Terahertz light-emitting graphene-channel transistor toward single-mode lasing

2.1 Design and fabrication details

The cross-sectional schematic of the device is shown in Figure 1A. First, epitaxial graphene was synthesized by the thermal decomposition of a SiC substrate; this method provides both easiness of fabricating the device and high crystallinity of the film [53]. C-face is specifically chosen to obtain non-Bernal stacking of multiple undoped graphene layers excluding the heavily doped buffer layer that is substantially made for Si-face decomposition. Lattice structure and crystal quality were first characterized by Raman spectroscopy at 300 K. The Raman shift spectrum obtained is shown in Figure 1B and C. No peak at the D band and sharp mono-peaks at the G and G′ bands with G′/G peak intensity ratio being 2.11 confirmed a high-quality, few-layer non-Bernal stacked graphene. Then the surface morphology of the synthesized epitaxial graphene was investigated by low-energy electron microscope (LEEM) at 300 K. Very large grains (>50 μm) consisting mainly of two-layer graphene were observed. Figure 1D shows that graphene is homogeneous in a rather large area; the lighter central area consists of two layers, whereas the darker area outside its edges contains three to six graphene layers [52]. This bilayer nature of the central grain area was also confirmed by the presence of the two dips in electron reflectance spectra between 0 and 8 eV, as shown in the inset in Figure 1D. Figure 1E shows an angle resolved photoelectron spectroscopy (ARPES) image, manifesting that the main band holds a linear dispersion and is divided into two groups and Fermi level lies at 0 eV, confirming the high-quality, non-Bernal stacked, double-layer graphene with no unintentional doping [52, 54]. By using this epitaxial graphene, GFET was fabricated by a standard photolithography process involving a gate stack of SiN dielectric layer, providing an excellent intrinsic field-effect mobility exceeding 100,000 cm²/Vs at 300 K at the maximal transconductance [55]. Throughout this gate stack process, the epitaxial graphene layer was encapsulated between the SiC substrate and the SiN gate dielectric layer, preventing the exposure of the graphene surface to the air and thus from the chemical reactions of unintentional doping even under varying the temperatures.

Figure 1:

The Raman spectrum (B, C), the LEEM image (D), and the ARPES image (E) confirms D-peak free, high crystal quality, double-layered large (>50 µm) grain, and non-Bernal stacked linear dispersion with not unintentional doping, respectively.

(A) Device cross-section, (B) Raman spectroscopy results of the epitaxial graphene on 4H-SiC substarte, (C) Lorentzian curve fitting of G′ peak confirming the presence of only one peak at 2700 cm⁻¹ with FWHM=28.52 cm⁻¹, (D) LEEM image and electron reflectance spectrum of epitaxial grapheme © Jpn Soc Appl Phys [52], and (E) ARPES image © Jpn Soc Appl Phys [52].

A pair of toothbrush-shaped gate electrodes was patterned to form a DFB cavity in which the active gain area and corresponding gain coefficient are spatially modulated [55] (see Figure 2A and B). The number of DFB periods N_DFB was designed to be N_DFB=16, resulting in active graphene channel width of ~200 μm, as shown in Figure 2B. Designed grating period Λ, the effective refractive index n_eff, the Bragg wavelength λ_dfb, and the principal mode f_P are 12 μm, 2.52, 60.5 μm, and 4.96 THz, respectively, as shown in Figure 2C. In this work, we carried experiments on two devices that are similar in design but slightly differ in the substrate thickness and DFB design parameters. The DFB modulation indices for device 1 (showing broadband emission) and device 2 (showing single mode emission) are L_int/L_dfb=20/15 and 20/18, respectively. Also, the carrier momentum relaxation time of these two devices, which were extracted from the slope of the ambipolar current-voltage curves, has different values: device 1 having longer values (ranging from 1.5 to 4 ps at temperatures 300~100 K) than those for device 2 (ranging from 0.8 to 2 ps at temperatures 300~100 K).

