Er³⁺ doped ZnO powders were prepared via controlled solid state reaction route at high temperature. The samples were prepared by thorough mixing of ZnO (Sigma aldrich product −99.99% purity) and Er₂O₃ (Sigma aldrich product −99.99% purity) and made in to slurry by adding LiOH.H₂O (merck product −99.99% purity) and ethanol (merck product −99.99% purity). In this study LiOH act as a heat transfer medium. The slurry then dried at 100˚C in an oven. Then obtained powder sample was well ground for 1hr using a mortar and pestle and made in to pellets using hydraulic pelletizer at a pressure of 8 Torr. The pellets were packed in a quartz boat and fired at 900˚C. The heat treated pellets were again ground for 15 minutes and used as the sample. Five batches of samples were prepared by varying the wt% of erbium as 0.3 wt%, 0.6 wt%, 0.9 wt% and 1.2 wt% of total amount of the powder sample.

The phase purity and structural informations were obtained by using Rigaku Miniflex 600 machine with Cu Kα radiation (1.5406 Å). The powder X, PDXL: Integrated powder X-ray diffraction software and ICDD data base were used for phase determination, peak reflection assignments and to analyse variations in peak positions and intensities. The purity of samples was confirmed with Energy Dispersive X-ray Analysis (EDAX) equipment of Hitatchi. The dielectric studies were done with Hioki 3532-50 LCR HiTESTER.

The crystallinity and structure of the synthesised samples were analysed by X-ray diffraction data recorded. The intensity data was collected over a 2θ range of 10˚ - 90˚. Powder X-ray diffraction patterns of undoped and Er- doped ZnO samples plotted in the Figure 1. All patterns are well matched with the standard X-ray diffraction pattern indicating hexagonal wurtzite structure of bulk ZnO. Diffraction peaks corresponding to reflections from planes (100), (002), (101), (102), (110), (103), (112) of Wurtzite ZnO structure, which are consistent with the standard ICDD Card no.01-074-9940. When the concentration of erbium was increased further, extra phase related to Er₂O₃ arises and is observed in Figure 2. It indicates that at this concentration the solubility limit of erbium in ZnO has exceeded. And thus multiphase formation occurs at this concentration.

Using Scherrer formula, D = 0.9λ/βcosθ, where λ is the wavelength of CuKα radiation (1.514 Å), θ is the peak position and β is the FWHM, the average crystallite size of the samples was estimated [5] . It is found that average crystallite size decreases with increase in doping concentration. The average crystallite size of pure ZnO nanoparticle was 57.71 nm. It is decreased to 45.26 nm with 1.2 wt% doping of erbium. The decrease in crystallite size is due to the distortion of host ZnO lattice by RE³⁺ ions, which actually reduces the nucleation and subsequent growth rate of ZnO crystals.

In order to confirm the chemical composition of the samples, Energy Dispersive Spectra were taken. The sam-ples were cleaned by Ar+ ion beam sputtering to remove surface contamination if any. Figure 3(a) is the energy dispersive spectra of undoped ZnO. Figure 3(b) is the energy dispersive spectra of doped (Er³⁺ −1.2 wt%) ZnO ceramics. From Figure 3(a), the purity of parent sample is confirmed. There are no impurities in the parent ZnO sample. The incorporation of Er³⁺ ions in ZnO crystal lattice are confirmed from the Figure 3(b).

