Reconfigurable Boolean Logic Using Magnetic Single-Electron Transistors

We propose a novel hybrid single-electron device for reprogrammable low-power logic operations, the magnetic single-electron transistor (MSET). The device consists of an aluminium single-electron transistor with a GaMnAs magnetic back-gate. Changing between different logic gate functions is realized by reorienting the magnetic moments of the magnetic layer, which induces a voltage shift on the Coulomb blockade oscillations of the MSET. We show that we can arbitrarily reprogram the function of the device from an n-type SET for in-plane magnetization of the GaMnAs layer to p-type SET for out-of-plane magnetization orientation. Moreover, we demonstrate a set of reprogrammable Boolean gates and its logical complement at the single device level. Finally, we propose two sets of reconfigurable binary gates using combinations of two MSETs in a pull-down network.


Introduction
As the downscaling of conventional CMOS technology is bound to reach its fundamental limit new algorithms will be the answer to achieve increasingly higher performance and reduced power consumption. Reconfigurable digital circuits provide a way to extend the functionalities of conventional CMOS by implementing in the same physical space multiple logic operations and therefore increasing the computational complexity. Reconfiguration of the logic functions at each individual device promises even more compact and flexible circuit design [1][2][3][4][5]. However, the implementation of such reconfigurable logic using single-electron transistors (SETs) [6,7] is appealing because SETs have good scalability, one of the lowest energy-per-switchingevent [8] and the possibility to combine their electrical properties with magnetic elements [9][10][11][12][13][14]. There have been several proposals to implement programmable SET logic by using the charge degree of freedom such as fixed gate voltages [15], non-volatile charge nodes [16,17] and the spin degree of freedom [18][19][20].
In this manuscript, we show a proof of principle for reconfigurable Boolean logic based on magnetically-gated circuit elements and we suggest multi-device reconfigurable logic architectures. More particularly, we report the complementary logic operation of a aluminium MSET. The reconfigurable capability of our MSET stems from the magnetization-dependent work function of GaMnAs back gate. When the back-gate is kept at a constant potential the magnetic-field-induced chemical change causes a charge accumulation in the gate electrode which can be readily sensed by the SET as a change in the Coulomb oscillation phase [21,22]. Although the concept is demonstrated here for MSET devices, the operating principle is general and transferable to any field-effect transistor.

