U.S. patent application number 16/294011 was filed with the patent office on 2022-09-08 for superconductivity device comprising a phononic crystal.
The applicant listed for this patent is National Technology & Engineering Solutions of Sandia, LLC. Invention is credited to Matt Eichenfield, Ihab Fathy El-Kady, Michael David Henry, Rupert M. Lewis.
Application Number | 20220285603 16/294011 |
Document ID | / |
Family ID | 1000006549533 |
Filed Date | 2022-09-08 |
United States Patent
Application |
20220285603 |
Kind Code |
A1 |
El-Kady; Ihab Fathy ; et
al. |
September 8, 2022 |
Superconductivity device comprising a phononic crystal
Abstract
The invention is directed to a device and method to engineer the
superconducting transition width by suppressing the phonon
populations responsible for the Cooper-pair decoherence below the
superconducting transition temperature via phononic bandgap
engineering. The device uses phononic crystals to engineer a
phononic frequency gap that suppresses the decohering thermal
phonon population just below the Cooper-frequency, and thus the
normal conduction electron population. For example, such
engineering can relax the cooling requirements for a variety of
circuits yielding higher operational quality factors for
superconducting electronics and interconnects.
Inventors: |
El-Kady; Ihab Fathy;
(Albuquerque, NM) ; Lewis; Rupert M.;
(Albuquerque, NM) ; Henry; Michael David;
(Albuquerque, NM) ; Eichenfield; Matt;
(Albuquerque, NM) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
National Technology & Engineering Solutions of Sandia,
LLC |
Albuquerque |
NM |
US |
|
|
Family ID: |
1000006549533 |
Appl. No.: |
16/294011 |
Filed: |
March 6, 2019 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
62639362 |
Mar 6, 2018 |
|
|
|
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H01L 39/08 20130101;
H01L 39/12 20130101 |
International
Class: |
H01L 39/12 20060101
H01L039/12; H01L 39/08 20060101 H01L039/08 |
Goverment Interests
STATEMENT OF GOVERNMENT INTEREST
[0002] This invention was made with Government support under
Contract No. DE-NA0003525 awarded by the United States Department
of Energy/National Nuclear Security Administration. The Government
has certain rights in the invention.
Claims
1. A superconducting device, comprising: a two-dimensional phononic
crystal comprising a periodic array of holes or plugs in a
superconducting matrix material, wherein the holes or plug material
provide an acoustic impedance mismatch with the matrix material,
wherein the matrix material has a superconducting transition
temperature T.sub.c, and wherein the phononic crystal has a
phononic bandgap at a frequency that suppresses a decohering
thermal phonon population just below the Cooper-frequency of the
matrix material, thereby suppressing the normal conduction electron
population near T.sub.c and narrowing the width of the
superconducting transition.
2. The superconducting device of claim 1, wherein the
superconducting transition temperature of the plug material is less
than T.sub.c.
3. The superconducting device of claim 1, wherein the plug material
comprises a metal.
4. The superconducting device of claim 3, wherein the plug material
comprises tungsten.
5. The superconducting device of claim 1, wherein the matrix
material comprises a metal.
6. The superconducting device of claim 1, wherein the matrix
material comprises aluminum, tantalum, iridium, tin, lead, niobium,
titanium, palladium, indium, vanadium, or alloys thereof.
7. The superconducting device of claim 1, wherein the matrix
material comprises a compound.
8. The superconducting device of claim 1, wherein the unit cell
size of the phononic crystal is less than the acoustic wavelength
of the Cooper-frequency of the matrix material.
9. The superconducting device of claim 1, wherein the unit cell
size of the periodic array is less than 300 nm.
10. The superconducting device of claim 1, wherein the periodic
array comprises a square or hexagonal lattice.
Description
CROSS-REFERENCE TO RELATED APPLICATION
[0001] This application claims the benefit of U.S. Provisional
Application No. 62/639,362, filed Mar. 6, 2018, which is
incorporated herein by reference.
FIELD OF THE INVENTION
[0003] The present invention relates to superconductivity and, in
particular, to a superconducting device and a method to engineer
superconductivity using a phononic crystal.