Figure 2:

The DFB modulation index is given by L_int/L_dfb.

(A) Schematic of DFB DG-GFET, (B) device SEM and photo images, (C) design parameters for the DFB structure: L_{sg, dg}=2 μm, L_g1,2=15 μm, L_int=20 μm, L_dfb=18 μm, W_dfb=6 μm, λ_dfb=12 μm, f_dfb=4.96 THz, and N_DFB=16.

2.2 Principles of operation

The operation principle called current injection THz lasing is as follows: when the dual-gate electrodes are applied with complementary biases (V_g=−V_g1=+V_g2), electrons or holes are injected underneath each gate electrode. The level of V_g determines the carrier injection level and corresponding Fermi level ε_F. With no applied source to drain bias V_d, the electrons and holes diffuse into the ungated i region and are recombined together to annihilate. Application of V_d, on the other hand, shifts the quasi-Fermi level of electrons and holes injected into the ungated i region to form a population inversion, and the recombination of those electrons and holes having an energy difference of several meV gives rise to spontaneous THz photon emission [42].

The real part of the dynamic conductivity Re σ(ω) in graphene under current-injection pumping is given by the sum of the intraband Drude-like component and the interband transition-related component as follows [42], [43]:

where e is the elementary charge, f(ε) is the Fermi-Dirac distribution function for electrons, ħ is the reduced Planck’s constant, k_B is the Boltzmann constant, T is the carrier temperature, τ is the momentum relaxation time, v_F is the Fermi velocity, κ is the permittivity of the gate dielectric layer, and d is the gate-dielectric layer thickness. Re σ^intra(ω) always takes positive values and has the dependence of τ1+ω2τ2 monotonically decreasing with increasing ω. The roll off frequency is given by ω_roll−off~1/τ⋅Re σ^inter(ω) causes its transition at around ħω~2ε_F and takes the upper plateau approaching e24ℏ at high frequencies ħω≫2ε_F and the lower plateau approaching 0 at low frequencies ħω≪2ε_F when the carrier populations are equilibrated. When the carrier populations are inverted by the carrier-injection pumping with a certain value of V_d, on the contrary, the minimal plateau of Re σ^inter(ω) may shift to the negative level (as low as –e24ℏ). As a consequence, if ħω_roll−off≪2ε_F, there exists a certain frequency range in which Re σ(ω) takes negative values. How widely and deeply the conductivity goes in negative at a given V_d depend directly on momentum relaxation time τ and carrier temperature T [42], [43]. A longer τ lowers the roll-off frequency and the conductivity values at higher frequencies (ωτ≫1). A lower T helps increase the population inversion to the higher levels and sharpens the transition on Re σ^inter(ω) at around ħω~2ε_F, enlarging the upper cuttoff frequency of the negative conductivity (gain) spectrum. To obtain a rather wide gain spectrum in the THz range, τ should be as long as possible (at least picoseconds) and T should be as low as possible.

Figure 3 plots the simulated real part of the dynamic conductivities of the DG-GFET at a constant carrier temperature of 300 K for different complementary gate biases (V_g=−V_g1=+V_g2) and drain-source biases V_d conditions according to Eqs. (1)–(4). The values of κ, d, τ, and T are assumed to be 4.7, 50 nm, 1 ps, and 300 K, respectively. When V_g=1.0 V, a weakly biased condition giving rise to doping with a Fermi level εF of 24.5 meV, as shown in Figure 3A, rather weak V_d beyond the threshold level of ~20 mV causes carrier population inversion and real net gain (negative dynamic conductivity) around 2 THz. Increasing the V_d value up to a certain level (V_d~30 mV in Figure 3A), which shifts the quasi-Fermi level equal to the magnitude of the original Fermi level at zero-V_d, can increase both the gain and its bandwidth. The lower and upper cutoff frequencies are situated between 0.7 and 7 THz. Further increase in V_d increases the channel electric field intensity resulting in carrier heating and weakening the gain. With increasing V_g, the carrier injection increases so that larger and wider gain bandwidths are obtained, as shown in Figure 3B and C. As abovementioned, a longer τ, meaning a higher carrier mobility, gives a higher THz gain with its peak at lower frequency, as shown in Figure 3D in comparison with Figure 3B. Hence, to realize a current injection THz lasing, realization of GFET with high carrier mobility is indispensable. In real operating conditions, as is described in detail in Ref. [42], carrier temperature T may change depending on the current-injection levels, modifying the gain spectral profiles. This effect will be discussed to interpret the experimental results in the next section.

