Heterogeneously integrated flexible microwave amplifiers on a cellulose nanofibril substrate

Low-cost flexible microwave circuits with compact size and light weight are highly desirable for flexible wireless communication and other miniaturized microwave systems. However, the prevalent studies on flexible microwave electronics have only focused on individual flexible microwave elements such as transistors, inductors, capacitors, and transmission lines. Thinning down supporting substrate of rigid chip-based monolithic microwave integrated circuits has been the only approach toward flexible microwave integrated circuits. Here, we report a flexible microwave integrated circuit strategy integrating membrane AlGaN/GaN high electron mobility transistor with passive impedance matching networks on cellulose nanofibril paper. The strategy enables a heterogeneously integrated and, to our knowledge, the first flexible microwave amplifier that can output 10 mW power beyond 5 GHz and can also be easily disposed of due to the use of cellulose nanofibril paper as the circuit substrate. The demonstration represents a critical step forward in realizing flexible wireless communication devices. Though flexible microwave integrated circuits (MICs) are desirable for the construction of functional microwave amplifier circuits, realizing low cost III-V-based MMICs remains a challenge. Here, the authors report a heterogeneous integration strategy for the fabrication of flexible low-cost MICs.

M icrowave circuits are essential components in modern wireless electronic devices, which generate, process, transmit, and receive signals beyond gigahertz (GHz). To date, microwave circuits have been mainly constructed on integrated semiconductor chips and/or on printed circuits boards (PCBs), both in rigid form. However, there are a number of existing and emerging applications that cannot be (or easily) addressed by the rigid form-based microwave electronics. For example, large-area (e.g., >several square meters) microwave systems (e.g., phased array systems) require individual chip packaging, module assembly, and inter-connections, thereby making such systems bulky and heavy weight with jeopardized operation reliability 1,2 . This renders the rigid-chip-based solution a very disadvantageous one. In addition, rigid-chip microwave electronics are also unable to address applications where light weight and low-cost electronic systems need to be squeezed in limited/irregular spaces such as small-footprint gadgets, e.g., wearable devices, drones, etc.
To address the existing and emerging microwave applications, the concept of flexible microwave electronics was initiated and has been explored for the last decade or so. Although individual flexible microwave active and discrete/distributed passive components [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] , and some simple flexible passive circuits 3,10,20 , have been demonstrated, using these components [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] to construct a functional microwave amplifier circuit, one of the most important types of circuits in microwave systems, has never been reported. To date, the only reported approach to fabricating bendable/ flexible microwave integrated circuits (MIC) is to thin down the substrates of rigid-chip-based monolithic MIC (MMIC) [21][22][23] and yield flexible MMIC. The fabrication cost of this approach includes rigid-chip fabrication cost (substrate plus processing) and the thinning down cost (processing). Although the substrate cost of Si-based MMIC 22,23 is a small portion of the total cost and thinning down the Si substrate to convert MMIC to flexible MMIC can be considered reasonably cost-effective, the same approach 21 to fabricating III-V-based MMIC becomes costineffective due to the high cost of III-V substrates and the epitaxy layers grown on them. Furthermore, substrate thinning down renders the chip brittle, increases handling challenges and possibly leads to limited yield, particularly for large-area chips 24 , which could further increase the final cost of a flexible chip.
When a thinned microwave chip is transferred to a microwavecompatible flexible substrate, heat dissipation of the active devices becomes a big concern, as the majority of available flexible substrates are known to have much lower thermal conductivities than semiconductor substrates. As a result, active devices that are robust against self-heating are much preferred over InP-and Sibased transistors [21][22][23] for reliable operation. Furthermore, considering the environmental impact 10,25-27 of flexible microwave electronics under the present situation of frequent upgrading/ discarding of microwave systems-containing gadgets, environment-friendly flexible MIC (fMIC) that can be easily disposed of with the minimum amount of waste is highly desirable.
In this study, we present a novel heterogeneous integration approach to realizing III-V-based fMIC, where the simple fabrication procedures of III-V-based MMIC are inherited in the fabrication but without wasting expensive III-V substrates or epitaxial layers as opposed to MMIC substrate thinning, thus substantially reducing the materials cost. We chose to employ AlGaN/GaN high electron mobility transistor (HEMT) as the active device in this work considering its superior microwave properties 28 29 . We further demonstrated the integration of the GaN-based fMIC on wood-derived cellulose nanofibril (CNF) substrate, which has been previously demonstrated to be microwave compatible and biodegradable 10 , and convenient disposal of the fMIC through incineration for easy adoption into mainstream municipal waste treatments 30 . As the first of its kind, the costeffective GaN HEMT-based fMIC amplifier shows excellent small-signal and large-signal microwave performances even under severe mechanical bending.

