Ultrafast van der Waals diode using graphene quantum capacitance and Fermi-level depinning

Abstract

Graphene, with superior electrical tunabilities, has arisen as a multifunctional insertion layer in vertically stacked devices. Although the role of graphene inserted in metal-semiconductor junctions has been well investigated in quasi-static charge transport regime, the implication of graphene insertion at ultrahigh frequencies has rarely been considered. Here, we demonstrate the diode operation of vertical Pt/n-MoSe₂/graphene/Au assemblies at ~200-GHz cutoff frequency (f_C). The electric charge modulation by the inserted graphene becomes essentially frozen above a few GHz frequencies due to graphene quantum capacitance–induced delay, so that the Ohmic graphene/MoSe₂ junction may be transformed to a pinning-free Schottky junction. Our diodes exhibit much lower total capacitance than devices without graphene insertion, deriving an order of magnitude higher f_C, which clearly demonstrates the merit of graphene at high frequencies.

Graphene insertion paves the way to effortlessly achieve 6G sub-THz communication devices.

INTRODUCTION

Two-dimensional (2D) van der Waals (vdW) semiconductors have been extensively studied as active components for advanced electronic devices (1–6). The high charge carrier mobilities and associated physical properties along the in-plane direction have been the main subjects of 2D crystals. In this regard, one of the main challenges in 2D crystal-based electronic device applications has been the high contact resistance (R_C) (7, 8). Previous reports have shown various ways to mitigate this issue, which includes identification of new Ohmic contact materials (7, 9), development of new strategy to deposit metals on 2D semiconductor (10, 11), and the adaptation of a vertical device geometry with larger contact area (12). Owing to the recent advancement of R_C engineering, a few high-frequency devices based on 2D semiconductors have been recently reported (11–15). Still, high cutoff frequency over 100 GHz seems not possible to achieve from R_C improvement alone.

Graphene, the most extensively studied 2D crystal with large electrical tunability and chemical stability (16), can be inserted as a multifunctional layer in various vdW heterostructures (17–19). For example, inserted graphene has been previously used as a layer for barristor device (17). Moreover, the in-plane charge transport behavior of graphene itself has also been studied well at DC and high frequencies (20–23). However, vertical charge transport across inserted graphene and its implication for device performance at high frequencies have been largely neglected. In particular, considering the capacitance is one of the key parameters for high-frequency devices (11), the role of graphene insertion regarding device capacitance should be properly addressed to understand the fundamental limitation on the high-frequency performance of vdW 2D devices.

Here, we demonstrate the operation of vertical Schottky diodes with high cutoff frequencies (f_C) of ~200 GHz at maximum via graphene insertion, which covers millimeter wave (mm-Wave) range for signal reception and energy harvesting (24, 25). We fabricate Pt/n-MoSe₂ vertical Schottky diodes with various Ohmic contacts and elucidate the role of graphene insertion regarding the modification of device capacitance at high frequency. We find that the electrical charge modulation by graphene is essentially frozen above a few gigahertz frequencies due to the delay associated with the quantum capacitance of graphene (C_GR), while charge modulation needs a minimum time longer than the delay. Ohmic Au/graphene/n-MoSe₂ junction transforms to an ideal pinning-free Schottky junction above a few gigahertz frequencies, which leads to lower total capacitance and order-of-magnitude higher cutoff frequencies than devices without graphene insertion. In addition, 28-GHz mixer applications are demonstrated by using two graphene-inserted Schottky diodes, which clearly displays the merit of graphene-insertion at high frequencies. Our work elucidates the role of graphene insertion at high frequencies and paves the way for improving the high-frequency performance of vertically stacked vdW devices.

RESULTS

Vertical Schottky diodes incorporating layered 2D semiconductor with various kinds of electrodes were fabricated. Figure 1A displays a 3D schematic of the vertical Schottky diode with Pt/n-MoSe₂/graphene/Au. Top Pt electrode with relatively thick (~160 nm) 2H-MoSe₂ flake serves as almost an ideal metal-semiconductor Schottky junction. Raman spectroscopy and atomic force microscopy (AFM) results for MoSe₂ flakes are shown in figs. S1A and S2, respectively. Au (with and without graphene insertion) was chosen as Ohmic contact as the other side (bottom-contact) of contact, so that Pt/n-MoSe₂/graphene/Au may form a vertical diode. Similar Ohmic contacts were observed with different graphene thickness for insertion, from monolayer (1L) to thick graphite or multilayer graphene (ML). Fabrication details are described in Methods. We also note that Ti contact (of Au/Ti bilayer form) can support better Ohmic behavior than Au, but here, Au as a bottom electrode was mainly discussed because of the suitable comparison between control groups and its superior air stability to Ti. Figure S3 shows the effects of source/drain top contact metals (Pt, Ti, and Au) on MoSe₂ channel field effect transistor and also displays the effects of top and bottom Au on a vertical MoSe₂ diode, where bottom Au contact clearly shows quiet an Ohmic behavior.

