A hybrid method for calorimetry with subnanolitre samples using Schottky junctions

0.41 MB·English

by  T. K. Hakala

A hybrid method for calorimetry with subnanolitre samples using Schottky junctions
T. K. Hakala, J. J. Toppari, and P. T¨orm¨a
Nanoscience Center, Department of Physics, P.O.Box 35 (YN), FIN-40014 University of Jyv¨askyl¨a, Finland
Aµm-scalecalorimeterrealizedbyusingSchottkyjunctionsasathermometerispresented. Com-
bined with a hybrid experimental method, it enables simultaneous time-resolved measurements of
variations in both theenergy and the heat capacity of subnanolitre samples.
7
I. INTRODUCTION nm) SiN-layer (see Fig. 1). The samples were fabricated
0
on a lightly boron doped (12 Ωcm) Si chip having a SiN
0
layeronbothsides. ByusingphotolithographyandReac-
2 Thepresentmicromachiningtechniquesallowthescal-
n ing of the calorimeter dimensions down to micrometer tive IonEtching(RIE),a squareopening(1.2×1.2mm2)
was etched on the SiN layer on one side. The opening
a or even submicrometer scale, which results in high sen-
J sitivity and rapid response times. For instance, ther- was then used as a mask for chemical KOH etching to
form a Si well. The etching was interrupted when there
4 mopiles fabricated on a thin SiN membrane have been
used to determine the catalase activity within a single was still about 5–10 µm of Si at the bottom of the well,

] mouse hepatocyte.1 Recently, nanowatt sensitivity and under which there was the SiN layer of the other side.
t
e time constant of millisecond was achieved by optimiz- After that the well was covered with SiN using PECVD
d ing such a structure.2 In general, membrane based mi- deposition. ThisSiN layerwasfurther e-beampatterned
- and RIE etched by using PMMA as a mask, to leave
s crocalorimeters using dc-methods have lately been un-
n der extensive study.3,4,5,6,7 Additionally, ac-calorimetry only a small SiN square at the center of the well bot-
.i methods8 have been developed for measurement of heat tom. A second KOH etching was applied to form a sep-
cs capacity9,10 and thermal conductivity11 of increasingly arate Si island onto the SiN membrane. On the other
side of that SiN membrane, openings on the SiN for the
i small samples.
s Schottky junctions to the Si island were done by e-beam
y In this paper we describe the first µm-scale calorime-
lithography and RIE. The chip was exposed to chemical
h ter realized by using Schottky junctions as a thermome-
p ter. The ability to use present IC fabrication techniques cleaning {procedure consisting of 2% HF (20s)/Piranha
[ (5min)/2% HF (20s)}13 prior to deposition of Ti, that
makes Schottky junctions a very attractive choice for
actedasametalforSchottkyjunctions. Tiwasdeposited
1 mass produced, low cost and high throughput calorime-
by e-beam evaporator in UHV chamber. Ti layer was
v ters for a variety of applications. Moreover, we utilize a
then patterned and (RIE) etched to form a heating ele-
4 novelmeasurementmethodwhichenablesmeasurements
4 of energy changes to be performed simultaneously with ment and the Schottky junctions onto the membrane.
0 ac-calorimetry.12 Combined with a short time constant
1
(∼20 ms) of the device, it allows direct time-resolved
0
7 measurements of both the variations in the sample heat
0 capacity and the energy changes due to for example a
/ phase transition or other phenomena. The calorimeter
s
c may be used in ambient conditions and with liquid sam-
i ples allowingalso realtime monitoring,e.g., under a mi-
s
y croscope, and the operation is near isothermal utilizing
h only low heating rates, thus making it particularly suit-
p able for biological applications. The performance and
:
v reliability of the device and method were tested. We
i used subnanolitre drops of DI-water as samples2,4 and
X
measured, simultaneously, the change of the heat capac-
r ity and the latent heat related to the evaporation of the
a
drop.
FIG. 1: A schematic and a micrograph (close-up) of the fab-
ricated sample and themeasurement principle.
