Electronic Ferroelectricity in II-VI Semiconductor ZnO

II-VI semiconductor Zinc oxide (ZnO) is a well-known electronic material [1-3]. Because of large piezoelectric constant and electromechanical-coupling constant, ZnO has been applied to ultrasonic transducer, SAW filter, gas sensor etc [3-5]. In addition, ZnO has been used widely as pigment and UV cut cosmetics extensively, so it is a safe material for our living environment, compared with heavy metals used in semiconducting process and materials science. Recently, ZnO has been studied as a material for the solar cell, transparent conduc‐ tors formed on liquid crystal displays, and the blue laser [6]. Then, p-type ZnO was found by Joseph et al [7].


Introduction
II-VI semiconductor Zinc oxide (ZnO) is a well-known electronic material [1][2][3]. Because of large piezoelectric constant and electromechanical-coupling constant, ZnO has been applied to ultrasonic transducer, SAW filter, gas sensor etc [3][4][5]. In addition, ZnO has been used widely as pigment and UV cut cosmetics extensively, so it is a safe material for our living environment, compared with heavy metals used in semiconducting process and materials science. Recently, ZnO has been studied as a material for the solar cell, transparent conductors formed on liquid crystal displays, and the blue laser [6]. Then, p-type ZnO was found by Joseph et al [7].
Ferroelectricity is recognized to appear mainly by the delicate balance between a long-range dipole-dipole interaction and a short-range interaction. When electrons should be well localized in dielectrics, the electronic distribution in the unit cell is determined by atomic positions of constituent ions. Slight distortion of electronic distribution due to structural changes in dielectrics gives a rise of dipole moments. From this point of view, the ferroelectric phase transition should be understood as a structural phase transition from the paraelectric phase with high symmetry to the ferroelectric phase with low symmetry. The atomic displacements are generally 0.01~0.1 Å, which are small compared with Bohr radius ( 0.53 Å). Therefore ferroelectrics are considered as a group of materials which are sensitive to structural changes. In this sense, the ferroelectric phase transition is classified into one of the structural phase transitions.
The basic Hamiltonian is generally given as

H= H(phonon) + H(electron) + H(electron-phonon),
where H(phonon) and H(electron) are due to motions of ion cores and valence electrons, and H(electron-phonon) presents interactions between ions and valence electrons. In dielec-tric materials, the contribution of electron systems is usually omitted since the band gap is generally wide. However, it should be necessary to consider the electron-phonon interaction in the case of ferroelectric semiconductors, since the correlation energy of dipole-dipole interaction (about 0.2 eV) is comparable with band-gap energy in some narrow-gap and widegap semiconductors. For this type of compounds, the electronic contribution due to bond charges and conduction electrons should play a key role and must be taken into account for understanding the nature of ferroelectricity. For long time, the importance of electronic contribution has been pointed out in the field of ferroelectrics, since the simple superposition of electronic polarizability does not hold in many ferroelectric substances. Recently, the novel ferroelectricity was discovered in narrow-gap and wide-gap semiconductors such as Pb 1-x Ge x Te [8], Cd 1-x Zn x Te [9] and Zn 1-x Li x O [10].The appearance of ferroelectricity is primarily due to electronic origin in Zn 1-x Li x O. Although the ferroelectric phase transition accompanies with structural distortions in usual ferroelectrics, only small structural changes of the order of 10 -3 Å are observed in Zn 1-x Li x O. The change in d-p hybridization caused by Li-substitution is responsible for the novel ferroelectricity and dielectric properties. In this chapter, we summarized recent works mainly onZnO.

