Thickness Effect on Microwave Permeability of CoFeB Films on Flexible Substrate

Abstract

Microwave permeability of amorphous Co₆₇Fe₇B₂₆ films deposited on a flexible substrate was studied in a wide range of film thicknesses up to 1.40 μm. Microwave permeability measurements were carried out using the coaxial technique in the frequency range from 0.1 to 10 GHz. It was found that both the static permeability and the ferromagnetic resonance frequency depend weakly on the film thickness. Analysis of the microwave data showed that the studied films possess in-plane magnetic anisotropy. The influence of the skin effect on the frequency dependence of the microwave permeability was modeled using an analytical approach. It was demonstrated that the decrease in the peak of the imaginary part of the microwave permeability with film thickness growth is related to the skin effect. The results obtained may be useful for microwave applications of soft magnetic CoFeB films.

1. Introduction

Microwave properties of ferromagnetic films are currently being intensively studied [1,2,3,4,5,6]. Static and dynamic magnetic properties of these films are of interest both from a fundamental point of view and for numerous potential applications in microwave devices. The key parameter governing the properties of a ferromagnetic material in the microwave range is the dynamic permeability, which has certain limitations. For bulk magnetic materials, according to the Snoek limit, the initial permeability is inversely proportional to the ferromagnetic resonance frequency under a certain saturation magnetization [7]. Ferromagnetic films with in-plane magnetic anisotropy have some advantages over other magnetic materials in their microwave behavior, since they can exceed the Snoek limit, allowing for a wider operating frequency range of microwave devices [8,9,10]. This is associated with a strongly pronounced shape anisotropy, which prevents the exit of the magnetization from the film plane. To attain high values of the microwave permeability, ferromagnetic films should possess a high saturation magnetization and anisotropy field. Furthermore, to reduce the skin effect, the films should also have high resistivity [11]. In recent decades, much attention has been paid to the study of microwave properties of various nanocrystalline soft magnetic films that possess the above-mentioned properties. In addition to nanocrystalline films, amorphous films with high saturation magnetization are promising for microwave applications.

Amorphous CoFeB films exhibit excellent soft magnetic properties and have a ferromagnetic resonance frequency above 1 GHz [12,13]. The dynamic magnetic properties of CoFeB films on rigid [4,6,12,13,14,15,16,17,18,19,20,21,22,23,24,25] and flexible [26,27,28,29,30,31] substrates have been investigated over the past decades. However, all studies of CoFeB films were carried out for ultra-thin films and were limited to a film thickness of 500 nm. Investigations of the dynamic magnetic properties for thicker CoFeB films are lacking.

At the same time, some applications of ferromagnetic films require relatively high film thickness. It is well known that in ferromagnetic films, an increase in film thickness leads to changes in the microstructure and magnetic anisotropy. Out-of-plane magnetic anisotropy can appear in various nanocrystalline [32,33,34] and amorphous [18,35,36,37,38,39] films with the growth of film thickness. The origin of out-of-plane anisotropy in amorphous films is associated with magnetoelastic effects. It has been found that the appearance of out-of-plane magnetic anisotropy depends on the film thickness, amorphous alloy composition, fabrication process and distribution of residual stress [36,38,39]. The appearance of out-of-plane magnetic anisotropy in a film leads to a decrease in the ferromagnetic resonance frequency, which worsens the microwave magnetic performance of the films.

Another mechanism affecting the microwave magnetic properties of ferromagnetic films is related to the skin effect. For relatively thick ferromagnetic films, the frequency dependence of the dynamic permeability can be governed by the effect of eddy currents, which leads to a sharp decrease in the permeability at high frequencies [40]. Therefore, the study of physical reasons leading to a decrease in the dynamic permeability with the growth of film thickness is an important task from the point of view of microwave applications.

In this paper, we systematically investigate the thickness effect on the microwave properties of amorphous Co₆₇Fe₇B₂₆ films on a flexible substrate obtained by DC magnetron sputtering. The microwave permeability was measured using the coaxial technique. The measured frequency dependences of permeability were approximated by the Lorentzian dispersion law. The possible appearance of out-of-plane magnetic anisotropy with the film thickness growth and the influence of the skin effect on the frequency dependence of the microwave permeability are analyzed.

