Oxidation Behavior, Insulation Resistance, and Permeability of FeSiCr Alloys for Multilayer Inductors

: FeSiCr alloys are used as soft magnetic materials for power multilayer inductors. The alloys are typically annealed at intermediate temperatures in air during inductor fabrication to form an insulating chromium oxide layer around the alloy particles. The variation of the annealing temperature between 700 ◦ C and 900 ◦ C in air, and, for the ﬁrst time, the variation of the oxygen partial pressure during annealing at 900 ◦ C are studied, and their effects on the alloy’s oxidation behavior, phase formation, insulation resistance, and permeability are demonstrated. The chromium oxide content increases up to about 12 wt% with annealing temperature in air, whereas it decreases to 8.2 wt% after annealing at 900 ◦ C and 0.001% O 2 . The observed mass changes during annealing conﬁrm the various tendencies towards oxidation. This oxidation behavior is reﬂected in an increase in the insulation resistance with annealing temperature or in a resistance reduction with decreasing oxygen partial pressure. The permeability decreases from µ = 22 after annealing at 700 ◦ C to µ = 18.5 at 900 ◦ C in air. The reduction of p O2 during annealing at 900 ◦ C leads to an increase in permeability up to µ = 22.5 at p O2 = 0.001% O 2 . The results can be used to design coﬁring strategies using reduced oxygen partial pressure for new composite multilayer inductive components consisting of FeSiCr-and ferrite layers in combination with silver metallization.


Introduction
Soft magnetic materials and composites (SMC) have numerous applications in modern portable electronic device applications [1]. The need of miniaturization and the low profile of inductive components for portable devices has led to the development of new power inductive devices. This is in line with the observed trend from one DC-DC converter in the power circuitry to a point-of-load (POL) concept with many smaller converters as a power source for individual ICs or modules. Moreover, the operating voltages of modules in a device might be different, requiring individual and miniaturized DC-DC converters to convert the power provided by the battery into the various circuit blocks. FeSiCr alloys have been proposed as suitable magnetic materials for the fabrication of power multilayer inductors [2,3]. As compared to Ni-Cu-Zn ferrites, which are typically used in multilayer inductors, the soft magnetic alloys have benefits of high saturation magnetization and good DC-superposition characteristics and, hence, are able to withstand higher current densities without a significant reduction of the inductance [2,3]. One critical issue is the low resistivity of the alloy. Low power losses, P v , of the soft magnetic alloy are required for high-frequency applications. Since eddy current losses P e are a major contribution to P v , the resistivity of the alloy needs to be increased in order to reduce P e . Therefore, it is very important to provide sufficient insulation resistance, which is realized by creating a thin insulating oxide layer at the surface of the alloy particles during annealing and multilayer fabrication. It was demonstrated that high compaction pressures are needed to achieve sufficient densification, and that subsequent annealing in the temperature range between 700 • C and 850 • C leads to the formation of an insulating chromia layer with the Alloys 2022, 1 289 resistivity increasing with annealing temperature [4]. Many other studies have focused on increasing the resistivity by coating the alloy particles. Insulating coatings are typically classified as organic, inorganic, and composite coatings. Organic coatings are primarily thermosetting materials, such as epoxy resins, phenolic resins or polyimides. Examples of inorganic coatings include phosphates [5], silica [6], MgO [7], alumina [8], or ferrites [9].
Another problem in multilayer chip fabrication arises from the interaction of FeSiCr with the Ag inner electrode material during thermal processing in air. It was observed that Ag reacts with the Cr 2 O 3 layer to form semiconducting AgCrO 2 delafossite-type oxide, reducing the insulation resistance and decreasing the inductor performance [10]. It has been observed that the annealing of FeSiCr-based multilayer inductors in nitrogen allows us to enhance the inductance by suppressing non-magnetic phase formation, but re-annealing in air is required to generate sufficient insulation resistance [11]. Thus, it seems that the oxygen partial pressure is another variable in addition to the annealing temperature to tailor the electromagnetic properties of FeSiCr alloys and the corresponding inductors. However, the effect of oxygen partial pressure upon annealing on the oxidation layer formation and the corresponding electromagnetic properties has not been systematically studied. Hence, it is desirable to investigate the role of oxygen partial pressure during annealing for the performance optimization of FeSiCr-based power multilayer inductors. In addition, a new concept of combining FeSiCr and Ni-Cu-Zn ferrites with Ag metallization to give a composite multilayer inductor was proposed recently [12], and annealing protocols include T and p O2 as variables as well.
