Giant tunnelling electroresistance in atomic-scale ferroelectric tunnel junctions

Ferroelectric tunnel junctions are promising towards high-reliability and low-power non-volatile memories and computing devices. Yet it is challenging to maintain a high tunnelling electroresistance when the ferroelectric layer is thinned down towards atomic scale because of the ferroelectric structural instability and large depolarization field. Here we report ferroelectric tunnel junctions based on samarium-substituted layered bismuth oxide, which can maintain tunnelling electroresistance of 7 × 105 with the samarium-substituted bismuth oxide film down to one nanometer, three orders of magnitude higher than previous reports with such thickness, owing to efficient barrier modulation by the large ferroelectric polarization. These ferroelectric tunnel junctions demonstrate up to 32 resistance states without any write-verify technique, high endurance (over 5 × 109), high linearity of conductance modulation, and long retention time (10 years). Furthermore, tunnelling electroresistance over 109 is achieved in ferroelectric tunnel junctions with 4.6-nanometer samarium-substituted bismuth oxide layer, which is higher than commercial flash memories. The results show high potential towards multi-level and reliable non-volatile memories.


Transport Mechanism for BSO-based FTJs (1.1) Direct tunnelling (DT)
The direct tunnelling current through a trapezoidal potential barrier is described as 1 ( ) where A is the device lateral size, Ф1,2 is the barrier height at the metal/ferroelectric (Cr/BSO) and ferroelectric/semiconductor (BSO/NSTO) interface, n m  is the effective mass of electrons in NSTO, is the reduced Planck constant, and d is the BSO thickness.

(1.2) Thermally assisted tunnelling
The thermally assisted tunnelling current is 2 : where q is the electron charge, V is the applied voltage, E0 is a temperature-dependent energy given by: where n is the ideality factor which equals to unity for ideal thermionic emission over a Schottky-type barrier, kB is Boltzmann constant, and T is temperature.
The temperature-dependent saturation current J0 in Supplementary equation ( 4) is given by: ( ) where Vbi is the built-in potential of the Schottky-like barrier due to the surface depletion, εr(T) is the temperature-dependent relative permittivity of NSTO which can be described by the Barrett's formula 3 : ( ) ϕn is the difference between the conduction band minimum (EC) and the Fermi level of NSTO (EF), which can be estimated using the effective mass of electrons ( n m  ) in NSTO 4 : where ND is the doping concentration, NC is the density of states (DOS) close to EC of NSTO given by: The effective Richardson constant of NSTO in Schottky junction is 156 A/(K 2 cm 2 ), and . 5 The electron affinity of NSTO is 4.08 eV.

(1.3) Discussion on theoretical investigations of transport properties
Although the tunnelling mechanism in the ferroelectric tunnel junctions employing doped semiconducting electrodes as in this work has been elucidated in a former study by Shen et al 6 , further theoretical investigations based on density functional non-equilibrium Green's function methods are worth carrying out to supplement the tunnelling model for fully understanding the transport properties of our studied ferroelectric tunnel junctions.

Energy Barrier in NSTO Depletion Region.
When the Au/Cr/BSO/BSTO FTJs are in HRS, the depletion region and extra energy barrier at NSTO surface are formed.Thermally assisted tunnelling exists, leading to an ideality factor n>1.In this case, n = 1+Cd/Cf, where Cd and Cf are the high-frequency capacitances of the depletion region in NSTO and the ferroelectric barrier in the BSO layer, respectively 7,8 .The build-in potential of a typical Schottky-like junction can be obtained through capacitance-voltage (C-V) measurement.For a semiconductor depletion region, the capacitance is calculated as 4 : 1/2 2

(
) where Vd is the reverse-bias voltage that drops across the depletion region.The equation can be rewritten as: It can be found that the In our metal/ferroelectric/semiconductor FTJs, the capacitance Cf for the BSO layer and the capacitance Cd for the space charge region are connected in series.The total capacitance C can then be obtained from 1/C = 1/Cd + 1/Cf = n/Cd.The reverse-bias voltage that drops across the depletion region (Vd) is then V/n, where V is the total reversed biased voltage applied on the whole junction.By linearly fitting to the plots, the doping concentration of NSTO and the build-in potential Vbi can be obtained (Supplementary Fig. 18), and the depletion width in the BSO/NSTO interface is calculated.

