Power gain and transistor operation in a three-terminal GaMnAs quantum-well double-barrier resonant-tunneling spin device

A three-terminal ferromagnetic-semiconductor heterostructure with a 2.5 nm GaMnAs quantum well (QW) embedded between AlMnAs and AlAs tunnel barriers was shown in 2010 to allow electrical, in-situ control of spin-dependent resonant levels by a ring-shaped electrode contacting the QW, modulating the magneto-current of the resonant tunneling. However, the device has no power gain: the QW-control electrode is galvanically connected to the QW, and a large leakage current between the top electrode and the QW electrode dissipates the input drive, while the usable level-tuning range saturates beyond about 0.2 V of control voltage. The open problem is to engineer this device class — barrier between the top and QW electrodes, electrode geometry, voltage partitioning, and the metallicity/Curie-temperature trade-off of the GaMnAs QW — so that spin-dependent resonant tunneling and usable level control are preserved while the modulated output signal power exceeds the control-input power, i.e., genuine spin-transistor operation. No device of this class with power gain has been reported: the original group's successor devices used non-resonant electrostatic-gate architectures and report no power gain, and reviews still treat the spin resonant-tunneling transistor as prospective.

Background

Dilute ferromagnetic semiconductor (Ga,Mn)As — Mn substituting for Ga in GaAs, with hole-mediated ferromagnetism and a Curie temperature ($T_C$, below which ferromagnetic order persists) of at most about 185–200 K — is the prototypical ferromagnetic semiconductor grown epitaxially on III–V substrates. Because its carriers are valence-band holes, a thin (Ga,Mn)As layer can act simultaneously as a ferromagnetic electrode and as a quantum well (QW): a layer so thin (nanometre scale) that hole motion normal to it is quantized into discrete subbands, conventionally labelled HH1, LH1, HH2, ... for the heavy-hole ground state, light-hole ground state, heavy-hole first excited state, and so on. In a quantum-well double-barrier (QWDB) structure — the (Ga,Mn)As QW sandwiched between two thin tunnel barriers — holes tunnel resonantly whenever a quantized subband aligns with the emitter's occupied states, and because the subbands of a ferromagnetic QW are spin split, the tunneling current depends on the magnetization configuration. Two-terminal (Ga,Mn)As QWDB devices had shown resonant tunneling and resonant enhancement of the tunneling magnetoresistance (TMR, the relative resistance change between parallel and antiparallel magnetizations of two ferromagnetic layers) (Ohya et al., Physical Review B 2007), but the quantum levels could not be tuned from outside.

Ohya, Muneta, and Tanaka (Applied Physics Letters 96, 052505 (2010)) demonstrated the three-terminal step. Their layer stack, grown by molecular-beam epitaxy (MBE; slow, layer-by-layer epitaxial crystal growth in ultra-high vacuum) on p-GaAs(001), is (from the surface) Ga$_{0.94}$Mn$_{0.06}$As (10 nm, top electrode TOP) / GaAs / AlMnAs (4 nm; a paramagnetic tunnel barrier of unusually low height, about 110 meV) / GaAs / Ga$_{0.94}$Mn$_{0.06}$As QW (2.5 nm) / GaAs / AlAs (4 nm) / GaAs:Be (substrate electrode SUB). A small central TOP electrode is surrounded by a ring-shaped 'QW electrode' contacting the GaMnAs QW, with an area 36 times the TOP area; the region between the two electrodes is etched down to the AlMnAs barrier. Applying a voltage $V_{QW}$ to the QW electrode shifts the HH1, LH1, and HH2 resonances in the TOP-collected differential conductance by roughly 0.05 V of substrate bias per 0.1 V of $V_{QW}$ in the linear regime, and modulates the magneto-current ratio

$$MC=\frac{I_P-I_{AP}}{I_{AP}},$$

where $I_P$ ($I_{AP}$) is the current collected at TOP for parallel (antiparallel) magnetization of the top GaMnAs electrode and the GaMnAs QW; for example, the MC peak associated with the HH2 resonance grows from roughly 2% to 6% as $V_{QW}$ goes from 0 to −0.1 V (all at 3.6 K, with $T_C\approx 60$ K for the GaMnAs layers). This was the first external, electrical control of spin-dependent quantum levels in a ferromagnetic semiconductor — in the words of the Dietl–Ohno review (2014), 'a valuable step towards development of a spin transistor'.