Zinc oxide
The crystal Structure of ZnO is wurtzite-type (P6 3 mc) as shown in Fig. 1, which belongs to hexagonal system. It does not have the center of symmetry, and is polar along the c-axis. Although it has been pointed out that the structure of pure ZnO has the possibility to exhibit ferroelectricity, the polarization switching does not observed until its melting point (1975 o C) because of large activation energy accompanied by dipole switching process. The lattice constants are a = 3.249858 Å, c= 5.206619 Å at room temperature (298 K) [11]. Zn and O ions are bonded tetrahedrally and form ZnO 4 groups. This tetrahedron is not perfect: the apical bond length of Zn-O is 1.992 Å (parallel to the c-axis) and the basal one is 1.973 Å. Bond length along the c-axis is longer than other three bonds by 0.96%: the ZnO 4 tetrahedra distort along the c-axis, which result in dipole moment. According to recent first-principles studies, it was reported that the hybridization between the Zn 3d-electron and the O 2pelectron plays an important role for dielectric properties of ZnO [12,13].The energy gap E g is 3.44 eV [14]. Although stoichiometric ZnO is an insulator (intrinsic semiconductor), it exhibits n-type conductivity because of excess Zn atoms. The resistivity is about 300 Ωcm, which, however, changes drastically by doping various impurities. By doping of trivalent ions, such as Al 3+ , In 3+ , Ga 3+ , it reduces to the order of 10 -4 Ωcm and shows the conductivity near that of metals [15].
Although p-type conductivity is expected by doping of monovalent Li + ions, ZnO becomes an insulator and the resistivity increases to as much as 10 10 Ωcm [16][17][18]. It is remarkable that the change in resistivity reaches over the order of 10 14 , which covers from metal-like to insulating region. It suggests that the physical nature in this material changes drastically by a little amount of dopant.

Electronic structure
Electronic structure of ZnO has been studied by LMTO (linear muffin-tin orbital) method [19] and by LAPW (linearized augmented-plane-wave) method using LDA (local density approximation). Band structure and the density of states is shown in Figs. 2 and 3 [20]. Around -17 eV, there are two bands originating from the O 2s-states. The narrow bands between -6 and -4 eV consist mainly of the Zn 3d-orbitals, and moderately dispersive bands from -4 to 0 eV consist mainly of the O 2p-orbitals. Figure 4 shows significant d-p hybridization. The 3d derived bands split into two groups, leading to double-peak structure in DOS (density of states). The lower peak is characterized by a strong d-p hybridization. The sharp upper peak between -4.8 and -4.2 eV has strong Zn 3d character and the hybridization with the O 2p-state is very small. Band gap is 0.77 eV. Discrepancy with the experimental value is larger than that of LMTO. It is due to the LDA gap error [21].

Ferroelectricity in binary semiconductors
Recently, the novel ferroelectricity was found in Li-doped ZnO [10,22,23], although pure ZnO has not shown any evidence of ferroelectricity. Generally representative ferroelectrics have complicate crystal structures such as Rochelle salt (KNaC 4 H 4 O 6 4H 2 O), TGS (tri-glycine sulfate, (NH 3 CH 2 COOH) 3 H 2 SO 4 ) and BaTiO 3 . Since ZnO is a simple binary compound, it is very convenient to study the microscopic mechanism and its electronic contribution for the appearance of ferroelectricity. Besides ZnO, IV-VI narrow-gap semiconductor Pb 1-x Ge x Te and II-VI wide-gap semiconductor Cd 1-x Zn x Te, are known as materials of binary crystals accompanying ferroelectricity.