In this study, we have investigated, for the first time, the influence of oxygen partial pressure during annealing at 900 • C of a FeSiCr alloy on the phase formation, insulating Cr oxide layer formation, resistivity, and permeability. We contrast the effect of the annealing temperature in air with that of the oxygen partial pressure (from 0.21 atm down to 10 −5 atm) during the annealing of FeSiCr compacts at 900 • C. The results indicate that annealing at 900 • C under lower p O2 leads to decreasing insulation resistance and higher permeability. Annealing at intermediate p O2 , on the other hand, provides sufficient insulation resistance and opens a new process window for the firing of multilayer power inductors.

Materials and Methods
A commercial FeSiCr powder was used with a composition of 90.3 wt% Fe, 5.4 wt% Si, and 4.3 wt% Cr (Chung Yo Materials Co., Ltd., Kaohsiung, Taiwan). The powder was mixed with a polyvinyl alcohol solution and dried at 95 • C. Pellets and toroids were uniaxially dry pressed with a pressure of 100 MPa. The samples were heated for binder burnout with 1 K/min to 300 • C and annealed for 5 h in air. In the first experimental series, the samples were further annealed with a 5 K/min heating and cooling rate to temperatures between 700 • C and 900 • C with a dwell time of 1 h. In the second series, the samples were annealed at 900 • C with a 1 h dwell time in a gas atmosphere with oxygen partial pressures between 0.21 atm (21%) and 10 −5 atm (0.001%) using a computer-controlled gas-mixing unit with mass flow controllers. The p O2 was measured directly at the sample position in the tube furnace with a zirconia-based oxygen sensor system (Zirox GmbH, Greifswald, Germany).
The specific surface area S of the powders was determined from nitrogen adsorption isotherms (BET, Nova 2000, Quantachrome Instruments, Boynton Beach, FL, USA); a mean particle size d BET was estimated using as d BET = 6/ρ·S (with density ρ; assuming spherical particles). The particle size was characterized using laser diffraction (Mastersizer, Malvern Panalytical GmbH, Kassel, Germany). The shrinkage of a cylindrical compact was measured using a Netzsch DIL402 dilatometer (Netzsch-Gerätebau GmbH, Germany) during heating to 1000 • C with a 5 K/min heating rate. Thermal analysis was performed using a TG/DTA 92-16.18 system (Seteram, Caluire, France). The microstructure of the samples was studied on polished samples with a scanning electron microscope (SEM, Ultra 55, Zeiss Microscopy GmbH, Jena, Germany). Elemental analysis was performed using a Bruker EDX system. The phase formation of the materials was evaluated using X-ray diffraction (XRD) with Cu-K α radiation (15-90 • , 3 s, 0.015 • /step, Advance D8, Bruker Alloys 2022, 1 290 AXS, Karlsruhe, Germany). Rietveld refinements were performed using the software Topas version 6 (Bruker AXS). The resistivity of the samples was measured using a two-point measurement set-up after contacting the samples with silver paste. The permeability of sintered toroids was measured using an Agilent E4991A impedance/material analyzer (Keysight Techn., Santa Rosa, CA, USA) in the frequency range from 1 MHz to 1 GHz.

