The Kirkendall effect, which was discovered by Kirkendall [1] and Smigelskas [2], is a classical metallurgy phenomenon. It basically refers to the unequal atomic mobilities of different species through an interface accompanying the vacancy migration [3,4]. Typically, the Kirkendall voids tend to form in the fast-diffusion side due to the condensation of excess vacancies [5,6]. The diffusion-driven formation of Kirkendall voids in bulks materials is normally considered to deteriorate the interface performance [[7], [8], [9]]. For instance, formation of the Kirkendall voids reducing the area of the joining interface might cause solder joints failure in printed circuit board [10]. During last decade, studies of the Kirkendall effect have been extended from macroscopic to micro- and nanoscales [[11], [12], [13]]. This destructive effect is further applied to design hollow nanostructures of diverse morphologies [14] (i.e. nanoplatelets [15], nanotube [16] and nanocrystals [17]) and positively applied in various fields, including capacitors [18], ion batteries [19], photoelectrochemical performance [20] and microwave absorption [21]. Therefore, it is highly desirable for developing a method to modulate morphology and properties by controlling the Kirkendall effect in consideration of nontoxic, environmental friendless and non-contamination.

High magnetic fields (HMFs) with advantages of multifunctional efficiency and contactless interaction are verified to have effects on atom movement and vacancy migration [[22], [23], [24]]. This was first found in 1964 by Youdelis et al. [25]. They found that a 3 T magnetic field retarded the diffusivity of Cu in the Al/Al-3%Cu diffusion couples. Since then, the diffusion-related phenomena that occurred in the presence of HMFs attracted much attention of researchers [[26], [27], [28]]. Extensive efforts have been made on the application of HMFs to control mass transfer in bulk materials [[29], [30], [31]]. Nakajima et al. [32] observed that a 4 T magnetic field had no effect on the diffusion of Ni in Ti. Ren et al. [33] suggested that the growth of intermetallic phase in Ni-Al diffusion couples reduced by a 12 T magnetic field. Zhao et al. [34] reported that the interdiffusion coefficient of the Sn-3Ag-0.5Cu/Cu solder joints increased with increasing intensity of a high magnetic field during thermal aging treatment. Furthermore, our group carried out a lot of research on the diffusion with the application of HMFs in bulk materials [[35], [36], [37]] and in thin films diffusion couples [38,39]. It is worth mentioning that HMFs enhancing the Kirkendall effect in Cu-Ni bulk diffusion couple has been found in our previous study [40]. Recently, magnetic fields promoting the Kirekndall effect in silicon nanosphere has been discussed [41]. However, especially for thin films, the exact mechanism by which the HMFs influence the diffusion is still not understood well. Therefore, study of the mechanism how magnetic fields plays a role in the Kirkendall effect could contribute to better control of diffusion-related phenomenon, subsequent morphology evolution and properties improvement.

In consideration of the fast process from formation to evolution, it is not easy to observe the Kirkendall voids in thin films. Fortunately, the formation of Kirkendall voids indeed took place in Co films-native oxide Si (100) system in our previous work [42]. In the Co films-native oxide Si (100) substrate system, voids formation started in the Co films near the interface between Co and native oxide layer. The formation of the voids was attributed to the Kirkendall effect associated with the different diffusion rates of Co and Si atoms moving across the native oxide layer on Si (100) substrate surface. Motivated by the successful studies related to investigating the influence of HMFs on Kirkendall effect in bulk materials and nanoparticles, an 11.5 T magnetic field is applied to the Co films-native oxide Si (100) system during annealing in this paper. To the best of our knowledge, this is the first report in regard to the role of an HMF on the Kirkendall effect in thin films. Co films and Si substrate being selected is not only of academic interest but also of importance for practical applications [[43], [44], [45]].

Polycrystalline Co films were deposited onto the native oxide Si (100) substrate at an ambient temperature using home-made molecular beam vapor deposition (MBVD) device. The base pressure was 1.0 × 10^-4 Pa and remained in the 2.5 × 10^-4 Pa range during the sample preparation. Prior to the deposition process, the Si (100) substrates with native oxide layer were cleaned in alcohol and acetone in an ultrasonic tank, followed by deionized water rinsing and dried by using an argon gun with an ultra-high pressure. The Co films/native oxide Si (100) substrates used as the specimen of diffusion couple were put into an alumina crucible shown in Fig. 1(b).

