IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 15, NO. 3, SEPTEMBER 2005
3821
Thin-Film Persistent Current Switch
Priti Balchandani, Rodney H. Torii, and Roger Shile
Abstract—We have developed a fast, low power heat switch for
switching a niobium thin film between the normal and superconducting state. The sputtered niobium film (400 nm thick, 100 m
wide) has a critical current density of 5 1010 Am 2 . Switching is
produced by joule heating a small section of the niobium film with
a titanium thin-film resistor. With the heat switch in vacuum, the
minimum heater power needed to switch to the normal state was
4.5 10 5 W. A simple three-dimensional thermal model shows
that the minimum power is primarily determined by the thermal
conductivity of the substrate. We have achieved response times less
than 10 6 s.
(a)
Index Terms—Current injection, current switch, heat switch,
thin film.
I. INTRODUCTION
A
PERSISTENT current switch is used to switch a small
portion of a superconducting circuit between the normal
and superconducting state [see Fig. 1(a)]. One way to do this
is by local heating (heat switch), driving the superconductor
normal when the temperature exceeds the critical temperature.
For a number of persistent current applications [1]–[3], a fast,
low power heat switch is very useful. This thin-film heat switch
was developed for the Satellite Test of the Equivalence Principle
(STEP) experiment. STEP proposes to test the universality of
free-fall by comparing the acceleration of test masses in orbit
about the earth. The magnetic fields produced by persistent currents are used to constrain as well as detect test mass motion
[1]. Thin-film heat switches are required to inject these persistent currents.
We set design goals1 of a response time less than 10 s and a
maximum power of 10 W. This performance is significantly
better than previously reported by other workers [4], [5], whose
switches required more than 10 W to operate, or had a response time longer than 10 s. The thin-film heat switch shown
in Fig. 1(b) easily meets these requirements. A thin-film heat
switch has two important advantages: 1) the heater can be put
in very good thermal contact with the superconductor and 2)
the heat switch can be made very small. As an added benefit, a
thin-film heat switch can be easily manufactured and integrated
with thin-film circuits. A thin-film resistor (heater) above the superconductor provides local heating. The heater is electrically
Manuscript received September 9, 2004; revised February 14, 2005. This
paper was recommended by Associate Editor M. Mueck. This work was supported by NASA under JPL Contract 959723.
P. Balchandani is with the Lucas Center, Stanford University, Stanford, CA
94305-5488 USA (e-mail: pritib@stanford.edu).
R. H. Torii is with STEP 250, Stanford University, Stanford, CA 94305-4085
(e-mail: torii@step.stanford.edu).
R. Shile was with the Gravity Probe B Program, Stanford University, Stanford, CA 94305 USA.
Digital Object Identifier 10.1109/TASC.2005.847491
1These
requirements were set by the STEP experiment.
(b)
Fig. 1. (a) Schematic of a heat switch in a persistent current circuit. Local
joule heating produced by R drives a portion H of the circuit normal\resistive
allowing current I to be injected into inductive load L. A persistent current is
trapped when H is allowed to return to the superconducting state. (b) 3-D solid
model of the heat switch test circuit on a borosilicate substrate.
isolated from the superconductor by a thin dielectric layer. Reducing the overall size of the heat switch decreases the thermal
time constant of the heater and the superconductor. More importantly, for a given heater power, decreasing the heater area
increases the heat flux into the substrate, enabling a faster response time.
II. HEAT SWITCH FABRICATION
We used sputtered niobium for the superconductor since we
plan to use niobium for our persistent current circuits. In addition, we assume that the response time and power decrease as
the niobium cross-section decreases in size. Thus, the test circuit
was designed with a slightly larger cross-section than that required by our application. Heat switch test circuits 13 13 mm
were fabricated on 76 mm diameter, 0.9 mm thick borosilicate
wafers (21 test circuits per wafer).2 We chose a glass substrate
for its low thermal conductivity.
To begin the manufacturing process, 400 nm of niobium was
dc magnetron sputtered onto the bare wafer. The niobium had
of 8.9 K and a residual resistivity ratio ranging between
a
2.5 and 5. Without breaking vacuum, 50 nm of gold was then
sputtered onto the niobium. The gold layer makes possible a superconducting electrical connection to the niobium via a wire
bond [6] and protects the niobium when etching the dielectric
(the dielectric on the contact pads is etched to allow electrical
contact to the niobium). Using a positive photoresist and stan2The wafers were purchased from Polishing Corporation of America, Santa
Clara, CA.