Fig. 1. Structure and DC properties of vertical Schottky diodes.

(A) Schematic of the Pt/n-MoSe₂/graphene/Au vertical Schottky diode. (B) OM image and 2D schematic (inset) of Pt/n-MoSe₂/graphene/Au diode. (C) OM image and 2D schematic (inset) of Pt/n-MoSe₂/Au diode. (D) TEM images of Au/monolayer graphene/MoSe₂, Au/4 ~ five-layer graphene/n-MoSe₂, Au/graphite/n-MoSe₂, and Pt/n-MoSe₂ interfaces (from left to right). Pt/n-MoSe₂ image is obtained by scanning TEM mode. (E and F) DC I-V characteristics of Pt/n-MoSe₂/graphene/Au and Pt/n-MoSe₂/Au diodes. (G) Current responsivity and nonlinearity (inset) of Pt/n-MoSe₂/graphene/Au diode. (H) 1/C²-V curve with calculated carrier concentration and built-in potential.

Schottky diodes with graphene insertion of various thickness (and without graphene insertion) were fabricated in a coplanar waveguide (CPW) device pattern for radiofrequency (RF) probing. Figure 1B (with graphene) and Fig. 1C (without graphene) show optical microscopy (OM) images of the diodes in a CPW pattern. The yellow dashed line in Fig. 1B traces the patterned chemical vapor deposited (CVD) graphene on the bottom Au electrode, and the vertical contact area is 10 × 10 μm² as patterned (red dashed line). Figure 1D shows cross-sectional high-resolution transmission electron microscopy (HRTEM) images of the MoSe₂/graphene/Au Ohmic junction with various graphene thickness, including the image of Pt/MoSe₂ junction. HRTEM images confirm the thickness of graphene insertion and show the clean interfaces without noticeable process-related residues at the junction.

The DC current-voltage (I-V) characteristics of the vertical diodes with (and without) graphene insertion are shown in Fig. 1E (and Fig. 1F). The ideality factors from each semilog-scale I-V plot were estimated to be 1.15 (n-MoSe₂/graphene/Au) and 1.20 (n-MoSe₂/Au). (The extraction and fitting of ideality factors are introduced in Supplementary Text 1). Low-temperature I-V characteristics were also measured in the range of 80 to 300 K, as depicted in fig. S4, where a Schottky barrier of ~0.17 eV at the Pt-MoSe₂ junction was consistently measured. The Schottky barrier height (qΦ_B,Pt) is quite small, and we attribute it to the existence of Fermi pinning effects between the Pt contact and n-MoSe₂ (26) as the origin of such a small qΦ_B.

The responsivity and the nonlinearity [i.e., the ratio of the rectified DC current and the RF power delivered to nonlinear devices and a measure of the deviation from a linear device, respectively (27)] are the important figures of merits (FOMs) in RF rectifier applications as estimated from the I-V characteristics. Figure 1G displays the responsivity and the nonlinearity (inset) plots of the graphene/Au-contact device, where their peak values are calculated as 22.7 A/W and 5.29, respectively. These numbers are regarded as high compared to those of reported Schottky devices (11, 28). These values were also extracted for Au-contact device, as plotted in fig. S5. In general, a diode rectifier should satisfy the conditions of certain responsivity (> 7 A/W) and nonlinearity (> 3) for RF applications (27), which means that our Schottky devices have strong potential for RF rectifiers. For more information on the Schottky junction characteristics of the Pt/n-MoSe₂/Au diode, a Mott-Schottky plot was (29) obtained from the capacitance-voltage (C-V) measurement. As shown in the 1/C²-V plot of Fig. 1H, we extracted the built-in potential (ϕ_i,Pt = 0.146 V) at the Pt/n-MoSe₂ junction and carrier concentration of MoSe₂ (n = 7.13 × 10¹⁶ cm⁻³).

