A. Fabrication

Standard microfabrication techniques were used to produce an array of NiFe bottom electrodes on an SiO₂/silicon wafer. A single sheet of graphene, grown by chemical vapor deposition (CVD), ^{Reference Li, Magnuson, Venugopal, Tromp, Hannon, Vogel, Colombo and Ruoff36} was transferred from its original copper foil substrate to the electrode array and patterned using polymethyl methacrylate (PMMA) resist and deep-UV photolithography. The graphene's conductive edge states are buried in a layer of SiN and a Co top electrode is deposited. ^{Reference Cobas, Friedman, van 't Erve, Robinson and Jonker24} A schematic of a device is shown in Fig. 1.

FIG. 1.

Schematic cross-sectional diagram of a graphene MTJ and optical photo of a junction prior to top contact deposition.

B. Results

Initial room temperature I–V characterization shows a nonOhmic junction with the increased low bias resistivity typical of tunnel junctions (Fig. 2). The temperature dependence of the junctions' zero bias resistance (ZBR), a characteristic measure of tunnel barrier quality, ^{Reference Jonsson-Akerman, Escudero, Leighton, Kim, Schuller and Rabson37} shows the weak decrease with the temperature characteristic of tunneling transport rather than the weak increase or dramatic decrease in resistance characteristic of metal and semiconductor transport, respectively. ^{Reference Sze and Ng38} Normalizing the individual junction resistances to their room temperature values shows that the junction resistances fall by a factor of about 3.5 in the temperature range 10–300 K (Fig. 2, inset), comparable to factors of 2.5 reported for high quality tunnel junctions. ^{Reference Jonsson-Akerman, Escudero, Leighton, Kim, Schuller and Rabson37}

FIG. 2.

Typical nonlinear current–voltage characteristics of a graphene tunnel junction at various temperatures. Inset: ZBR of several graphene MTJs normalized to their room temperature resistances, showing a weak temperature dependence.

In canonical tunnel junctions, the resistance depends on the ability of electrons from the emitter to tunnel into available states of matching polarization in the collector. When the electrodes are oppositely magnetized, the majority-spin density of states in the emitter corresponds to the smaller minority spin density of states in the collector and vice versa. Consequently, resistance is higher in the antiparallel configuration than in the parallel case where majority-spin states in the electrodes have the same polarization.

When an in-plane magnetic field is applied, the magnetizations of the NiFe and Co electrodes reverse at fields corresponding to their respective coercivities, with the NiFe switching at a much lower field than the Co. Their magnetizations can thus be aligned either parallel or antiparallel, and two distinct resistance states are observed in the data, as seen in Fig. 3. The junction resistance can be controllably and reversibly switched from a low-resistance parallel state to a higher resistance antiparallel state with the applied field. At low temperatures and low biases, where the physics of tunneling are simplest and most evident, the tunnel magnetoresistance (TMR) reaches a value of 2%. ^{Reference Cobas, Friedman, van 't Erve, Robinson and Jonker24,Reference Cobas, Friedman, van 't Erve, Robinson and Jonker25}

FIG. 3.

Graphene junction TMR curves at a low temperature (T = 4 K), showing the typical MTJ switching behavior at low bias voltages of 0.125 and 0.250 mV. The arrows indicate the relative orientation of the NiFe and Co contacts.

Several authors have predicted a large spin-filtering effect at the interface between graphene and various FM metals including nickel, cobalt, and iron. ^{Reference Yazyev and Pasquarello9,Reference Karpan, Khomyakov, Starikov, Giovannetti, Zwierzycki, Talanana, Brocks, van den Brink and Kelly39} The theoretical prediction rests on the peculiar band structure of graphene at the Fermi level and its interaction with the spin-polarized band structure of the metals. This prediction is similar to that of spin filtering at Fe/MgO interfaces ^{Reference Butler, Zhang, Schulthess and MacLaren40,Reference Mathon and Umerski41} which was quickly verified experimentally ^{Reference Bowen, Cros, Petroff, Fert, Martinez Boubeta, Costa-Kramer, Anguita, Cebollada, Briones, de Teresa, Morellon, Ibarra, Guell, Peiro and Cornet42} and has since led to room temperature TMR in excess of 200%. ^{Reference Parkin, Kaiser, Panchula, Rice, Hughes, Samant and Yang43,Reference Yuasa, Nagahama, Fukushima, Suzuki and Ando44} The mechanisms leading to spin filtering are quite different, however. In Fe/MgO, it derives from band symmetry effects, while in FM/graphene it derives from band alignments, i.e., the positions of the majority/minority spin bands relative to E _F.

We have recently shown that using multi-layer graphene as the tunnel barrier between NiFe and Co produces a negative magnetoresistance of 20%, which is a direct consequence of the spin-filtering qualities of graphene. ^{Reference Cobas, van 't Erve, Robinson and Jonker45}

A. The devices

Three types of tunnel barriers, SiO₂, Al₂O₃, and graphene, were fabricated on identical Si substrates. Here, 2 nm of SiO₂ was grown on HF etched Si using plasma oxidation to obtain pinhole-free barriers. Al₂O₃ tunnel barriers are routinely used in research grade and commercially available MTJs. Here, a 1.5 nm thick Al₂O₃ layer is grown in situ by a two-step natural oxidation process. Finally, Graphene was synthesized via low-pressure CVD on a copper foil substrate using methane gas and transferred onto hydrogenated Silicon using conventional wet chemical processing. ^{Reference Li, Magnuson, Venugopal, Tromp, Hannon, Vogel, Colombo and Ruoff36} The typical grain size of the graphene films is of several hundred micrometers. The quality of the graphene was assessed using Raman spectroscopy, the absence of the “D” line (∼1350 cm⁻¹) associated with defects, and the widths and ratios of the “G” (∼1580 cm⁻¹) and “2D” (∼2700 cm⁻¹) lines confirm that the graphene is of high quality with minimal defects.

During device fabrication, care was taken to isolate conducting edges of graphene ^{Reference Chae, Jung, Woo, Baek, Ha, Song, Son, Zhitenev, Stroscio and Kuk62} by burying them in a layer of sputter-deposited Si₃N₄. For this study, n-type Si (001) wafers with donor concentrations of 1 × 10¹⁹, 3 × 10¹⁹, and 6 × 10¹⁹ were used. The top electrode for all three types of tunnel barriers is sputter-deposited Ni₈₀Fe₂₀. A schematic of the device used in this study is found in Fig. 4.

FIG. 4.

(a) Schematic view of the 3T device, contacts 1 and 3 are Ohmic, contact 2 is a Au capped Ni₈₀Fe₂₀/graphene tunnel barrier. (b) Schematic of the nonlocal spin-valve device, contacts 1 and 4 are ohmic contacts applied directly to the Si substrate, and contacts 2 (1 μm wide) and 3 (200 nm wide) are Au capped Ni₈₀Fe₂₀/graphene tunnel barriers for electrical spin injection and detection.

B. The results

Electrical measurements were performed in a cryogen-free cryostat and electromagnet set-up using 3- and 4-terminal configurations, as depicted in Fig. 4(a) and described below.

