Introduction

The favourable electrical and optical properties of zinc oxide made it promising for applications in opto-electronics1, sensor technology2, UV light emitting diodes3, and photovoltaic devices. In the field of spintronics, special attention has been given to oxygen-deficient magnetic ZnO thin films with substitutional 3d transition metal ions4,5,6. Observed spontaneous magnetization has been related with the formation of stable Bound Magnetic polarons (BMP)7. The BMP concept was first introduced to explain metal-insulator transition in oxygen-deficient EuO8. BMPs are formed by the s-d exchange interactions between the electron spin of a singly charged oxygen vacancy \({V}_{o}^{+}\) in the center of the BMP and the electron spins of substitutional 3d transition metal ions in a sphere with Bohr radius rB9,10,11. The Bohr radius is proportional to the static dielectric constant. Due to the s-d exchange interaction between the spin of singly charged oxygen vacancy \({V}_{o}^{+}\) and the spins of the 3d transition metal ions in the sphere with Bohr radius rB, the spins of the 3d transition metal ions the align in same direction and sum up to the collective spin of the BMP. For example, spontaneous magnetization due to collective spins of BMPs in CdTe with substitutional Mn ions was reported by Peter and Eucharista12. From magnetic n-CdS13,14 and n-CdSe15,16 there is abundant evidence that the electron localized at the impurity in the BMP center can induce sizable magnetization in its vicinity, often having magnetic moments exceeding 25 μB17. Interestingly, so far the focus in the BMP research was more on the formation of BMP and not on the increase of the static dielectric constant in the dilute magnetic semiconductor in comparison to the semiconductor host without substitutional magnetic ions. For example, the static dielectric constant of ZnO amounts to 8.5–9.518,19,20 and we have observed an increase of the static dielectric constant of ZnCoO up to 25.0 if 4 at.% Co is added7. Investigations of dielectric constant of ZnCoO powders modelled from measured shift in bandgap showed that it is not possible to achieve significant increase in dielectric constant. This may be due to the absence of singly ionised oxygen vacancies (\({V}_{o}^{+}\)) in ZnCoO powders enabling s-d exchange interaction and bound magnetic polaron formation which would enhance the static dielectric constant of ZnCoO powders. In this work we determine the magnetic species and concentration dependent static dielectric constant εr of two ZnO thin films and eight magnetic ZnO thin films with 2 at.% and 5 at.% substitutional Co2+ and Mn2+ ions from analysis of capacitive metal/n-ZnO semiconductor/Si3N4 insulator/p-Si semiconductor (MSIS) structures. The oxygen partial pressure during growth of the magnetic n-ZnO films by pulsed laser deposition (PLD) mainly determines the concentration of oxygen vacancies which are intrinsic donors and may form the center of BMP in magnetic ZnO. The intrinsic oxygen vacancy defects are donors that can be estimated from room temperature sheet resistance. This work proposes an approach to determine intrinsic defects from measured sheet resistance and volume of bound magnetic polaron which are the main ingredients that guide researchers towards ferromagnetism in transparent spintronics. The static dielectric constant has been modelled from the measured frequency dependent capacitance characteristics (C-F) of MSIS structures. The simpler metal insulator metal (MIM) structure for evaluation of static dielectric constant of magnetic, n-type conducting ZnO layers would be problematic for modelling frequency dependent capacitance data. This is because even nominally insulating ZnO thin films in MIM structures are leaky insulators and such MIM structures are not suitable for analysing non-linear frequency dependent impedance. And also, the analysis of current voltage (IV) and impedance (CV) data of Schottky diodes with completely depleted ZnO thin films have too many unknown implicit parameters to extract the static dielectric constant of the ZnO thin film in a Schottky diode from the IV and CV data. Schottky diodes with n-type conducting Zn0.95Co0.05O thin films have been investigated by Kasper et al.7. Kasper et al. used a static dielectric constant of εr = 2521. It was not possible to extract the static dielectric constant of Zn0.95Co0.05O. Therefore, we chose a MSIS heterostructure in order to extract the static dielectric constant of magnetic, n-type conducting ZnO layers.

