Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
  • G01N25/00—Investigating or analyzing materials by the use of thermal means
  • G01N25/18—Investigating or analyzing materials by the use of thermal means by investigating thermal conductivity

Definitions

• the invention relates to the field of thermal characterization of materials, and more particularly to a method of thermal characterization of a portion of material for determining the thermal conductivity of this portion of material.
• the 3 ⁇ method allows to thermally characterize layers of materials by determining the thermal conductivity of these layers. This method is described in D.G. Cahill and R.O. Pohl's "Thermal conductivity of amorphous solids above the plateau", Physical Review B, vol. 35, March 1987, page 4067.
• a test structure such as that shown in FIG. 1 comprising a micro-wire 4 based on a metal material, of width equal to 2b (b corresponding to half the width of the micro-wire), forming a metal line deposited on a layer of material 8, called sample, whose thermal conductivity is to be measured.
• sample is itself placed on a substrate 2.
• a measurement TCR, or measurement of the coefficient of variation of the temperature resistance, of the metallic line 4 is first performed. This measurement consists in arranging the test structure on a heating support and to measure the value of the electrical resistance R of the metal line 4 as a function of the different temperatures T to which the test structure is subjected.
• the characteristic R (T) obtained is adjusted by a polynomial of order 2 in order to calculate the coefficient of variation of the temperature resistance R of the metallic line 4 such that:
• a sinusoidal electric current i (t) of frequency ⁇ and amplitude I o is circulated in the metal line 4.
• This heating leads to a temperature variation ⁇ in the metallic line 4 of frequency 2 ⁇ such that:
• V3 m 3 ⁇ of the voltage across the metallic line 4
• the substrate 2 is homogeneous, isotropic and semi-infinite in the depth (which is to say that ⁇ lq s "d s with d s : thickness of the substrate 2)
• the heat source formed by the metal line 4 is linear, that is to say that the metal line 4 has a width 2b that is negligible compared to the depth of penetration of the thermal wave 1 / q s (expressed as b " ⁇ / Q s ),
• the material of the sample 8 allows the heat flow to pass through the sample 8 perpendicularly to the plane of the layer forming the sample 8 (parallel to the (X, Z) plane shown in FIG. 1),
• the width 2b of the metal line 4 is much greater than the thickness d F of the sample 8.
• the temperature increase ⁇ 3 in the substrate 2 may be approximated by the following formula:
• an electrically insulating film for example based on SiO 2 and of known thickness, is interposed in order to prevent any electrical short circuit between the metallic line. 4 and sample 8.
• C thermal conductivity contrast factor between the sample and the substrate
• S lateral dispersion effect of heat
• k Fx , y representing the spatial pulsation of the thermal wave in the sample respectively along the x or y axis
• X Fx , y representing the thermal conductivity of the sample respectively along the x or y axis
• ⁇ being a integration variable
• T F 1D is the expression of T F when the assumptions of one-dimensional flow of heat are respected.
• T F is inversely proportional to b.
• An increase of b therefore implies reducing T F , which can lead to a signal that is difficult to measure for films with good thermal conductors.
• An object of the present invention is to propose a method of thermal characterization of a portion of material that does not have the drawbacks of the prior art, that is to say making it possible to measure the thermal conductivity of a very thin or very thick portion, and / or may have a strong anisotropy and / or is based on a high thermal conductivity material.
• a thermal characterization method is proposed for a portion of at least one elongate first material on which at least a portion of at least one elongate second electrically conductive material is disposed, the method comprising at least Steps :
• a width of the portion of the first material being between about 0.9L and 1.1L, with L: width of the portion of the second electrically conductive material.
• the portion of the first material is surrounded by at least one material forming a thermal insulator vis-à-vis the portion of the first material.
• This method therefore makes it possible to apply the principle of the method 3 ⁇ to material ranges whose value of the term CS is different from 1, for example materials whose thermal conductivity and / or anisotropy are too important to be compatible with with the conventional method 3 ⁇ of the prior art, such as for example germanium whose thermal conductivity coefficient is equal to about 60 W / m / K, or titanium whose thermal conductivity coefficient is equal to about 46 W / m / K, or still platinum whose thermal conductivity coefficient is equal to about 72 W / m / K, and / or portions of materials whose thicknesses, which are too thin or too thick in relation to the conductivities, are incompatible with the implementation of the classical method 3 ⁇ of the prior art.
• This method also makes it possible, for materials compatible with the 3 ⁇ method of the prior art, to improve the measurement accuracy of the thermal conductivity since the heat flux passing through the portion of the first material is unidimensional, that is to say said direction in the same direction (in the direction of the thickness of the portion of the first material) throughout the volume of the portion of the first material, unlike the flow through a layer based on the first material, and that it is sufficient for example to reduce the width 2b to obtain a measurable signal without excessive error.
• the portions of the first and second material have an elongate shape, i.e. a shape whose length is greater than the width, for example such that the length is greater than about 10 times the width.
