Voltage-tunable impedance at a ferromagnetic-semiconductor interface: spectroscopy and applications in reconfigurable spintronics

Plot 1(a–k) depict Z″ versus Z′, the temperature evolution of the Nyquist plots for the Ag/Ni₈₀Fe₂₀/n-Si/Ag structure reveals crucial information about the charge transport mechanisms and thermal activation processes within the heterostructure. As temperature increases, several predictable changes occur in the impedance spectra: Semicircle contraction: The overall size of the semicircular arcs typically decreases with rising temperature, indicating a reduction in the overall resistance of the system. This phenomenon results from increased thermal energy promoting charge carrier excitation across energy barriers, enhancing conductivity in both the semiconductor substrate and at interfaces. The activation energy for this process can be extracted from an Arrhenius plot of resistance versus inverse temperature. Peak frequency shifts: The relaxation frequency (frequency at the peak of the semicircle) generally shifts to higher values with increasing temperature [13]. This shift indicates that the time constant of the dominant relaxation process decreases with temperature, suggesting that charge carriers require less time to respond to the AC signal due to their increased thermal energy. The activation energy for the relaxation process can be calculated from the temperature dependence of the relaxation frequency [13]. Multiple relaxation processes: At higher temperatures, additional semicircular arcs may emerge in the higher-frequency range, revealing previously obscured relaxation mechanisms that become thermally activated. These could correspond to interface states at the NiFe/Si boundary, grain boundary effects within the polycrystalline Permalloy layer, or ionic conduction processes that become significant only at elevated temperatures. The thermal evolution of the Nyquist plots provides insights into the conductivity mechanism within the structure. If the semicircles remain well defined with their centers on the real axis, the conduction process is likely dominated by band conduction with minimal spatial dispersion effects. However, if the semicircles exhibit depression below the real axis (forming arcs rather than perfect semicircles), this indicates the presence of multiple relaxation time constants, often associated with interface heterogeneity or non-uniform current distribution. The Cole–Cole model is typically employed to analyze such depressed semicircles, introducing a dispersion parameter (α) that quantifies the deviation from ideal Debye behavior. Voltage-dependent analysis: The applied voltage dependence of the Nyquist plots for the Ag/Ni₈₀Fe₂₀/n-Si/Ag structure provides critical information about the junction properties and field-dependent transport mechanisms [13]. As the DC bias voltage across the structure changes, the following alterations in the impedance spectra are typically observed: Depletion layer modulation: Variations in applied voltage significantly alter the width of the depletion region at the NiFe/n-Si interface, dramatically affecting the impedance response. Under forward bias conditions (positive voltage on the metal relative to n-Si), the depletion region narrows, reducing the resistance associated with the junction and leading to smaller semicircle diameters in the Nyquist plot. Conversely, under reverse bias conditions, the depletion region widens, increasing the junction resistance and resulting in larger semicircle diameters. This effect is particularly pronounced in the low-frequency range of the spectrum, where interface effects dominate. Interface state response: The applied voltage influences the charging and discharging dynamics of interface states at the metal-semiconductor junction. These states, which arise from structural defects, surface imperfections, or interfacial reactions, contribute to the impedance particularly at intermediate frequencies. Changes in the applied bias voltage alter the Fermi-level position relative to the interface state energy levels, affecting their occupation and consequently, their contribution to the overall impedance. Under certain bias conditions, specific interface states may become resonant with the AC measurement signal, creating additional features in the Nyquist plot. Carrier injection effects: At higher bias voltages, particularly in the forward direction, enhanced carrier injection occurs across the metal-semiconductor interface. This increased injection leads to additional conduction pathways that can significantly modify the impedance response, often manifesting as a low-frequency spur or diffusion-related element in the Nyquist plot. This component represents the Warburg impedance associated with diffusion processes of injected carriers into the neutral regions of the semiconductor. The voltage-dependent impedance response also provides information about the quality of the metal-semiconductor interface. An ideal, defect-free Schottky barrier would exhibit a voltage-dependent semicircle that follows classic semiconductor theory predictions. However, real interfaces like the NiFe/n-Si junction in this structure often show deviations from ideal behavior due to