II. EXPERIMENTS
A. Sample fabrication B. Experimental methods
The fabricated calorimeter is composed of two Si/Ti It is well known that Schottky diodes can be used as
Schottky junctions as a thermometer and a Ti heating accuratethermometer atroomtemperature. The charge
element on a small Si island supported by a thin (600 transport through Schottky junctions with low semicon-
2
ductor doping concentrationis dominated by thermionic where the term ∆C describes the heat capacity of the
emission, which yields an exponential dependence be- sample which can also slowly vary in time, e.g., due to
tween the current and the temperature given by I = evaporation of a liquid sample drop. Thus, by simulta-
tot
AJ [exp(qV/k T)−1].14 Here V is the voltage across neous measurement of the dc and ac signals, one is able
ST B
the junction, A the area of the junction, q the electron todetectboththevariationintemperatureandthevari-
charge, k the Boltzmann constant and T the absolute ation in heat capacity, respectively.
B
temperature. The saturation current density J is de- The simultaneous monitoring of the dc and ac signals
ST
fined by JST ≡ A∗T2exp(−qφB/kBT), where A∗ is the was performed by using a measurement setup shown in
effective Richardsonconstant and φ the barrier height. Fig. 2. The dc-bias of the Schottky junctions was set to
B
We consider temperature changes ∆T small enough so 60 mV and the sinusoidal signal for the heating element
thatthedependenceofthecurrentontemperature,I(T), hadrmspowerof37µWandafrequencyof10Hz corre-
canbelinearized,i.e.I(T)∝(dI/dT)∆T. Inthepresent spondingtothesituationω ∼τ−1. Thedccomponentof
configuration there are two Schottky junctions in series, the temperature sensitive current through the Schottky
onebeingalwaysforwardbiasedandtheotherreversebi- junctions was measured directly using DL Instruments
ased. The zero bias resistance of the fabricated samples lownoisevoltagepreamplifier1201andtomeasurethe20
with35×45µm2Schottkycontactsinambientconditions Hz accomponent, StanfordResearchSR830digitallock-
is5-10MΩandthevariationofresistanceabout10%/K. in amplifier was used. These both signals were recorded
At the equilibrium, the temperature ofthe Si islandT byacomputerwithasamplingrateof1kHz. Thefluctu-
is governed by the net power P applied to it, and by ating ac signal component was extracted from the mea-
in
the heat conductance K [W/K] of the SiN membrane to sured dc signal by digital notch filtering.
a heat bath formed by the Si chip at temperature T . In
0
general, one can write
T =T +P /K, (1)
0 in
if the variations in P are slower than time constant of
in
the calorimeter τ = (C +∆C)/K. Here C +∆C is the
totalheatcapacityoftheSiisland(C)andpossiblesam-
ple on it (∆C). An ac voltage V = V sin(ωt) applied
0
via the Ti-heater,i.e., the powerP =V2/R×sin2(ωt),
H 0
where R is the resistance of the heating element, pro-
duces by Joule heating a temperature fluctuation of the
sample with a frequency 2ω. If ω ∼τ−1, the equilibrium
result does not apply anymore and one obtains for the FIG. 2: A schematic of the measurement setup.
temperature of the island
V2 e−t/τ cos(2ωt+ϕ) P
T=T + 0 1− − + S, (2)
0 2RK" 1+(2ωτ)−2 1+(2ωτ)2# K C. Sample delivery
p
where ϕ = arctan(2ωτ) and PS is the power produced The sample to be measured, i.e., drop of DI-water is
by the sample (e.g. due to a chemical or biological re- delivered to the Si island of the calorimeter constructed
action), or by some external source. Consequently, the onto the center of the SiN membrane (see Figs. 1 and 3)
dc-biasedSchottkyjunctionswillcarryacurrent,directly using a very narrow pulled glass pipette. The injection
proportionaltoT above,withonecomponenthavingthe iscarriedoutbyhavingthepipettebackendattachedto
frequencyof2ωandanotherbeingthedccomponentpro- a pressuredevice (ASI MPPI-2microinjector)which can
portionaltoPS andtheconstantrmspowerfedinviathe supply a short pressure pulse with adjustable pressure
heater, V02/2RK. and pulse time. In principle, this device allows one to
Our calorimeter function is based upon the combina- precisely and reproducibly (from measurement to mea-
tion of two calorimeter operation modes: the heat con- surement) control the amount of liquid injected. How-
duction mode, which measures PS/K via the dc compo- ever, it is not possible to quantify the amount since the
nent, and the ac-calorimeter mode with an ac voltage of total amount depends on the viscosity of the liquid, the
frequencyω ∼τ−1 appliedtotheheater(seeFigs. 1and surface effects between the liquid and the pipette, the
2). According to Eq. (2), the amplitude of the produced pipette dimensions, etc.
