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3. plastics and polymers

Design and Fabrication of a Sample
Holder for sub-mK Temperatures
Semester Project
Supervisor: Prof. Dr. D. Zumb¨
uhl
Quantum Coherence Lab - Institute of Physics
Abstract
The aim of this semester project was to design, build and characterize a sample holder suitable for sub-mK temperatures. This sample
holder should fix and protect the sample and connect it with the wires
that lead out of the dilution refrigerator. As little material as possible
was used to minimize the heat release of the sample holder. Further
the wires were designed to establish a good thermal connection down
to the 100µK regime between the sample and the copper pieces of a
nuclear demagnetization stage. To achieve this, the wires were made
from high purity silver (5N) and annealed at 820◦ C, resulting in residual resistivity ratios exceeding 1’000.
July 15, 2009
Dario Maradan
Student of the Nanosciences Curriculum
University of Basel, Switzerland
Contents
1 Introduction
1
2 Theory
2.1 Four-Point-Measurement . . . . . . . . . . . . . . . . . . . . .
2.2 Thermal Conduction . . . . . . . . . . . . . . . . . . . . . . .
2.3 Thermal Expansion . . . . . . . . . . . . . . . . . . . . . . . .
2
2
2
3
3 Materials and Methods
3.1 Epoxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Silver Wires . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
4
5
4 Procedure
4.1 CAD Modeling . . . . . . . . . .
4.2 Wire Preparation . . . . . . . . .
4.3 Teflon Form . . . . . . . . . . . .
4.4 Epoxy Preparation and Handling
4.5 Machining . . . . . . . . . . . . .
4.6 Glueing and Bonding . . . . . . .
4.7 RRR Measurement . . . . . . . .
6
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5 Results
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6 Discussion and Conclusion
17
7 Acknowledgements
18
References
18
I
1
Introduction
The invention of dilution refrigerators and their use in ultra-low temperature
physics opened a new door to explore for example transport phenomena by
observing single electrons. This achievement led to the experimental description of effects like Kondo states [1] and the fractional quantum Hall effect
[2]. A major obstacle to cooling down to the millikelvin regime is the thermal connection between the sample and the helium mixture in the mixing
chamber, which is the coldest point in the dilution refrigerator system.
Whilst at temperatures of a few kelvin, most of the energy or heat,
respectively, is stored in the electrons, it is stored in the nuclei at even
lower temperatures (see subsection 3.2). In the range of a few hundred microkelvins, it has been predicted by Simon, Braunecker and Loss [3] [4] that
the gallium-arsenide lattice will order its nuclear spins, so-called magnetic
ordering. The aim of the group which I was part of is to verify and measure
this phase transition. Dilution refrigerators with a 3 He/4 He mixture are
limited to temperatures of a few millikelvin. So, to achieve such low temperatures, a new technique named ”Adiabatic Demagnetization” is applied.
Adiabatic demagnetization of paramagnets is a very powerful technique to
reach the microkelvin regime [5] and hold the system at such temperatures
(for extended but finite periods of time). Magnetic cooling is relying on
the adiabatic demagnetization of nuclear magnetic moments (spins): In the
cooling cycle, the magnetic field is decreased very slowly (adiabatic) so that
there is no change in the entropy. Because the entropy is proportional to
B 2
, the temperature is decreased with the magnetic field. Further inforT
mation about magnetic cooling can be found in ”Matter and methods at
low temperatures” by Frank Pobell, page 215ff [6].
My task was to built a sample holder for this measuring chamber that
fits and fulfills the following needs [7] [8]:
• 16 contacts to connect the sample with the wires,
• the sample holder itself has to be insulating,
• it should have a good thermal conductivity and a minimal heat release,
• and last but not least it should be easy to fix and remove.
This semester project report contains a short theoretical overview about
the four-point-measurement technique and problems like heat conduction
and thermal expansion. This section is followed by a detailed description
of the materials that were used and the exact procedure for the fabrication
of the sample holder. At the end, some measurements were done and a few
pictures of the final sample holder were shown.