Results
Strategies of fMIC fabrication. Figure 1 presents schematic illustrations of two manufacturing processes that can be used for fabricating bendable MICs: flexible MMIC and fMIC. In the chip thinning down approach 21,31 as shown in Fig. 1a, MMICs were built on III-V semiconductor epitaxial wafers that were thinned down to flexible form. The total number of MMICs that can be fabricated out of one epitaxial wafer using this approach is about (slightly smaller than) the area ratio between a wafer area (A wafer ) and a circuit area (A circuit ), which is similar to the turnout of previously demonstrated flexible electronics approaches [32][33][34][35] . For silicon-integrated circuits with a high density of transistors and for Si-substrate MMICs 22,23 , chip thin-down represents the most convenient approach to producing bendable chips and favorable cost advantages [36][37][38] , particularly considering the very low cost of Si substrates. However, for (majority of) MMIC chips built on epitaxial substrates (e.g., GaAs, InP, Sapphire, SiC, etc.), as the majority of the chip area is occupied by area-consuming passive components (e.g., inductors, capacitors, and transmission lines, etc.), the chip thin-down approach is no longer cost-effective due to the high cost of the epitaxial substrates.
The cost-effective approach to fabricate fMICs demonstrated herein, as shown in Fig. 1b, is to heterogeneously integrate membrane transistors 39,40 transferred from a dense transistorpacked source epitaxial substrate, which have maximized the use of expensive source substrate, with passive components on an inexpensive, microwave-compatible destination substrate, thus avoiding the occupation of the source substrate by large-area passives. It is noted that the fabrication procedures and, therefore, the processing cost of both the active transistors and passive components are identical in the two approaches illustrated in Fig. 1. However, the substantial increase in the number of active transistors fabricated on the source substrate, now determined by the area ratio between A wafer and the area of the transistors (A transistors ), leads to the same number increase in fabricated fMIC (~13 times of A wafer /A circuit as in Fig. 1a, detailed in Supplementary Note 2). It is also noted that the cost of the substrates of fMIC shown in Fig. 1b (CNF) is nearly negligible in comparison with that used in Fig. 1a. The only extra fabrication procedure used in Fig. 1b was transfer printing. As the transfer-printing techniques and the relevant tools have already been adopted for other mass-production applications 41,42 and proven to be a lowcost addition in the applications, they also represent minimal cost additions in handling active transistors and passives upon adopting the present demonstration for massive production. As a result, the fMIC approach shown in Fig. 1b suggests substantial cost advantages. Figure 2a, b show photographs of a flexible microwave amplifier circuit on a transparent CNF substrate fabricated using the approach illustrated in Fig. 1b. The fMIC amplifier consists of AlGaN/GaN HEMT, which is readily available from large-size AlGaN/GaN-on-Si wafer 43 and can be released in membrane form 13 . Figure 2c shows the circuit diagram of the flexible microwave amplifier. The designed operating frequency range of the amplifier is 5-6 GHz, which can address many commercial applications 44   It is noted that the HEMT size/area is still mainly dominated by the coplanar ground-signal-ground (G-S-G) probing pads needed for on-chip radio frequency (RF) characterizations. After dicing, an individual HEMT (or multiple HEMTs as needed) was picked up with a polydimethylsiloxane (PDMS) stamp after coating the HEMT with SiO 2 by plasmaenhanced chemical vapor deposition (PECVD). The Si-handling substrate of the HEMT was then fully etched away using XeF 2 etching ( Supplementary Fig. 4c), leaving a membrane HEMT of about 3.5 μm-thick finished. The membrane HEMT on top of the PDMS stamp was then transfer printed to CNF substrates precoated with adhesion layers with the assistance of an MJB-3 contact aligner ( Supplementary Fig. 5), of which the operation principle is the same as the commercial tools 41,42 . The images of HEMT sitting on CNF substrates are shown in Supplementary  Fig. 6.