Figure 5(a) shows the typical I–V curve at 300 K for NiFe/monolayer graphene/Si (6 × 10¹⁹ cm⁻³) contacts and NiFe/Si (6 × 10¹⁹ cm⁻³) contacts. The I–V curve for the contact without graphene is completely linear, as is expected, for this type of Ohmic contact. However the inclusion of a single layer of graphene completely changes the nature of this contact and a nonlinear I–V curve is observed. The weak temperature dependence of the ZBR of the NiFe/graphene/Si contact confirms that transport occurs by tunneling through a pinhole free tunnel barrier, ^{Reference Jonsson-Akerman, Escudero, Leighton, Kim, Schuller and Rabson37} and provides a more definitive test for tunneling than fitting to a parabolic model. ^{Reference Simmons63,Reference Brinkman, Dynes and Rowell64}

FIG. 5.

(a) I–V curve at 300 K. The ohmic NiFe/Si contacts exhibit metallic behavior and the NiFe/graphene/Si is nonlinear. (b) The normalized ZBR shows a weak insulator-like temperature dependence for the NiFe/graphene/Si contact, confirming tunnel transport. A metallic behavior of the NiFe/Si contact is observed. (c) The current–voltage curves and corresponding RA products of NiFe/Si, NiFe/graphene/Si, and NiFe/2 nm SiO₂/Si contacts. The Si electron density is 6 × 10¹⁹ cm⁻³.

Graphene serves as a highly conductive tunnel barrier, as demonstrated in Fig. 5(c) by a comparison of the room temperature zero bias RA products and current density versus voltage curves of three types of contacts to the Si (6 × 10¹⁹ cm⁻³) substrate: NiFe/Si (ohmic), NiFe/graphene/Si (tunneling), and NiFe/2 nm SiO₂/Si (tunneling) contacts. NiFe deposited directly on the Si forms an ohmic contact with a zero bias RA product of 0.4 kΩ μm², and the conductivity increases with decreasing temperature [metallic-like, Fig. 5(b)]. When a single layer of graphene is inserted between the NiFe and the Si, tunneling behavior dominates, but the RA product increases to only 6 kΩ μm². In contrast, a NiFe/2 nm SiO₂ tunnel contact on the same substrate has a much larger RA product of 15 MΩ μm², with a corresponding decrease in the tunnel current of over 10³ at a given bias voltage. A similar trend is observed for contacts to the Si (1 × 10¹⁹ cm⁻³) substrate, although the NiFe/Si contact is Schottky-like rather than ohmic. Thus the uniform, atomically thin character of graphene provides a superior tunnel barrier with a low RA product.

Using a ferromagnet like NiFe as the top electrode ensures that the tunnel current is spin polarized ^{Reference Meservey and Tedrow65} and the tunnel barrier allows for a spin accumulation to occur underneath the tunnel barrier contact.

Spin accumulation and precession directly under the magnetic tunnel barrier contact interface can be observed using a single contact for both spin injection and detection, as shown in Fig. 5(a). A current is applied to contacts 1 and 2, and a voltage is measured across contacts 2 and 3. The injection of spin-polarized carriers from FM contact 2 produces a net spin accumulation in the Si described by the splitting of the spin-dependent electrochemical potential, Δμ = μ_up − μ_down, which is detected as a voltage ΔV _3T = γΔμ/2e, where γ is the tunneling spin polarization of the magnetic tunnel contact.

Spin lifetime and spin diffusion lengths are important figures of merit for spin devices. For a practical device the spin diffusion length (L _SD = (Dτ_s)^1/2) in the semiconductor channel has to be longer than the device dimensions, where L _SD is the spin diffusion length, D is the diffusion constant and τ_s is the spin lifetime. Hanle spin precession measurements (precession caused by dephasing of electron spins in an applied magnetic field) are used to determine spin lifetimes and spin diffusion lengths. The top three curves in Fig. 6 are the Hanle measurements of the Al₂O₃, SiO₂, and graphene tunnel barrier samples at room temperature. For all three barriers, a negative magnetoresistance was observed with a Lorentzian line-shape caused by field-induced precession, confirming successful spin accumulation in silicon. The bottom two measurements of Fig. 6 are for the NiFe/Si (1 × 10¹⁹) reference sample and a nonmagnetic/graphene/Si (1 × 10¹⁹) control sample, measured at 10 K. No magnetic field dependence is observed and none is expected. Although NiFe/Si (1 × 10¹⁹) forms a Schottky contact and spin-polarized electrons could, in principle, tunnel across this barrier, silicide formation and diffusion of metallic ions from the NiFe are likely, suppressing spin injection for this contact. The top three Hanle curves can be fit with a Lorentzian line-shape given by ΔV _3T(B _z) = ΔV _3T(0)/[1 + (ω_Lτ_s)²], where ω_L is the Lamor frequency and τ_s is the spin lifetime. Fits to this line-shape (shown in Fig. 6) give a lower bound of τ_s ∼ 150 ps for each of the tunnel barrier materials used (graphene, SiO₂, and Al₂O₃), demonstrating that the lifetime measured is not dominated by some characteristic of the tunnel barrier. This is also explicitly demonstrated in Fig. 7, where we plot the spin lifetime obtained from three-terminal Hanle data on n-Si as a function of electron density for three different tunnel barrier materials (graphene, Al₂O₃, and SiO₂) and three different magnetic metal contacts (Fe, CoFe, and NiFe). The spin lifetime measured with the three-terminal Hanle geometry shows a clear dependence only on electron density, and the dependence is consistent with literature electron spin resonance data on bulk Si. The spin lifetime is completely independent of the tunnel barrier material or magnetic metal used for the contact. The values for the graphene tunnel barriers fall directly on the curve. These data confirm that the spin accumulation occurs in the Si, and not in the graphene or possible interface trap states (Fig. 8).

FIG. 6.

Hanle spin precession measurements, graphs are offset for clarity. Room temperature Hanle data for spin injection NiFe/Al₂O₃/Si (3 × 10¹⁹), NiFe/SiO₂/Si (3 × 10¹⁹) and NiFe/graphene/Si (1 × 10¹⁹). Also shown are the control samples; nonmagnetic/graphene/Si (1 × 10¹⁹) and NiFe/Si (1 × 10¹⁹) measured at 10 K.

FIG. 7.

Spin lifetimes obtained from three-terminal Hanle measurements at 10 K as a function of the Si electron density for the tunnel barrier materials indicated and different FM metal contacts (Fe, CoFe, and NiFe). The symbol shape distinguishes the tunnel barrier material: triangles—SiO₂, circles—Al₂O₃ and stars—graphene. Solid symbols correspond to devices with Ni_0.8Fe_0.2 contacts, half-solid symbols to Fe contacts, and open symbols to Co_0.9Fe_0.1 contacts. The spin lifetimes show a pronounced dependence on the Si doping level, and little dependence on the choice of tunnel barrier or magnetic metal.

FIG. 8.

Nonlocal resistance versus in-plane magnetic field measured using lock in techniques. Clear parallel and antiparallel magnetic states are observed.

The 3T devices with graphene tunnel barriers provide insight into the properties of a spin-polarized electron current and spin accumulation that occur directly underneath the injecting contact. To study the physics of a pure spin current which is away from the injecting contact, one can use a four-terminal (4T) nonlocal spin-valve (NLSV) contact geometry, as illustrated in Fig. 4(b). In the nonlocal detection geometry, spin-polarized electrons are injected into the Si from contact 2, producing both a spin-polarized electron drift/diffusion current which flows with an applied bias from contact 2 to 1, and a diffusive spin current which flows to the right from contact 2. This pure spin current produces a net spin polarization and an imbalance in the spin-dependent electrochemical potential, which is detected as a voltage by the magnetic contact 3 relative to the reference contact 4. No charge current flows in the detection circuit defined by reference contact 3 and magnetic detector contact 4, and thus excluding spurious contributions from anisotropic and local Hall effects. The voltage measured at contact 3 is sensitive to the relative orientation of the contact magnetization and the net spin orientation in the Si itself.

