WO2008068386A1

WO2008068386A1 - An elongated nanofiber with an improved prevention of thermal conductance and method to prevent thermal conductance in the nanofiber

Info

Publication number: WO2008068386A1
Application number: PCT/FI2007/050665
Authority: WO
Inventors: Lev M. Baskin; Pekka Neittaanmäki; Boris A. Plamenevsky; Alexey A. Pozharsky
Original assignee: Jyväskylän Yliopisto
Priority date: 2006-12-05
Filing date: 2007-12-05
Publication date: 2008-06-12
Also published as: FI20065776A0

Abstract

The present invention relates to an elongated nanofiber (12) in a temperature sensitive device (10) connected to two opposite connection ends (11, 13) of the device (10), the connection ends (11, 13) having distinct temperatures (T1, T2) and where a thermal energy is carried through the nanofiber (12) by propagating non-interacting elastic waves (14 - 16). The nanofiber (12) includes deformation structures (17.1 - 17.4) arranged to prevent the propagation of at least a part of the elastic waves (14 - 16). In addition, the invention also relates to a corresponding method to prevent thermal conductance in the nanofiber.

Description

AN ELONGATED NANOFIBER WITH AN IMPROVED PREVENTION OF THERMAL CONDUCTANCE AND METHOD TO PREVENT THERMAL CONDUCTANCE IN THE NANOFIBER

The present invention concerns an elongated nanofiber in a temperature sensitive device connected to two opposite connection ends of the device, the connection ends having distinct temperatures, and where a thermal energy is carried through the nanofiber by propagating non-interacting elastic waves. In addition, the invention also concerns a corresponding method to prevent thermal conductance in the nanofiber.

From the prior art there are known various kinds of temperature sensitive applications in which the effect of the thermal conductance should be eliminated. One example is the temperature measurements performed at the low temperature. In particular, bolometers of various types are examples of such devices in which a good thermal insulation is required between the bolometric material sensing the temperature and the substrate, frame or a corresponding support to which the active part has been adjoined. When the temperature to be measured is extremely low then the prevention of the thermal conductance from the environment to the measuring unit should be particularly well to increase the sensitivity.

The prior art solution relating to diminishing the thermal conductance between the active part including bolometric material and the substrate is presented in US-patent 7,268,350 B1. This solution is based on the "constriction" phenomenon. This phenomenon shows itself only if the phonon-phonon interaction length is much less than the size of system (collision regime). In the method of decreasing thermal conductance at the collision regime is produced a point-type thermal contact or a contact having an extremely small cross-sectional area between two materials. The contact causes a constriction of the flux lines which results in a significant increase in the thermal contact resistance. In addition, the constrictions have been made to the ends of the studs or posts which support the active part with the embedded bolometric material. The thermo insulating properties of the system according to this publication can not manifest themselves at the extreme conditions in which the temperature is very low.

However, as regards the state of the art, several practical problems relate to the implementation of nanofibers to be used, for example, in temperature sensitive applications.

It is a purpose of the present invention to provide a new kind of nanofiber structure arranged to a temperature sensitive device. With the invention, the thermal conductivity of the nanofiber is an essentially diminished compared with the known prior art solutions. The characteristic features of the nanofiber according to the invention are presented in the appended claim 1 , while the characteristic features of the method are presented in claim 18.

The nanofiber according to the invention includes deformation structures arranged to prevent the propagation of at least a part of the elastic waves. In the method according to the invention at least part of the thermal flux carried by the elastic waves in the nanofiber is prevented by reflecting at least a part of the elastic waves in the opposite direction relative to their incoming direction.

The nanofiber according to the invention is designed to work at ballistic regime. In this kind of collisionless conditions the size of the nanofiber is not greater than the phonon- phonon interaction length. Ballistic regime exists only at low temperature where the thermal conductivity is a quantum phenomenon.

According to one embodiment the deformation structures are arranged to reflect at least a part of the elastic waves in the opposite direction relative to their incoming direction. According to one embodiment the deformation structures are arranged to dilate the cross-section of the nanofiber. The dilatations may have different kind of implementation as regards their forms and periodicity. According to one embodiment the periodicity of dilatations may be monotonously increasing. By this kind of arrangement, the frequency band of the waves to be prevented may be made essentially broader.

