Rapid and up-scalable manufacturing of gigahertz nanogap diodes

The massive deployment of fifth generation and internet of things technologies requires precise and high-throughput fabrication techniques for the mass production of radio frequency electronics. We use printable indium-gallium-zinc-oxide semiconductor in spontaneously formed self-aligned <10 nm nanogaps and flash-lamp annealing to demonstrate rapid manufacturing of nanogap Schottky diodes over arbitrary size substrates operating in 5 G frequencies. These diodes combine low junction capacitance with low turn-on voltage while exhibiting cut-off frequencies (intrinsic) of >100 GHz. Rectifier circuits constructed with these co-planar diodes can operate at ~47 GHz (extrinsic), making them the fastest large-area electronic devices demonstrated to date.

SI-3 measurement the films have to adhere on the substrate so that the change in radius of curvature can be measured before and after the film deposition and then can be used to elucidate the stresses.
In a study by Lee et al. 3 , the authors used this method to measure the stresses induced in Ti-Pt films (10-100 nm) deposited on flat Si/SiO2 and found values in the range of 700-800 MPa. When the same films were instead deposited over a Si/SiO2 mesh pattern, the bilayer metal film started to form Ti-Pt microtubes of approximately 25 µm diameter. This compares well to the microtube diameters obtained in our own experiments.
The FLX-2320-S stress measurement system uses two lasers at 670 nm and 780 nm and 4 mW to scan a substrate's surface before and after a film is deposited onto it. The lasers raster the surface and measure the change in curvature radius caused by the stress in the film. The interior chamber supports circular wafers of 8", 6", and 4" diameters. The accompanying software uses the collected radius of curvature measurements and known material constants and applies the following Stoney's equation to calculate the stress in the film. (S1) Where is Young's modulus, ℎ is the substrate thickness, is Poisson's ratio, is the substrate radius of curvature, is the film thickness, is the average film stress, and (1− ) is the biaxial elastic modulus of the substrate. To measure the stress in our Ti-Pt thin films, we deposited them sequentially onto a Si/SiO2 wafer and measured the stress. The deposited layers were 10 nm Ti and 90 nm Pt. The calculated stress in the Ti layer on the Si/SiO2 substrate is 613 MPa (tensile) and the final stress when the Pt layer is deposited is 972 MPa (tensile). This agrees with stress values reported by Lee et al., and consequently our Ti-Pt films exhibit internal stresses within a similar range.
Contrary to Ti-Pt, self-peeling has not been observed for aluminum, gold, or titanium (as M2 electrodes) deposited using the same process and parameters. A possible explanation is that the residual strain induced during (electron-beam) deposition of other M2 (Al, Au and Ti) is insufficient 3,4 . In addition to that, the Ti-Pt bilayer only self-peels at a critical thickness once the platinum layer is approximately ≥ 95 nm. At smaller thicknesses of Ti and Pt, the bilayer is too SI-4 thin, and immediate delamination is not observed. This could be due to the lack of insufficient stress at lower thickness 3,5 .

ST 3. Geometric considerations for diodes:
The co-planar nanogap electrodes designed in this work are illustrated in Supplementary Fig.   5 where we clearly define the all the specific dimensions of the diodes in the top and cross-section schemes. The channel length (L) i.e., the size of the nanogap between the Al (M1) and Ti-Pt (M2) electrodes, also known as inter-electrode distance, is typically < 10 nm. The thickness of the electrodes, denoted as height (H), is kept as 100 nm. The inner Ti-Pt (M2) electrodes' diameter, d, Due to the 250 µm pitch size of our GSG picoprobes (from GGB industries), smaller diodes of diameters 100 and 300 µm could be easily probed but, for larger diodes (600 µm and 900 µm diameter), a notch was added to the design to facilitate the landing of GSG probe for RF measurements.

ST 4. Average nanogap size extraction:
To elucidate the nanogap length between two metal electrodes, we have used two different approaches that are detailed below. These methods that were successfully employed in previous works allow us to calculate the average nanogap size and distribution 6,7 .
Method 1: In method 1, the software ImageJ 8 was used to load a high-resolution SEM image of a nanogap and then calibrated using the embedded scale bar to obtain the pixel-to-nanometer conversion factor. Next, using the measure function in the software, the nanogap size was measured manually, multiple times across the nanogap, as shown in Supplementary Fig. 7a- The area S of the gap is determined from the total number of pixels within the gap (black pixels). The perimeter (P) was found by removing pixels from the inside of the nanogap space, i.e., only selecting the outer pixels surrounding the nanogap space. Thus, the average gap size was calculated in units of pixels/nm and afterward converted to nanometer from the pixel-to-nm conversion factor, which is determined while calibrating the image as mentioned above in method 1. Other than the manual method 1, the procedure described by Kano et al. yields the average gap size but does not lead to a histogram of size distribution.
The mean nanogap size extracted by these two methods is approximately 16 nm, which is slightly higher than the 10 nm that were determined from cross-sectional TEM image as shown in to a certain degree, this final placement lies in the judgment of the user. Using an automated algorithm for this purpose (as suggested by Kano et al.) can aid in this process. However, even in this method, the user has to adjust the level of thresholds for the accurate conversion into a binary image. Hence, some degree of uncertainty still remains to determine the precise nanogap length.