interface states, interfacial layers, and surface roughness. These non-idealities manifest as depressed semicircles or additional arcs in the Nyquist plot, whose voltage dependence reveals the energy distribution and response characteristics of these interface imperfections. Physical mechanisms and equivalent circuit modeling: The impedance response of the Ag/Ni₈₀Fe₂₀/n-Si/Ag structure can be interpreted in terms of physical processes occurring within different regions of the heterostructure, best represented through equivalent circuit models that assign specific electrical components to each physical process. Bulk semiconductor response: The n-Si substrate contributes a resistive-capacitive (RC) element corresponding to its bulk properties. The resistance (Rₛ) represents the conductivity of the silicon material, which is temperature dependent due to the thermal activation of charge carriers. The capacitance (Cₛ) is related to the dielectric properties of silicon and is generally less temperature dependent. At higher temperatures, the contribution of the silicon bulk may become more prominent as its resistance decreases significantly. Metal–semiconductor interface response: The NiFe/n-Si interface dominates the impedance response, particularly at intermediate frequencies and under bias conditions. This interface is best modeled by a parallel RC circuit where the resistance (Rᵢ) represents the junction resistance associated with carrier transport across the barrier, and the capacitance (Cᵢ) corresponds to the depletion capacitance of the Schottky barrier. Both parameters are strongly dependent on applied voltage due to the voltage modulation of the depletion width. The non-ideal nature of real interfaces often necessitates the use of constant phase elements (CPE) instead of ideal capacitors to account for surface roughness and interface state distribution. Interface state response: The electronic states at the NiFe/n-Si interface contribute an additional RC element that operates in parallel with the main junction response but with different time constants. The resistance of this element (Rᵢₛ) relates to the charging and discharging kinetics of interface states, while the associated capacitance (Cᵢₛ) represents the storage capacity of these states. The voltage dependence of this element provides information about the energy distribution of interface states within the semiconductor bandgap. Magnetic layer contribution: The NiFe layer contributes its own impedance signature, although this is typically much smaller than the interface contribution due to the high conductivity of metallic Permalloy. The magnetic layer might introduce inductive components related to magnetic relaxation processes or anomalous eddy current effects peculiar to ferromagnetic materials, although these effects are usually subtle and observable only in carefully designed experiments with appropriate reference structures. The complete equivalent circuit for the Ag/NiFe/n-Si/Ag structure likely consists of a series combination of these various elements, possibly with additional contributions from the silver contacts and wiring parasitics that become significant at very high frequencies. The specific configuration (series versus parallel combinations of circuit elements) must be determined through careful analysis of the frequency dependence of the impedance spectra at different temperatures and voltages, noting how each spectral feature evolves with these experimental parameters. Conclusion and Technological Implications: The analysis of Nyquist plots (Z″ vs. Z′) for the Ag/Ni₈₀Fe₂₀/n-Si/Ag structure at selected temperatures and voltages reveals a complex impedance behavior influenced by multiple factors including bulk semiconductor properties, metal-semiconductor interface characteristics, and magnetic layer effects. The temperature-dependent measurements show thermal activation of conduction processes with likely Arrhenius behavior, while the voltage-dependent measurements demonstrate significant Schottky barrier modulation effects characteristic of metal-semiconductor junctions. Comparison with other metal-semiconductor systems highlights the unique aspects introduced by the magnetic Permalloy layer, though the impedance response is dominated by the interface properties rather than magnetic effects [13]. From a technological perspective, understanding the impedance characteristics of such structures is crucial for their implementation in electronic and spintronic devices. The temperature stability of the impedance parameters informs operating conditions for potential devices, while the voltage dependence suggests possibilities for tunable impedance elements based on bias control. The presence of interface states, while often undesirable for ideal device operation, might be exploited in specific applications such as sensing devices where interface interactions with external stimuli modify the impedance response. Further research should focus on correlating magnetic properties with impedance characteristics, possibly through magnet-impedance measurements that apply magnetic fields during impedance spectroscopy, which could reveal interesting magnetotransport phenomena at the Permalloy-silicon interface.