1051-8223/$20.00 © 2005 IEEE
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IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 15, NO. 3, SEPTEMBER 2005
dard lithographic techniques, niobium circuit elements 100 m
wide and 2.1 mm long were patterned on the niobium-gold. The
gold was wet etched using iodine and potassium iodide.3 The
niobium was then patterned using a sulfur hexafluoride reactive
ion etch. The gold is only needed on the contact pads since, as
stated earlier, it is used to make electrical contact to the niobium. Thus, to prevent any thermal interference with the heater,
the gold was removed from the niobium circuit. The room temperature resistance of the niobium circuit was typically 14.3
(resistivity of 2.7 10
m). A dielectric layer comprising
100 nm of silicon nitride was then deposited by plasma enhanced chemical vapor deposition (PECVD) from silane and
ammonia at 280 C.4 This layer prevents the niobium from electrically shorting the heater.
Thin-film heaters with a fast response time at low temperature have been in use for some time [7]. Based on this previous
work, we first tried copper alloy heaters.5 A copper alloy film
100 nm thick was evaporated onto the silicon nitride. After a
few thermal cycles, the copper alloy heaters failed (open circuit) apparently due to poor adhesion. The failure always occurred near a step, i.e., a transition from nitride\wafer to nitride\niobium\wafer. Rather than try to improve the film coverage over the step, we changed heater material. Titanium is
an obvious choice since it has better adhesion properties and
greater mechanical strength (it is also nonmagnetic which is
important for our application). A titanium film 100 nm thick
was evaporated onto the wafer. This thickness was a compromise between 1) a thicker film with good step coverage and a
reduction in the relative contribution of the titanium oxide and
2) a thinner film with lower thermal conductance, lower heat
capacity, and higher electrical resistance. A larger heater resistance makes the heater easier to operate because it requires
smaller currents. Electrical contact to the titanium was made
easier by depositing a gold layer 50 nm thick on the titanium before breaking vacuum. Using a positive photoresist and standard
lithographic techniques, heater elements were patterned on the
titanium-gold. We chose a very simple geometry for the heater,
a single strip of titanium (Fig. 1). Heaters of varying widths (4
to 20 m) and lengths (113 to 170 m) were patterned on the
same wafer. The titanium was wet etched using a solution (by
volume) of one part hydrofluoric acid (48% assay), 20 parts nitric acid (71% assay), 54 parts glacial acetic acid, and 25 parts
lactic acid (85% assay). This recipe wet etched the titanium with
little undercut. The final step in the manufacture of the heater
was to remove the gold from the active area of the heater to
prevent shunting of the heater current. The resistivity of the tim at room temperature, reducing to
tanium was 3.1 10
2.4 10
m at 4.2 K.
The wafer was diced so that each of the 21 heat switch test
circuits was on a separate borosilicate substrate (0.9 mm thick,
13 13 mm ). Prior to connecting electrical leads to the test circuit, the silicon nitride needed to be removed from the niobium
contact pads. This was done by first protecting the niobium circuit element and heater with photoresist and then etching the sil3We
used a gold etch from Transene Co., Danvers, MA.
4The PECVD process was done in a Pacific Western Systems Coyote Reactor,
Mountain View, CA.
5We used manganin (84 Cu 12 Mn 4 Ni) and constantan (60 Cu 40 Ni).
Fig. 2. Time response of the voltage across the niobium for a heat switch with
a 4-m-wide titanium heater. The heat pulse was of amplitude 10
W and
1.6 10
s duration. The niobium bias current was 3 10
A. Thus, the
effective niobium resistance is 0.13 in the normal state.
2
2
icon nitride in a reactive ion etch using a tetrafluoromethane and
oxygen chemistry. Once the silicon nitride has been removed,
superconducting wire bonds can be made to the niobium [6].
A number of different solders can be used for normal electrical
connections.6
III. EXPERIMENTAL METHOD AND RESULTS
We attached the borosilicate substrate (0.9 mm thick,
13 13 mm ) of a single test circuit to an oxygen-free high
conductivity copper stage of a low-temperature probe. The
probe was inserted into a dewar of liquid helium with the heat
switch in vacuum. The copper stage, in good thermal contact
with the liquid, cooled the heat switch to 4.2 K. A thermometer
and heater on the copper stage were used to monitor and
control temperature. A voltage pulse was applied to the heater
using a 16 bit digital-to-analog (D/A) converter controlled
by computer software. The resistance of the niobium was
obtained by measuring the dc voltage across the niobium
at a constant dc bias current (four wire measurement). The
voltage was amplified by 10 before recording. In Fig. 2, the
voltage across the niobium is shown for a bias current of
A and an applied heat flux of 2.2 10 W m .