1
2
2.1
Theory
Four-Point-Measurement
When we measure the resistance of a device by the usual two-point-measurement,
we get one resistance value for the whole circuit, including the resistances of
the wires. This can be avoided with a four-point-measurement (see figure 1).
Two wires were used to apply a current through the device. The current is
thereby measured by an amperemeter A.
Figure 1: Four-point-measurement of the resistance Rsubject . The arrows
indicate the amount of current (not to scale).[9]
It is assumed that the current is constant in the whole circuit according
to the Kirchhoff’s circuit laws. Because the internal resistance of the voltmeter V is very high, there is almost no current flowing so that there is no
voltage drop across the wires from the voltagemeter to the device, but we
can measure the voltage drop across the device. So, we can easily calculate
the resistance of the device by deviding the voltage drop across the device
by the current measured by the amperemeter. The value we get does not
include any resistances from wires.[9]
2.2
Thermal Conduction
One of the most important things, if not the most important at all, when one
wants to accomplish experiments and measurements in a temperature range
of a few kelvins or less, is thermal conduction. If one is not able to isolate
the measurement chamber from the outside, the heat will flow in through
the wires and other connections and the sample will never get really cold.
To be able to estimate the thermal conduction of a material, one refers
often to the law of Wiedemann and Franz [10]. This law describes the correlation between the thermal conductivity κ and the electrical conductivity σ,
which is easy to measure with a four-point-measurement described in section
2.1.
2
κ
3
= ·
σ
2
kB
e
2
·T
(1)
where kB is the Boltzmann constant, T the temperature in Kelvin and e the
charge of the electron. According to equation 1, the thermal and the electrical conduction are directly related with each other. This equation most
often holds at low temperatures, where the impurity scattering is dominant
ΘAg
(T < 10
where ΘAg = 227 K is the Debye temperature of silver), and at
high temperatures (T ≥ ΘAg ), where the phonon scattering is dominant. In
between, there may be some deviations due to ballistic thermal conduction
caused by energy losses of the order kB T associated with electron-phonon
collisions.[6]
In the few-kelvin-range, in which we are interested, resistivity is caused
by lattice defects and impurities of the conducting material. The fraction
caused by phonons is negligible because there are almost no phonons existing. If we want to achieve a good thermal conductivity between the dilution
unit and the sample, all wires that lay between should have the lowest possible resistivity. The so-called ”residual resistivity ratio” value (RRR) is an
estimation of the purity of a metallic conductor. It probes the resistivity
in the absence of phonon scattering. It is defined as the ratio between the
resistance at room temperature and the resistance at the temperature of
liquid helium (4.2 K).[6]
Thermal annealing of the metal can reduce the scattering centers like
vacancies and defects in the lattice and therefore lead to a higher conductivity. Impurities by iron atoms for example can be oxidized to Fe-O molecules
that form clusters. Thereby the number of scattering centers is reduced.[6]
To achieve an ideal diffusion of molecules from the gas phase, a small flow is
brought to the annealing furnace. The furnace has a temperature between
a few hundred to more than thousand degrees Celsius.
2.3
Thermal Expansion
Every material contracts or expands when the temperature is changed. Most
materials expand when the temperature is increased and shrink when the
temperature is decreased, but in a few cases (like freezing water) its contrary
and the thermal expansion coefficient is negative. The thermal expansion
coefficient is a thermodynamic property of a material. One differentiates
linear thermal expansion, area thermal expansion and volumetric thermal
expansion coefficients, but these values are closely related so that we only
take a look at the linear coefficient. This value itself is temperature dependent. Hence the linear coefficient of thermal expansion α is defined as
α=
1 ∂l
·
l ∂T
3
(2)
where l is the length and T the temperature.[6]
When we work with cold temperatures in the laboratory, or more precisely with large temperature differences, it is very important to be always
attentive to this fact. For example, when a device is fixed with a screw,
this screw may get loose when it is cooled down from room temperature to
liquid helium temperature and the device may not be fixed anymore. In
the other case, one can assure that the screw holds even stronger if one
uses appropriate materials. Another example: When one wants to isolate
the measurement chamber thermally or one wants to produce a high vacuum, there may be some small leaks arising from thermal expansion (or
contraction, respectively) if one does not consider the thermal expansion
coefficients. According to this the tube with the largest thermal expansion
coefficients should be on the outside so that the joints are not pulled open
during the cooldown.