IV-VI Narrow-gap semiconductor
Among IV-VI semiconductor, Pb 1-x Ge x Te has been investigated extensively about its ferroelectricity [8]. Pb 1-x Ge x Te has a NaCl (rock-salt) type structure at room temperature. Although any ferroelectric activities have not been observed in pure PbTe and GeTe crystals, the ferroelectric phase transition is induced only in solid solution Pb 1-x Ge x Te. In the low temperature phase of Pb 1-x Ge x Te, the crystal becomes rhombohedral and exhibits ferroelectric activity. In the case of x = 0.003, it shows a large dielectric anomaly of the order of 10 3 at T = 100 K as shown in Fig. 5 and the softening of TO mode was observed.
The energy gap of Pb 1-x Ge x Te is no more than 0.3 eV, which is 3000 K in temperature. This value is comparable to the energy of the Lorentz field of dielectrics, (4π/3)P. Therefore, conduction electrons can couple strongly with phonons in this solid solution. The electron-phonon interaction decreases the frequency of TO phonon mode which results in the ferroelectric phase transition. In Pb 1-x Ge x Te, doped Ge ions displace from the center position of Pb ion by 0.8 Å and behave as off-center ions because of the ionic size-mismatch between Pb ion (the ionic radius: 1.2 Å) and Ge ion (the ionic radius: 0.73 Å) [24]. The direction of displacement is the eight equivalent [111] directions, which is spatially vacant and polar in the rock-salt structure. Above T c , the ions shift toward any one of these directions at random, but its displacement would be ordered along the trigonal axis below T c . The ordering of the off-center ion triggers the softening of TO phonon mode and induces rhombohedral distortion in the way such as ‧‧‧Pb 2+ -Te 2-‧‧‧Pb 2+ -Te 2-‧‧‧Pb 2+ -Te 2-‧‧‧or ‧‧‧Te 2--Pb 2+ ‧‧‧Te 2--Pb 2+ ‧‧‧ Te 2--Pb 2+ ‧‧‧. This structural ordering generates spontaneous polarization. However, in Pb 1- x Ge x Te, the D-E hysteresis loop has not been observed, while it is a direct evidence of the ferroelectricity. Whereas traditional dielectric measurements are performed on a parallelplate capacitor, it is difficult to measure dielectric constant of such lossy Pb 1-x Ge x Te because of current leaks. Therefore dielectric constant is determined by the C-V measurement or the optical reflectiveity, which are commonly used in semiconductors. The large dielectric anomaly and soft mode of Pb 1-x Ge x Te suggest the ferroelectric activity.

II-VI Wide-gap semiconductor Cd 1-x Zn x Te
Among many wide-gap semiconductors, the ferroelectricity of Cd 1-x Zn x Te was discovered by R. Weil et al in 1988 [9,25]. The E g of Cd 1-x Zn x Te is 1.53 eV. It is a wide-gap semiconductor unlike the narrow-gap IV-VI Pb 1-x Ge x Te. The crystal structure is cubic zinc-blende-type. Cd(Zn) ion is surrounded by four Te ions tetrahedrally. The center of symmetry in this compound does not exist. When x=0.1, the crystal exhibits a dielectric anomaly at 393 K as shoen in Fig. 6. The peak value of dielectric constant (ε peak ) is only 50, which is smaller by about two orders than that of BaTiO 3 (~14000) and that of Pb 1-x Ge x Te (~1000). Because of the large E g and the resistivity (~kΩ), a ferroelectric D-E hysteresis loop was successfully observed in the low-temperature phase. The direction of spontaneous polarization is along the apex of a tetrahedron, [111], which is reported as P s = 0.0035 μC/cm 2 in their first paper, and 5 μC/cm 2 in the second paper. Because the ionic radius of Zn ion (0.83 Å) is smaller than that of Cd ion (1.03 Å), Zn ion also locates at the off-center position which deviates from the center of tetrahedra toward the apex. According to the result of EXAFS (X-ray absorption fine structure), it shifts by 0.04 Å [26]. It is considered that the ordering of off-center ions causes rhombohedral distortion of the cubic lattice by about 0.01 Å, and induces ferroelectricity.
In Cd 1-x Zn x Te, the soft mode has not been observed and the dielectric anomaly is small. These dielectric properties are different from those found in Pb 1-x Ge x Te, which are summarized in Table 1. These facts are consistent each other when one consider the LST (Lyddane-Sachs-Teller) relation (ω LO 2 /ω TO 2 = ε/ε ∞ ). In Pb 1-x Ge x Te, the existence of soft mode is responsible for large dielectric anomaly. Although the behavior of off-center ions plays an important role in this ferroelectricity like Pb 1-x Ge x Te, the occurrence of phase transition seems to be driven in different way from that of Pb 1-x Ge x Te, because of the different dielectric properties described above. Furthermore, the band gap is much larger than that of the narrowgap ferroelectric semiconductors, which suggests that the electron-phonon coupling is not so strong in Cd 1-x Zn x Te solid solutions.