Experiments were carried out under vacuum (1 × 10^-3 Pa) at the temperatures of 873, 973 and 1073 K for 30 min (heating rate is 5 K/min) in a vertical furnace located inside a superconducting magnet (JMTD-12T100, JASTEC, JPN), as shown in Fig. 1(a). Temperature was controlled by a programming thermometer with an R-type thermal couple (with the precision of ±1 K). The specimen was cooled to ambient temperature by furnace cooling after annealing. 0 and 11.5 T magnetic fields were applied to the diffusion couple during annealing. The direction of the external magnetic field was perpendicular to the Co film plane.

The thickness of Co films was maintained at 120 ± 2 nm, which was measured by using a Stylus Surface Profiler (DEKTAK 150, VEECO, USA). The surface morphology was detected by scanning electron microscopy (SEM, SU8010 N, HITACHI, Japan) equipped with energy dispersive spectroscopy (EDS). Transmission electron microscopy (TEM, JEM-2100 F, JEOL, Japan) was applied to investigate the morphology of the samples in cross-section. The magnetic properties of the Co films were determined by using a vibrating sample magnetometer (VSM, MODEL 7407, LAKESHORE, USA). The concentration-depth profiles were examined by X-ray photoelectron spectroscopy (XPS, ESCALAB 250, THERMO VG, USA).

Fig. 2 shows the results obtained from SEM imaging of samples annealed at 873, 973 and 1073 K under high magnetic fields of 0 and 11.5 T. It can be seen a slightly different contrast in brightness in Fig. 2(a), which reveal that the Co films annealed at 873 K were not fully homogeneous without a magnetic field. The Co films were more inhomogeneous at 873 K under an HMF because the brightness contrast became evident, as shown in Fig. 2(b). Upon further increase in annealing temperature to 973 K, highly dense voids occurred in Fig. 2(c). With the application of an 11.5 T magnetic field, some separated voids were clearly observed at 973 K in Fig. 2(d). Finally the network-like Co nanostructure geometry was seen at 1073 K shown in Fig. 2(e). Apparently, more isolated Co particles were formed and the spacing among the network-like nanostructures widened under HMF annealing shown in Fig. 2(f).

EDS mapping was used to identify the surface component of the Co films-native oxide Si (100) samples after annealing. Fig. 3 shows the EDS maps of the Co films-native oxide Si (100) samples with an HMF annealed at 873 and 1073 K. The light feature regions surrounded by a dark background were visible in the SEM images presented in Fig. 3(a) and (d). The Co maps are shown in Fig. 3(b) and (e), and Si maps in Fig. 3(c) and (f). It can be seen that Co atoms covered all substrate at 873 K, as shown in Fig. 3(b). However, the brightness of Co element in the light feature regions in Fig. 3(b) was much more obvious than that in the dark background. This verified the inhomogeneity of Co films. Upon annealing at 1073 K, the Co element was mainly distributed at the position of the light regions, while the Si element was distributed at the dark background, as shown in Fig. 3(e) and (f). This confirmed that the continuous Co films transformed into network-like nanostructures and then the substrate exposed. In order to quantitatively analyze the effects of high magnetic fields on the surface morphology of Co films on native oxide Si (100), the exposed area ratio of native oxide Si (100) substrate at 1073 K with and without high magnetic fields were measured from three SEM images of each sample by using the image analysis tool of Win ROOF software (MITANI, Japan). The percentage of exposed substrate areas were 49.1% ± 1.3% under a 0 T magnetic field and 61.3% ± 2.4% under an 11.5 T magnetic field, respectively. The HMF significantly promoted the substrate exposing.

To correlate with evolution of the surface morphology, cross-sectional TEM was examined shown in Fig. 4. Fig. 4(a) was the sample annealed at 873 K without an 11.5 T magnetic field. Some voids appeared near the interface of Co films and native oxide layer which highlighted by the white arrows. However, in the case of an 11.5 T magnetic field in Fig. 4(b), the voids already reached the substrate and some already merged due to voids growth. Upon further annealing, the voids continued to grow towards the substrate and Co free surface, as shown in Fig. 4(c). After applying a HMF in Fig. 4(d), the voids already reached the substrate and the Co free surface shown. The Co films dispersed into relatively large Co islands at 1073 K, as seen in Fig. 4(e). With the application of a HMF in Fig. 4(f), more sphere-like particles were formed. It can be clearly observed that the Co films increased in thickness and decreased in length with the increase of temperature and the application of an HMF.