With the promising DC diode performance, high-frequency performance including f_C measurements were conducted using a network analyzer. Figure 2 (A and B, respectively) shows the circuit diagram and CPW device scheme with the ground–signal–ground (G-S-G) configuration (30) for the one-port S-parameter measurement. A small-signal equivalent circuit of the Schottky diode is included as the device under test (red box) in the diagram of Fig. 2A. One-port scattering parameters (S₁₁) for each diode were achieved from 50 MHz to 40 GHz using a network analyzer and subsidiary circuitry. S₁₁ in the one-port network equals the voltage reflection coefficient, Γ = (Z_L – Z₀)/(Z_L + Z₀) (30), where Z_L and Z₀ are the impedances of each diode and the transmission line (= 50 ohm in this case), respectively. Thus, the impedance of each device can be extracted from its S₁₁ parameter chart, the Smith chart in Fig. 2C. Figure 2D shows the series resistance (real part, solid) and capacitive reactance (imaginary part, dot) in log-scale impedance plots, as extracted.

Fig. 2. S-parameter and RF characteristics of vertical Schottky diodes.

(A) Circuit diagram of the test setup for S-parameter measurement including the small-signal equivalent circuit of the Schottky diode. C_p indicates the parasitic capacitance. (B) 3D schematic of the G-S-G patterned device. (C) The Smith chart on S₁₁ parameters of Pt/n-MoSe₂/1L graphene/Au (red), Pt/n-MoSe₂/3L graphene/Au (green), and Pt/n-MoSe₂/Au (blue) diodes. (D) Impedance-frequency plot of of Pt/n-MoSe₂/1L graphene/Au (red), Pt/n-MoSe₂/3L graphene/Au (green), and Pt/n-MoSe₂/Au (blue) diodes with extracted cutoff frequencies (inset). (E) Impedance-frequency plot of Pt/60-nm n-MoSe₂/1L graphene/Au diode as compared with Pt/160-nm n-MoSe₂/1L graphene/Au diode. Inset shows the cutoff frequencies extracted from the devices with 60-, 128-, 160-nm-thick MoSe₂. The bars in the inset graphs for 1L Gr.-inserted device with 160-nm MoSe₂ indicates all three measured f_C (110, 145, and 220 GHz).

The impedances for three Schottky diodes of Pt/MoSe₂/1L graphene/Au (red), Pt/MoSe₂/3L graphene/Au (green), and Pt/MoSe₂/Au (blue) are displayed separately in Fig. 2D. The cutoff frequency of devices can be determined as the intersection of resistance and capacitive reactance in the impedance plot (31) and 1L graphene–inserted device shows an order of magnitude higher f_C of 220 GHz than those of Au-contact (25.9 GHz) and 3L graphene–inserted (33.5 GHz) device. This ultrahigh f_c can be attributed to two factors: low series resistance R_S and low junction capacitance C_j. According to the small-signal equivalent circuit, the junction resistance (R_j) and C_j originate from the depletion region at the Schottky junction, whereas R_S is composed of the contact resistance (R_C) and undepleted region resistance (R_I). The total impedance, Z_L, can be expressed as

$$Z_{\mathrm{L}}=[R_s+\frac{R_{\mathrm{j}}}{1+{(2\mathrm{\pi }f{R}_{\mathrm{j}}{C}_{\mathrm{j}})}^2}]-j\left[\frac{2\mathrm{\pi }f{R}_j^2{C}_{\mathrm{j}}}{1+{(2\mathrm{\pi }f{R}_{\mathrm{j}}{C}_{\mathrm{j}})}^2}\right]$$ (1)

and Z_L ≅ R_s − j∣X_c∣ = R_s − j∣1/2πfC_j∣ at f ≫ 1/2πR_jC_j. According to simple mathematics to justify the approximation in Supplementary Text 2, |Im(Z_L)| maximum (in the imaginary part of Z_L) should appear at the frequency of $\frac{1}{2\mathrm{\pi }{R}_j{C}_j}$, which is experimentally found to be ~100 MHz or less as shown in fig. S6. Hence, the criteria f ≫ 1/2πR_jC_jfor our approximation could be well satisfied at gigahertz frequencies; the real and imaginary parts of impedance at the frequencies higher than a few gigahertz can be interpreted as the series resistance (R_S) and the capacitive reactance (X_C), respectively. In this respect, the capacitance of 1L graphene–inserted device must be smaller than that of Au- or 3L graphene–inserted device at a same high frequency (Fig. 2D). Furthermore, at their cutoff frequencies, 1L graphene–inserted device shows quite lower R_S (~22 ohm) than those (40 to 55 ohm) of Au contact and 3L graphene–inserted devices as indicated by dashed arrows.