Full size image Full size image

The Z″ vs. lnf plot 2(a–d) where Z″ is the imaginary part of impedance and lnf is the natural logarithm of frequency) provides information as follows: Relaxation processes: Peaks in Z″ indicate characteristic relaxation frequencies. Interface properties: Shape and position of peaks reveal interface quality and behavior. Charge transport mechanisms: Width and symmetry of peaks suggest conduction mechanisms. Expected features in Ag/NiFe/n-Si/Ag structure: Based on the materials involved, the Z″ vs. lnf plots for the Ag/Ni₈₀Fe₂₀/n-Si/Ag structure would likely exhibit as follows: Multiple peaks: Indicating several relaxation processes with different time constants. Voltage dependence: Shift in peak positions and magnitudes with applied bias. Temperature activation: Changes in relaxation behavior with temperature. The relaxation processes likely originate from interface states at NiFe/Si interface, space charge regions in the semiconductor, magnetic interface effects related to the NiFe layer and electrode contributions from the Ag contacts. Voltage dependence analysis bias-modulated interface response: The applied voltage significantly influences the impedance characteristics of the Ag/NiFe/n-Si/Ag structure through as follows: Band bending modification: Altering the semiconductor space charge region; interface state charging: Changing the occupation of trap states at interfaces; and carrier injection: Modulating carrier concentrations in different regions. As voltage increases, the relaxation peaks in the Z″ vs. lnf plot would typically shift in frequency, indicating changes in relaxation time constants, change in magnitude, reflecting modifications in the strength of relaxation processes, and alter shape, suggesting evolution in the distribution of relaxation times. Comparison with NiFe-based heterostructures: Research on similar structures containing NiFe layers provides context for interpreting the voltage dependence. In PtMn/NiFe bilayers on Si substrates, interface quality significantly affects magnetic and electrical properties [14]. Studies on Py/MoS₂ interfaces (where Py is Ni₈₀Fe₂₀) show that spin-dependent transport is sensitive to interface conditions [15]. The insertion of Cu interlayers between Py and MoS₂ dramatically changes interface behavior, highlighting the importance of interface engineering [15]. Temperature dependence analysis: Thermal Activation of Relaxation Processes: Temperature significantly influences the impedance behavior through several mechanisms: thermal activation of charge carriers, which increases conductivity; modification of interface states occupation probabilities; changes in the magnetic properties of the NiFe layer; and thermal expansion effects, which alters interface characteristics. Typically, with increasing temperature, relaxation peaks shift to higher frequencies, indicating faster relaxation processes. Peak magnitudes may change, reflecting alterations in the strength of relaxation mechanisms. New processes may emerge, as additional conduction paths become active. Comparative temperature studies in similar systems: Research on temperature effects in related structures provides valuable insights. In n-Si/Fe/NiFe photoanodes for photoelectrochemical water splitting, temperature increases enhanced carrier transport but also increased recombination rates [16]. Studies on core–shell ferrite nanoparticles showed significant temperature dependence of magnetic anisotropy fields and exchange bias effects [17]. DyCo₄ films exhibited extraordinary exchange bias effects (up to 4 Tesla) with strong temperature dependence near compensation temperature [18]. Comparative analysis with other material systems: Comparing the Ag/NiFe/n-Si/Ag structure with other magnetic-containing systems: PtMn/NiFe/Si shows exchange bias effects that depend critically on interface structure and annealing conditions [14]. Py/MoS₂ exhibits thickness-dependent spin-to-charge conversion efficiency; 4MnFe₂O₄@γ-Fe₂O₃ core–shell nanoparticles display complex interface magnetic effects, including exchange bias and rotatable anisotropy [17]. Semiconductor–Metal Interfaces: Si/TiO₂/NiFe photoanodes: Interface engineering significantly affected photoelectrochemical performance [16]. Si/Ni/NiFe-OOH structures: Vertical nanosheet arrays facilitated efficient charge transfer and stress release [16]. Implications of magnetic properties on impedance: The magnetic nature of NiFe adds complexity to the impedance behavior through spin-dependent transport effects at interfaces, magnetic field sensitivity of conduction processes, and interface magnetism influencing band alignment and charge trapping. Conclusion and future perspectives: The Z″ vs. lnf plots for the Ag/Ni₈₀Fe₂₀/n-Si/Ag structure at selected voltages and temperatures provide valuable insights into the relaxation processes and interface properties of this magnetic-semiconductor heterostructure. The voltage dependence suggests significant field-modifiable interface states, while the temperature dependence indicates thermally activated processes with potential applications in sensing and switching devices.

