Counterfeit band gaps caused by microstructural voids in photo-ferroelectric ceramics

In recent years, conventional wide band gap ferroelectric ceramics have been engineered by doping to obtain reduced band gaps. The band gaps in these engineered ceramics are usually determined according to the optical absorption measurement. However, this raises a potential problem in the research of these presumed narrow band gap ferroelectric ceramics as the results of the absorption measurement may give incorrect information of band gaps. This paper demonstrates how microstructural voids, i.e. micron-sized intra- and inter-granular pores in the ceramics formed with improper sintering conditions, can create additional absorption peaks thus leading to counterfeit band gaps. Two types of Ba/Ni co-doped (K,Na)NbO 3 (KNN) photo-ferroelectric ceramics with rela- tively wide (~3 eV) and narrow (~2 eV) band gaps are used to explain the potential problem. This paper hopes to encourage photo-ferroelectric ceramics researchers to use methods other than the optical absorption to determine band gaps in future works.


Introduction
Ferroelectrics, mostly oxide perovskites, are conventionally considered insulators or semiconductors with wide optical band gaps [1,2]. For instance, BiFeO 3 and BaTiO 3 have band gaps of 2.7 eV and >3 eV respectively, which are beyond the majority part of visible light (1.8-3.1 eV) [3,4]. Apart from being broadly used in electromechanical components (e.g. piezoelectrics), ferroelectrics are also found to be able to exhibit bulk photovoltaic effect upon absorbing photon energy higher than the band gaps. The photovoltaic effect in ferroelectrics is possible to generate above band gap, ultra-high photovoltages and a photovoltaic energy conversion efficiency breaking the physical (Shockley-Queisser) limit which is theoretically predicted for conventional semiconducting p-n junction solar cells [4,5]. However, the wide band gaps of conventional ferroelectrics hinder the effective absorption of visible light thus the generation of photo-excited charge carriers. For instance, a band gap of 1.3-1.4 eV is the most ideal for photovoltaic applications in order to achieve the maximum Shockley-Queisser limit and a possibly larger energy conversion efficiency [6]. On the other hand, to enable opto-ferroelectric devices to distinguish the wavelengths of incident lights and hence the domain wall motions react correspondingly, the band gaps should be tuneable within the visible range [7,8].
In recent years, intensive attempts have been made to reduce the band gaps of ferroelectrics in order to achieve a more efficient visible light absorption. For instance, the introduction of nickel ion-oxygen vacancy (Ni 2þ -V O ) defect dipoles is reported to be able to significantly reduce the band gaps of KNbO 3 (KN), (K,Na)NbO 3 (KNN), (Bi,Na)TiO 3 (BNT) and BaTiO 3 (BT) based compositions from 3-4 eV to 1-2.5 eV [3,[9][10][11][12]. Meanwhile, Ti/Mo and Sr/Fe co-doping methods are presented to have a similar effect to bring the band gap of KN compositions down to 2-2.5 eV [13,14]. However, a significant issue is also raised in band gap engineered ferroelectrics. In particular, some Ni 2þ -V O doped KNN and BNT-BT based compositions exhibited multiple optical absorption peaks within the visible light range [10,11]. In-gap states rather than a directly eased band-band transition (i.e. a truly reduced band gap) may have been formed as discussed in literature [15,16].
Apart from the possible in-gap states, this paper reports another factor that can affect the optical absorption behavior of band gap engineered ferroelectrics. It is found that intra-and/or inter-granular pores with sizes of 200 nm to 1 μm could be formed in ferroelectric ceramics due to improper sintering conditions. The dimension of these pores is similar to the wavelengths of visible light, causing reflection, refraction or scattering and thus apparent absorption peaks. Alternatively, these pores may trap charges which may become mobile under illumination. However, these additional absorption peaks induced by the pores are not able to generate electron-hole pairs or excite band-band transition in the materials. Since the optical absorption behavior is widely used to determine band gaps, the above-mentioned additional absorption peaks E-mail address: yang.bai@oulu.fi. may have chances to be determined as band gaps or gap states but they are actually incorrect. It is empirically known that the optical absorption is an unreliable method for polycrystalline and inhomogeneous materials. This paper provides an experimental evidence.