Results
The morphological properties of the FeSiCr powder were studied. The particle size distribution as obtained from laser diffraction revealed a mean particle site of d 50 = 10.3 µm (Figure 1a) with a broad distribution of sizes (d 10 = 4.1 µm, d 90 = 28.6 µm). The specific surface area was found to be S = 0.3 m 2 /g. This translates into a mean particle size of the primary particles of d BET = 2.6 µm. SEM micrographs confirmed that the powder consisted of agglomerates with a size between 5 and 30 µm, built from smaller particles of around 1-3 µm in size.
performed using a TG/DTA 92-16.18 system (Seteram, Caluire, France). The microstructure of the samples was studied on polished samples with a scanning electron microscope (SEM, Ultra 55, Zeiss Microscopy GmbH, Jena, Germany). Elemental analysis was performed using a Bruker EDX system. The phase formation of the materials was evaluated using X-ray diffraction (XRD) with Cu-Kα radiation (15-90°, 3 s, 0.015 °/step, Advance D8, Bruker AXS, Karlsruhe, Germany). Rietveld refinements were performed using the software Topas version 6 (Bruker AXS). The resistivity of the samples was measured using a two-point measurement set-up after contacting the samples with silver paste. The permeability of sintered toroids was measured using an Agilent E4991A impedance/material analyzer (Keysight Techn., Santa Rosa, CA, USA) in the frequency range from 1 MHz to 1 GHz.

Results
The morphological properties of the FeSiCr powder were studied. The particle size distribution as obtained from laser diffraction revealed a mean particle site of d50 = 10.3 µm (Figure 1a) with a broad distribution of sizes (d10 = 4.1 µm, d90 = 28.6 µm). The specific surface area was found to be S = 0.3 m 2 /g. This translates into a mean particle size of the primary particles of dBET = 2.6 µm. SEM micrographs confirmed that the powder consisted of agglomerates with a size between 5 and 30 µm, built from smaller particles of around 1-3 µm in size. The oxidation behavior of the FeSiCr powder was investigated using thermal analysis. The mass gain of the powder as a function of temperature, as determined with thermogravimetry (TG), signaled the start of an oxidation process at about 300 °C in air (Figure 2a), slowly increasing into a significant mass increase at about 600 °C, and reaching a mass gain of about 1.2% at 900 °C. Contrarily, no mass gain was observed in a gas atmosphere with pO2 = 10 −5 atm. Simultaneously, the expansion of a powder pellet as a function of temperature in air atmosphere determined using a dilatometer indicated an almost constant expansion up to a maximum at about 625 °C, where the thermal expansion of the FeSiCr phase seemed to be overshadowed by another process leading to shrinkage at a higher temperature (Figure 2a). The observed mass gain originated from partial oxidation of the alloy and the formation of a layer of Cr2O3 (as shown later). This tendency towards oxidation was also monitored by measuring the weight change of the samples upon annealing. Annealing for 1 h in air led to a mass gain increasing with temperature ( Figure  2b), reaching 2% at 900 °C. On the other hand, the observed mass gain decreased with decreasing partial pressure in the atmosphere during annealing for 1 h at 900 °C ( Figure  2c), indicating a significant lower tendency towards oxidation and Cr2O3 formation. The oxidation behavior of the FeSiCr powder was investigated using thermal analysis. The mass gain of the powder as a function of temperature, as determined with thermogravimetry (TG), signaled the start of an oxidation process at about 300 • C in air (Figure 2a), slowly increasing into a significant mass increase at about 600 • C, and reaching a mass gain of about 1.2% at 900 • C. Contrarily, no mass gain was observed in a gas atmosphere with p O2 = 10 −5 atm. Simultaneously, the expansion of a powder pellet as a function of temperature in air atmosphere determined using a dilatometer indicated an almost constant expansion up to a maximum at about 625 • C, where the thermal expansion of the FeSiCr phase seemed to be overshadowed by another process leading to shrinkage at a higher temperature ( Figure 2a). The observed mass gain originated from partial oxidation of the alloy and the formation of a layer of Cr 2 O 3 (as shown later). This tendency towards oxidation was also monitored by measuring the weight change of the samples upon annealing. Annealing for 1 h in air led to a mass gain increasing with temperature ( Figure 2b), reaching 2% at 900 • C. On the other hand, the observed