2. Materials and Methods

CoFeB amorphous films were deposited using DC magnetron sputtering onto a flexible polyethylene terephthalate (PET) substrate. Co₆₇Fe₇B₂₆ alloy was used as a target material. This composition was chosen due to its high saturation magnetization and high dynamic permeability in the range of several GHz [13]. The films were deposited in an argon atmosphere at a pressure of 10⁻³ Torr. The PET substrate of a thickness of 12 μm was fixed on a rotating barrel-type substrate holder. The sputtering target to substrate distance was 5 cm. Films with thicknesses in the range from 0.19 to 1.40 µm were obtained.

The thickness of the obtained films was determined by two methods: measuring the film mass and monitoring the film cross-section using scanning electron microscopy (SEM) JEOL JCM-7000 (JEOL, Tokyo, Japan). To obtain the thickness by the mass of the film, the mass of a 20 × 20 cm² square was measured before and after deposition of the film on a PET substrate. The density of the magnetic layer was found by measuring the volume and mass of the target material. To obtain SEM images, a sharp blade was used to cut off a smooth edge of the film, with the film cut oriented parallel to the incident electron beam. The film thickness was evaluated by the average value obtained from the SEM image data analysis at several points of the film. A typical SEM image is shown in Figure 1 for a 1.40 µm thick film. Note that the two methods mentioned above give similar results for a film thickness within 0.01 µm.

The film resistivity was measured using the four-probe method for a 1.40 µm thick film. The resistivity value was 140 μOhm·cm. Magnetostatic properties were studied using a vibrating sample magnetometer (VSM). For the VSM measurements, the 7 mm diameter discs were cut from the film. Hysteresis loops were measured in the film plane in a magnetic field range of ±1 kOe.

The microwave permeability was studied using a 7/3 coaxial measurement line. A detailed description of the measurement method can be found elsewhere [41,42]. Samples for microwave measurements were 5 mm wide strips cut from film. The strips were cut perpendicular to the direction of the barrel axis. The strips were wound into a hollow cylindrical roll with inner and outer diameters of 3 and 7 mm, respectively. The frequency dependence of microwave permeability was measured in the range of 0.1 to 10 GHz using the Nicolson–Ross–Weir technique. Additionally, microwave measurements were determined under a bias magnetic field of up to 800 Oe. The bias magnetic field was applied along the axis of the measurement line.

Measurements of resistivity, magnetostatic and microwave properties were carried out at room temperature.

The measured frequency dependence of the permeability μ = μ′ + iμ″ was approximated by the Lorentzian dispersion law:

$$\mu =1+{\displaystyle \frac{{\mu }_{\mathrm{s}}-1}{1-i\beta (f/f_{\mathrm{res}})-{(f/f_{\mathrm{res}})}^2}}.$$

(1)

Here, μ_s is the static permeability, β is the damping factor, f is the frequency and f_res is the ferromagnetic resonance frequency.

As a result of the fitting, the static permeability μ_s and the ferromagnetic resonance frequency f_res of the film were estimated. Based on the static permeability and the ferromagnetic resonance frequency, the microwave magnetic performance of the films was analyzed by using the Acher parameter k_A, which is defined as follows [10]:

$$k_{\mathrm{A}}={\displaystyle \frac{({\mu }_{\mathrm{s}}-1)f_{\mathrm{res}}^2}{{(\gamma 4\pi M_0)}^2}},$$

(2)

where M₀ is the saturation magnetization of the material, and γ ≈ 3 GHz/kOe is the gyromagnetic ratio.

The Acher parameter describes the fraction of magnetic moments of a material that are involved in the precession excited by a microwave magnetic field. For a uniformly magnetized film with in-plane magnetic anisotropy, the Acher parameter equals unity when the microwave magnetic field is transverse to the anisotropy axis of the film. The case of k_A < 1 may be related to the appearance of out-of-plane magnetic anisotropy [10,43,44].

3. Results and Discussion

Figure 2 shows the in-plane hysteresis loops for a 0.63 µm thick film. The measurements were carried out in a field directed along the symmetry axis of the barrel and perpendicular to this axis. The film exhibited uniaxial in-plane magnetic anisotropy. The easy magnetization axis coincided with the axis of the barrel. The coercivity values were 1.7 and 1.9 Oe for easy and hard axes, respectively. The measured saturation magnetization was 780 G. Note that the hysteresis loops for the other films under study had a shape similar to that shown in Figure 2.

