Solid-Solid Interface
Narrow Depletion and Defect Assisted Tunneling
- Narrow Depletion
The depletion layer can become narrower when a reverse-bias voltage is applied to defective (Ba,Sr)TiO3 thin films since the dielectric constant in the depletion layer is decreased by the reverse-bias voltage [T. Hara, "Electrical characteristics of (Ba,Sr)TiO3 films accounted by partially depleted model", Microelectron. Eng. 75 (2004) 316.], and since deep-level donors are ionized [T. Hara, "Electron-detrapping from localized states in the band gap of (Ba,Sr)TiO3", Solid State Commun. 132 (2004) 109.].
In “pure” semiconductors without deep-level donors, conduction electrons are discharged from an n-type semiconductor toward the electrode on the forward-bias side; however, on the reverse-bias side, hardly any electrons are supplied from the electrode that forms Schottky contact to the n-type semiconductor because of the Schottky barrier. Thus, when only shallow-level donors exist in the depletion layer, the depletion layer is widened (this is the deep depletion) by the ionization of these shallow-level donors to flow electrons.
In contrast, in “impure” semiconductors with deep-level donors, the deep-level donors are ionized as a result of the lowering of quasi-Fermi level EImref. The density of the ionized donors increases and the depletion layer becomes narrow. Note that the depletion layer of some conventional semiconductors with a low purity becomes narrow owing to the ionization of the deep-level donors [C. W. Jen, C. L. Lee, Solid-State Electron. 24 (1981) 949; E. H. Rhoderick, Rev. Phys. Technol. 1 (1970) 81; K. Maeda, J. Vac. Sci. Technol. B 19 (2001) 268]. It has been reported that Cr3+, which serves as an acceptor in the Sr(Ti,Cr)O3 used in resistance random access memories (RRAMs), is oxidized to Cr4+ on both the anode and cathode sides [M. Janousch et al., Adv. Mater. 19 (2007) 2232].
- Defect-assisted tunneling
Tunneling at room temperature can occur. When the density of oxygen vacancies is intentionally increased, the Schottky barrier becomes narrow, causing tunneling (which is considered to be trap-assisted tunneling). This is a technique generally used to decrease the contact resistance between conventional semiconductors and electrodes. The ideality factor should be considered since it is very difficult to form a complete Schottky contact even using Si and GaAs. It has been pointed out that thermally assisted tunneling, instead of “pure” thermionic emission, should be considered for the Schottky contact of organic semiconductors with many vacancies [L. Burgi et al., J. Appl. Phys. 94 (2003) 6129].
In contrast to many thin film capacitor researchers' belief, I-V curves can be fitted to a space-charge-limited current (SCLC) only at low bias voltages [H. F. Tian et al., Appl. Phys. A 102 (2011) 939].
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Let us consider a conductive path with a length of 40 nm on a LaAlO3/SrTiO3 interface by applying a positive-bias voltage, and generate an asymmetric potential profile by controlling the negative bias to determine the I-V characteristics. In such a case, we can observe tunneling [D. F. Bogorin et al., Appl. Phys. Lett. 97 (2010) 013102 ; C. Cen et al., Science 323 (2009) 1026]. Recently, some researchers have reported a change in the tunneling resistance of several orders of magnitude that was induced by the polarization switching of ferroelectric BaTiO3 with a width of several unit cells [V. Garcia et al., Nature 460 (2009) 81]. It was explained that this phenomenon is caused by the change in the tunneling probability rather than merely the change in the density of states [E. Y. Tsymbal, H. Kohlstedt, Science 313 (2006) 181]. Concretely, the tunneling probability changes when the shape of the Ti 3d orbital evanescent waves on the BaTiO3 surface changes in accordance with the polarization direction, and its consistency with the shape of the evanescent waves that propagate in the electrode on the BaTiO3 side changes [J. P. Velev et al., Phys. Rev. Lett. 98 (2007) 137201; J. P. Velev et al., Nano Lett. 9 (2009) 427].
If one metal is a “good” metal (e.g., Pt) with a short Thomas-Fermi screening length (e.g., 70 pm) and the other metal is a “bad” metal (e.g., SrRuO3) with a long Thomas-Fermi screening length (e.g., 1 nm), an asymmetric potential is formed to make the barrier width and barrier height changeable depending on the polarization direction, which will lead to a change in resistance of severalfold to three orders of magnitude for the combination of Pt/BaTiO3 (thickness of 3 to 10 unit cells)/SrRuO3 [M. Y. Zhuravlev et al., Phys. Rev. Lett. 94 (2005) 246802; H. Kohlstedt et al., Phys. Rev. B 72 (2005) 125341]. To increase the change in resistance, the film thickness should be increased as much as possible. Garcia et al. obtained a change in resistance of three orders of magnitude for a 3 nm ferroelectric film. Kohlstedt et al. predicted that the changes in the barrier width, effective mass, and the position of the conduction band edge due to the inverse piezoelectric effect will also contribute to the change in resistance. Burton and Tsymbal predicted that an electrode that is hole-doped with slightly less than half of the conventional number of holes can serve as a spin valve in accordance with the polarization direction of BaTiO3 when asymmetrically hole-doped (La,Sr)MnO3 is used as the electrode [ J. D. Burton, E. Y. Tsymbal, Phys. Rev. Lett. 106 (2011) 157203]. In this case, the calculated tunneling probability, k||(=kx, ky), significantly changes although the barrier width and barrier height scarcely change, which indicates that an antiferromagnetic order is generated at the interface on the side of the electrode, which serves as a spin valve.