2ωtemperaturecomponentdependsontheheatcapacity All the time during the sample delivery and the mea-
of the sample as surement,theendofthepipetteisattheverynearprox-
imityoftheSiislandofthecalorimeter. Thisisnecessary
V2 1 since, due to high surface tension of the water,the small
δT = , (3)
2R K2+(2ω)2(C+∆C)2 drops used in this experiment will not have sufficient
p
3
mass to detach from the tip of the pipette unless they
touch the Si island surface. During the pressure pulse,
the drop size increases until it touches the hydrophilic
surface of the Si island and spreads on. After the pulse,
the dropsizestartstodecreasedue toevaporationofthe
drop and also due to the reflux of the water back to the
injector as will be discussed later.
After the evaporation of the drop, a small amount of
water is left to thermally bridge the pipette and the Si
island (see Fig. 3). This is due to hydrophilicity of the
surface of the Si island and the surface tension of wa-
ter, and it creates an additional pathway for heat trans-
fer between the calorimeter and the environment. Since
the relative positioning of the tip of the pipette and the
calorimeter remains constant throughout the whole ex-
periment, it is expected that this additional pathway for
heat transfer will simply increase the total heat conduc-
tivity K in our simple model by a constant factor which FIG.3: (a)–(d)Cartoonofevaporationofawaterdropafter
injection. Intheend,asmallamountofwaterstaystobridge
can be experimentally determined. Thus the total ther-
the end of the pipette and the Si island of the calorimeter.
mal conductivity may be assumed to be constant over
Thisconfiguration,shownin(d),isconsideredasthe”empty
the time span of the experiment.
device”. ThethermalconductivityKandtheheatcapacityC
Prior to measurement of the device parameters (see
are determined for this ”empty device”, thus accurately and
nextsection),adropofwaterwasinjectedontotheSiis- systematically including theeffect of thepipette.
landsurfacewhichwasthenallowedtoevaporatetoform
thewaterbridgebetweenthecalorimeterandthepipette
asdescribedabove. Thisconfigurationisnowconsidered which yielded a value of 1.53×10−6 J/K.
tobetheemptydevice,sinceaftereachinjectionthesys-
temreturnstothisstate. Thepipetteiskeptonitsplace
during all the further experiments. Thus, the obtained III. RESULTS AND DISCUSSION
parameter values already include the effect of the addi-
tionalheatconductivitythroughthewater,i.e.,theeffect
A. Measured signals for subnanolitre drops of
of the pipette slightly touching the device. Importantly, water
this effect can be accurately measured, and it remains
constantthroughthe whole measurementprocess,which
Thevalidityofourmeasurementmethodwasevaluated
makes it controllable. However, for more practical use
by injecting several subnanolitre-scale drops of DI-water
ofthe device,other deliverysystems,e.g.,microfluidistic
withdifferent(undetermined)volumesontothecalorime-
channels, could be implemented.
ter, and by measuring the ac and dc responses as func-
tions of time as explained in section IIB. In Fig. 4a) is
shownthedcandacsignalsofthethermometerwithsev-
D. Calibration eral injection times of the nanoinjector, ranging from 10
ms up to 60 ms (injection pressure being constant ∼0.5
The dc signal (with 60 mV dc-bias) dependence on Bar). During all the measurements, the pipette was in
the temperature was calibrated by using a Pt-100 ther- thermal contact with the device as described above in
mometerasareference,resultinginalinearrelationwith section IIC.