mass gain decreased with decreasing partial pressure in the atmosphere during annealing for 1 h at 900 • C (Figure 2c We also monitored the temperature and oxygen partial pressure during annealing in the furnace next to the sample position. The obtained in situ annealing protocols are shown in Figure 3. For annealing at various temperatures in air, the observed temperature-time protocols indicated a regular annealing process; the pO2 was close to the expected value of 0.21 atm ( Figure 3a). However, during annealing at various oxygen partial pressures, a different picture emerged: the pO2 remained stable and constant in air atmosphere, but with nominally decreasing oxygen partial pressure, the pO2 signal from the oxygen sensor decreased below the nominal pO2 value already during the heating period, showing much lower values of pO2 during the dwell time of the anneals. For example, at nominal pO2 = 10 −5 atm, the pO2 close to the sample position rapidly decreased upon heating and reached values as low as 10 −16 atm during heating at 900 °C. This behavior demonstrated that FeSiCr soaked up all available oxygen in the gas atmosphere with reduced oxygen concentration, thus locally generating very reducing atmospheric conditions.  We also monitored the temperature and oxygen partial pressure during annealing in the furnace next to the sample position. The obtained in situ annealing protocols are shown in Figure 3. For annealing at various temperatures in air, the observed temperature-time protocols indicated a regular annealing process; the p O2 was close to the expected value of 0.21 atm (Figure 3a). However, during annealing at various oxygen partial pressures, a different picture emerged: the p O2 remained stable and constant in air atmosphere, but with nominally decreasing oxygen partial pressure, the p O2 signal from the oxygen sensor decreased below the nominal p O2 value already during the heating period, showing much lower values of p O2 during the dwell time of the anneals. For example, at nominal p O2 = 10 −5 atm, the p O2 close to the sample position rapidly decreased upon heating and reached values as low as 10 −16 atm during heating at 900 • C. This behavior demonstrated that FeSiCr soaked up all available oxygen in the gas atmosphere with reduced oxygen concentration, thus locally generating very reducing atmospheric conditions. We also monitored the temperature and oxygen partial pressure during annealing in the furnace next to the sample position. The obtained in situ annealing protocols are shown in Figure 3. For annealing at various temperatures in air, the observed temperature-time protocols indicated a regular annealing process; the pO2 was close to the expected value of 0.21 atm (Figure 3a). However, during annealing at various oxygen partial pressures, a different picture emerged: the pO2 remained stable and constant in air atmosphere, but with nominally decreasing oxygen partial pressure, the pO2 signal from the oxygen sensor decreased below the nominal pO2 value already during the heating period, showing much lower values of pO2 during the dwell time of the anneals. For example, at nominal pO2 = 10 −5 atm, the pO2 close to the sample position rapidly decreased upon heating and reached values as low as 10 −16 atm during heating at 900 °C. This behavior demonstrated that FeSiCr soaked up all available oxygen in the gas atmosphere with reduced oxygen concentration, thus locally generating very reducing atmospheric conditions. The samples obtained after annealing at different temperatures in air, or at different pO2 values at 900 °C, were investigated using electron microscopy. EDX maps of samples annealed in air between 700 and 900 °C indicated the formation of a Cr2O3 layer at the surface of the alloy particles (Figure 4). The O-and Cr-maps showed a layer of Cr and O The samples obtained after annealing at different temperatures in air, or at different p O2 values at 900 • C, were investigated using electron microscopy. EDX maps of samples annealed in air between 700 and 900 • C indicated the formation of a Cr 2 O 3 layer at the surface of the alloy particles (Figure 4). The O-and Cr-maps showed a layer of Cr and O connecting the larger alloy particles, with the thickness of the Cr 2 O 3 layer increasing with annealing temperature (Figure 4). This tendency towards oxidation and the oxide layer formation agrees well with the results from thermogravimetry (TG, Figure 2a) and the mass change during annealing (Figure 2b), indicating an enhancement of mass with annealing temperature.