Results

Oxygen vacancies in n-ZnO are intrinsic donors and increase the concentration of the electron majority charge carriers n. If the carrier concentration n is small, the ZnO thin films in the metal/n-ZnO semiconductor/Si3N4 insulator/p-Si semiconductor MSIS structures are insulating. With decreasing n the carrier mobility μ increases and influences the dc transport properties of the ZnO in the (MSIS) structures. The ZnO, ZnCoO, and ZnMnO thin films have been grown by PLD on insulator-semiconductor (Si3N4/p-Si) MIS structures for investigating the static dielectric constant of the magnetic ZnO thin films (Fig. 1). In the following we show how measured impedance has been modelled and how the extracted capacitance of the magnetic ZnO thin films has been used to extract the static dielectric constant of magnetic ZnO in dependence on the species and concentration of magnetic ions. The polarity and strength of the applied bias on the Al/ZnO interface determines the ionization of donor oxygen vacancies (\({V}_{o}\)) (Fig. 1(a–c)). The mobile defects in Si3N4 are redistributed in Si3N4 under a bias applied to the MSIS structure, namely with large negative applied bias in accumulation towards the ZnO/Si3N4 interface (Fig. 1(a)) and for a large positive applied bias inversion towards the Si3N4/p-Si interface (Fig. 1(c)). The flat band voltage lies in the negative bias range (Fig. S3 in supplementary) for both ramping directions, namely from accumulation (Fig. 1a) to inversion (Fig. 1c) and from inversion to accumulation. This indicates the presence of positive charge defects in Si3N4 (Fig. S3 in supplementary). Si3N4 contains both mobile (~) and fixed (▫) positive charge defects. The presence of fixed impurities and mobile positive charge defects in insulating Si3N4 can be recognized from shift flat band voltage and midgap voltage of conductance and capacitance hysteresis measurements, respectively (Fig. S3). First the distribution of mobile defects in Si3N4 is changed when the dc bias is ramped from +10 V to −15 V (accumulation in Fig. 1(a)) or when the dc bias is ramped from −15 V to +10 V (depletion-inversion in Fig. 1(b,c)). The positive fixed and mobile charge defects in the insulating Si3N4 layer cause a shift of the flat band voltage to larger negative bias. The mobility of the mobile defects in Si3N4 depends on the PLD growth temperature during deposition of the n-type semiconductor on the insulator Si3N4, namely 550 °C for the deposition of ZnO in this work and 380 °C for the deposition of BiFeO3 in a previous work22. It has been reported that the threshold temperature for the formation of defects in Si3N4 lies at circa 500 °C23.

Figure 1
figure 1

Schematic representation of charge distribution in the n-ZnO layer, the Si3N4 layer and the p-Si in the metal/n-ZnO semiconductor/Si3N4 insulator/p-Si semiconductor (MSIS) structure and corresponding band diagram in (a) accumulation (b) depletion and (c) inversion. There are mirror charges on Al top electrode to compensate the charges in p-Si accumulated at the interface Si3N4/p-Si. There are singly ionized oxygen vacancies in accumulation and depletion and single and double ionized oxygen vacancies in inversion in ZnO. The majority charge carriers are accumulated at the opposite interface of the ZnO layer. Si3N4 contains both mobile (~) and fixed (▫) positively charged impurities. The existence of the positive impurity charges are expected from the shift of the flat-band voltage towards more negative biases in the negative bias range. Due to the thickness (~110 nm) of the n-type ZnO thin film, only fully depleted or fully accumulated regime band diagram is shown in the figure. Work function of ΦM for aluminium metal is 4.3 eV, electron affinity of ZnO χZnO is 4.2 eV, electron affinity of Si3N4 χi is 1.8 eV and electron affinity of p-Si χs is 4.15 eV. Band gap of ZnO \({{\rm{E}}}_{g}^{ZnO}\) is 3.3 eV, band gap of p-Si \({{\rm{E}}}_{g}^{Si}\) is 1.1 eV and bulk potential φb of p-Si is 0.36 eV.

Full size image

The small signal analysis of Al/n-ZnO semiconductor/Si3N4 insulator/p-Si semiconductor structures was performed for obtaining the static dielectric constant of completely depleted ZnO, ZnCoO, and ZnMnO thin films (Fig. 1(c)). The MSIS equivalent circuit model in strong inversion is shown in Fig. 2(b)) and accounts for all RC elements in the interfaces and layers of the MSIS structure. The equivalent circuit model describes the measured nonlinear behaviour of the frequency dependent capacitance (C-F) and conductance (G-F) curve (Fig. S5 in supplementary) of samples grown under different oxygen partial pressures 6.5 × 10−3 mbar (LP), 3.91 × 10−2 mbar (HP) for two top contact areas A1 (5.026 × 10−7 m2) and A2 (2.827 × 10−7 m2).