Figure 3:

Real part of the conductivity spectra of a complementary dual-gate-biased DG-GFET at 300 K for different drain-source bias voltages.

The vertical axis is normalized to the fundamental conductivity (e²/4h) corresponding to 2.3% absorbance of monolayer graphene. The value of τ=1 ps for (A) V_g (=−V_g1=+V_g2)=1.0 V, (B) V_g=5.0 V, (C) V_g=10.0 V, and (D) τ=5 ps for V_g=5.0 V.

Another important criterion of the device operation is choosing the lasing frequency. The conductivity profile shows negative gain for a wide range of THz frequencies. To make single-mode lasing, one needs to implement a pertinent high-Q laser cavity structure in which the gain medium of the graphene under carrier injection pumping is accommodated. Such a laser cavity can be realized by using the gate electrodes as a DFB type waveguide structure. As shown in Figure 2B, the DFB structure periodically modulates the distance between the two gate electrodes along the length of the device. This results in periodic modulation of the gain coefficient given by the conductivity and the gain overlapping factor (the ratio of the areal integration of the THz photon electric field overlapped with the gain area to that of the entire area) [55]. At the Bragg wavelength (λ_B=2n_effλ_dfb), determined by the modulation period λ_dfb and the effective refractive index n_eff of the gain coefficient, the spontaneously emitted THz photons intensify each other, in each period, along the dual-gate direction. At that resonance frequency, single-mode oscillation can be obtained if the current-injection gain at only the maximal mode exceeds the laser oscillation threshold. Figure 4A shows the quality factors for in-plane waveguided modes of the DFB-DG-GFET structure for different quality graphene samples having τ of 0.1, 1.0, 3.0, 5.0, and 7.0 ps at a weak drain bias of 30 mV. For longer τ of 5~7 ps, the spectra exhibit high Q factors up to 150 over a broader frequency range, suggesting LED-like broadband spontaneous emission. The modal gain for this case is ~−30 cm⁻¹ (losses are greater than gain, limiting the possible operation to spontaneous emission). Varying the DFB design parameters, quality of graphene layer, and thickness of substrate can largely affect the confinement of THz photon electric fields on to the active gain area, which can hugely alter the gain profile. The other important parameter is the drain bias V_d that determines the level of carrier population inversion. Figure 4B shows the numerically calculated quality factors for the case of device 2, with different V_d levels of 30, 50, 70, 100, and 150 mV for a relatively shorter fixed τ value of 3.5 ps. When V_d is relatively high at around 70~100 mV, the spectra exhibit single peak at the designed fundamental DFB mode at ~5 THz, suggesting the single-mode lasing operation. The modal gain in this case is ~5 cm⁻¹. Further increase in V_d to 150 mV totally vanishes the peak profile, reflecting the carrier heating and making the net THz gain disappear. These results suggest that graphene quality and carrier temperature reflecting τ values, drain bias reflecting the level of population inversion, and DFB modulation index reflecting the Q factor determine the overall spectral profile of the THz photon emission.

Figure 4:

Simulated quality factors for in-plane waveguided modes (A) for different quality graphene samples having τ of 0.1, 1.0, 3.0, 5.0, and 7.0 ps at a fixed weak drain bias of 30 mV and (B) for different drain bias conditions at 30, 50, 70, 100, and 150 mV at a fixed τ of 3.5 ps.

