Phonon disruptors for increased thermal resistance without sacrificing electrical signal quality in thermal sensors using alloy and intermetallic materials
Sensor interconnects and supports and methods of making them utilize phonon disruptors for increased thermal resistance while maintaining acceptable electrical signal quality in materials. Phonon disruptors include the use of an electrically conductive alloy material or intermetallic material of at least two or more elements to promote scattering of phonons. These materials are selected to scatter heat carriers while allowing electrons to pass through the material.
1. A thermal sensor device comprising:
a substrate;
read-out circuitry;
a thermal sensor element; and
at least one conductive leg that constitutes a conductive path of enhanced thermal resistance extending between the thermal sensor element and the read-out circuitry configured for conducting an electrical signal between the thermal sensor element and the read-out circuitry, the at least one conductive leg having a thermal resistance and comprising an electrically conductive alloy material or intermetallic material of at least two or more elements having an electrical conductivity (o) no less than about 1.9×10 5 S/m and a thermal conductivity (k) no more than about 22 Wm −1 K −1 .
2. The device of claim 1 , wherein the alloy material or the intermetallic material is a binary alloy composed of only two elements.
3. The device of claim 1 , wherein the alloy material or the intermetallic material is a ternary, quaternary or higher alloy composed of three, four or more elements, wherein the additional element or elements beyond two increase scattering and transport disruption of the phonons through the at least one conductive leg compared to a binary material composed of only two elements.
4. The device of claim 1 , wherein the at least one conductive leg is provided as a homogenous film or a trace.
5. The device of claim 1 , wherein the material is an intermetallic having a B1, B2, B3, B4, B10, B17, B19 or B20 crystal packing structure.
6. The device of claim 1 , wherein the alloy material or the intermetallic material are formed of only metal atoms.
7. The device of claim 1 , wherein the alloy material is clad with a cladding material.
8. The device of claim 1 , wherein the thermal resistance and electrical conductivity of the electrically conductive alloy material or the intermetallic material are determined using the Klemens analytical model and the Nordheim rule, respectively.
9. The device of claim 1 , wherein the phonon mean free path is greater than the electron mean free path through the conductive path of enhanced thermal resistance.
10. A method for forming the thermal sensor device of claim 1 , the method comprising:
selecting an electrically conductive alloy material or intermetallic material of at least two or more elements to promote scattering of phonons; and
forming, as part of the at least one conductive leg extending between the thermal sensor element and the read-out circuitry, the phonon transport disrupting structure from the selected electrically conductive alloy material or intermetallic material for conducting an electrical signal between the thermal sensor element and the read-out circuitry.
11. The device of claim 2 , wherein the material comprises: Ni X Ti 1-X 0.45<x<0.55 , Co X Ga 1-X X≈0.5 , or Al X Fe 1-X X≈0.5 , if an intermetallic, or a-NiTi, CuNi, or TiN, if an alloy.
12. The device of claim 3 , wherein the material comprises: NiTiHf, NiTiCoHf, or hcp-GeSbTe, if an intermetallic, or Fe 0.55 Ni 0.2 Cr 0.25 , Zr 0.55 Al 0.1 Ni 0.05 Cu 0.3 , Pd 0.4 Ni 0.4 P 0.2 , if a binary alloy.
13. The device of claim 8 , wherein the thermal resistance of the electrically conductive alloy material or the intermetallic material is determined according to the following equation:
k
L
k
0
=
tan
-
1
u
u
,
where
u
=
(
(
6
π
5
V
2
)
1
3
2
k
B
v
s
k
0
Γ
)
1
/
2
,
where
Γ
=
〈
Δ
M
2
_
〉
〈
M
2
_
〉
,
〈
Δ
M
2
_
〉
is the average mass variance, ( M 2 ) is the average mass squared, k 0 is the thermal conductivity of a pure material, k L is the lattice thermal conductivity of the alloy, V is the volume of a unit cell of the compound, and v s is the average speed of sound in the material.
14. The device of claim 8 , wherein the electrical conductivity of the electrically conductive alloy material or the intermetallic material is determined according to the following equation:
σ
=
1
C
X
(
1
-
X
)
,
where C is the Nordheim coefficient of one material in a solution of the other and X is the atomic fraction of the element being added to the solution.
15. The device of claim 14 , wherein for material concentrations beyond the solubility limit, two phase solutions exist, determined according to the following equation:
σ=σ A X+σ B (1− X ),
where σ A and σ B are the electrical conductivity of a first material A and second material B, respectively.
16. The device of claim 9 , wherein the thickness of the conductive path of enhanced thermal resistance is determined by a Fuchs-Sondheimer solution.
17. The device of claim 16 , wherein a thickness d film of the conductive path of enhanced thermal resistance is determined is according to the following equations:
k
film
k
bulk
=
1
-
3
ξ
p
h
o
n
o
n
(
1
-
p
)
2
∫
0
1
(
μ
-
μ
3
)
1
-
exp
(
-
ξ
p
h
o
n
o
n
μ
)
1
-
p
exp
(
-
ξ
p
h
o
n
o
n
μ
)
d
μ
,
where k film is the thermal conductivity of the thin film, k bulk is the corresponding bulk thermal conductivity, p is the fraction of energy carriers specularly reflected at the interface, μ is a variable of integration, and ξ phonon =d film /Λ phonon , where Λ phonon is the phonon mean free path; and
σ
film
σ
bulk
=
1
-
3
ξ
e
l
e
c
t
r
o
n
(
1
-
p
)
2
∫
0
1
(
μ
-
μ
3
)
1
-
exp
(
-
ξ
e
l
e
c
t
r
o
n
μ
)
1
-
p
exp
(
-
ξ
e
l
e
c
t
r
o
n
μ
)
d
μ
,
where σ film a is the electrical conductivity of the thin film, σ bulk is the corresponding bulk electrical conductivity, p is the fraction of energy carriers specularly reflected at the interface, μ is a variable of integration, and ξ electron =d film /Λ electron , where Λ electron is the electron mean free path.
18. The device of claim 17 , wherein the thickness d is selected so that Λ phonon >d film >Λ electron .
19. The device of claim 17 , wherein Λ electron is 3 nm and Λ phonon is 30 nm; and p is 0.
20. The method of claim 10 , wherein the selecting of an electrically conductive alloy material or intermetallic material includes: selecting the electrically conductive alloy material or intermetallic material to have a thermal conductivity (k) no more than about 22 Wm −1 K −1 and an electrical conductivity (σ) no less than about 1.9×10 5 S/m.
21. The method of claim 10 , wherein the forming of the phonon transport disrupting structure includes: forming a film by: physical vapor deposition; chemical vapor deposition, evaporation, epitaxial growth, pulsed laser deposition, selective laser melting/sintering, or arc melt spinning.
22. The method of claim 10 , wherein the at least one conductive leg is a conductive trace which is patterned and etched or milled.