Figure 2
figure 2

Modelled static dielectric constant of ZnO (°), ZnCoO (▫), and ZnMnO (◊) for top contact area (a) A1 [5.026 × 10−7 m2] and (c) A2 [2.827 × 10−7 m2]. The variation of the static dielectric constant which is extracted from CZnO used for modelling [1 ± (Δ/2)] × CZnO (s.a. error of CZnO in Table 1) is indicated as an error bar. Samples grown under low oxygen partial pressure (LP) with 6.50 × 10−3 mbar and under high oxygen partial pressure (HP) samples with 3.91 × 10−2 mbar are shown in open and closed symbols respectively. (b) Equivalent circuit model for Al/ZnO/Si3N4/p-Si/Au MSIS structure at inversion regime (Fig. 1(c)).

Full size image

The equivalent circuit model describes the impedance characteristics of each region in the MSIS structure that includes each material and the interface regions between the materials. The small signal impedance of MIS and of MSIS structures is analyzed in strong inversion (s.a. supplementary). An equivalent circuit model describing the frequency dependent capacitance (C-F) and conductance (G-F) of the reference structure, namely of Al/Si3N4/p-Si/Au metal/insulator/semiconductor (MIS) structures, is presented in ref. 24. In this work we also extended the MOS equivalent circuit model to describe voltage dependent impedance (C-V and G-V))24 to the MSIS equivalent circuit model with a n-ZnO semiconductor layer (Fig. 2(b)) (s.a. supplementary). The modelled parameters of the MIS structure (reference samples) have been used as an estimate for the corresponding parameters of the MSIS structures (s.a. S3.1). The modelling of small signal impedance of the MSIS structure always starts in the high frequency range where the leaky Si3N4 does not dominate frequency dependent small signal impedance (s.a. S3.2). Afterwards the small signal impedance has been modelled in the whole frequency range (s.a. S3.3). CZnO is the parameter which is finally used to extract the static dielectric constant of the ZnO layer in the MSIS structures.

The equivalent circuit model of the MSIS structure is given in Fig. 2(b). It describes the impedance characteristics of each layer in the MSIS structure and the interface regions between each layer. The capacitor Ci represents the Si3N4 capacitance. The p-Si region consists of p-Si depletion capacitance Cdep in series with the Si3N4 capacitor. The sharp termination of p-Si at the Si3N4/p-Si interface causes formation of surface states in p-Si. Those surface states are occupied during strong inversion24. The MSIS equivalent circuit model accounts for slow and fast surface states with capacitance/resistance Css/Rss and Cfss/Rfss, respectively, in parallel to the p-Si depletion capacitance Cdep. The series resistance RS includes resistances from undepleted p-Si in series with top electrode and bottom electrode. The bottom contact capacitance Cst in parallel with the resistor Rst in the circuit model emulates the Schottky junction between the bottom gold contact and semiconductor. The barrier height calculated from the modelled capacitance of bottom contact agrees with the calculation of barrier height from difference in work function of gold (4.8 eV)25 and work function of Si (5.07 eV)26. The sharp interface between ZnO and Si3N4 causes the formation of surface states in ZnO at the ZnO/Si3N4 interface. The MSIS equivalent circuit model (Fig. 2(b)) also accounts for the slow and fast surface states in ZnO with capacitance/resistance CZss/RZss and CZfss/RZfss in parallel with the depletion capacitance CZnO in ZnO, respectively. Also, charges at the interface of top contact aluminium (Al) and ZnO are taken into account with capacitance CAl in parallel with the resistance RAl. Additional resistive elements RZI and RIS (RZI = RIS) which describe the conductivity changes in the defective Si3N4 at the ZnO/Si3N4 and Si3N4/Si interfaces, respectively, have been incorporated into the MSIS equivalent circuit model to describe the defects in the Si3N4 (S3.4). In Fig. 2, dotted vertical lines indicate the interface between each layer. We show arrows at the interface position of ZnO/Si3N4 and Si3N4/ZnO to sketch that RZI and RIS are finite and belong to the leaky Si3N4 dielectric. We see a frequency dependent capacitance for Si3N4 in small signal ac analysis. Also, a voltage dependent dc conduction is seen in leaky Si3N4. Therefore, Si3N4 can be considered as a broken ac channel with same dc conduction and for small signal equivalent circuit. Analytically we considered a capacitor with reduction in effective thickness described by Beaumont and Jacobs model27. Because ac conduction does not go through the Si3N4 at all frequencies and because of charge neutrality, the resistance change due to accumulation of charges at the interface ZnO/Si3N4 (RZI) and at the interface Si3N4/p-Si (RIS) the corresponding resistance change is the same, i.e. RZI = RIS.