a slope of 9.5×10−10 A/K between the current and the The figure 4b) illustrates the function of the sensor in
◦
temperature near the operation temperature 23 C. Ad- detail for 60 ms injection time. From the figure one can
ditionally, the relaxation method was used to determine see the abrupt change in the two signals when the injec-
thethermalconductance,K,andheatcapacity,C,ofthe tion of drop takes place, i.e., at around 288.5 s. The dc
empty device (including the pipette for water, see above signalincreases,indicatingthetemperaturedecreasedue
and Fig. 3) without the sample: To obtain the thermal to evaporation of the drop while the ac signal decreases
conductance according to the Eq. (1), we measured the due to increase in heat capacity of the system. Between
dccurrentasafunctionofslowlyincreasingdcpower(ap- thetime289–295.5sthedcsignalremainsapproximately
pliedtotheheatingelement),yielding6.95×10−5W/K. constant,whichimplies thatthe powerconsumptiondue
The time constant of the calorimeter was determined by to evaporation (P in Eq. (2)) and thus the surface area
S
measuring the dc signal response to the step pulse fed of the drop, remains almost constant. This is due to hy-
into the heater, resulting in a time constant of 21 ms. drophilicity of the Si island surface, which causes a flat
Finally, the calorimeter heat capacity was obtained as shape of the drop and the height of it to vanish almost
the product of the time constant and the conductance completely before the horizontal area starts to decrease
4
duringevaporation(seeFig.3). Thisalsoimpliesthatthe B. Detection of nonidealities in sample delivery
volume of the evaporated part of the drop is decreasing
withapproximatelyconstantrate. Duringthistimeframe
In general, the heat capacity, ∆C of the sample can
the ac signalis increasing whichis due to continuous de-
be expressed in terms of specific heat c and mass m of
crease in heat capacity, ∆C, of the system as the drop
the sample as ∆C=cm. Furthermore, for samples that
evaporates,which is alsoshownasa dash-dotted(green)
evaporate, ∆C=cm=cE/ℓ, where E is the total energy
curve in Fig. 4b). As the heat capacity is proportional
required for evaporation of a drop and ℓ is the latent
to volume, this is consistent with the conclusions made
heat of evaporation. From the measured dc signal one
from the dc signal.
is able to obtain the energy E as the time integral of
the signal, and the variation of the heat capacity of the
In figure 4b) the dashed line shows the calculated system is related to the ac signal via Eq. (3). Such com-
(alongEq.(3))variationofacsignalamplitudeasafunc- plementary information allows to understand details of
tionoftimeassumingaconstantreducingrateofvolume theprocessandeliminatetheeffectofmeasurementnon-
after the injection. Also, a finite time for injection, dur- idealities (which are of increasing importance when the
ing whichthe dropis growinglinearly, is assumedincal- sample volume decreases), as will be shown in the fol-
culation. These assumptions canbe clearly verifiedfrom lowing. Furthermore,for evaporatingsamples, it offers a
the curve showing ∆C as a function of time. Heat ca- test of consistency since the heat capacity can be deter-
pacity of the drop, ∆C, as well as the heat capacity, C, mined in two ways: from the ac signal, and, in addition,
and conductance, K, of the calorimeter for the calcula- from the dc signal via the relation ∆C=cE/ℓ.
tion are obtained from the measurement and calibration As the main non-ideality in the measurement, it was
data. The excellent agreement of the calculated curve observed that the non-ideal backpressure applied to the
with the measured one further verifies that the reducing nanoinjector produced a reflux of the injected drop back
rate of the total heat capacity of the sample during the into the pipette during evaporation (the backpressure is
evaporationis approximatelyconstantin time, as the dc used to compensate the capillary forces that result in a
signal already suggested for the evaporated part. Since reflux of the injected liquid back to the pipette). There-
the total reduction of the heat capacity is due to evap- fore the energy of evaporation E obtained by integrat-
oration and also due to the reflux of the injected water ing the dc signal does not give, without a correction,
back to the pipette, as will be further explained in next the initial heat capacity of the sample from ∆C=cE/ℓ.
section, this implies that also the reflux happens at a Therequiredcorrectionwasobtainedbyperformingmea-
constant rate. surementsfordropsofdifferent(unknown)volumesuntil
they were fully evaporated, and by 1) determining the
mass of the initial drop from the ac signal as the ratio
m = ∆C/c of the maximum variation of heat capac-
C
ity ∆C and the specific heat of water c, 2) determining
the mass of the evaporated part of drop from the dc sig-
nal as the ratio m = E/ℓ of the energy required for
E
evaporation E and the latent heat of water ℓ. The dif-
ference between the mass of the initial drop and that of
the evaporatedpart then gives the mass of the part that
was refluxed to the injector.
A plotting of m against m for each drop, as shown
C E
inFig.5,revealsthatthe massm obtainedfromevapo-
E
rationenergyissystematicallysmallerthanthemassm
C
obtained from minimum of the ac signal. This result is
easytounderstandbynotingthatsincethepipettesucks
someofthe liquidbackduringthe evaporation,the mass
m obtained from evaporation energy must be smaller
E
than the mass m obtained from the initial heat capac-
FIG. 4: (a) The dc (blue) and ac (red) signals of the ther- C
ity of the drop(ac signal). Furthermore,since the reflux
mometerforseveralconsequentinjections,theinjectiontimes
ranging from 10 ms up to 60 ms. (b) A closeup of both sig- is due to a constantpressuredifference, it is supposedto
nals with 60 ms injection time. The dash-dotted (green) line happen at approximately constant rate, which can also
is the heat capacity of the drop, ∆C, obtained from the ac be verifiedfrom the signals in Fig. 4 as explained in pre-
signalasafunctionoftimeandthedashedline(black)shows vious section IIIB. As shown by the Fig. 5, as much
thetheoreticalsignalcalculatedalongEq.(3)assuminglinear as 72% of the initial mass is lost by the reflux in every
decreasein∆C. Thetwoarrowsshowthecorrespondingaxes pipetting.
for the curves.