The capacitances of various devices with the same 160-nm-thick MoSe₂ are compared. According to the Smith chart in Fig. 2C, the three clockwise circles end to meet different capacitive reactance (−2.0j versus ~ −0.6j) at the same 40 GHz. This clearly indicates that the capacitance of 1L graphene–inserted device must be about three times lower than those of Au- and 3L graphene–inserted diodes, although MoSe₂ thickness in each device is almost the same, to be ~160 nm. The impedance feature of 3L graphene–inserted device seems similar to that of Au-contact device, resulting in a f_C of 33.5 GHz. This behavior from 3L graphene appears quite similar to those of another device with a few nanometer-thin graphite (f_C ~ 20 GHz for 4L and 10L graphene, fig. S7). We have also fabricated a few more 1L graphene–inserted devices with ~160-nm-thick MoSe₂, which consistently exhibit high f_C of 110 to 220 GHz (see fig. S8). The inset graph of Fig. 2D summarizes f_C results from the diodes with 1L ~ ML graphene and from Au-contact diode.

We also studied the effect of MoSe₂ thickness in our vertical devices. We found that, even with 1L graphene insertion, the f_C decreases below 100 GHz if MoSe₂ thickness is not thick enough. According to Fig. 2E, f_C of the device with 60-nm-thin MoSe₂ is limited to 37.3 GHz, resulting from smaller R_S and X_C than those of our main device with 160-nm-thick MoSe₂. R_S comprises undepleted thickness-induced R_I and R_C (constant), and thinner MoSe₂ thus brings relatively smaller R_S (due to smaller R_I) in favor of high f_C. However, thinner MoSe₂ also causes smaller X_C with higher C_j, which would be critically opposed to increasing f_C. Likewise, f_C of the device with 128-nm-thin MoSe₂ was ~67 GHz (fig. S9), which is higher than 37.3 GHz but lower than 110 GHz (the smallest f_C of L graphene–inserted diode with 160-nm-thick MoSe₂). The inset graph of Fig. 2E summarizes measured f_C results according to MoSe₂ thickness. Regarding an optimum MoSe₂ thickness for maximum f_C (from smallest R_S and C_j), further study would be necessary on the basis of any precise information on the carrier concentration in working MoSe₂ and its dielectric constant.

Apart from above device performances, another important feature of the vertical diodes to note is their ageing stability and reproducibility; even if they are kept in ambient air (45% relative humidity at room temperature) for more than a week, they show no difference in terms of the RF impedance feature and the f_C behavior (see figs. S8, S10, and S11 for more details including reproducibility). We attribute such a stability to encapsulation effects probably achieved from the top Pt electrode covering the thick MoSe₂. Last, Ti-contact device with a different architecture (Pt/MoSe₂/Ti) was also fabricated and its f_C (24.4 GHz) appears very comparable to that of Au-contact device (25.9 GHz). According to fig. S12, those two devices with different Ohmic contact seem to have almost identical impedance characteristics in high-frequency regime, where the Pt/MoSe₂ junction capacitance must be the control factor for impedance.

DISCUSSION

To elucidate the role of graphene (Gr) insertion in vdW Schottky diode, the junction capacitance values of each diode were extracted from the imaginary part of impedances as shown in Fig. 3A. Although the three diodes with 160-nm-thick MoSe₂ initially show almost the same capacitance (C_j ~ 110 nF/cm²), each becomes to display different behavior as frequency increases. Schottky diode without graphene insertion seems to show a constant capacitance regardless of frequency. Because the diode capacitance mostly originates from the depletion thickness in MoSe₂, the observed constant capacitance could be attributed to the fixed depletion thickness at Pt/n-MoSe₂ Schottky junction. On the other hand, the capacitance of 1L graphene–inserted diode largely decreases with the input frequency reaching to ~43 nF/cm² at 20-GHz input frequency, and it is almost three times smaller value than that of Au-contact case. The capacitance of ML (or 3L) graphene–inserted diode appears to moderately decrease to ~88 nF/cm². The observed frequency-dependent capacitance from graphene-inserted devices strongly suggests that the charge depletion at the MoSe₂/Gr junction arises under high-frequency operation; reduction in total capacitance takes place because of series capacitance effects. According to the detailed calculation in fig. S13 and Supplementary Text 3, the total capacitance [C_j,tot, or C_j,high = C_j,PtC_j,Au-Gr/(C_j,Pt + C_j,Au-Gr)] at high frequencies (> 40 GHz) becomes ~4 times smaller than that (C_j,low = C_j,Pt) of the Pt/n-MoSe₂/Au diode if the MoSe₂ flake is sufficiently thick. C_j,Pt and C_j,Au-Gr indicate the junction capacitances due to depleted MoSe₂ near Pt and Au/Gr, respectively. These explanations are consistent with the result of Figs. 3A and 2D. Along with the decrease in C_j,tot, R_S (= R_C + R_I) simultaneously decreases, because R_I decreases with the increase of depletion thickness at high frequencies. R_S thus becomes small with the frequency increase, resulting in a markedly high f_C as combined with the effects of small C_j,tot.