Significant advantages are achieved with the invention in comparison with the state of the art. In addition, the nanofiber will not suffer structural weakening owing to the deformation structures broadening the frequency band. The deformation structures are not in connection with the ends of the nanofiber but more on its centre area. Owing to this the nanofiber may be easily connected and/or formed i.e. fabricated when arranging that to the temperature sensitive device. Other features characterising the invention emerge from the appended claims and more possible advantages are listed in the specification.

The invention, which is not limited to the embodiments presented hereinafter, will be described in greater detail with reference to the appended figures, wherein

Figure 1 shows a scheme of a microbolometer, or more generally, one device in connection with a nanofiber according to the invention may be applied as an example of use, Figure 2 shows an example of a periodically deformed nanofiber to prevent the propagation of longitudinal waves, Figure 3 shows an example of a deformed nanofiber with monotonously increasing period structure to prevent the propagation of longitudinal waves, Figure 4 shows an example of a periodically deformed nanofiber to prevent the propagation of torsional waves,

Figure 5 shows a scheme of a nanofiber including three deformation regions with monotonously increasing dilatations, Figure 6 shows the transmission probability of longitudinal waves for a deformation structure with 150 monotonously increasing periods, Figure 7 shows the transmission probability for flexural waves in a nanofiber with periodic deformation structure containing 20 periods and Figure 8 shows the transmission probability of flexural waves in a nanofiber with deformation structure containing 150 monotonously increasing periods.

The method according to the invention is arranged to diminish essentially the thermal conductance of an elongated dielectric nanofiber 12 at low temperatures (* 1K, or more generally, for example, 0.1 - 10 K). These kinds of nanofibers 12 may have several different kinds of applications, for example, in a temperature sensitive devices 10 and applications. Such fibers can be taken as suspenders 12, for example, for microbolometers 10 designed for measuring small thermal fluxes. A very simplified example of this kind of bolometer 10 has been presented in the Figure 1. Of course, the invention may also be applied in several different kinds of applications in which a thermal conductance is to be diminished and thus the bolometer presented herein is not an exclusive example.

The sensor 11 of a microbolometer 10 with diameter, for example, about 10 mem (mcm=micrometer), more generally, for example, 2 - 20 mem, is kept by several elongated nanofibers 12 of length about 200 mem, more generally, for example, 10 - 500 mem, and of the cross-section diameter « 0.1 mem, more generally, for example, 0.05 - 0.5 mem. The sensor is an active part 11 including a bolometric material. The opposite connection end 13' of the nanofiber 12 relative to the connection end 11' next to the sensor 11 is connected to the frame 13, or corresponding support of the bolometer 10. In other words, the active part 11 and the support 13 may be connected together by suspenders 12 being now nanofibers. The connection ends 11 , 13 have distinct temperatures conditions Ti, T2 in which Ti > T2. The sensitivity of the device 10 is increasing when the thermal conductance of the suspenders 12 is diminishing. More generally, the dimensions of the nanofiber 12 according to the invention may be, for example, the length L 10 - 500 mem and the diameter of the basic cross-section, for example, 0.05 - 0.5 mem. The cross-section of the basic profile 18 of the nanofiber 12 may be, for example, non-circular (rectangular, triangular, etc.). Under the above temperature and scale conditions the thermal energy is carried through the nanofiber 12 i.e. from its one connection end 13' to the opposite connection end 11 ' by propagating, non-interacting elastic waves 14 - 16. The propagation i.e. the input direction of the elastic waves 14 - 16 is from the temperature Ti towards the temperature T₂. This means that at these temperature and scale conditions the thermal flux propagates within the ballistic regime. Under such collisionless conditions the size of the nanofiber 12 is not greater than the phonon-phonon interaction length. In other words, in the nanofiber 12 the phonon-phonon interaction cross-section is so small that the collisions between phonons have no significant effect on the system. Ballistic regime exists only at low temperature where the thermal conductance is a quantum phenomenon. It has been observed that the main contribution to the conductance is due to the elastic waves (in the form of phonons) with frequencies close to ω₀ = k_BT/fi, where k_B and fi are the Boltzmann and reduced Planck constants and T is a temperature to which the frequency is connected, too. In thin wires, like defined above, and at low temperature, such waves are classified into the three types:

1 ) longitudinal (the displacements of the waves 14 are parallel to the axis of the nanofiber 12);

2) flexural (the displacements of the waves 15 are orthogonal to the axis of the nanofiber 12);

3) torsional 16.

