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Large-Velocity Saturation in Thin-Film Black Phosphorus Transistors Xiaolong Chen,†,# Chen Chen,†,# Adi Levi,‡ Lothar Houben,§ Bingchen Deng,† Shaofan Yuan,† Chao Ma,† Kenji Watanabe,∥ Takashi Taniguchi,∥ Doron Naveh,‡ Xu Du,*,⊥ and Fengnian Xia*,† †
Department of Electrical Engineering, Yale University, 15 Prospect Street, Becton 519, New Haven, Connecticut 06511, United States ‡ Faculty of Engineering and Bar-Ilan Institute for Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel § Department of Chemical Research Support, Weizmann Institute of Science, Rehovot 76100 Israel ∥ National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan ⊥ Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, United States S Supporting Information *
ABSTRACT: A high saturation velocity semiconductor is appealing for applications in electronics and optoelectronics. Thin-film black phosphorus (BP), an emerging layered semiconductor, shows a high carrier mobility and strong mid-infrared photoresponse at room temperature. Here, we report the observation of high intrinsic saturation velocity in 7 to 11 nm thick BP for both electrons and holes as a function of charge-carrier density, temperature, and crystalline direction. We distinguish a drift velocity transition point due to the competition between the electron-impurity and electron−phonon scatterings. We further achieve a room-temperature saturation velocity of 1.2 (1.0) × 107 cm s−1 for hole (electron) carriers at a critical electric field of 14 (13) kV cm−1, indicating an intrinsic current-gain cutoff frequency ∼20 GHz·μm for radio frequency applications. Moreover, the current density is as high as 580 μA μm−1 at a low electric field of 10 kV cm−1. Our studies demonstrate that thin-film BP outperforms silicon in terms of saturation velocity and critical field, revealing its great potential in radio-frequency electronics, high-speed mid-infrared photodetectors, and optical modulators. KEYWORDS: black phosphorus, drift velocity, saturation velocity, electron-impurity scattering, electron−phonon scattering, field-effect transistors lack phosphorus (BP)1−5 electronic and optoelectronic devices have been extensively investigated, taking advantage of its high carrier mobility,6−9 thicknessand gate-tunable bandgap,10−12 and high in-plane anisotropy.1,2 For example, radio-frequency transistors based on BP can operate at a high frequency of 10 GHz,13,14 and phototransistors show a desirable broadband responsivity from visible to mid-infrared.15−19 For these devices, their performance highly depends on the intrinsic transit frequency of carriers, which is defined as f T = νd/2πL.13,14 Here, νd is the drift velocity of carriers and L is the carrier transit length. In a diffusive transport system, the carrier drift velocity increases linearly with a low electric field, while at a high field it saturates to a constant value νsat due to the dynamic balance between the energy gain from electric field and the energy loss through inelastic scatterings. Hence, at a fixed channel length, the saturation velocity determines the ultimate performance of
B
© XXXX American Chemical Society
high-frequency transistors and phototransistors. Achieving a high saturation velocity is desirable for realizing high performance devices. Despite the progress in developing BP-based transistors, such an important quantity has not yet been experimentally investigated in BP thin films. Here, we systematically investigated the intrinsic drift and saturation velocity in high-quality BP thin-film field-effect transistors (FETs) as a function of temperature, carrier density, crystalline direction, and electric field. The BP transistors, encapsulated by hexagonal boron nitride (hBN), show robust air stability and high field-effect hole mobility over 1000 cm2 V−1 s−1 at room temperature and 3000 cm2 V−1 s−1 at 80 K. We Received: March 27, 2018 Accepted: April 26, 2018
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DOI: 10.1021/acsnano.8b02295 ACS Nano XXXX, XXX, XXX−XXX
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ACS Nano identified a crossover region in the drift velocity−electric field diagram, arising from the interplay of different carrier-scattering mechanisms. In low electric field, the drift velocity decreases with decreasing carrier density, indicating an electron-impuritydominated scattering mechanism. In high electric field, the drift velocity increases with decreasing carrier density due to the dominant electron−phonon scattering. Based on the drifted Fermi−Dirac distribution model,20 we elucidated the temperature-, carrier-density-, and crystalline-direction- dependent saturation velocity in BP thin films. We achieved a hole saturation velocity of ∼1.2 × 107 cm s−1 at room temperature at a critical electric field of 14 kV cm−1. Moreover, we were able to access the electron branch with a saturation velocity of 1 × 107 cm s−1 at room temperature. Our comprehensive studies on the drift and saturation velocity in the BP thin film, together with recent progress in the synthesis of black phosphorus,21 reveal it as a promising material for ultrafast electronic and optoelectronic applications.