Discussion

The dielectric constant of the ZnO layer in the MSIS structure has been determined from the modelled CZnO (Fig. 2(b)) using the area of the Al top contacts and the ZnO thickness from SEM measurements (Table S1 in supplementary). The static dielectric constant εr (Table 1) calculated for ZnO, ZnCoO, and ZnMnO grown at 6.50 × 10−3 mbar (LP), 3.91 × 10−2 mbar (HP) oxygen partial pressure is plotted in Fig. 2(a) for contact area A1 and in Fig. 2(c) for contact area A2 (A1 = 5.026 × 10−7 m2 and A2 = 2.827 × 10−7 m2). The modelled static dielectric constant of ZnO ranges between 8.2 and 9.3 and is in good agreement with literature values in the range between 8.5 and 9.5. A strongly increased static dielectric constant has been deduced from CZnO of MSIS structures with ZnCoO and ZnMnO thin films. We also see a slight increase of dielectric constant for ZnO_LP and ZnO_HP in comparison to bulk ZnO. However, it is not proven so far that the observed increase of dielectric constant in ZnO can be related with magnetism in ZnO, e.g. with magnetism due to the formation of bound magnetic polarons (BMPs). One could speculate that for ZnO_LP which has been grown at low oxygen partial pressure and which has a larger concentration of intrinsic donors, more donors are available as centres for BMPs. One possible type of ferromagnetic s-d exchange interaction in pure ZnO is the s-d exchange interaction between 3d electrons of Zn ions and electron spin of oxygen vacancies (Vo+). Therefore, we expect an increased volume of bound magnetic polarons (Eq. (1)) in magnetic ZnO in comparison to unmagnetic ZnO.

Table 1 Modelled static dielectric constant of the ZnO thin films for ZnO_LP, ZnO_HP, Zn1−xCoxO_LP, Zn1−xCoxO_HP, Zn1−xMnxO_LP, and Zn1−xMnxO_HP from modelled capacitance (CZnO) and measured SEM thickness (s.a. Supplementary Table S1).
Full size table

The resistance of the ZnO has been measured and the transport properties are classified28,29 by ranges of resistance in Table 1. Insulating ZnO thin films have lower εr while low conducting ZnO and moderate conducting ZnO thin films have higher εr which is an indication of the dielectric constant dependence on donor concentration. Here the donors are intrinsic donors formed in ZnO by oxygen vacancies (\({V}_{o}\)) whose concentration depends on the oxygen partial pressure during PLD growth of ZnO. One might expect smaller dielectric constant in higher pressure (HP) samples in comparison to lower pressure (LP) samples, because electrically polarizable BMP represent a collective spin of 3d spins of Mn2+ in ZnMnO and of Co2+ spins in ZnCoO which is mediated by s-d exchange interaction between 3d wavefunction of 3d spins and s wavefunction of the electron spin of Vo+ in the centre of the bound magnetic polaron30. More BMPs are expected for a larger number of oxygen vacancies in lower pressure samples.

