JP5598813B2 - Thin film thermophysical property measuring device and method of measuring thermal conductivity and interfacial thermal resistance using this measuring device - Google Patents

Description

The present invention relates to a thermophysical property measuring apparatus for examining a thermophysical property of an object having a thin film on the surface, and a technique for measuring the thermal conductivity and interfacial thermal resistance of the thin film.

Patent Documents 1 and 2 are already known as means for measuring the thermal conductivity and interfacial thermal resistance of a thin film.
Since Patent Document 1 uses an analysis theory that requires a condition in which the thermal diffusion length is sufficiently smaller than the film thickness, there is a lower limit to the measurable film thickness. Cannot handle film thickness of several microns or less. Of course, it was impossible to measure the interfacial thermal resistance.
In Patent Document 2, in metals and semiconductors, alternating current heats layers other than the metal thin film, so that the boundary condition of the heat conduction equation is not satisfied, and thus the substance to be measured is limited. Cannot handle metals and semiconductors.

The present invention has been made in view of the above circumstances, and an object of the present invention is to obtain a means for measuring thermal conductivity and interfacial thermal resistance even if the thin film is a metal and the thickness is several microns or less. .

The thermophysical property measurement method of the present invention measures heating light irradiation means for irradiating an object with alternating-current pump light of a predetermined frequency, and an AC temperature response on the surface of the object caused by the irradiation of the pump light. The thermophysical property of the object is examined using a thermophysical property measuring apparatus having means for measuring the reflectance of the probe light reflected from the surface and means for measuring the amplitude and phase of the probe light reflected from the surface. In the measurement method, the substrate of the object is standardized even if the absolute value of the heat flow (Q) per unit area by the irradiation of the pump light is unknown from the measurement result of the amplitude and phase of the AC temperature response. The analysis is performed using the thermophysical value as the substance, and the sum of the thermal resistance and the interfacial thermal resistance value of the thin film layer on the surface of the object is obtained.
In the thermophysical property measuring method of the present invention, preferably, the heat flow (Q) per unit area by the irradiation of the pump light is obtained by the following formula (9);

Here, Q is the amount of heat generated per unit area by pump light irradiation, λ is the thermal conductivity, C is the volume specific heat capacity, I _AC is the AC component of the reflected light amount , I _DC is the DC component of the reflected light amount, and α is the thermo− The reflectance coefficient, ω, is the angular frequency.

It is possible to measure the thermal conductivity and interfacial thermal resistance of an extremely thin film without the need for a thin film standard sample, and it is also possible to measure a metal film by adopting a heating / temperature measurement method using a complete optical means. It was.

The figure explaining the sample structure (3 layer heat system) of thin film thermal conductivity measurement. The figure explaining the sample structure (2 layer heat system) of interface thermal resistance measurement. The example of the graph which shows the relationship between (Formula 12) and (omega) ^-1/2 . The figure explaining the thermophysical property measuring apparatus of this invention. Example of a graph showing the relationship between the apparent thermal resistance relative to the thickness of the thin film to be measured (d _1). The thermal conductivity (λ ₁ ) of the thin film is obtained from the slope (Slp) of the linear regression. Example of a graph showing the relationship between the apparent thermal resistance with respect to the thickness of the metal thin film (d _0). The thermal conductivity (λ ₀ ) of the metal thin film is obtained from the slope (Slp) of the linear regression, and the interface thermal resistance (R ₀ ) is obtained from the Y-axis intercept (Int). The flowchart which shows the measurement outline | summary 1. FIG. The flowchart which shows the measurement outline | summary 2. FIG. The flowchart which shows the subroutine of FIG.