Fig. 3. Capacitance lowering at high-frequency regime and its explanation.

(A) Capacitance-frequency plot that is extracted from the imaginary part of the impedance of each diode in Fig. 2. (B) Band diagram of Pt/n-MoSe₂/1L-graphene/Au and Pt/n-MoSe₂/ML-graphene/Au diode at DC and high-frequency AC. Trapping-induced modulation is frozen at high AC frequencies. (C) Plot of MoSe₂ depletion thickness (x_d,Au-Gr) as a function of frequency (D) Plots of built-in potential ϕ_i,Au−Gr between MoSe₂ and graphene as a function of frequency. Max. ϕ_i,Au−Gr between MoSe₂ and graphene appears to be ~1.3 V which well matches with the theoretical work function difference (qW_Au-qW_MoSe2 ≃ 1.3 eV) between Au and n-MoSe₂. It means that graphene’s Fermi level decreases down to E_O,Gr at high frequency although initial maximum of E_F,Gr-E_O,Gr was 1.3 eV, the same as work function difference between Au and MoSe₂. (E) Accumulated total electron charge density, N versus frequency plot, which unintentionally follows exponential form. Inset logarithmic plot results in f_O of ~4.18 GHz, to be a characteristic frequency.

The rise of depletion thickness in MoSe₂ near Gr could be attributed to the graphene’s failure in its charge modulation at high frequencies. According to previous studies on DC operation (32), 1L graphene between two materials acts as a tunneling layer that is nearly transparent to the vertically transported electrons, while such vertical tunneling originates from momentum mismatch. Moreover, graphene can modulate the potential difference (ΔV) between the two materials due to the graphene-captured charges (Q_e) and quantum capacitance (C_GR); ΔV = Q_e/C_GR. Under DC voltage sweep, the Schottky barrier at the graphene/MoSe₂ junction is effectively nullified, so that the Fermi level of each material may be aligned maintaining an equilibrium Ohmic junction at a certain temperature (Fig. 3B, upper band diagram). However, at much high frequencies, the electrical behavior of the Au/1L graphene/MoSe₂ junction seems not Ohmic anymore but rather ideal Schottky, as shown in the band diagrams (Fig. 3B, middle). It is probably because tunneling electrons may not be captured by the graphene layer in such a short duration. As a result, charge modulation is prevented and 1L graphene only plays as a tunneling layer. It must be also considered that C_GR-induced delay (R_SC_GR) exists in the AC behavior. Charge trapping in graphene might need a minimum time (scattering-induced mean free time, τ) which would be longer than R_SC_GR delay. At such a high frequency (f ≫ 1/ R_SC_GR), charge modulation may largely be frozen.

