Ultrafast 27 GHz cutoff frequency in vertical WSe2 Schottky diodes with extremely low contact resistance

Ultra-thin two-dimensional semiconducting crystals in their monolayer and few-layer forms show promising aspects in nanoelectronic applications. However, the ultra-thin nature of two-dimensional crystals inevitably results in high contact resistance from limited channel/contact volume as well as device-to-device variability, which seriously limit reliable applications using two-dimensional semiconductors. Here, we incorporate rather thick two-dimensional layered semiconducting crystals for reliable vertical diodes showing excellent Ohmic and Schottky contacts. Using the vertical transport of WSe2, we demonstrate devices which are functional at various frequency ranges from megahertz AM demodulation of audio signals, to gigahertz rectification for fifth-generation wireless electronics, to ultraviolet–visible photodetection. The WSe2 exhibits an excellent Ohmic contact to bottom platinum electrode with record-low contact resistance (~50 Ω) and an exemplary Schottky junction to top transparent conducting oxide electrode. Our semitransparent vertical WSe2 Schottky diodes could be a key component of future high frequency electronics in the era of fifth-generation wireless communication.

L ayered semiconducting crystals have been extensively studied in many aspects of scientific features and device applications [1][2][3] . Representative transition metal dichalcogenides (TMDs) and black phosphorus have been used for device applications, such as field effect transistors (FETs) [4][5][6][7] and PN diodes 8,9 , complementary metal oxide semiconductor inverters 10 , photovoltaic diode circuits 11,12 , FET circuits for light emitting diodes 13,14 , and ring oscillators. Most of the previous devices have utilized the lateral electrical transport as well as the ultra-thin nature of semiconducting two-dimensional (2D) crystals. However, the ultra-thin nature of 2D crystals inevitably results in high contact resistance from limited channel/contact volume. Moreover, the issues from surface adsorbates and defects introduced during device fabrication processing become more pronounced as we deal with thinner 2D crystals. Because of these technical challenges, the reliable applications using ultra-thin 2D semiconductors, especially in ultrahigh frequencies, have been extremely difficult, although a few recent attempts show~10 GHz of state-of-the-art operating frequency in 2D-like thin TMD Schottky diode 15,16 .
The vertical transistors and diodes could be alternative device designs for 2D electronic applications. Vertically stacked layered crystals have been used in different device designs and have shown great advantages over lateral devices, such as tunneling or ultrafast charge transfer-mediated device operation 8,[17][18][19][20][21][22] . The band alignment through a combination of 2D crystals and contact engineering in these vertical devices is very crucial to achieve highperformance electron devices [23][24][25] . In particular, contact engineering to van der Waals 2D semiconductors is timely important, whether the device structure is for the lateral or vertical direction. Even though recent works using van der Waals contacts of metals or graphene electrodes to 2D semiconductors provided potentially useful methods to engineer contact properties [26][27][28][29][30] , the realization of the ultra-low contact resistance together with ultrahigh frequency in vertical device geometry has yet to be reported.
In the present study for high frequency devices, we circumvent the serious parasitic resistance issues of 2D semiconductors by incorporating rather thick 2D layered TMD and achieving excellent Ohmic and Schottky contacts in vertical diodes. We find that, in a vertical diode, relatively thick (a few tens of nanometer) TMD can serve as an ideal platform for achieving ultra-low contact resistance and capacitance. We demonstrate that excellent Ohmic contact using semitransparent platinum (Pt) to WSe 2 with recordlow series resistance (~50 Ω) and low specific contact resistance of 3.4 × 10 −5 Ω cm 2 . The top transparent electrode (indium tin oxide: ITO) on WSe 2 serves as an exemplary Schottky junction. Some other part of the top surface is electrically isolated by thin aluminum oxide (Al 2 O 3 ), which becomes a self-aligned parallel capacitor suitable for amplitude modulation (AM) demodulation circuits on glass substrate. More importantly, by modulating the thick 2D layered crystals in the vertical diodes with capacitive dimension, very low series resistance and capacitance (0.145 pF) are simultaneously achieved, allowing an ultrahigh cutoff frequency up to record high 27.1 GHz 22,31 . Equipped with practically facile fabrication process using thick and large-area van der Waals TMD crystals, our vertical TMD Schottky diodes exhibit high device stability and reproducibility. In fact, such vertical Schottky or PN diodes have been well known in conventional semiconductor materials, among which the highest frequencies come from single-crystalline Si and GaAs. However, according to Supplementary Table 1, other thin-film-based candidates might not be able to exceed fifth-generation (5G) compatible frequencies higher than 20 GHz. We believe that our semitransparent WSe 2 Schottky diode would find breakthroughs in perspectives of future 5G communications and automobile electronics toward high frequency (K-band: 18-27 GHz) applications 32,33 .