(1) In this measurement method, a metal thin film was formed on the surface of a thin film sample formed on a substrate, and modulated at a low frequency so that the thermal diffusion length was sufficiently larger than the thickness of the thin film layer.
The “condition that the thermal diffusion length is sufficiently larger than the film thickness of the thin film layer” is a condition that satisfies the approximate expression. The condition kd << 1 presented by the mathematical expression in the above approximate expression derivation process is expressed in words.
The approximate expression is obtained by expanding the exp, sinh, and cosh functions with respect to kd and ignoring the higher-order terms of kd, and the condition for that is kd << 1.
(2) Uniform and large-diameter pump light is irradiated to the surface of the metal thin film and AC heated to infiltrate a one-dimensional temperature wave into the thin film layer and the substrate layer, and the AC temperature response on the surface of the metal thin film is reflected by thermoreflectance. Measure the amplitude and phase of the thermoreflectance detected by the lock-in amplifier.
The boundary condition of the heat conduction equation of the present invention is premised on a one-dimensional heat flow. One-dimensional heat flow is ensured by making the diameter of the pump laser light on the surface of the metal thin film sufficiently larger than the diameter of the probe laser light.
(3) When the thermal diffusion length is sufficiently larger than the thickness of the thin film, the thermal conductivity of the thin film is analyzed by analyzing based on the approximate equation of the solution of the thermal conduction equation of the thermal system including the metal thin film layer. And determine the interfacial thermal resistance.
Specifically, the wave number k is a function of the thermal diffusivity and the frequency, and the reciprocal of the thermal diffusion length. Let kd be the film thickness d divided by the thermal diffusion length k- ¹ .
First, the film thickness d of the thin film is measured. The value of k that satisfies the condition is determined. The thermal diffusivity D of the thin film is estimated, and the frequency is calculated according to the definition formula of k. Test measurement is performed, and k value is obtained from the actual measurement result of thermal conductivity. It is determined whether or not the k value satisfies the condition. If not, change the frequency and execute the above procedure again.
(4) In this measurement method, the absolute values of the thermal conductivity and interfacial thermal resistance of the thin film can be determined using known thermophysical values of the substrate.
(5) In this measurement method, the thermal conductivity and interface thermal resistance of a thin film layer whose film thickness is sufficiently smaller than the thermal diffusion length can be measured. The condition of kd << 1 is satisfied even if d of the metal thin film or the thin film is thin. (D in the formula kd << 1 is the film thickness.) The upper limit of the k value is determined by the thermal properties (thermal diffusivity and thickness) of the substrate and does not depend on the film thickness of the thin film. If d is as close as possible to zero when k is constant, kd will approach zero as much as possible, so this satisfies the equation kd << 1. Incidentally, in the measurement method of Document 1, kd >> 1, which is completely opposite to the present invention, is a condition. In this case, the film thickness naturally has a lower limit.
(6) Since this measurement method uses optical heating without using Joule heating, it can measure the thermal conductivity and interfacial thermal resistance of not only insulators but also metals and semiconductors.

<Measurement outline 1>
The measurement method in the heat system (three-layer heat system) for measuring the thermal conductivity of the thin film shown in the schematic diagram of FIG. 1 will be described below.
FIG. 4 is a conceptual diagram of a thin film thermal conduction / interfacial thermal resistance measuring apparatus of the present invention.
Pump laser light (L2) (LD) modulated by an AC signal (C1) output from a signal generator built in the lock-in amplifier (10) is transmitted from a laser transmitter (8). The pump laser light (L2) is reflected at right angles by a PBS (polarizing beam splitter) (9), collected by a lens (11), and irradiated onto the sample (12) with a constant diameter. On the other hand, the probe laser beam (L1) (HeNe) transmitted from the probe laser transmitter (1) is transmitted through the λ / 2 wavelength plate (2) and then divided into two by a CBS (cube beam splitter) (5). . The beam (L12) reflected by the CBS (5) passes through the NDF (4), changes its direction by 180 degrees with the right-angle prism (3), and again passes through the NDF (4) and the CBS (5). (Photodiode) Incident on one cell (7a) of (7). On the other hand, the beam (L13) first divided into two by CBS (5) and transmitted through CBS (5) is transmitted through PBS (9), condensed by lens (11), and pump laser on metal thin film surface (12). The focal point is set at the center of the irradiation region of the light (L2). The light (L14) reflected by the surface of the metal thin film is transmitted again through the lens (11) and the PBS (9), is reflected by the CBS (5), and enters the other cell (7b) of the differential PD (7). .
Rotating the λ / 2 plate (λ / 2 wavelength plate) (2) around the optical axis to change the polarization state, thereby adjusting the amount of light transmitted by the probe laser light (L1) through the PBS (9). Can do. In this way, the amount of light incident on the differential PD (7) both cells (7a) and (7b) can be balanced. Since such a differential optical system reduces common mode noise of the probe laser, it is possible to measure a weak reflected light amount change with high accuracy.
The photocurrent difference of the differential PD (7) is converted into a voltage by an IV-amplifier (not shown), and the voltage signal (C2) is locked-in detected by the lock-in amplifier (10) (the amplitude of the input AC voltage and DC voltage proportional to the phase is output respectively) and input from the computer terminal (13) to a computer (not shown) operating a predetermined processing method (processing based on the following equations) program, Calculation based on the signal (C2) is performed, and the thermal conductivity and the like are calculated.
The BPF (band pass filter) (6) transmits the probe laser beam (L14) and does not transmit the pump laser beam (L2). The NDF (ND filter) (4) attenuates the amount of light reflected by the prism (3).

