1 Introduction

Zinc oxide (ZnO) is a II–VI semiconductors material with exciton binding energy of 60 meV at room temperature, a direct wide band gap of 3.37 eV which are attractive physical and chemical properties for various optoelectronic applications, i.e., gas sensor, photodetectors, blue light-emitting diodes and laser diodes [1–15]. Furthermore, ZnO is a promising material for piezoelectric sensors and mechanical actuators due to its strong piezoelectric and pyroelectric properties arising from large electrochemical coupling and the vacancies in its wurtzite structure with a hexagonal lattice (a = 0.325 nm, c = 0.521 nm) [16].

Electro-optical and structural properties of ZnO nanomaterials can be controlled and improved by doping process. As is well known that the rare earth (RE) ion doped ZnO have received considerable attention for use in optical devices. The trivalent RE ions enhance optical properties of ZnO due to its partially filled 4f energy level, surrounded by full 5s and 5p orbitals.

Many different physical and chemical techniques have been developed to synthesize Er and Yb doped-ZnO nanostructures e.g. wet chemical method [17–20], sol–gel method [21], chemical method [22], magnetron reactive sputtering [23, 24], solid state reaction [25, 26], spray pyrolysis [27].

The hydrothermal synthesis of fabricating ZnO nanostructures comes to fore among the other technics due to its suitability to any type of doping and easy control of dopant concentration, good potential for environmentally-safe large scale production, tolerable growth condition and low reaction temperature adaptable to the plastic electronics and microelectronics.

Contrary to the superior properties of hydrothermal method, the number of studies of Er [28–30] doped ZnO is scarce in the literature. Especially, Yb doped ZnO prepared by hydrothermal method is not reported previously. In this regard, this is a novel study which studies the effect of Er and Yb doped ZnO nanostructures synthesized by hydrothermal method. In this paper, undoped and RE (Er, Yb) doped ZnO nanopowders have been synthesized using hydrothermal method. Our aim is to comparatively investigate the effect of Er and Yb doping influence on structural, optical and electrical properties of ZnO nanopowders by using XRD, SEM, EDS, UV–visible diffuse reflectance spectroscopy techniques, and Hall effect measurements.

2 Experimental details

ZnO nanoparticles doped with Erbium and Ytterbium were prepared by hydrothermal synthesis method to study their structural, optical and electrical properties. The chemicals used in the experiment are Zinc acetate dihydrate (Zn(CH3COO)22H2O) (Merck), Erbium(III)acetate tetrahydrate (Er(CH3COO)24H2O) (Merck), Ytterbium(III)acetate tetrahydrate, (Yb(CH3COO)24H2O) (Merck), hexamethylenetetramine (HMT) (Merck). Firstly, 0.2 M equimolar aqueous solution of Zinc acetate and 5 % mol of Er acetate and Yb acetate were dissolved in distilled water, separately. Each of the obtained solutions were added 0.56076 g of hexamethylenetetramine and kept under magnetic stirring for 2 h. Then solutions were transferred into the Teflon-lined autoclave. The reaction was conducted in an electric oven at 120 °C for 18 h. Er-doped ZnO powder and Yb-doped ZnO powder were separated from the solution by using centrifuge and washed with deionized water and dried in air. The undoped, Erbium and Ytterbium doped ZnO samples are labeled as ZnO, Zn0.95Er0.05O, and Zn0.95Yb0.05O, respectively. Finally, the powders were calcined in a muffle furnace at 600 °C for 1 h. The flow chart of the sample preparation is shown in Fig. 1.

Fig. 1
figure 1

Flowchart showing the procedure of preparing the undoped, Er-doped and Yb-doped ZnO nanoparticles

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The structural properties of the samples were studied using Rigaku Multiflex X-ray diffraction (XRD) instrument at room temperature, with monochromated Cu Kα (λ = 1.5418 Å), in the scan range of 2θ between 20° and 80° with a scan speed of 3°/min and a step increment of 0.02. The surface morphologies of the samples were evaluated by scanning electron microscopy SEM (FEI Quanta Feg 250). The diffuse reflectance of UV–Vis spectra of the samples were measured by Shimadzu UV-2600 spectrophotometer.