Alloys 2022, 2, FOR PEER REVIEW connecting the larger alloy particles, with the thickness of the Cr2O3 layer increasin annealing temperature (Figure 4). This tendency towards oxidation and the oxide formation agrees well with the results from thermogravimetry (TG, Figure 2a) an mass change during annealing (Figure 2b), indicating an enhancement of mass wi nealing temperature. Annealing of the samples at 900 °C at different reduced oxygen partial pre from 0.21 atm down to 10 −5 atm was mirrored in less intense oxidation and Cr2O3 s layer formation as compared to air ( Figure 5). Correspondingly, the TG curve rec during annealing in nitrogen with pO2 = 10 −5 atm did not reveal any mass uptake ( 2a), and the mass change of the samples during a 1 h anneal at 900 °C in that gas a phere was very small (Figure 2c). These findings indicate that the formation of a surface layer was less pronounced under decreasing pO2 in the surrounding gas a phere.  Annealing of the samples at 900 • C at different reduced oxygen partial pressures from 0.21 atm down to 10 −5 atm was mirrored in less intense oxidation and Cr 2 O 3 surface layer formation as compared to air ( Figure 5). Correspondingly, the TG curve recorded during annealing in nitrogen with p O2 = 10 −5 atm did not reveal any mass uptake (Figure 2a), and the mass change of the samples during a 1 h anneal at 900 • C in that gas atmosphere was very small (Figure 2c). These findings indicate that the formation of a Cr 2 O 3 surface layer was less pronounced under decreasing p O2 in the surrounding gas atmosphere.
Alloys 2022, 2, FOR PEER REVIEW connecting the larger alloy particles, with the thickness of the Cr2O3 layer increasing annealing temperature (Figure 4). This tendency towards oxidation and the oxide formation agrees well with the results from thermogravimetry (TG, Figure 2a) an mass change during annealing (Figure 2b), indicating an enhancement of mass wit nealing temperature. Annealing of the samples at 900 °C at different reduced oxygen partial pres from 0.21 atm down to 10 −5 atm was mirrored in less intense oxidation and Cr2O3 su layer formation as compared to air ( Figure 5). Correspondingly, the TG curve reco during annealing in nitrogen with pO2 = 10 −5 atm did not reveal any mass uptake (F 2a), and the mass change of the samples during a 1 h anneal at 900 °C in that gas at phere was very small (Figure 2c). These findings indicate that the formation of a C surface layer was less pronounced under decreasing pO2 in the surrounding gas at phere.  In addition, the element concentrations of Fe, Si, and Cr in the FeSiCr particles were determined using EDX (measurement of five point-scans in the particle centers). It is interesting to note, that after annealing in air, the Cr concentration within the alloy particles decreased with increasing annealing temperature, whereas the Fe concentration increased, and the Si content remained more or less unchanged (Figure 6a). This observation might be interpreted as the increasing diffusion of Cr out of the alloy particles with increasing annealing temperature, as the formation of the Cr 2 O 3 surface layer requires the diffusion of Cr from the bulk of the particles to the surface. After annealing at 900 • C, the Cr concentration in the alloy particles decreased to about 1 wt% as compared to about 4% in the initial alloy. Consequently, the Fe concentration in the alloy particles increased. If the samples were annealed at 900 • C in reduced p O2 , the Cr concentration in the alloy slightly increased with decreasing p O2 , indicating the reduced formation of a chromia surface layer and, hence, increased Cr content in the alloy particles (Figure 6b).