We use electron-beam lithography to define the magnetic contacts that are 200 nm wide and 1 µm wide contact separated by 200 nm. E-beam evaporation was used to deposit 150 Å Ni₈₀Fe₂₀/50 Å Ti/300 Å Au. These contacts were then used as a hard mask to etch away the exposed graphene by a light oxygen plasma, confirmed by a resistance check.

At large negative magnetic fields applied along the long axis of the contacts, the magnetizations of the 200 nm and 1 µm wide contacts are parallel, and the nonlocal resistance is at the maximum. As the field is increased, the 1 µm contact switches, resulting in an antiparallel orientation and the minimum nonlocal resistance. As the field increases further, the 200 nm contact also switches, so that the contact magnetizations are again parallel, and the nonlocal resistance returns to its maximum value. The sequence is reversed as the magnetic field is swept from positive to negative. The maximum resistance change is ∼2.5 mΩ, close to the value that has been observed previously with MgO barriers. ^{Reference Sasaki, Oikawa, Suzuki, Shiraishi, Suzuki and Noguchi66–Reference Shiraishi, Honda, Shikoh, Suzuki, Shinjo, Sasaki, Oikawa, Noguchi and Suzuki68} We observed clear switching for the inplane NLSV devices, see Fig. 8. From the nonlocal Hanle data, we obtained spin lifetimes of 140 ps in the NLSV devices at 10 K, consistent with the 3T measurements described above.

In addition to good spin properties, a spin contact must also exhibit a low conventional RA product. The magnetic contact's conventional RA product is an important parameter in determining the practical application of spin-based semiconductor devices. Calculations have shown that significant local MR can be achieved only if the contact RA product falls within a range, which depends upon the Si channel conductivity, the spin lifetime and the contact spacing. ^{Reference Min, Motohashi, Lodder and Jansen69} The RA products of all magnetic tunnel barrier contacts, to date, have been much larger than required, making such devices unattainable. However, the low RA products provided by the graphene tunnel barriers fall within this window, and enable realization of these and other important spintronic devices. We calculated the range of optimum RA products and the corresponding local MR as a function of the Si electron density using the contact geometry shown as the inset in Fig. 9. The geometric parameters are chosen to be consistent with the node anticipated for Si device technology within the next few years. The color code in Fig. 9 identifies the range of useful MR and the corresponding window of contact RA products required. Reducing the RA product also has a positive effect on the electrical properties of the spin device, as lowering the resistance reduces noise and increases the speed of an electrical circuit.

FIG. 9.

Calculation of the local (two terminal) magnetoresistance as a function of the contact's conventional RA product and the Si electron density for the device geometry shown in the inset. The data points are the RA products measured for our FM metal/tunnel barrier/Si contacts using 2 nm SiO₂ (triangles), 1.5 nm AlO _x (squares) and monolayer graphene (circles) tunnel barriers prepared from identical Si wafers in our lab. The FM metal/graphene RA products fall within the window of useful MR values. W = w = 11 nm.

Another application where RA product is crucially important is nanowire devices, because of the exceedingly small contact area, which can be of order 100 nm². ^{Reference Mohney, Wang, Cabassi, Lew, Dey, Redwing and Mayer70,Reference Leonard and Talin71}

Nanowires are 1D structures and are a natural way to keep reducing the dimensions of electronic devices. Adding spins to nanowire circuits will offer enhanced functionality, such as built-in nonvolatile memory and reprogrammable logic.

Electrical spin injection that enables this enhanced functionality depends critically on the interface resistance between the spin injecting FM metal contact and the semiconductor.

Standard oxide tunnel barriers grown on nanowires in our lab were found to be too resistive to yield reliable and consistent results. We have fabricated nanoscale spintronic devices comprising of a Si nanowire spin transport channel with a low resistance tunnel barrier of single layer graphene for electrical spin injection and detection of pure spin currents. We used both four-terminal NLSV (Refs. Reference Johnson and Silsbee72 and Reference Jedema, Nijboer, Filip and van Wees73) and three-terminal (3T) ^{Reference Lou, Adelmann, Furis, Crooker, Palmstrøm and Crowell74} geometries to probe the spin accumulation and transport properties.

Si nanowires were grown using gold seeded vapor–liquid–solid techniques with a 〈111〉 growth axis. ^{Reference Cui, Lauhon, Gudiksen, Wang and Lieber75} The wires were phosphorous doped to an electron concentration n ∼ 3 × 10¹⁹ cm⁻³. They were removed from the growth substrate by sonication and dispersed on a Si₃N₄/Si substrate. Appropriate nanowires ∼100–150 nm in diameter were chosen optically, and two outer ohmic contacts were made using electron-beam lithography. A buffered hydrofluoric acid based solution was used to remove any thin oxide layer and hydrogen passivates the nanowires. Graphene grown by low-pressure CVD within Cu foil enclosures ^{Reference Li, Magnuson, Venugopal, Tromp, Hannon, Vogel, Colombo and Ruoff36} was transferred onto the hydrogen passivated nanowires using mechanical transfer techniques. The magnetic contacts, Au 300 Å/NiFe 100 Å, were defined by electron-beam lithography using a PMMA resist and deposited by electron-beam evaporation to form the devices illustrated in Fig. 10. These contacts are then used as a hard mask to remove the excess graphene by a light O₂ plasma etch. Complete removal of excess graphene was confirmed when the resistance between these electrodes increased by three orders of magnitude.

FIG. 10.

(a) Schematic of 4T nanowire device; contacts 1 and 4 are ohmic contacts applied directly to the nanowire, and contacts 2 (1 μm wide) and 3 (200 nm wide) are NiFe/graphene tunnel barriers for electrical spin injection and detection. The edge-to-edge separation of contacts 2 and 3 is 200 nm. (b) AFM image of graphene covered nanowire, green line is line scan shown in (c), (c) line scan of graphene covered nanowire. (d) scanning electron microscope (SEM) image of a NiFe/graphene contact on nanowire (NW). The graphene smoothly bridges the nanowire so that the NiFe film is smooth and continuous, scale bar is 1 μm, and (e) SEM image of an Au contact on a NW showing discontinuous portions of the metallization at the nanowire, scale bar is 1 μm.

Figure 10(b) shows an atomic force microscopy (AFM) image and line scan across the wire directly after the graphene transfer onto a 100 nm diameter Si nanowire. As reported in Ref. Reference Jin, Lee, Hwang, Kim, Kim, Son, Whang and Hwang76, the graphene smoothly bridges the nanowire and forms freely suspended graphene for approximately the width of the nanowire on each side, like a blanket on a clothesline. This free hanging graphene is robust to electron-beam evaporation of NiFe, and produces a smooth and continuous NiFe film across the nanowire as is evident from the SEM image in Fig. 10(c). The smooth bridging provided by graphene results in clean switching of the contact magnetization, because it minimizes the formation of complicated magnetic domains which have been found to compromise the magnetic behavior. In contrast, the SEM image of the Au reference contact, Fig. 10(d), shows that this metal layer without graphene underneath attempts to be highly conformal to the NW, resulting in discontinuous portions of the metallization.