BACKGROUND OF THE INVENTION
[0004] According to BCS theory, superconductivity arises from the
creation of Cooper-pairs, a coherent interaction of two
opposite-spin electrons coupled by a lattice phonon. As the
temperature rises, approaching the transition temperature
(T.sub.c), interactions with thermal phonons result in Cooper-pair
decoherence and loss of superconductivity. Thus, there exists two
electron populations in a superconductor: superconducting
Cooper-pairs and unpaired, normal-conducting electrons. In the
neighborhood of T.sub.c, resistive losses start increasing due to
the increase in the thermal phonon noise and the subsequent
disruption of the Cooper-pairs. As such, almost all superconducting
applications require cooling well below T.sub.c to ensure a
lossless system, which increases the required overhead in terms of
cost and time. The ability to narrow the transition width
.DELTA.T.sub.c, as shown in FIG. 1A, would result in relaxing the
cooling requirements, thereby enabling higher quality factors for
superconducting resonators, transmission lines, and detectors, and
potentially enhancing the sensitivity and reducing the dead-time of
transition-edge single photon detectors.
[0005] As shown in FIG. 1B, in the two-fluid model of
superconductivity by Casimir and Gorter, the ratio of
superconducting electrons to normal conducting electrons is given
by:
n S N = 1 - ( T T C ) .gamma. , ##EQU00001##
where n.sub.s is the number of superconducting electrons, n.sub.e
is the number of normal conducting electrons, N=n.sub.s+n.sub.e is
the total number of electrons, and .gamma..about.4, based on
experiment. This equation suggests that the order parameter .gamma.
can be engineered by controlling the phonon population. Further,
the population of "Cooper-pairs" can be changed by manipulating the
"Cooper phonons" that couple the electron pairs.
SUMMARY OF THE INVENTION
[0006] According to the present invention, the superconducting
transition width can be engineered by suppressing the phonon
populations responsible for the Cooper-pair decoherence below the
superconducting transition temperature (T.sub.c) via phononic
bandgap engineering. The invention is directed to a superconducting
device comprising a two-dimensional phononic crystal (PnC)
comprising a periodic array of holes or plugs in a superconducting
matrix material, wherein the holes or plug material provide an
acoustic impedance mismatch with the matrix material, wherein the
matrix material has a superconducting transition temperature
T.sub.c, and wherein the phononic crystal has a phononic bandgap at
a frequency that suppresses a decohering thermal phonon population
just below the Cooper-frequency of the matrix material, thereby
suppressing the normal conduction electron population near T.sub.c
and narrowing the width of the superconducting transition.
BRIEF DESCRIPTION OF THE DRAWINGS
[0007] The detailed description will refer to the following
drawings, wherein like elements are referred to by like
numbers.
[0008] FIG. 1A is a graph of resistivity .rho. verses temperature
T. The short-dashed line indicates the resistivity of a normal
conductor, the solid line indicates the resistivity of an ideal
superconductor, and the long-dashed fine indicates the resistivity
of an actual conductor. Near T.sub.c, an actual superconductor
transitions from no resistivity to normal resistivity over a
transition width, .DELTA.T.sub.c. FIG. 1B is a graph of the
fraction of superconducting electrons n.sub.s/N versus temperature
T for a number of .gamma..
[0009] FIGS. 2A and 2B are graphs of the band structure of two
phononic crystal designs comprising air holes in an aluminum slab
or plate. The two designs have identical hole sizes and number but
arranged in different lattices. PnC-1 has a square lattice. PnC-2
has a hexagonal lattice.
[0010] FIGS. 3A-H are graphs of band structure calculations for the
two different PnCs comprising air holes in a tantalum matrix. FIGS.
3A-D show band structure calculations for a square lattice with
slab thicknesses from 50 to 100 nm. FIGS. 3E-H show band structure
calculations for a hexagonal lattice with slab thicknesses from 50
to 100 nm.
[0011] FIGS. 4A and 4B are graphs of the calculated band
structures, along with the corresponding density of phonon states,
for a PnC with a hexagonal lattice.
[0012] FIGS. 4C and 4D are graphs of the calculated band
structures, along with the corresponding density of phonon states,
for a PnC with a square lattice.
[0013] FIGS. 5A and 5B are scanning electron micrographs of e-beam
write fabrications of a square lattice of silicon pillars at low
and high magnification. The fabrications comprise 42 nm diameter,
140 nm tall silicon pillars on a period of 75 nm and a unit cell of
150 nm.