Numerically calculated Q factors for the case when τ is ~3.5 ps at relatively high drain bias conditions exhibit slightly better THz photon field confinement.

3.1 Broadband THz light emission

The emission results from device 1 are summarized in Figure 6. A rather strong emission at 100 K, stronger than that at higher temperatures from 300 to 150 K (Figure 6A), was observed in 1–7.6-THz range when V_d is forward-biased to a certain level under symmetric electron-hole injection conditions leading to carrier population inversion (see inset of Figure 5B: V_g1=−2.28 V and V_g2=4.56 V at 100 K). The emission power from the device integrated over 1–7.6 THz is of the order of ~80 μW at most. The shape of emission spectra reflects superimposed effects of the graphene-original conductivity profile, which gives larger gain at lower frequencies [43] and the DFB cavity effects that have the fundamental mode peak at ~4.96 THz. Regarding the former, as the device is kept at low temperatures, scattering processes in graphene are suppressed, which means longer momentum relaxation time of the carriers present in the channel (see Figure 5D), thereby enabling the achievement of higher negative conductivity in the wide THz range and resultant broadband spontaneous THz emission (see Figure 3D). To obtain single-mode lasing, improvement on the Q factor of the DFB cavity with larger numbers of the DFB periods and/or deeper DFB modulation indices would be a possible solution (see Figure S2 in Supplemental Material). Further precise identification of the threshold temperature to the spontaneous THz emission is a next subject.

Figure 6:

The threshold temperature for amplified spontaneous broadband THz emission stays between 100 and 150 K. The device also exhibits double-threshold-like behavior with respect to V_d and injection current.

(A) Temperature dependence of the observed emission spectra in a fabricated DFB-DG-GFET (device 1) under carrier population inversion (V_g2=4.56 V, V_g1=−2.28 V). (B) Observed emission spectra of the device under population inversion for different values of drain voltage at 100 K. (C) Measured THz emission power (left axis) and dc power consumption (right axis) versus drain voltage V_d and drain injection current.

With increasing V_d, the emission power increases non-monotonically while preserving its spectral shape, as shown in Figure 6B. Apart from temperature-dependent spontaneous THz emission, the device also exhibited double-threshold-like behavior with respect to V_d and drain injection current, as shown in Figure 6C. The first threshold current to the spontaneous THz emission stays below 0.1 mA, whereas the second threshold current does around 0.9 mA. Such a double-threshold-like behavior may be due to the carrier overcooling effect [39], [42]. As theoretically predicted in Refs. [39] and [42], when carriers are excited, their energy is relaxed mainly via emission of optical phonons (including interband emission). The optical phonon decay rate, which depends on the overall thermal conductivity of the device, modifies the energy relaxation dynamics and carrier cooling decay. The existence of the scattering factors with a finite value of τ gives rise to the imaginary part of the conductivity, Im σ, which is known as the origin of the kinetic inductance of carriers. Such an inductive inertia of carriers may cause an overshoot on their energy transfer to the lattice phonons, resulting in carrier overcooling even below the lattice temperature in a limited time scale in a rather weak carrier-injection pumping regime [42]. Continuous injection pumping at a low V_d level may cause carrier overcooling steadily, which in turn enhances the carrier population inversion and contributes to promote the THz gain. When the carrier injection level rises further with increasing V_d and dc power consumption (see Figure 6C), carrier heating is dominated, which prevails over the cooling effect, resulting in net carrier heating and reduction of the THz gain. Further increase in V_d increases the level of population inversion, recovering the net THz gain. As a consequence, the carrier temperature changes non-monotonically along with the increase in V_d [42]. This is thought to be a possible interpretation for the cause of such non-monotonic double-threshold-like behavior.