• This elongated shape can example correspond to a rectangular parallelepiped shape, wire, cylinder, or more generally a substantially rectilinear shape of uniform width.
• the thickness of the portion of the second electrically conductive material may be less than or equal to about 0.1. L, and / or the length of the portion of the second electrically conductive material may be greater than or equal to about 10. L.
• the length of the portion of the first material may be greater than or equal to about 10 times the width of the portion of the first material, and / or the thickness of the portion of the first material may be less than the penetration length of a flow thermal generated during step b) in the portion of the first material, the heat flow reaching the substrate which can then be seen as a heat sink.
• the portion of the first material and / or the portion of the second electrically conductive material may have a substantially rectangular parallelepiped shape.
• the portion of the first material may be disposed between the portion of the second electrically conductive material and a substrate, the substrate may be based on at least one semiconductor.
• the substrate may have a thickness equal to or greater than about 10 times the penetration length of a thermal flux generated during step b) in the substrate and / or a width equal to or greater than about 10 times the width of the portion of the first material.
• the second electrically conductive material may be a metal.
• a portion of a dielectric material may be disposed between the portion of the first material and the portion of the second electrically conductive material, thereby electrically isolating the portion of the first material relative to the portion second electrically conductive material.
• the calculation of the thermal conductivity coefficient of the portion of the first material may comprise at least the steps of:
• the portions of the first and second material can be made by implementing the following steps:
• a layer based on a dielectric material can be deposited on the layer based on the first material, the layer based on the second electrically conductive material can then be deposited on the layer based on the dielectric material, the layer based on the dielectric material can also be etched according to the pattern of the engraving mask.
• the value of the thermal conductivity coefficient of the material surrounding the portion of the first material may be less than or equal to about one tenth of the value of the thermal conductivity coefficient of the portion of the first material.
• the value of the thermal conductivity coefficient of the material surrounding the portion of the first material may be less than or equal to the value of the thermal conductivity coefficient of the portion of the first material, and a thickness of the material surrounding the portion of the first material may be less than or equal to about one-tenth of a thickness of the portion of the first material.
• FIG. 1 represents a sectional view of a test structure used during the implementation of a method for measuring the conductivity of a thin layer of material according to the method 3 ⁇ of the prior art
• FIGS. 2A, 2B and 3 respectively represent sectional views and a top view of a test structure used during the implementation of a method for thermal characterization of a portion of material according to one embodiment. particular of the invention.
• FIG. 2A represents an example of a test structure 100 used during the implementation of a method of thermal characterization of a portion of material 104 according to a particular embodiment.
• the test structure 100 includes a substrate 102, here based on silicon and with a thickness d s for example between about 100 .mu.m and 1 cm, on which is formed a thick portion 104 of F, by example between about 100 nm and 10 ⁇ m, which is to measure the thermal conductivity.
• the portions 104 and 106 both have an elongate shape, that is to say having a length (dimension along the Z axis perpendicular to the x axis and shown in FIG. 2A) greater than at least 10 times their width.
• the width 2b is for example between about 1 ⁇ m and 30 ⁇ m, and the length of the portions 104 and 106 is for example between about 10 ⁇ m and 1 cm.
• the material whose thermal conductivity is to be measured is not in the form of a thin layer, but in the form of the portion 104 which here comprises a width (dimension according to FIG. x axis) equal to 2b, that is to say equal to the width of the portion 106.
• the portion 106 thus forms a metal line disposed on the portion 104 which will be called "sample”.
• the metal line 106 and the sample 104 thus form a mesa type structure, the shape of the sample 104 in a plane parallel to the (X, Z) plane of FIG. 2A (plane parallel to the face of the substrate 102 on which are made the sample 104 and the metal line 106) being substantially similar to the shape of the metal line 106 in this same plane.
• the sample 104 by making the sample 104 such that its width is substantially equal to that of the metal line 106, it blocks the lateral dispersion of the heat emitted by the metal line 106, and whatever the physical properties of the sample 104, that is to say whatever its thickness or the nature of its material.
• the blocking of this lateral dispersion of the heat emitted by the metal line 106 is also obtained thanks to the fact that the portion 104 is surrounded by a material 112 forming a thermal insulation around this portion 104.
• the value of the thermal conductivity coefficient of this material 112, in this case air is less than or equal to about one-tenth of the value of the thermal conductivity coefficient of the portion 104.
• the air 112 being around the Sample 104 forms an excellent thermal insulator.
• a heat flux 108 created by the metal line 106 passing through the sample 104 is therefore unidimensional and directed in a single direction perpendicular to the face of the substrate 102 on which the sample 104 and the line are made.
• metal 106 (direction parallel to the y-axis shown in Figure 2A).
• the test structure 100 is also shown in FIG. 3, seen from above.
• four electrical contacts 110a, 110b are electrically connected to the ends of the metal line 106.