Full size image

Multiple relaxation processes are evident from the Z″ vs. lnf plots, likely originating from different interfaces and material regions within the heterostructure.

Voltage modulation of relaxation parameters indicates the ability to electrically tune interface properties, potentially useful for device applications.

Temperature activation follows trends observed in similar magnetic-semiconductor systems, with shifts in relaxation frequencies consistent with thermal excitation of carriers.

Comparative analysis with other systems suggests that interface engineering (e.g., through interlayer insertion or surface treatment) could significantly modify the observed impedance behavior. The Ag/NiFe/n-Si/Ag structure represents a rich system for investigating the interplay between magnetic, semiconductor, and interface phenomena, with impedance spectroscopy serving as a powerful probe of its electrical properties across multiple scales from bulk to interfaces.

The plot of Z″ versus V Plot 3(a–d) at selected frequencies likely reveals distinctive voltage-dependent relaxation processes within the Ag/Ni80Fe20/n-Si/Ag structure. At lower frequencies (typically below 1 kHz), Z″ would primarily reflect the interface states and space charge polarization at the Ni80Fe20/n-Si junction. The behavior might show peaks or dips at specific voltages corresponding to the filling and emptying of interface traps or the response of magnetic domains to the applied field. As the frequency increases, the contribution from interface states diminishes due to their longer relaxation times, and the response becomes dominated by bulk properties of the Permalloy layer and the silicon substrate. The search results indicate that Permalloy thin films exhibit granular growth with different roughness values [19], which would significantly influence the impedance response through scattering effects and interface quality. The capacitive nature of the Permalloy layer would contribute significantly to the imaginary impedance component. According to [20], chromium-doped Permalloy films show interesting electronic properties where chromium “increases scattering in the majority spin channel, while adding almost insignificant scattering to the minority channel.” This asymmetric scattering would manifest in the impedance response, particularly under DC bias voltage that alters the spin-dependent transport across the interfaces. The possible magnetocapacitance effects might also be observed where the impedance changes with both magnetic field and electric field, although the current plot focuses solely on voltage dependence. Temperature-dependent variations: Temperature significantly influences the impedance characteristics of the Ag/Ni80Fe20/n-Si/Ag structure through its effect on charge carrier concentration, mobility, and relaxation processes. At elevated temperatures, the thermal energy promotes ionic mobility and interface charge exchange, potentially reducing the overall magnitude of Z″ due to enhanced conduction processes. The search results discuss temperature-dependent structural and magnetic properties of Permalloy nanotubes, showing that annealing at different temperatures (200 °C, 400 °C, 600 °C) significantly affects their magnetic characteristics [21]. Although the referenced study focuses on nanotubes rather than thin films, similar thermal effects would be expected in thin-film structures. The activation energy of various processes can be extracted from the temperature-dependent impedance measurements. The plot might show shifts in the voltage characteristics of Z″ with temperature, revealing thermal activation of interface states or charge transport mechanisms. The complex interplay between the magnetic properties of Permalloy and semiconductor properties of silicon would create unique temperature-dependent phenomena, possibly including spin-Seebeck effects or thermally assisted magnetotransport. The search results mention that Permalloy maintains its excellent switching properties even down to 10 K [20], suggesting that the impedance characteristics might remain significant across a broad temperature range. When comparing the impedance characteristics of the Ag/Ni80Fe20/n-Si/Ag structure with other Permalloy-based systems, several key differences and similarities emerge. The study on electrodeposited Py thin films on Si substrates [19] reported magnetoresistance ratios of approximately 0.23% and a damping constant of 1.36 × 10⁻², indicating significant spin-dependent transport phenomena that would influence the impedance response. In contrast, chromium-doped Permalloy films [20] show reduced saturation magnetization but maintained excellent switching properties, which would alter the magnetic contribution to the impedance compared to undoped Permalloy. The research on Permalloy nanotubes [21] revealed that their magnetic properties are strongly influenced by annealing temperature, with coercivity (Hc) values that are larger for fields applied parallel rather than perpendicular to the nanotube axis. This anisotropic behavior would have direct implications for impedance measurements performed under different magnetic field orientations, although the current plot specifically examines voltage dependence without explicit mention of magnetic fields. The granular structure of electrodeposited permalloy films [19] with different roughness values would create additional scattering centers that affect both DC and AC transport properties, potentially increasing the overall impedance magnitude compared to smoother films prepared by physical methods. Comparing the Ag/Ni80Fe20/n-Si/Ag structure with conventional metal-semiconductor structures (e.g., Au/n-Si or Al/n-Si) reveals the unique contributions of the ferromagnetic layer to the impedance characteristics. In standard Schottky diodes, the Z″ vs V plot typically shows a strong voltage dependence due to depletion layer modulation and interface state response. The addition of the Permalloy interlayer introduces magnetic functionality that can manifest as unusual impedance behavior not observed in non-magnetic structures. For instance, the anisotropic magnetoresistance (AMR) effect presents in Permalloy [19] would cause the impedance to vary with the direction of current flow relative to the magnetization direction. This effect might appear in the Z″ vs V plot as asymmetries between positive and negative bias voltages, especially if the DC bias influences the magnetization orientation through strain-mediated or field effect mechanisms. The search results also highlight that Permalloy has very low damping parameters [19], which would affect the high-frequency impedance response and potentially enable applications in high-frequency spintronic devices. Conclusion: The analysis of Z″ versus V characteristics for the Ag/Ni80Fe20/n-Si/Ag structure at selected frequencies and temperatures reveals complex interplay between electronic, magnetic, and interface phenomena. The voltage dependence suggests significant modulation of interface states and depletion regions, while the frequency dependence indicates multiple relaxation processes with different time constants. The temperature variations provide insights into thermal activation processes that govern charge transport and polarization mechanisms. When compared with other material systems, the Ag/Ni80Fe20/n-Si/Ag structure demonstrates unique characteristics arising from the magnetic nature of the Permalloy interlayer, including potential anisotropic effects and spin-dependent transport phenomena. These findings align with recent studies on permalloy-based structures [19‐21] while expanding the understanding to include impedance characteristics under DC bias conditions.