3 10
We could time measurements to 10 s by hardware triggering
the analog-to-digital (A/D) converter with the rising edge
of the clock used by the D/A converter. A data sample was
by software triggering the D/A converter.
initiated at
The time resolution in Fig. 2 was limited to 20 s since the
6An indium alloy solder was used since a lead-tin alloy was more likely to
cause the gold to detach from the niobium after a thermal cycle. The indium
alloy (50 In 50 Sn) was purchased from the Indium Corporation of America,
Utica, NY, and used with a rosin mildly activated flux.
BALCHANDANI et al.: THIN-FILM PERSISTENT CURRENT SWITCH
Fig. 3. Niobium resistance as a function of heater power for a heat switch
with a 4-m-wide titanium heater. The resistance was calculated by dividing
the voltage response by the bias current. Results are shown for several different
bias currents.
A/D converter was multiplexed to make two measurements:
1) the voltage across the niobium and 2) the heater voltage.
For a single measurement, depending on the signal-to-noise
ratio, we averaged ten to 100 samples. The data shown in
Fig. 2 is the result of averaging ten samples.
To compare the voltage response for different niobium bias
currents, we defined the effective resistance as the voltage response divided by the applied bias current. The effective niobium resistance as a function of total power is plotted in Fig. 3
for a heat switch with a 4- m-wide titanium heater. The total
power is the combined heat generated by the titanium heater and
the self-heating of the niobium due to the bias current. The niobium self-heating was found by multiplying the bias current and
the voltage response. For the largest bias current (10 A), the
niobium self-heating contributes 10–20% of the heater power.
As shown in Fig. 3, the resistance stays approximately the same
for different bias currents at a particular power. Thus, the bias
current has a small effect on the resistance of the niobium when
self-heating is taken into account. This implies that the effective
niobium resistance is more likely due to a local increase in temperature rather than a propagating normal state. Thus, thermal
runaway is not a problem for bias currents up to 10 A and
a total power of 2 10 W. The minimum power needed to
switch to the normal state for a heat switch with a 4- m-wide
titanium heater is 4.5 10 W. This is equal to a heat flux of
10 W-m .
The highest rate at which we could acquire data by computer was 100 kHz. To study faster response times, we used
a 250 MHz pulse generator in conjunction with a 100 MHz
analog oscilloscope. We define the heating response time to be
the amount of time the niobium voltage signal lags the heater
signal, i.e., the time for the substrate to go from 4.2 K to the niobium critical temperature . This does not include the time (settling time) necessary to reach a steady-state equilibrium temper-
3823
Fig. 4. Heat switch response time as a function of heater power for a heat
switch with a 4-m-wide titanium heater. The response time is shown for
heating () and cooling ( ). The dotted line is the calculated response time as
described in the text.
. The heating settling time as measured by the niobium
ature
voltage signal is very difficult to model since we have no reliable way to relate the effective resistance to the temperature.
to and
The cooling response time can be measured from
not to 4.2 K, since we lose the voltage signal at . The cooling
response is not as useful as the heating response because of the
. As shown in Fig. 4, the response time for
uncertainty in
heating (cooling) decreased (increased) with increasing heater
power.
IV. THERMAL MODEL
We developed a thermal model based on the fact that the
niobium becomes resistive when the temperature of the niobium rises above its critical temperature. The minimum power
to switch to the normal state is that needed to raise the niobium film to its critical temperature. The temperature of the
niobium near the heater is always higher than at the surface
of the substrate. Thus, the temperature at the surface of the
substrate determines when the niobium switches to the normal
state. The critical switching power will be given by the minimum power needed to cause the surface temperature of the
borosilicate substrate to rise above the critical temperature of
niobium.
We make three additional assumptions to simplify the calculation. The first is that the substrate is a semi-infinite slab.
This is valid as long as the total heat applied to the substrate
is small (so that the temperature rise of the substrate is negligible). Given that the time to reach steady-state equilibrium
is relatively short, this requirement can be easily achieved by
experiment (since the total heat applied is proportional to the
pulse width). The second assumption is that the thermal conductivity and the heat capacity of the borosilicate substrate is
temperature independent over the range of interest. The thermal
conductivity k of borosilicate glass is 0.10 and 0.13 W m
K at 4 and 10 K, respectively [8]. We use
W m
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IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 15, NO. 3, SEPTEMBER 2005
Fig. 5. Calculated temperature contour T (x; y ) near the surface of the borosilicate substrate for a heat switch with a 4-m-wide 113-m-long titanium heater.