In order to prevent or at least considerably restrict the propagation of thermal flux in the case of waves of every type or at least some of them, small deformation structures 17.2 - 17.4 have been arranged to a nanofiber 12. The deformation structures 17.2 - 17.4 cause the reflection of the desired waves 14 - 16 or all of them and due to this reason those will prevent the propagation of the thermal flux between the ends 11 ', 13' of the nanofiber 12. The reflection of the waves 14 - 16 will take place in the opposite direction relative to their incoming direction. On the other hand, due to the reflections the waves 14 - 16 can also be fade out from the structures of the nanofiber 12. Thus, the propagation of the wave(s) 14 - 16 is prevented in such a way that the thermal effect to the temperature sensitive target 11 is diminished regardless of the thermal source. Being small, the deformations 17.2 - 17.4 do not affect the mechanical strength of the nanofiber 12.

Prevention of the propagation of the longitudinal waves

Figure 2 shows a simplified example of an elongated nanofiber 12 including periodical deformation structure 17.1 arranged to prevent the propagation of longitudinal waves 14 by reflection. As Figure 1 shows, a part of the nanofiber 12 is deformed relative to its basic cross-sectional profile 18 so that the area S(z) of the cross-section of the nanofiber 12 varies in a periodic way along the nanofiber 12, z being an axial coordinate. The deformation structure 17.1 dilates i.e. extends the cross-section area of the basic profile 18 of the nanofiber 12. In the regions before and after the deformation structure 17.1 the nanofiber 12 has a straight elongated form.

Now the deformation structure 17.1 include discrete locally dilations 19.1 which are periodically along the axial direction of the nanofiber 12. The dilations 19.1 have the same cross-sectional profile as the basic nanofiber structure 18. This may be, for example, a circle. The period L₀ of the dilations 19.1 may be arranged to be dependent on the propagation speed of the longitudinal elastic wave 14. According to one embodiment, the period L₀ may be defined by the relation L₀= V|

where V| is the propagation speed of longitudinal oscillations and h is the Planck's constant. It should be also notified that periodicity is also a function of temperature T.

Numerical results show that if min S/max S ^s 0.8 and the number of the periods N = IO, then the transmission coefficients of the waves 14 with frequencies close to ωo diminishes as much as 10 times. However, this kind of evenly periodically deformation setup 17.1 provides quite narrow reflection band.

Figure 3 shows a simplified example of a nanofiber 12 equipped with deformation structure 17.2 in which the frequency band corresponding to the intensive reflection is extended relative to the deformation structure 17.1 presented in Figure 2. Now the strictly periodic goffered deformation structure region 17.1 presented in Figure 2 has been replaced by a deformation structure 17.2 with monotonously varying "period" in which monotonously increasing period structure 17.2 increases monotonously in the propagation direction of the elastic longitudinal waves 14 and prevents the propagation of the longitudinal waves 14. This kind of "chirped" deformation structure 17.2 extends the reflection band essentially and provides thus a better blocking of thermal conductance.

To reflect elastic waves with frequencies within the interval (ω_o/5, 5ω₀), where ω_o = k_BT lti , the "period" of the chirped deformation structure 17.2 is now monotonously (for example, linearly) increasing from πv/5 ω₀ to 5πv/ω₀ . It should be notified that the propagation speed v is different for the waves 14 - 16. Typical values of the variation of period are given at Figures 6 and 8. According to preliminary calculations, for a chirp containing about 150 periods varying from L₀/5 to 5L₀, the transmission coefficient diminishes about 10 times for the waves 14 with frequencies within the interval (ωo/5, 5ωo). Generally, the number of periods of the chirp 17.2 may be, for example, 100 - 300. In its general form, the monotonously increasing period L₀ may be defined by the relation L₀(z) = L₀(O) (1 + B_oz), where the constant B₀ depends on the propagation speed of the longitudinal waves 14 and the frequency band of the longitudinal waves 14 propagation of which is arranged to be prevented. The more specific theoretical background will be described later. Owing to this the periods in the original propagation direction of the wave 14 will be L₀(zi) < L₀(Z₂) < L₀(Z₃) < L₀(Z₄) <... < L₀(Z_N).