Results
Electrical properties of vertical Schottky diode circuit. Figure 1a, b shows a three-dimensional (3D) device schematic diagram and an optical micrographic (OM) image of ITO/p-WSe 2 Schottky diode, which has a relatively thin Al 2 O 3 as a parallel capacitor (Type A). Depending on the overlap area of bottom Pt electrode  and Al 2 O 3 , we categorize devices into Type A (large overlap area) and Type B (small overlap area). All the device fabrication processes including atomic layer deposition (ALD) of 50 nm-thick Al 2 O 3 are shown in Supplementary Fig. 1. Transmission electron microscopy (TEM) imaging and energy dispersive X-ray spectroscopic (EDS) mapping at the ITO/p-WSe 2 junction show a very thin (0.7 nm) uniform interfacial layer as shown in Fig. 1c and Supplementary Fig. 2. Raman spectroscopy as shown in Supplementary Fig. 3 confirms the multilayer WSe 2 34 . The energy band diagram of ITO/p-WSe 2 junction is estimated along with the Schottky barrier height as shown in Fig. 1d. For the Schottky barrier height and energy band estimation, temperaturedependent current density-voltage (J-V) measurements and Richardson's equation have been utilized as shown in Supplementary Fig. 4 [35][36][37] . The work function of the bottom Pt electrode matches well with the valence band edge of p-WSe 2 , which provides an excellent Ohmic contact to p-WSe 2 . The current-voltage (I-V) characteristics of the Type A Schottky diode show a high ON/OFF current ratio of~10 5 and an ideality factor (η) of 1.23 (Fig. 1e). Some of non-ideality (η > 1) may come from possible junction defects at the ITO/p-WSe 2 interface, as conjectured from TEM observation. The detailed characteristics of Schottky diodes using different WSe 2 thicknesses are shown in Supplementary Fig. 5 22 . Figure 1f shows the junction capacitance-voltage (C j -V or 1/C j 2 -V) characteristics for our Schottky diode. Both the C j -V measurements and the atomic force microscopy (AFM) imaging give consistent thickness values of WSe 2 flake, 50.4 nm (C j -V) and 55.2 nm (AFM) (Supplementary Fig. 6). The full depletion thickness (X d ) of the diodes under reverse bias would approach to the physical thickness of WSe 2 flake, and it is estimated from saturated C j value (= ε WSe2 A j /X d ; ε WSe2 is the dielectric constant of 7.9ε o and A j is the junction area of 2.02 × 10 -6 cm 2 ) [38][39][40] . Here, C j (= 0.292 pF) is extracted out by removing parallel Al 2 O 3 capacitance (C ox is the oxide capacitance of 0.456 pF and A ox is the oxide area of 2.95 × 10 −6 cm 2 ) from the raw total C-V curve results (C tot = 0.748 pF). Based on these C j -V results, we could even estimate the hole density (~10 17 cm −3 ) in the thick p-WSe 2 flake using the slope of 1/C j 2 -V plot. From the 1/C j 2 -V plot, built-in potential can also be found to be 0.514 V.