DETAILED DESCRIPTION OF THE INVENTION
[0014] According to the present invention, the distribution of
superconducting Cooper-pairs and unpaired normal-conducting
electrons can be modified by selectively engineering which phonons
can propagate in the superconductor. Changing the thermal
background seen by the electrons can result in fewer quasi-particle
excitations (i.e., normal electrons). Fundamentally, this phonon
engineering route requires suppression of the phonon heat capacity
of the superconductor near T.sub.c. In particular, a phononic
crystal (PnC) can be used to engineer a phononic frequency gap that
suppresses the decohering thermal phonon population just below the
Cooper-frequency (f.sub.c), and thus the normal conduction electron
population. PnCs comprise periodic arrangements of phonon
scattering centers embedded in a homogeneous background matrix with
lattice spacing comparable to the acoustic wavelength. The
scattering material has a density and/or elastic constant that is
different than the matrix material. When properly designed, a
superposition of Bragg and Mie resonant scattering results in the
opening of a frequency gap over which there can be no propagation
of elastic waves in the crystal, regardless of direction. This
property makes PnCs particularly attractive for their ability to
manipulate and control phonon propagation.
[0015] The Cooper-frequency is related to the energy needed to
break a Cooper-pair. Specifically, the Cooper-frequency is related
to the energy gap of the superconductor by
f.sub.c*h=.DELTA.
where f.sub.c is the frequency of phonons, h is the Planck
constant, and .DELTA. is the superconducting energy gap of the
matrix material. For example, the superconducting transition
temperature for aluminum is T.sub.c.about.1.25 K. The energy gap is
about 190 .mu.V at temperatures well below the transition
temperature, giving a Cooper-frequency of about 46 GHz. The PnC can
be designed to have a phononic bandgap at the Cooper-frequency of
the matrix material, thereby suppressing the normal conduction
electron population near the transition temperature and narrowing
the width of the superconducting transition.
[0016] The present invention phononically engineers the
superconducting state. By doing so, a sharp superconducting
transition at T.sub.c can be achieved. By reducing or eliminating
the transition tail, it can be possible to operate closer to
T.sub.c, hence relaxing the cooling requirements. Further, by
suppressing the phonon heat capacity, it may be possible to achieve
higher intrinsic quality factors (Q) for superconducting devices
and single phonon sensitivity. To achieve these objectives requires
tight fabrication tolerances, low temperature facilities for
cooling and measurement, and the ability to deposit and
micromachine high-quality superconducting films.
[0017] If the superconducting matrix material is dense and has a
high velocity of sound, gas or vacuum provide a good acoustic
impedance mismatch to the matrix material (e.g., vacuum has no
density or sound velocity). As an example of the invention, the
two-dimensional PnC can comprise air-holes in a metallic matrix. To
demonstrate the ability of the present invention to control the
superconducting transition via phononic engineering, two phononic
crystals (PnC-1 and PnC-2) are compared conceptually using
identical hole sizes and filling fraction, differing only in the
geometric arrangement of the holes. Therefore, PnC-1 can be
designed to have a phononic bandgap that encompasses the
Cooper-frequency; while PnC-2 can be designed to not have a
phononic bandgap at all. Since the two PnCs are identical in
everything but their geometry and can be fabricated using the same
process and on the same material slab, then the loss of the
superconductivity in one PnC but not the other PnC can only be
attributed to phonon engineering.
[0018] FIGS. 2A and 2B are schematic illustrations of two exemplary
PnCs comprising two-dimensional periodic arrays of circular air
holes in an aluminum slab or plate, along with their calculated
band structures. The band structures are calculated accounting for
the thickness of the PnC slab, and hence the gap is not perturbed
by any surface states. PnC-1, shown in FIG. 2A, has a square
lattice structure. This PnC has a phononic bandgap centered as the
Cooper-frequency (shown as We). PnC-2, shown in FIG. 2B, has a
hexagonal lattice structure. This PnC does not have a phononic
bandgap. In this example, the superconducting transition is
suppressed only in PnC-1 while it persists in PnC-2
[0019] A variety of low-temperature superconducting materials can
be used as the matrix material. For example, superconducting metals
(i.e., Type I or "BCS" superconductors) can be used as the matrix
material, including aluminum (Al), tantalum (Ta), iridium (Ir),
niobium (Nb), titanium (Ti), palladium (Pd), indium (In), tin (Sn),
lead (Pb), vanadium (V), and alloys thereof. Other superconducting
materials (i.e., Type II superconductors) can also be used, such as
niobium compounds (e.g., NbN, NbTi, or NbTiN), vanadium compounds
(e.g., V.sub.3Si), and germanium compounds. For very
low-temperature superconducting materials, the cell size can be up
to about 300 nm (since the Cooper-pair wavelength and, therefore,
the PnC cell size is inversely proportional to T.sub.c). The
thickness of the two-dimensional PnC slab, or plate, can be
comparable or less than the cell size. The PnC slab can be
supported by a thin membrane or substrate that is insulating and
has a good acoustic impedance mismatch with the matrix
material.