Following analysis may support aforementioned statements. The high frequency–induced MoSe₂ depletion thickness (x_d,Au-Gr) of Fig. 3B (middle) at 1L graphene/MoSe₂ junction can be extracted out by considering blue and red plots for capacitance in Fig. 3A which reflect upper and middle band diagrams of Fig. 3B, respectively. Calculation details found in fig. S14, which include a formula (1/C_j,Au-Gr = x_d,Au-Gr/ɛ_MoSe2, ɛ_MoSe2 is dielectric permittivity). The calculation results in frequency-dependent plot of x_d,Au-Gr as seen in Fig. 3C, where at 40 GHz the thickness saturates to ~137 nm. Since we know ɛ_MoSe2 (~ 8.5ɛ_o) and N_d (7.13 × 10¹⁶ cm⁻³) in the inset equation (x_d,Au-Gr = $\sqrt{\frac{2{\epsilon }_{MoSe2}{\mathrm{\varphi }}_{i,Au-Gr}}{q{N}_d}}$), the built-in potential ϕ_i,Au−Gr between MoSe₂ and graphene can be plotted as a function of frequency in Fig. 3D, where 1.3 V appears to be a maximum. A voltage of 1.3 V well matches with the theoretical work function difference (qW_Au − qW_MoSe2 = ~1.3 eV) (29, 33) between Au and n-MoSe₂. This result indicates that pinning-free Schottky barrier certainly arises at the high frequency due to the failure of graphene’s charge modulation and the maximum attains to 1.3 eV. Likewise, the frequency-dependent Schottky barrier comes from frequency-limited charge trapping or modulation limit in inserted graphene layer, which means that graphene’s Fermi level (E_F,Gr) decreases as a function of frequency as described with E_F,Gr- E_O,Gr where E_O,Gr is constant as a minimum Fermi level. Maximum of E_F,Gr- E_O,Gr becomes 1.3 eV, the same as work function difference between Au and MoSe₂. Now, frequency-dependent E_F,Gr- E_O,Gr is plotted along in Fig. 3D, and in Fig. 3E it is converted to accumulated (total) electron charge density, N which can be obtained by integrating the density of states (dN/dE) with energy via a relationship (dN/dE ∝ √N). Theoretical analysis and calculation details are in Supplementary Text 4. According to Fig. 3E, N is accidentally well fitted to an exponential form as frequency varies, and the slope of inset logarithmic plot shows a characteristic frequency f_O, to be ~4.18 GHz which is for 36% charge accumulation in the Dirac cone. τ (= 1/f_O) becomes ~0.24 ns. On the basis of τ (= R_SC_GR) value, approximate C_GR can be worked out to be ~1.14 μF/cm² (R_S = ~210 ohm at 4.18 GHz, and diode area = ~100 μm²), which is a quite comparable to number values of undoped graphene’s quantum capacitance (34, 35).

For ML graphene–inserted devices, the RC delay associated with the quantum capacitance of graphene is still effective and the depletion thickness should have the frequency dependence. However, graphite will replace the position of Au as shown in another band diagram of Fig. 3B (bottom). Graphite has much smaller work function than Au, which results in a limited depletion thickness of MoSe₂ and moderate decrease of C_j,tot. Consequently, ML (over 3L) graphene–inserted diodes behave similar to Au-contact device at high frequencies. More analysis details including the plots analogous to Fig. 3 (C to E) are found in fig. S15.

We designed another vertical vdW devices to more directly confirm the graphene’s role under high-frequency operations. Here, we fabricated devices with Ti/n-MoSe₂/1L graphene/Au junction as schematically presented in Fig. 4A, which should exhibit Ohmic characteristics under DC operation. We found that the device indeed exhibits quasi-Ohmic characteristics as shown in Fig. 4B, which confirms that both junctions at graphene/MoSe₂ and Ti/MoSe₂ interface have ignorable barrier under DC condition. Under RF conditions, however, the device exhibits totally different results as seen in the equivalent circuit of Fig. 4C. One-port S-parameter measurement was conducted with a similar setup to Fig. 2A, but this time, graphene/Au electrode is forwardly biased with DC voltage ranging from 0 to 1 V as depicted in Fig. 4 (A and C). As a result, the Smith chart of Fig. 4D shows diode-like behavior with circular contour in lower plane, which implies the existence of junction capacitance under RF input signal. In addition, the circular contour varies with applied DC voltage. According to more detailed analysis in Fig. 4E, R_j values (real part in impedance) decrease with the forward bias voltage at low 50 MHz while total capacitance increases with the voltage at high 20 GHz (because depletion thickness decreases as described in Fig. 4G). On the basis of the Eq. 1 and the circuit of Fig. 4C, it is expected that the impedance Z under low-frequency AC input approaches to junction resistance, R_j (≅ R_S + R_j) because R_j is much larger than R_S in this low-frequency regime. As the frequency increases, Z approaches to R_S – j/2πfC_j by ignoring R_j. At gigahertz high frequencies, imaginary part (−j/2πfC_j) becomes much more important than R_S, so that C_j is extracted. Likewise, Fig. 4 (D and E) directly indicate a diode-like behavior of our new device under forward DC bias conditions. The underlying principle of this behavior is presented graphically in Fig. 4G where the depletion thickness is modulated by forward DC bias. The impedance plots in Fig. 4F for Ti/n-MoSe₂/1 L graphene show f_C of 33 GHz resembling the behavior of Pt/n-MoSe₂/1 L graphene diode.

Fig. 4. Experiment for clarifying the formation of barrier at Au/1L graphene/n-MoSe₂ interface.