Transistor action, however, demands power gain: the change in output signal power must exceed the power consumed by the control input. This device lacks it. The TOP-collected current decomposes as $I=I'-I''$, where $I'$ is the direct TOP-to-SUB resonant tunneling current through both barriers, and $I''$ is a leakage current flowing from TOP through the thin AlMnAs barrier beneath it and laterally through the metallic QW plane to the QW electrode. Because the QW electrode is galvanically connected to the QW, the control drive burns power in the large leakage $I''$, so the modulation it buys cannot exceed the input. The paper identifies three coupled limitations. First, no power gain because of the large $I''$; the authors propose that inserting a thicker barrier of suitably low barrier height between TOP and QW could reduce $I''$ without suppressing the magneto-current, but did not implement or test this. Second, the resonance shift saturates for $|V_{QW}|\gtrsim 0.2$ V: $V_{QW}$ divides between the AlMnAs tunnel resistance (which falls with growing bias, because of the low barrier height) and the bias-independent sheet resistance of the QW plane, so most additional drive is dropped laterally in the QW rather than shifting its levels, which caps the usable tuning range. Third, across their devices the level-shift controllability grows with the QW's $T_C$ (its metallic character), but more metallic, magnetically stronger (Ga,Mn)As grown at low temperature is more disordered, and the trade-off between magnetic/metallic quality and visible spin-dependent resonances was not mapped.

For context: three-terminal resonant-tunneling transistors with current gain are long established in non-magnetic III–V heterostructures (for example the resonant-tunneling hot-electron transistor with current gain of 5, Mori et al. 1986), so the obstacle here is specific to combining a galvanically connected, spin-dependent quantum well with amplification. The intended applications of the magnetic version — the spin resonant-tunneling transistor and the magnetic monostable-bistable transition logic element (a logic concept in which a magnetic tunnel element is electrically switched between monostable and bistable output states) — require exactly this amplification. Metal-based magnetic tunnel transistors, the main alternative three-terminal spin devices, are limited to current transfer ratios of at most $10^{-2}$ (Tanaka, Ohya, and Hai, Applied Physics Reviews 2014).

Problem Statement

The problem is to realize the three-terminal (Ga,Mn)As quantum-well double-barrier (QWDB) device as a genuine spin resonant-tunneling transistor — that is, to find and implement a design of this device class in which all of the following hold simultaneously, and to demonstrate that they hold. (1) Power gain: the leakage current $I''$ between the top (TOP) electrode and the quantum-well (QW) electrode is suppressed — whether by a thicker TOP–QW tunnel barrier of appropriately low barrier height as proposed by the authors, by altering barrier properties, by reducing the in-plane resistance of the QW, by changing the electrode geometry, or by any other band-engineering means — so that the power drawn by the QW-electrode control input is smaller than the modulated output signal power it produces at the collector. (2) Preserved spin-dependent resonant transport: the heavy-hole and light-hole resonances of the GaMnAs QW remain identifiable, and the magneto-current (or tunneling magnetoresistance) at the resonances remains a substantial, measurable signal under the modified structure, ideally maintaining high spin polarization at resonant conditions. (3) Usable level control: the QW resonant levels remain tunable by the QW-electrode voltage over a range sufficient for transistor operation, rather than saturating at roughly 0.2 V as in the original device. (4) Reproducible device performance with a defensible materials choice: the metallicity and Curie temperature of the GaMnAs QW are chosen so that level-shift controllability and resonant-tunneling visibility are jointly adequate for the device, in light of the observed growth of level-shift controllability with the QW's Curie temperature and of the disorder accompanying more metallic, magnetically stronger material. These four requirements are jointly one objective — a single three-terminal (Ga,Mn)As QWDB device exhibiting transistor-like power gain together with a magnetization-dependent output signal at its resonances — because the same TOP–QW leakage path that forbids gain is also what saturates the level tuning, and the QW material quality underlies both. No numerical threshold for 'gain', 'substantial', or 'sufficient range' is imposed beyond standard field usage: the output modulation power must exceed the input control power, and the spin-dependent signal must remain a resonance-correlated feature distinguishable from background; operation is within the ferromagnetic phase of the GaMnAs layers used. A quantitatively justified design that demonstrates, through a transport and power-balance analysis, that the modulated output signal power exceeds the control-input power while preserving spin-dependent resonant transport and usable level control resolves the task; experimental fabrication and measurement are not required.

References

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