Spin-Orbit Torque (SOT) Rectifier

Figure 1: A new mechanism for rectification and comparison with existing technologies.

Conventional semiconductor diode operations are fundamentally limited by the thermal voltage (kBT/q), which in turn limits the sensitivity of radio-frequency (RF) detection applications and also limits the energy harvesting from weak ambient RF sources. Harvesting ambient radio-frequency (RF) is attractive for powering the edge devices in the era of internet-of-things. Although backward tunnel diodes can break this limit and operate ~2x below the thermal voltage, they do not show much efficiency when the input RF power is below 1 micro-Watt. A new mechanism of rectification is needed that can operate far beyond this fundamental limit and enable exciting new applications, e.g., wireless or self-powered devices and medical implants. Furthermore, a new rectifier capable of operating at weak RF can yield significant improvements in the RF detection and imaging applications including radar sensors for autonomous vehicles and anti-drone technologies.

I have shown for the first time that the integration of spin-orbit and magnetic materials onto conventional semiconductors can lead to a novel spin-orbit torque (SOT) rectifier that can operate far beyond the fundamental limit in conventional rectifiers. While the curvature coefficient (γ = d2I/dV2) of Schottky diodes is limited by the thermal voltage, this new SOT rectifier promises to operate ~300x below this limit (see Fig. 2), which will be of great interest for highly sensitive RF detection. Besides, the SOT rectifier made using existing materials promises to harvest ambient RF power in the 100 nW range with ~71% efficiency, a regime where existing technologies do not show much efficiency (see Fig. 1). This will be of great interest for energy harvesting from ambient RF sources. Furthermore, I have designed a circuit using SOT rectifiers that promise to provide up to 0.5 V DC by harvesting such weak ambient RF energy while matching the low impedance of antennas. This will be of great interest for self-powered voltage-controlled electronics.

The basic idea is to divide a RF current between a Hall bar and a spin-orbit torque material. The current in the spin-orbit torque material applies a torque to an adjacent magnet according to the current direction, and saturates the magnet in a particular direction if the strength of the current is higher than a minimum value (Imin). If the current direction is reversed, the magnet becomes saturated in the opposite direction. The magnet applies a magnetic field to the Hall bar, which in conjunction with the current in the Hall bar (a fraction of the total current) yields a transverse Hall voltage, which is unidirectional irrespective of the current direction.

where M is the normalized magnetization vector, ρH is the Hall resistivity, tH is the thickness of the Hall bar, and IRF is the RF current.

The underlying mechanisms, the Hall effect and the SOT, are proportional to the current density, which improves inversely with device cross-sectional area, providing the largest signals at the nanoscale. In order to enhance the SOT rectifier performance, we need a material with high SOT efficiency, a magnet with high saturation magnetization, and a Hall material with large Hall coefficient. In order to achieve a rectification from weak RF, we use a weak magnet. While conventional magnetic devices focus on magnetic bits with a large anisotropy energy >40kBT for a long memory retention time, we use a magnet with a much lower anisotropy energy, ~2kBT, that on average follows the current as

Using existing materials, a single device with reasonable dimensions can provide ~200 μV DC from 500 nW of RF power. However, for practical applications, especially for self-powered technologies, we need to have a DC voltage in the order of 0.8 ~ 1 V. I have designed an array of such rectifiers (see Fig. 3) that can efficiently provide ~0.5V DC from a RF power in the order of 100 nW. In the array, the ac paths of the devices are connected along the parallel connected columns of the array. The number of columns (K) and the number of devices in each column (N) are set such that the overall impedance matches with the antenna and the captured RF current divides equally in each of the parallel branches. We also need to make sure that the strength of the current in each of the parallel branches is above the Imin. Finally, the DC paths of all the devices are connected in series using inductors, which act like short circuits for DC and add the voltages from each devices to yield a larger output DC voltage. The RF paths are also connected using capacitive connectors to avoid DC leakage. Note that the capacitors and inductors need to be such that their reactances cancel out for impedance matching purpose. Presence of inductors and capacitors can narrow down the bandwidth of operation.

The bandwidth of each rectifier is very wide and can operate from DC to ~10 GHz (see Fig. 4). The bandwidth of such rectification is determined by the physics of angular momentum conservation between the spin current (IS) generated from the SOT materials and the total number of equilibrium spins (NS) in the magnet. The relation can be expressed as

where q is the electron charge. The numerator suggests that a larger spin current from the SOT material can enhance the bandwidth, which in turn means that we need a material with a large SOT efficiency. The denominator suggests that a magnet with lower total magnetic moment can enhance the bandwidth of operation. Such lowering of the total magnetic moment can be achieved by lowering the switching field and the volume of the magnet. We can also lower the saturation magnetization of the magnet to lower the total magnetic moment, but that will also reduce the strength of the DC voltage.

Related manuscript:

  • S. Sayed, S. Salahuddin, and E. Yablonovitch, "Spin-Orbit Rectifier for Weak RF Energy Harvesting", Appl. Phys. Lett. 118, 052408, Feb 2021. (Link).

  • S. Sayed, K. Y. Camsari, R. Faria, and S. Datta, "Rectification in spin-orbit materials using low-energy-barrier magnets'', Phys. Rev. Applied 11, 054063, May 2019. (Link).

Related patent:

  • S. Sayed, S. Salahuddin, and E. Yablonovitch, "Spin-Orbit Rectifier for Weak RF Energy Harvesting", UC case number: BK-2021-041.

Figure 2: The calculated curvature coefficient of the SOT rectifier is ~300x higher than the fundamental high limit in Schottky diodes.




Figure 3: Circuit design for an array of rectifier that enhances the output DC voltage from a given RF power.



Figure 4: Frequency response of a single SOT rectifier.