The electrical properties of the samples were performed by using an Ecopia HMS-5000 Hall Effect Measurement System using the four-point van der Pauw method. The system allows for variable temperature readings between 77 and 350 K with fixed magneto-flux density of 0.51 T and injected current that can be controlled between 1 nA and 20 mA. The sample powders were pressed as disc shaped pellets, and the four corners were soldered by silver blobs for the ohmic contacts.

3 Results and discussion

The XRD patterns of the undoped and rare-earth (Er, Yb) doped ZnO nanostructures are shown in Fig. 2. As shown in the figure the characteristic peaks related to Er and Yb impurities do not appear in XRD patterns in comparison with the standard XRD patterns of bulk ZnO (JCPDS 36-1451), which indicate that all Er and Yb atoms have entered into ZnO lattice. All the samples have wurtzite hexagonal structure with the preferred orientation along the (100) direction. The intensity of (100) peak is reduced with the addition of Yb (5 %) while (002) peak intensity slightly increases. The addition of Er (5 %) causes notable increase in both (100) and (002) peak intensities. More intense and sharper diffraction peaks of Er doped sample point out that Er doping enhances crystallinity compared to other samples.

Fig. 2
figure 2

XRD patterns for undoped and rare-earth (Er, Yb) doped ZnO nanoparticles

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The hexagonal lattice constants a and c were calculated from the interplanar spacing, dhkl, of (hkl) planes obtainable from XRD peaks and using the following equation,

$$\frac{1}{{d^{2} }} = \frac{4}{3}\left( {\frac{{h^{2} + hk + k^{2} }}{{a^{2} }}} \right) + \left( {\frac{{l^{2} }}{{c^{2} }}} \right)$$

The lattice parameters a and c for undoped, Er-doped and Yb-doped ZnO nanopowders are given in Table 1. The average grain sizes (D) of samples were calculated using Scherrer’s formula [31]

$$D = \frac{0.9\lambda }{B\cos \theta }$$

where λ is the wavelength of incident X-ray, \(B = \sqrt {b_{m}^{2} - b_{0}^{2} }\) is the line broadening, b m and b 0 are the full width at half maximum of the XRD peak of the sample and the silicon standard. The average grain sizes were obtained using the full width at half maximum of (101), (002), and (100) characteristic peaks and the results are listed in Table 1. Both lattice parameters and the grain sizes increase with Yb and Er doping as predicted, comparing the difference between the ionic radii of Yb3+ (0.87 Å) and Er3+ (0.89 Å) to Zn2+ (0.74 Å). The increase in grain size of Er doped samples is more than Yb doped samples due to larger ionic radius of Er3+. The increase in crystal parameters indicate distortion of the crystal lattice when Yb3+ and Er3+ ions enter into the ZnO lattice. The crystal lattice distortion degree is calculated by following relation [32]:

$$R = \frac{{2a\left( {2 /3} \right)^{1 /2} }}{c}$$

here a and c are calculated lattice constants from the XRD data. Table 1 clearly suggests that, the lattice distortion increases with Yb3+ and Er3+ doping into the ZnO lattice.

Table 1 The unit cell parameters, crystallite sizes, and lattice distortion degrees calculated from XRD data of the samples
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The mechanism for the formation of ZnO crystals using methenamine, also known as hexamethylenetetramine or hexamine can be summarized in the following chemical reactions [2]:

$$\left( {{\text{CH}}_{2} } \right)_{6} {\text{N}}_{4} + 6{\text{H}}_{2} {\text{O}} \leftrightarrow 6{\text{HCHO}} + 4{\text{NH}}_{3}$$
(1)
$${\text{NH}}_{3} + {\text{H}}_{2} {\text{O}} \leftrightarrow {\text{NH}}_{4}^{ + } + {\text{OH}}^{ - }$$
(2)
$$2{\text{OH}}^{ - } + {\text{Zn}}^{2 + } \leftrightarrow {\text{ZnO}} + {\text{H}}_{2} {\text{O}}$$
(3)

In the hydrothermal processes, if the amount of Zn2+ and OH− ions pass over the critical value, the precipitation form of these ions occurs as ZnO nuclei as shown in reaction (3). The OH− ions play an important role in the nucleation and growth of the hexagonal ZnO structure.

