Electrons transmitted across a ballistic semiconductor junction are expected to undergo refraction, analogous to light rays across an optical boundary. In graphene, the linear dispersion and zero-gap band structure admit highly transparent p-n junctions by simple electrostatic gating. Here, we employ transverse magnetic focusing to probe the propagation of carriers across an electrostatically defined graphene junction. We find agreement with the predicted Snell's law for electrons, including the observation of both positive and negative refraction. Resonant transmission across the p-n junction provides a direct measurement of the angle-dependent transmission coefficient. Comparing experimental data with simulations reveals the crucial role played by the effective junction width, providing guidance for future device design. Our results pave the way for realizing electron optics based on graphene p-n junctions.
We present a quantum switch based on analogous Dirac fermion optics (DFO), in which the angle dependence of Klein tunneling is explicitly utilized to build tunable collimators and reflectors for the quantum wave function of Dirac fermions. We employ a dualsource design with a single flat reflector, which minimizes diffusive edge scattering and suppresses the background incoherent transmission. Our gate-tunable collimator-reflector device design enables the quantitative measurement of the net DFO contribution in the switching device operation. We obtain a full set of transmission coefficients between multiple leads of the device, separating the classical contribution from the coherent transport contribution. The DFO behavior demonstrated in this work requires no explicit energy gap. We demonstrate its robustness against thermal fluctuations up to 230 K and large bias current density up to 10 2 A/m, over a wide range of carrier densities. The characterizable and tunable optical components (collimatorreflector) coupled with the conjugated source electrodes developed in this work provide essential building blocks toward more advanced DFO circuits such as quantum interferometers. The capability of building optical circuit analogies at a microscopic scale with highly tunable electron wavelength paves a path toward highly integrated and electrically tunable electron-optical components and circuits. graphene | Dirac fermion | electron optics | quantum transport
The kinetics of persistent photoconductivity (PPC) in A1Q 3GaQ 7As and ZnQ 3CdQ 7Se has been investigated. The PPC relaxation behaviors in both materials can be well described by stretched-exponential functions, Ippc(t) =Ippc(0)exp[ (t/r) ]l (P(l). For Alo 36ao 7As, the relaxation-time constant r, as a function of the relative photoexcited electron concentration n, is measured through the variation of the excitation photon dose in the temperature region T 10 K. At low temperatures, we found that in A1Q 3GaQ 7As, v decreases and reaches a minimum value as n increases in the low-concentration region but it increases with increasing n in the higher-concentration region. Such a turning-over behavior observed in AlQ, GaQ 7As is believed to be due to the crossover from a nondegenerate to a degenerate regime as the electron concentration increases. At higher temperatures,~observed in A1Q 3GaQ7As decreases monotonically with increasing electron concentration, which is consistent with the fact that the degenerate carrier concentration is more difficult to attain at higher temperatures. The PPC-buildup transients in A1Q 3GaQ 7As and ZnQ 3CdQ 7Se have also been measured and formulated at different conditions and are shown to be very different. These results have shown that the PPC-buildup transients contain information not only about electron excitation but also electron recapture. The photoionization cross section of DX centers, o», in A1Q 3GaQ7As has been obtained from the PPC-buildup-transient measurements. The experimental results indicate that the transport properties in AlQ 3GaQ 7As are controlled by DX centers as expected, but in II-VI semiconductor alloys in the low-electron-concentration region they are governed nonetheless by tail states induced by compositional fluctuations.
Graphene p-n junctions offer a potentially powerful approach towards controlling electron trajectories via collimation and focusing in ballistic solid-state devices. The ability of p-n junctions to control electron trajectories depends crucially on the doping profile and roughness of the junction. Here, we use four-probe scanning tunneling microscopy and spectroscopy (STM/STS) to characterize two state-of-the-art graphene p-n junction geometries at the atomic scale, one with CMOS polySi gates and another with naturally cleaved graphite gates. Using spectroscopic imaging, we characterize the local doping profile across and along the p-n junctions. We find that realistic junctions exhibit non-ideality both in their geometry as well as in the doping profile across the junction. We show that the geometry of the junction can be improved by using the cleaved edge of van der Waals metals such as graphite to define the junction. We quantify the geometric roughness and doping profiles of junctions experimentally and use these parameters in Nonequilibrium Green's Function based simulations of focusing and collimation in these realistic junctions. We find that for realizing Veselago focusing, it is crucial to minimize lateral interface roughness which only natural graphite gates achieve, and to reduce junction width, in which both devices under investigation underperform. We also find that carrier collimation is currently limited by the non-linearity of the doping profile across the junction. Our work provides benchmarks of the current graphene p-n junction quality and provides guidance for future improvements.
We propose Graphene Klein tunnel transistors (GKTFET) as a way to enforce current saturation while maintaining large mobility for high speed radio frequency (RF) applications. The GKTFET consists of a sequence of angled graphene p-n junctions (GPNJs). Klein tunneling creates a collimation of electrons across each GPNJ, so that the lack of substantial overlap between transmission lobes across successive junctions creates a gate-tunable transport gap without significantly compromising the on-current. Electron scattering at the device edge tends to bleed parasitic states into the gap, but the resulting pseudogap is still sufficient to create a saturated output (I D–V D) characteristic and a high output resistance. The modulated density of states generates a higher transconductance (g m) and unity current gain cut-off frequency (f T) than GFETs. More significantly the high output resistance makes the unity power gain cut-off frequency (f max) of GKTFETs considerably larger than GFETs, making analog GKTFET potentially useful for RF electronics. Our estimation shows the f T /f max of a GKTFET with 1 μm channel reaches 33 GHz/17 GHz, and scale up to 350 GHz/53 GHz for 100 nm channel (assuming a single, scalable trapezoidal gate). The f max of a GKTFET is 10 times higher than a GFET with the same channel length.
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