Alloys 2022, 2, FOR PEER REVIEW 6 In addition, the element concentrations of Fe, Si, and Cr in the FeSiCr particles were determined using EDX (measurement of five point-scans in the particle centers). It is interesting to note, that after annealing in air, the Cr concentration within the alloy particles decreased with increasing annealing temperature, whereas the Fe concentration increased, and the Si content remained more or less unchanged (Figure 6a). This observation might be interpreted as the increasing diffusion of Cr out of the alloy particles with increasing annealing temperature, as the formation of the Cr2O3 surface layer requires the diffusion of Cr from the bulk of the particles to the surface. After annealing at 900 °C, the Cr concentration in the alloy particles decreased to about 1 wt% as compared to about 4% in the initial alloy. Consequently, the Fe concentration in the alloy particles increased. If the samples were annealed at 900 °C in reduced pO2, the Cr concentration in the alloy slightly increased with decreasing pO2, indicating the reduced formation of a chromia surface layer and, hence, increased Cr content in the alloy particles (Figure 6b). The results of an XRD study confirm the tendency towards oxidation upon annealing in air (Figure 7a). The initial alloy powder exhibited peaks of the alloy with a body-centered lattice typical of α-Fe [13]. Peaks of a corundum-type structured Cr2O3 phase [14] started to appear at 750 °C with their intensity increasing with the annealing temperature. After annealing at 900 °C, the main peaks of chromia clearly appeared. The concentration of the formed Cr2O3 phase was determined using Rietveld refinements, and the results are shown in Figure 8a. The chromia content was practically zero in the initial powder and increased to 12.2(3) % after annealing at 900 °C. Simultaneously, the lattice parameter a0 of the body-centered cubic alloy phase decreased from a0 = 2.8601(1) Å of the initial alloy to a0 = 2.8580(1) Å for the 900 °C annealed sample. The decrease in the cubic lattice parameter reflects the change in the alloy composition, as Cr tended to diffuse to the alloy particle surface to be oxidized into Cr2O3; therefore, the alloy contained less Cr and more Fe with increasing annealing temperature (Figure 6a). It has been demonstrated that the cubic lattice parameter in the body-centered Fe-Cr alloy system increases with the Cr content, even more than expected according to linear Vegard's rule [15,16]. The results of an XRD study confirm the tendency towards oxidation upon annealing in air (Figure 7a). The initial alloy powder exhibited peaks of the alloy with a body-centered lattice typical of α-Fe [13]. Peaks of a corundum-type structured Cr 2 O 3 phase [14] started to appear at 750 • C with their intensity increasing with the annealing temperature. After annealing at 900 • C, the main peaks of chromia clearly appeared. The concentration of the formed Cr 2 O 3 phase was determined using Rietveld refinements, and the results are shown in Figure 8a. The chromia content was practically zero in the initial powder and increased to 12.2(3) % after annealing at 900 • C. Simultaneously, the lattice parameter a 0 of the body-centered cubic alloy phase decreased from a 0 = 2.8601(1) Å of the initial alloy to a 0 = 2.8580(1) Å for the 900 • C annealed sample. The decrease in the cubic lattice parameter reflects the change in the alloy composition, as Cr tended to diffuse to the alloy particle surface to be oxidized into Cr 2 O 3 ; therefore, the alloy contained less Cr and more Fe with increasing annealing temperature (Figure 6a). It has been demonstrated that the cubic lattice parameter in the body-centered Fe-Cr alloy system increases with the Cr content, even more than expected according to linear Vegard's rule [15,16]. Alloys 2022, 2, FOR PEER REVIEW 7  If the samples were annealed at 900 °C in various oxygen partial pressures, then the tendency towards the formation of Cr2O3, as observed in air, was significantly reduced. After annealing in gas atmospheres with lower pO2, the intensity of the Cr2O3 peaks decreased (Figure 7b). Rietveld refinements confirmed a decrease in the Cr2O3 concentration in the annealed samples and reached about 8(1) wt% at pO2 = 10 −5 atm (Figure 8b). At the same time, the cubic alloy lattice parameter increased with decreasing pO2, indicating an increase in the Cr content in the alloy and, consequently, less Cr2O3 surface layer formation (Figure 8b).
The formation of insulating Cr2O3 layers at the surface of the alloy particles directly affected the electrical resistivity. The increasing Cr2O3 layer thickness formed with increasing annealing temperature in air led to an increase in resistivity by about one order of magnitude (Figure 9a). Similar results were reported by Hsiang et al. [4]. On the other hand, a decrease in pO2 at 900 °C tended to slow down the formation of this chromia surface layer (Figure 8b). Consequently, a reduction of resistivity by about one order of magnitude was observed upon changing the pO2 from air to 10 −5 atm (Figure 9b).  If the samples were annealed at 900 °C in various oxygen partial pressures, then the tendency towards the formation of Cr2O3, as observed in air, was significantly reduced. After annealing in gas atmospheres with lower pO2, the intensity of the Cr2O3 peaks decreased (Figure 7b). Rietveld refinements confirmed a decrease in the Cr2O3 concentration in the annealed samples and reached about 8(1) wt% at pO2 = 10 −5 atm (Figure 8b). At the same time, the cubic alloy lattice parameter increased with decreasing pO2, indicating an increase in the Cr content in the alloy and, consequently, less Cr2O3 surface layer formation (Figure 8b).