Such measurements can also be used to calibrate
the pipette for different liquids, surfaces, etc., which
is often found to be a problem in nano- and subnano-
5
litre injections. Therefore, the hybrid method and used in this analysis are taken from the measured cali-
the device we use allow to accurately distinguish vari- bration data. From the value givenfor c/ℓ by the fitting
ous non-idealities of the measurement from the chem- and using the known value for c or ℓ, we obtain the cor-
ical/physical/biological phenomena of interest. This is rect value for ℓ or c, respectively, with the accuracy of
certainly a strength, especially at nanoscale where non- about7%. Thisaccuracycharacterizestheoverallperfor-
idealities in the measurements are difficult to avoid. manceofthedeviceandmethodatthisstage,andcanbe
improved by optimizing the sample fabrication and the
measurement setup. Note that for evaporating samples
whereoneoftheparametersc,ℓorvolumeisknown,the
method can used for determining the two others.
The acsignalalsoallowshighaccuracymassmeasure-
ments: the smallest measured change of heat capacity
(for 10 ms injection time) was approximately 10−7 J/K
which, for water, corresponds to 20 ng mass. This could
be extremely useful for example when measuring a re-
actionheatofsomechemicalorbiologicalreaction,since
oneisabletosimultaneouslymeasuretheamountsofthe
reagentsaddedandtheenergyproducedorconsumedby
the reaction.
FIG.5: RelationbetweentheinitialmassofthedropmC and
the mass of the evaporated part mE. Circles correspond to
themeasured data and line is a linear fit to it.
C. Evaluation of the calorimeter
Finally,asatestofperformanceandconsistencyofour
method,wepresentinfigure6thefollowinganalysis: We
performed measurements for different sizes of the drops.
For each drop, the information given by the two signals,
acanddc,isplottedasapointinatwodimensionalgraph
whereoneaxisistheminimumofthenormalizedaclock- FIG. 6: The measured minimum values of the normalized ac
in signal (corresponds to the heat capacity of the initial signal and themeasured total energy required for drop evap-
sample via Eq. (3)), and the other axis is the integrated oration (with the reflux correction), together with the theo-
dc signal giving the evaporation energy E. The latter retical fit obtained using the relation of evaporation energy
yields the mass of the evaporated part of the drop m and heat capacity and Eq.(3).
E
via the relation m =E/ℓ. However, we cannot use the
E
mass m as such since it excludes the part gone back to
E
the pipette by the reflux, and when considering e.g. the
minimum value of the ac signal, one has to use the mass
ofthe initialdrop,whichincludesthe partthatlaterwill
IV. CONCLUSIONS
be gone back to the pipette by the reflux. From the
analysispresentedabove,we knowthe ratio betweenthe
evaporatedandtheinitialmassestobeconstant,∼0.28. In summary, we have developed a microcalorimeter
Thereby we can use a corrected value of mass, i.e. m = capable of providing simultaneous quantitative time-
mC ≈ mE/0.28 = E/(0.28ℓ) and thus corrected energy resolved information of the sample temperature, power
EC ≡E/0.28,which is plotted as x-axis in 6. and total energy production/consumption as well as of
As a fit to the theory and test of consistency, we sample heat capacity and its variations. The small heat
then take the measured values of E, use the relation capacity of the device which enables fast and sensitive
∆C = cm = (c/ℓ)E (with c/ℓ as the only fitting pa- measurementscarriedoutinroomtemperature,together
C
rameter),insertthisvalueof∆C inEq.(3),andplotthe withthemassproductionpotentialoftheSchottkyjunc-
resulting curve in the figure. It corresponds excellently tions, holda promisefor highthroughput andcosteffec-
to the measured data points. The values for C and K tive tool for biological and chemical applications.
6
ACKNOWLEDGMENTS
We thank Academy of Finland and EUROHORCs
(EURYI award, Academy project number 205470).
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