(Invited) 2D Transport and Velocity Modulation in Black Phosphorus Field Effect Transistors
Authors: Szkopek Thomas , Gervais Guillaume , Hemsworth Nicholas , Tayari Vahid 
Published: February 2020

Black phosphorus (bP) is an elemental allotrope with a layered crystal structure of puckered honeycombs that can be mechanically exfoliated down to atomic layer thickness. First synthesized over a century ago, bP has been previously studied as a bulk semiconductor [1,2] and is subject to a resurgence of interest as a 2D semiconductor with properties complementary to the 2D semi-metal graphene [3]. bP is the most thermodynamically stable allotrope of phosphorus but is nonetheless subject to photo-oxidation in the presence of water, oxygen and visible light with a reaction rate that increases as bP layer thickness decreases [4].
We have fabricated bP quantum wells in both back-gated and dual-gated field effect transistor (FET) geometries with bP thicknesses ranging from 6±1 nm to 47±1 nm. Stability under ambient conditions was achieved in back-gated FETs by encapsulation with a layer of poly methyl methacrylate (PMMA), while dual-gated FETs were additionaly protected by a combination of Al2O3 deposited by atomic layer deposition and optically opaque gold metallization.
Charge transport measurements reveal ambipolar conduction, field effect mobilities of up to 900 cm2/Vs for holes at low temperatures ( T< 100 K ), current saturation as expected of a bona fide semiconductor, and on/off current ratios exceeding 105 at room temperature [5]. Shubnikov-de Haas (SdH) oscillations were observed in bP FETs at 300 mK to 30 K and magnetic fields of up to 35 T. Lifshitz-Kosevich analysis of the SdH oscillations indicates the presence of a 2-D hole gas with Schrödinger fermion character in an accumulation layer at the bP surface. A simple Schrödinger-Poisson analysis predicts accumulation of holes in a single 2-D sub-band at 300 mK over the range of applied electric fields used in our experiments. Analysis of the thermal activation of SdH oscillations yields a hole effective mass of m*=0.36±0.03m0. Improvements to bP device quality by the independent Y. Zhang group has led to the observation of the quantum Hall effect [6].
The top gate of dual-gate bP FETs was found to be effective at modulating both carrier mobility and contact resistance [7]. The mobility modulation effect enables operation of the dual-gate bP FET as a velocity modulated transistor (VMT), first proposed by Sakaki [8] to overcome the limitation on transistor switching frequency imposed by the channel transit time of charge carriers. The mobility of charge carriers within an assymetric bP FET structure is dependent upon the charge carrier density distribution, and is thereby dependent upon the externally applied electric field of the top gate. A two-fold mobility modulation and a two-fold contact resistance modulation leads to a four-fold modulation of transconductance at a fixed hole density.
The observation of mobility modulation effects in dual-gate bP FETs demonstrates the capacity for bP to function as a room temperature VMT. Charge density distribution plays an important role in the charge transport properties of 2D atomic crystals, where the exposed surfaces of naked quantum well structures can lead to a strong spatial dependence of charge carrier scattering rates. The recent observation in angle resolved photo-emission spectroscopy of bandgap tuning and a semiconductor to semi-metal transition in K-doped bP via a giant Stark effect [9] suggests the possibility of electric field tuning of bP bandgap in bP FETs. Further work is required to improve the quality of bP/dielectric interfaces and to increase the applied electric field strength to access electric field tunable bandgap devices with bP.
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