Dielectric measurements of the undoped and erbium doped ZnO were carried out as a function of frequency at room temperature using an LCR meter. The samples were pelletized by using a hydraulic press and this pellet was placed between the electrodes. The dielectric constant (ε_r) is calculated using the relation ε_{r =} Cd/ε₀A and the ac conductivity is calculated by the relation, σ_ac = ε₀ε_rωtan(Δ), where C is the capacitance, d is the thickness, A is the area of cross section of the pellet and tan(Δ) is the dielectric relaxation of the sample. It is observed that the dielectric constant decreases with increasing frequency for all samples. This is evident in the low frequency region and is shown in Figure 4. At high frequencies the dielectric constant becomes frequency independent. Maxwell-Weigner model can be used to explain the dielectric properties of the homogeneous double structure systems. According to this model the dielectric medium is made of well conducting grains with poorly conducting or resistive grain boundaries. Thus by the application of external electric field, the charge carriers easily moves, but will be accumulated at the grain boundaries. This process causes large polarization and high dielectric constant produced by the sample. At low frequency, the small conductivity of grain boundary contributes to the high value of dielectric constant. The interfacial/space charge polarization due to inhomogeneous dielectric structure can also be considered as the reason for high dielectric constant. Beyond certain level of frequency of external field, the hopping between different metal ions (Zn²⁺, Er³⁺) can not follow the alternating field [2] . This is why the dielectric constant becomes frequency independent beyond certain limit. The decrease in dielectric constant with increase in frequency in the lower frequency range can be considered as a natural phenomenon because any species contributing to polarizability is found to show lagging behind the applied field at higher and higher frequencies.

In order to investigate further the effect of erbium doping, the dielectric constant of material is re plotted in

Figure 5 as a function of concentration of erbium. The dielectric constant is found to be decreased first withsmall amount of erbium incorporation (0.3 wt%). It is striking to see that the dielectric constant increases dramatically while the concentration of erbium is increased to 0.6 wt%. Further increase in erbium concentration decreases the dielectric constant of ZnO. The incorporation of small amount of Erbium ions produces distortion and an abrupt unstability in the crystal lattice of ZnO, which results in the decrease of dielectric constant of the material. But when the concentration is increased to an optimum concentration of 0.6 wt%, the system gets stabilized and results in the reduction of the number of oxygen vacancies [18] . This leads to an increase in the dielectric constant. Further increase of erbium content would result in the unit cell contraction and hence the free volume available for the displacement of ions gets reduced. This results in the decrease of dielectric polarization and dielectric constant.

An important observation from Figure 5 is the frequency dependence of the dielectric constant of the samples with erbium concentration 0.6 wt% and 0.9 wt% and the frequency independent behaviour of dielectric constant of samples with 0.3 wt% and 1.2 wt% erbium incorporation. This observation will be very useful in the practical applications of these materials. It is interesting to note that the sample with 0.6 wt% erbium incorporation appears to be the best dielectric material than the parent ZnO at 100 Hz, 10 KHz, 100 KHz and 1000 KHz. This helps us to optimize the concentration of erbium in ZnO for making good dielectric material.

Figure 6 shows the variation of ac conductivity of undoped and Erbium doped samples with frequency. The ac conductivity of all the samples gets increased with increase in frequency. But the maximum ac conductivity is seen for undoped ZnO sample and which decreases with the erbium incorporation. The production of defects like zinc interstitials in the ZnO host system by erbium ions can be considered as the reason for this reduction in ac conductivity. It is very relevant that the doping percentage plays important role in tuning the electrical property of the sample. Because the 0.6 wt% erbium incorporation show maximum ac conductivity as compared to other doped samples. After this optimum doping percentage the ac conductivity is found to be decreased with increase in doping percentage. This decrease may be due to the defects produced by erbium ions in ZnO host matrix. As doping concentration increases, the defect ions which facilitates the formation of grain boundary defect barrier, leading to blockage to the flow of charge carriers. This in turn decreases the conductivity of the system on doping.

Figure 7 shows the variation of dielectric loss values tan(δ) with frequency of the un doped and erbium doped ZnO samples. Loss tangent i.e. tan(δ) is the energy dissipation in the dielectric system. It is found to be maximum for undoped ZnO samples. As erbium doping increases, this loss factor is decreased to a large extend. The decrease of tan(δ) with increase in frequency seen in erbium doped samples is due to the space charge polarization. This peculiar behaviour as well as the very low loss factor compared to the parent ZnO makes the prepared samples suitable for high frequency device applications.