• the contacts 110a will be used thereafter to circulate a current in the metal line 106 while the contacts 110b will be used to measure a voltage across the metal line 106.
• the thickness of the metal line 106 is for example between about 100 nm and 1 ⁇ m, and for example equal to 400 nm.
• This thickness is chosen to be sufficiently thick so that, when the contacts 110a, 110b are made from the same layer of material as that used to make the metal line 106, electrical contacts with the devices intended to circulate the current in the metal line 106 and measuring the voltage across the metal line 106 can be created, and thin enough so that the heat is not stored in the metal line 106 and / or the contacts 110a, 110b when circulating a current in the metal line 106.
• the test structure 100 can be made according to one of the different possible configurations for applying a measurement method of the "four-point" type or of the "Van der Pauw" type. ".
• the width 2b will be chosen as low as possible in order to have the largest possible value of T F , which makes it possible to reduce the error on the value of T F , and thus also on the thermal conductivity X F.
• the sample 104 is based on an electrically conductive material, is interposed, between the metal line 106 and the sample 104, a portion of a dielectric material, for example based on S10 2 , to avoid a short circuit between the metal line 106 and the sample 104.
• the section, in a plane parallel to the plane (X, Z) shown in Figure 3, of this portion of dielectric material is for example similar to the section of the sample 104 and / or the metal line 106 in this same plane.
• Such a test structure 100 is obtained by first producing a deposit, on the substrate 102, of a layer based on the material intended to form the sample 104, then the deposition of a dielectric layer if the sample 104 is based on an electrically conductive material, and the deposition of a layer based on the electrically conductive material intended to form the metal line 106.
• An etching mask for example based on resin, is produced on the layer to be base of the electrically conductive material.
• the pattern of the etching mask corresponds for example to the pattern of the metal line 106 and the contacts 110a, 110b shown in FIG. 3.
• the various layers previously deposited on the substrate 102 are then etched according to the pattern of the etching mask, forming the sample 104 and the metal line 106 and the contacts 110a, 110b.
• the engraving mask is then removed.
• the material 112 surrounding the portion 104 may be vacuum or a gas such as air, an inert gas (nitrogen, argon, helium, etc.), or a solid composed of plastics, rubber or epoxy, of polystyrene, or any other material whose value of the thermal conductivity coefficient is less than or equal to about one tenth of the value of the thermal conductivity coefficient of the portion of the first material.
• a gas such as air, an inert gas (nitrogen, argon, helium, etc.), or a solid composed of plastics, rubber or epoxy, of polystyrene, or any other material whose value of the thermal conductivity coefficient is less than or equal to about one tenth of the value of the thermal conductivity coefficient of the portion of the first material.
• FIG. 2B Another alternative embodiment of the test structure 100 is shown in FIG. 2B.
• the portion 104 is surrounded by a material 114 whose value of the thermal conductivity coefficient is less than or equal to the value of the thermal conductivity coefficient of the portion 104 of the first material.
• the thickness (dimension along the y-axis shown in FIG. 2B) of the material 114 surrounding the portion 104 is less than or equal to about one-tenth of the thickness (dimension along the y axis) of the portion 104.
• the material 114 partially surrounding the portion 104 is formed as a layer of silicon or silicon nitride.
• the portion 104 is also traversed by a substantially unidimensional heat flux 108 through the portion 104.
• the rest of the portion 104 is for example surrounded by a material forming a thermal insulator, for example air.
• the value of the thermal conductivity coefficient of the portion 104 is then calculated. An example is given below for carry out this calculation.
• heating means per unit length of the metal line 106 ⁇ 3 thermal conductivity coefficient of the substrate 102, p s density of the substrate 102, and c pS mass thermal capacity of the substrate 102.
• the method according to the invention therefore makes it possible to thermally characterize a whole range of materials that can not be characterized by the 3 ⁇ method of the prior art, for example very thin or very thick portions, with high anisotropy or very good conductors. thermal.
• this method makes it possible to improve the measurement accuracy of the thermal conductivity of these materials.
• the sample and the thin layer are arranged in two separate test structures, each comprising a silicon substrate whose characteristics are:
• T FID measured temperature variations of the sample
• T FCOUCHE thin layer
• This difference in value is due in particular to a high heat dispersion occurring in the thin layer due to the high thermal conductivity of the material (30 W / m / K). It is also seen that by increasing the width of the metal line, the difference between the measured values T Fcouche and T F i D is reduced. However, this increase in the width of the metal line causes a drop in the temperature to be measured, which then becomes difficult to measure and increases the probability of errors in the measurement.
• the silicon substrate used is similar to that described above.
• the thickness of the thin layer and the sample is equal to 1 ⁇ m.
• the applied linear power is equal to 30 W / m.
• T FID The values of the measured temperature variations of the sample (T FID ) and of the thin layer (T F- layer) for different values of b are:

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