ITO/p-WSe 2 Schottky diode with a parallel capacitor can be used for signal rectification up to megahertz (MHz) frequency range. Figure 1g shows the input voltage-output voltage (V in -V out ) plots obtained from the inset circuit with the different external load resistors of 100 MΩ and 1 GΩ. According to Fig. 1h, under 100 Hz 1 V amplitude alternating current (AC) input, the dynamic rectification curve exactly shows the half-wave rectification output voltage whose peak value should be related to the plot in Fig. 1g. However, at 1 kHz, resistive-capacitive delay in output voltage signal is clearly shown as coupled with the parallel capacitance ( Supplementary Fig. 7b), and almost perfect direct current (DC) output voltage of 0.6 V is observed at 10 kHz (Fig. 1i) 41 . Decreased DC output level at higher frequencies ( Supplementary Fig. 7d, e) is not an intrinsic device property but rather due to an inductive impedance ωL ext (L ext is external inductance of coaxial cable) 42 . Figure 1j shows such decreased DC output voltage at 13.56 MHz, which is a well-known standard radio frequency (RF). At 13.56 MHz, DC output voltage appears to be as small as 0.2 V, but it is enough to be used for demodulation of AM radio signals.
AM demodulation for radio reception. We demonstrate successful demodulation of AM radio signals using the Schottky diode. The dashed square part including antenna was simulated by using a function generator, and the Schottky diode integrated with a parallel capacitor and an external series resistor served as the main components of the demodulator (Fig. 2a). Carrier frequencies (f c ) of 500 kHz, 1 MHz, and 1.5 MHz and the low modulating frequencies (f m ) of 0.5, 1, and 5 kHz were selected for audio signal frequencies at a modulation index of 100% 43 . 20   Supplementary Fig. 8). Figure 2d shows the frequency domain signals of AM input (black signal; 5 kHz and 1.5 MHz) and demodulated output (red signal). Unlike the input showing large voltage signals near 1.5 MHz, the output shows at least two orders of magnitude reduced voltage signals at 1.5 MHz, while it also presents large demodulated voltage signals near 5 kHz. This indicates that the demodulation by our device is very effective. Figure 2e, f presents the zoomed views of signals near 1.5 MHz and 5 kHz, respectively (see more details in Supplementary Fig. 9). The demodulation of real audio signals carried at 1.5 MHz was tested as shown in Fig. 2g, h. The oscilloscope-captured signals clearly display the three different profiles from real audio, AM modulating function generator, and demodulation signals (Fig. 2i). The demodulated signals resemble those of real audio in profile with very slight distortion, and even a Korean pop music was successfully demodulated (see the experimental setup in Supplementary Fig. 10 for more details) 44 .
Gigahertz frequency rectification behavior. With intrinsically high cutoff frequencies of our ITO/WSe 2 Schottky diodes, even successful gigahertz (GHz) rectification can be demonstrated. RF probing was performed from 45 MHz to 40 GHz for one-port scattering (S 11 ) parameter measurements on our Schottky diodes as seen in the photograph of Fig. 3a. For the S 11 parameter measurement, the Schottky diode (Type B) was prepared on the mesa structure pattern with 100 μm ground-signal-ground (G-S-G) pitch. The OM images of Fig. 3b, c show semitransparency and zoomed details of the device, respectively. Coplanar waveguide (CPW) configuration is shown in the inset of Fig. 3c and Fig. 3d, as fabricated with a characteristic impedance which is close to 50 Ω based on the dielectric constant of glass and dimension of metal pads 45,46 . In the CPW pattern of the Type B diode (the top inset in Fig. 3d), the junction area is reduced to 0.69 × 10 −6 cm 2 which is~3 times smaller than the Type A diode, while the parallel oxide-capacitive area (0.26 × 10 −6 cm 2 ) is an 5 MHz with f m = 5 kHz. e Zoomed FFT spectra for symmetric baseband which consists of three fine peaks at 1.5 MHz and ±5 kHz apart from the central 1.5 MHz (carrier feed-through signal peak). They also show much reduced AM input, which indicates demodulation effects. f Zoomed FFT spectra near 5 kHz, showing main peaks of demodulated signals at 0 Hz and 5 kHz along with distortioninduced small signals at 10 and 15 kHz. Schematic illustration (g) and photograph (h) of practical AM demodulator setup to test our Schottky device performance as composed of audio source (laptop computer), three channel oscilloscope, AM modulator (function generator), AM demodulator (ITO/p-WSe 2 Schottky diode circuit), and speaker. i Three different profiles from real audio (yellow), AM modulating function generator (sky blue), and demodulation (pink) signals. Note that the demodulated signals quite resemble those of real audio as an envelope of AM signals. Supplementary Fig. 10 would explain more. order of magnitude (or 12 times) smaller (the inset of Fig. 1a). Figure 3e shows the I-V characteristics of the Type B diode, showing much improved DC properties compared with those of the Type A device: three orders of magnitude lower reverse leakage current (110 fA) and two order of magnitude higher ON/ OFF ratio (~10 7 ) along with an improved ideality factor of 1.12.