The surface of the metal thin film is irradiated with pump laser light (L2) having a predetermined diameter and subjected to AC heating to generate an AC heat flow in the X-axis direction (arrow pointing downward in the figure). By detecting the temperature response at the center of the pump laser beam (L2) irradiation region with thermoreflectance (a phenomenon in which the reflectance changes with temperature), specifically, by detecting the voltage signal (C2) in FIG. 4 and lock-in detection. Measure AC temperature response (amplitude and phase) of metal thin film surface by one-dimensional AC heat flow. The solution of the heat conduction equation of this heat system is given by (Equation 1).
<Formula 1>

(Expression 1) is expanded and simplified in the case of (Expression 13) and (Expression 14), and (Expression 2) is established.
<Formula 2>

When only the real part of (Expression 2) is written, (Expression 3) is obtained.
Here, (Formula 15) is a real part (In-phase Amplitude) of the AC temperature response on the surface of the metal thin film.
<Formula 3>

<Measurement outline 2>
Next, a measurement method for the sample configuration (two-layer heat system) for measuring the interface thermal resistance shown in FIG. 2 will be described.
As shown in the measurement outline 1, the apparatus shown in FIG. 4 is used.
In the same manner as in measurement outline 1, the AC temperature response (amplitude and phase) of the metal thin film surface by a one-dimensional AC heat flow, specifically, the output of the lock-in detection in FIG. 4 is measured. The solution of the heat conduction equation of this heat system is given by (Equation 4).
<Formula 4>

(Expression 4) is expanded and simplified in the case of (Expression 13), and (Expression 5) is established.
<Formula 5>

If only the real part of (Expression 5) is written out, (Expression 6) is obtained.
Here, (Formula 15) is a real part (In-phase Amplitude) of the AC temperature response on the surface of the metal thin film.
<Formula 6>

The right side of both the approximate solution of the three-layer thermal system (Equation 3) and the approximate solution of the two-layer thermal system (Equation 6) is a linear expression of ω ^−1/2 . That is, the first term on the right side is proportional to ω ^−1/2 , and the second and subsequent terms on the right side are real constants independent of ω ^−1/2 . Therefore, the sum R ^* of the constant term on the right side is obtained from the Y-axis intercept (Int) of the linear regression of (Equation 12) versus ω ^−1/2 plot.
An example of a graph showing the relationship between (Equation 12) and ω ^−1/2 is shown in FIG. However, in order to determine the absolute value of the sum R ^* of the constant terms, in addition to the actual measurement value of the AC component of the reflectance (or amount of reflected light) on the metal surface, the thermo-reflection coefficient
The absolute value of the heat flow Q per unit area by pump laser light irradiation (determined using (Equation 9) according to the following procedure) is also considered necessary.