The easiest way to avoid such incidents is to use materials with similar
expansion coefficients. One trick is to improve the thermal contact after
cooldown by adding a washer of a material with a low thermal expansion
coefficient such as Mo or W. The problem is that they are both superconductors at very low temperatures, but there are also applications where this
is not important.[6]
3
3.1
Materials and Methods
Epoxy
The demands on the material are quite numerous and hard to combine: it
should be an electrical insulator, easy to handle and cast (low viscosity), fast
cure within hours, undergo extreme temperature difference from room temperature to a few millikelvin without cracking or getting brittle by repeating
the cooling cycle many times. Further the thermal expansion coefficient has
to be similar to that of the silver wires, and it should be generally small
because the glued sample may get loose if the sample holder expands or
contracts too much.
Every kind of epoxy consists of polymer and has therefore a high thermal
R
expansion coefficient. Though we decided to use the epoxy STYCAST
2850 FT with the catalyst 23 LV from Emerson & Cuming [11]. Its coefficient
of thermal expansion is α = 39.4 · 10−6 K −1 at 300 K when used with the
catalyst 23 LV. As it is shown in figure 2, the thermal expansion coefficients
of silver (Ag) is very similar to the value of the epoxy that we used here.
R
The STYCAST
2850 FT is a black two component, thermally conductive
epoxy and has a relatively low coefficient of thermal expansion, compared
to similar encapsulants. The Brookfield viscosity is indicated as η = 5.6
P a · s with the catalyst 23 LV, compared to viscosities of about 58 P a · s
and 64 P a · s if it is used catalyst 9 or catalyst 11, respectively. For this
4
reason we decided to use the catalyst 23 LV. It allows a working life for
about 60 minutes at room temperature and then cures at room temperature
within 16-24 hours. The mix ratio is 7.5 parts of catalyst per 100 parts of
epoxy. (All information from Datasheet, [11].)
R
To lubricate the teflon form before pouring the epoxy in, Dow Corning
High Vacuum Grease was used.
3.2
Silver Wires
The choice to use silver wires was easy: Silver has a very high conductivity
and is not superconducting even at very low temperatures, like gold as well.
Further, silver has a nuclear spin of only 1/2, compared to other elements
like copper or gold with spin 3/2. Additionally, it has also a very small
magnetic nuclear moment: µ = 0.11µN where µN = 5.05 · 10−27 JT −1 is the
nuclear magneton whilst most materials have a µ ∼ 1µN . This properties
of the silver nuclei lead to a low heat capacity Cn as shown in the Schottky
law (equation 3) and the definition of the molar nuclear Curie constant λn
(equation 4).
Cn =
λn B 2
µ0 Tn2
λn = N0 I (I + 1) µ0 µ2n gn2 /3kB
(3)
(4)
where B is the magnetic field, Tn the temperature of the nuclear spin
system, N0 the number of nuclei, I the nuclear spin (1/2 for silver) and
gn = µ/I the nuclear g-factor.[6] When the magnetic field is going to zero,
we see in equation 3 that the heat capacity should also go to zero. As this is
not the case, the electronic heat capacity gets dominant. This means that
with silver, we have a very small heat capacity, and that is another reason
to choose silver.
Our silver wires have a quality of 5N and a diameter of 1.27 mm and
were obtained from ESPI Metals, USA. The annotation 5N stands for ”5
nine”, so it is 99.999 % pure silver. The possible impurity is declared with
2 ppm Fe, 0.6 ppm Cu and Pd and less than 0.2 ppm Bi. According to
manufacturer information the silver wires have a thermal conductivity of
4.29 W cm−1 K −1 at 298.2 K. The melting point of this high purity silver is
indicated as 961.93◦ C.[12]
The wires were prepared and then annealed at about 820◦ C for 5-7 hours
in a N2 flow with 5N purity of 500 cc/min. Before annealing, they had a
RRR values of about 40, and after annealing of about 1900. Out of this
we can conclude that the annealing is extremely useful and eliminates a lof
of scattering centers. The wires are very smooth and easy to bend after
5
annealing, and when they are bent a few times the RRR declines to about
400 caused by induced strain and lattice distortions.[13] As we know from
section 2.2, a low resistance means a high electrical conductivity and that
implies a good thermal conductivity according to the law of Wiedemann
and Franz.