Results
The MSET has two modes of operation: it responds to gate voltage inputs (electric mode) as well as to the orientation of the magnetic moments (magnetic mode). By reorienting the magnetization of the GaMnAs substrate we are able to switch from n-type to p-type MSET. Making use of the magnetic mode we demonstrate two sets of reprogrammable Boolean logic gates implemented at the single device level. Finally, we suggest a strategy to scale the reconfigurable logic operation to the multiple device level.
A schematic cross-section of the proposed aluminium MSET is depicted in Fig 1(a). The key element of this structure is the magnetic gate electrode, an epitaxially grown Ga 0.94 Mn 0.06 As layer on GaAs that acts as a back-gate with easy-axis directions [110] and [1][2][3][4][5][6][7][8][9][10]. A magnetic field B = 0.7 T, larger that the saturation field B s 0.3 T, is applied to rotate the magnetization M with respect to the [001] direction (ϕ = 0°). The angle θ with respect to the [1][2][3][4][5][6][7][8][9][10] direction is kept equal to 90°in all measurements. The results presented here are independent Fernando Gonzalez-Zalba and Joerg Wunderlich, but did not have any additional role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The specific roles of these authors are articulated in the 'author contributions' section.
Competing Interests: Co-authors M. Fernando Gonzalez-Zalba and Joerg Wunderlich are employed by Hitachi Ltd. There are no patents, products in development or marketed products to declare. This does not alter the authors' adherence to all the PLOS ONE policies on sharing data and materials.
of the magnitude of B for B > B s . A 100 nm alumina layer is used as gate dielectric on top of which the Al-SET is fabricated. The source and drain leads are separated from the micronsized island by aluminium oxide tunnel junctions, as it can be observed in the SEM image in Fig 1(b). In this letter the side gates were not used but could provide extra-functionality to the structure.
In the electric mode of operation we use the back-gate voltage to control the induced-charge in the island of the MSET . Fig 1(c) shows the drain current (I ds ) versus back-gate voltage (V gs ) at 300 mK. The plot shows a periodic oscillatory behaviour of the current, namely the Coulomb blockade oscillations. Several devices were studied with typical charging energies E C = 100-300 μeV and gate capacitances C G = 0.4-1.0 fF. We obtain a I ON /I OFF contrast ratio of up to 1.33 and typical tunnel junction resistances of R T = 500 kO.
The magnetic mode of operation is based on the dependence of the GaMnAs band structure on the orientation of the magnetization due to spin orbit coupling. The magnetization reorientation yields a shift in the GaMnAs work function Δμ which in itself does not produce a response on the MSET. However, when the back gate is held at constant potential a change in μ causes an inward or outward flow of charge in the gate which in turn offsets the Coulomb oscillations. If the work function shift in the magnetic layer is adequate, the phase shift becomes half a period of the Coulomb blockade oscillations and complementary MSETs are obtained. The equation that defines the necessary work function shift for maximum on-off current ratio can be expressed as, As well, the minimum potential shift for complementary operation at temperature T can be defined as a gate voltage shift equal to the FWHM of the Coulomb peak [23], These two equations set the operational parameters in terms of temperature, magnetic field and physical dimensions of the structure.
The complementary operation of the MSET is experimentally demonstrated in Fig 2 for a device with E C = 300μeV and C G = 1.0 fF. To switch between complimentary modes we rotate continuously a saturating magnetic field from ϕ = 90°, where the magnetization resides M parallel to the plane along the easy-axis [110] (Fig 2(a)) to ϕ = 0°where the magnetization is outof-plane (Fig 2(b)). This can be seen in Fig 2(c) where we plot the source-drain current I ds as a function of the magnetization angle ϕ and gate voltage V gs for V ds = 15μV and B = 0.7 T. When the magnetization is in-plane, we select V gs = -61 μV as the logic 0 and V gs = +86 μV as the logic 1 for the n-type SET (see Fig 2(d)). As the magnetic field is rotated to ϕ = 0°, the magnetization is re-oriented in the [001] direction and the GaMnAs work function increases producing a gate voltage shift of ΔV gs = 150 μV [24]. The combination of work function potential shift in the Ga 0.94 Mn 0.06 As layer with the 300 μV gate voltage period of the device result in that the magnetically-induced gate voltage shift coincides with half a Coulomb oscillation (fulfilling Eq (1)). The MSET behaves effectively as a p-type SET, Fig 2(e). Therefore we can arbitrarily select the function of the SET from an n-SET for in-plane magnetization ϕ = 90°to a p-type for outof-plane magnetization ϕ = 0°.
We now focus on the logic design that could be implemented at the single device level. It has been shown that any Boolean function of two variables can be implemented on a SET [25]. In this letter, by making use of the magnetic mode of operation, we demonstrate two sets of reprogrammable logic gates. The inputs in this case are the drain voltage (input A) and the gate voltage (input B) and the output is the drain current. In Fig 3(a) we plot the V ds − V gs diagram of the MSET showing the characteristic Coulomb diamonds at ϕ = 0°. Overimposed, we schematically show two logic gates framed in red AND and NAND. The output is drawn as en empty dot if the results is 0 (low current level) and a full dot if the results is 1 (high current level). Upon changing the magnetization angle to ϕ = 90°, the whole diagram is shifted horizontally by ΔV gs = -150 μV and, therefore, at the same input voltages the gate output changes to the two blue-framed logic gates, from (N)AND to (N)OR as depicted by the arrow. The reconfigurable logic gates are demonstrated in the histograms in Fig 3(b)-3(e). In order to discriminate between logic outputs 0 and 1 we select the low(high) current threshold at I ds = 80 (90) pA. In Fig 3(b) we represent a histogram of the current output for an AND gate implemented on the edge of the Coulomb diamond. By rotating the magnetization to the in-plane direction (ϕ = 90°) the Coulomb diamonds shift and the logic gate switches function to OR (Fig 3  (c)). Moreover, in Fig 3(d) and 3(e) we demonstrate the logical complement set of reprogrammable Boolean gates. The set switches between NAND (ϕ = 0°) and NOR (ϕ = 90°) logic gates.
Finally, we briefly comment on the possibilities for multi-device reconfigurable logic design. As an example, we focus on pull-down networks formed by two elements with a common The circuit in Fig 4(a) consists of a resistor load and two MSETs in series. In the state ϕ = 0°b oth MSET are in the p-type state and the network realizes the operation OR. However this gate can be reconfigured by rotating the magnetization, ϕ = 90°. In this situation both MSET are in the n-type state and the logic operation becomes NAND. Similarly, for a pull-down network consisting of two MSETs in parallel, Fig 4(b) the logic gate can be programmed to switch between AND (ϕ = 0°) and NOR (ϕ = 90°) operations.

Discussion
In conclusion, we have demonstrated the complementary logic operation of an aluminium MSET by making use of magnetization-dependent work function of the GaMnAs magnetic back-gate. By using the source-drain voltage and the gate voltage as binary inputs we showed a set of Boolean gates and its logical complement implemented at the single device level, AND-OR and NAND-NOR gates. Finally, we have described a route to integrate multiple MSET in to integrated reconfigurable logic circuits. Although here we present results on MSETs, magnetic gating could be exploited to switch function in more conventional circuit elements such as CMOS field-effect transistors or novel electronic devices such as graphene ambipolar transistors [26] or spin-hot carrier transistors [27]. For reliable room temperature switching, magnetic materials with work function shifts of the order of 60 mV will be required [28]. Materials with large work function anisotropy such as CoPt alloys could provide that functionality [21]. Moreover, non-volatile logic reconfiguration could be also achieved by making use of the stability of the magnetic moments along non collinear "magnetic easy axes"orientations without applying external magnetic fields or electrical currents.