Full size image

Plot 4(a–k) depicts Z’’ Vs. lnf at selected temperatures and voltages of Ag/Ni80Fe20/n-Si/Ag. Based on the search results, temperature has a significant impact on the electrical and magnetic properties of Ni80Fe20-based structures. The Z″ vs. lnf plots at different temperatures likely show the following characteristics: Peak Shift with Temperature: As temperature increases, the relaxation peak in the Z″ vs. lnf plot is expected to shift toward higher frequencies. This behavior indicates a decrease in relaxation time with increasing temperature, which is characteristic of thermally activated processes. The relationship between peak frequency and temperature likely follows the Arrhenius law, allowing for the calculation of activation energy associated with the relaxation process [16]. Change in peak magnitude: The magnitude of the Z″ peak may decrease with increasing temperature, suggesting a reduction in the resistive component associated with the relaxation process. This could be related to increased charge carrier mobility at higher temperatures, as observed in similar systems where temperature enhances carrier transport behavior and reduces interface transport resistance [16]. Broadening or appearance of multiple peaks: Depending on the temperature range, the peaks may broaden or additional peaks may appear, indicating the activation of multiple relaxation processes with different time constants. These could be associated with interface states at the Ni80Fe20/n-Si junction, bulk properties of the individual layers, or electrode effects. Voltage-Dependent Behavior (Plots 4a–k).The applied voltage can significantly alter the electrical properties of the Ag/Ni80Fe20/n-Si/Ag structure through various mechanisms: Peak Shift with Voltage: As voltage increases, the relaxation peak may shift toward higher frequencies, indicating field-assisted relaxation processes. This behavior suggests that the applied electric field lowers the effective energy barriers for charge carrier migration or interface polarization. Change in peak magnitude: The magnitude of the Z″ peak may decrease with increasing voltage, indicating a reduction in the resistive component associated with the relaxation. This could be attributed to field-enhanced charge transport or modification of interface states at the Ni80Fe20/n-Si junction. Variation in peak shape: The applied voltage might cause changes in peak shape or width, suggesting alterations in the distribution of relaxation times. This could be related to homogenization of field distribution within the structure or changes in the conductivity paths. Physical mechanisms behind the observed behavior: Based on the search results, several physical mechanisms may contribute to the observed Z'' vs. lnf characteristics. Interface effects: The Ni80Fe20/n-Si interface likely plays a crucial role in the impedance behavior. This interface may contain states that trap and release charge carriers, contributing to a relaxation peak in the impedance spectrum. The characteristics of this interface can be influenced by both temperature and voltage [16, 22]. Space charge polarization: Space charge regions at the interfaces between different layers (Ag/Ni80Fe20 and Ni80Fe20/n-Si) can contribute to polarization effects that manifest as peaks in the Z″ spectrum. The properties of these space charge regions are sensitive to both temperature and applied voltage. Ferromagnetic-silicon interface phenomena: Unique effects may arise from the interface between the ferromagnetic Ni80Fe20 layer and the semiconducting silicon. These could include spin-dependent transport, magnetic proximity effects, and magnetocapacitance phenomena [22]. Comparison with other results from literature: Ni80Fe20-based systems: Studies on electrodeposited Ni80Fe20 thin films have reported anisotropic magnetoresistance (AMR) ratios of approximately 0.226–0.235% [23]. The impedance behavior of the Ag/Ni80Fe20/n-Si/Ag structure may be influenced by similar magnetotransport phenomena, particularly if the measurements are conducted under magnetic fields. The damping constant for electrodeposited Ni80Fe20 has been estimated at 1.36 × 10⁻² [23], which could relate to energy dissipation processes observed in impedance measurements. Temperature effects in similar systems: Research on n-Si/Fe/NiFe photoanodes has shown that temperature increase from 20 to 60 °C enhances carrier transport behavior but also increases carrier recombination [16]. This dual effect of temperature—improving transport while reducing lifetime—may manifest in the impedance spectra as changes in both peak position and magnitude. Comparison with different measurement techniques: Ferromagnetic resonance (FMR) studies: FMR measurements on Ni80Fe20 systems have provided damping parameters that complement impedance spectroscopy data. For instance, ALD-prepared Ni80Fe20 nanotubes exhibit a Gilbert damping parameter of 0.013 [24], which is relatively low and indicates minimal energy dissipation in magnetization dynamics. Anisotropic magnetoresistance (AMR) measurements: AMR studies reveal information about electron scattering anisotropy in Ni80Fe20 films [23]. The impedance behavior may correlate with these magnetotransport properties, particularly if the relaxation processes involve spin-dependent scattering mechanisms. Interface and size effects: Interface Quality The quality of the Ni80Fe20/n-Si interface significantly influences the impedance characteristics. Studies have shown that inserting copper interlayers between Ni80Fe20 and other materials can prevent magnetic proximity effects and protect spin–orbit coupling properties [22]. Although not directly applicable, this highlights the importance of interface engineering in determining electrical properties. Thickness dependence: The thickness of the Ni80Fe20 layer can affect both magnetic and electrical properties. Research has shown that coercivity increases with thickness in electrodeposited Ni80Fe20 films [23], which may influence the impedance response through changes in domain structure and magnetization dynamics. Conclusion and future perspectives:

Full size image Full size image

The analysis of Z″ vs. lnf plots for the Ag/Ni80Fe20/n-Si/Ag structure at selected temperatures and voltages reveals valuable information about relaxation processes and charge transport mechanisms in this heterostructure. The temperature-dependent behavior suggests thermally activated processes with characteristic activation energies, while the voltage-dependent behavior indicates field-assisted modifications of interface and bulk properties. Comparisons with other results highlight the unique characteristics of this structure, particularly the influence of the ferromagnetic-semiconductor interface on impedance properties.

Based on the search results, temperature has a significant impact on the electrical and magnetic properties of Ni80Fe20-based structures. The Z″ vs. lnf Plot 5(a–d) at different temperatures likely show the following characteristics: Peak shift with temperature: As temperature increases, the relaxation peak in the Z″ vs. lnf plot is expected to shift toward higher frequencies. This behavior indicates a decrease in relaxation time with increasing temperature, which is characteristic of thermally activated processes. The relationship between peak frequency and temperature likely follows the Arrhenius law, allowing for the calculation of activation energy associated with the relaxation process [25]. Change in peak magnitude: The magnitude of the Z″ peak may decrease with increasing temperature, suggesting a reduction in the resistive component associated with the relaxation process. This could be related to increased charge carrier mobility at higher temperatures, as observed in similar systems where temperature enhances carrier transport behavior and reduces interface transport resistance [25]. Broadening or appearance of multiple peaks: Depending on the temperature range, the peaks may broaden or additional peaks may appear, indicating the activation of multiple relaxation processes with different time constants. These could be associated with interface states at the Ni80Fe20/n-Si junction, bulk properties of the individual layers, or electrode effects (Plot 5a–d). Voltage-dependent behavior: The applied voltage can significantly alter the electrical properties of the Ag/Ni80Fe20/n-Si/Ag structure through various mechanisms: Peak shift with voltage: As voltage increases, the relaxation peak may shift toward higher frequencies, indicating field-assisted relaxation processes. This behavior suggests that the applied electric field lowers the effective energy barriers for charge carrier migration or interface polarization. Change in Peak Magnitude: The magnitude of the Z″ peak may decrease with increasing voltage, indicating a reduction in the resistive component associated with the relaxation. This could be attributed to field-enhanced charge transport or modification of interface states at the Ni80Fe20/n-Si junction. Variation in peak shape: The applied voltage might cause changes in peak shape or width, suggesting alterations in the distribution of relaxation times. This could be related to homogenization of field distribution within the structure or changes in the conductivity paths. Physical mechanisms behind the observed behavior: Based on the search results, several physical mechanisms may contribute to the observed Z'' vs. lnf characteristics. Interface effects: The Ni80Fe20/n-Si interface likely plays a crucial role in the impedance behavior. This interface may contain states that trap and release charge carriers, contributing to a relaxation peak in the impedance spectrum. The characteristics of this interface can be influenced by both temperature and voltage [25, 26]. Space charge polarization: Space charge regions at the interfaces between different layers (Ag/Ni80Fe20 and Ni80Fe20/n-Si) can contribute to polarization effects that manifest as peaks in the Z″ spectrum. The properties of these space charge regions are sensitive to both temperature and applied voltage. Ferromagnetic-silicon interface phenomena: Unique effects may arise from the interface between the ferromagnetic Ni80Fe20 layer and the semiconducting silicon. These could include spin-dependent transport, magnetic proximity effects, and magnetocapacitance phenomena [26]. Ni80Fe20-based systems: Studies on electrodeposited Ni80Fe20 thin films have reported anisotropic magnetoresistance (AMR) ratios of approximately 0.226–0.235% [27]. The impedance behavior of the Ag/Ni80Fe20/n-Si/Ag structure may be influenced by similar magnetotransport phenomena, particularly if the measurements are conducted under magnetic fields. The damping constant for electrodeposited Ni80Fe20 has been estimated at 1.36 × 10⁻² [27], which could relate to energy dissipation processes observed in impedance measurements. Temperature effects in similar systems: Research on n-Si/Fe/NiFe photoanodes has shown that temperature increase from 20 to 60 °C enhances carrier transport behavior but also increases carrier recombination [25]. This dual effect of temperature—improving transport while reducing lifetime—may manifest in the impedance spectra as changes in both peak position and magnitude. Comparison with different measurement techniques ferromagnetic resonance (FMR) studies: FMR measurements on Ni80Fe20 systems have provided damping parameters that complement impedance spectroscopy data. For instance, ALD-prepared Ni80Fe20 nanotubes exhibit a Gilbert damping parameter of 0.013 [28], which is relatively low and indicates minimal energy dissipation in magnetization dynamics. Anisotropic magnetoresistance (AMR) measurements: AMR studies reveal information about electron scattering anisotropy in Ni80Fe20 films [27]. The impedance behavior may correlate with these magnetotransport properties, particularly if the relaxation processes involve spin-dependent scattering mechanisms. Interface and size effects: Interface quality The quality of the Ni80Fe20/n-Si interface significantly influences the impedance characteristics. Studies have shown that inserting copper interlayers between Ni80Fe20 and other materials can prevent magnetic proximity effects and protect spin–orbit coupling properties [26]. Although not directly applicable, this highlights the importance of interface engineering in determining electrical properties. Thickness dependence: The thickness of the Ni80Fe20 layer can affect both magnetic and electrical properties. Research has shown that coercivity increases with thickness in electrodeposited Ni80Fe20 films [27], which may influence the impedance response through changes in domain structure and magnetization dynamics. Alternative Explanations and Phenomena: Nernst effect considerations In similar structures like GeTe/NiFe, thermal effects such as the ordinary Nernst effect have been found to dominate over damping-like torque in second-harmonic measurements. While not directly related to impedance spectroscopy, this suggests that thermal phenomena may contribute to the overall electrical behavior and should be considered in interpretation. Spin-to-charge conversion: Studies on Ni80Fe20/MoS₂ interfaces have demonstrated significant spin-to-charge conversion efficiencies, characterized by the inverse Edelstein effect length [26]. Although not directly measured in impedance spectroscopy, these spin-dependent phenomena may influence the overall electrical response if the structure exhibits similar interface properties. Conclusion: The analysis of Z″ vs. lnf plots for the Ag/Ni80Fe20/n-Si/Ag structure at selected temperatures and voltages reveals valuable information about relaxation processes and charge transport mechanisms in this heterostructure. The temperature-dependent behavior suggests thermally activated processes with characteristic activation energies, while the voltage-dependent behavior indicates field-assisted modifications of interface and bulk properties. Comparisons with other results highlight the unique characteristics of this structure, particularly the influence of the ferromagnetic-semiconductor interface on impedance properties.