Normalized ambient temperature hysteresis loops of Co-native oxide Si (100) samples annealed at different temperatures are shown in Fig. 5. The in-plane directions of all samples in Fig. 5(a) were considered an easy-axis of magnetization by comparing the out-of-plane M‒H curves in Fig. 5(b) owing to the smaller value of applied magnetic field required to reach the saturation. The out-of-plane M-H curves of in Fig. 5(b) show an almost linear behavior of magnetization and not reaching the saturation even at 4 kOe, indicating that this direction was a hard-axis of magnetization. The in-plane M‒H curves of the sample annealed at 873 K was typical of soft magnetic materials with a rather rectangle shape because of small coercive field and high remanence. See the blue hollow triangle symbol as shown in Fig. 5(a). With increasing annealing temperature further, the rectangle shape became weaker due to the larger coercive field and lower remanence. See the green solid circle and pink hollow diamond symbols as shown in Fig. 5(a).

Fig. 6 shows the normalized in-plane hysteresis loops measured at ambient temperature for the Co films annealed at 873, 973 and 1073 K on the native oxide Si (100). The hysteresis curves of Co films on native oxide Si annealed at 873 K shows typical soft magnetic properties. The Co films can reach the saturation with a small value of magnetic field. As the annealing temperature increased, the Co films cannot reach the saturation by applying the same value of magnetic field. The coercivity increased at 873 and 973 K but decreased at 1073 K under HMF annealing, which can be clearly seen from the insets in Fig. 6.

From the results above, notable surface morphology evolution of Co films on native oxide Si (100) during annealing under a magnetic field of 11.5 T were observed. The surface morphology changed via the voids initiating in the Co films near the interface of Co films and native oxide layer on Si (100) at 873 K, as shown by TEM results (Fig. 4(a)). The voids formation can be attributed to the nanoscale Kirkendall effect. This diffusion process was detected by XPS. Fig. 7 shows the Co and Si concentration profiles of the Co films-native oxide Si (100) samples vs. etching time. The two crossed curves represented atomic transport across the interface during annealing. An asymmetry in the concentration profiles demonstrated that Co diffusion into the Si substrate was more intensive than Si diffusion into the Co films. Upon annealing at 873 K shown in Fig. 7(a), Co concentration firstly decreased from 100 to 93 at.% and Si concentration increased from 0 to 7 at.% before 120 s of etching time without an HMF. Until 850 s of etching time, the Co concentration began to decrease gradually. After applying an 11.5 T magnetic field, the concentration of Co firstly decreased from 100 to 87 at.% and Si increased from 0 to 13 at.% before 120 s of etching time. Then the Co concentration began to decrease from 500 s of etching time. This indicates that an HMF promoted the interdiffusion process of Co and Si atoms which resulted in the decrease of Co concentration and increase of Si concentration compared with non-field case. It is worth noting that the Co concentration decreased to 0 at.% at 1700s with a 0 T magnetic field while decreased to 0 at.% at 1850s with an 11.5 T magnetic field. The Co atoms diffused deeper into the Si substrate by an HMF. Furthermore, the Si concentration overpassed that of Co from 1100s in the non-field case but from 800 s in the HMF case. It is because the voids became larger (Fig. 4(a) and (b)) as a result of accelerating Kirkendall effect caused by an HMF. Hence, the etching time was shorter since less Co left. Upon further increase in annealing temperature to 973 K in Fig. 7(b), there was a definite segregation of Si atoms at the free surface of Co films. In the non-field case, the concentration of Co firstly decreased to 80 at.% and Si increased to 20 at.% before 1000s of etching time. The decrease of Co concentration and increase of Si concentration were due to the enhanced interdiffusion with increasing annealing temperature. Then the Co concentration gradually decreased to 0 at.% at 3000 s of etching time. The Co atoms diffused deeper into the Si substrate with the increase of annealing temperature. Under an HMF, the concentration of Co firstly decreased to 80 at.% and Si increased to 20 at.% before 1250s of etching time. The HMF accelerating the diffusion of Co atoms into the Si substrate led to the Co concentration decreasing to 0 at.% at 3250 s of etching time. However, the Si concentration overpassed that of Co from 1600s of the sample annealed with an HMF. The etching time became longer than in the non-field case (1400s) at 973 K. Changes in the concentration profiles were pronounced at elevated temperature, as shown in Fig. 7(c). There was an increased segregation of Si towards the free surface. The Co concentration decreased to 0 at.% at 4500 s of etching time with a 0 T magnetic field. There was an increased interdiffusion of Co and Si atoms when the temperature was up to 1073 K. After 240 s of etching time, the Si concentration began to increase because of the substrate exposure. In addition, the Co and Si elements were strongly intermixed from 400 to 2000s of etching time. After applying a magnetic field of 11.5 T, the Si concentration began to increase after 100 s of etching time. This etching time became shorter because the exposed substrate areas were larger than non-field case, which was visible seen from Fig. 2(e) and (f). When the concentration profile went from 300 to 1500s of etching time, the compositions of Co and Si elements levelled off. It seems that Co and Si formed a fairly homogeneous intermixed layer (The atomic ratio of Co:Si was 4:6). However, note that the Co signal should originate from the Co islands on the substrate and the Si signal should originate from the substrate. The etching time of Co concentration decreasing to 0 at.% was more than 4500 s because the diffusion of Co atoms was promoted by an 11.5 T magnetic field.