The measured frequency dependence of the microwave permeability for films of various thicknesses is presented in Figure 3. The lines in Figure 3 show the fitting of the measured permeability by the Lorentzian dispersion law, Equation (1). The frequency dependence of the imaginary part of the permeability for all films shows one peak, which is attributed to the ferromagnetic resonance. For films of thickness 0.33 µm or higher, both the static permeability and the ferromagnetic resonance frequency depend weakly on the film thickness. The resonance frequency is approximately 2 GHz.

The film of 0.19 µm in thickness has a lower value of the static permeability and a higher resonance frequency of 2.3 GHz. This is due to a higher magnetic anisotropy field in the thinnest film under study. The increase in the anisotropy field in this film is probably related to the magnetoelastic effect, which has been shown to be significant in amorphous CoFeB films [26,45,46]. When the studied film is rolled into a cylinder for the microwave measurements, stresses arise in the film that result in an additional contribution to the anisotropy field [42]. It was shown previously for cobalt films [47] that the relative contribution of the magnetoelastic effect to the microwave properties is significant for thin films and decreases with increasing film thickness. However, further studies of the influence of the magnetoelastic effect on the dynamic permeability of CoFeB films are needed.

It follows from Figure 3 that for films with a thickness of 0.33 µm and higher, the peak of the imaginary part of the permeability broadens, and the peak amplitude decreases with increasing film thickness. This may be related to the appearance of out-of-plane magnetic anisotropy and the exit of magnetization from the film plane. The Acher parameter k_A was calculated by using the fitting of the measured frequency dependences of the permeability by the Lorentzian dispersion law in order to study the appearance of out-of-plane magnetic anisotropy. To calculate the Acher parameter, we use the saturation magnetization value M₀ = 780 G obtained from magnetostatic measurements. The calculated Acher parameter depends slightly on the film thickness, and k_A ≈ 0.9 (see inset in Figure 3b).

The appearance of out-of-plane magnetic anisotropy has been observed previously in various nanocrystalline films. In particular, out-of-plane magnetic anisotropy in permalloy films can lead to the transition into a “transcritical state” [33,34,48,49,50]. This transition takes place when the film thickness exceeds a certain critical value. The critical thickness depends on the substrate properties and the film sputtering conditions and is typically several hundred nanometers [33,49]. The transition to a “transcritical state” leads to an increase in the coercivity of the film and a deterioration in its soft magnetic properties. As for the microwave properties of permalloy films, the appearance of out-of-plane magnetic anisotropy is accompanied by a decrease in both the static permeability and the ferromagnetic resonance frequency. As a result, the Acher parameter drops sharply by approximately two orders of magnitude with an increase in the film thickness [44,51]. A significant decrease in the Acher parameter was also observed in cobalt films on a PET substrate when the film thickness exceeded 100 nm [47]. In the studied CoFeB films, the Acher parameter is nearly constant up to a film thickness of 1.40 µm, and its value is close to unity. Therefore, thick CoFeB films retain in-plane magnetic anisotropy, and these films have an advantage over nanocrystalline films.

The deviation of the Acher parameter from unity may be related to the scattering of the anisotropy axis directions in the films under study. To suppress magnetic non-uniformity, the frequency dependence of the microwave permeability was measured under the bias magnetic field applied along the axis of the coaxial line. Figure 4 shows the measured frequency dependence of the permeability for the 0.33 µm thick film at different values of the bias field. With the magnetic field increase, the resonance frequency shifts toward higher frequencies, and the width of the peak of the imaginary part of the permeability becomes narrower. The calculated values of the Acher parameter increase monotonically from 0.90 to 1 with the bias field (see inset in Figure 4b). For all the films studied, the Acher parameter is equal to unity at a magnetic field of 800 Oe, which indicates that the films are in a saturated isotropic state.

Since out-of-plane magnetic anisotropy does not appear in the CoFeB films under study, it could be assumed that an increase in the damping factor β with the film thickness is related to the skin effect. The skin effect is caused by eddy currents induced by the microwave magnetic field. As a result of the influence of eddy currents, the measured permeability μ differs from the intrinsic permeability of the material μ_in [52]. The relationship between the measured and intrinsic permeability for a film of thickness d is given by the well-known expression [53]:

$$\mu ={\mu }_{\mathrm{in}}{\displaystyle \frac{\tan \mathrm{h}(kd/2)}{kd/2}}.$$

(3)

$$k=(1-i)2\pi {({\mu }_{\mathrm{in}}f/\rho c^2)}^{1/2}$$

(4)

Here, k is the wave propagation constant, ρ is the film resistivity, and c is the speed of light in a vacuum.