Zn 1-x Li x O
Dielectric constants of Zn 1-x Li x O ceramics with x=0.09 show an anomaly at 470 K (T c ) ( Fig. 7), although a high purity of ZnO does not show any anomaly from 20 K to 700 K [27]. The peak value of dielectric anomaly is 21 ( x=0.1), which is the same order with Cd 1-x Zn x Te (ε ~ 50), but much smaller than ordinal ferroelectrics by 2~4 orders. This means that the dipole-dipole correlation accompanied with this ferroelectric phase transition is not so large in Zn 1-x Li x O. In the measurement of D-E hysteresis loop, a small and clear hysteresis curve was observed. The spontaneous polarization varies by samples from 0.05 μC/cm 2 to 0.59 μC/cm 2 . This is due to that the preferred orientation of the c-axis, the direction of P s of the samples varies depending on samples. Naturally, powder of ZnO has egg-shaped grains which are elongated along the c-axis due to the anisotropy of elastic constants. Therefore, the orientation of the ceramic sample depends on the condition of the pressing process in the sample preparation. After the correction of the preferred orientation by using X-ray diffraction, the value of spontaneous polarizations of each sample converges to 0.9 μC/cm 2 as shown in Fig. 8 [28,29]. The transition temperature, T c , depends on the Li concentration. The phase diagram between T c and x is shown in Fig. 9. As temperature increases, T c becomes higher,which reminds us the phase diagram of quantum ferroelectrics such as KTa 1-x Nb x O 3 and Sr 1-x Ca x TiO 3 .   Specific heat anomaly is small at the ferroelectric-paraelectric phase transition temperature. The transition entropy ΔS is almost 0. If Li ions which substitute Zn ions occupy the off-center position and behave an order-disorder motion, ΔS must be about Rln 2. If the nature of the transition is displacive type, ΔS≏0. The observed thermal behavior suggests displacive nature, but, however, no soft mode was observed in Raman scattering measurement [30]. The small dielectric anomaly and the absence of soft mode are consistent each other, when we consider the LSTrelation. Relaxation mode corresponding to an order-disorder motion has not been found also by Raman scattering [31]. These peculiar dielectric properties of Zn 1-x Li x O is resemble to those of Cd 1-x Zn x Te. These evidences suggests a new type of ferroelectric phase transition.

Electronic ferroelectricity in ZnO
It is considered that the replacement of host Zn atoms by substitutional Li atoms plays an primary role for the appearance of ferroelectricity in ZnO. The problem is the effect of Lidoping. Here we consider the following two models [32].

i.
Structural size-mismatch model Pure ZnO is polar along the c-axis and has dipole moments in crystals. Because of the sizemismatch between Zn ion (the ionic radius: 0.74 Å) and Li ion (the ionic radius: 0.60 Å), substituted Li ions displace from the Zn positions. These displacements may force to induce extra dipole moments locally. It is considered that these local dipoles couple with dipoles of the mother ZnO crystal and the structural ordering of local dipoles triggers to induce a ferroelectric phase transition. ii.

Electronic model
According to the first-principle study by Corso et al [10], the hybridization between Zn 3d electron and O 2p electron plays an important role in dielectric properties of ZnO. As the Li atom has no d-electrons, it is considered that the partial replacement of Zn ions by Li ions changes the nature of d the d-p hybridization. Therefore this doping is considered to induce local extra dipole moments. These extra local dipoles couple with parent dipoles and induce a new type of ferroelectricity.
To clarify which model is effective in the appearance of ferroelectricity in ZnO, the following structural and dielectric measurements were performed.