All of these positive effects should be related to the reduced junction and oxide-capacitive area. Moreover, such a reduced junction area leads to smaller junction capacitance (0.10-0.12 pF) as well as the total capacitance. The C-V characteristics in Fig. 3f  Both of approximate C j and C tot (= C j +C ox ) with parallel Al 2 O 3 are displayed. g Smith chart from 45 MHz to 40 GHz under forward DC biases (0 to +1 V) as obtained from S 11 parameter measurement. As a positive voltage is applied, the red curve goes inward. Magnitude (h) and phase angle (i) plots of S 11 parameters in the Schottky device. j R s and |X c |(= 1/ωC tot ) plots as a function of frequency at 0 V (battery free). The cutoff frequency is found at 27.1 GHz. The plots are without de-embedding. k Average rectified V out as a function of frequency of the input AC signal with an amplitude of 1 V. Inset circuit is for rectified DC output voltage measurements. According to h, j, and k, cutoff frequency should be much higher than 10 GHz and approaches to~27 GHz. show the total capacitance (0.15 pF) with 48 nm-thick WSe 2 in Supplementary Fig. 11, which is five times smaller than that (0.75 pF) of the Type A diode with similar thickness (55 nm) of WSe 2 . The Type B Schottky diodes with reduced junction and oxidecapacitive area are thus expected to achieve a superior cutoff frequency performance in RF measurements. Figure 3g shows that the Smith chart results from the Schottky diode as measured from 45 MHz to 40 GHz under different DC forward biases from 0 to +1 V. The bottom inset of Fig. 3d is an equivalent small signal circuit model of high frequency RF measurements on device under test (DUT) structure. Since Al 2 O 3 is deposited on WSe 2 flake rather than Pt electrode, oxideinduced capacitance (C ox ) is parallel to junction resistance (R j ) and junction capacitance (C j ) 22 . At a sufficiently high frequency, the C j dominates the R j . The resultant total resistance is series resistance (R s ) which is now mostly covered by contact resistance (R c ), because the R j becomes negligible at high frequency. Accordingly, a useful "figure of merit" would be the frequency at which total capacitive reactance (|X c | = 1/ωC tot where C tot = C j + C ox ; C ox would be <40 fF) equals to R s , and it is called the cutoff frequency (f cutoff ) as it also matched to the −3 dB power loss point [47][48][49] . Although there must exist the effects of parasitic components for the 48.3 nm-thick WSe 2 Schottky diode, the diode well displays S 11 plots for magnitude and phase angle in Fig. 3h and i, respectively. According to Fig. 3h, −3 dB power loss is expected at much higher than 10 GHz. Figure 3j shows the value of R s and |X c |(= 1/ωC tot ) extracted from S 11 results at zero DC bias (V DC = 0 V) as a function of frequency. It is expected from the plots that the diode with 48.3 nm-thick WSe 2 has a cutoff frequency of over 27 GHz, and such a high cutoff frequency stems from extremely low R s value (~50 Ω), mostly of contact resistance. As the frequency of the input signal increases, the value of the rectified output signal slightly decreases from V out maximum (0.80 V) but is still maintained to be 0.65 V (V out /V out, max =~81%) at 10 GHz as shown in Fig. 3k [50][51][52][53] . Such voltage rectification at even higher frequencies has been again confirmed from two-port Schottky device architecture, according to which the f cutoff is observed at~25 GHz with a similar WSe 2 thickness of 50 nm (Supplementary Fig. 12). The thickness of WSe 2 can be utilized to modulate the cutoff frequency of the Schottky diode effectively. Figure 4a displays cutoff frequency (Type B) with different WSe 2 thicknesses of 7.53, 23.6, and 48.3 nm. Interestingly, the Schottky diodes incorporating thinner WSe 2 (7.53 and 23.6 nm) show lower cutoff frequencies at 5.92 and 14.7 GHz, respectively. The C tot extracted from |X c |(= 1/ωC tot ) plot of Fig. 4a shows the generally inversely proportional value with respect to the thickness of WSe 2 (Fig. 4b,  c). On the other hand, the R s values show nearly constant values around~50 Ω regardless of WSe 2 thickness (Fig. 4c). The f cutoff equation below genuinely explains the above thickness-dependent results, but we also calculated f cutoff following Eq. (1) and confirmed that calculation results are almost the same as the measured value in each thickness 22,49 : The thickness-dependent f cutoff results signify that f cutoff even higher than 27 GHz is possibly achievable by optimally modulating the WSe 2 thickness. More details on each DUT Schottky device of 27.1, 14.7, and 5.92 GHz are displayed in Supplementary  Figs. 13-15. The observed ultra-low R s of~50 Ω, independent of WSe 2 thickness in high frequency regime, mainly originates from the R c , which must be constant for either RF or DC measurement. In order to confirm such a low R c , we conducted DC regime J-V characteristics on Pt-WSe 2 -Pt diode with three different thicknesses of WSe 2 . This experiment could be regarded as a modified transmission line measurement because it suitably provides R c 54 . Figure 4d displays the J-V characteristics of the Pt-WSe 2 -Pt diodes with different WSe 2 thicknesses of 12.1, 28.3, and 51.2 nm. Those J-V curves show straight ohmic behavior, and R c is estimated to be 65 Ω, which is quite similar to R s in RF measurements (Fig. 4e). Extremely small specific contact resistance, R ct (= R c × A ct ) is thus estimated to be 3.4-4.2 × 10 −5 Ω cm 2 (A ct is the contact area of 0.69 × 10 −6 cm 2 and L T is the characteristic transfer length of 28.2 nm as measured from x-axis intercept). The measured contact resistance of 50-65 Ω is a record-low R c value for 2D layered semiconducting crystals, to the best of our limited knowledge. According to Fig. 4f, g and Supplementary Table 1, the highest f cutoff is found to be over 1 THz and 400 GHz, which are, respectively, from vertical GaAsand Si-based bulk single-crystalline Schottky diodes, since R ct values of those devices are extremely low (10 −7 -10 −8 Ω cm 2 ) and the devices are fabricated with low capacitances 55,56 . Our f cutoff value (27.1 GHz) is located right after them, showing that ours is still outstanding among all other thin-film semiconductors. Outof-plane linear mobility (μ) of 2.2 cm 2 V −1 s −1 is also extracted from the slope (r th = 1/pqμA ct ) of 4.8 Ω nm −1 , where hole concentration (p) in WSe 2 is assumed to be~10 17 cm −3 from Supplementary Fig. 11 40 .
Ultraviolet-visible photodetection. Our ITO/p-WSe 2 diodes are equipped with a transparent electrode window and can be functional under visible photons. According to the photocurrent-voltage (I ph -V) and responsivity plots shown in Supplementary Fig. 16, the photoelectric and photovoltaic properties of ITO/p-WSe 2 Schottky diode are well noted in the visible range 57,58 .

Discussion
In summary, our Schottky diodes incorporating rather thick WSe 2 provide an alternative approach to utilize layered van der Waals semiconductors for device applications. Our results show that the cutoff frequency of Schottky diodes can be increased as we incorporate thicker 2D layered crystals. The reliable excellent Schottky junction and Ohmic contact to WSe 2 were successfully achieved using conventional device fabrication processes compatible with semiconductor industry. The demonstrated 27.1 GHz cutoff frequency is matched with 5G era wireless communication as the highest among cutoff frequency reports from 2D materialor 3D thin-film-based diodes (Supplementary Table 1). Conventional thin-film deposition techniques could also be employed to grow quite thick large-area WSe 2 or other TMDs 59,60 . Controlling the density of defects, the grain size, and the thickness of WSe 2 from thin-film growth would be the key requirement for our high frequency applications. Considering the demonstrated cutoff frequency of 27.1 GHz with exfoliated samples is approximately an upper limit, we believe that the device performance with large-area samples could be good enough for at least a few GHz applications. We thus conclude that our vertical semitransparent Schottky diode would be a breakthrough device toward ubiquitous 5G wireless communications and automobile electronics while serving as a key component built in window glass.