(A) 2D schematic and (B) DC I-V characteristic on the cross-section of the device which has Ohmic contacts at each terminal, one of which is Au/1L graphene contact. (C) Circuit diagram of the measurement including the small-signal equivalent circuit of the device. (D) S₁₁ parameter of the device on the Smith chart in which characteristic semicircle contour of diode can be seen. (E) Extracted resistance under 50 MHz and junction capacitance under 20 GHz AC input signal with different DC forward bias from 0 to 1 V. (F) Impedance-frequency plot under zero DC bias. (G) Band diagram which shows the change of Schottky barrier and junction capacitance at Au/1L graphene/n-MoSe₂ junction under forward bias.

As our last work, we have fabricated a high-frequency mixer using two Pt/n-MoSe₂/graphene/Au diodes, to more demonstrate the validity of our Schottky diode with inserted graphene. Figure S16 (A to F) displays 28-GHz mixer applications using two graphene-inserted Schottky diodes, which clearly displays the merit of graphene-insertion at high frequencies.

In summary, we have elucidated the implication of graphene insertion in vdW layered vertical devices at ultrahigh frequencies. The Pt/n-MoSe₂ Schottky diode with graphene/Au contact shows an extremely high f_C of approximately 220 GHz in maximum, which would be applied to high-frequency mixer and mm-Wave energy harvesting. The mechanism of such a high f_C is attributed to the fact that quantum capacitance–driven charge modulation by the inserted graphene becomes essentially frozen above gigahertz frequencies, so that the Ohmic graphene/MoSe₂ junction may be transformed to a pinning-free Schottky junction. By integrating the diodes within a peripheral circuit, we successfully demonstrate an RF mixer for 5G communication. Although high cutoff frequencies over ~100 GHz have been reported for devices with single-crystalline Si (28, 36, 37) and GaAs (38, 39), achieving 5G-compatible frequencies (> 28 GHz) using thin film–based devices is challenging (40, 41) (see fig. S17 for comparison.) We believe that our vertical device geometry is essentially compatible with the conventional fabrication process and has great potential in high-frequency applications. Equipped with month-long ambient stability and fabrication ease, we conclude that our vertical diode with inserted graphene enlightens a new possibility toward future RF devices with 2D layered semiconductors.

MATERIALS AND METHODS

Device fabrication

For all diodes in this study, a glass substrate (Eagle XG) was sequentially cleaned with acetone, ethanol, and deionized water using an ultrasonicator. Then, 10-nm Al₂O₃ was deposited using an atomic layer deposition (ALD) system as a buffer layer. For the Pt/n-MoSe₂/1 L graphene/Au diode, a 5 nm Ti/10 nm Au bottom electrode was patterned by conventional photolithography and deposited using a DC magnetron sputter. For the wet-transfer, polystyrene (PS) was initially spin-coated onto CVD monolayer graphene on the 285 nm SiO₂/p⁺-Si substrate (Graphene Supermarket). Then, the monolayer graphene film was separated from the SiO₂/p⁺-Si substrate using deionized water to be wet-transferred onto the bottom electrode. After wet-transfer, PS was removed by toluene. A 2H-MoSe₂ flake (HQ Graphene) was then mechanically exfoliated and dry-transferred onto the bottom electrode. As a last step, a 150-nm Pt top electrode was patterned by the same method used for the bottom electrode. For the case of the Pt/n-MoSe₂/Au diode, all the processes were same but the wet transfer process of graphene sheet that was omitted.

Last, for the mixer application, two Pt/n-MoSe₂/graphene/Au diodes with similar characteristics were selected, and the glass substrate was diced except for the area containing the device. The device was then connected by silver paste to a mixer circuit board. All Schottky diodes were fabricated according to the guidelines for the CPW pattern (I-V, C-V, S₁₁ parameter, and power spectrum measurements) or mixer pattern.

Material characterization

Noncontact mode AFM (NX-10, Park Systems) was used to characterize the surface topography as well as the thickness of 2H-MoSe₂ flakes. Raman spectroscopy was conducted by using a 532-nm laser source with a Raman spectrometer (LabRam Aramis, and Horriba). TEM samples were prepared using a focused ion beam (Crossbeam 540, ZEISS). TEM and STEM images were acquired with double Cs-aberration corrected JEOL ARM-200F, which operated at 200 kV.

DC electrical measurements

DC current-voltage (I-V) characteristic measurements were carried out by using a semiconductor parameter analyzer (HP4155C, Agilent Technologies). Low-temperature measurements were performed in the dark under vacuum (~1.5 mtorr). DC capacitance-voltage (C-V) measurements were conducted by using a precision LCR meter (HP4284A, Agilent Technologies) under a small signal frequency of 1 MHz.