There exist three types of known native donors in ZnO oxide, i.e., O vacancies (Vo), Zn interstitials (IZn), and H related defects (Hi)31 which play crucial roles in determining the transport and optical properties of zinc oxide. We investigated the species of shallow donors in ZnO thin films grown by pulsed laser deposition by assuming two different donors with two thermal activation energies in the ZnO. For example, in our previous work Vegesna et al.28 the existence of two different donors could (\({{\rm{E}}}_{a}^{1}\) = 1.54 meV and \({{\rm{E}}}_{a}^{2}\) = 82.75 meV) be proven by modeling the temperature dependent free carrier concentration. This thermal activation energy hints towards hydrogen related defects and zinc interstitials. Because the thermal activation energy of oxygen vacancies amounts to 300 meV Hofmann et al.32, it is not possible to prove existence of oxygen vacancies in ZnO by temperature dependent transport measurements. Hoffman et al. used photoluminescence measurements and related the green emission from ZnO with the existence of oxygen vacancies. In a recent work Liu et al.33 showed that oxygen vacancies are the dominant defects in n-type conducting ZnO using oxygen isotope diffusion which depends on the concentration of oxygen vacancies. Here we focus on native point defects providing a single electron spin for the formation of BMP in magnetic, intrinsically n-type conducting ZnO. The only native donor in n-ZnO carrying a single electron spin is the O vacancy (\({V}_{o}^{+}\)). Zinc interstitials occur exclusively in the 2+ charge state, i.e., \({I}_{Zn}^{++}\)34. Therefore, formation of bound magnetic polarons with \({I}_{Zn}^{++}\) (no electron, S = 0), IZn (paired electrons, S = 0) and \({H}_{i}^{+}\) (no electrons, S = 0) is not possible. Only singly ionised oxygen vacancy (\({V}_{o}^{+}\)) (single electron, S = 1/2) can form the center of BMP. \({V}_{o}\) (paired electrons, S = 0) and \({V}_{o}^{2+}\) (no electron, S = 0) with zero-valued electron spin cannot be the center of the a donor-BMP35.

The spin interaction volume in BMP constitutes30 represent a collective spin of 3d spins of Mn2+ and Co2+ which is mediated by s-d exchange interaction between 3d wavefunction of 3d spins and s wavefunction of the spin of \({V}_{o}^{+}\) in the center of the bound magnetic polaron. The volume of bound magnetic polaron defined by the Bohr radius is proportional to the static dielectric constant. The Bohr radius can be calculated using following equation

$${r}_{b}=\frac{4\pi {\varepsilon }_{0}{\varepsilon }_{r}\hslash }{m{e}^{2}},$$
(1)

where ε0 is permittivity of free space, \(\hslash \) is reduced Planck's constant, εr is static dielectric constant, m is effective mass (0.24m0)36 and e is elementary charge.

The bound magnetic polaron (BMP) in ZnCoO and in ZnMnO has a huge collective spin, if many 3d ions lie in the volume of the bound magnetic polaron. The larger the number of 3d ions in the BMP volume, the more spins of 3d ions can be aligned in parallel by the s-d exchange between the spin of the oxygen vacancy (\({V}_{o}^{+}\)) in the center of the BMP and the spins of the 3d ions in the BMP volume within the Bohr radius37. The BMP will increase the polarizability of magnetic ZnO.

In our work, we have extracted the static dielectric constant from frequency dependent impedance data measured on ZnO coated MSIS structures. The model does not capture frequency dependence of the dielectric constant of ZnO. In the measured frequency region up to 1 MHz the dielectric constant of ZnO are expected to be constant. Therefore, a time dependent switching characteristics of static dielectric constant in ZnO can only be studied if the switching is non-volatile. For example, the model could possibly be used to investigate the dynamics of spin alignment in BMPs in magnetic, n-ZnO if single magnetic field pulses of different lengths are applied before the measurement of impedance data in dependence on the magnetic field pulse length. Before applying subsequent magnetic field pulse and before measuring the resulting frequency dependent impedance data, the spin alignment in the BMP has to be destroyed, e.g. by an ac magnetic field. We expect that the dynamics of the spin alignment in BMPs will depend on the volume and on the material dependent ferromagnetic s-d exchange parameter. A direct measurement of the spin dynamics in BMP would be possible if the frequency dependence of the dielectric constant could be measured in the several hundred GHz frequency range, e.g. by microwave measurements.

In the following we discuss possible percolation of BMP in ZnO with dependence on the static dielectric constant and the concentration of oxygen vacancies. Coey and Venkatesan30 estimated the concentration of defects in ZnO for polaron percolation based on a static dielectric constant of ZnO of (εr) and Bohr radius (rH). A threshold concentration of defects inZnO of 4 × 1019 cm−3 has been obtained for εr = 4.0 and rH = 0.76 nm from (\({n}_{\square }^{crit}\))1/3 rH ≈ 0.2638, where \({n}_{\square }^{crit}\) is the critical defect concentration for delocalization of the impurity band states. In Fig. 3 we show the calculated BMP diameter in ZnO thin films with different static dielectric constants (εr(A1) = 8.39 (ZnO_LP), 17.71 (Zn0.95Co0.05O_LP), 21.74 (Zn0.95Co0.02O_LP), 27.00 (Zn0.95Mn0.05O_LP), and 30.49 (Zn0.95Mn0.02O_LP)) and with the density of oxygen vacancies ranging from 1016 cm−3 to 1022 cm−3. For simplicity, for the determination of the distance between oxygen vacancies we have considered a homogeneous oxygen vacancy distribution. The diagonal black solid line gives the distance between two oxygen vacancies in dependence on concentration of oxygen vacancies. If the distance between the oxygen vacancies is smaller than the diameter of BMP, BMPs coalesce and overlap. Such overlap of bound magnetic polarons possibly induces ferromagnetism in magnetic ZnO at room temperature39,40 if the orientation of the electron spin of the oxygen vacancy in the center of BMP is stable and not continuously changing due to hopping transport of free carriers via oxygen vacancies.