These contacts were initially characterized using I–V measurements demonstrating that this contact is a high quality, pinhole-free tunnel barrier. An in-plane magnetic field is used to switch the magnetizations of the two electrodes independently, producing parallel and antiparallel alignments. A net change in the nonlocal resistance of ∼0.7 mΩ was measured at 10 K, see Fig. 11.

FIG. 11.

Nonlocal spin-valve and Hanle measurements. (a) NLSV data on 150 nm wide nanowire, contacts are 200 nm and 1 μm wide with a 200 nm edge-to-edge spacing. The arrows indicate the relative orientation of the magnetizations of the injector and detector contacts, and the blue and red traces indicate increasing and decreasing magnetic field sweeps. (b) NLSV Hanle data after background subtraction. All data are for a bias current of −200 μA at T = 10 K, peak is 5 mΩ.

The magnetizations of the two contacts reverse cleanly at well-defined coercive fields consistent with shape anisotropy, so that both parallel and antiparallel alignments of the injector/detector magnetizations are realized. We attributed this to the smooth bridging of the NW by the graphene layer as discussed above producing a more gradual variation in the contact topography to which the NiFe film conforms. In contrast, magnetic metal/oxide tunnel contacts applied directly to the NW exhibit poorly defined switching characteristics attributed to local domain patterns arising from the more complex morphology created as the contact attempts to conform to the NW sidewalls. ^{Reference Zhang, Dayeh, Li, Crooker, Smith and Picraux77}

The amplitude of the nonlocal Hanle signal measured at contact 2 is 1 μV or 5 mΩ, and can be modeled using the integral spin diffusion approach described in the literature. ^{Reference Jedema, Nijboer, Filip and van Wees73,Reference Lou, Adelmann, Crooker, Garlid, Zhang, Reddy, Flexner, Palmstrøm and Crowell78} The model fits the experimental data well, as shown by the red curve in Fig. 10(d), and yields values for the diffusion constant D = 0.00047 m²/s and the NLSV spin lifetime of 190 ± 10 ps, consistent with the values observed for the bulk silicon samples described above.

A. In summary

This work is the first demonstration of the use of a single layer of graphene as a tunnel barrier. By incorporating a single layer of CVD-grown graphene into an MTJ structure, we have shown that charge and spin transport across the graphene occurs by tunneling and preserves the spin polarization of the tunneling carriers. Using FM-graphene tunnel contacts to inject spin into a silicon channel, we have shown that such contacts achieve dramatically lower resistance than equivalent oxide-based tunnel contacts. We have also shown that functionalized graphene can be used as an effective tunnel barrier on graphene, creating a homoepitaxial spintronic graphene device. These discoveries pave the way for a new generation of spintronic devices using graphene in an unconventional way, but providing unparalleled potential for better state-of-the-art performance. Utilizing intrinsic 2D layers, such as graphene or hexagonal boron nitride, as tunnel contacts on nanowires offers many advantages over conventional materials deposited by vapor deposition (e.g., Al₂O₃ or MgO), enabling a path to highly scaled electronic and spintronic silicon or graphene devices.

A. Introduction

TMDs are of keen interest for emerging electronic applications. ^{Reference Jariwala, Sangwan, Lauhon, Marks and Hersam108,Reference Wang, Kalantar-Zadeh, Kis, Coleman and Strano111,Reference Radisavljevic, Radenovic, Brivio, Giacometti and Kis122,Reference Yoon, Ganapathi and Salahuddin166,Reference Alam and Lake167} In contrast with their indirect gap character in the bulk, single monolayer TMDs of the family MX₂ (M = Mo, W and X = S, Se, and Te) are direct-gap semiconductors with a range of band gaps in the visible regime ^{Reference Mak, He, Shan and Heinz118,Reference Splendiani, Sun, Zhang, Li, Kim, Chim, Galli and Wang121,Reference Gutiérrez, Perea-López, Elías, Berkdemir, Wang, Lv, López-Urías, Crespi, Terrones and Terrones148} suitable for a host of optoelectronic, ^{Reference Wang, Kalantar-Zadeh, Kis, Coleman and Strano111} light harvesting ^{Reference Feng, Qian, Huang and Li168,Reference Bernardi, Palummo and Grossman169,} chemical sensor, ^{Reference Perkins, Friedman, Cobas, Campbell, Jernigan and Jonker117,Reference Liu, Chen, Liu, Abbas, Fathi and Zhou170} and spin-valley coupling based ^{Reference Xiao, Liu, Feng, Xu and Yao171–Reference Mak, McGill, Park and McEuen173} applications.

A single layer of MoX₂, schematically shown in Fig. 19(a), consists of a plane of transition metal atoms sandwiched by layers of chalcogen atoms. The Brillouin zone of this system is shown in Fig. 19(b). In single layer form, the direct gap occurs at the K-point, and the optical properties of these materials are governed by strong excitonic transitions, both neutral and charged.

FIG. 19.

(a) Crystal structure of a single-layer transition-metal dichalcogenide. A central layer of transition metal atoms is sandwiched by layers of chalcogens. (b) Brillouin zone for a reduced dimensional hexagonal lattice. Some relevant high symmetry points are indicated. (c) Schematic of the single-particle band structure at K and K′ valleys. The arrows denote the A (solid line) and B (dashed line) excitons. Each valley can only be excited with a specific helicity, σ⁺ or σ⁻.

These excitons are strongly bound, with the neutral exciton having binding energies in the order of 0.5–0.8 eV (Refs. Reference Qiu, da Jornada and Louie174–Reference Chernikov, Berkelbach, Hill, Rigosi, Li, Aslan, Reichman, Hybertsen and Heinz178) and the charged exciton (trion) having a binding energy of 20–30 meV. ^{Reference Mak, He, Lee, Lee, Hone, Heinz and Shan179,Reference Ross, Wu, Yu, Ghimire, Jones, Aivazian, Yan, Mandrus, Xiao, Yao and Xu180} In addition to being optically active with strong PL, they also have unique optical selection rules [Fig. 19(c)]. Time reversal symmetry and strong orbital-hybridization couples the valley and spin indices. This enables access to a single valley using polarized light, since the angular momentum of incident circularly polarized light interacts with carriers to produce specific spin states. ^{Reference Mak, He, Shan and Heinz118,Reference Kioseoglou, Hanbicki, Currie, Friedman, Gunlycke and Jonker119,Reference Cao, Wang, Han, Ye, Zhu, Shi, Niu, Tan, Wang, Liu and Feng172,Reference Mak, He, Lee, Lee, Hone, Heinz and Shan179,Reference Sallen, Bouet, Marie, Wang, Zhu, Han, Lu, Tan, Amand, Liu and Urbaszek181,Reference Zeng, Dai, Yao, Xiao and Cui182} In other words, the symmetry properties of the two inequivalent valleys lead to a difference in the absorption of circularly polarized light, either positive (σ ⁺ ) or negative (σ ⁻ ) helicity, resulting in a strong chiral selectivity.

Despite recent progress, there are many gaps in our understanding of the fundamental interactions which lead to the striking optical and electronic properties these monolayer semiconductor materials exhibit, including very basic electron–hole interactions. Here we will review four topics that highlight the novelty, subtlety, and unexpected behavior present in these fascinating materials. This includes the extremely high binding energy of optically generated electron–hole pairs, intervalley scattering, and the profound effect of the environment on these mostly surface materials.