Prevention of the propagation of the torsional waves

Figure 4 shows a simplified example of nanofiber 12 arranged to prevent the propagation of torsional waves 16 by reflection. The dilations 19.2 of the deformation structure 17.3 again locally dilate i.e. increase the width of the cross-section of the basic profile 18 of the nanofiber 12. However, it has been observed that the deformation structures 17.3 of nanofiber 12 that change the area of cross-sections without changing their cross-section forms do not affect the propagation of the torsional waves 16. Therefore to reflect such waves 16, the form of the cross-section of the nanofiber 12 is varied in a periodic way. One way to implement this is to vary the cross- section profile between circle and ellipse (for example, circle → ellipse →circle). The eccentricity of the dilations 19.2 relative to the basic cross-section profile 18 of the nanofiber 12 may be in the interval 0,05 - 0,7, for example.

Owing to this the nanofiber 12 includes discrete locally elliptic dilations 19.2 which are periodically along the axial direction of nanofiber 12. The period Li of the changes in the form of the cross-section of the basic profile 18 of nanofiber 12 may be dependent on the propagation speed of the elastic torsional wave 16. The period of deformation 17.3 may be defined by L₁ = v_t r/(2k_BT), where v_t is the propagation speed of torsional waves 16. However, this kind of strictly periodically dilation structure 17.3 provides again a quite narrow reflection band. As in the case of longitudinal waves 14, an extension of the range of reflected waves 16 can be provided by a chirp deformation structure 17.3 (Figure 5) in which the period Li of the changes in the form of the cross- section of the basic profile 18 of nanofiber 12 increases monotonously in the propagation direction of the elastic torsional wave 16. In its general form, the monotonously increasing period Li may be defined by the relation l_i(z) = l_i(0) (1 + B₁Z), where the constant B₁ depends again on the propagation speed of the torsional elastic waves 16 and the frequency band of the torsional waves 16 propagation of which is arranged to be prevented. Owing to this the period in the original propagation direction of the wave 16 will be L₁(Z₁) < L₁^) < L₁(Zs) < L₁(Z₄) <... < L₁(Z_N) in which N may be in the interval 100 - 300.

Prevention of the propagation of the flexural waves

The velocity of flexural waves 15 depends on the cross-section diameter of nanofiber 12 and can be essentially less than that of the other elastic waves 14, 16. A deformation structure 17.4 of nanofiber 12 including discrete locally dilations 19.3 (Figure 5) which are periodically along the axial direction of the nanofiber 12 can be chosen on the same principle as for the longitudinal waves 14 except for the fact that the period L₂ has to be diminished in accordance with the diminution of the wave propagation speed.

A nanofiber including a goffered part reflecting waves of all the three types

Figure 5 presents an example of nanofiber 12 including three separately located goffered deformation structure regions 17.2 - 17.4. Owing to this kind of nanofiber 12 each deformation region reflects waves belonging to one of the above types. It has been observed that the waves of each type 14 - 16 interact with only one chirped deformation structure region 17.2 - 17.4 (designed to reflect such a type of waves). Therefore the nanofiber 12 reflects the waves of all the three types 14 - 16 and in doing so essentially reduces the thermal conductance of the nanofiber 12. Of course, implementing only one goffered deformation structure region (belonging to one of the types 17.1 - 17.4), it is possible to provide reflecting one type of waves 14 - 16, i.e., in the general case, about 1/3 of the thermal flux carried by the nanofiber 12. This is also an improvement relative to the Prior Art.

The typical length LCDS of every chirped deformation structure region 17.2 - 17.4 is no greater than, for example, 90 mem at temperature T = I K. When the length L of the whole nanofiber 12 is, for example, about 400 mem, then all the deformed regions 17.2 - 17.4 may occupies no more than one half of the wire 12. It should be notified that the Figure 5 may not be realistic in this sense. More generally, the lengths LCDS of the each deformation region 17.2 - 17.4 may be, for example, 5 - 30 % and the total length of all three deformation regions 17.2 - 17.4 may be, for example, 15 - 80 % of the whole length L of the nanofiber 12. The distance a between the deformation regions 17.2 - 17.4 may be, for example, 0 - 50 mem. The distance b between the end 11 ', 13' of the nanofiber 12 and the deformation structure 17.2, 17.4 may be, for example, 0 - 20 % of the total length L of the nanofiber 12. If the regions 17.2 - 17.4 are not immediately at the ends 11 ', 13' of the nanofiber 12 the advantage is that those may be easily to be fabricated, for example. This may also affect the strength of the nanofiber 12.

The profile of the chirped deformation structure regions 17.1 - 17.4 may be selected quite freely. Generally, choosing a more (less) indent profile, it is possible to get a desired reflection band implementing a shorter (longer) chirped deformation region.