Nonlinearity and responsivity FOM from DC I-V characteristic

The nonlinearity FOM of a diode is the ratio of the differential conductance to the conductance, i.e.

$$Nonlinearity=\frac{dI(V)}{dV}/\frac{I(V)}{V}$$ (2)

and is a measure of the deviation from a linear resistor (27).

On the other hand, the responsivity FOM is defined as the ratio of the rectified DC current and the RF input power that is delivered to device (11) i.e.

$$Responsivity=\frac{I_{DC}}{P_{in}}$$ (3)

For a nonlinear device, current as a function of voltage can be expanded in a Taylor series at V = V₀

$$I(V)=I(V_0)+{\frac{dI}{dV}|}_{V=V_0}(V-V_0)+\frac{1}{2}{\frac{d^{2}I}{d{V}^2}|}_{V=V_0}{(V-V_0)}^2+\frac{1}{6}{\frac{d^{3}I}{d{V}^3}|}_{V=V_0}{(V-V_0)}^3+\cdots$$ (4)

If an external voltage V = V₀ + vcosωt is applied across the device, the current can be expressed as

$$\begin{array}{c}{\displaystyle I(t)=I(V_0)+{\frac{dI}{dV}|}_{V=V_0}v\cos \mathrm{\omega }t}\\ {\displaystyle +\frac{1}{2}{\frac{d^{2}I}{d{V}^2}|}_{V=V_0}{v}^2{\cos }^2\mathrm{\omega }t+\frac{1}{6}{\frac{d^{3}I}{d{V}^3}|}_{V=V_0}{v}^3{\cos }^3\mathrm{\omega }t+\cdots }\\ {\displaystyle =[I(V_0)+\frac{v^2}{4}{\frac{d^{2}I}{d{V}^2}|}_{V=V_0}+\cdots ]+[v{\frac{dI}{dV}|}_{V=V_0}+{\frac{v^3}{8}\frac{d^{3}I}{d{V}^3}|}_{V=V_0}+\cdots ]}\\ {\displaystyle \cos \mathrm{\omega }t+[{\frac{v^2}{4}\frac{d^{2}I}{d{V}^2}|}_{V=V_0}+\frac{v^4}{48}{\frac{d^{4}I}{d{V}^4}|}_{V=V_0}+\cdots ]\cos 2\mathrm{\omega }t+\cdots }\end{array}$$ (5)

Therefore, if the amplitude of applied AC input signal v is small enough, the rectified current due to AC signal is approximately

$$\frac{v^2}{4}{\frac{d^{2}I}{d{V}^2}|}_{V=V_0}$$ (6)

And for small signal AC input v(t) = vcosωt, time-averaged power P_in is calculated as

$$\begin{array}{c}{P}_{in}=\frac{1}{T}{\displaystyle {\int }_0^T}v(t)I(t)dt\\ {\displaystyle \approx \frac{1}{T}{\displaystyle {\int }_0^T}{v}^2{\frac{dI}{dV}|}_{V=V_0}{\cos }^2\mathrm{\omega }tdt=}\\ {\displaystyle \frac{v^2}{2}{\frac{dI}{dV}|}_{V=V_0}}\end{array}$$ (7)

Then, the responsivity FOM can be expressed as

$$Responsivity=\frac{{\displaystyle {\frac{d^{2}I}{d{V}^2}|}_{V=V_0}}}{2{\displaystyle {\frac{dI}{dV}|}_{V=V_0}}}$$ (8)

The nonlinearities the responsivities in fig. S5 and Fig. 1 are calculated from I-V characteristics in Fig. 1 (E and F).

S-parameter and f_C measurement

A 1-port network was constructed by using a reference G-S-G CPW pattern with a characteristic impedance of 50 ohm. Scattering parameter S₁₁ measurements were performed by using a vector network analyzer (MS4647B, Anritsu) after calibration. The RF input signal was set to sweep from 50 MHz to 40 GHz.

Power spectrum and mixer measurement

For output power spectrum measurements using two terminals, an RF signal generator (MG3695A, Anritsu) was connected to the input terminal of devices. A spectrum analyzer (MS2850A-046, Anritsu) was then connected to the output terminal of the devices so that the output signal could be analyzed. For mixer demonstration, two RF signal generators were used along with two Schottky diodes, where the generators were connected to the RF and LO terminals.

Supplementary Materials

This PDF file includes:

Supplementary Texts 1 to 4

Figs. S1 to S17

References