Methods
Device fabrication. A glass substrate (Eagle XG) was ultrasonically cleaned by acetone, ethanol, and deionized water and then dried by N 2 gas flow. A Pt bottom electrode (10 nm) was patterned with photolithography and deposited on the glass substrate by DC magnetron sputtering. Thick p-type WSe 2 flakes (HQ Graphene) were mechanically exfoliated and transferred onto the Pt electrode. For the ITO/p-WSe 2 Schottky diode, the device was annealed in air ambient at 300°C for 10 min. A 50 nm-thick high-k dielectric Al 2 O 3 was patterned by conventional photolithography and deposited by the ALD system at the edge of the WSe 2 flake. Then, an ITO top electrode (100 nm) was patterned by the photolithography and deposited by DC magnetron sputtering on the side where Al 2 O 3 was deposited. Besides Schottky diodes, Pt-WSe 2 -Pt diodes were also fabricated, to obtain the information on R c , as follows. First, a Pt bottom electrode (10 nm) was patterned with the photolithography and deposited on the glass substrate by DC magnetron sputtering. The WSe 2 flakes with different thicknesses were mechanically exfoliated and transferred onto the bottom electrode. Then, a Pt top electrode (100 nm) was patterned by the photolithography and deposited by DC magnetron sputtering on the WSe 2 flake. In air ambient, the device was annealed at 300°C for 10 min. For DUT structure in RF measurements which use the characteristic impedance in transmission lines with 50 Ω for RF matching, the width of the signal metal pad was designed to be 80 μm, and the distance between the signal and ground   pad was designed as 13 μm, based on glass substrate with a dielectric constant (5.181) and thickness (0.5 mm). Our devices were mostly reproducible in their fabrication and DC performances when at least four batches were measured for 32 device samples in total. Four batches are categorized by WSe 2 thickness:~10,~30, 50, and~70 nm. All the samples endured more than a month without visible property degradation in air ambient. More details are found in Supplementary  Fig. 5.
Materials characterization. AFM equipment (XE-100, park systems) was used to measure the WSe 2 thickness, and Raman spectroscopy (LabRam Aramis, Horriba Jovin Yvon) was performed by using 532 nm laser source.
TEM characterization. All of the cross-sectional TEM samples were fabricated with an FEI Helios 650 dual beam focused ion beam. TEM imaging and EDS mapping were performed with transmission electron microscopes (JEOL JEM-F200 and 2100-plus), operated at 200 kV.
Half-wave rectification and AM demodulation measurement. All AC input voltage signals were applied by increasing ten units from 100 Hz to 20 MHz under the conditions that the peak voltage was +1 V, and the offset was 0 V with a function generator (AFG 3022B, Tektronix). The AC input voltage and rectified output voltage were measured with a four channel digital storage oscilloscope (TDS 2014B, Tektronix). In the same conditions of the peak voltage and offset, amplitude modulated input voltage signals were applied with 1.5 MHz carrier frequency and signal/modulating frequencies of 0.5, 1, and 5 kHz, respectively, at 100% modulation index. The input amplitude modulated voltage and output demodulated voltage were measured by the same oscilloscope.
Cutoff frequency measurement. One-port scattering (S 11 ) parameter measurements were performed by a vector network analyzer (VNA; E8364A, Agilent Technologies) after calibration. The RF source was set to sweep from 45 MHz to 40 GHz with 12,800 interval points, and an internal reflectometer was used to detect the incident and reflected RF wave signals. The magnitude and phase of S 11 were measured and recorded. S 11 represents the reflection coefficient, which is the ratio of reflected signal voltage to the incident signal voltage at one single port. The real part and imaginary part of impedance are calculated by S 11 = (Z 11 − Z 0 )/ (Z 11 + Z 0 ), where Z 0 = 50 Ω. The S 11 parameter measurements were repeated under different applied forward bias voltages from 0 to +1 V. For rectified V out measurement, AC input signal of 1 V was generated by a signal generator (N5183A, Agilent Technologies) so that the rectified DC output signal was measured by an oscilloscope (DSO81004B, Agilent Technologies) with impedance of 1 MΩ.