B. Experimental background

Before discussing the fascinating science inherent in these systems, it is instructive to review some basic properties of these materials. TMD samples can be prepared in several ways. One common method is to mechanically exfoliate flakes from bulk single crystals and deposit them onto substrates such as SiO₂/Si. If the SiO₂ thickness is chosen judicously monolayer regions can be readily identified in an optical microscope because of the optical contrast. ^{Reference Blake, Hill, Castro Neto, Novoselov, Jiang, Yang, Booth and Geim183,Reference Benameur, Radisavljevic, Héron, Sahoo, Berger and Kis184}

This method usually yields monolayer regions that are typically 5–10 µm across. An example of exfoliated monolayers is shown in Fig. 20. Another method that is becoming increasingly popular is to grow material via CVD. This technique can lead to large area samples and is discussed at length in the previous section. Independent of preparation technique, the single layer nature of the TMD to be interrogated can be confirmed based on the Raman signature. ^{Reference Tonndorf, Schmidt, Böttger, Zhang, Börner, Liebig, Albrecht, Kloc, Gordan, Zahn, Michaelis de Vasconcellos and Bratschitsch155,Reference Lee, Yan, Brus, Heinz, Hone and Ryu185–Reference Terrones, Corro, Feng, Poumirol, Rhodes, Smirnov, Pradhan, Lin, Nguyen, Elías, Mallouk, Balicas, Pimenta and Terrones189} For example, with MoS₂ and WS₂ the separation of the in-plane ${\rm{E}}_{2{\rm{g}}}^1$ and out-of-plane ${\rm{A}}_{\rm{g}}^1$ Raman modes varies as a function of temperature. In the single layer limit, the energy difference for MoS₂ is 18 cm⁻¹ while for the bulk it is 23 cm⁻¹. ^{Reference Tonndorf, Schmidt, Böttger, Zhang, Börner, Liebig, Albrecht, Kloc, Gordan, Zahn, Michaelis de Vasconcellos and Bratschitsch155,Reference Lee, Yan, Brus, Heinz, Hone and Ryu185,Reference Molina-Sánchez and Wirtz186,Reference Terrones, Corro, Feng, Poumirol, Rhodes, Smirnov, Pradhan, Lin, Nguyen, Elías, Mallouk, Balicas, Pimenta and Terrones189} In WS₂ a single layer shows a separation of 60–61 cm⁻¹ while for the bulk it is 65 cm⁻¹. ^{Reference Molina-Sánchez and Wirtz186,Reference Berkdemir, Gutiérrez, Botello-Méndez, Perea-López, Elías, Chia, Wang, Crespi, López-Urías, Charlier, Terrones and Terrones187,Reference Terrones, Corro, Feng, Poumirol, Rhodes, Smirnov, Pradhan, Lin, Nguyen, Elías, Mallouk, Balicas, Pimenta and Terrones189} For WSe₂, the bulk in-plane and the out-of-plane modes are degenerate (E = 250 cm⁻¹), but this degeneracy is lifted for few and single layers. The resulting splitting is 12 cm⁻¹ for a single layer and 6 cm⁻¹ for the bilayer. ^{Reference Tonndorf, Schmidt, Böttger, Zhang, Börner, Liebig, Albrecht, Kloc, Gordan, Zahn, Michaelis de Vasconcellos and Bratschitsch155,Reference Sahin, Tongay, Horzum, Fan, Zhou, Li, Wu and Peeters188,Reference Terrones, Corro, Feng, Poumirol, Rhodes, Smirnov, Pradhan, Lin, Nguyen, Elías, Mallouk, Balicas, Pimenta and Terrones189} The identification of single layer MoSe₂ is based on the absence of the B_2g mode at 353 cm⁻¹. ^{Reference Terrones, Corro, Feng, Poumirol, Rhodes, Smirnov, Pradhan, Lin, Nguyen, Elías, Mallouk, Balicas, Pimenta and Terrones189} Representative Raman spectra from each of these materials are presented in Fig. 21.

FIG. 20.

Optical image of (a) MoS₂, (b) MoSe₂, (c) WS₂, and (d) WSe₂ flakes exfoliated from bulk crystals.

FIG. 21.

Representative room temperature Raman spectra of the four TMDs shown in Fig. 20, (a) MoS₂, (b) MoSe₂, (c) WS₂, and (d) WSe₂.

As discussed, when reduced to single monolayer, the TMDs become direct band gap semiconductors. Therefore, it is common to measure PL to further confirm the single layer nature of these materials. Room temperature PL emission from the four different samples is presented in Fig. 22. In these spectra, the dominant emission peak is the A-exciton, a feature that originates from the lowest energy transition at the K-point of the Brillouin zone [see Fig. 19(c)]. While each material emits at a wave length characterized by the band gap, the specific energy of emission can vary somewhat based on the quality and environment of the flake. For instance, the environment has a profound effect on the emission characteristics. ^{Reference Tongay, Zhou, Ataca, Liu, Kang, Matthews, You, Li, Grossman and Wu190–Reference Currie, Hanbicki, Kioseoglou and Jonker196} The emission energy can vary by as much as 50 meV. ^{Reference Kioseoglou, Hanbicki, Currie, Friedman, Gunlycke and Jonker119,Reference Lin, Ling, Yu, Huang, Hsu, Lee, Kong, Dresselhaus and Palacios194,Reference Mouri, Miyauchi and Matsuda195,Reference Plechinger, Schrettenbrunner, Eroms, Weiss, Schüller and Korn197} Multiple features associated with charged and neutral excitons can also be present in the spectra. ^{Reference Ross, Wu, Yu, Ghimire, Jones, Aivazian, Yan, Mandrus, Xiao, Yao and Xu180,Reference Currie, Hanbicki, Kioseoglou and Jonker196,Reference Jones, Yu, Ghimire, Wu, Aivazian, Ross, Zhao, Yan, Mandrus, Xiao, Yao and Xu198}

FIG. 22.

Representative PL spectra of the four TMDs shown in Fig. 20, (a) MoS₂, (b) MoSe₂, (c) WS₂, and (d) WSe₂.

More detail on this aspect of the PL will be discussed later. To probe the electronic transitions in these monolayers, light from a broad-band radiation source is focused on the sample and the reflected intensity is measured. Because the flakes are atomically thin and are usually on a substrate, the reflected light spectra include the illumination source profile, the sample transmission and absorption, the substrate reflection and absorption, and potential resonant effects due to the thickness of the substrate. To distinguish the contribution from the monolayer TMD flake, one takes the difference between the intensity measured from the flake, I _on, and from the substrate just off the flake, I _off, and normalizes to the intensity from the substrate, I* = (I _on − I _off)/I _off. This is commonly referred to as reflectivity, but is also called differential reflectivity or reflectance contrast. Figure 23 shows some representative reflectivity spectra from various TMDs.

FIG. 23.

Representative low temperature reflectivity spectra of the four TMDs shown in Fig. 20, (a) MoS₂, (b) MoSe₂, (c) WS₂, and (d) WSe₂.