4
4.1
Procedure
CAD Modeling
Figure 3 shows an overview of different parts modeled with the CAD (Computer Aided Design) software ”CoCreate Modeling Personal Edition 2.0”
from Parametric Technology Corporation.
4.2
Wire Preparation
One of the major problems was the wire for the middle hole. This wire was
thought to ground the sample and to carry the heat away from the sample
at the same time. We planed to weld together four of our 1.27 mm wires,
but a lot of trials were unsuccessful. At the end we decided to mill a little
piece out of a 4N silver plate. So we had to weld only once to connect this
piece with one of our wires. We cut 17 pieces of about 12 cm length from
the 5N silver wire from ESPI metals [12]. 16 of them were bent in a ninety
degree angle at about 1 cm of one end. This length of about 1 cm slightly
differed for the 16 wires: to ensure enough place for all the wires, that ones
from the back should lie a little bit higher than the ones on the front. This
small difference can be seen in figure 4 in the following section 4.3.
The thought behind this 1 cm was that about 5 mm go into the teflon
form and about 3-4 mm will be covered by the epoxy. In the part that will be
covered by epoxy we added some small slots using pliers to supplementary
fix the wires and prevent them from torsion: Every smallest torsion will
remove the sensitive gold wires that connect the sample with the sample
holder. But squeezing them too much will lower their electric conductance.
After this threatment the wires were polished with a fine-grained sandpaper and wiped with ethanol to remove dirt like grease or impurities from
oxidation with the environment. The cleaning was followed by the thermal
annealing at about 820◦ C for 5-7 hours, accomplished by Tobias Bandi as
described in section 3.2. Once annealed, we tried to avoid every smallest
bending or other modification on the wires.
4.3
Teflon Form
According to the model in figure 3 and the precise dimensions (see figure
8 in section 5) the shop cut a teflon form with the relevant measures. The
6
holes in the bottom part have a depth of about 5 mm. This depth and
the diameter of 1.3 mm make sure that the silver wires with a diameter of
1.27 mm can be pushed into the holes and are then fixed. At the same time,
the sample holder was really hard to remove from the teflon form after the
epoxy is cured; so we had to find a middle course.
R
The teflon form was then lubricated with Dow Corning
High Vacuum
Grease to make the removal easier. Teflon is an ideal material for such applications per se because it is repellent to different kinds of sticky materials.
After lubricating, the prepared silver wires were pushed in the holes and
bound together at the other end to assure the right positioning.
It is very important that the distance from the spacer of the sample
holder on one side to the curved wires on the other side is smaller than
18 mm. If it is larger, the wires will touch the refrigerator and generate a
short! Every single wire will be protected by an insulation, but nevertheless
it must not touch any part of the refrigerator.
4.4
Epoxy Preparation and Handling
Due to the long storage time, the epoxy had little chunks and could not
be stirred homogeneously. So it was heated to about 50◦ C and stirred continuously. After the chunks were disappeared, we let it cool down to room
temperature because the working life would be decreased when we mix it
with the catalyst while it is still warm. Based on estimations and experiR
ences from the first trial, 14.48 g of the STYCAST
2850 FT were mixed
with 1.08 g of catalyst 23 LV under continuous stirring until the compound
is homogeneous. To prevent air bubbles in the sample holder, the compound
was then put under a bell jar with small low-pressure to degas. Due to the
stirring there is a lot of air in the mixture and the low-pressure causes a
foam that is quickly expanding. To prevent a pollution of the bell jar by the
foam, one has to slightly slow down the low-pressure by an air inlet. After
several minutes, the foam is diminishing and then disappearing what means
that the compound is now degassed. As already mentioned before, every
inhomogeneity like air bubbles or other enclosures can lead to an instability
and therefore damage the sample holder during the cooling cycle.