JUSTIFICATION OF THE METHOD

Physical background

A method to lower the thermal flux is suggested for a dielectric wire G connecting two ends (reservoirs) R₁ and R₂ with distinct temperatures T₁ and T₂ , respectively. The phonon free path is substantially greater than the length of the wire 12, i.e., the thermal flux carried by the wire 12 is within the ballistic regime.

The thermal phonon distribution at T₁ is given by

n_t (ω) = (exp(hω/ k_BT_t ) - 1)^"1 ,

where h = 2πtι and k_B are the Planck and Boltzmann constants. Denote by p_a{co) the transmission probability through the wire 12 for the phonon of a mode a with frequency ω in G . Then the energy flux dQ/dt in G is defined by

dQ/dt [n₂(ω) -n_ι(ω)]p_a(ω)dω , (1 )

where ω_a>mm and <y_{α max} stand for the minimal and maximal frequencies of the mode a [1] . In the case T₁ - T₂ « UImJr₁, T₂} , the thermal conductance Ω = {dQI dt)l(T₂ -T₁) can be represented in the form

W ^■\lth β = (k_BT)-^ι , T = T_λ * T₂.

If βfιω_{a min} » 1 , then the contribution of mode a to Ω is exponentially small and can be neglected. We have either ω_{a min} = 0 or ω_{a min} ~ const nv₅ ID , where D is the diameter of cross-section of the fiber G , v_s the sound speed in G , and n=1 , 2, ...

For small /J⁾ (<100nm) and low temperature T (<1K), only the modes with ω_{a min} = 0 contribute to Ω (the so-called massless modes). Moreover, at low temperature the main contribution to the thermal conductance is due to the phonons with frequency ω « k_BT Ih and wave length λ_ph ~ hv_s I k_BT . When T < 1 K and v_s > 10³ m/sec the

inequality λ_ph > 4 - 10^~8 m shows that λ_ph is at least 100 times greater than the period of lattice. Therefore the dispersion of acoustic wave speed can be neglected as well as the effect of optical phonons on the thermal conductance. This means that the wave propagation should be considered in the framework of elasticity theory.

At low temperature for a sufficiently thin wire 12 (so that the length of elastic wave 14 - 16 is greater than the diameter of cross-section) the massless modes can be classified into the following three types: a) a longitudinal wave 14 (the direction of oscillation is parallel to the axis of wire 12); b) two independent flexural waves 15 (the direction of oscillation is orthogonal to the axis of wire 12); c) a torsional wave 16. We first separately discuss for the waves of every mentioned type 14 - 16 how they can be kept from passing through the wire 12. Then it is described how to implement a wire 12 with a deformed part 17.2 - 17.4 that reflects all the waves 14 - 16 with energies within a range corresponding to a basic thermal transfer.

Reflection of longitudinal waves

Assume that the area S(z) of the cross-section of a wire is slowly varying along the axis z. The propagation of longitudinal waves is described by the equation [2]

J-±(s_(z) *L \ ₌ P &L_{t (3)}

S(z) dz { dzj E dt²

where u(z, t) is a displacement along the axis. The density p and Young modulus E are supposed to be constant. In the case S(z) = const , the wave propagation speed is

equal

According to numerical results, if S(z) periodically depends on z with

period L₀ , then the longitudinal waves with frequencies ω ∞ {πl L₀)^E I p are intensively being reflected. Devising a long wire even with a short goffered part (10-12 periods), where S(z) is slightly varying, one can get an almost complete reflection in a

narrow spectral band centered approximately at ω ∞

To widen such a band the invention suggest changing the periodically goffered part for a corrugated part 17.2with a "perturbed period" that linearly increases along the wire ("chirped" goffer). Then different parts of the chirp operate in their own spectral ranges forming together a sufficiently wide reflection band.

Figure 6 shows the transmission probability for a chirp region 17.2 with 150 "periods" providing a wide band of practically complete reflection. For a goffer 17.2 of length 95 mem the cross-section radius is defined by R(z) = R₀[l + 0.2ύn(2π z / L₀(Z))], ^Lo(^z) = °_> ^{56 •} 10^~7 + 8.82- 10 ^{3 •} z (m), 0 < z < 9,5 ^• 10 ⁵ (m)

In its general form the radius of the dilations 19.1 , 19.3 may be expressed as

R(Z) = R₀[I + W sin (2π z /L_{0 2}(z))J , where W is in the interval (0,05 ÷ 0,4). In general, the linear sizes of the basic cross-section of nanofiber 12 may be, for example 60 - 95% of those of the cross-sections of the dilatations 19.1 - 19.3 of the deformation structure 17.2 - 17.4.