C. High exciton binding energy

Photoexcitation in semiconductors is usually performed by promoting an electron directly from the valence band to the conduction band. A subsequent coulomb interaction, mitigated by dielectric screening from the surrounding lattice, leads to spatial confinement of the electron–hole pair. The resulting bound quasiparticle is known as an exciton. In bulk materials, excitons have binding energies less than 0.1 eV (e.g., ∼40 meV in bulk MoS₂), so that the ground state of the exciton is just below the true band gap energy determined by the electronic band structure. In reduced dimensions dielectric screening is greatly reduced, which is predicted to lead to exciton binding energies ten times larger than in the bulk. ^{Reference Qiu, da Jornada and Louie174,Reference Ramasubramaniam176,Reference Cheiwchanchamnangij and Lambrecht199–Reference Liang, Huang, Soklaski and Yang201} These high binding energy excitons exhibit behavior similar to excited atoms, with energy levels designated 1s, 2s, 2p and so on. The observation of both ground (1s) and excited (2p) states is therefore one way to determine a lower bound for the exciton binding energy.

Table IV shows a summary of the dispersion of theoretical and experimental results for the binding energy of WS₂ and WSe₂ as found in the literature. As mentioned, one way to interrogate the band gap is to measure the optical reflectivity/absorption. Figure 24 displays the differential reflectivity from several single monolayer samples of WS₂ [Fig. 24(a)] and WSe₂ [Fig. 24(b)] in the energy range of 1.5–3.3 eV and temperatures of 4–300 K. ^{Reference Hanbicki, Currie, Kioseoglou, Friedman and Jonker175}

TABLE IV.

Summary of exciton binding energies reported in the literature.

FIG. 24.

Derivative of differential reflectivity from several single monolayer samples of (a) WS₂ and (b) WSe₂ in the energy range of 1.5–3.3 eV and temperatures of 4–300 K.

For each sample, there are peaks corresponding to the ground state exciton associated with the direct gap (A-exciton, $E_{1{\rm{s}}}^{\rm{A}}$ ), and the exciton associated with the spin–orbit splitting of the direct gap valence band (B-exciton, $E_{1{\rm{s}}}^{\rm{B}}$ ) occurring at the K/K′ points in the Brillouin zone. Similar features are reported in monolayer MoS₂. ^{Reference Mak, He, Shan and Heinz118,Reference Splendiani, Sun, Zhang, Li, Kim, Chim, Galli and Wang121} By measuring to an energy of 3.3 eV, it is possible to observe distinct spectral features associated with the 2s excited state, $E_{{\rm{2s}}}^{\rm{A}}$ , of the A-exciton in both WS₂ and WSe₂. From these energy levels it is possible to derive a lower bound for the exciton binding energy as $E_{{\rm{2s}}}^{\rm{A}} \minus E_{1{\rm{s}}}^{\rm{A}}$ of 0.83 and 0.79 eV for WS₂ and WSe₂, respectively, and a lower bound for the corresponding band gaps ${E_{\rm{g}}} \ge E_{{\rm{2s}}}^{\rm{A}}$ of 2.90 and 2.53 eV at 4 K. ^{Reference Hanbicki, Currie, Kioseoglou, Friedman and Jonker175} These values compare well with theoretical predictions (binding energies of 1.04 and 0.9 eV for WS₂ and WSe₂, respectively). ^{Reference Ramasubramaniam176} These experimental values are significantly larger than the 0.37 eV binding energy reported by He et al. ^{Reference He, Kumar, Zhao, Wang, Mak, Zhao and Shan177} for WSe₂, but are similar to the 0.7 eV binding energy reported by Ye et al. ^{Reference Ye, Cao, O'Brien, Zhu, Yin, Wang, Louie and Zhang203} for WS₂. Both of these groups use two-photon PL spectroscopy measurements. A third group, also using absorption/reflectivity measurements, reported a binding energy of 0.32 eV in WS₂ (Ref. Reference Chernikov, Berkelbach, Hill, Rigosi, Li, Aslan, Reichman, Hybertsen and Heinz178) based on a series of Rydberg-like states just above the A-exciton.

These remarkably high exciton binding energies imply that excitonic behavior dominates to room temperature and above, and as can be seen in Fig. 25, it is indeed possible to follow the evolution of these features to 300 K. Furthermore, because the binding energies are large, the electronic band gap (sometimes referred to as the true band gap) is substantially higher (∼1 eV) than the dominant excitonic spectral feature commonly observed with PL (the optical gap), and the exciton can be created directly using photoexcitation energies well below the true band gap. This has been an implicit, and to date largely unappreciated assumption of much experimental work. In contrast with most common semiconductors, excitons in these novel monolayer materials exist even at room temperature, and an excitonic band structure and framework should be used as a starting point to further understand their basic properties. ^{Reference Song and Dery208} More advanced theoretical treatments ^{Reference Qiu, da Jornada and Louie174,Reference Ramasubramaniam176,Reference Komsa and Krasheninnikov200} may provide more accurate estimates of the exciton binding energies, band gaps, and corresponding properties. It is clear from the broad dispersion of results in the community that further work is necessary to fully understand these novel 2D materials.

FIG. 25.

PL spectra at T = 5 K analyzed for σ⁺ and σ⁻at selected photoexcitation energies for (a) MoS₂ and (b) MoSe₂.

D. Intervalley scattering

Another interesting property of these TMD materials is the spin-valley coupling that leads to rather unique optical selection rules [Fig. 19(c)]. When single-layer TMDs are excited with circularly polarized light, excitons are created in a single valley. The radiative decay of excitons within this valley subsequently produces circularly polarized light due to these optical selection rules. Therefore, measuring the circular polarization of electroluminescence or PL provides a direct way to monitor valley populations. The degree of circular polarization is defined as P _circ = (I ₊ − I ₋)/(I ₊ + I ₋), where I ₊ (I ₋) is the intensity of the σ ⁺ (σ⁻) component of the PL. Valley populations are altered by intervalley scattering, a process that is enabled by either phonons or the Coulomb interaction. ^{Reference Kioseoglou, Hanbicki, Currie, Friedman, Gunlycke and Jonker119,Reference Song and Dery208,Reference Glazov, Amand, Marie, Lagarde, Bouet and Urbaszek209} At high temperatures or high photoexcitation energy, large phonon populations can readily couple the valleys, reducing valley specific populations.

Polarization-resolved PL of single layer MoS₂ has been extensively studied, and a high initial circular polarization was reported with a circularly polarized pump. ^{Reference Mak, He, Shan and Heinz118,Reference Sallen, Bouet, Marie, Wang, Zhu, Han, Lu, Tan, Amand, Liu and Urbaszek181} In contrast, there are few polarization-dependent studies for MoSe₂ at zero magnetic field. One recent study ^{Reference Wang, Palleau, Amand, Tongay, Marie and Urbaszek210} reported very low initial circular polarization in the PL which is surprising since one expects members of the MoX₂ family to behave similarly. Several other recent studies, ^{Reference MacNeill, Heikes, Mak, Anderson, Kormányos, Zólyomi, Park and Ralph211,Reference Li, Ludwig, Low, Chernikov, Cui, Arefe, Kim, van der Zande, Rigosi, Hill, Kim, Hone, Li, Smirnov and Heinz212} demonstrated generation of valley polarization in MoSe₂ by applying external magnetic fields up to 10 T perpendicular to the sample. In particular, MacNeil et al. ^{Reference MacNeill, Heikes, Mak, Anderson, Kormányos, Zólyomi, Park and Ralph211} observed a maximum polarization of 14% for the charged and 9% for the neutral exciton at 4.2 K and 6.7 T attributed to the magnetic field breaking the K/K′ valley-degeneracy.