Since the proportionality coefficient on the right side of (Equation 3) and (6) is a function of only the thermal permeability of the substrate layer (Equation 16), it can be theoretically calculated if the thermal permeability of the substrate layer (Equation 16) is known. Using this theoretical value, the absolute value of (Equation 12) can be determined. The procedure is as follows. First, (Expression 3) and (6) are rewritten to the general form of (Expression 7).
<Formula 7>

(Expression 8) is obtained by multiplying both sides of (Expression 7) by (Expression 17).
<Formula 8>

If (Equation 18) is actually measured for a plurality of ω, the unknown coefficient (Equation 17) can be determined according to (Equation 9).
Here, the numerator on the right side of (Equation 9) is an actually measured value of the gradient of (Equation 18) versus ω ^−1/2 plot, and the denominator is the theoretical value of the gradient of (Equation 12) vs. ω ^−1/2 plot. is there.
<Formula 9>

Thus, in this measurement method, the substrate serves as a standard substance. Since the substrate is a bulk material, in many cases there are already reliable thermophysical values (reference values for thermal conductivity and volumetric specific heat capacity). In particular, a silicon substrate is a high-purity single crystal and is supplied in a large amount, so that it becomes an excellent standard substance.

The right side of (Expression 10) is a constant term after the second term on the right side of (Expression 3). As mentioned above, the sum R ^* of these constant terms can be determined experimentally. The first term is the interfacial thermal resistance between the substrate layer and the thin film layer, the second term is the apparent thermal resistance of the thin film layer, the third term is the interfacial thermal resistance between the thin film layer and the metal thin film layer, and the fourth term is metal. Each corresponds to the thermal resistance of the thin film layer. Since the entire right side is a linear expression of the film thickness d ₁ of the thin film, the total sum R ^* of the constant terms on the right side is measured, and linear regression is performed using a function of the film thickness d ₁ , so that the thin film is known from the gradient. The thermal conductivity of the thin film can be obtained using the volume specific heat capacity C _{1 of} the substrate and the known thermal permeability of the substrate (Equation 16).
<Formula 10>

The right side of (Expression 11) is a constant term after the second term on the right side of (Expression 6). As mentioned above, the sum R ^* of these constant terms can be determined experimentally. The first term corresponds to the interfacial thermal resistance R ₀ between the metal thin film layer and the substrate layer, and the second term on the right side corresponds to the thermal resistance of the metal thin film layer. Since the entire right side is a linear expression of the film thickness d ₀ of the metal thin film, by measuring the sum R ^* of the constant terms on the right side and performing a linear regression with a function of the film thickness d ₀ , from the Y-axis intercept, The interfacial thermal resistance _R0 between the substrate layer and the metal thin film layer is obtained. Further, from the gradient, the thermal conductivity of the metal thin film can be obtained using the known volume specific heat capacity C ₀ of the metal thin film and the known heat permeability of the substrate (Equation 16). Thus, since the two-layer heat system has only one interface, there is an advantage that the interface thermal resistance can be uniquely determined.
<Formula 11>

<Formula 12>

<Formula 13>

<Formula 14>

<Formula 15>

<Formula 16>

<Formula 17>

<Formula 18>

As measurement example the measurement overview 2 thermal oxidation SiO ₂ thin film thermal conductivity, an example of measurement by forming a gold thin film on the thermally oxidized SiO ₂ film sample.
Samples 1 and 2 shown in Table 3 are formed by depositing thermally oxidized SiO ₂ thin films having different thicknesses on a silicon single crystal substrate. A plot of the apparent thermal resistance versus film thickness of the thermally oxidized SiO ₂ thin film is shown in FIG. Table 1 summarizes the thermal properties of the thermally oxidized SiO ₂ thin film samples used in the experiment. Table 2 shows the thermal conductivity measurement results of the thermally oxidized SiO ₂ thin film.
The wavelength of the pump laser is 405 nm, and the wavelength of the probe laser is 632 nm. The diameter of the pump laser is 1 mm, and the diameter of the probe laser is 30 μm. Both the modulation frequency of the pump laser and the frequency of lock-in detection are 2, 3, 8, and 12 kHz. The probe laser is CW transmission. The calculation formula was calculated using (Formula 11).
In this embodiment, the signal (C1) is an ON-OFF signal (digital signal (TTL)) having an amplitude of about 5V.
The signal (C2) is a DC component 1.0 V, which is the _{I DC,} but AC component is the level of several 0.1μV several .mu.V, need not be measured at this stage. This AC component is accurately measured by the lock-in amplifier (10).
The two samples differ only in film thickness, and the others are common. What is obtained for each sample is only the sum of the constant terms, and one thermal conductivity common to the two samples is determined.

