(Color online) Schematic band diagram of the MIM capacitor structure consisting of the bottom electrode (BE), the dielectric, and the top electrode (TE). A defect band Φtrap below the dielectric conduction band minimum is responsible for leakage at high temperatures (Poole–Frenkel mechanism, PF) and at low temperatures (TAT). Barrier Φb and band gap Eg have been determined from optical measurements.
(Color online) High-T leakage (symbols) in STO films with (a) RuOx and (b) Ru bottom electrodes. The leakage can be well described by the Poole–Frenkel mechanism [Eq. (1) , lines].
(Color online) Low-T leakage (symbols) in STO films with (a) RuOx and (b) Ru bottom electrodes. The leakage at higher VG can be well described by T-independent TAT mechanism [Eq. (3) , lines]. The apparent leakage at low VG is at the edge of instrument resolution and is ascribed to relaxation current.
(Color online) Calculated imaginary bands plotted vs the absolute value of the imaginary component of the wavenumber κ, allowing for easier comparison between different materials. Recall that the intrinsic tunneling current is proportional to exp(−2 κ tox ) (Ref. 4 ). The dashed red and the solid green lines demarcate, respectively, the parabolic and the nonparabolic approximations (Ref. 12 ), while the arrow indicates the energy at which Eq. (6) is evaluated.
(Color online) Calculated intrinsic (i.e., trap-free) leakage at VG = 1 V for a given electrode/dielectric barrier Φb , different effective tunneling masses mtunnel , and dielectric physical thicknesses tox . The minimum tox to achieve 10−7 A cm−2 at 1 V (dashed line) can be readily read off of the graph.
(Color online) Calculation of the minimum physical thickness tox required to obtain intrinsic direct-tunneling leakage of 10−7 A cm−2 at 1 V (cf. Fig. 5 ) and the corresponding ε value assuming EOT of 0.4 nm for different combinations of Φb and mtunnel .
STO and r-TiO parameters extracted from optical and electrical measurements.
Extracted and calculated values for rutile TiO2.
Extracted and calculated values for STO.
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