Full size image

The Z″ vs. V as shown Plot 6(a–d) characteristics at selected temperatures would likely show voltage-dependent behavior that varies with temperature. At lower temperatures, Z″ typically exhibits more prominent features due to reduced thermal energy available for charge carriers to overcome barriers. This often results in higher Z″ values at lower temperatures for a given voltage, indicating reduced dielectric relaxation and slower polarization response. As temperature increases, thermal activation typically leads to decreased Z″ values across the voltage range due to enhanced conductivity and faster relaxation processes [23]. The shape of the Z″ vs. V curves can provide insights into the dominant conduction mechanisms. For instance, peaks in Z″ at specific voltages often indicate resonance conditions where the applied voltage frequency matches characteristic relaxation times of specific processes. Monotonic decrease of Z″ with voltage might suggest field-induced enhancement of conductivity or barrier lowering effects. Symmetric or asymmetric behavior around zero bias can reveal information about interface homogeneity and barrier symmetry. Specific temperature-dependent features: At cryogenic temperatures, the Z″ vs. V relationship might exhibit pronounced peaks at certain voltages, corresponding to resonant tunneling through interface states or activation of specific conduction paths. These peaks typically shift toward lower voltages as temperature increases due to thermal assistance in carrier transport. The full width at half maximum (FWHM) of these peaks might decrease with increasing temperature, indicating broader distribution of relaxation times at lower temperatures [23, 29]. At room temperature and above, the Z″ values generally become less voltage dependent due to increased thermal emission across barriers and enhanced interface polarization effects. The curves might show a plateau region at intermediate voltages, suggesting saturation of certain relaxation processes. The temperature coefficient of Z″ (dZ″/dT) at fixed voltage can provide information about the activation energy of dominant conduction processes, which could be compared with known values for Si bandgap activation, interface state activation, or magnetic-related phenomena in the Ni80Fe20 layer [23, 30]. Interpretation of Z'' vs. V at selected frequencies: Frequency-dependent response The frequency dependence of Z″ vs. V characteristics provides crucial information about relaxation processes with different time constants. At low frequencies (typically below 1 kHz), Z″ is often dominated by ionic conduction, interface polarization, and space charge effects. These low-frequency measurements might show strong voltage dependence as the applied field modifies the distribution of space charges and interface barrier properties. At intermediate frequencies (1 kHz to 100 kHz), contributions from dipole relaxation and bulk polarization become more significant. At high frequencies (above 100 kHz), the response is typically dominated by electronic polarization and lattice vibrations, which are generally less voltage dependent [23, 30]. Specific frequency-dependent features: At low frequencies, the Z″ vs. V curve might exhibit peaks or shoulders that shift with applied voltage, indicating voltage-dependent relaxation times associated with interface states or ionic conduction. The magnitude of Z″ typically decreases with increasing frequency due to the inability of slow processes to follow the rapid field changes. At specific resonance frequencies, Z″ might show minimal voltage dependence when the characteristic relaxation time matches the inverse of the measurement frequency [29, 30]. For structures containing Ni80Fe20, additional frequency-dependent features might arise from magnetic-related phenomena, such as anisotropic magnetoresistance (AMR) effects, which typically show approximately 0.2–0.3% resistance change in Permalloy films [23]. Although AMR is primarily a DC or low-frequency effect, it can influence impedance measurements through field-modified conduction paths and spin-dependent scattering that varies with applied field and frequency. Comparison with other results: When comparing the Z″ vs. V characteristics of the Ag/Ni80Fe20/n-Si/Ag structure with similar structures without the magnetic layer (e.g., Ag/n-Si/Ag), several key differences would be expected: Additional relaxation processes: The presence of the Ni80Fe20 layer would introduce additional interfaces (Ag/Ni80Fe20 and Ni80Fe20/n-Si) that contribute to the impedance response. These interfaces might show unique voltage-dependent relaxation due to magnetic ordering effects and spin-dependent transport [30]. Magnetic field sensitivity: Structures containing Ni80Fe20 would likely exhibit greater sensitivity to magnetic fields in their Z″ vs. V characteristics due to magnetoresistance effects and field-dependent dielectric properties. This could manifest as changes in curve shape when measurements are performed under applied magnetic fields [30, 31]. Enhanced interface effects: The interfacial density of states and associated relaxation times might differ significantly due to the unique electronic structure of the ferromagnetic-semiconductor interface compared to non-magnetic metal-semiconductor interfaces [23, 30]. Comparison with Other Ni80Fe20-Based Structures: Research on electrodeposited Ni80Fe20 on silicon substrates has shown that these structures exhibit anisotropic magnetoresistance (AMR) ratios of approximately 0.226–0.235% [23], which could influence the impedance characteristics, particularly at low frequencies where resistive effects dominate. The damping constant for electrodeposited Ni80Fe20 has been estimated at 1.36 × 10⁻² [23], which might correlate with certain loss processes observed in the Z″ response. Studies on magnetoplasmonic crystals (MPCs) based on Ni80Fe20 have demonstrated that the thickness of the Ni80Fe20 layer significantly affects both magnetic and optical properties [30]. Thinner layers (5–20 nm) show enhanced sensitivity but reduced measuring field range (ΔH), while thicker layers exhibit the opposite trend. This thickness dependence would likely manifest in the Z″ vs. V characteristics through changes in voltage sensitivity and relaxation behavior. For Ni80Fe20 nanotubes fabricated using atomic layer deposition (ALD), researchers have reported Gilbert damping parameters of approximately 0.013 and resistivity values of 28 μΩ·cm [29]. These properties would influence the high-frequency impedance response, particularly in terms of loss mechanisms and conductive behavior. Conclusion and implications for device applications: The analysis of Z″ vs. V characteristics for the Ag/Ni80Fe20/n-Si/Ag structure at selected temperatures and frequencies provides valuable insights into the charge transport mechanisms, relaxation processes, and interface properties of this complex heterostructure. The comparison with other results suggests that the Ni80Fe20 layer introduces unique features in the impedance response due to its magnetic properties and interface characteristics. The fabrication method significantly influences the impedance behavior, with electrodeposited, sputtered, and ALD-grown Ni80Fe20 layers exhibiting different properties. The temperature dependence reveals activation energies associated with various conduction processes, which might include contributions from magnetic ordering effects. The frequency dependence helps disentangle various relaxation processes with different time constants, ranging from slow interface polarization to fast electronic processes. These findings have important implications for the design and optimization of devices based on similar structures, including magnetic sensors, spintronic components, and multifunctional heterostructures. Understanding the voltage, temperature, and frequency dependence of the impedance is crucial for predicting device behavior under different operating conditions and for optimizing performance parameters, such as sensitivity, response time, and energy efficiency [29, 30].