Measurement example of thermal conductivity of Bi thin film and Bi-sapphire interface thermal resistance Bi films having different thicknesses are formed on a sapphire single crystal substrate, and samples 3, 4 and 5 in Table 6 are prepared. Table 4 shows the thermophysical values (document values) of the substances used in the experiment. Table 5 shows the measurement results of the thermal conductivity of the Bi thin film and the Bi-sapphire interface thermal resistance. A plot of the apparent thermal resistance versus film thickness of the Bi thin film is shown in FIG.
The diameter of the pump laser when irradiating the sample is 1 mm, and the diameter of the probe laser is 30 μm. Both the pump laser modulation frequency and the lock-in detection frequency were set to 2, 3, 8, and 12 kHz. The probe laser is CW transmission. The calculation formula was calculated using <Formula> 10.
The three samples differ only in film thickness, and the others are common. What is obtained for each sample is only the sum of the constant terms, and the thermal conductivity and interfacial thermal resistance common to the three samples are determined one by one.

T (0): AC temperature response of metal thin film surface
l _j : thermal conductivity (j = 0, metal thin film; j = 1, thin film; j = S, substrate)
d _j : film thickness (j = 0, metal thin film; j = 1, thin film)
C _j : unit volume heat capacity (j = 0, metal thin film; j = 1, thin film; j = S, substrate)
R _j : interface thermal resistance (j = 0, interface between metal thin film and thin film; j = 1, interface between thin film and substrate)
Q: Heat flow per unit area (1) Probe laser transmitter (2) λ / 2 wave plate (3) Right angle prism (4) NDF (ND filter)
(5) CBS (cube beam splitter)
(6) BPF (band pass filter)
(7) Differential PD (photodiode)
(7a) (7b) Cell (8) Laser transmitter (9) PBS (polarization beam splitter)
(10) Lock-in amplifier (11) Lens (12) Sample (metal thin film surface)
(13) Computer terminal (C1) AC signal (C2) Voltage signal (L1) Probe laser beam (L12) Reflected beam (L13) Transmitted beam (L14) Light reflected on metal thin film surface (L2) Pump laser beam

Japanese Patent No. 3294206 JP 2002-303597 A

Claims (2)

Heating light irradiating means for irradiating the object with AC pump light of a predetermined frequency, and probe light reflected from the surface for measuring the AC temperature response of the object surface caused by the irradiation of the pump light means for measuring the reflectance of a measurement method for examining the thermal properties of the object using a thermal property measurement apparatus having means for measuring the probe light amplitude and phase of reflected from said surface,
From the measurement results of the amplitude and phase of the AC temperature response, even if the absolute value of the heat flow (Q) per unit area due to the irradiation of the pump light is unknown, the thermophysical value using the substrate of the object as a standard material And measuring the sum of the thermal resistance and interfacial thermal resistance of the thin film layer on the surface of the object. The thermophysical property measuring method according to claim 1, wherein the heat flow (Q) per unit area by the irradiation of the pump light is obtained by the following equation.

Here, Q is the amount of heat generated per unit area by pump light irradiation, λ is the thermal conductivity, C is the volume specific heat capacity, I _AC is the AC component of the reflected light amount , I _DC is the DC component of the reflected light amount, and α is the thermo− The reflectance coefficient, ω, is the angular frequency.