Rietveld analysis of structural changes in Zn 1-x Li x O ceramics
Structural changes associated with Li-substitution were studied by X-ray powder diffraction [33]. Ceramic samples of Zn 1-x Li x O prepared by using a SPS (spark plasma sintering) method were used in this experiment. The nominal value of x is 0.1 for the first sample. The T c of the sample was 470 K which is determined by dielectric constant measurements. The systematic check of the absence of possible reflections (h-k=3n and l= odd for (hkl), n = integer) suggests that the space group of the ferroelectric phase still remains P6 3 mc, which is same as pure ZnO. The obtained pattern was analyzed by the Rietveld method including the Li concentration, x, as a refinable parameter. All parameters refined are shown in

Effect of Be and Mg dopants on T c
The effect of dopants on T c was studied based on the two models mentioned above. If the ionic size-mismatch between the substituted and the host ions is important for ferroelectricity, the introduction of Be ions should be more effective than Li and Mg doping.  Fig. 10. The series of dielectric measurements show that the introduction of Mg 2+ suppresses T c , while isoelectronic Be 2+ shows almost the same T c .
It is considered that the appearance of ferroelectricity in ZnO is primarily due to electronic origin. The change in d-p hybridization caused by Li-substitution is responsible for this novel ferroelectricity and dielectric properties.  In the next section, we shall study the change in electronic distribution, especially in the nature of d-p hybridization by Li-doping directly by X-ray diffraction, and discuss new electronic ferroelectricity in ZnO.

X-ray study of electronic density distribution
X-ray diffraction measurements were performed for single crystals of pure ZnO and Zn 1- x Li x O at 297 K and 19 K in order to investigate the changes in the crystal structure and the electronic density distribution by Li-substitution in detail. Single crystal of pure ZnO was prepared by the hydrothermal method [34]. The content of excess Zn ions of obtained single crystal was 1.7 ppm and color was light yellowish (Fig. 11). In this hydrothermal method, it is rather difficult to add a large amount of Li ions into single crystal. In order to dope Li ions, several c-plate samples (0.16 mm thick) were annealed at an atmosphere of Li ions at 920 K for 24 hours. The light yellowish color of as-grown single crystal became transparent after this doping as shown in Fig. 12. Li concentration x was measured by chemical analysis and it is confirmed that x = 0.082~0.086.   Accurate electron densities of single crystals of paraelectricZnO and ferroelectric Li-doped ZnO at 19 K were analyzed by the maximum-entropy method (MEM) [36]. The MEM analyses were performed using the MEED (maximum-entropy electron density) program [37].

Crystal structures of single crystals of ZnO and Li-doped ZnO at 293 K
The final positional parameters and thermal factors at 293 K are given with their estimated standard deviation in The bond lengths and angles of ZnO 4 group are shown in  The distributions of electronic density around Zn and O atoms at 293 K are obtained by using Fourier analysis (Fig. 13). The difference Fourier maps between observed distribution ρ obs and calculated distribution ρ cal in the (110)

Bond electron densities at 19 K
The discrepancy factors of MEM analysis for pure ZnO at 19 K are R(F)=1.20 % and R w (F)=1.39 % [40]. The electron density map of ZnO in the (110) plane is shown in Fig. 18

Difference between Li-doped ZnO and pure ZnO
The difference of the charge densities between two crystals is calculated by subtracting the MEM charge densities of pure ZnO from those of Zn 1-x Li x O as in Fig. 19 [40].   In Li-doped ZnO, negative peaks around Zn atom corresponding to 3d z 2 orbital were observed in difference Fourier map, and also in the MEM difference map between the ferroelectric phase and the paraelectric phase. These results may be related to the existence of localized d-holes in Li-doped ZnO. It is considered that 3d z 2 electrons transfer to bonding region and play a role for contribution for the covalence observed from the result of the MEM analysis. Furthermore, the antibonding orbital of 2p electron is observed in difference Fourier map of Li-doped ZnO. It is suggested that the interaction between d-holes and p-electrons should be closely related to the appearance of the ferroelectricity in Lidoped ZnO.