SI-6
The nanogap size and distribution relies on various factors, including the properties of Al (M1) such as thickness, roughness and grain size influenced by deposition rate (since the nanogap forms along the boundary line of M1). So, these factors play a significant role in the process, and careful tuning of these parameters need to be considered. The temperature rise in Ti-Pt (α) is significantly higher than in Al (γ) due to the higher absorption in the former case (~× 4) and the small heat decay length in glass = √ ≅ 21 µm, where = / is the corresponding heat diffusion coefficient. However, within the nanogap (β) the temperature is practically uniform. As shown in Supplementary Fig. 12g, the power deposited in each contact (when the pulse is on) comes from the product of source power ( Supplementary Fig. 12f) and contact absorptivity (Supplementary Fig. 12e). The temporal profile of the absorbed heat which was used in the COMSOL thermal simulations 10 have shown in Supplementary Fig. 12h. The boundary conditions are convective cooling with ℎ 1 = 10 W/m 2 K from the top (free convection) and ℎ 2 = 150 W/m 2 K from the back surfaces (loose contact with metal holder) 11 as well as the radiative cooling from the top. Given the very short pule duty cycle (DC = × = 0.09%) however, the latter has a minor role with the former determining the saturation background substrate temperature according to respectively, as shown in Supplementary Fig. 12h. Overall, FLA allows targeted, fast and precise energy delivery in nanochannel (< 10 nm) within short time frame (< 10 s) leaving the substrates intact.

ST 6. Important figures of merit for RF Schottky diodes:
For RF applications, Schottky diodes are preferred over conventional PN junction diodes as they possess a low turn-on voltage, are easy to fabricate, and are compatible with a large range of semi-conductor and substrate materials 12 . There are several important figures of merit that can be used to assess Schottky diodes in RF device applications. Here, we discuss those quantities that plays a crucial role in rectifying RF input signals into DC output voltage.

ST 6a. Rectification ratio, non-linearity, and responsivity of the RF diodes:
The rectification ratio is defined as the ratio of the forward to the reverse current at the same (absolute) voltage and it is a measure of the diode's asymmetry 7,13 .
The non-linearity of the Schottky diode is a measure of the deviation from a linear resistor. It is defined as the ratio of the differential conductance (dI/dV) to the conductance (I/V) of the diode.
A non-linearity of > 3 is preferred for RF device applications 7,13 .
Quasi-DC responsivity (or current sensitivity) is a measure of the change in the DC output current for a given RF input power. It is calculated in a small-signal approximation from the currentvoltage (I-V) measurements. It is defined as the ratio of the second derivative of the I-V to the differential conductance 7, 14 . SI-8

ST 6b. Series resistance calculation from I-V measurements:
The diode's series resistance, RS, was calculated from the I-V measurements using the method proposed by Cheung et al. 15 . The thermionic emission region of the I-V curve chosen for applying the Cheung method was adopted from the well-known thermionic equation as follows, where Io is the reverse bias saturation current given as = * 2 ( | ) . Here, n is the ideality factor, S is the diode area (cm 2 ), ΦB is the barrier height, and A* is the effective Richardson constant (41 A/cm 2 K 2 for IGZO) 16 . From equation S5, the equation can be expanded to include the effect of series resistance RS as where, β = q/kT. By plotting d(V)/d(lnI) and fitting the linear region, RS can be obtained from the slope and n from the intersect and we define equation H(I) as: The plot of H(I) and a fit of the linear region are used to obtain a second approximation of RS from the slope and ΦB from the intersect.

ST 6c.Temperature-dependent charge transport analysis:
Temperature-dependent I-V characteristics are used to estimate the barrier height (ΦB) and effective Richardson constant (A * ). Supplementary Fig. 16 shows the I-V characteristics of IGZO diodes measured from 140 K to 300 K. Using this data and considering the thermionic emission model, the standard Richardson plot can be obtained by plotting ln ( Here ΦB0 is the apparent barrier height at T = 0, and a, b are constants, and T is temperature.
Equation S10 allows to calculate the apparent ΦB0 but not the true flat band barrier height ΦBfb,.
This can be obtained by using Where NC is the density of states in the conduction band, and the ND is the carrier concentration.
The modified saturation current then becomes n(T)ln ( was plotted and the best fit for the data yields a value for A = 41.6 ± 6 A cm -2 K -2 and the barrier height at T = 300 K (ΦB) of 0.75 ± 0.2 eV has been found. The ΦB value is in good agreement with previously reported barrier height 18 .

ST 6d. Schottky barrier height and dopant concentrations
C-V measurements are considered as an alternative method to extract the Schottky barrier height.
This approach is regarded as most practical as the value of flat band barrier height is determined, and the effects of image force lowering are negligible 19 . In the C-V data, we apply the Mott-Schottky plot, 1 2 = ( ), to calculate the built-in voltage, Vbi, namely the voltage at which there is no band bending, or charge depletion that separates depletion from accumulation region, and the dopant concentration NA/D. Here the extrinsic capacitance due to 3D coupling of the electrodes with an empty nanogap, i.e. no semiconductor material present (0.17 pF), has been subtracted from the raw data to assure the measured capacitance values come only from the complete device 20 .
The Schottky barrier height, ΦB, can then be calculated from the Vbi and NA/D: Where NCB is the effective density of states in the conduction band and is calculated as follows: For IGZO, given m* = 0.27m0 16 , and the calculated NCB = 3.5×10 18 cm -3 .

