crystals Review Ferroelectricity in Simple Binary Crystals Akira Onodera * and Masaki Takesada Department of Physics, Faculty of Science, Hokkaido University, Sapporo 060-0810, Japan; [email protected] * Correspondence: [email protected]; Tel.: +81-11-706-2680 Academic Editor: Stevin Snellius Pramana Received: 28 April 2017; Accepted: 23 May 2017; Published: 28 July 2017 Abstract: The origin of ferroelectricity in doped binary crystals, Pb1−xGexTe, Cd1−xZnxTe, Zn1−xLixO, and Hf1−xZrxO2 is discussed, while no binary ferroelectrics have been reported except for two crystals, HCl and HBr. The ferroelectricity is induced only in doped crystals, which shows an importance of electronic modification in chemical bonds by dopants. The phenomenological and microscopic treatments are given for the appearance of ferroelectric activity. The discovery of ferroelectricity in binary crystals such as ZnO and HfO2 is of high interest in fundamental science and also in application for complementary metal–oxide semiconductor (CMOS) technology. Keywords: ferroelectric; binary crystal; ZnO; HfO2; mixed bond 1. Introduction Ferroelectrics are expected as a key material for next-generation nonvolatile ferroelectric memories (FeRAM), piezoelectric actuators, high-k gate-materials for high-speed FET (field effect transistor), and optoelectronic devices [1–6]. Particularly, ferroelectric thin films such as perovskite PZT (PbZr1−xTixO3) and Bi-layered perovskite SBT (SrBi2Ta2O9) have been investigated extensively for FeRAM, because of their excellent dielectric properties, i.e., high dielectric constant and large spontaneous polarization. However, it is not so easy to fabricate good quality ferroelectric thin films on silicon substrate and integrate into devices overcoming degradation of ferroelectric properties due to the so-called size effect. Many ferroelectrics have crystal structures consisting of more than three atoms. For example, BaTiO3, known as a typical ferroelectric with a perovskite structure, consists of three atoms. New materials with a simple structure are not only preferable for understanding the microscopic origin of ferroelectricity, but are also easy for integrating into modern ferroelectric devices. No ferroelectrics with two atoms have been reported except for two molecular crystals, HCl and HBr (Table1)[ 7]. In 1969, Cochran developed the theory of lattice dynamics for alkali halide crystals such NaCl and discussed the possibility of ferroelectricity, which revealed a real alkali halide crystal is not a ferroelectric, because a short-range restoring contribution is about twice as great as a long-range Coulomb contribution as discussed later [8–10]. However, it is important to point out that these two contributions are the same order for alkali halide crystals. We will show in this article that this balance of these two contributions may be modified by introducing some dopants, strain or defects in crystals. Crystals 2017, 7, 232; doi:10.3390/cryst7080232 www.mdpi.com/journal/crystals Crystals 2017, 7, 232 2 of 15 Table 1. Phase diagram of HCl and HBr after Hoshino et al. [7]. Crystals 2017, 7, 232 2 of 14 Phase III Phase II Paraelectric Phase I Liquid FerroelectricTable 1. Phase diagram of HCl and HBr after Hoshino et al. [7]. Orthorhombic-Bb21m Cubic-Fm3m Liquid HCl Phase III Ferroelectric Phase II Paraelectric Phase I Liquid Orthorhombic-Below 98Bb2 K1m Cubic- 98~159Fm3 Km AboveLiquid 159 K HCl Below 98 K Phase IIc 98~159 K Phase IIa Above 159 K Orthorhombic-Bb2 m Phase IIb Cubic Liquid HBr 1 Orthorhombic-Phase IIc Bbcm Cubic-Fm3m Orthorhombic-Bb21m Phase IIb Cubic Phase IIa Cubic-Fm3m Liquid Orthorhombic-Bbcm HBr Below 90 K 90~114 K 114~117 K 117~186 K Above 186 K Below 90 K 90~114 K 114~117 K 117~186 K Above 186 K TheThe electronicelectronic ferroelectricityferroelectricity was was foundfound inin wide-gapwide-gap semiconductorsemiconductor ZnOZnO byby introducingintroducing aa smallsmall amountamount ofof Li Li dopants, dopants, although although pure pure ZnO ZnO does does not no showt show any any evidence evidence of ferroelectricity of ferroelectricity [11–15 [11–15].]