Electron-phonon instability in graphene revealed by global and local noise probes

April 24, 2019 3:47 PM by admin

[ad_1]

Electron-phonon instability in graphene revealed by global and local noise probes

Non-equilibrium dynamics in graphene, sounded both globally and locally. (A) Schematic of the device: graphene device encapsulated by hBN (hexagonal boron nitride) on a diamond substrate containing NV centers (Nitrogen-Vacany) for nanomagnetometry. (Framed) Optical image of the device A1 clean and encapsulated in hBN (6 μm x5.4 μm) (B) Condition of emission of phonons by Cerenkov: when vD> vs, the stimulated phonon emission ( ph) overrides absorption (right). (C) Resistance to two probes as a function of the carrier density of the device A1 (T = 10 K). (D) Density of current as a function of the applied electric field (T = 80 K) in the clean devices A1 (blue) and disordered B1 (7 μm on 18 μm, black). The dashed gray line indicates where vD = vs for the longitudinal acoustic mode. (E) Overall electronic noise PSD (average of 100 to 300 MHz) as a function of the polarization power of the devices A1 (blue) and B1 (black). The blue curve verifies vD> vs for P> 0.12 μW / μm2. (F) Local magnetic noise (measured by NV nanomagnetometry) relative to the bias power applied in the clean device C1 on a diamond substrate. The error bars represent 95% confidence intervals. Credit: Science, doi: 10.1126 / science.aaw2104

Understanding out-of-equilibrium phenomena to control them effectively is a major challenge in science and engineering. In a recent study, Trond. I. Andersen and colleagues from the physics, chemistry, material science, and engineering departments of the United States, Japan, and Canada used electricity to unbalance ultra-transparent graphene devices and observe the instability manifested in the form of current fluctuations and suppressed conductivity at microwave frequencies.

Using the experimental setup, they found that DC at high drift rates generated a large increase in noise at gigahertz and that noise increased exponentially in the direction of the current. Andersen and his collaborators attributed the observed emission mechanism to Cerenkov acoustic phonon amplification (a characteristic blue glow resulting from the passage of charged particles through an insulator at a speed greater than that of light in that medium) and have published the results on Science.

Scientists spatially mapped non-equilibrium current fluctuations using magnetic field sensors at the nanoscale, in order to reveal their exponential growth in the direction of the carrier flow. Andersen et al. credited with the observed dependence of the phenomenon on density and temperature, electron-phonon instability of Cerenkov at supersonic drift velocities. Supersonic drift velocities appeared when the population of some phonons increased over time due to the forced emission of Cerenkov, when the drift velocity of electronic conduction was greater than the speed of sound (V_re> V_S) in the middle. Experimental results can provide the ability to generate adjustable terahertz frequencies and build active phonon devices on two-dimensional materials.

Non-equilibrium phenomena in electronic and optical systems display a rich dynamic that can be exploited for applications such as Gunn diodes and lasers. Two-dimensional materials such as graphene are a new and increasingly popular platform for exploring such phenomena. For example, modern ultraclean graphene devices exhibit high mobility and can be driven at high electron speeds with instabilities predicted to include hydrodynamic instabilities in electronic fluids and Dyakonov-Shur instabilities where driven electrons can amplify plasmons .

TOP: Measuring circuit. Circuit diagram for noise measurement (red box) and differential conductivity AC (yellow box). LEFT: Manufacture of the device on a diamond substrate. (A) Schematic of the apparatus: Single layer graphene (gray chain) was contacted with graphite and encapsulated with hexagonal boron nitride (hBN). Reduced-layer graphene (FLG) was used as a topgate. (B-H) Micrographs of the device manufacturing, with a graduated scale of 40 μm in (B) – (G) and 500 μm in (H). (B) Exfoliated graphene. The white dotted line indicates the monolayer region. (C) Full diamond-substrate stack with shallow implant centers (40-60 nm deep). (D) Initial contacts and wire for supplying the reference noise (leftmost electrode). (E) Device after etching to define the geometry. (F) Edge contacts built by etching and thermal evaporation. (G) Device with etching mask to disconnect the topgate from the edge contacts. Note that visible ripples in the image are entirely contained in the upper grid graphene and should not affect the transport properties of channel graphene, due to the thick hBN dielectric (~ 90 nm). (H) Whole monocrystalline diamond (2 × 2 mm2), with wire bonding device. RIGHT: Manufacture of the device on Si / SiO2 substrate. (A) Schematic of the apparatus: The monolayer graphene (gray chain) was encapsulated with hexagonal boron nitride (hBN). The silicon substrate has been used as a global back door. (B) – (F) Device fabrication micrographs, with a 20 μm scale bar. (B) Exfoliated graphene. (C) Completing the battery on the substrate. (D) First contacts. (E) Edge contacts built by etching and thermal evaporation. (F) Device after etching defining the geometry. Credit: Science, doi: 10.1126 / science.aaw2104

The study of the electronic properties of graphene under extreme conditions of non-equilibrium is therefore a productive test bench for evaluating and monitoring exotic transport phenomena. Besides the use of high frequency signal generation, Andersen et al. have studied the underlying non-equilibrium dynamics during electron transport in ultraclean graphene devices containing an extremely high electron drift velocity. Understanding non-equilibrium dynamics is vital for many graphene technical applications; including high frequency transistors, high-speed light sources and flexible transport interconnects. However, it is difficult to achieve the electronic stabilities in practice because of the increased phonon scattering at high drift rates.