Here we introduce some measurements of the energy-dependent valley polarization in both MoS₂ and MoSe₂ under zero magnetic field, and present a model for the polarization relaxation. ^{Reference Kioseoglou, Hanbicki, Currie, Friedman and Jonker213} We probe the valley population dynamics in MoSe₂ and MoS₂ by selectively populating the K and K′ valleys with circularly polarized light [light of positive (σ⁺) or negative (σ⁻) helicity] while systematically varying the laser excitation energy. Figure 25 shows some PL spectra for MoS₂ [Fig. 25(a)] and MoSe₂ [Fig. 25(b)] analyzed for positive and negative helicity at T = 5 K at selected σ⁺ excitation energies. For both systems, the difference in the excitation energy and PL emission energy, ΔE = E _pump − E _PL, governs the depopulation of carriers in each valley. This can be seen most effectively in a plot of polarization versus ∆E (Fig. 26). In this figure it is clear that as the excess energy increases, the polarization decreases monotonically. Moreover, there is an energy threshold that needs to be surmounted before depolarization begins.

FIG. 26.

Degree of circular polarization of the emitted PL as a function of excess energy, ΔE.

Again, the degree of circular polarization is shown as a function of the excess energy in Fig. 26. The inset of this figure is a graphical representation of excess energy. Data from our group are plotted for MoSe₂ (solid red circles) and MoS₂ (solid blue circles) and are derived from spectra where the temperature was held constant and the laser energy was varied, or the laser energy was fixed and the emission energy was varied via a change in temperature. ^{Reference Mak, Lee, Hone, Shan and Heinz116,Reference Kioseoglou, Hanbicki, Currie, Friedman, Gunlycke and Jonker119,Reference Sallen, Bouet, Marie, Wang, Zhu, Han, Lu, Tan, Amand, Liu and Urbaszek181} Other data for MoS₂ from the literature are also plotted in Fig. 26. The open circles and the open triangles are data from Refs. Reference Mak, Lee, Hone, Shan and Heinz116 and Reference Zeng, Dai, Yao, Xiao and Cui182 (respectively) taken at 5 K, and the open squares are data from Ref. Reference Sallen, Bouet, Marie, Wang, Zhu, Han, Lu, Tan, Amand, Liu and Urbaszek181 obtained at fixed excitation energy but at different temperatures. All data follow the same depolarization trend line when plotted as a function of excess energy. Using this methodology, all of the data collapse onto a single curve for each material, independent of whether the polarization of the trion or neutral exciton is considered. The data clearly demonstrate that as the excess energy increases the emitted circular polarization decreases.

To explain this behavior, we begin by noting that intervalley scattering can account for the reduced polarization observed, and the change in momentum necessary for such scattering implicates a phonon-mediated process. ^{Reference Mak, He, Shan and Heinz118,Reference Kioseoglou, Hanbicki, Currie, Friedman, Gunlycke and Jonker119} Close to resonance, the emitted circular polarization is expected to be essentially 100%, since there is not enough energy in the system to facilitate intervalley scattering. As the laser excitation energy increases or as the temperature changes for a fixed pumping energy, the available excess energy ∆E increases and phonon-assisted scattering is enabled above some material-dependent energy threshold. For MoS₂, the combined data set clearly interpolate to 100% polarization at ∆E = 60 meV. This distinct threshold is the same energy as twice the longitudinal acoustic (LA) phonon characteristic of MoS₂ [30 meV for MoS₂ (Ref. Reference Molina-Sánchez and Wirtz186)]. The MoSe₂ data (solid red symbols) exhibit a similar behavior—the measured polarization rapidly increases as the excess energy ∆E decreases. The solid red line in Fig. 27 is a model fit described below, and intercepts 100% polarization at ∆E = 38 meV, corresponding to twice the MoSe₂ LA phonon energy of 19 meV from the literature. ^{Reference Horzum, Sahin, Cahangirov, Cudazzo, Rubio, Serin and Peeters214} These data make it clear that depolarization and intervalley scattering are governed by the excess energy, ∆E, imparted to the photoexcited carriers through optical pumping.

FIG. 27.

Photoluminescence of WS₂ monolayer as a function of excitation power at room temperature for samples in (a) air and (b) vacuum.

To model this behavior, we begin with a familiar rate equation model in which the emitted circular polarization can be expressed as $P_{{\rm{circ}}} = {1 \mathord{\left/ {\vphantom {1 {\left( {1 + 2{{\tau _{\rm{r}} } \over {\tau _{\rm{s}} }}} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {1 + 2{{\tau _{\rm{r}} } \over {\tau _{\rm{s}} }}} \right)}}$ , where τ_r is the exciton lifetime and τ_s the intervalley scattering time. ^{Reference Mak, He, Shan and Heinz118,Reference Kioseoglou, Hanbicki, Currie, Friedman, Gunlycke and Jonker119} The increase in the excess energy ∆E, leads to an increase of the phonon population. Assuming τ_r to be linearly dependent on temperature ^{Reference Palummo, Bernardi and Grossman215} and the scattering rate τ_s ⁻¹ to be proportional to the phonon population $\langle n\rangle = {1 \mathord{\left/ {\vphantom {1 {\left( {{\rm{e}}^{{{\hbar \omega _{\rm{q}} } \mathord{\left/ {\vphantom {{\hbar \omega _{\rm{q}} } {kT}}} \right. \kern-\nulldelimiterspace} {kT}}} - 1} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {{\rm{e}}^{{{\hbar \omega _{\rm{q}} } \mathord{\left/ {\vphantom {{\hbar \omega _{\rm{q}} } {kT}}} \right. \kern-\nulldelimiterspace} {kT}}} - 1} \right)}}$ , we can fit the data using the relationship $P = {1 \mathord{\left/ {\vphantom {1 {\left( {{{1 + C\Delta E} \mathord{\left/ {\vphantom {{1 + C\Delta E} {\left( {{\rm{e}}^{{{\hbar \omega _{\rm{q}} } \mathord{\left/ {\vphantom {{\hbar \omega _{\rm{q}} } {\left( {\Delta E - \hbar \omega _q } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\Delta E - \hbar \omega _q } \right)}}} - 1} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {{\rm{e}}^{{{\hbar \omega _{\rm{q}} } \mathord{\left/ {\vphantom {{\hbar \omega _{\rm{q}} } {\left( {\Delta E - \hbar \omega _q } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\Delta E - \hbar \omega _q } \right)}}} - 1} \right)}}} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {{{1 + C\Delta E} \mathord{\left/ {\vphantom {{1 + C\Delta E} {\left( {{\rm{e}}^{{{\hbar \omega _{\rm{q}} } \mathord{\left/ {\vphantom {{\hbar \omega _{\rm{q}} } {\left( {\Delta E - \hbar \omega _q } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\Delta E - \hbar \omega _q } \right)}}} - 1} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {{\rm{e}}^{{{\hbar \omega _{\rm{q}} } \mathord{\left/ {\vphantom {{\hbar \omega _{\rm{q}} } {\left( {\Delta E - \hbar \omega _q } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {\Delta E - \hbar \omega _q } \right)}}} - 1} \right)}}} \right)}}$ , where ħω_q is twice the LA phonon energy, the minimum energy necessary for the exciton (electron and hole) to scatter from one valley to the other and reduce the optical polarization. The only fitting parameters are then a scaling constant C and ħω_q. The solid lines in Fig. 26 are fits to the data and yield values for 2LA of 54 meV for MoS₂ and 38 meV for the MoSe₂, in good agreement with the respective literature values of 60 and 38 meV ^{Reference Molina-Sánchez and Wirtz186,Reference Horzum, Sahin, Cahangirov, Cudazzo, Rubio, Serin and Peeters214}

In summary, depolarization of both MoS₂ or MoSe₂ can be modeled by a single depolarization mechanism: intervalley scattering mediated by LA phonons. The threshold needed for depolarization is found to be twice the LA phonon energy of the corresponding material, and the exciton kinetic energy greater than this is the key parameter for the depolarization. Generating high chirality PL in Mo-based two-dimensional structures enables applications in valley-photonics.