Reflection of torsional waves

Such waves 16 are described by an equation of the form

V " fo-r. ' (z) * - OZ

where v_tor = ^C{z)l pl{z) is the wave propagation speed along a rod 12, C(z) being the twisting rigidity of the rod, p the density (supposed to be constant), I(z) the moment of inertia of the cross-section (with respect to its center of inertia), and φ{z,t) is the torsion angle. For a rod with circular cross-section the equality C{z) = μπR^A(z) l2 holds while R(z) is the radius of cross-section and μ the shear

modulus (which is constant). Then I(z) = πR^A 12 and the propagation speed ^v _tor = Λ//^{/ /} P ^{V of} torsional oscillations is independent of the radius of cross-section.

Therefore the variation of R(z) does not affect the reflection of torsional oscillation. For a rod 12 with elliptic cross-section, the propagation speed is defined by

where a = a{z) and b = b(z) are the semiaxes of the ellipse. Denoting the eccentricity by ε (z), it is obtained

and if ε{z) = const , then v_tor (z) =const. Thus, the corrugated part 17.3 with elliptic cross-sections such that ε{z) = const cannot be used to lower the contribution of torsional waves 16 into the thermal conductance of a wire 12.

In order for a periodically goffered part 17.3 of a wire 12 to reflect the torsional waves 16 of frequency ω , it is suggested to apply a nontrivial periodic function z — » v(z) (not

identically equal to a constant) with period L₁ ∞ (π/ω)_*Jμ/ p . To this end it is suggested to periodically vary the form of cross-section along the axis of wire 12. For instance, a periodic passage from a circle to an ellipse with ε=0.8 (i.e. b/a = 0.6 ) and back leads to the speed v such that (v_max -v_min )/v_max « 0.12 ; in the case ε = 0.85 (i.e. b/ a = 0.52 ), it is obtained 0.18 instead of 0.12.

As in the case of longitudinal oscillation, the spectral band corresponding to an intensive reflection of torsional waves 16 can be widen by a monotone dilation of the "period" of deformation 17.3 along the axis. Estimations show that the monotone

dilation of L from with number of periods ~ 150 allows to

reflect all the torsional phonons with energies within the interval 0.2k_BT < hω < 5k_BT . Reflection of flexural waves

Let a thin rod 12 is parallel to the axis z . Let's consider its flexural oscillations along the axis x . Such waves 15 are described by the equation

where u{z,t) is a displacement (along the axis x ), S the area of cross-section, and I_y the moment of inertia of the cross-section with respect to the axis y ,

/, = 1 \ x²dS .

For a thin circular cross-section, / = πR⁴ /4 so the equation (5) takes the form

Flexural waves 15 possess strong dispersion

where ω is a frequency and A: is a wave number. The group velocity

depends on the wave number. For a rod of circular cross-section,

Since for thin rods Rh = 2πR/ λ « 1 , the propagation speed of flexural waves 15 is less than that of waves of the other types 14, 16.

For the frequency ω₀ = k_BT Ih , the wave number k and the propagation speed are defined by the equalities

If the area S(z) of the cross-section at z is slowly varying along the axis z, then

Provided L-periodically varying S(z) , there arise intensive reflected waves with length λ = 2L₂. In view of (6) and (7) it is obtained

Figure 7 shows the transmission probability p(ω) for a fiber with periodic goffer containing 20 periods. As well as in the case of longitudinal waves 14, using chirped goffer, it is possible to essentially widen the reflection band. The transmission probability for a fiber with chirped goffer containing 150 "periods" in the deformation structure 17.4 is represented by Figure 8. For a goffer of length 20 mem the cross-section radius is defined by

R(z) = R₀ [1 + 0.3 sin (2^- z /Z₂ (z))], Z₂ (z) = 0,5 - 10^"7 + 3,5 - 10^"3 - z (m), 0 < z < 2 - 10^"5 (m)

Emphasize that for flexural waves 15 the period L is determined not only by a frequency ω and elastic properties of a nanofiber 12 but by the radius of cross-section as well.

Reflection of waves in the general case

Generally all three types of elastic waves 14 - 16 simultaneously contribute into a thermal flux through a nanofiber 12. Endowing the nanofiber 12 with three separate chirped deformation structure regions 17.2 - 17.4 of different types, it is possible to drastically lower its thermal conductance. An example of this kind of nanofiber 12 has been presented in Figure 5.