Materials and methods
Two compositions with nominal chemical formulae of (K 0.51 Na 0.44 Ba 0.04 )(Nb 0.98 Ni 0.02 )O 2.985 (Type I) and (K 0.45 Na 0.37 Ba 0.05 ) (Nb 0.98 Ni 0.02 )O 2.93 (Type II) were synthesized via solid-state reaction. Type I was designed to have fully occupied A-site in the ABO 3 perovskite structure while Type II was designed to have about 10 mol.% A-site deficit. Detailed reasons for such designs and corresponding works have been reported elsewhere [17]. Starting reactants of K 2 CO 3 (!99%, J.T. Baker, USA), Na 2 CO 3 (!99%, Sigma-Aldrich, USA), BaCO 3 (99.98%, Aldrich Chemistry, USA), NiO (99.999%, Aldrich Chemistry, USA) and Nb 2 O 5 (99.9%, Aldrich Chemistry, USA) were weighed and mixed on a planetary ball mill in ethanol. The slurries were dried at 80 C and calcined at 825 C in air for 4 hours (heating rate: 3 C/minute, cooling rate: 10 C/minute). The calcined powders were milled and dried as presented above and were subsequently shaped into green bodies with diameter of 14.5 and thickness of 1.5 mm under 90 MPa uniaxial pressure. 5 wt.% polyvinyl alcohol dissolved in deionized water was used as the binder. After shaping, the binder was burnt off at 550 C for 10 hours (heating rate: 1 C/minute, cooling rate: 10 C/minute).
The green bodies were sintered for 2 hours in two ways: (1) at 1130-1150 C where the samples were placed in a powder bed with sacrificial powder of the same composition and were sealed in a crucible, and (2) at 1150 C in air (not in powder bed or sealed). During sintering, the heating and cooling rates were 5 C/minute and 10 C/minute, respectively. The sintered samples were polished down to 400 μm thick with a surface roughness of 50-60 nm. The polished samples were measured under XRD (X-ray diffraction, D8 Discover, Bruker, USA) for structural identification and with a UV-Vis-NIR spectrophotometer (Cary 500 Scan, Varian, USA) for characterization of absorption behavior.
A part of the samples was thermally etched at 960 C for 1 hour and then, together with un-etched samples, was imaged under FESEM (field emission scanning electron microscope, ULTRA plus, Zeiss, Germany) for microstructural characterization. The rest of the samples were coated with 200 nm thick ITO (indium tin oxide) on both surfaces as transparent electrodes. A ferroelectric evaluation system (Precision LCII, Radiant Technologies Inc., USA) was used to measure ferroelectric hysteresis loops at 1 Hz and large-signal conductivity. The electrical signal for the hysteresis measurement was in a bipolar triangular shape with linear change of the input electric field as a function of time. Small-signal conductivity was measured with a 4-terminal configuration using a SourceMeter (Model 2450, Keithley, USA). In the small signal measurement, transient current was excluded by collecting stabilized current data at each applied voltage. Both the conductivity measurements were carried out in the dark as well as under laser illuminations (OBIS LX/LS series, Coherent, USA) with output power of 20 mW and wavelengths of 405 nm, 552 nm and 660 nm and beam diameters at e À2 of 0.8 AE 0.1 mm, 0.7 AE 0.05 mm and 0.9 AE 0.1 mm, respectively.
The samples were finally poled with electric field of 4 kV/mm for 30 minutes in silicone oil at room temperature and in the dark. Piezoelectric coefficient (d 33 ) was measured with a Berlincourt piezoelectric meter (YE2730A, APC International Ltd., USA) at 110 Hz after shorting the two electrodes of each poled sample for 24 hours.  Fig. 1 shows the XRD patterns of the Type I and Type II ceramics sintered under different conditions. Both the Type I samples obtained single perovskites phases. Type II samples formed major perovskite phases with minor tungsten bronze phases. Table 1 lists the lattice parameters of the perovskite phases. It can be seen in Fig. 1 that the Type I samples sintered at 1130 C and 1140 C under powder bed and sealed condition (as presented in Section 2 above) had very similar XRD patterns ( Fig. 1(a) and (b)) with larger b/a and c/a ratios for the sample sintered at 1140 C (Table 1). This indicates an increased asymmetry thus a more complete sintering occurred in the 1140 C sintered sample compared to that in the 1130 C sintered sample. Based on previous research in literature, it is reasonable that such a 10 C difference of sintering temperature could significantly influence the microstructure of KNN-based compositions which are proved to be sensitive to sintering temperature [18][19][20][21].

