a sample which must be prepared at high
temperatures. However, due to the complicated processing
steps required to incorporate the polysilicon into our membrane device, we prefer to use the amorphous Nb-Si thermometers described above.
Doped epitaxial Si is a widely used low-temperature
thermometer, 1*9p20123
but one which is incompatible with
the microcalorimeter processing because it cannot be prepared on an amorphous substrate (the nitride membrane).
Conduction in doped polysilicon has been studied at temperatures above 77 K (Refs. 24-32) and the material has
been used as a thermometer at high temperatures,33 but the
presence of grain boundaries makes extrapolation to low
temperatures difficult. To the best of our knowledge, the
resistivity of doped polysilicon has never been measured
below 77 K. We have found that heavily doped polysilicon
makes an excellent low-temperature resistance thermometer, with a thermally activated temperature dependence.
Boron was chosen as the dopant as it does not chemically
segregate to grain boundaries.24
The polysilicon thermometer that we have developed
has two levels of doping: the active temperature-sensing
portion has a concentration of about 1.6 x 1Or9cm-s while
a doping of 2 x 102’ cmw3 is used to provide lower resistance leads and to make an ohmic contact with Au-Pd
pads on the frame. By using polysilicon itself as the material for the leads, instead of the Au-Pd, we avoid the possibility of exothermic reactions taking place on the membrane should we use the devices at high temperatures.
(Reactions between Au and Si, for example, occur not far
above room temperature). As with the Nb-Si thermometers described above, we use two thermometers with different geometries of the actively doped area to span the
temperature region from 1.5 to 40 K [see Fig. 3 (a)]. A plot
of the resistance of the two thermometers is shown in Fig.
3 (b). An insert shows the temperature dependence of the
resistivity plotted as log(p) vs 1/T1’4; the data are consistent with thermally activated variable range hopping.34
Polysilicon is thus a very satisfactory thermometer, but
for our particular devices, owing to the fabrication of the
membrane, its use leads to more complicated processing
steps. The difficulty lies in the fact that the polysilicon
thermometer must be made prior to etching the silicon
away and forming the membrane since the membranes
cannot stand up to the polysilicon processing. This means
that an approximately 100 nm thick polysilicon layer must
be protected while the 330 pm thick Si wafer is etched in
KOH. We have found that the LPCVD Si-N is the only
mask which stands up against this KOH step. We therefore
must deposit the nitride for the membrane in two layers,
sandwiching the polysilicon thermometer between two 90
nm thick films of nitride.
We start by depositing the first 90 nm nitride t?lm. We
then deposit approximately 110 nm of polysilicon in an
Thin film calorimeter
949
nitride process is prone to developing particulates which
are incorporated in the film and can lead to pinholes. This
sets a lower limit of approximately 50 nm on the thickness
of nitride which makes a sufficient mask in KOH, 90 nm is
our usual choice.
After the Si wafer is etched in KOH to form the membrane, electrical contact to the polysilicon thermometers
must be made on the Si frame. We use a plasma etcher to
etch small holes in the second nitride layer. Care must be
taken not to etch too far, as once the nitride is etched away,
the polysilicon etches very rapidly. The wafer is dipped in
HF to remove the silicon oxide immediately prior to the
Ti/Au-Pd evaporation which forms the contacts for the
polysilicon thermometers. Using this technique we have
found that the metal makes good ohmic contact to the
polysilicon leads.
1.5
s
C. Microcalorimeter
0
20
40
Temperature
60
80
(K)
ON
PIG. 3. (a) Diagram of two polysilicon low-temperature thermometers
with different active area geometries. Leads are heavily doped polysilicon,
while the active area (at the center of each strip) is masked from the
heavy doping and receives a lighter dose. Photolithographically delined
SiOa masks (shaded) define a straight (narrow path) and serpentine
(wide path) active area. (b) Resistance of the active area of the polysilicon low-temperature thermometers (lead resistance has been subtracted)
with boron concentration of 1.25~ lOI cmd3 and polysilicon leads with
boron concentration of 3 x low cmm3. Inset shows log(p) vs 1/T”4 for
the active area, the temperature dependence expected for variable range
hopping (see Ref. 34).
LPCVD furnace at 605 “C and auneal it for 1 h at 1000 “C.
The wafers are then commercially ion implanted with the
first of two implant? and annealed at 900 “C for 30 min to
activate the doping. We use boron at an energy of 20 keV
which puts the peak of the implant distribution near the
middle of the layer.36 Boron concentrations between
1.25~ 1019and 2.0X 1019crn3 (1.38~ 1014and 2.2~ 1014
cmm2 area dose) were successfully used for this hrst implant which creates the active temperature sensing areas.
In the next step, 450 nm of SiOZ is deposited, again in an
LPCVD furnace, and patterned to act as a mask for several
small areas against a second high dose implant which creates the leads (2 x 102’cmm3; 2.2 x 1015cme2 area dose of
B at 20 keV, also annealed at 900 “C for 30 min) . The leads
develop a relatively low and temperature-independent resistivity (about 750 $I cm) with any concentration above
1 x 10”’ cmw3. The temperature dependence of the lead
and active area resistances are shown in Fig. 3 (b) .
The Si02 mask is a relatively tall and narrow structure
and can lead to problems with nitride coverage if the second nitride layer is deposited on top of it. We therefore
remove the Si02 after the heavy implant. The polysilicon is
then patterned into the strips shown in Fig. 3(a) after
which the second nitride layer is deposited. The low-stress
950
Rev. Sci. Instrum.,
Vol. 65, No. 4, April 1994
mounting
The Si frame of the microcalorimeter is attached to a
removable copper mount with either Apiezon II or N
grease37 and pressed down using phosphor-bronze pins.
Electrical connections are made by bonding 0.001 in. gold
wires from the Au-Pd contact pads on the Si frame to gold
pads (cut from ceramic integrated circuit mounts) epoxied
on the copper mount. The copper mount (with the sample) is pressed onto a Cu block in a cryostat by screws,
again using Apiezon H or N to ensure thermal contact.