The periods L₀, Li, L₂ of deformations regions 17.2 - 17.4 presented in Figure 5 are different relative to each other (L₀ for the longitudinal waves 14, Li for the torsional waves 16, and L₂ for the flexural waves 15). In the general form, the periods are defined by L,(z) =L,(0)(1+B ^*z), where B₁ is a constant depending on the type of elastic waves and the frequency band to be prevented. In order that the waves of every type be effectively reflecting within the frequency range (ω_o/5, 5ω₀), where the basic part of the thermal flow is supported, each array 17.2 - 17.4 may include N ~ 100 ÷300 (more generally 50 - 450) deformation periods. The part of array with minimal period L₁(O) reflects the maximal frequencies ~ 5ω₀ while L₁(O) = πv,/(5ω₀), (8)

v, being the propagation speed of the corresponding waves. The part of array with maximal period reflects the waves with minimal frequencies ~ ω_o/5, and the maximal period is defined by L,(z_N) = 5πv/ωo. To ensure that the reflection coefficient remains constant for the frequency range (ω_o/5, 5ω₀), the periods are to form a geometric progression with ratio α. It follows that α = 25^1/N. For N » 1 it will be obtained that

B, « (α - 1 ) / L₁(O). (9)

If the range (ω_o/5, 5ω₀) is changed for (ω_o/ci, c₂ω₀), all remains true with α = (Ci c₂)^1/N.

In generally, L₁(O) is a coefficient dependent on the maximum frequency range c₂ω₀ to be reflected and v, is the propagation speed of the corresponding waves. B₁ is a coefficient by means of which the reflection coefficient is arranged to be kept constant for the frequency range ω_o/ci - c₂ω₀ where Ci is in the interval 1/10 ÷ 1/2 and C₂ is in the interval 1 ÷ 8 and Ci < C₂.

It should be notified that the deformation periods are different for different types of waves because the propagation speeds of the waves are different.

Conclusion

A method of diminishing phonon thermal conductance is suggested for dielectric rods 12 in ballistic regime. The thermal conductance in a thin rod 12 is performed by elastic oscillations of the following three types: longitudinal 14, torsional 16, and flexural 15. In the invention has been disclosed a small deformation structure regions 17.2 - 17.4 of a rod 12 providing the reflection of the elastic waves 14 - 16 within energy ranges related to the basic thermal conductance. A carbon nanofiber 12 with needed deformations 17.2 - 17.4 can be obtained by Standard methods of, for example, roentgen or electron lithography followed by etching. The deformations 17.2 - 17.4 can also be scorched by a focused electron beam. The nanofiber 12 may be also made by any dielectric material which possesses a required strength. Examples of such may be diamond, titanium nitride, silicon nitride etc..

The dielectric rods of low thermal conductance are of use for implementing various insulating structures. For instance, such wires can be taken as suspenders (legs) 12 to keep microthermometers and microbolometers 10 (thermal detectors).

It should be understood that the above specification and the figures relating to it are only intended to illustrate the present invention. Thus, the invention is not limited only to the embodiments presented above or to those defined in the claims, but many such different variations and modifications of the invention will be obvious to the professional in the art, which are possible within the scope of the inventive idea defined in the appended claims.

REFERENCES:

1. L.G.C.Rego and G.Kirczenow Phys.Rev.l_etters81 :232, 1998.

2. K.F.Graff. Wave Motion in Elastic Solids. Ohio State University, Columbus, 1975.

Claims

1. An elongated nanofiber (12) in a temperature sensitive device (10) connected to two opposite connection ends (1 1 , 13) of the device (10), the connection ends (1 1 , 13) having distinct temperatures (Ti, T₂) and where a thermal energy is carried through the nanofiber (12) by propagating non-interacting elastic waves (14 - 16), characterized in that, the nanofiber (12) includes deformation structures (17.1 - 17.4) arranged to prevent the propagation of at least a part of the elastic waves (14 - 16).

2. An elongated nanofiber (12) according to claim 1 , characterized in that, the deformation structures (17.1 - 17.4) are arranged to reflect at least a part of the elastic waves (14 - 16) in the opposite direction relative to their incoming direction.

3. An elongated nanofiber (12) according to claim 1 or 2, characterized in that, the deformation structures (17.1 - 17.4) are arranged to dilate a basic profile (18) of the nanofiber (12).