In principle, although loss of phonon scattering is generally irreversible, long-lived phonons may be a dominant source of instability in the experimental setting. When the electronic drift speed (V_re) exceeds the speed of sound (V_S), the phonon emission becomes greater than the phonon uptake, resulting in an exponential growth of the phonon population, known as Cerenkov phonon amplification. The phenomenon has long been theoretically explored as a technique for producing high frequency acoustic waves, with associated experimental evidence in global systems and semiconductor superlattices obtained using acoustic and optical measurements.

Spatially resolved local noise measurements with NV magnetometry. (A) Fluorescence image of the NV centers under the C2 device, with false contacts and false colors. (B) NV spin relaxation from the polarized to thermal state (dashed line), when the current densities j = 0 mA / μm (dark blue) and j = -0.19 mA / μm (light blue) cross the device. The solid lines are adjustments. ms, quantum number of spin. (C) Local magnetic noise near the drain contact as a function of graphene current density (device C1) in the electron (e) and hole (h) doped regime (blue and red respectively). (D) Spatial map of the local magnetic noise (device C2) at j = 0.18 mA / μm and n = 0.92 × 1012 cm – 2. The spatial pattern is compatible with the exponential phonon growth due to amplification of Cerenkov (comic strip, above). The dashed black curve shows the theoretically expected surplus of the phonon population (compensated for background noise). a.u., arbitrary units. (E) The direction of growth is reversed by changing the current direction (left) or the sign of the load support (right). The error bars represent 95% confidence intervals. Credit: Science, doi: 10.1126 / science.aaw2104

In the present work, Andersen et al. used electrically tempered graphene devices manufactured on diamond and silicon / silicon dioxide substrates, encapsulated in hexagonal boron nitride (hBN) at cryogenic temperatures (T = 10 to 80 K) to conduct the proposed experiments. The experimental setup provided low-bias transport properties for the ultraclean graphene system with a mobility range of 20 to 40 m²/V.s at a density of carriers (2 x 10¹²cm^-2), corresponding to an almost ballistic transport. Because of their high mobility, carriers could be accelerated by an electric field at high drift rates to observe non-linear current response, while a disordered device would exhibit linear ohmic behavior.

To study out of equilibrium behavior, first, Andersen et al. measured the overall noise in the source-drain current with a spectrum analyzer, while varying the bias power applied (P). The results indicated a new source of noise in low-mess graphene devices encapsulated in hBN. In order to better understand the anomaly observed, scientists performed spatially resolved noise measurements by constructing graphene devices on diamond substrates with center-of-color impurities at the shallow nitrogen slot of 40 to 60 nm deep. They measured atom – type spin qubits using confocal microscopy and probed current noise at the nanoscale by measuring the resulting magnetic fields.

Andersen et al. have probed the spatial dependence of abnormal noise by optically observing simple NV centers along the device to measure their spin relaxation rate. The noise presented a clear symmetry with the direction of the current, an unexpected result since the overall noise and the transport properties are independent of the direction of the current. Then, using the door of the device, Andersen et al. demonstrated that the local noise signal depended on the flow direction of the momentum and not the load. The scientists also showed that the noise was low at the point of entry of the carrier, but that it increased exponentially as the carrier crossed the device by 17 μm in length.

Slow dynamics in global electronic measurements. (A) Overall noise spectrum at n = 2 × 1012 cm – 2. Color curves: clean A2 device (9.5 μm on 11 μm) with polarization from 0 to 0.8 V (from bottom to top). Black curve: Disordered device B1 at maximum power applied to device A2 (7 × scale). (B) Differential conductivity spectrum Ac (excitation: -20 dBm) (19) with polarization from 0 to 0.8 V [top to bottom, colors same as in (A)]. The real (Re) component is suppressed at low frequencies. Gray curve: imaginary component (Im) at 0.8 V. The black curves are adjustments. (C and D) The characteristics of the noise and conductivity spectra are shifted to higher frequencies in a shorter device (6 μm) (device A1) under an electric field similar to the maximum in (A) and (B). (E and F) Travel times extracted from (B) and (D) as a function of the drift rate and the length of the device. Dotted curves correspond to the speed of sound in graphene [light gray, transverse acoustic (TA); dark gray, longitudinal acoustic (LA)]. (G) Cartoon of significant rates in the electron-phonon driven system. During Cerenkov amplification, the correlation time observed in the electronic measurements is limited by the phonon traversal time, tT = L / vs.. Credit: Science, doi: 10.1126 / science.aaw2104

Scientists have consistently explained all observations using the instability of Cerenkov at the electro-phonon. As a key piece of information from the study, Andersen et al. showed that when the electronic drift velocity exceeded the velocity of sound (supersonic drift velocity), acoustic phonons moving forward had a higher simulated emission rate than absorption. Virgin graphene also exhibited a long lifespan of acoustic phonons; therefore, a phonon emitted could stimulate the exponential growth emission in the configuration.

When they mathematically modeled these effects, the results were in good agreement with the experimental results, while the abnormal noise increased as the length of the device increased. The model predicts that the observed electron-phonon instability would give rise to a conductivity spectrum. Scientists continued to explore off-equilibrium dynamics using models of the electron-phonon system.

Depends on bath temperature and charge density. (A) Global noise PSD as a function of bath temperature at constant drift velocities and n = 2 × 10 ^ 12 cm – 2. (B) Calculated maximum phonon emission frequency, which can be set via the density of graphene carriers (blue: Te = 0 K, red: Te = 320 K). (C) Normalized global current noise as a function of carrier density for different lengths of the device (j = 0.6 mA / μm). The solid lines indicate the estimated total emission of phonons. (D) The charge density at which the noise peaks (npeak) for a wider variety of samples than in (C), with adjustment (blue). Error bars represent the sampling spacing of carrier densities. Credit: Science, doi: 10.1126 / science.aaw2104.