Copper wires soldered onto the other end of the gold pads
connect to the wires in the cryostat sample chamber via
gold pins. Commercially calibrated Ge (Ref. 38) and Pt
(Ref. 39) thermometers are pressed into holes in the Cu
block close to the sample mount attachment point, using
copper-filled conducting grease. Two more calibrated thermometers are mounted on top of the sample chamber for
routine calibration checks.
This whole assembly is inside a relatively standard
immersion-type vacuum cryostat with a variable heat link
to the bath.40 For measurements below 77 K, the cryostat
is evacuated, sealed, precooled with LN2, and immersed in
LHe. For all measurements above 77 K (including those to
date above room temperature), the cryostat is immersed in
liquid nitrogen and is continuously pumped with a turbo
pump. In the latter case, the pressure at the top of the
cryostat is typically around 6x 10Y7 Torr, and is lower at
the sample space due to cryopumping by the LN2-cooled
walls.
D. Electronics
An ac bridge technique is used in which the bridge is
balanced when the sample and block are at To and the
small temperature rise ST of the sample relative to the
block is detected as an off-null signal by a lock-in amplifier.
The sample thermometer R, and the matching thermometer on the Si frame, R, (see Fig. 1) serve as the arms of
the bridge. A schematic of the essential components of the
bridge is shown in Fig. 4. Having the matching resistor on
the device itself makes the wiring and stray capacitances of
the two arms more symmetric than the usual approach of
Thin film calorimeter
COARSE ADJ.
L-
+=
FROM OSC
r
FIG. 4. A schematic of the ac bridge. R, is the sample thermometer; R, is the matching thermometer on the Si frame. R, is used to measure the current
in the bridge. The bridge is balanced by changing RY which varies the voltages at op-amps 3 and 4. Transformers Tl and T2 are used for isolation. The
oscillator signal is amplified by a programmable amplifier 1, and buffered by op-amp 2. The phase shifters needed to balance the reactive component of
the bridge for the high resistance thermometers at low temperatures are the RC circuit elements next to op-amps 3 and 4.
an external matching resistor. For the Pt thermometers,
R, is typically 1000-1600 fi and is within 100 fi of R,.
For the low-temperature thermometers (both Nb-Si and
doped polysilicon), R, varies from 10 to 300 kfi as a
function of temperature. Referring again to Fig. 4, RA is a
resistor allowing the measurement of the current through
the bridge for thermometer resistance measurements, and
RB is an identical resistor added to keep the bridge symmetric.
A Philips PM5 110 oscillator provides the excitation
voltage for the bridge and the reference for. the Stanford
Research SR530 lock-in amplifier. The bridge is balanced
by changing R,, which varies the voltages to op-amps 3
and 4 (which are on a single chip), thereby changing Vi
and Vz, the voltages across the sample and matching thermometers, respectively. The magnitudes of the bridge excitation voltages Vi and I’, are a compromise between
minimizing self-heating and making measurements of the
off-null voltage possible at a lock-in gain which results in a
full scale range of at least 2 ,!.iV. Irl and V2 are typically
10-13 mV for the Pt thermometer, giving a self-heating of
<2 mK at room temperature, about 4 mK at 80 K, and
< 10 mK around 40 K. For the low-temperature thermometers, larger excitation voltages can be used; at every temperature, self-heating is kept to less than 0.03% of To.41
RV consists of two helipots connected to dc motors for
automated coarse and fine adjustments. The resistorcapacitor (RC) components next to the op-amps serve to
balance the reactive part of the bridge.
The center tap of the bridge provides the input to the
lock-in amplifier. The output* of the lock-in amplifier is
recorded by a 1 MHz, 1Zbit RC electronics computer oscilloscope, allowing averaging of many relaxation sweeps.
Data acquisition is automated by a pc-compatible 386 comRev. Sci. Instrum.,
Vol. 65, No. 4, April 1994
puter and communication between equipment is made
through a GPIB interface.
The frequency used for the bridge when using the Pt
thermometer is 733 Hz, which is fast enough for the time
constants encountered above 40 K (see Table I). At low
temperatures, the faster relaxation time constants (as little
as a few ms) necessitate a frequency of 1500 Hz or greater.
The block temperature iS read and controlled by a
Quantum Design 401802 Digital R/G Bridge. Stability is
approximately It2 mK at 80 K and better than f4 mK
above room temperature using the Pt block thermometer,
and 0.002%-0.005% at lower temperatures with the Ge
thermometer.
TABLE I. Addenda and time constants for microcalorimeters with Au
sample.
Sample thickness
(lo-” m)
1000
1000
loo0
1000
2OuO
2000
10000
T
6)
1
4.3
10
40
100
300
900
Ti”tc
4
@J/K)
(ms)
bs)
5 x 1o-5
2 x 10-3
1 x lo-*
0.18
1.2
4.0
6
0.03 1
0.22
1.4
4.4
6.9
11
7
0.55
2.7
22
150
380
240
95
c addenda
h
CT-(PJAQ
7.2 x 1o-5
1.9 x 10-3
2.7 x lo-’
0.68
2.6
3.1
18
‘Specific heat of metal layers based on Ref. 42.
hMeasured values except 1 and 900 K which were extrapolated from
measured values.
“ri,,=&/2K
where d=0.125 cm, the distance to the edge and K is the
thermal diffusivity of the bilayer consisting of the gold sample layer
membrane under
it.
and the nitride
lY=
CKnittni*+
K.4utAu)/
~~~~~~~~~~~~~~~~~~~~~~~
) where fi are the thicknesses, ar the thermal conductivifies, q the specific heats, and pi the densities of the layers, determined as discussed in the text.
dMeasured external relaxation time constant; values for the thicknesses
shown were calculated by scaling the data from a 307 nm gold sample.
Thin film calorimeter
951
I in cryostat
2OK
20K
To computer
FIG. 5. A schematic diagram of the filtered switch for the current to the
sample heater. The switch is a MOSFET 2N7OC0.
used with any of the small sample calorimetry techniques.
The microcalorimeter with its thin film sample [see Figs.