The SEM figures of the undoped, Yb-doped, and Er-doped ZnO samples are shown in Figs. 3, 4, and 5, respectively. These figures clearly show that the formation of hexagonal ZnO nanostructures varied with different dopant ions. Figure 6a–c show EDS spectrum of undoped, Yb-doped, and Er-doped ZnO powders respectively. It is observed that the undoped ZnO nanoparticles are tiny clamped rectangular and rod-shaped crystals. Rod-like particles ranging from 35 to 40 nm in size were formed. The EDS spectrum (Fig. 6a) shows the presence of Zn and O for undoped ZnO powders. For the Yb doped ZnO nanoparticles, rice kernel-like ZnO nanostructures formed as depicted in Fig. 4. The average lengths of the rice kernel-like Yb doped ZnO nanorods are about 300–400 nm. The EDS spectrum of Yb doped ZnO in Fig. 6b indicates the presence of Yb atoms along with zinc and oxygen. Figure 5 shows that Er doped ZnO sample has hexagonal prism-like ZnO structure. Each prism is about 1 µm in diameter and 2 µm in length. EDS spectrum of Er doped ZnO sample in Fig. 6c shows the presence of Er, Zn, and oxygen atoms.

Fig. 3
figure 3

SEM images of the undoped-ZnO nanoparticle with a 50,000 magnification, b 100,000 magnification

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Fig. 4
figure 4

SEM images of the Zn0.95Yb0.05O nanoparticle with a 40,000 magnification, b 80,000 magnification, c 160,000 magnification

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Fig. 5
figure 5

SEM images of the Zn0.95Er0.05O nanoparticle with a 5000 magnification, b 10,000 magnification, c 50,000 magnification

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Fig. 6
figure 6

EDS image of a undoped ZnO, b Zn0.95Yb0.05O, c Zn0.95Er0.05O nanoparticles

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3.1 Optical properties

The reflectance spectra of undoped, Yb and Er doped ZnO samples obtained by UV–Vis diffuse reflectance measurements in the range 300–600 nm wavelength are shown in Fig. 7. In this figure, all samples have a sharp decrease of reflectance intensity around 380 nm as expected for ZnO structures. The reflectance intensities of the samples are around 80 % for wavelengths higher than 420 nm, while they are around 5 % for wavelengths shorter than 370 nm. The optical band gap of the samples are obtained by plotting the (dR/dλ) versus (λ) graph as in Fig. 8 and plugging the wavelength values of the maximum peaks (λ max ) into the equation [33]

$$E_{g} = \frac{hc}{{\lambda_{\hbox{max} } }}$$

where h is the Planck’s constant and c is the speed of light. The obtained Eg values of undoped, Er, and Yb doped ZnO powders are 3.24, 3.23, and 3.22 eV, respectively. The decrease of Eg values with Er and Yb doping is also evident as a red shift of the maximum peaks in Fig. 8. This might be due to the increased defects introduced by Er and Yb doping. Higher defects makes the electronic transitions from the filled valence band to the energy levels of the defects more probable than the transitions to the conduction band.

Fig. 7
figure 7

The reflectance spectra of the undoped-ZnO, Er-doped ZnO and Yb-doped ZnO nanoparticles

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Fig. 8
figure 8

The plots of dR/dλ as a function of wavelength for the undoped-ZnO, Er-doped ZnO, and Yb-doped ZnO nanoparticles

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3.2 Electrical properties

The electrical characterization of semiconductor materials gives valuable information about the quality of the materials for use in optoelectronic applications. To investigate the electrical properties of the samples, the carrier concentration (n), Hall mobility (μH) and electrical resistivity (ρ) are measured using a Hall effect measurement system based on the Van der Pauw method. The results of measurements at room temperature are listed in Table 2. As shown in Table 2, the carrier concentration of ZnO decreases, while the mobility and resistivity increases with Er and Yb doping. Similar decrease of carrier concentration and increase of resistivity and mobility are observed for 1.1 % and higher ratios of Er doping into ZnO [34].