[0020] FIGS. 3A-D and 3E-H show the computational outcomes for
tantalum as a matrix metal, for both square and hexagonal lattices,
respectively. As can be seen, gaps can be designed for one PnC and
gaps can be avoided in the other PnC, both having the same unit
cell size (140 nm) and slab thickness t (e.g., compare PnCs with
t=60 nm in FIGS. 3B and 3F). Furthermore, the gaps can be tuned and
moved away from the Cooper-frequency in one PnC and centered at the
correct frequency in the other (e.g., compare PnCs with t=100 nm in
FIGS. 3D and 3H). The two PnCs can be fabricated using E-beam
writes followed by etch chemistry. The tether size (neck between
the air holes) is about 22 nm for these PnCs. This small tether can
make fabrication difficult. The process can be modified to relax
the dimensions of the PnC lattice to more readily fabricable
sizes.
[0021] As another example of the invention, the PnCs can comprise
solid plugs in a superconducting matrix. If the matrix material is
light and/or has a low sound velocity, the plugs need to be dense
and have a high sound velocity. Specifically, the plug material
needs to have a high enough acoustic impedance mismatch with
respect to the superconducting matrix material so that phonons in
the matrix material are reflecting strongly by the solid plugs to
allow for a phononic bandgap to be opened. Therefore, the plug
material can be a metal or a non-metal having a good acoustic
mismatch with the matrix material. Further, it is preferable to use
a matrix material with low T.sub.c, to allow for PnC features to be
larger in size, but still avoid the need for dilution
refrigeration. The plug material also should be normal conducting
at the T.sub.c of the matrix material.
[0022] For this example, the PnC can be fabricated out of tungsten
(W) plugs in an aluminum (Al) matrix. Tungsten is dense and has a
high sound velocity and, therefore, provides a strong acoustic
impedance mismatch with the lighter Al matrix. The transition
temperature for Al is T.sub.c.about.1.25 K. Tungsten has a T.sub.c
of 1.5 mK, thus W will not be superconducting when the Al
transition temperature is realized. This avoids the problem of
carrier hopping between superconducting plugs. FIG. 4A shows the
calculated band structure of a hexagonal lattice PnC, and FIG. 3B
shows the corresponding density of phonon states. This PnC has a
bandgap. FIGS. 4C and 4D show the calculated band structure and
corresponding density of phonon states for a square lattice PnC.
This PnC does not display a phononic bandgap. As can be seen the
tether size of this PnC is a more manageable dimension of 33
nm.
[0023] The fabrication process for these PnCs can comprise the
following steps: [0024] 1. E-beam write photoresist on a silicon
substrate [0025] 2. Use resist as etch mask [0026] 3. Etch away,
leaving Si pillars [0027] 4. Sputter/vapor deposit Al film on the
Si pillars [0028] 5. Etch away Si leaving holes in the Al film
[0029] 6. Back-fill the holes with tungsten FIGS. 5A and 5B show
the result of an E-beam write and etching to form Si pillars (step
3), prior to Al deposition, Si etching, and W backfill (steps
4-6).
[0030] The invention can greatly improve superconducting
electronics for high performance computing at the heart of current
encryption and secure communications. The invention may enable more
tunable parameters for detection and sensing technology and the
reliable detection at the single quanta. The invention may also
enable quantum computing which holds the future of secure
communication. The reduction of the superconducting transition
width may enable higher quality factor (Q) superconducting
circuits, transmission lines, and resonators. The invention can
greatly relax the cooling requirements necessary for
superconducting operations.
[0031] For example, the invention can provide a highly sensitive
transition edge single photon detector (SPD) in a PnC. A PnC film
can be placed on top of an optical wave guide. The PnC bandgap can
be designed to encompass f.sub.c. A serpentine line defect can then
be created in the PnC such that it meanders over the waveguide.
Thus, a superconducting state will exist only in the serpentine. By
operating at the critical current density (J.sub.c) of the
serpentine, the absorption of a single photon can then be detected
as a calorimetric change in the serpentine resistance. While the
geometry and principal of operation is similar to the
state-of-the-art superconducting nanowire SPD, the ability to
dispose of the generated normal electron pairs through the PnC
normal conducting region rather than forcing them to propagate
through a lengthy serpentine reduces detector dead-time while
maintaining photon number resolution and detection efficiency.
[0032] The present invention has been described as a
superconducting device and method to engineer superconductivity
using phononic crystals. It will be understood that the above
description is merely illustrative of the applications of the
principles of the present invention, the scope of which is to be
determined by the claims viewed in light of the specification.
Other variants and modifications of the invention will be apparent
to those of skill in the art.
* * * * *