1 (f)-1 (g)] is pressed against a copper block at temperature Ta. A small dc current (typically 5-300 PA) is supplied to the thin film sample heater, causing the temperature of the sample and the addenda (the amorphous Si-N
membrane under the sample, the thin film sample thermometers, and the thin film heater itself) to rise to a temperature T,+ST. 6T is determined by the thermal link
between the sample and the outside world, Ker, which
includes conduction through the Au-Pd leads .and the
amorphous Si-N “border” and, at higher temperatures,
radiation. We then turn off the sample heater and measure
the relaxation of the sample temperature back to the block
temperature. The temperature decays exponentially
T-
Current to the sample heater is supplied by a Keithley
Model 2243 programmable current source and is turned on
and off using a metal-oxide-semiconductor field-effect transistor (MOSFET) 2N7000 switch. There is significant capacitance between the Pt thermometer and the heater
through the sample (which acts like a ground plane), and
between their respective leads and pads on the frame (via
the semiconducting Si frame). The capacitance via the
sample is approximately 40-80 pF and that via the Si
frame is approximately 400 pF at room temperature and
decreases with decreasing temperature as the Si becomes
more insulating. Due to these capacitances, the sample
heater with its relatively high voltage is capacitively coupled to the low-voltage bridge thermometers. An abrupt
change in the heater voltage introduces a high frequency
spike into the bridge and overloads the lock-in amplifier.
To avoid the high frequencies associated with an abrupt
transition, we filter the trigger to the heater switch (see
Fig. 5) in order to turn the heater off more slowly than a
step function. This filter time constant has to be much less
than the relaxation time constant being measured, but long
enough to minimize interference and prevent the lock-in
from overloading. A Computer Boards CIO-D1024 card
provides the trigger and also controls the relays via a ribbon cable.
Work at low temperatures (below 10 K) is complicated by noise and capacitance problems. Typical resistances of the polysilicon thermometers at 4 K are greater
than 100 kfi, and typical stray capacitances are 0.1 nF. For
an excitation frequency of 1500 Hz, wR,C is approximately 0.1, introducing attenuations into measurements of
R, and AR,. This problem necessitates the use of two
frequencies in the measurement. For measuring the resistance R, and AR, (see section on thermal conductance)
we use 100 Hz, and for measuring the relaxation curves,
where the attenuation of the signal is irrelevant because
only the determination of Q-matters, we use frequencies of
1500 Hz or greater.
III. EXPERIMENTAL
METHOD
We use the relaxation method4 to measure heat capacity, although we note that the microcalorimeters may be
952
Rev. Sci. Instrum.,
Vol. 65, No. 4, April 1994
T,+ST
exp( -UT),
where r= C/K,, and C is the sum of the sample heat capacity and the contributions from the various addenda.
The determination of the sample specific heat using the
relaxation method thus involves four separate measurements: the time constant of the relaxation 7, the thermal
link Ker, the heat capacity of the addenda which must be
subtracted from the total C, and the sample volume or
weight which is used to convert heat capacity into specific
heat. In this section, we discuss the range of validity for
this technique and how each of these measurements are
implemented for the microcalorimeters.
A. Internal and external time constants
The bridge is balanced with the temperature of the
block (and sample) stable at a temperature To. The sample heater is turned on, changing R T and driving the bridge
off balance. The current to the sample heater is chosen
such that 6T<0.003To to ensure that the values of C and K
change by less than 1% within the temperature interval.”
At time t=O, the sample heater is turned off and the offnull signal of the bridge (proportional to ST) is recorded
up to tz2.5~. Several sweeps (25 to 225) are taken, averaged, and fitted to an exponential. A rounding of the signal
near t=O is introduced by the lock-in filter time constant
and by the filtered heater switch (see Fig. 5), both of
which are set to <~/lo. Fitting is done from t=O.lT
(away from the rounding) to 1.17. Figure 6 shows an example of a measured relaxation curve out to 77. For To
above 40 K, we find no detectable drifts in the base line,
allowing the base line to be recorded before and after the
set of sweeps and averaged. Below 40 K, the noise in the
base line is greater (due to the larger resistances of the
low-temperature thermometers and the shorter time constants). We therefore record and subtract the base line
after each sweep.
A simple exponential decay is dependent on the condition that internal time constants Tint (through the sample
and between the sample, the heater, and the thermometer)
are much faster than the external time constant 7. Physically, the sample must be isothermal during the relaxation
to the block temperature and must be at the same temperature as the thermometers. The internal time constants are
Thin film calorimeter
Time
0
500
1000
(ms)
1500
2000
10
Time (ms)
FIG. 6. A typical relaxation curve (averaged over 100 sweeps) with
r==252.3 m s at room temperature. This data was taken with a sampling
time of 2 ms, sample heater power of 30 mW, lock-in amplifier full scale
range of 5 pV, and integration time of 10 ms. Inset shows the log plot of
the same relaxation curve. Note the linearity down to 77 indicating a
single time constant.
controlled by the thermal diffusivities of the various components and by the distances involved. The time constant
associated with thermal diffusion through the thickness of
the sample/membrane/thermometers
is extremely fast
since the sample, the thermometers, and the heater are
evaporated directly onto the 180 nm thick membrane. The
internal time constant associated with lateral thermal diffusion is slower due to the much longer distances involved.
To ensure that this time constant is sufficiently fast requires that the thermal conductance of the sample be large
compared to K,,. This requirement is met when the sample
is conducting or when a parallel conducting layer such as
gold or aluminum is deposited either under or over the
sample. An “empty” device therefore cannot be measured
because 7int is not (7.