E. Effect of environment

When TMDs are optically pumped, the resultant PL is characterized by excitonic emission. In an undoped material, the main emission feature is from the neutral exciton, X⁰. Charged excitons, or trions, become important in doped systems and have emission energies 30–50 meV below the neutral exciton. ^{Reference Mak, He, Lee, Lee, Hone, Heinz and Shan179} The dynamic behavior of photoexcited carriers in MX₂ materials are governed by strong Coulomb interactions. These interactions have a profound influence on the charge concentration which in turn influences physical properties. Modification of the carrier concentration in MoS₂, has been achieved by applying a gate bias (in FET devices), ^{Reference Mak, He, Lee, Lee, Hone, Heinz and Shan179} physisorption, ^{Reference Tongay, Zhou, Ataca, Liu, Kang, Matthews, You, Li, Grossman and Wu190} chemical doping, ^{Reference Mouri, Miyauchi and Matsuda195} and functionalization. ^{Reference Lin, Han, Wang, Wang, Xiang, Qin, Zhang, Wang, Zhang, Wee and Chen216} Changes in carrier density can enhance the formation of charged excitons (trions) and manipulation of trions in both MoS₂ and MoSe₂ using electrostatic gating has been demonstrated. ^{Reference Mak, He, Lee, Lee, Hone, Heinz and Shan179,Reference Ross, Wu, Yu, Ghimire, Jones, Aivazian, Yan, Mandrus, Xiao, Yao and Xu180}

There are a myriad of ways in which changes to the carrier concentration in MX₂ materials influence the optical properties, and more specifically the PL. For example, in MoS₂, increased electron doping suppresses optical absorption near the exciton peaks resulting in diminished exciton PL intensity. Concurrent with this intensity reduction is the emergence of a trion peak. ^{Reference Mak, He, Lee, Lee, Hone, Heinz and Shan179} Conversely, MoS₂, which is typically n-type, can be transformed to heavily p-type via chemical absorption of oxygen at defect sites formed during annealing. This process converts negatively charged trions back to neutral excitons, resulting in an enhancement of the neutral exciton PL. ^{Reference Nan, Wang, Wang, Liang, Lu, Chen, He, Tan, Miao, Wang, Wang and Ni191}

Similarly, physisorbed molecules (e.g., O₂ and H₂O) were shown to influence the PL in MoS₂, MoSe₂, and WSe₂. ^{Reference Tongay, Zhou, Ataca, Liu, Kang, Matthews, You, Li, Grossman and Wu190} Annealing produced a large increase in the PL intensity for MoS₂ and MoSe₂ samples in O₂ and H₂O environments, while PL decreased for WSe₂ samples. These changes are reversible and result from carrier transfer between the gas and the 2D material. ^{Reference Tongay, Zhou, Ataca, Liu, Kang, Matthews, You, Li, Grossman and Wu190} Finally, large PL intensity was observed from induced defects (specifically MoS₂, MoSe₂, and WSe₂), ^{Reference Tongay, Zhou, Ataca, Liu, Kang, Matthews, You, Li, Grossman and Wu190} where point defects were created by either high-temperature annealing or by alpha-particle irradiation. ^{Reference Tongay, Suh, Ataca, Fan, Luce, Kang, Liu, Ko, Raghunathanan, Zhou, Ogletree, Li, Grossman and Wu217} The point defects consist of anion vacancies which in turn enable bound exciton formation. Gas molecules that interact with defect sites can enhance PL by draining electrons, shifting charged excitons to neutral excitons. The surface sensitivity we observe is likely responsible for many emission characteristics seen in all TMDs, since these materials are dominated by their surface properties.

In addition to modifying the carrier concentration via external perturbations, such as with the addition of adsorbates, it is also possible to optically prepare monolayers such that the emission is from either only the neutral exciton or only the charged exciton (trion) state. Reliably and reproducibly controlling TMD absorption and emission behavior is important for physical measurements (e.g., time-resolved measurements of the pure exciton/trion state) as well as for most applications of these materials.

The emission spectrum of WS₂ in ambient atmosphere is dominated by the neutral exciton low power while the trion is the dominant peak at high excitation power, and this process is completely reversible. This is not the case in vacuum. The PL spectra as a function of increasing excitation power for the sample in vacuum are shown in Fig. 27. Once the trion is stabilized by exciting with high power, even after reducing the excitation power to nanowatt levels, the trion emission remains dominant.

To reverse this state and regain the neutral exciton emission the sample must be exposed to air. If the sample is exposed to only nitrogen or helium, the neutral exciton will not be recovered.

To facilitate the transition from the neutral exciton to the trion, we focused a 532-nm laser on the sample to provide a 200-kW/cm² irradiance. We then raster scanned the laser thoroughly over the entire monolayer region of WS₂ (in vacuum). This caused a complete shift in the PL spectrum from the purely neutral exciton PL, as it is in ambient atmosphere, to a purely charged exciton PL. The resulting trion PL is independent of the probing PL excitation power, and further rastering produced no additional change demonstrating the saturation of this process for this optical power level. Thus, we are able to create an optically prepared system in WS₂ where either the exciton or trion exists. This effect can be achieved in seconds, which is much faster than hour-long annealing processes used in the studies described above. ^{Reference Tongay, Zhou, Ataca, Liu, Kang, Matthews, You, Li, Grossman and Wu190}

Luminescence changes appear to be quenched by surface interactions with the ambient environment, evidenced by the fact that the optically prepared state is reversible by exposing the sample to air. This enables deliberate investigation of specific surface properties for WS₂ and other 2D materials. For instance, optical preparation allows isolated examination of pure trion or exciton states, necessary for observing many physical processes, e.g., time-resolved exciton measurements. This also provides a tool to modify optical emission energy and could potentially modify the band structure in 2D materials enabling applications in optical modulation, tunable optical sources and detectors as well as all-optical sensors. The methodology described here lends itself to optical control of charged exciton states in WS₂ (and potentially all TMD and 2D materials) by merely exposing the material to light in controlled environments.

A. Summary

In this section we have shown that, in contrast to the linear gapless energy dispersion of graphene that we talked about in Sec. I, single layer TMDs are direct-gap semiconductors. TMDs have shown reasonable electronic mobility, high optical responsivity, environmental sensitivity, high valley polarization and long spin lifetimes, making this class of materials promising for optoelectronic components, chemical sensing, and valleytronic applications. We have shown that there are several promising routes to make large-area monolayer TMDs. We have used optical methods to probe the fundamental interactions in monolayer TMDs and compared them to results from the literature. Finally, we showed one specific example where a single layer of MoS₂ is used as a selective chemical vapor sensor.