Despite the small Brookfield viscosity indicated as η = 5.6, the mixture
was quite viscous and it was hard to pour it into the teflon form, because
there was not much space left beside all the wires. For this reason we used a
micropipette and enlarged the plastic aperture by cutting off a piece. With
this tool it was still painful but possible. So the compound was poured drop
by drop into the teflon form until the desired height of 3-4 mm was reached.
With a toothpick, the compound was agglutinated to the wires to achieve a
better stability and prevent torsion (see figure 5).
24 hours later the compound was cured and one could remove the teflon
form. Due to the grease, it was quite easy to remove the outer cylindrical
7
part of the form. To peel off the inner form was, as expected, arduous. On
the one hand, the epoxy adhered to the teflon form and there may be a small
vacuum when one tries to remove it. On the other hand, the 17 wires were
all plugged in the about 5 mm deep holes. Thus it was important to remove
it in very small steps without tilting the sample holder. The more it was
tilted the harder it adhered. We finally achieved it with a razor blade and
a little screwdriver. The sample holder looked then as shown in figure 6.
4.5
Machining
The shop cut 3 mm away on the right and left side of the sample holder and
milled down the wires and the whole outer cylinder (except the spacers) to
one single plain. They drilled a hole with 2 mm diameter for the screw.
Later on the sample holder could be fixed with an M2 screw to the sample
stage in the refrigerator. Then the sample holder was rubbed with a finegrained sandpaper and a polishing towel. We suspect that there may be
some silver sulfite disposal on the wires, so we dipped the wires in 50 %
nitric acid and paid attention that the epoxy was not in direct contact with
the acid.
4.6
Glueing and Bonding
We used varnish to glue a test sample on the sample holder. This may not
be the optimal glue but it is fast and easy to handle. The sample was fixed
by the varnish and we had no problems to cool down the sample holder with
the sample to 4 K and warm it up several times. To remove the sample from
the sample holder, we used acetone. Maybe one could also try ethanol, but
isopropanol did not work. When real samples were measured, the sample
could be glued with liquid gallium. This would assure a better electrical
and thermal contact of the sample to the grouding wire in the middle of the
sample holder.
Wire bonding was one of the most laborious tasks in the whole project.
First of all, it was not possible to use the standard tower which fixes the
sample holder. So we found a grey plastic tube with a diameter similar to the
sample holder (∼26 mm) to fix the sample holder on the desired height under
the bonder. This tube was referred to as ”sample holder holder”. Caused by
the milled slot which was added afterwards, an additional plate with a height
of 5 mm was necessary to reach the ideal work distance. Unfortunately this
construction was quite instable and it was hard to make reliable bonds. We
used the old bonder in manual mode with a standard gold wire to bond the
sample to the sample holder. Because there were no parameters for bonding
gold wire on a silver surface, it was hard to find a working adjustment. As
a basis, the gold-wire-bonding program (number 5) of Sarah Heizmann was
used. A working set of parameters is shown in table 1 for bonds from one
8
silver contact to another and in table 2 for bonds from a silver contact to
the sample. Since it was difficult to decide which parameters are more and
which are less important, nearly all parameters are listed in the tables. The
parameters written in italic were supposed to be critical ones. A bonded
sample glued on the sample holder is shown in figure 9 in section 5.
Table 1: Bonding parameters for cross-bonds (bonds from one silver contact
to another).
1st bond: silver contact 2nd bond: silver contact
Search: 0.54
Search: 0.31
Power: 3.72
Power: 3.99
Time: 5.0
Time: 5.0
Force: 1.4
Force: 1.4
Step: 1.9
Tail: 1.5
Kink: 0.2
Tear: 3.3
Reverse: 0.0
Time: Long
Yspeed: 0.2
Tail: Long
Loop: 2.3
Auto: Off
Table 2: Bonding parameters to wire-bond the sample holder with the sample. The parameters of the first bond are equal to the parameters given in
table 1 except the values for Step and Loop.