The lateral internal time constant is estimated based on
thermal diffusion through a bilayer or trilayer consisting of
the sample, the nitride membrane, and any parallel conducting layer. The thermal diffusivity of a bilayer is given
by
K=
Kltl +Kz tz
w1t1+
P2 c2 t2 ’
where ti are the thicknesses, Ki the thermal conductivities,
cf the specific heats, and pi the densities of the layers. The
time constant q,,, is equal to d2/2K where d=O. 125 cm, the
distance from the center of the sample to the edge. The
density, thermal conductivity, and specific heat for the conducting layer are based on literature values’7p42assuming a
mean free path limited by an approximate grain size of 100
nm. The density, thermal conductivity, and specific heat
for the Si-N membrane are based on measurements made
on this material at room temperature by Mastrangelo
et a1.43The values at other temperatures were calculated
by scaling the values for vitreous silica42,44to the room
Rev. Sci. Instrum.,
Vol. 65, No. 4, April 1994
15
20
25
30
Time (ms)
FIG. 7. Relaxation curves (r=7.35 ms) at 10 K using a boron-doped
polycrystalline Si resistance thermometer. This figure shows the relaxation curves for three different sample heater currents giving three different powers: 30.02, 37.99, and 46.90 nW. The largest current gives 6V
=12.2 pV, which corresponds to 6T=25 mK. The inset shows the
logarithm of all three curves, scaled by Z”, which is proportional to the
relative power input. Note that they lie on top of each other, indicating
not only a single time constant but the same time constant and thermal
conductance. The high frequency oscillation is the incompletely filtered
2f component of the bridge excitation.
temperature nitride values. Table I shows estimates of 7int
at various temperatures together with the measured external relaxation time constant 7 for a typical microcalorimeter with a 100-200 nm Au sample. Typical Caddenda
are
also shown and will be discussed below. W e note that these
estimates of 7int are worst case estimates since we neglect
the Pt thermometer and heater which have good thermal
conductivity and will decrease the internal time constant,
and since we believe from measurements of the addenda
that the room temperature value (and hence the values at
all temperatures) for c&d& may be overestimated (discussed below). Faster internal time constants are obtained
by using Al for a conducting layer instead of Au due to
both higher thermal conductivity and lower specific heat.
Experimental data for the relaxation shows one time
constant from 0.17 up to 7~, beyond which the signal is
dominated by noise (see Figs. 6 and 7) .45This observation
supports the conclusion of Table I that, with an appropriate choice of conducting layer, CTint<T.Figure 7 shows relaxation curves of 153 nm (2.6 lug) Al taken at 10 K for
several values of sample heater current. The curves scale
with the power (as shown in the inset), as expected, showing that the thermal conductance and the heat capacity are
not changing appreciably within the temperature throw ST
and giving further credibility to the simple time constant
analysis.46
B. Thermal conductance
After measuring the time constant 7, we measure the
heat link Ker between the sample and the block. The current source is used to provide electrical power P to the
sample heater, producing a steady-state temperature rise
Thin film calorimeter
953
AT (typically larger than 6T used for the determination of
7). In steady-state conditions, the power in (P) equals the
power out. Therefore,
P=K,,dAT+a~[(To+AT)‘-~]
I
=: (Kco,d+4~cAT;)AT=Ke~AT,
where Kcondis the thermal conductance of the Au/Pd leads
and the Si-N membrane border, u is the Stefan-Boltzmann
constant, E and A are, respectively, the emissivity and surface area of the sample/membrane/thermometers.
The
contribution to the power from radiation assumes an isothermal environment held at To. This is ensured by a copper heat shield surrounding the block. Note that we do not
need to calculate any of these quantities; K,, is found by
measuring P and AT. Typical values used for AT are
O.O2T,; the averaging of K,, over AT is removed by interpolation once we know the functional form of the temperature dependence of KeE.
To measure AT, we calibrate the sample thermometers
during each measurement using the commercially calibrated block thermometers. This process is somewhat
more involved than the techniques described in Refs. 1, 3,
4, and 20 because the matching resistor R, on the Si frame
also depends on temperature. With the heater turned off
and both the sample and block at To, VI, and V, (see Fig.
4) are adjusted to balance the bridge ( Vs=O) . The current
I through the bridge is determined by the voltage V, across
RA . When power P is input, RT changes to R,+ AR,, and
the bridge is driven off balance with an off-null signal A Vc .
The temperature rise AT=AR,(dRT/dT)-‘.
For the
closely matched case RTzRM, VlzV,,
and AR, is approximately given by 2AV,,/I (the exact solution is given
in Ref. 47 ) . To determine dR r/dT, R T is measured at each
block temperature To. The voltage V, across R, is measured and the current is simply I= VA/RA, so that
R,=R,VR/V,.
The voltages V,, V,, V,, V,, and AV,
are all measured with the lock-in amplifier, using low-noise
relays to switch measurements between them. R, measurements are made to better than 0.5%. Measurements are
carried out over some temperature range with r, P/AR=,
and R, versus temperature stored in a file. R,(T) is fit to
a spline and the derivative dRT/dT calculated. AR, is then
converted to AT, which together with r and P/ART, yields
K,,(T) and C(T). Typical dR/dT for the Pt thermometers is 2.5 R/K and does not vary greatly for a given thermometer from 40 to 360 K. For the polysilicon or the
Nb-Si thermometers, dR/dT is a strongly varying function
of temperature (see Figs. 2 and 3).
C. Addenda
Because it is not possible with our microcalorimeters
to measure an empty device, the most accurate method for
determining the heat capacity addenda is to use a differential technique. First we deposit a conducting layer and
measure the heat capacity, which becomes the addenda for
the subsequent layer. We then deposit the sample, remeasure the heat capacity, and take the difference. The first
(conducting) layer must be thick enough to ensure a re954
Rev. Sci. Instrum.,
Vol. 65, No. 4, April 1994
laxation curve with a single time constant. 250 nm of Al or
Au is sufficient for measurements around room temperature. Thinner layers are sufficient at low temperatures
where the specific heat and the thermal conductivity of the
metal samples become much larger than that of the silicon
nitride.
For some samples, it is desirable to deposit them directly on the Si-N membrane, rather than on an Al or Au
film. In this case, if a conducting layer is needed, it must be
deposited on top of the sample and the differential technique is not possible. We will show in the Results section
that the addenda varies very little between different devices
and hence an approximate value can be used if high accuracy is not needed or if only the temperature dependence
through a phase transition is wanted. To improve on the
accuracy of the estimated addenda, the usual technique
used, for example, in Refs. 1, 3,4, and 20 is to calculate the
addenda based on measurements of specific heat for the
various contributions and determinations of the mass of
each contribution (e.g., the mass of the sapphire substrate
and of the wires used for electrical leads). In the ideal case,
a sample with substrate and thermometers with infinite
thermal conductivity is attached to the block by leads with
no heat capacity and finite thermal conductivity KL. In
this case, r= C/KL, where C= C,+C,.