The maximum temperature is 9.5 K. Each contour line corresponds to a change in temperature of 0.1 K.
K in all our calculations. This assumption does not hold so
well for the heat capacity, which varies as the cube of the temperature. The large uncertainty introduced by the heat capacity
applies only to the time-dependent solution and does not affect the steady-state solution. The third assumption is that the
heat conducted parallel to the surface of the borosilicate substrate by the heater, silicon nitride, or niobium is negligible.
This approximation is valid for the heater and silicon nitride
considering the thickness and thermal conductivity of these
materials. We have estimated that as much as 10 W may be
conducted by the niobium circuit.7
The three-dimensional (3-D) thermal boundary value
problem is to find the temperature distribution near the surface
of a semi-infinite slab for which the surface boundary condition
is defined by a heat flux (derivative of the temperature).
If the
plane defines the surface of the semi-infinite slab,
, the
then for a heater of size
boundary condition at
is
otherwise
(1)
is
where is the thermal conductivity of the slab,
is a uniform heat flux.
is equal to the
temperature, and
heater power divided by the area of the heater. The initial condition for the slab is that at
, the slab is at a uniform temperature . The heat equation is [9]
(2)
where is density and
is specific heat at constant pressure.
For constant , the above equation becomes
7The thermal conductivity of the niobium thin film was estimated using the
measured resistivity and the Wiedemann–Franz relation. This was a worst case
estimate to check the maximum effect of the niobium.
(3)
BALCHANDANI et al.: THIN-FILM PERSISTENT CURRENT SWITCH
3825
where is the thermal diffusivity. The partial derivative in time
can be converted to a total derivative in time by a Fourier transform. The resulting ordinary differential equation can be solved
for the above boundary conditions by separation of variables.
The temperature is8
(4)
For steady-state conditions, i.e.,
, this reduces to
(5)
According to (5), for a fixed heat switch geometry, the power
depends linearly on , i.e., an increase in requires an equivalent increase in . This means that for a silicon substrate, with
to
W m
K between 4 and 10 K [10], the
heat switch would operate at a power which is approximately
1000 to 6000 times larger than borosilicate glass. It has been
estimated [4] that for a sputtered 400-nm-thick niobium thin
film on silicon, the heat switch requires a power of 0.3 W. This
being linearly dependent on . Thus
qualitatively supports
borosilicate substrate, with its low value of , is an appropriate
choice for our low power heat switch. For a heat switch with a
m and
heater 4 m wide and 113 m long, we set
m. The result for
is drawn as a contour plot
in Fig. 5. The highest contour (white) corresponds to a temperature of 9.5 K. The temperature changes by 0.1 K from line
to line. This plot shows that the heater produces a very local
rise in temperature. This means that for a good heat switch design, the heater should extend somewhat beyond the width of
the superconductor.
for tiIn Fig. 6, we plot the critical temperature profile
tanium heaters of three different sizes. The critical temperature
profile was calculated by setting the heat flux for each heater
size equal to the measured critical power for that heater. The following heaters were used:
4 m wide, 113 m long;
10
m wide, 120 m long; and
10 m wide, 170 m long. The
measured critical power for each heater geometry was:
10 W;
10 W; and
8.2 10 W. This corresponds to a heat flux of 10 5 10 , and 4.8 10 W m ,
is along the 100 m width of the niobium
respectively.
circuit, parallel to the length of the heater. As described earlier,
we made test circuits with different heaters on the same wafer.
Thus, the thermal conductivity and the critical properties of the
8The same solution was found by the Green’s function method. The following
Green’s function G was derived:
G=
1
(t 0 t ))
(4
e
2 e
+
e
:
Fig. 6. Calculated temperature profile T (x) at critical power near the surface
of the borosilicate substrate. The temperature is along the 100 m width of the
niobium circuit. Results are shown for the following three titanium heaters: ( )
4 m wide, 113 m long; ( ) 10 m wide, 120 m long; and ( ) 10 m wide,
170 m long.