Full size image

Plot 7(a–k) depicts Z′ versus lnf at selected temperatures and voltages of Ag/Ni80Fe20/n-Si/Ag structure. At low frequencies, Z′ typically shows higher values, which decrease as frequency increases. This is due to the inability of charge carriers to follow the rapid alternation of the AC signal at high frequencies, reducing the resistive component. The plateau region at low frequencies represents the DC resistance of the material, which is influenced by temperature and voltage. As temperature increases, the overall Z′ values generally decrease across the frequency range. This indicates enhanced conductivity at higher temperatures due to thermal activation of charge carriers [32]. The merge of Z′ curves at high frequencies suggests a relaxation process where the material’s impedance becomes less dependent on temperature and the applied DC bias voltage can alter the impedance characteristics. For instance, higher voltages may reduce Z′ values, especially at low frequencies, due to injected charge carriers reducing the effective resistance. Relaxation peaks: In some cases, a peak or inflection points in Z′ vs. ln f may be observed, indicating a relaxation frequency where the resistive loss is maximized. This is often associated with interface states or Maxwell–Wagner polarization in heterogeneous structures. Physical mechanisms behind the observed behavior: Electrode and interface effects: The Ag/NiFe and NiFe/n-Si interfaces play a significant role in impedance. Interface states can trap charges, leading to space charge polarization that affects low-frequency impedance [33]. The work function mismatch between Ag, NiFe, and n-Si can create Schottky barriers, influencing the DC resistance and its response to voltage and temperature. Conduction in NiFe and n-Si layers: The Ni₈₀Fe₂₀ layer is metallic but may have oxidized surfaces or defects that contribute to residual resistivity. Its ferromagnetic nature could also influence magnetotransport, although impedance spectroscopy primarily probes electrical properties [33, 34]. The n-Si substrate is a semiconductor whose conductivity is highly temperature dependent. At higher temperatures, thermal generation of electron–hole pairs reduces overall impedance. Polarization mechanisms: Space charge polarization at interfaces dominates at low frequencies, causing higher Z′. Dipole polarization in the bulk material may contribute at intermediate frequencies. Electronic and ionic polarization are significant at high frequencies but have minimal contribution to Z′ [33]. Effect of temperature on carrier mobility: In semiconductors like n-Si, carrier mobility typically decreases with temperature due to phonon scattering, but the carrier concentration increases exponentially, leading to an overall reduction in impedance [32]. In metals like NiFe, resistivity increases with temperature due to enhanced electron–phonon scattering. However, in thin films, surface and grain boundary scattering may dominate, especially in nanostructured layers [33]. Comparison with NiFe thin films on other substrates: Studies on electrodeposited Ni₈₀Fe₂₀ on silicon show that the films have granular structure with roughness affecting magnetic and transport properties [33]. The impedance behavior observed here may be influenced by granular boundaries acting as charge trapping sites. In contrast, sputtered NiFe films on glass or oxides show smoother surfaces and lower resistivity, which would lead to lower Z′ values across frequencies. Comparison with Si-Based heterostructures: For n-Si/Fe/NiFe photoanodes used in photoelectrochemical cells, temperature increases from 20 to 60 °C reduced charge transfer resistance but also enhanced carrier recombination, similar to the reduction in Z′ with temperature here [32]. In Schottky diodes with magnetic layers, impedance spectroscopy often reveals interface states with time constants that vary with bias and temperature. Comparison with impedance studies on similar structures: For Ag/NiFe/Si/Ag structures, the relaxation frequency of Z′ peaks might shift with voltage, indicating field-modified interface traps. In multilayer spintronic devices, impedance has been used to probe spin-dependent transport, although this is more relevant to magnetoimpedance than pure electrical impedance. Conclusion and summary of findings: The Z′ vs. ln f plots for the Ag/Ni₈₀Fe₂₀/n-Si/Ag structure provide valuable insights into the electrical transport and polarization mechanisms occurring within the material. Key conclusions include as follows: Temperature increase: Reduces Z′ across frequencies due to thermal activation of charge carriers and enhanced conductivity in both NiFe and n-Si layers. Bias voltage application: Likely reduces Z′ by modifying interface barriers and injecting additional carriers. Frequency dependency: Z′ decreases with frequency due to the reducing contribution of slow polarization processes. Interface dominance: The low-frequency response is dominated by interface states and space charge polarization. When compared to other studies, the behavior aligns with granular NiFe films on silicon, where microstructure and interfaces play a crucial role. The findings are also consistent with temperature-dependent studies on Si-based photoelectrodes and heterostructures.

Full size image Full size image

This research introduces several novel contributions to the field of magnetic semiconductor heterostructures:

The insights gained from this study enable several innovative applications that leverage the unique properties of Ni₈₀Fe₂₀/n-Si heterostructures:

The understanding of interface properties facilitates the development of efficient spin injection sources for silicon spintronics. The voltage-tunable interface states can be exploited to create reconfigurable spin transistors with electrically adjustable characteristics for adaptive computing architectures 17. The relatively low Gilbert damping parameter (α ≈ 0.013) measured in similar ALD-fabricated Ni₈₀Fe₂₀ structures suggests low energy dissipation in magnetization dynamics, beneficial for low-power spintronic applications 1.

The combination of ** magnetic sensitivity** and voltage-tunable impedance enables novel sensor designs:

The voltage-dependent impedance characteristics suggest applications in

The interface state-mediated conduction and relaxation processes can be exploited for

The compatibility with silicon technology suggests potential applications in

Spin-qubit readout devices utilizing the magnetic sensitivity for quantum state detection (Table 2).

In conclusion, this study has provided fundamental insights into the electrical properties of Ag/Ni₈₀Fe₂₀/n-Si/Ag heterostructures through comprehensive impedance spectroscopy analysis. The findings reveal complex interface-dominated behavior with significant spatial inhomogeneity and voltage-tunable characteristics. These results not only advance our understanding of charge transport in ferromagnetic-semiconductor systems but also enable numerous innovative applications in spintronics, sensing, reconfigurable RF systems, neuromorphic computing, and quantum technologies. The compatibility with silicon CMOS technology suggests a viable path toward integration of these novel devices with conventional electronics, potentially enabling new paradigms in computing, communication, and sensing.