Evaluation of Nonlinearity for Potentiation and Depression Processes
The conductance (G) update process with pulse number (N) for long-term potentiation (LTP) and long-term depression (LTD) is given by Supplementary equations (14-16) 9 : where Nmax, Gmin, and Gmax represent the maximum pulse number, minimum conductance, and maximum conductance values, respectively.Ap and Ad are the fitting parameters related to the nonlinearity of the potentiation and depression processes, respectively.
The nonlinearity factor (α) of conductance for potentiation (αp) and depression (αd) can be calculated from: / / 1.727 By fitting to the experimentally measured conductance vs. pulse number data using Supplementary equations ( 14) or (15), the values of Ap/d can be extracted, and the nonlinearity factor α is then obtained.The curve will be more linear when α is much closer to zero.1.2×10 9 TER value with -7 V reset voltage is obtained (Fig. 2d).vice can sustain a TER over 10 5 for more than 10 6 cycles, with a total endurance cycle over 5×10 9 .b, The I-V switching characteristics measured during the endurance test.The device performance slightly degrades after 10 7 endurance cycles, and the switching window further shrinks as the endurance cycle further increases.For FTJs with 1-nm-thick BSO, the V bi is extracted to be 1.35 V, and the corresponding depletion width (W d ) is 9.72 nm.For FTJs with 4.6-nm-thick BSO, the V bi is extracted as

2 dC
− shows a linear dependent on Vd.Therefore, the doping concentration of NSTO can be calculated from the slope and the build-in potential Vbi can be extracted from the intercept.Besides, the depletion region width Wd can be estimated based on the extracted Vbi and ND:

FigureFigureFigure S4 .
Figure S1.The atomic model of BSO thin film, with the dashed blue box showing the BSO film illustrated in Fig. 1b.In the grown BSO film, some regions have three Bi-O layers, while some regions may have four Bi-O layers.In regions with three Bi-O layers,the thickness is ~0.9 nm; and in regions with four Bi-O layers, the thickness can reach ~1.1 nm.The X-ray reflectivity measurements and the fitting results confirm that the thickness of the BSO film is 1 nm with a surface roughness of 0.173 nm.

Figure S5 .
Figure S5.Giant TER in 2.1-nm-BSO-based FTJ.a, I-V sweep of the FTJ device with BSO thickness of 1 nm.Inset: resistance distribution of low resistance state and high resistance state.b, TER over 1.5×10 8 is achieved with -0.1 V read voltage.

Figure S6 .Figure S7 .
Figure S6.Fitting to the measured I-V curve for a FTJ in LRS.The I-V curve at low voltage can be well fitted by the direct tunnelling model.The barrier height at the metal/ferroelectric (Cr/BSO) and ferroelectric/semiconductor (BSO/NSTO) interface are extracted as 1.92 eV and 0.25 eV, respectively.

Figure S8 :
Figure S8: The DFT results of the BSO/NSTO interface.a, Interface structure of BSO/NSTO; b, Interface states of Ti, calculated using the Hubbard U of 6 eV and J of 0.855 eV for Sm.c, The comparison between Sm DOS and total DOS, showing that the states near the Fermi level are very weak, and the dominating electronic states of Sm lie as deep as around -20 eV.Therefore, excluding the Sm will not strongly affect the electronic properties at the interface.

Figure S9 :
Figure S9: Charge density difference at the interface between ferroelectric bismuth oxide and metallic chromium layers, with the bismuth oxide layer showing (a) upward, and (b) downward polarizations.

Figure S10 .Figure S11 .Figure S12 .
Figure S10.The conductance modulation using the incremental step pulse programming (ISPP) technique, for another two FTJs with 1-nm-thick BSO film.a, Measurement results for FTJ Device #2.b, Measurement results for FTJ Device #3.The programming conditions are the same as that in Fig. 3d in the Main Text.The nonlinearities for potentiation (αp) are extracted as -0.109 and -0.103, and the nonlinearity for depression (αd) are extracted as -0.134 and -0.128, for Device #2 and Device #3, respectively, showing consistent linear conductance tuning properties among different devices.

Figure S13 .
Figure S13.The measured endurance properties of the 1-nm-BSO-based FTJ.a, The I-V switching characteristics before the endurance measurement and after 10 8 and 5×10 9 endurance cycles.There is no significant degradation of the device performance after 10 8 endurance cycles, while the resistance window shrinks after 5×10 9 endurance cycles.b, The HRS and LRS resistances after 5×10 9 endurance cycles, showing that the resistance window degrades under the same programming voltage pulses shown in Fig. 5a in the Main Text.The resistance window can be recovered by slightly increasing the programming voltage amplitudes (Fig. 5b in the Main Text).

Figure S15 .Figure S16 .Figure S17 .Figure S18 .
Figure S15.The retention properties of 1-nm-BSO-based FTJ for 4 typical intermediate resistance states.There is no significant shift of the resistance levels, which is consistent with the trend shown in Fig.5cin the Main Text.