4. An elongated nanofiber (12) according to any of claims 1 - 3, characterized in that, the deformation structures (17.1 - 17.4) include discrete locally dilations (19.1 - 19.3) which are arranged periodically along an axial direction of the nanofiber (12).

5. An elongated nanofiber (12) according to any of claims 1 - 4, characterized in that, the elastic waves propagation of which is arranged to be prevented are torsional waves (16) and a cross-section of the nanofiber (12) is arranged to be varied in a periodic way.

6. An elongated nanofiber (12) according to claim 5, characterized in that, the cross- section of the nanofiber (12) is arranged to be varied between a circle and an ellipse.

7. An elongated nanofiber (12) according to any of claims 3 - 6, characterized in that, the periods L₀, Li, L₂ Of the dilations (19.1 - 19.3) are arranged to be dependent on the propagation speed of the elastic wave type (14 - 16).

8. An elongated nanofiber (12) according to claim 7, characterized in that, the periods Lo, ₁, ₂ of the dilations (19.1 - 19.3) are defined by the relation L₁ = V₁ fV(2k_BT), wherein v, is the propagation speed of the elastic wave type (14 - 16) in question and where k_B and h are the Boltzmann and Planck constants.

9. An elongated nanofiber (12) according to any of claims 1 - 7, characterized in that, the periods L₀, i, ₂ of the dilations (19.1 - 19.3) are arranged to be increased monotonously in the propagation direction of the elastic waves (14 - 16).

10. An elongated nanofiber (12) according to any of claims 1 - 9, characterized in that, the each deformation region (17.2 - 17.4) include 100 - 300 dilations (19.1 - 19.3).

1 1. An elongated nanofiber (12) according to claim 9 or 10, characterized in that, the monotonously increasing period L₁ is defined by the relation L,(z) = L₁(O) (1 + B,z), wherein L,(0) is a coefficient dependent on the maximum frequency range C2(JU_O to be reflected, v, is the propagation speed of the corresponding waves and B₁ is a coefficient by means of which the reflection coefficient is arranged to be kept constant for the frequency range ωo/Ci - C2(JU_O where Ci is in the interval 1/10 ÷ 1/2 and C₂ is in the interval 1 ÷ 8 and Ci < C₂.

12. An elongated nanofiber (12) according to claim 1 1 , characterized in that, the coefficients L₁(O) and B₁ are defined by the relations L₁(O) = πv,/(c₂ωo) and B₁ «(α - 1 ) / L₁(O) wherein α « (C₁ ^* c₂)^1/N.

13. An elongated nanofiber (12) according to any of claims 6 - 12, characterized in that, the eccentricity of the dilations (19.2) relative to the basic profile (18) of the nanofiber (12) is in the interval 0,05 ÷ 0,7.

14. An elongated nanofiber (12) according to any of claims 4 - 13, characterized in that, the radius of the dilations (19.1 , 19.3) is R(z) = R₀[l + W ύn(lπ z / L_{0 1}(z))] , in which W is in the interval 0,05 ÷ 0,4.

15. An elongated nanofiber (12) according to any of claims 1 - 14, characterized in that, the nanofiber (12) includes three deformation structures (17.2 - 17.4) arranged to be in the nanofiber (12) separate relative to each other and each of which deformation structures (17.2 - 17.4) is arranged to prevent the propagation of one type of waves being longitudinal, torsional and flexural waves (14 - 16).

16. A device (10) including at least one elongated nanofiber (12) according to any of claims 1 - 15, characterized in that, the device is a thermal detector device, such as, for example, a micro-thermometer or a bolometer (10).

17. A thermal detector device (10) including an active part (11 ) and a support (13) and which active part (11 ) and the support (13) are connected together by suspenders (12), characterized in that, at least part of the suspenders (12) include deformation structures (17.2 - 17.4) arranged to prevent the propagation of at least a part of the elastic waves (14 - 16) carrying the thermal energy.

18. A method to diminish a thermal conductance of a nanofiber (12) where a thermal flux is carried through the nanofiber (12) by non-interacting elastic waves (14 - 16), characterized in that, at least part of the thermal flux carried by the elastic waves (14 - 16) is prevented by reflecting at least a part of the elastic waves (14 - 16) in the opposite direction relative to their incoming direction.

19. The method according to claim 18, characterized in that, the elastic waves (14 - 16) to be reflected are selected from at least one of the longitudinal, flexural or torsional waves (14 - 16).