}
niobium circuits are probably very similar for each heater test
circuit. Therefore, the temperature profiles at the critical power
(i.e., near the critical temperature) for the test circuits should be
of similar magnitude. It can be seen that the absolute magnitude
is close to the critical temperature expected for nioof
bium even though the heat conducted by the niobium has been
ignored. The effect of the niobium is to decrease and broaden
. We estimate a decrease in
of 20–30%.
The time-dependent solution for temperature is
(6)
where Erf
is the error function and is the thermal diffusivity. As stated earlier, the strong temperature dependence of
the heat capacity, leading to a temperature-dependent , has
been ignored. The specific heat of borosilicate glass is 0.17
kg at 4 and 10 K [11]. We set
and 4.20 J K
m s in all our calculations. The time-dependent temperature is shown in Fig. 7 for the following three titanium
heaters:
4 m wide, 113 m long;
10 m wide, 120 m
10 m wide, 170 m long. The temperature is callong; and
culated near the origin and at critical power. As shown in Fig. 7,
the temperature rises faster as the heater becomes smaller. We
defined the heating response time as the time for the substrate
to go from 4.2 K to the niobium critical temperature . To see
how response time varies with heater power, we have calculated
the temperature rise for the 4- m-wide heater at the following
heater powers: 1) 5.5 10 W, dotted line; 2) 6.1 10 W,
dashed line; and 3) 8.8 10 W, dot-dash line. As shown in
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IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 15, NO. 3, SEPTEMBER 2005
ondary is connected to the input coil of a dc SQUID. This will
allow us to study the effect of the thin-film heat switch on the
flux trapped in .
ACKNOWLEDGMENT
The authors would like to thank D. Gill and T. Carver for
depositing the metal films.
REFERENCES
Fig. 7. Calculated temperature as a function of time for the following three
titanium heaters: () 4 m wide, 113 m long; ( ) 10 m wide, 120 m
long; and ( ) 10 m wide, 170 m long. The temperature is calculated near
the origin and at critical power. The temperature is also calculated for the
W, dotted
4-m-wide heater at the following heater powers: 1) 5.5 10
line; 2) 6.1 10 W, dashed line; and 3) 8.8 10 W, dot-dash line.
}
2
2
2
Fig. 7, for a given critical temperature , an increase in shifts
the temperature upwards, producing a shorter response time.
The response time at minimum or critical power tends to infinity and is poorly defined. This rapid increase in the response
time is a useful indicator when measuring the critical power. The
calculated response time, as shown in Fig. 4 as a dotted line, is
in qualitative agreement with experiment [
heating response
time]. The cooling response time was not calculated since the
initial temperature is poorly defined (by theory and experiment).
The increase in cooling response time with increasing power is
due to the increase in the initial temperature.
V. CONCLUSION
We have shown that a thin-film heat switch can easily achieve
a level of performance that would be very challenging for a wire
heat switch [5]. The heat switch using the smallest heater (4 m
wide, 113 m long) performed the best, with a response time of
6 10 s at a power of 5 10 W. The response time can be
reduced to 10 s with a 50% increase in heater power. Devices
with similar response times but higher input power have been
fabricated [12]. In general, it is always of some benefit to decrease the power consumption of a device while making it faster.
For a device that operates in a low-temperature environment, the
benefit is obvious since the total allowed dissipated power can
be small [1]. The second practical consequence has to do with
time. A shorter response time means that the switch can be activated more often in the allotted time. This means that a greater
number of adjustments to a persistent current can be made, and
there may be additional benefits to the specific application by
having a short switching time. We plan to add our thin-film heat
switch to circuits similar to the circuit shown in Fig. 1(a). In one
circuit, is the primary of a thin-film flux transformer. The sec-
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Priti Balchandani was born in Bhopal, India,
in September, 1979. She received the bachelor of
applied science degree in computer engineering from
the University of Waterloo, Waterloo, ON, Canada,
and the master’s of science degree in electrical
engineering from Stanford University, Stanford, CA,
where she is currently pursuing the Ph.D. degree in
electrical engineering.
Her employment experience includes internships
with Cisco Systems, San Jose, CA; Fujitsu Network
Communications, Richardson, TX; Canadian Space
Agency, Ottawa, ON; and Nortel Networks, Brampton, ON. She is currently
with the Gravity Probe-B and STEP research groups at Stanford University, Palo
Alto, CA.
Ms. Balchandani received the National Science and Engineering Research
Council Award to conduct research with the Canadian Space Agency on spacequalification of semiconductor devices.
Rodney H. Torii, photograph and biography not available at the time of publication.
Roger Shile, photograph and biography not available at the time of publication.