C, is the sample
heat capacity and C, is the combined heat capacity of the
substrate (i.e., the membrane beneath the sample), the
thermometers, and the heater. A correction can be made to
include the effect of finite lead heat capacity CL. Specifito within
1%
when
c=c*+c,+
1/3CL
cally,
CL/( C,+ C,) < 0. 1.4 This still gives a single time constant
r= C/K,. For the microcalorimeters, the Au-Pd leads
and the Si-N border around the sample contribute to the
total thermal conductance and hence to the heat capacity.
The heat capacity C, of the Si-N border is relatively large,
so that we must consider (CL+ C,)/( C,+ C,) which may
be nearer the value of 0.7-1.0, making the expansion which
led to the correction 1/3CL invalid. We performed a finite
element heat flow calculation to determine the effect of this
large heat capacity and found that l/3 (CL+ C’) still gave
an adequate approximation to the addenda heat capacity
(within a few percent for the sample and membrane thicknesses described in this article). This calculation will be
described below.
The high heat capacity of the Si-N border also led us
to consider the potential problem of heat flow from the
border back to the sample, which would give rise to multiple time constants. [Note, however, that the observation
of a single time constant experimentally (Figs. 6 and 7)
gives confidence that heat flow back from the border is not
a problem for the devices and conducting layers we use.] In
other words, can the Si-N border act as a heat reservoir,
storing heat and eventually reintroducing it back to the
sample? A complication in analyzing the Si-N border is
that it constitutes a two-dimensional heat flow problem.
The square nitride membrane border can be reduced to an
effective one-dimensional problem by replacing it in the
calculation with nitride “leads” which are the width of the
sample, correcting for the missing corners by slightly inThin film calorimeter
creasing the conductivity and specific heat. Using a simple
graphical method in determining the shape factor,48 the
conductance increases by approximately 20% when the
corners are included. To test the importance of heat flowing back to the sample, and to determine what contribution
the Si-N border makes to the heat capacity addenda [i.e.,
whether using l/3( C,+C,)
is appropriate], a onedimensional problem with two different parallel conducting paths was analyzed. We solved the time-dependent heat
flow equation for a sample with a given heat capacity C,
and thermal conductance K, connected to the block by two
leads, one with high conductivity but low heat capacity
(representing the metallic leads) and one with low conductivity but greater heat capacity (representing the Si-N border) using finite differences4’ We examined the relaxation
curve generated in this simulation and determined whether
it fit a simple exponential form with a time constant
r= C/K, where C= C,+ l/3 (CL + Cb) . ( C’ in this simulation includes the heat capacity of the sample, the heater,
the thermometers, and the portion of the membrane under
the sample.)
We found from this calculation that the total heat capacity which should be included as addenda depends on
the ratios CJC, and C/C, and on the ratios KJK, and
KJKb, where the subscript b refers to the Si-N border, L
to the Au-Pd leads, and C and K to the extensive quantities of heat capacity and thermal conductance, respeo
tively. The danger therefore is that even our differential
technique for determining the addenda might lead to an
error as the ratios CJC, and CJC, change with the addition of a second sample layer. We have found, however,
that the corrections to the simple l/3( C,+C,> addenda
contribution are quite small (less than 3% ) for all cases
relevant to the microcalorimeters, that is, when r&r.
For
example, at room temperature, CJC, is approximately 1.6
for a 250 nm Al layer, CJC, is approximately 18, KJK,
is approximately 11, and KJKb is approximately 25. With
these numbers, the calculation shows a single relaxation
time constant with r= C/K, where K= KL+Kb
and
C= C,+ l/3 ( CL+ C,), with C, determined to an accuracy
of 3%. For this case, the ratio of thermal conductance
through the Au-Pd leads to that through the Si-N border
KJKb is 2.3. If KL/Kb increases above 3, deviations from
one time constant appear in the calculation. For larger
values of C/C,, i.e., thicker films or lower temperatures,
the accuracy improves to better than l%, and in fact the
limit on the ratio of KL/Kb for observation of a single time
constant can be relaxed. In practice, these limits are the
same as those that ensure q&r.
D. Sample volume determination
The sample area is known to high accuracy as it is
photolithographically determined either by etching or by
deposition through the evaporation masks shown in Fig.
1 (g). The sample thickness is determined by measuring
neighboring samples from the same deposition, using either
Rutherford backscattering or a profilometer technique.
Rev. Sci. Instrum.,
Vol. 65, No. 4, April 1994
1”‘,““,“,,,“‘,
50
40 30 20 10 0
0
ltll’(*I~‘illl’ll~~
100
200
Temperature
300
400
(K)
FIG. 8. Typical measured thermal link KeR. K,, can be written as
K,,=a+b~7’+cT~.
The linear term (shown in the figure with circles) is
from conduction through the Au-Pd leads and S-N border and the cubic
term from radiation with c=4aui where A is the sample/membrane/
thermometers surface area , ~,2(0.25 cm)* and (Tis the Stefan-Boltzmann
constant. For this particular device and sample (aluminum), the emissivity E is found from the fit to be -0.1.
IV. RESULTS
A. Thermal conductance
The effective thermal link Ker= Kand + 4~x54T3 can be
written as a+ bT+cT3, where a and b are constants related to the thermal conductance of the leads and c=4mA.
