In-plane tunnelling field-effect transistor integrated on Silicon

Silicon has persevered as the primary substrate of microelectronics during last decades. During last years, it has been gradually embracing the integration of ferroelectricity and ferromagnetism. The successful incorporation of these two functionalities to silicon has delivered the desired non-volatility via charge-effects and giant magneto-resistance. On the other hand, there has been a numerous demonstrations of the so-called magnetoelectric effect (coupling between ferroelectric and ferromagnetic order) using nearly-perfect heterostructures. However, the scrutiny of the ingredients that lead to magnetoelectric coupling, namely magnetic moment and a conducting channel, does not necessarily require structural perfection. In this work, we circumvent the stringent requirements for epilayers while preserving the magnetoelectric functionality in a silicon-integrated device. Additionally, we have identified an in-plane tunnelling mechanism which responds to a vertical electric field. This genuine electroresistance effect is distinct from known resistive-switching or tunnel electro resistance.


Supplementary information S1
The surface morphology of the samples was investigated using a Digital Instrument D-5000 atomic force microscope AFM. In figure S1, the AFM scan on the LSMO layer before the deposition of the top PZT layer shows a grainy morphology with sizes <50 nm. Figure S1. Deflection AFM image of the LSMO film before PZT deposition.

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2 Supplementary information S2 X-ray diffraction (XRD) analyses were carried out using a Siemens D500 diffractometer with Cu-Kalpha radiation in Bragg-Brentano geometry. In order to avoid the strong diffraction from the single crystalline Si substrate and increase the contribution of the thin films we intentionally tilted the sample leading to the observation of only the diffuse scattering around the Si (004) Bragg diffraction position.
The signal of the bilayer is not affected by aforementioned tilt due to its polycrystalline nature. ). High Resolution The X-ray diffraction (XRD) pattern (figure S2) of our bilayer shows several diffraction peaks due to the polycrystalline nature of the films. These correspond to the PZT layer (with lattice parameters a=3.95(1) Å and c=4.08(1) Å, P4mm notation, close to the bulk ones) and except one corresponding to the single crystalline Si substrate.

Supplementary information S4
The magnetic characterization was performed with a Quantum Design SQUID magnetometer. Raw measurements of the magnetization vs applied magnetic field were corrected for the contributions from the substrate by substracting the linear response measured at high fields.   Figure S5 shows the temperature dependence of the conductivity in the Arrhenius T -1/4 representation for an epitaxial SrTiO 3 (001)/LSMO/PZT sample. Further details on sample growth along with structural and morphological characterization can be found elsewhere s1 . As a result, from the linear extrapolation of both (T) curves at low temperature, T 0 values of 6.2x10 6 and 1.8x10 6 K, were obtained for P down and P up states, respectively. Interestingly, the ratio between the T 0 values calculated for P down and P up states is near 4, much larger than the one calculated for the investigated sample in the main manuscript. Additionally (assuming that the localization length a for each states remains constant), the scenario in which the transport is dictated by a modulation of the number of carriers upon ferroelectric switching is in agreement with the trend of the aforementioned ratio value. Indeed, P down sets the electronic state of depletion with a subsequent decrease of charge carriers (transport in LSMO is dictated by holes), it is clear that T 0 must be larger for this electronic state (T 0  1/N(E F )).

Supplementary information S6
In table S6, the results of the fittings according to the Glazrnan-Matveev equation for the three ferrolectric polar states are summarized. The remarkably smaller G 0 +G 1 and G 2 for Pdown indicate much less probability of tunnelling across the averaged barrier. Instead, G 3 is constant for the three evaluated polar states. Remarkable, is the fact that for P down the  2 is smaller, indicating that the data is better described by the equation and that the tunnelling is more important. Table S6. Summary of the fitting parameters obtained using the equation I = V·G(V), where G(V)= G 0 +G 1 +G 2 V 4/3 +G 3 V 5/2 is fitted to the data of the figure 2c.

Supplementary informationS7
In figure S7, it is shown the cross-section used to determine the layers thickness.