Discussion
The ferroelectric phase transition accompanies with structural distortions in usual ferroelectrics. Portengen, Ostreich and Sham reported the theory of electronic ferroelectricity [41], which examined possibilities of electronic ferroelectricity, based on the spinless Falikov-Kimball (FK) model [42] with a k-dependence hybridization in Hartree-Fock approximation. The FK model introduces two types of electrons, itinerant d-electrons and localized f-electrons. The valence transition is driven by on-site Coulomb repulsion between the d-electrons and f-electrons. They found that the Coulomb interaction between itinerant d-electrons and the localized f-electrons give rise to an excitonic<d + f> expectation value, which breaks the center of symmetry of the crystal and leads to electronic ferroelectricity in mixed-valent compounds. In this electronic model, the transition involves a change in the electronic structure rather than the structural one. The estimated spontaneous polarization is of the order of 10 μC/cm 2 , which is comparable to those in displacive type ferroelectrics such as BaTiO 3 .
In the case of Li-doped ZnO, the d-p hybridization should be changed by Li-doping. The dholes and itinerant electrons should be closely related to the appearance of Li-doped ZnO. It should be further detailed studies would be necessary whether this proposed theory is applicable for the electronic ferroelectricity found in ZnO or not.
Recently Glinchuk et al propose the mechanism of impurities induced ferroelectricity in nonperovskite semiconductor matrices due to indirect dipole interaction via free carriers [43]. They showed that the ferroelectricity in Li-doped ZnO might appear due to indirect interaction of dipoles, formed by off-center impurities, via free charge carriers, namely, the Ruderman-Kittel-Kasuya-Yosida (RKKY)-like indirect interaction of impurity dipoles via free charge carriers. They estimated that the typical semiconducting concentration of the carriers like 10 17 cm −3 is sufficient for the realization of the ferroelectricity. The finite conductivity does not mean complete destruction of possible ferroelectric order and shows rather many interesting effects. In this theory, they have succeeded to obtain the spontaneous polarization and the phase diagram of T c vs. impurity molar ratio (x) as shown in Fig. 21.
Experimental results suggest the existence of localized d-holes and p-electrons in Li-doped ZnO. We consider that the interaction between d-holes and p-electrons may be related to the appearance of the ferroelectricity in Li-doped ZnO. However, there are many proposals for this peculir novel ferroelectricity in ZnO. Scott and Zubko have pointed out the possibility of a classic electret mechanism for Li-doped ZnO [44]. Tagantsev discussed a Landau theory, where a crystal on cooling from a state with polar symmetry exhibits a maximum of dielectric permittivity and D-E hysteresis loops [45]. He proposed that these ferroelectric like phenomena corresponds to the case for Li-doped ZnO. Furthermore, the multiferroic behavior has been reported in impurity-doped ZnO [46]. At present, further detailed experiments should be expected to clarify the nature of Li-doped ZnO.

Conclusion
Dielectric properties and crystal structures and electron density distributions studied on pure ZnO and Zn 1-x Li x O by the precise X-ray diffraction are reviewed in comparison with ferroelectric semiconductors Pb 1-x Ge x Te and Cd 1-x Zn x Te. It is considered that the appearance of ferroelectricity in ZnO is primarily due to electronic origin. The change in d-p hybridization caused by Li-substitution is considered to be responsible for this novel ferroelectricity and dielectric properties. Although the ferroelectric phase transition accompanies with structural distortions in usual ferroelectrics, the structural changes observed in Zn 1-x Li x O are the order of 10 -3 Å. The clear change of Zn 3d-electron is observed. It suggests Zn 3d-electron of Zn 1- x Li x O transfers from Zn atom to the bonding. The positive electronic density is observed near the O atom. It corresponds to the antibonding orbital of O 2p-electron. These results suggest the existence of localized d-holes and p-electrons in Li-doped ZnO. It may be probable that the interaction between d-holes and p-electrons may be related to the appearance of the ferroelectricity in Li-doped ZnO.
For long time, the importance of electronic contribution has been pointed out in the field of ferroelectrics, since the simple superposition of electronic polarizability does not hold in many ferroelectric substances. Many efforts have been done in vain because of complexity of crystal structures of ferroelectrics. As the crystal structure of ZnO is very simple, the electronic contribution could be observed rather easily. It is considered that this result is the first example to discuss the electronic contribution for ferroelectricity.