Typical measurements shown in Fig. 8 show that indeed
K,, has this temperature dependence, which allows us to
extract an approximate value for the emissivity (assuming
A=0.125 cm2, typical values determined for E are 0.1, a
reasonable number). The T3 (radiation) contribution to
K,, is extremely small until we reach temperatures above
200 K.
B. Addenda
We measured a series of samples (Au, Cu, and Al) of
different thicknesses (200 to 1000 nm). The heat capacity
of the Au, Cu, or Al (calculated from literature values42)
was subtracted from the total measured heat capacity. This
process is shown graphically in Figs. 9 (a>-9( c) . The addenda for a number of microcalorimeters from different
processing batches are shown in Fig. 10; results are remarkably similar to each other. Au and Al have very different Debye temperatures and hence their specific heats
have very different temperature dependencies in the temperature interval studied. The similarity of the addenda for
such different thicknesses of different types of samples supports the reliability of the measurement. The small differences that are seen are due to differences in the nitride and
metallization thicknesses, and can be corrected for since
these thicknesses are readily measured on each device. (In
fact, these thickness variations have been much reduced in
recent batches, as is evidenced by the similarity of batch B
and C in the figure).
Thin film calorimeter
955
5p
total
G
r;
2
measured
Q
heat copocity +H+w++
0.8
l
+++
++++
++++
+f’ literature value for Al
-.
+if
- --,-.-’- -5z-..
--
//--- C’
_._’
,,0
_.f / / ,/ .’ &dendo = Ctotol-CA,
/
, .fl
0.0 t --+-I'
0
-3
vx3
.e
ki
Q2
s
:
-:
-
%I2
-
14
A++++@+
.A’
' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' 1
300
400
100
200
Temperature
(4
-5’ 1.3
‘23
u
n
F
+
+
+
r”
01,
0
(K)
/’
8”,”
I1,1111,1111j
--Batch
A
- -Batch
C
-‘.“. Batch
B
3 ’ 1 ”
b 3-t ’ * ’ * I ”
100
200
300
Temperature
(K)
9 t 81
400
FIG. 10. Addenda for six different devices from three different processing
batches determined as shown in Fig. 9. Note the similarity especially in
the B and C devices. Batch A has about 165 nm nitride thickness while B
and C have about 199 nm. The thicknesses and areas of the metallic leads
and thermometers are also slightly different for these three batches.
//
:~:~/,
,(,I-jI:~~~:~:__‘_i
. 30
40
50
total
measured
0
ICI
70
80
(K)
heat capacity,,’
I
(4
60
Temperature
04
/
+/
/
f,’
/
/
/’ literature
/ ’ value for Au
addenda =
20
Temperature
30
40
50
(K)
FIG. 9. Measurement of the heat capacity of microcalorimeter plus aluminum or gold sample. (a) 278 nm (4.7 pg) of Al on 199 nm nitride
membrane from 80 to 370 K; includes addenda data from (b) and (c);
(b) 345 nm (5.8 pg) of Al on 165 nm nitride from 40 to 70 K; (c) 307
nm (37 pg) of Au on 199 mn nitride from 4 to 40 K. The literature values
for the specific heat for Au and Al are from Ref. 42. The sample areas
were defined photolithographically; the sample thicknesses were from a
crystal monitor. Subtracting the heat capacity of the Au or Al from the
total measured heat capacity gives the addenda shown on each figure.
Figure 11 shows calculations of the various contributions to the addenda as a function of temperature, compared to a typical measured value. The largest contribution
at higher temperatures comes from the nitride membrane,
both the portion under the sample and the border outside
the sample area (which contributes l/3 of its total heat
956
Rev. Sci. Instrum.,
capacity). The thermometers, heater, and Au-Pd (or
heavily doped polysilicon) leads contribute about 12% of
the total addenda above 77 K, and increasing amounts at
lower temperatures. The heat capacity of the nitride membrane is calculated from the specific heat for vitreous silica
(from Refs. 42 and 44) since the room temperature value
agrees with the single measurement for amorphous siliconrich silicon nitride (0.7 J/g K, from Ref. 43). The calculated total addenda exceeds the measured values by a significant amount at all temperatures; since the nitride
membrane is the dominant contribution, the most likely
Vol. 65, No. 4, April 1994
CD0
@“‘*
///
I
:
“Jf,./
_.C’
y,H.y~H’~ji$kme
‘.
sample
1
0
0
100
200
Temperature
300
(K)
400
FIG. 11. Comparison of measured and calculated addenda. (0) are
typical addenda, determined as shown in Fig. 9. (- -) represents the total
addenda calculated for the metallic portions of the microcalorimeters.
(-.-a ) represents the heat capacity of the nitride membrane directly
beneath the sample, assuming the nitride specific heat to be the same as
that of vitreous silica. (-) shows the calculated total addenda. This
calculation exceeds the measurement while scaling the nitride specific
heat to a room temperature value of 0.5 J/g K fits our data better.
Thin film calorimeter
2.0x1 o-” 1”
,
s?
--'I.5
2
x
2
g 1.0 a
s
$J 0.5 -
Au sample+Au
layer+addenda
I2
o.o-
0
r ' * t ' a ‘ * t ' * ‘ t "
100
200
300
Temperature
(4
2.5x10-5~
5 '
c;32.0
=-, .A=!
iiEk
cl1.0
5 -
'
'
1 I
'
8 '
q '
400
(K)
1 '
'
4 '
t+
,t+
1 '
'
'
+++c2
The literature value for gold is 7X 10e9 J/K; the addenda
is therefore approximately 2 x 10M9 J/K. At lower temperatures, we have extrapolated the addenda, based on literature values for a-SiOz,44 to give a value of approximately
1 X lo-*’ J/K at 1.5 K. These lowest temperature measurements are currently in progress.
At present we do not have an apparatus capable of
making specific heat measurements above 360 K, but microcalorimeters with samples, Pt thermometers and heaters, and Au/Pd leads on them have been cycled in a furnace up to 800 K without damage. The Pt thermometers
have been measured up to 800 K; their temperature sensitivity does not change. We do not, therefore, anticipate any
problems with using these devices up to at least this temperature.