Figure 3
figure 3

Calculated distance between the homogeneously distributed oxygen vacancies (black line) for ZnO in dependence on oxygen vacancy concentration (\({{\rm{V}}}_{o}^{+}\)) in logarithmic scale. Calculated sample dependent bound magnetic polaron (BMP) diameter represented in the same range of \({{\rm{V}}}_{o}^{+}\). Oxygen vacancies overlap in the dotted area for \({{\rm{V}}}_{o}^{+}\) concentrations larger than the \({{\rm{V}}}_{o}^{+}\) concentration (intersection of colored lines and black line) where BMP diameter and distance between \({{\rm{V}}}_{o}^{+}\) are equal.

Full size image

We describe the frequency dependent capacitance (C-F) behaviour of the Al/n-ZnO semiconductor/Si3N4 insulator/p-Si semiconductor MSIS structure with an equivalent circuit model in strong inversion regime where each layer and interface has been described. Static dielectric constant of ZnO has been extracted from modelled capacitance of the ZnO layer. The dielectric constant of ZnO lies in the expected range from 8.1 to 9.3. We observed strongly increased static dielectric constant in magnetic ZnO in dependence on the concentration of magnetic ions and on the concentration of oxygen vacancies. The dielectric constant in ZnMnO with 5 at. % Mn is 28.3 and with 2 at. % Mn is 31.8. The dielectric constant in ZnCoO with 5 at. % Co is 17.7 and with 2 at. % Co is 22.0. The ferromagnetic s-d exchange interaction between electron spin of donors (\({V}_{o}^{+}\)) in the center of the bound magnetic poloron (BMP) and the electron spin of substitutional magnetic ions is partially superimposed by the anti-ferromagnetic coupling between nearest neighbours substitutional magnetic ions. With increasing concentration of substitutional magnetic ions it is expected that the anti-ferromagnetic coupling which excludes ferromagnetic s-d coupling increases and weakens the formation of BMPs. This is the possible reason why we see a larger static dielectric constant in magnetic ZnO with 2 at. % substitutional magnetic ions in comparison to magnetic ZnO with 5 at. % substitutional magnetic ions. The observed trend is in agreement with the observations from Franco et al.41 on powdered ZnCoO who observed a maximum of static dielectric constant in powdered ZnCoO around 2 at. % Co. We related the increased static dielectric constant in magnetic ZnO with the formation of partially overlapping bound magnetic polarons and their contribution to the electrical polarizability of magnetic ZnO.

Finally, we estimated the contribution of the BMP in ZnO to the polarizability of ZnO. The resonance of BMP typically lies in the several hundred GHz range. Here we chose the same resonance of BMP in magnetic ZnO as shown for the magnetic semiconductor CdMnTe where an additional absorption due to BMP has been observed at 120 GHz by Raman shift measurements (4 cm−1)42. We assumed an additional polarizability of magnetic ZnO due to BMP and added this to the modelled imaginary part (ε2) of the dielectric constant (Fig. 4(b,d,f)).

$${\varepsilon }_{2}(x)={\varepsilon }_{2}^{BMP}(x)+{\varepsilon }_{2}^{Phonon}(x)+{\varepsilon }_{2}^{Electronic}(x)$$
(2)

where \({\varepsilon }_{2}^{BMP}\) is the contribution due to BMP, \({\varepsilon }_{2}^{Phonon}\) is the contribution due to phonons in ZnO43 and where \({\varepsilon }_{2}^{Electronic}\) is the contribution due to electronic transitions in ZnO44. \({\varepsilon }_{2}^{BMP}\) has been described with a Lorentz oscillator model as follows:

$${\varepsilon }_{2}=1+{N}_{peak}\frac{\Gamma \omega }{{({\omega }_{o}^{2}-{\omega }^{2})}^{2}+{\Gamma }^{2}{\omega }^{2}}$$
(3)

where ωo is the BMP peak position (ωo = 120 GHz), Npeak is the peak strength and Γ is the FWHM. We calculated the real part (ε1) of the dielectric constant (Fig. 4(a)) using Kramers-Kronig relation (Eq. (4)) for ZnO with the electronic44 and phonon43 contribution to ε2. Additionally, the FWHM of a Lorentz oscillator with a fixed peak strength(Npeak = 350) and fixed peak position has been varied to change the contribution from \({\varepsilon }_{2}^{BMP}\) to ε2 in Fig. 4(d,f)) and derived ε1 of magnetic ZnO in Fig. 4(c,e), respectively, using Kramers-Kronig relation (Eq. (4)) \({\varepsilon }_{2}^{BMP}\) as long as static dielectric constant ε1 from Eq. (4) was the same as the modelled static dielectric constant from impedance measurements (εr).

$${\varepsilon }_{1}(\omega )={\varepsilon }_{\infty }+\frac{2}{\Pi }{\int }_{0}^{\infty }\frac{x\cdot {\varepsilon }_{2}(x)}{{x}^{2}-{\omega }^{2}}$$
(4)

Estimated FWHM for Zn0.95Co0.05O is Γ = 0.7 GHz, Zn0.95Mn0.05O is Γ = 4.1 GHz, Zn0.98Co0.02O is Γ = 0.8 GHz, and Zn0.98Mn0.02O is Γ = 6.1 GHz.

We expect that the dielectric constant peak position can be tuned via the material dependent ferromagnetic s-d exchange parameter. Here we rather focused on the amplitude of the additional absorption \({\varepsilon }_{2}^{BMP}\) in the several hundred GHz range. We expect that the amplitude can be tuned via via the volume of the BMP. Dielectric constant shown in Fig. 4 represents the dielectric constant of magnetic ZnO layer in the MSIS structure. So far, we have not directly investigated the properties of BMPs in the several hundred GHz range.

Figure 4
figure 4

Real part (ε1) of dielectric constant for (a) ZnO, (c) Zn0.95Co0.05O, Zn0.95Mn0.05O, and (e) Zn0.98Co0.02O, Zn0.98Mn0.02O has been estimated by applying Kramers-Kronig tranformation to imaginary part (ε2) of dielectric constant for (b) ZnO, (d) Zn0.95Co0.05O, Zn0.95Mn0.05O, and (f) Zn0.98Co0.02O, Zn0.98Mn0.02O, respectively. The electronic44 and phonon43 contribution to ε2 has been taken from literature43,44. An additional contribution to ε2 due to BMP at 120 GHz has been assumed in such a way that ε1 agrees with modelled εr.

Full size image

ZnO coated Si3N4/p-Si metal insulator semiconductor (MSIS) structures with nominal concentration of 2 at.% and 5 at.% Co2+, Mn2+ ions at 6.50 × 10−3 mbar, 3.91 × 10−2 mbar oxygen partial pressure are grown by pulse layer deposition (PLD). Voltage dependent capacitance (C-V) and frequency dependent capacitance (C-F) characteristics have been measured. Thickness of ZnO layer and Si3N4 is obtained from secondary electron microscopy (SEM) cross section images. Measured C-F characteristics at strong inversion regime of ZnO coated MSIS structure shows, nonlinear behaviour of the capacitance. To describe the nonlinear behaviour of the C-F characteristics we proposed an equivalent circuit model at strong inversion regime. The RC equivalent circuit model gives the description of each region of Al/ZnO/Si3N4/p-Si/Au MIS structure such as metal, insulator, semiconductor including interface region between materials. Dielectric constant is obtained from modelled ZnO capacitance value and with the thickness of ZnO from SEM measurements. Dielectric constant for ZnO is obtained in the expected range εr = 8.17–9.34. We determined the static dielectric constant in magnetic, n-type conducting ZnO thin films with different Co and Mn concentration. With 2 at. % it is 31.84 and for 5 at.% Mn sample dielectric constant is 28.31 and for 2 at.% Co samples dielectric constant is 22.31 and for 5 at.% Co sample it is 17.71. We attribute the increase of the static dielectric constant to the contribution of bound magnetic polarons to the electrical polarization of magnetic, n-type conducting ZnO.