fabrication processes are summarized in Figure S2 (Supporting Information). High Mobility and Current Density in BP FET. Figure 2a shows the sheet conductance G= Ids/(V1 − V2) of the 11 nm thick BP transistor along the X- (armchair) direction (as illustrated in the right panel of Figure 1), measured in a fourprobe configuration to eliminate the contribution from contact resistance. Here, Ids is the source−drain current, and voltages V1 and V2 are collected by probes 1 and 2, respectively, as shown in Figure 1b. The measured conductance shows the ambipolar transport property of BP thin film. In order to accurately determine the field-effect and Hall mobilities of the hBNencapsulated BP transistor, we performed Hall measurement in a perpendicular magnetic field to extract its carrier density n. As shown in Figure S3 (Supporting Information), the extracted carrier density from Hall conductance linearly depends on the gate voltage (Vg). The slop of the n−Vg curve gives a geometric capacitance Cg = 0.994 × 10−8 F cm−2, and the intersection with the x-axis shows a threshold voltage Vth of 9.3 V for hole branch and 19.8 V for electron branch. Hence, the carrier density can be expressed as n = Cg(Vg − Vth)/e, where e is the elementary charge. With this information, we extracted the L 1 dG field-effect mobility ( μFET = W12 · e · dn ) and Hall mobility
RESULTS AND DISCUSSION Parts a and b of Figure 1 show the schematic and false-color atomic force microscopy (AFM) images of a hBN/BP/hBN
L
1 G
( μH = W12 · e · n ) at various temperatures from 77 to 297 K, where L12 = 4.4 μm is the channel length between probes 1 and 2 and W = 1.25 μm is the channel width, accurately determined by AFM (see Figure 1b). As shown in Figure 2b, the device has a high field-effect (Hall) mobility of 1432 (1012) cm2 V−1 s−1 at n = −4.4 × 1012 cm−2 on the hole side and 616 (590) cm2 V−1 s−1 at n = 2.4 × 1012 cm−2 on the electron side at room temperature. At 77 K, the field-effect (Hall) mobility increases to 3388 (2024) cm2 V−1 s−1 at n = −4.4 × 1012 cm−2 on the hole side and 2434 (1877) cm2 V−1 s−1 at n = 2.4 × 1012 cm−2 on the electron side. Such high carrier mobility enables a high current density and drift velocity at a low electric field (defined as F=(V1 − V2)/L12 for intrinsic electric field and Fds = Vds/Lds for extrinsic electric field including the contribution from the contact resistance, where Lds is the channel length between source and drain electrodes). The current density (J = Ids/W) as a function of the intrinsic electric field F at different gate voltages from −25 to −60 V is plotted in Figure 2c. In low fields, the current increases linearly with the electric field and starts to show the tendency of saturation rapidly when F > 1 kV cm−1. High current densities of 430 μA μm−1 at room temperature and 580 μA μm−1 at 80 K are achieved at an intrinsic electric field of 10 kV cm−1 (see Figure 2d) and a gate voltage of −60 V. Even for extrinsic twoprobe measurements, these high current density values are reached at a low extrinsic electric field of 11.7 kV cm−1 (Figure 2d). Comparing the performance of our hBN-sandwiched BP device with previous works2,13,14,22−27 on BP transistors in terms of the current density and extrinsic electric field, our BP transistors show the highest current density at a low extrinsic electric field,due to the preservation of their intrinsic properties. Drift Velocity Dominated by Electron-Impurity and Electron−Phonon Scatterings in BP. Drift velocity, defined as νd = J/(en), is shown in Figure 3a. Here n ≈ Cg(Vg − Vth − Vds/2) denotes the average carrier density, considering the nonuniformity caused by a large source-drain bias Vds. Since similar results are observed on both electron and hole sides, we mainly focus on the drift velocity at hole side here. As shown in Figure 3a, the drift velocity is larger at a higher carrier density
Figure 1. Device configuration. (a) Schematic image of the hBN/ BP/hBN field-effect transistor. The right panel shows the schematic crystalline structure of BP. (b) False-color AFM image of the 11 nm-thick BP field-effect transistor. The scale bar is 2 μm. (c) Falsecolor cross-sectional high-resolution TEM image of the 11 nm thick devices. The scale bar is 5 nm.
device fabricated on a 285 nm thick silicon dioxide (SiO2) covered silicon substrate. BP thin flakes were exfoliated and encapsulated by hBN in an argon-filled glovebox (with oxygen and water concentration below 1 ppm) to prevent BP from oxidation. The cross-sectional high-resolution transmission electron microscope (HRTEM) image further confirmed the high quality of the BP−hBN interfaces (Figure 1c). The thickness of BP shown in this device is accurately determined to be 11 nm. Right after encapsulation, Raman spectroscopy was used to characterize the crystalline direction of BP flakes (see Figure S1, Supporting Information). Chromium/gold (3/40 nm) were used as contact metals, and the device was shaped into Hall-bar geometry using reactive ion etching. Detailed B
DOI: 10.1021/acsnano.8b02295 ACS Nano XXXX, XXX, XXX−XXX
Article
ACS Nano
Figure 2. Transport and mobility characterization in the 11 nm thick BP FET. (a) Sheet conductance as a function of gate voltages at various temperatures. (b) FET and Hall mobilites (at Vg = −60 V for holes and +60 V for electrons) as a function of temperature. (c) Current density as a function of the intrinsic electric field at 80 K. The step of gate voltage is 5 V. (d) Current density as a function of the intrinsic and extrinsic electric fields at 297 and 80 K (at Vg = −60 V).