Results and discussions
The Type II sample sintered in air ( Fig. 1(d)) had a slightly larger concentration of the tungsten bronze phase than the one sintered under powder bed and sealed condition (Fig. 1(c)). The role of the tungsten bronze phase for the change of ferroelectric/piezoelectric properties and band gap has been studied in other works, and, it is less relevant for the topic of this paper [17]. The b/a and c/a ratios of the perovskite phases slightly increased from the Type II sample sintered under powder bed/sealed condition to the one sintered in air (Table 1). Fig. 2 shows the FESEM images of the Type I and Type II ceramics sintered under different conditions. The densities of these samples measured Table 1 Lattice parameters of the perovskite phases shown in Fig. 1.

Amm2
Orthorhombic  by the Archimedes' method were all similar (%4.55-4.60 g/cm 3 ). However, it is obvious that for Type I samples, the one sintered at 1130 C ( Fig. 2(a) and (c)) contained inter-granular pores of about 200 nm to 1 μm. In comparison, the sample sintered at 1140 C ( Fig. 2(b) and (d)) showed a better densification given the same sintering condition (in powder bed and sealed). This indicates the pores in the 1130 C sintered sample were formed due to relatively low sintering temperature thus insufficient densification. Different from Type I samples in which inter-granular pores were found, in Type II samples intra-granular pores of about 200 nm to 1 μm were formed when being sintered at 1150 C in air ( Fig. 2(f)). For the one sintered at the same temperature but under powder bed and sealed condition ( Fig. 2(e)), intra-granular pores could hardly be seen. The formation of intra-granular pores was likely to be due to excess Nb, or equivalently A-site deficit, as have been reported in literature [22]. It implies the alkaline elements may have escaped from the sample when being sintered in air, which may also be the reason of the increased concentration of the tungsten bronze phase (Fig. 1). Although a minor amount of Ba and Ni were doped into KNN in this research, the sintering showed comparable results to those of pure KNN discussed in literature [19]. This convinces the observed microstructure in this research. Fig. 3 shows the ferroelectric hysteresis loops and piezoelectric coefficients of the Type I and Type II ceramics. Regardless of the difference in microstructure, the Type I samples exhibited the same ferroelectric and piezoelectric properties (Fig. 3(a)). The remanent polarization of the Type II sample sintered in air was slightly larger than that of the one sintered under powder bed and sealed condition (Fig. 3(b)). This could be attributed to the slightly larger asymmetry in the sample sintered in air (Table 1). Despite this slight difference of remanent polarization, the d 33 values of the Type II samples were similar (Fig. 3(b)). The spontaneous/ remanent polarizations and piezoelectric properties of the Type II samples were significantly larger than those of the Type I samples (Fig. 3). Such a difference has been studied and discussed in detail in other works [17]. Briefly, there were perovskite-tungsten bronze phase boundaries in the Type II samples which acted as pseudo-morphotropic phase boundaries (MPB) mimicking proper MPB typically existing in good ferroelectric and piezoelectric compositions such as Pb(Zr 0.52 Ti 0.48 )O 3 . The pseudo-MPB formed between the orthorhombic perovskite and tetragonal tungsten bronze phases promoted domain wall motion, inducing larger ferroelectric and piezoelectric properties in the Type II samples [17]. Fig. 3 indicates that the differences of ferroelectric and piezoelectric properties between the two Type I samples, and between the two Type II samples, were negligible. Fig. 4 shows the absorbance and F(R) measured with the Type I and Type II ceramics, where F(R) ¼ (1-R) 2 /2R and R is reflectance. F(R) has been used to help to determine band gaps of Ni 2þ -V O doped KN and KNN ceramics [9,23]. Although as discussed above with Fig. 3 the difference within the same type of samples was negligible, different sintering conditions clearly induced different absorption behaviors as shown in Fig. 4. In general, the samples with pores in the microstructure tended to exhibit multiple absorption peaks while the relatively dense samples tended to exhibit a single absorption.