' 4
1
C. Calibration
samples
A variety of samples have been prepared and measured
using these devices. As discussed in the section on process1.5
ing, samples have been prepared by evaporating or sputtering onto the back side of the membrane, then spinning
on photoresist at the bottom of the etch pit and photolithographically defining the sample area. As a simpler alternative, we use evaporation masks [see Fig. 1 (g)] which fit
0.5
down into the pit, approximately 25 pm away from the
membrane. This close fit is needed to avoid shadowing
0.01,
* B I ' * * * t "
I ' 1 ' p t t .-i
effects, particularly when coevaporating materials. For
0
100
200
300
400
samples where the differential method is used, the first
Temperature
(K)
(b)
(highly conducting) layer is made with a slightly larger
area than the second (sample) layer to ensure that the
FIG. 12. Total heat capacity of a microcalorimeter with the first (conducting) layer (0 ), with the iirst and second (sample) layer ( + ), and
sample lies completely within the highly conducting area
the difference between these (A). (a) The first layer is 290 nm (35 pg) of
defined by the first layer.
Au and the second (sample) layer is 390 *40 nm (47 S=5 pg) of Au. The
Figures 9 and 10 show measurements which were
difference of the measurements fits the literature value for 425 nm (51 ,ug)
made
on single layers of either Au or Al on several devices
of Au. (b) First layer is 595 nm (10 pg) of Al and second layer is
470+50 nm (57*6 pg) of Au. The difference data fits the literature
from different batches at temperatures ranging from 4 to
value for 532 mn (64 pg) of Au. Literature values are from Ref. 42.
360 K. Sample thicknesses ranged from 150 to 600 nm.
For a better test of the microcalorimeters, we measured a series of gold samples deposited as the second layer
onto previously measured microcalorimeters with various
explanation is an overestimate of its specific heat.
types of first layers. Figures 12(a) and 12 (b) show the
At low temperatures (below 40 K), the difficulties asresults of the first measurement, the second measurement,
sociated with attenuation from using high bridge frequenand the difference between the two which should be the
cies (necessitated by fast time constants) and with the
heat capacity of the gold sample. The thickness (and hence
large temperature dependence of dR/dT have delayed the
the volume and weight) of the gold layer is uncertain to
completion of measurements to the same accuracy that we
approximately 10% due to the sample preparation techhave achieved above 40 K. Values of KeE are currently
nique used. This measured heat capacity is shown comuncertain to approximately 10% with corresponding unpared with the literature values for bulk gold,42 with the
certainties in the total heat capacity C and hence Caddenda. sample volume as the single adjustable parameter. In each
We have solved the attenuation problem by using two meacase, the difference between the two measurements fits the
surement frequencies (as previously discussed), but we
literature value for Au to the accuracy of the film thickhave not yet completed calibration runs to the accuracy
ness. In particular, the temperature dependence is well fit.
shown in Figs. 9(a), 10, and 12. A relaxation curve taken
at 10 K was shown in Fig. 7, demonstrating that the techV. CONCLUSION
nique works. Figure 9(c) shows preliminary results of
We have developed a thin tllm microcalorimeter which
measurements from 4.3 to 40 K with a sample of Au. Al
is capable of measuring the specific heat of thin film samsamples have also been measured. For the purposes of deples as small as a few micrograms over a wide temperature
termining addenda, a few measurements were made near
range. The contribution of the addenda for these devices is
4.2 K where the total heat capacity for a 307 nm (37 pg)
more than two orders of magnitude less than addenda for
Au sample plus addenda was found to be 9 X lo-’ J/K.
Rev. Sci. Inetrum.,
,+++++iu
samD!etAi
faddenda
Vol. 65, No. 4, April 1994
layer
r
j
Thin film calorimeter
957
any comparable system capable of measuring thin films.
Measurements to date have been made from 4.3 to 360 K;
the thermometers have a sensitivity which allows their use
down to 1.5 K. Devices have been thermally cycled to 800
K and the temperature dependence of the Pt thermometers
successfully measured, we anticipate no problems extending specific heat measurements up to 800 K.
ACKNOWLEDGMENTS
We would like to thank J. Birmingham, E. D. Dahlberg, R. C. Dynes, T. H. Geballe, A. M. Goldman, P. L.
Richards, and G. R. Stewart for useful discussions concerning specific heat measurements and for assistance in
writing this manuscript. For numerous resistivity measurements, we would like to thank Erica Perry Lewis, Dennis
Palmer, and Nancy H. Trissel. For assistance in the development of the microcalorimeter, we would like to thank R.
S. Muller, R. M. White, and the staff and students at the
UC Berkeley Microlab: Katalin Voros, Bob Hamilton,
Kris Pister, Debra Hebert, Dave Hebert, James Bustillo,
William Flounders, Leslie Field, and Phil1 Guillory. We
would also like to thank George Kassabian and Alan
White for their help in developing the electronics for the
experiment and Arnold Krause and Andy Pommer for
help in machining. This work has been supported by the
National Science Foundation (Grant Nos. DMR 9 l-09004
and DMR 88-10374).
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13Berkeley Microfabrication Laboratory, University of California, Berkeley, CA 94720.
14This large residual resistivity is due presumably to either impurity incorporation or grain boundary scattering, resulting from the relatively
low vacuum deposition system used for this step.
15To keep sensitivity constant with temperature T, the ac bridge offset
voltage SF, should be constant. This voltage can be written as SV,=
fL#WdT)&i,,,,,
. I,,, is determined by limiting the self-heating
of the thermometer ST, = ILR/K
to 0.0003 T. Koc T in the region of
interest, say K=aT.
Then ST, =I2 R/aT=O.O003T
or I,,,,,=
~O.O003u/RT. Therefore SV0=5‘? 0.0003a/RT(dR/dT)6T,,,,I,.
We
small to limit the averaging over the (temwould like to keep GTsnmple
perature dependent) specific heat to approximately 1%. Quantitatively
) - C( T,)]/C( To) ~0.01, where T, is
we want AC/C=[C( T0+6T,,,,,
the block temperature. We assume we are in a region where
C(T) =flT3 (the limitation on ST-,,, when C is linear in T is even
less stringent). Using C(T,+ST,,,,,)
=C( T, ) +GT,,,,,,dC/dT
we
fmd AC/C=36T,,,,,,
/T(O.Ol, or ST,,,,,,<O.O03T. Then the bridge
958
Rev. Sci. h-strum.,
Vol. 85, No. 4, April 1994
offset voltage becomes GV,,=a’( Tz/ fi) (dR/dT) where a’ is a constant. Integration shows that for constant 6 I’, we want Ra( l/p).
l6 CRC Handbook of Electrical Resistivities of Binary Metallic Alloys, edited by K. Schroder (CRC, Boca Raton, FL, 1983).