1st bond: silver contact 2nd bond: sample
Search: 0.54
Search: 0.31
Power: 3.72
Power: 5.25
Time: 5.0
Time: 6.3
Force: 1.4
Force: 4.0
Step: 2.5
Tail: 1.5
Kink: 0.2
Tear: 3.3
Reverse: 0.0
Time: Long
Yspeed: 0.2
Tail: Long
Loop: 2.6
Auto: Off
4.7
RRR Measurement
Two silver wires with contacts which were connected with a standard gold
bonding wire as described above were soldered together on the back side
of the sample holder each with a current and a voltage wire. The current
wire connections have to be further away from the sample holder. At room
temperature, a certain current was applied and the voltage drop was measured with a DMM (Digital Multi Meter). Different currents were applied
9
to calculate an average resistance of the little circuit. This procedure was
repeated after dipping the sample holder in liquid helium after equilibrating
for a few seconds. The data can be found in table 3 in the following section.
5
Results
Figure 7 shows the final model of the sample holder. Its dimensions are
depicted in figure 8. Figure 9 is a light microscope picture of the final
sample holder with some gold wires to measure the RRR.
The RRR measurements are shown in table 3. We made some cross
bonds on the silver contacts and measured the total resistance. Cross
bonds are shown in figure 9. The average resistance at room temperature is
87.43 mΩ and at 4 Kelvin it is 1.96 mΩ. So, the RRR value is 44.6. That
value corresponds to the RRR value of the thin gold wire and is not the
outcome of a high resistance of the silver wires, as it was shown in earlier
measurements [8]. This result does also imply that the bonds of the gold
wire from one to another silver contact are solid.
Table 3: Measurement of RRR ”Ag-contact to Au-wire to Ag-contact” at
room temperature and at 4 K. The resistance in the last column is calculated
from the average of the two measured voltage drops (at the same current
but in both directions) divided by the current.
# temperature current [mA] voltage [mV ] resistance [mΩ]
1
RT
+1
+0.08674
2
RT
-1
-0.08799
87.4
3
RT
+4
+0.34879
4
RT
-4
-0.35012
87.4
5
RT
+10
+0.87276
6
RT
-10
-0.87413
87.3
7
RT
+100
+8.7550
8
RT
-100
-8.7559
87.6
9
4K
+1
-0.008684
10
4K
-1
-0.012640
1.98
11
4K
+4
-0.002795
12
4K
-4
-0.018464
1.96
13
4K
+10
+0.00902
14
4K
-10
-0.03016
1.96
15
4K
+100
+0.18537
16
4K
-100
-0.20702
1.96
17
4K
+1000
+1.95119
18
4K
-1000
-1.97294
1.96
After the dip-in measurements, the sample holder did not show any
10
damage or cracks: warming up and cooling down from room temperature to
4 K seemed to be no problem for the epoxy and the embedded silver wires.
11
Figure 2: Linear thermal expansion coefficients of different materials.
(1) Invar (upper), Pyrex (lower), (2) W , (3) non-alloyed steel, (4) N i,
(5) Cu0.7 N i0.3 , (6) stainless steel, (7) Cu, (8) German silver, (9) brass,
(10) Al, (11) soft solder, (12) In, (13) Vespel SP22, (14) Hg, (15) ice,
(16) Araldite, (17) Stycast 1266, (18) PMMA, (19) Nylon, (20) Teflon. P t
is similar to (3); Ag is between (9) and (10); Stycast 2850 GT slightly larger
than (10); Stycast 2850 FT very similar to Stycast 2850 GT (from F. Pobell,
page 60, [6]).
12
Figure 3: Left: First ideas. The teflon form consists of three parts, whereat
the upper cylindric part somehow holds the wires and fits in the lower tubeshaped one. At the bottom of the tube-shaped part is the third piece. The
small channels in the upper part were thought to vent the air excess. Right:
Final model. The upper part has gone and the wires were held in place by
sticking them into holes at the bottom part shown above and below as set
in the cylindric part.