The nanoscale Kirkendall effect can be found in the Co films-native oxide Si (100) system owing to the different diffusion fluxes of Co and Si atoms moving across the native oxide layer on Si (100) substrate surface. The Si oxide layer acted as an effective diffusion barrier avoiding mobility of metal into Si substrate and Si out-diffusion during annealing [46,47]. However, several studies have been found that the metal in thin films can diffuse to the Si substrate without detectable modification of the amorphous oxide layer at a comparatively high annealing temperature, such as in Cu-Ni alloy/SiO₂/Si (100) [48], Ni/native SiO₂/Si (100) [49], and Co/SiO_x/ Si substrate [50]. Metal and Si atoms interdiffusion can be facilitated by high defects concentration in amorphous oxide layer [51]. In our case, the native oxide layer on the Si (100) was confirmed as amorphous SiO₂ by TEM and XPS in our pervious study [52]. Therefore, the diffusion path in the SiO₂ layer is the interstices of the very open SiO₂ structure [53,54]. The Co atoms migrate along the interstices as diffusion channels without any chemical interaction with SiO₂ layer. The faster Co diffusion rate in defect-rich areas leads to the Kirkendall effect in Co films-native oxide Si (100) system.

It is known that the real driving force for diffusion is the chemical potential gradient from the point of thermodynamics. For the diffusion of a constituent element i, the driving force ${{F}_{i}}$ is defined by:

Where, ${\mu }_{i}$ is the chemical potential, and $x$ is the displacement of the element $i$. The diffusion flux $J$ is expressed as:

Where, ${{\rho }_{i}}$ is the mass concentration of the element $i$, and ${{v}_{i}}$ is the average diffusion velocity. Here ${{v}_{i}}$ is directly proportional to ${{F}_{i}}$:

Where, ${{m}_{i}}$ is the velocity of unit driving force, i.e., the migration rate of element $i$. Substituting Eqs. (1) and (3) into Eq. (2) yields:

In the case of sample annealed without an HMF, the chemical potential of the constituent element $i$ is given by:

Where, ${{G}_{i}}$ is the standard Gibbs free energy, ${{\alpha }_{i}}$ is the activity of the constituent element, ${{\gamma }_{i}}$ is the activity coefficient, and ${{M}_{i}}$ is the mole percent. The diffusion flux in Eq. (4) can be calculated by employing Eq. (5):

According to the Fick’s first law:

Where, $D$ is the diffusion coefficient. Thus, the diffusion coefficient can be determined from Eqs. (6) and (7):

In the case of sample annealed with an HMF, the chemical potential in Eq. (5) should be modified to include an additional energy:

Where, $E$ is a term of magnetic free energy. Applying this relationship into Eq. (4), the diffusion flux under an HMF can be estimated as:

The diffusion coefficient with a high magnetic field would amount to:

.Comparing with the non-field condition, the ${{D}_{\text{H}}}$ is larger than the $D$ in Eq. (8) because of the additional item related to magnetic free energy $E$. Therefore, the application of an HMF accelerates the diffusion coefficient, and in turn enhances the nanoscale Kirkendall effect. Furthermore, E/kT decreasing results in a decrease in ${{D}_{\text{H}}}$ when the annealing temperature $T$ increases. This demonstrates that the effect of the magnetic field on diffusion is retarded with increasing thermal field.