The formation of insulating Cr2O3 layers at the surface of the alloy particles directly affected the electrical resistivity. The increasing Cr2O3 layer thickness formed with increasing annealing temperature in air led to an increase in resistivity by about one order of magnitude (Figure 9a). Similar results were reported by Hsiang et al. [4]. On the other hand, a decrease in pO2 at 900 °C tended to slow down the formation of this chromia surface layer (Figure 8b). Consequently, a reduction of resistivity by about one order of magnitude was observed upon changing the pO2 from air to 10 −5 atm (Figure 9b). If the samples were annealed at 900 • C in various oxygen partial pressures, then the tendency towards the formation of Cr 2 O 3 , as observed in air, was significantly reduced. After annealing in gas atmospheres with lower p O2 , the intensity of the Cr 2 O 3 peaks decreased (Figure 7b). Rietveld refinements confirmed a decrease in the Cr 2 O 3 concentration in the annealed samples and reached about 8(1) wt% at p O2 = 10 −5 atm (Figure 8b). At the same time, the cubic alloy lattice parameter increased with decreasing p O2 , indicating an increase in the Cr content in the alloy and, consequently, less Cr 2 O 3 surface layer formation (Figure 8b).
The formation of insulating Cr 2 O 3 layers at the surface of the alloy particles directly affected the electrical resistivity. The increasing Cr 2 O 3 layer thickness formed with increasing annealing temperature in air led to an increase in resistivity by about one order of magnitude (Figure 9a). Similar results were reported by Hsiang et al. [4]. On the other hand, a decrease in p O2 at 900 • C tended to slow down the formation of this chromia surface layer (Figure 8b). Consequently, a reduction of resistivity by about one order of magnitude was observed upon changing the p O2 from air to 10 −5 atm (Figure 9b). Alloys 2022, 2, FOR PEER REVIEW 8 The permeability at 1 MHz is shown as function of the annealing temperature in Figure 9, with the corresponding permeability spectra in Figure 10. Samples annealed at 700 °C exhibited a permeability of about µ′ = 22. It has been demonstrated that higher compaction pressure results in a larger final density of the pressed and annealed samples [4]. Compacting with 800 MPa pressure was shown to yield a permeability of µ′ = 34, and subsequent annealing at 750 °C was found to increase the permeability to about µ′ = 38 only [4]. This indicates that plastic deformation of the alloy particles seemed to be the major mechanism for the densification of the samples, whereas sintering and grain growth seemed to play a minor role only. This is consistent with the observed small shrinkage of the samples during annealing and with the almost zero shrinkage in the dilatometric curve (Figure 2a). The permeability spectra showed slight variations in the permeability with frequency up to about 30 MHz, followed by a stronger decay in the hundreds of MHz region up to a resonance frequency at about 1 GHz (Figure 10). FeSiCr samples with higher The permeability at 1 MHz is shown as function of the annealing temperature in Figure 9, with the corresponding permeability spectra in Figure 10. Samples annealed at 700 • C exhibited a permeability of about µ = 22. It has been demonstrated that higher compaction pressure results in a larger final density of the pressed and annealed samples [4]. Compacting with 800 MPa pressure was shown to yield a permeability of µ = 34, and subsequent annealing at 750 • C was found to increase the permeability to about µ = 38 only [4]. This indicates that plastic deformation of the alloy particles seemed to be the major mechanism for the densification of the samples, whereas sintering and grain growth seemed to play a minor role only. This is consistent with the observed small shrinkage of the samples during annealing and with the almost zero shrinkage in the dilatometric curve ( Figure 2a). The permeability at 1 MHz is shown as function of the annealing temperature in Figure 9, with the corresponding permeability spectra in Figure 10. Samples annealed at 700 °C exhibited a permeability of about µ′ = 22. It has been demonstrated that higher compaction pressure results in a larger final density of the pressed and annealed samples [4]. Compacting with 800 MPa pressure was shown to yield a permeability of µ′ = 34, and subsequent annealing at 750 °C was found to increase the permeability to about µ′ = 38 only [4]. This indicates that plastic deformation of the alloy particles seemed to be the major mechanism for the densification of the samples, whereas sintering and grain growth seemed to play a minor role only. This is consistent with the observed small shrinkage of the samples during annealing and with the almost zero shrinkage in the dilatometric curve (Figure 2a). The permeability spectra showed slight variations in the permeability with frequency up to about 30 MHz, followed by a stronger decay in the hundreds of MHz region up to a resonance frequency at about 1 GHz (Figure 10). FeSiCr samples with higher The permeability spectra showed slight variations in the permeability with frequency up to about 30 MHz, followed by a stronger decay in the hundreds of MHz region up to a resonance frequency at about 1 GHz (Figure 10). FeSiCr samples with higher permeability of µ = 44 as presented in ref. [2] exhibited their resonance frequency at a lower frequency of about 100 MHz in agreement with Snoek's law.