ST 7. Cut-off frequency estimation:
Cut off frequency of a Schottky diode is a somewhat generic term and can be referring to an intrinsic or extrinsic cut off frequency, depending on the context 12 . When the diodes are incorporated in rectifier circuits, the extrinsic cut off frequency (fC,ext) can be determined from the output voltage progression with frequency. The output voltage is subjected to losses due to reflection, impedance mismatch, skin depth effects, and dielectric losses 14 . The intrinsic cut off frequency (fC,int) on the other hand, measured via one port S11 reflection measurements, excludes those losses associated with the device and represents the theoretical upper limit. As a result, the intrinsic cut off frequency values are always higher than the extrinsic ones. There is consequently a need to elucidate both frequencies; hence we measured one port S11 measurement (to evaluate the intrinsic cut off frequency) and also incorporated our diodes into rectifier circuits to extract the extrinsic cut-off frequency. (S17)

SI-12
Where the series resistance, RS in series with nonlinear barrier resistance Rb, and the Xc is reactance associated with capacitance (Cj) given as Where f is the frequency in the equation S18. It is evident that at lower frequencies XC >> RS, the resistive elements mainly dominate the current transport and the rectification occurs. On the contrary, at higher frequencies, Xc << Rs, the current flow is shorted through the capacitive element, and the rectification ceases at reasonably high frequencies. The threshold frequency at which the latter happens is defined as the intrinsic cut-off frequency where the XC = RS 12 . From fC, the RC constant may also be determined. The underlying solution to find the intrinsic cut-off frequency of the Schottky diodes relies on the two essential factors, as mentioned above, series resistance (RS) and junction capacitance (Cj). The series resistance, RS, is due to the combination of intrinsic semiconductor resistance (RSP) and the contact resistance between metal and semiconductor RC (both Ohmic, Rohmic, and Schottky contact RSC). The series resistance can be calculated from either static I-V measurements using a method proposed by Cheung et al., 15 or from one port S11 dynamic reflection measurements.
However, the frequency-dependent series resistance and capacitance values are more reliable and are widely used to extract the impedance of the diode as well as to predict the intrinsic cut-off frequency 18,21,22 .
The extracted impedance of the Schottky diodes from S11 measurements, which consists of a real (series resistance, Rs) and imaginary part (reactance Xc, primarily due to capacitance Cj), is plotted against frequency. The crossover point at which the real and imaginary values meet is considered as the intrinsic cut-off frequency 18,22 , as shown in Supplementary Fig. 22. At this SI-13 point, the device impedance is matched with the input RF signal, and ideally, the device allows more than 90 % of the input signal. However, this does not ensure that all the signal will be transmitted to the device. This is where the losses, as mentioned above, play a significant role in rectifying the input signal.
To include such losses and re-evaluate the actual (extrinsic) cut off frequency (fC,ext), we conducted a rectifier circuit measurement where one can directly extract the -3dB point. The -3dB point is defined as the frequency at which the output voltage, VOUT, reaches     The non-linearity curve as a function of voltage. The non-linearity is a measure of the deviation from a linear resistor and is defined as the ratio of the differential conductance (dI/dV) to the conductance (I/V) 13 . A non-linearity > 3 (marked by the green area in the graph) is preferred for high performing RF diodes. diameter diodes. The current distribution for 100 and 300 µm appears to be uniform, but for 600 and 900 µm, the current is more concentrated near the probing region. This simulation reveals that at a larger device structure, launching and transmitting the RF signal becomes challenging.

SI-32
Supplementary Fig. 21 | High-frequency S11 measurements on several diodes: (a-d) the one port S11 measurement of 10 diodes for each diameter (900, 600, 300, and 100 µm) measured from 100 MHz to 40 GHz frequency range and showing consistent reflection results. In our co-planar devices most of the input RF signal is reflected and only small portion passes through the device.
The -10 dB point (red color dotted lines) is where the 90 % of the input signal assumed to passing through the device. The corresponding impedance and intrinsic cut-off frequency estimation of the diodes are shown in the following Supplementary Fig. 18. as a source of AC signal, the bias tee (used to allow the RF signal to nanogap diodes and divide the RF and DC signals back from the diode), and the load resistor, RL, used to measure the rectified DC voltage from nanogap diodes. (b-e) The rectified DC voltage output for 900, 600, 300, and 100 µm diodes, respectively. Around ten diodes were measured for each diameter and each show a consistent voltage output. The frequency range for rectifier measurements was 100 MHz to 18 GHz. As expected, a diode's rectified output voltage increases with its diameter.

Supplementary Tables
Supplementary Table 1. Thermal properties of the materials used in the opto-thermal calculations 24 .