Table 2 The carrier concentration, mobility, electrical resistivity and mean free path of the samples
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The decrease in carrier concentration may be due to the increase in grain boundary defects which act as free carrier traps. Since the doping ratio in our samples is high, the excess Er3+ and Yb3+ ions may lead to ionized impurities which can’t be observed in structural analysis.

The Hall mobility, resistivity, and mean free path depend mainly on charge carrier scattering in polycrystalline samples. Main scattering centers are impurities (especially the ionized impurities), crystal defects, phonons and grain boundaries. The effect of ionized impurities on scattering mechanism could result in increased Hall mobility and resistivity. The ionized impurity scattering mobility is given by

$$\mu_{i} = \left( {\frac{2}{{m^{*} }}} \right)^{1 /2} \frac{{\varepsilon^{1 /2} E_{F}^{3 /2} }}{{\pi e^{3} N_{i} Z^{2} }}\left[ {\ln \left( {1 + \frac{{\varepsilon E_{F} }}{{N_{i}^{1 /3} Ze^{2} }}} \right)^{2} } \right]^{ - 1}$$

where ε is the static dielectric constant, E F is the Fermi level, e is the electron charge, Z is the ion valence and m* denotes effective mass of electrons in conduction band. N i correspond to the concentration of scattering centers and can be defined to be closely equal to electron concentration (n e ) for degenerate semiconductors. Therefore, the contribution of ionized impurity scattering to carrier mobility is proportional to the inverse of carrier concentration.

When the mean free path of the free carriers is comparable to the grain size of the crystallites, the effect of grain boundary scattering becomes very important. The mean free path values of the free carriers as a function of carrier concentration and Hall mobility are calculated by the following relation [35]

$$l = \frac{h}{2e}\left( {\frac{{3n_{e} }}{\pi }} \right)^{1 /3} \mu_{H}$$

The calculated mean free path values are given in Table 2. The average grain sizes in our samples are about three orders of magnitude larger than the calculated mean free paths. Thus, the grain boundary scattering can not effect the observed carrier mobility.

Temperature dependent electrical resistivities in the range 280–350 K of the samples are shown in Fig. 9. It can be seen that resistivities of undoped and Yb doped ZnO decrease as the temperature increases. The carriers move more slowly spending more time passing an impurity ion at low temperatures. The ion impurity scatterings which have little impact on energetic electrons become dominant causing the resistivity to decrease as temperature increases. For Er doped sample interesting behavior of resistivity is observed. The resistivity decreases from 280 to 295 K, then it increases in the range 295–320 K, and finally it reaches an almost steady state in 320–350 K range. Therefore, the temperature dependence of resistivity of Er doped ZnO act as a metal–semiconductor transition (MST) at about 295 K. This type of MST behavior was reported for Er:ZnO [36], Al:ZnO [37], As:ZnO [38], Ga:ZnO [39]. Er doped ZnO displayed a negative temperature coefficient of resistance (TCR) below the MST which is a typical behavior of a semiconductor, and metal type positive TCR above MST. This effect can be explained by the formation of degenerate band appearing in heavily doped semiconductors, as suggested by Mott [40].

Fig. 9
figure 9

Temperature-dependent resistivity of undoped, Er and Yb doped ZnO nanoparticles

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4 Conclusions

In this study undoped ZnO, Zn0.95Er0.05O and Zn0.95Yb0.05O nanopowders have been successfully synthesized by hydrothermal method. The XRD results show that all samples have the preferential orientation along the (100) when the different rare earths (Er, Yb) are added. The SEM results display that the incorporation of rare earth ions in crystal structure of ZnO can change the morphology of ZnO nano particles from rod like to rice kernel and hexagonal prism for Erbium and Ytterbium doping, respectively. The optical properties have been studied by reflectance measurements. The optical band gaps are calculated as 3.24, 3.23, and 3.22 eV, for undoped, Er-doped and Yb-doped ZnO, respectively. The electrical measurements are made by van der Pauw method in the 280–350 K temperature range. The carrier concentration of ZnO decreases, while the mobility and resistivity increases with Er and Yb doping at room temperature. Yb doped ZnO showed characteristic semiconductor behavior while temperature dependent resistivity measurements of Er doped ZnO showed a metal–semiconductor transition at about 295 K.