. ZnO hasZnO a has simple a simple binary binary AB AB structure structure with with high-symmetry high-symmetry (wurtzite structure). structure). Besides Besides ZnO, ZnO, Ge- Ge-dopeddoped PbTe, PbTe, a aIV-VI IV-VI narrow-gap narrow-gap semiconducto semiconductorr [16], [16], and and Zn-doped Zn-doped CdTe, CdTe, a II-VIII-VI wide-gapwide-gap semiconductorsemiconductor [[17],17], havehave beenbeen investigatedinvestigated asas materialsmaterials ofof binarybinary crystalscrystals accompanyingaccompanying ferroelectricityferroelectricity (Figure(Figure1 ).1). Moreover,Moreover, recent recent works works showed showed that that thin thin films films of of HfO HfO2-ZrO2-ZrO2 2systems systems exhibitexhibit ferroelectricityferroelectricity [[18,19].18,19]. HafniaHafnia (HfO(HfO22)) andand ZirconiaZirconia (ZrO(ZrO22) havehave beenbeen wellwell studiedstudied asas high-high-kk dielectricdielectric materialsmaterials inin CMOSCMOS (complementary(complementary metal–oxidemetal–oxide semiconductor)semiconductor) technology.technology. PurePure HfOHfO22 crystalcrystal isis monoclinicmonoclinic withwith spacespace groupgroupP P221/1/c at roomroom temperaturetemperature andand atmosphericatmospheric pressure.pressure. OnlyOnly HfOHfO22 thinthin filmsfilms dopeddoped withwith Si,Si, Y,Y, AlAl andand ZrZr changechange thethe monoclinicmonoclinic crystalcrystal structurestructure toto aa polarpolar orthorhombicorthorhombic structure. structure. The The discovery discovery of of ferroelectricity ferroelectricity in in binary binary crystals crystals such such as ZnOas ZnO and and HfO HfO2 is2 of is highof high interest interest in fundamental in fundamental science science and alsoand inalso application in application fields. fields. Our concern Our concern is to study is to thestudy origin the oforigin this unexpectedof this unexpected appearance appearance of ferroelectricity of ferroelectricity in doped in doped binary binary crystals. crystals. We will We discusswill discuss why why the ferroelectricitythe ferroelectricity does does not appearnot appear in pure in pure systems systems but inbut doped in doped crystals. crystals. (a) (b) (c) Figure 1. Crystal structures of (a) Pb1-xGexTe, (b) Cd1-xZnxTe and (c) Zn1-xLixO. The lower figures are Figure 1. Crystal structures of (a) Pb Ge Te, (b) Cd Zn Te and (c) Zn Li O. The lower figures plots of cation (blue lines) and anion1− (redx xlines) layers1− alongx x the polar rhombohedral1−x x [111] direction are plots of cation (blue lines) and anion (red lines) layers along the polar rhombohedral [111] direction for Pb1-xGexTe and Cd1-xZnxTe, and polar [001] direction for Zn1-xLixO [15]. for Pb1−xGexTe and Cd1−xZnxTe, and polar [001] direction for Zn1−xLixO[15]. 2. Ferroelectricity in Binary Semiconductors 2. Ferroelectricity in Binary Semiconductors Ferroelectrics, in general, have complicated crystal structures, which undergo a phase transition fromFerroelectrics, a paraelectric inhigh-temperature general, have complicated phase with crystal decreasing structures, temperature, which undergo breaking a phasethe symmetry transition of from a paraelectric high-temperature phase with decreasing temperature, breaking the symmetry of inversion. The dielectric constant (ε) and the spontaneous polarization (Ps) are characterized in the mean field approximation as ε = C/(T − Tc) (1) Ps = Po (T − Tc)1/2 (2) Crystals 2017, 7, 232 3 of 15 inversion. The dielectric constant (") and the spontaneous polarization (Ps) are characterized in the mean field approximation as " = C/(T − Tc) (1) 1/2 Ps = Po (T − Tc) (2) where Tc is a critical temperature. Ferroelectrics are generally classified into order-disorder, displacive and improper types, though multiferroic materials have been reported recently. According to these types, they show the following characteristic dielectric properties as summarized in Table2[20]. Table 2. Typical values of the Curie-Weiss constant (C), the dielectric constant around Tc ("max), and the spontaneous polarization (Ps) according to the type of ferroelectrics. 2 Type of Ferroelectrics C [K] "max at Tc Ps [µC/cm ] Example Order-disorder 1~3 × 103 103 3~5 TGS § 5 4 Displacive 10 10 10~30 BaTiO3 Improper 10 10 Small ACS # Electronic - 21 0.9 ZnO § # TGS (NH3CH2COOH)3H2SO4), ACS ((NH4)2Cd2(SO4)3). Binary ferroelectric crystals show different but common dielectric behavior from those of the usual ferroelectrics described above; a small dielectric anomaly at Tc and relatively large Ps. We will review the ferroelectric properties of the ferroelectric binary semiconductors, PbTe, CdTe and ZnO, and a high-k dielectric HfO2, briefly in this section. More detailed discussion should be referred in a monograph [15]. 2.1. Narrow-Gap Ferroelectric Semiconductor PbTe The PbTe-GeTe system has been investigated extensively about its ferroelectricity among IV-VI semiconductors [16], which has a rock-salt type structure (Fm3m, a = 6.46 Å) at room temperature. The energy gap (Eg) is 0.3 eV, which is comparable to the Lorentz field (4π/3)P. The ferroelectricity 2+ 2− is observed in solid solution Pb1−xGexTe. The stacking Pb cation and Te anion layers dimerize along the rhombohedral [111] direction, as shown in Figure1. The crystal changes to a rhombohedral structure (R3m) which allows it to exhibit ferroelectric activity Pb1−xGexTe with x = 0.003 shows a large dielectric anomaly at T = 100 K. The large dielectric anomaly