Figure 4: Teflon form with wires. One can see the middle wire which was
milled out of a 4N silver plate and the small slots from the pliers that should
give additional rigidity. Before pouring the epoxy in, the middle part is
lowered by a few millimeters. The wires on the right are a little higher than
the ones at the left.
13
Figure 5: Photograph after pouring the epoxy-catalyst compound in the
teflon form and covering the wires with a toothpick. The cured epoxy will
give additional stability to the wires and the welded bond of the middle-wire.
Figure 6: Photograph of the sample holder after removing the teflon form.
The slightly sparkling tracks on the surface were relicts from the vacuum
grease. The screw hole will be added on the right side, where the distance
between the two middle wires is a little bit larger.
14
Figure 7: Silver wires are shown in yellow, spacers in black. In the foreground, the screw hole is visible. The spacers protect the sample from
mechanical damage.
Figure 8: Dimensions of the sample holder. Numbers in circles are diameters.
The diameter of the silver wire was 1.27 mm, the height of the spacers 3 mm
and the height of the epoxy in the middle area about 3-4 mm.
15
Figure 9: A light microscope picture of the sample holder wearing a sample
glued with varnish. Here, the screw hole is on the right side. One can see
the cross bonds of gold wires from one silver contact to another. With this
setup, the RRR values shown in table 3 were measured. There are also
bonds from the silver contact to the sample on the left side.
16
6
Discussion and Conclusion
One must not forget that this sample holder is a first prototype. There are
many things one can improve in the fabrication process. A few possibilites
to improve the procedure are listed here, but most of them will arise when
the sample holder is used regularly and frequently.
First of all the pouring of the epoxy compound into the teflon form
would be much easier if the compound was less viscous. Maybe one could
find another material with similar properties but a lower viscosity or even
better properties like a better thermal conduction value or a lower thermal
expansion coefficient.
This leads to the problem of the heat release. The more material we have
in the measurement chamber, the larger is the heat release. Therefore we
used as less epoxy as possible, but we still needed to assure that the wires
were strongly adhering to prevent torsion and gliding. We think that the
small slots we pressed in the wires with pliers are quite useful to fix them.
Maybe there are further possibilities to decrease the amount of material and
nevertheless have enough stability?
From the experience gained by peeling off the teflon form, we would
shorten the depth of the holes in the bottom part of the epoxy form to
about 2 mm or 3 mm (now: 5 mm). We think that the wires would still be
held in place and that the removal of the teflon form could be a bit easier.
Further it could be favourable to clean the silver contacts not only with a
sandpaper and a polishing towel, but with a chemical agent like nitric acid.
This could improve the cleanliness of the silver surface and therefore ease
the bonding process.
The wire-bonding is another crucial point in the fabrication process. One
day we tried for hours to make one single bond, and the day after we bonded
without any problems with the same parameters, the same sample and the
same sample holder. There seem to be some unknown influences we can
not explain. An important improvement that has to be done implicitly is
an enhancement of the sample holder holder. By reason of the additional
plastic plate, the composition is unstable and shaky. One has to fix the tube
by one hand while setting the bonds, and that is really hard to achieve. It
would be nice to have a heavy tube with a large foot that can be adjusted
in a small range of height.
17
7
Acknowledgements
A special thank goes to my supervisor Prof. Dr. Dominik Zumb¨
uhl. He
had always time to answer my questions and lead me back on the right
way. I enjoyed the group meetings with the exciting talks and learned
a lot by preparing and giving a little talk by myself about a paper from
H.O.H. Churchill et al. with the title ”Electron-nuclear interation in 13 C
nanotube double quantum dots”. Further thanks goes to Dr. Anthony Clark
and Kai Schwarzw¨alder for their help at all kind of ”lab-problems” and their
useful explications and hints during my practical work. Last but not least
I would like to thank Sascha Martin and his crew for all the precise manufacturing work and the whole Zumb¨
uhl-group for the good time I had.
References
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[8] Dr. A. Clark and K. Schwarzw¨alder. Personal discussions during and
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18
[11] Emerson & Cuming. http://www.emersoncuming.com.
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