In particular, the Type I sample sintered at 1130 C (with intergranular pores) showed two additional absorption peaks in the 1-2 eV range compared to the one sintered at 1140 C ( Fig. 4(a)). This resulted in two corresponding peaks in Fig. 4(c). If employing the previous method (Tauc fitting) to determine the band gaps (although will be proved incorrect later), the Type I sample sintered at 1130 C yielded band gaps or gap states of 0.9 eV, 1.6 eV and 2.5 eV. A similar phenomenon has also been observed with other compositions [10,11]. Differently, the nominal band gap of the Type I sample sintered at 1140 C determined with the same method was a single 2.9 eV. Similarly, the Type II sample sintered in air (with intra-granular pores) showed an additional absorption peak in the 1-2 eV range compared to the one sintered under powder bed/sealed condition (Fig. 4(b)). This gave the former two nominal band gaps/gap states of 1.6 and 2.2 eV and the latter a single nominal band gap of 2.4 eV (Fig. 4(d)). Fig . 5 plots the conductivity as a function of incident light photon energy obtained from the large-signal measurement. In the measurement, the input electric field was 1.5 kV/mm which, according to Fig. 3, was slightly above the coercive fields of all samples. Such an input electric field was chosen in order to exclude potential influence of mobile trapped charges/charged defects and/or domain switching current on the measured conductivity [2,24,25]. The soaking time and measuring time were 50 ms and 100 ms, respectively.
Contradictory to the observation in Fig. 4(a) and (c), Fig. 5(a) shows no evidence of the Type I sample sintered at 1130 C having narrower band gaps or additional gap states compared to the one sintered at 1140 C. The photoconductivity was proved to be similar for both the samples ( Fig. 5(a)). In this paper, E g * is introduced to reflect equivalent band gap, which is defined as the photon energy needed to induce an order of magnitude increase of conductivity. Fitted in Fig. 5(a), the E g * values were 2.9 eV and 2.6 eV for the Type I samples sintered at 1130 C and 1140 C, respectively. These E g * values are considered consistent with the widest nominal band gap defined with the optical method (~2.6 eV and~2.9 eV, respectively). However, the optical method (Fig. 4(c)) was concluded to be unreliable for samples with microstructural pores.
The same conclusion can be made based on the photoconductivity of the Type II samples (Fig. 5(b)). The E g * values of both the samples were considered identical (about 2 eV). This is also consistent with the correspondingly widest nominal band gaps determined in Fig. 4(d).
There is no evidence in Fig. 5(b) that shows a gap state at about 1.6 eV in the sample sintered in air. In order to further validate these preconclusions, Fig. 6 shows the small-signal current-voltage (I-V) curves and photoconductivity of the Type II samples.  Raw data directly obtained from the measurements are plotted in Fig. 6(a) and (b). The responses of the two Type II samples seemed to be different as the largest change of the I-V curve under illumination compared to that in the dark was achieved with the 405 nm laser for the sample sintered under powder bed and sealed condition ( Fig. 6(a)) while the largest change for the sample sintered in air was found with the 552 nm laser. As the transient current caused by domain wall motion was excluded (see Section 2), such a difference may be caused by trapped charges (e.g. by V O ) and less likely charged defects which could become mobile under illumination with certain wavelength [2]. This was also the reason of carrying out the large-signal measurements above. Regardless of this difference, the E g * values obtained in Fig. 6(c) and (d) are 2-2.2 eV, consistent with those obtained in Fig. 5(b).
Based on the evidences presented above, it can be concluded that the additional absorption peaks in the range of 1-2 eV were caused by microstructural voids, i.e. intra-and/or inter-granular pores with the size of 200 nm to 1 μm. Therefore, the band gaps or gap states determined according to the optical absorption measurement were counterfeit which could not effectively generate electron-hole pairs or excite band-band transition in the unit cells. These pores can affect the optical absorption in two possible ways. (1) The size of the pores was comparable to the wavelengths of visible light (400-700 nm), which may act as centers of reflection, refraction and scattering. (2) The pores may trap charges of which the energy levels were sitting in the band gap [2]. Such charges may become mobile or be excited to reach the conduction band (for trapped electrons, or valence band for holes) [2]. Nevertheless, neither of these ways was truly exciting band-band transition, thus leading to incorrectly determined band gaps.

Conclusion
This paper has demonstrated that improper sintering conditions can leave microstructural pores (intra-or inter-granular) for Ba/Ni co-doped KNN photo-ferroelectric ceramics. These pores are able to induce additional absorption peaks in the visible light range, imposing difficulties to correctly define the band gaps. The commonly used optical method is relatively reliable when defining the single band gaps of photoferroelectric ceramics with high-level densification and free from microstructural voids. For those without an extremely dense microstructure, the determination of band gaps using the conventional optical method becomes considerably unreliable. Therefore, researchers of photo-ferroelectric ceramics should either pay particular attention to microstructure or consider comprehensive methods including photoelectric and photovoltaic ones when assessing band gaps of newly developed materials in future works.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.