With increase in oxygen vacancies at the surface, bound magnetic polaron formed with oxygen vacancy as nucleus can overlap and provide ferromagnetic behaviour at room temperature45 Davies et al.46 and Kaspar et al.7 suggest that ferromagnetic features from bound magnetic polaron can be used in developing magnetic sensors, non-volatile memories in spintronics devices which are potentially expected to be energy-efficient devices. Application of BFO coated Si3N4 MIS structure as a photocapacitive detector has been studied by You et al.22. Because ZnO is transparent and because the ZnO coated Si3N4 MIS structure shows similar capacitance behaviour as the BFO coated Si3N4 MIS structure, the ZnO coated Si3N4 MIS structure is expected to reveal similar photocapacitive functionality as the BFO coated Si3N4 MIS structure to detect intensity and color of visible light by impedance measurements. In addition, we suggest to use the ZnO coated Si3N4 MIS capacitor as magneto-capacitive detector where the presence of a magnetic field can be detected via the increase of static dielectric constant due to the formation of BMPs with aligned spins of magnetic ions.

We propose to study change of static dielectric constant in magnetic transparent conducting oxides (TCO)47,48 by preparing metal/n-TCO/insulator/p-Si MSIS structures and by measuring and modelling the impedance in strong inversion. It is expected that also other magnetic n-type conducting TCOs reveal an increase of static dielectric constant due to the formation of bound magnetic polarons and due to the contribution of BMP to the polarizability of magnetic TCOs. Bound magnetic polarons strongly influence transport, magnetization and magnetooptical properties in magnetic semiconductors within the confined volume of BMPs. For example, ferromagnetic behaviour in magnetic ZnO at room temperature can be related with BMP45,49 and it has been suggested that ferromagnetic behavior related with BMP formation in magnetic n-type conducting TCOs can be used in developing magnetic sensors and non-volatile memories in spintronics devices with a low energy consumption7,50. If BMPs are coalescing, even at the room temperature strongest effect of BMPs on the transport, magnetization and magnetooptical properties51 of magnetic semiconductors can be expected.

Methods

First alpha silicon nitride (α-Si3N4) thin films with a nominal thickness of about 88 nm were deposited in a Roth and Rau AK1000 microwave PECVD reaction chamber. Afterwards ZnO, ZnCoO, and ZnMnO thin films with the nominal concentration of 2 at.% and 5 at.% Co and Mn have been grown on top of Si3N4/p-Si MIS structures by PLD with 700 1 Hz KrF excimer laser pulses with energy density of 1.60 Jcm−2 to ablate ZnO, ZnMnO, and ZnCoO ceramic targets at a substrate temperature of 550 °C with a constant oxygen flux of 4.50 sccm. Two different oxygen partial pressures, 6.50 × 10−3 mbar and 3.91 × 10−2 mbar, have been applied to control the concentration of oxygen vacancies in the magnetic ZnO thin films. The bottom of the p-Si has been coated with gold (Au) using dc magnetron sputtering at room temperature to form a bottom contact to the MIS structure. Circular dc magnetron sputtered aluminium dots of different size have been prepared on the ZnO films to form the top contacts on the MIS structure. For impedance measurements we have chosen Al contacts with and area of 5.026 × 10−7 m2 (A1) and of 2.827 × 10−7 m2 (A2).

Structural properties of investigated ten different metal/n-ZnO semiconductor/Si3N4Si3N4 insulator/p-Si semiconductor (MSIS) structures, mainly thickness of the n-ZnO and Si3N4, have been determined using secondary electron microscopy (SEM) cross section measurements (Sect. S1). Impedance of the MSIS structures with ten different ZnO, ZnCoO, and ZnMnO thin films grown on Si3N4/p-Si was measured versus voltage (V) and versus frequency (F) using the Agilent 4294A precision impedance analyzer. We determined the bias range for the different regimes in the MSIS structure (accumulation, depletion, inversion, strong inversion) by voltage dependent impedance measurements (Sect. S2). Nonlinear behaviour of the frequency dependent capacitance (C-F) and conductance (G-F) of all MSIS structure in strong inversion has been modelled with an equivalent circuit model which accounts for all RC elements in the interfaces and layers of the MSIS structure. The static dielectric constant of n-ZnO has been extracted from modelled capacitance (CZnO) of completely depleted n-ZnO layer of the MSIS structure (Sect. S3).