Figure 3. Drift velocities in the 11 nm-thick BP FET. (a) Drift velocity as a function of electric field at 80 K. The step of gate voltage is 5 V. (b) Hole mobility as a function of carrier density at different temperatures extracted from νd-F relation and Drude model. (c) Theoretical fittings of the drift velocities at 80 K. Inset shows the illustration of the drifted Fermi−Dirac distribution model at vanishing and high drift velocity.
for electric field F < 8.2 kV cm−1, while this trend is reversed at a higher electric field. It clearly indicates two competing electron scattering mechanisms at different electric field regimes. At low field regime, the drift velocity is proportional to the electric field by a ratio factor which is μ = νd/F.28 From this relation, we extract the mobility as a function of carrier
density at different temperatures. The mobility obtained from this method is consistent with that calculated by Drude model μH =
L12 1 G 28 · · . W e n
As shown in Figure 3b, a higher mobility is
observed at a higher carrier density in our BP transistors, which is contradictory to the observations in high mobility C
DOI: 10.1021/acsnano.8b02295 ACS Nano XXXX, XXX, XXX−XXX
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ACS Nano
Figure 4. Saturation velocity in the 11 nm thick BP FET. (a) Measured saturation velocity (scatters) and guiding lines (in the form of νsat = βn−1/η) as a function of the carrier density at different temperatures. (b) Measured saturation velocity (scatters) and theoretical fittings (solid lines) from eq 2 as a function of temperature at various carrier densities.
graphene.28 A similar μ−n relation has been observed in previous BP and MoS2 studies.6−8,29 This ascending μ−n relation can be attributed to carrier scatterings by long- and short-range impurities.29 Long-range impurities, such as interfacial and remote charged impurity, scatter carriers through long-range Coulomb interactions, while atomic-scale defects usually behave as short-range impurities with extremely localized scattering potential.29,30 While an individual charge carrier is vulnerable to long- and short-range impurity scatterings, it becomes more resistive to these impurity scatterings when surrounded by high density of carriers due to enhanced screening of the impurity potential. Hence, a higher mobility and drift velocity are expected at a higher carrier density, consistent with our observations. This indicates that electron-impurity scattering is the dominant scattering mechanism at low field regime. Next, we analyze the contribution of electron−phonon scattering to the drift velocity at different electric fields and carrier densities. As illustrated in the inset of Figure 3c, at a vanishing drift velocity (electric field), the population ρ is larger for charged carriers with smaller momentum (k), subjected to the standard Fermi−Dirac distribution, and the Fermi circle is centered at the origin in k-space.20 The anisotropic Fermi− Dirac distribution in BP arises from the anisotropic band structures along different crystalline directions. With a small finite electric field, the drifted Fermi−Dirac distribution is displaced from the origin to mνd/ℏ, where m is the carrier effective mass and ℏ is the reduced Planck constant. Here, the zero-field ρ-k relation still holds, indicating that charged carriers tend to absorb phonons rather than emit phonons (with a momentum q = k2 − k1) at low field. However, at a high drift velocity (inset of Figure 3c) the ρ−k relation is reversed, with a higher population for higher momentum carriers. In this case, the probability of phonon emission exceeds that of phonon absorption, leading to a phonon-generation gain20 G analogous to the photon gain in laser medium. Such gain depends on carrier density, carrier effective mass, and drift velocity, as a higher carrier density increases the number of carriers interacting with phonons and a larger drift velocity and carrier mass leads to a larger probability of phonon emission.20 Hence, it can be qualitatively expressed as G ∼ mnνdη, where η is a fitting factor with value between 2 and 4.20 Once the electric field exceeds the threshold value, the phonon gain will dominate in carrier-phonon scattering process, as observed in gallium nitride in ref 20. The excessive energy of carriers obtained from the applied field will be immediately transferred
to phonon emissions, leading to the saturation of the drift velocity. Since phonon gain is more accessible for a higher carrier density n, smaller saturation velocity νsat is observed to reach the threshold condition. In this qualitative physical picture,20 we have νsat ∼ n−1/η. This is consistent with our observations that the drift velocity at a high electric field (>8.2 kV cm−1) shows larger values at lower carrier densities (see Figure 3a), indicating an electron−phonon dominant scattering mechanism. Saturation Velocity in BP FETs. To extract the saturation velocity of our hBN-sandwiched BP transistor, we fit our data in Figure 3a using the equation in ref 31 νd =
μF [1 + (μF /νsat)γ ]1/ γ
(1)
where γ is a fitting factor with values between 0.6 to 2, depending on the temperature and carrier density. The mobility used for the fitting is extracted from μ = νd/F (Figure 3b), leaving saturation velocity νsat and γ as free fitting parameters. The theoretical fittings (solid line), shown in Figure 3c, match quite well with the experimental data (scatters) at different gate voltages. We notice that at high electric fields the experimental data exceed the theoretical fittings. This indicates an insignificant self-heating effect in our devices. Previous theoretical works32,33 predict that the strong self-heating at high electric fields would reduce the drift velocity and even result in a negative differential velocity. However, such a strong self-heating effect is insignificant in our measurements, probably due to the small Joule heating power