The permeability at 1 MHz occurred at about µ = 22 for samples sintered in air at 700 • C and 750 • C and started to decrease from µ = 21 after annealing at 800 • C down to µ = 18.5 for samples annealed at 900 • C (Figure 9a). A similar behavior with a decrease in permeability after annealing at T > 800 • C was reported in ref. [4]. This reduction in permeability originates from the insulating Cr 2 O 3 layer at the grain surfaces of the alloy particles. This layer seems to hinder domain wall motion and therefore lowers the permeability. Bulk chromium oxide Cr 2 O 3 itself is an antiferromagnetic material. After nano-structuring into ultra-thin layers or as nanosized particles, it exhibits a weak ferromagnetism that increases with decreasing particle size [17,18]. However, it is expected that the (less magnetic) chromia surface layer weakens the exchange across particles and contributes to the permeability reduction. For samples annealed at 900 • C at different p O2 values, the permeability increased from µ = 18.5 after annealing in air at 900 • C to about µ = 22.5 for samples annealed at p O2 = 10 −5 atm (Figure 9b). Such increased permeability is consistent with the observations of less Cr 2 O 3 formation under more reducing conditions.
FeSiCr alloys represent an interesting family of magnetic materials used for the fabrication of multilayer powder inductors. In this study, we compared the effect of the annealing temperature and oxygen partial pressure as parameters to tailor the oxidation state of the alloy particle surfaces and the corresponding performance of the material. It has been known that increasing annealing temperatures enhance the formation of a Cr 2 O 3 oxide surface layer and, hence, the resistivity of the alloy, but also reduce permeability. It has been documented here that a reduction of the oxygen partial pressure during annealing at 900 • C is an option to reduce and slow down the formation of a chromia layer of sufficient thickness and, simultaneously, avoid the reduction of permeability upon annealing at 900 • C. This offers new paths for firing multilayer inductors with enhanced performance including high insulation resistance and permeability, or inductance.

Conclusions
FeSiCr alloy is an important soft magnetic material for multilayer power inductors. Upon processing of the multilayer, the alloy is laminated at high pressure and annealed in air. During annealing, a surface layer of Cr 2 O 3 forms, which markedly affects the electromagnetic performance. We have studied the effect of annealing temperature in air and, alternatively, the effect of oxygen partial pressure during annealing at 900 • C on the formation of the surface oxide layer and the performance.
With increasing annealing temperature in air: -The alloy oxidation and chromia layer formation increased. - The alloy composition became more Fe-rich. - The insulation resistance increased and the permeability decreased.
With decreasing oxygen partial pressure in the gas atmosphere during annealing at 900 • C: -The formation of an insulating Cr 2 O 3 surface layer slowed down. - The resistivity decreased somewhat and the permeability increased.
This implies that the p O2 of the gas atmosphere is another important parameter that allows for tailoring the insulating layer thickness and hence the insulating resistance, as well as the electromagnetic performance of FeSiCr-based inductors. These findings will be used to derive optimum annealing regimes of FeSiCr/ferrite composite multilayer inductors with sufficient insulation resistance of the FeSiCr, with negligible Ag migration in the magnetic layers and/or less reaction between Ag and magnetic materials.