” Thermal Conductivity of Metals and Alloys at Low Temperatures, edited
by R. L. Powell and W. A. Blanpied, Natl. Bur. Stand. Cii. 556
(United States Department of Commerce, Washington, DC, 1954).
“M.
Hansen, Constitution of Binary Alloys, 2nd ed. (Genium,
Schnectady, NY, 1986).
“Au and Pd have similar vapor pressures (see R. E. Honig and D. A.
Kramer, RCA Rev. 30, 285 (1969). In addition, to ensure chemical
homogeneity, we weigh the appropriate amounts of each into the evaporafion boat, heat slowly to just below the temperature at which appreciable evaporation occurs, using a crystal oscillator to monitor evaporation, then turn up the power to the boat and evaporate rapidly to
completion. Rutherford backscattering measurements of this material
have shown reasonable uniformity.
z”S. R. Early, Ph.D. thesis, Stanford University, 1981.
*’ G. Hertel, D. J. Bishop, E. G. Spencer, J. M. Rowell, and R. C. Dynes,
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Dynes, Solid-State Electron. 28, 73 (1985).
22F. Helhnan, Appl. Phys. Lett. (to be published, April 1994).
“See, for example, C. Yamanouchi, K. Mizuguchi, and W. Sasaki, J.
Phys. Sot. Jpn. 22, 859 (1967).
“T. Kamins, Polyclystalline Silicon for Integrated Circuit Applications
(Kluwer Academic, Boston, MA, 1988), pp. 112-115.
25R. K. Ray and H. Y. Fan, Phys. Rev. 121, 768 (1961).
26P. Rai-Choudhury and P. L. Hower, J. Electrochetn. Sot. 120, 1761
(1973).
“J. Y. W. Seto, J. Appl. Phys. 46, 5247 (1975).
28G. Baccarani, B. Ricco, and G. Spadini, J. Appl. Phys. 49,5565 (1978).
2pG. J. Korsh and R. S. Muller, Solid-State Electron. 21, 1045 (1978).
30N. Chau-Chun Lu, L. Gerzberg, C.-Y. Lu, and J. D. Meindl, IEEE
Trans. Electron Devices ED-28, 8 18 ( 198 1).
3’N. Chau-Chun Lu, L. Gerzberg, C.-Y. Lu, and J. D. Meindl, IEEE
Trans. Electron Devices ED-30, 137 (1983).
32M. S. Rodder and D. A. Antoniadis, Mater. Res. Sot. Svmp. Proc. 106,
77 (1988).
“‘For example, M. A. Huff, S. D. Senturia, and R. T. Howe, 1988 Solid
State Sensor and Actuator Workshoo Technical Digest. Hilton Head
Island, SC, 1988 (IEEE, New York,*1988), p. 47. 34N. Mott, Conduction in Noncrysfalline Materials, 2nd ed. (Oxford University Press, Oxford, 1993).
“IICO, 3050 Oakmead Village Dr., Santa Clara, CA 95051.
36J. F. Gibbons, Projected Range Statistics Semiconductors and Related
Materials, 2nd ed. (Dowden, Hutchinson, and Ross, Stroudsburg, PA,
1975).
37GEC Alsthom (M&I) Ltd., Manchester England. Apiezon N is used
for work below room temnerature while Aniezon H is necessary if
temperatures are to exceed-30 “C (Apiezon N melts near 30 “C while
Apiezon H melts near 250 “C) .
“Model CR 2800, manufactured by CryoCal, Inc., St. Paul, MN 55114.
39Model Pt-11 1, manufactured by Lakeshore Cryotronics, Inc., Westerville, OH.
@J. M. E. Harper, Ph.D. thesis, Stanford University, 1975.
41Our criterion for self-heating (ST,, < O.O003T,=O. MT) is somewhat
unnecessarily stringent. A less stringent criterion would be that selfheating should not change over the temperature interval 6T (for relaxation time constant measurement; this is known as the aP correction in
Early’s work) or AT (Early also shows how to make corrections to
thermal conductance measurements); see Ref. 20. In this case, a larger
bridge excitation voltage could actually be used, which would improve
the signal to noise ratio.
42Specific Heat: Elements and Metallic Alloys, edited by Y. S. Touloukian
(HI/Plenum, New York, 1970).
43C H. Mastrangelo, Y.-C. Tai, and R. S. Muller, Sensors Actuators A
23, 856 (1990).
44R. C. Zeller and R. 0. Pohl, Phys. Rev. B 4, 2029 (1971).
45All devices which meet the criteria discussed in the text show a single
time constant, although not all devices were checked to >7r at all
temperatures to the accuracy shown in Fig. 6.
46Further confidence is given by the accuracy of the measurements of the
heat capacity of standard materials like Au and Al (see Results
section).
Thin film calorimeter
J7The resistance change AR, can be solved exactly. Note that V, and V,
stay constant and it is the current that changes when R, changes on
turning
on the sample heater. The off-null
voltage AV,
= V, -Z’(R,+RT+ART),
where I’ is the current when the bridge is
off-balance. Rearranging, ART= ( VI -A V,)/Z’VI/Z, where we have
used the condition at balance V,=Z(R,+
RT). The current I’ is related
Rev. Sci. Instrum.,
Vol. 65, No. 4, April 1994
to Z, i.e., Z’=Z[l +ART/(R,+RT+RB
+R,)]-’
Substituting I’ into
the expression for ART yields ART= (-AVdZ)[l(l+ V,/V,)-’
-tAVd(V,+ Vdl-‘, which reduces to AR, z -2AVdZ when
?~~Z v,.
4sF Kreith Principles of Heat Transfer (Harper and Row, New
York, 198;).
Thin film calorimeter
959