Also, the conductivity profile highly depends on the applied biases, as shown in Figure 3. Increasing the gate voltage increases the number of injected charge carriers, which thereby increase the gain bandwidth and the lower cutoff for gain [43]. The drain bias is also very important as it determines the shifting of quasi-Fermi level; higher voltage causes more injection current and hence more gains. However, it also increases the band slope and causes carrier heating, which sacrifices the injection beyond the Fermi level [42], [44]. Hence, there is both a lower and upper limit on gain with respect to V_d, as also observed in our experimental results.

Another factor causing the broadband nature of emission from device 1 is the poor DFB cavity effects (substrate-thickness-dependent THz photon field distribution [57] could not meet the maximal available gain-overlapping condition), which do not work properly as single-mode lasing but give a tendency of being transcended from spontaneous broadband THz emission to stimulated emission with a central peak at the DFB fundamental mode of ~5 THz. The simulated quality factor for the DFB cavity for excellent quality GFET at low value of V_d shows gain over a wide frequency range (as seen in Figure 4A) supporting the possibility of observing broadband emission spectra from these devices. If the photon electric fields could be concentrated effectively on the graphene gain area, by optimizing the substrate thickness as well as additional thick high-K dielectric layer on top of the gate stack, one can expect single-mode lasing from these structures.

3.2 Towards single-mode lasing

We repeated the experiment on another sample device 2 (having a bit smaller DFB modulation index and shorter momentum relaxation time than those in device 1, as mentioned in 2.1) and observed no emission at 300 K, but lowering the temperature down to 100 K showed current-injection-dependent (V_g2=7.3 V, V_g1=−4.8 V) emission, as shown in Figure 7A. This single-mode-like emission also exhibited a non-monotonic threshold behavior, i.e. the emission at 5.2 THz grows with increasing V_d from 0 to 0.1 V but weakens with further increasing V_d until 0.2 V. The emission grows again after increasing V_d from 0.2 to 0.5 V, giving a single-mode emission with the highest power of ~0.1 μW. Spectral narrowing with increasing the carrier injection around the threshold was also observed, as shown in Figure 7B. The emission spectra at V_d=0.5 V can fit to the Lorentzian curve with a Q factor of 170 (a linewidth of 30.6 GHz), which fairly agrees with the simulated values ~210, as shown in Figure 4B. Compared to the broadband emission obtained from device 1, such a sharp single-mode emission is thought to be caused by the shorter momentum relaxation time of graphene carriers in device 2, which could allow the net THz gain only at around the DFB fundamental mode frequency ~5 THz, as is simulated in Figure 4B. From the good correspondence between the experimental result and the analytical results for the gain spectra, it could be inferred that the obtained radiation is due to laser oscillation.

Figure 7:

The single-mode like emission peak at ~5.2 THz with Q factor of 170 fairly agrees with the simulated results (at ~4.96 THz with Q ~210).

(A) Observed spectra for device 2 at 100 K and (B) the fitting curve for the peak at ~5.2 THz showing Q factor to be 170.

Although device 2 shows single-mode emission, the peak power of emission is 3.5 times lower than that for device 1, which implies that high-quality GFET when paired with carefully designed DFB cavity could result in efficient THz lasing at higher THz frequencies. For example, numerical simulations suggest that an increase of N_DFB from 16 to 24 and an increase of the DFB cavity modulation index L_int/L_dfb from 20/15 to 20/8 give rise to an increase of the quality factor of the DFB cavity by two orders of magnitude, respectively (see Supplement 2 in detail). Also, pertinent waveguide structures with a thick dielectric layer on top of the GFET and/or ridge-waveguiding with thick dual-gate metal pillars as well as surface plasmon-polaritonic waveguiding may improve the THz photon field spatial confinement and the gain-overlapping factor.

Further investigation is needed to confirm if the observed emission is truly single-mode lasing. Also, as the drain bias dependence and device structure dependence of radiation spectrum are yet to be fully understood, we need to elucidate them by future experiments along with improving the device processing and integration to achieve high-power THz emission at room temperature.