The whole process of morphology evolution can be illustrated by a schematic diagram, as shown in Fig. 8. The diffusion of Co atoms is faster than that of the Si through the native oxide layer, which could produce a net flux of vacancies from Si substrate to Co films shown in Fig. 8(a). The Kirkendall voids nucleation in Fig. 8(c) via clustering of excess vacancies occurs near the interface of Co films and native oxide layer. Areas where the voids appear indicate the location of high defects concentration which provide preferential diffusion pathways for Co diffusion in native oxide layer. Owing to the appearance of the voids, the SEM image in Fig. 2(a) shows the different brightness contrast. The diffusion of Co atoms into the Si substrate is enhanced by enhanced Kirkendall effect under an HMF, as shown in Fig. 8(b). Therefore, the voids grow and subsequently touch the substrate shown in Fig. 8(d). When the voids reach the substrate, the enlargement of the Kirkendall voids could be contributed by the diffusion of Co atoms along the voids surface. The brightness contrast in Fig. 2(b) became evident because of the voids growth. The interdiffusion of Co and Si elements is reinforced at elevated temperature. The voids continue to grow and perforate the Co films, which cause the open holes and underlying substrate exposing (Fig. 2(c)). In the presence of an 11.5 T magnetic field, the density of open holes is increased by the enhanced diffusion of Co atoms (Fig. 2(d)). After annealing to 1073 K, the Co films become semicontinuous shown in Fig. 8(e). After applying an HMF, the Co films agglomerate into individual islands and nanoparticles shown in Fig. 8(f). This is because the remaining Co films will be thermodynamically unstable after the open holes formation. The total energy of Co films/native oxide Si (100) system tends to minimize. The HMF could facilitate to reduce the surface energy of Co films and interface energy of Co films-native oxide layer. The remaining Co films on the substrate tend to become a sphere to decrease the surface and interface area in the presence of an 11.5 T magnetic field. Therefore, the size and height of Co islands and nanopaticles increase under an HMF due to the Co islands retraction and more sphere-like Co particles, as observed from TEM and AMF results at 973 and 1073 K.

The magnetic properties have a significance relationship with the morphology evolution of Co films on native oxide Si (100) substrate. The morphology change begins with a continuous film to the islands and sphere-like shape particles. This morphology evolution causes a rearrangement of magnetization that is not forced into film plane any more but it lies into islands giving rise to a more isotropic magnetic behavior [55]. Thus though the magnetic easy axis was still the in-plane direction, the rectangle shape of soft magnetic films became weaker with increasing annealing temperature. We will only discuss the magnetic properties of magnetization easy-axis of Co-native oxide Si (100) samples annealed with and without high magnetic fields. Because the network-like Co islands annealed at 1073 K show much lower magnetic anisotropy than the Co films with increasing annealing temperature, the rectangle shape became weaker. The coercivity increased under an 11.5 T magnetic field at 873 and 973 K, as shown in Fig. 6(a) and (b). This can be attributed to the voids growth caused by the accelerating Kirkendall effect. It can be seen from the TEM results in Fig. 4(a) and (b), and SEM results in Fig. 2(c) and (d), the voids size and density were increased in the presence of an HMF. The voids acting as pinning site are further to impede domain wall motion under an HMF. However, the coercivity in Fig. 6(c) decreased after applying an 11.5 T magnetic field at 1073 K. The semi-continuous Co films transformed into isolated Co islands and nanopaticles (see Fig. 2(e) and (f)), which reduce the dipolar interactions between the islands and particles.

A high magnetic field was applied to the Co films-native oxide Si (100) system with increasing annealing temperature. The kirkendall voids enlarged in the presence of high magnetic fields. The enhanced nanoscale Kirkendall effect can result from an increase in the chemical potential gradient induced by magnetic free energy in a high magnetic field. The Co films on native oxide Si (100) transformed from continuous to isolated Co islands and particles as the annealing temperature increased to 1073 K under an 11.5 T magnetic field. The morphology of Co films changed dramatically along with the Kirkendall voids development and substrate exposure due to the lowering of total energy (surface energy of Co, and interface energy of Co and native oxide layer on Si). The increase of size and density of voids with an 11.5 T magnetic field resulted in the increase of coercivity at 873 and 973 K. Nevertheless, the coercivity was reduced by the increase of the spacing of Co islands with an 11.5 T magnetic field at 1073 K. The present exploration provides insights into the HMFs technique to tailor morphology and properties by accelerating Kirkendall effect in thin films.

This work was financially supported by the National Natural Science Foundation of China (Nos. 51425401, 51690162), Liaoning Innovative Research Team in University (No. LT2017011), the Fundamental Research Funds for the Central Universities (Nos. N160907001, N180915002 and N180912004).