In the case of a strong skin effect, kd/2 >> 1, the frequency dependence of the imaginary part of the permeability splits into two distinct peaks. The low-frequency peak is associated with the skin effect, and the high-frequency peak is due to the ferromagnetic resonance [10]. At a weak skin effect, kd/2 << 1, a broadening of the single peak at the resonance frequency can be observed. The latter corresponds to experimental data, so below, the case of a weak skin effect is analyzed.

Further, we assume that the frequency dependence of the intrinsic permeability is described by the Lorentzian law (1) with β = β_in corresponding to the damping factor of the material. In the case of a weak skin effect, kd/2 << 1, Equation (3) can be rewritten as follows [52]:

$$\mu ={\mu }_{\mathrm{in}}[1-{(kd/2)}^2/3].$$

(5)

Substituting Equation (1) with β = β_in into Equation (5) and taking into account that μ_s >> 1, after simple algebraic transformations, we obtain for the measured permeability:

$$\mu ={\displaystyle \frac{{\mu }_{\mathrm{s}}}{1-i{\beta }_1(f/f_{\mathrm{res}})-{(f/f_{\mathrm{res}})}^2}}.$$

(6)

Here, the damping factor β₁ is given by

$${\beta }_1={\beta }_{\mathrm{in}}+{\displaystyle \frac{8{\pi }^2{d}^2{\mu }_{\mathrm{s}}{f}_{\mathrm{res}}}{3\rho c^2}}$$

(7)

The last term on the right-hand side of Equation (7) is responsible for the broadening of the Lorentzian curve due to the skin effect. Figure 5 shows a comparison of the measured and calculated frequency dependences of the dynamic permeability for different values of the film thickness. The calculations were carried out using Equations (6) and (7). The value of the resistivity ρ = 140 μOhm·cm used in the calculations was measured for a 1.40 µm thick film. The static permeability μ_s and ferromagnetic resonance frequency f_res were found from the approximation of experimental data by the Lorentzian frequency dispersion law. The only fitting parameter used in the calculations was the damping factor β_in of the material.

It follows from Figure 5b that the calculated frequency dependences of the imaginary part of the dynamic permeability are in good agreement with the measurement data. The highest discrepancy between the measurement and calculation results is observed for a film with a thickness of 1.40 µm.

Table 1. The values of the damping factors β and β₁ as a function of the film thickness d. The factor β was estimated by fitting experimental data according to the Lorentzian frequency dispersion law, Equation (1). The factor β₁ was calculated using Equation (7).

Film Thickness d, μm	Damping Factor β	Damping Factor β1
0.33	0.80	0.79
0.63	0.89	0.85
1.40	1.27	1.17

presents a comparison of the damping factor β estimated from the approximation of experimental data by Equation (1) and the damping factor β₁ calculated using Equation (7) at different values of the film thicknesses. The difference in factors β and β₁ is insignificant, even for a 1.40 µm thick film. Note that for the thickest film studied, there is another contribution to the damping, which may be related to the greater non-uniformity of the film. Thus, it was concluded that in the films under study, changes in the frequency dependence of the dynamic permeability with film thickness are mainly due to the skin effect.

4. Conclusions

The thickness effect on the microwave permeability of amorphous Co₆₇Fe₇B₂₆ films deposited on a flexible substrate was studied. It was observed that both the static permeability and the ferromagnetic resonance frequency remain unchanged even for relatively thick films, while the peak in the imaginary part of the microwave permeability decreases with film thickness growth. The Acher parameter, Equation (2), was used to analyze the change in the microwave permeability as a function of the film thickness. It was found that the Acher parameter for all studied CoFeB films is close to unity, which indicates the presence of in-plane magnetic anisotropy in the films.

The influence of the skin effect on the frequency dependence of the microwave permeability of CoFeB films was studied within the framework of a simple analytical model. The calculated results satisfactorily describe the changes in the microwave permeability with film thickness growth. The analysis shows that an increase in the damping factor with the film thickness is indeed due to the skin effect. The results obtained demonstrate that relatively thick, soft magnetic amorphous CoFeB films may be promising for various microwave applications.