Direct current (DC) characteristics and S-parameters of the HEMT sitting on the original Si substrate and on CNF substrates were characterized, and the results are shown in Supplementary Figs. 7 and 8, respectively. Both drain current and peak transconductance were reduced after HEMT transfer to CNF substrates due to the increased self-heating effects in the device, which resulted from the low thermal conductivity of CNF substrate (~1 Wm −1 K −1 ) 45 compared with that of Si substrate (~156 Wm −1 K −1 ) 46 . The results shown here are consistent with other reports 13,47,48 . Improving the thermal conductivity of flexible substrates 49,50 is expected to improve the DC characteristics. Considering the low thermal conductivity of CNF and to avoid excessive heating, the HEMT was biased at a drain voltage (V DS ) of only 10 V, despite HEMTs' ability to sustain a much higher voltage (30 V) 51 .
The values of current gain (|H 21 | 2 ), Mason's unilateral power gain (U), and maximum available gain (MAG)/maximum stable gain (MSG) of the HEMTs were extracted from the measured Sparameters. The extracted values were plotted in Fig. 3d-f as a function of measurement frequency. Without de-embedding parasitic effects, the highest cut-off frequencies (f T ) of~34.1, 37.9, and~37.0 GHz, and the highest maximum oscillation frequencies (f max ) of~69.5,~87.8, and~75.0 GHz were obtained for HEMTs on Si, SU8/CNF, and polyimide (PI)/SU8/CNF substrates, respectively (Supplementary Table 2) 52 . The gate bias (V GS ) values where the highest f T and f max were obtained were −1, −1.5, and −1 V, respectively, on the three different substrates. The RF performances of the HEMT on the CNF substrates are comparable to reported similar HEMTs on other substrates (see Supplementary Note 5 and Supplementary  Table 3).
According to Eq. (1) 53 , it was expected that the HEMT on CNF substrate would have lower f T than that on Si substrate due to the reduced peak transconductance (g m ) on CNF. However, both f T and f max values on CNF substrates are higher than that on Si substrate. The reasons for the unexpected RF behavior were analyzed based on three-dimentional EM simulations using CST Microwave Studio ® ( Supplementary Fig. 9a, b). The CNF substrates have lower dielectric constant (ε r ) of~2.6 54 than Si (~8.9). The simulations show that the parasitic capacitance values (C PAR in Eq. (1)) caused by the metal probing pads of the HEMT on CNF substrates were significantly reduced in comparison with that on Si substrates, which is consistent with other reports 13 , due to the lower ε r of CNF (see Supplementary Fig. 9c-e and Supplementary Table 4). As no de-embedding of the parasitics were performed for the HEMTs, the parasitic effects were included in the measured (raw) HEMT S-parameters. The reduced parasitic effects of the HEMTs on CNF substrate have over-compensated for the adverse effects caused by the lower thermal conductivity of CNF substrate than Si on f T . As a result, higher f T values were obtained for the HEMTs on CNF than on Si. The increase in f max on CNF is primarily due to the increase in f T and partly to the reduced gate-to-drain capacitance (C GD ), which is also a consequence of the lower dielectric constant of CNF than Si as indicated in (2) 53 . As the HEMT on SU8/CNF does not have extra PI or oxide layers in comparison with PI/ SU8/CNF as shown in Fig. 3b, c, the former has less extrinsic parasitic capacitances between electrodes and thus higher f max values than the latter.
The HEMT on PI/SU8/CNF, which was used in amplifier circuit, was further tested under different mechanical bending conditions with bending radii (R) of 38.5 mm and 28.5 mm to study the influence of mechanical bending on the microwave performance of flexible HEMT (Fig. 3g). It was observed that the MAG of HEMT decreased very slightly in the interested frequency range as the bending radius became smaller (see the inset of Fig. 3g). The slight degradation of the small-signal power gain was due to the effects of external strain on the twodimensional electron gas in the AlGaN/GaN heterostructure through piezoelectric effect and surface states, as revealed previously 55,56 . Correspondingly, the drain current 57 and transconductance 58 of the HEMT were slightly reduced, which in turn degrades its microwave performance.
Design and fabrication of flexible microwave amplifier. The flexible microwave amplifier was designed using the characterized HEMT on PI/SU8/CNF, based on the circuit diagram shown in Fig. 2c. The passive components, two spiral inductors and one capacitor, consists of two layers of metal paths 10 . A layer of spin-cast PI isolates the two layers of metal path, which not only possesses good mechanical properties but also introduces low parasitic capacitances in the spiral inductors due to its low dielectric constant (~3.5). The optimized input impedance matching network contains a 2.5-turn spiral inductor connected in series with the input port. The optimized output impedance contains a low-pass inductor-capacitor network to suppress high-frequency harmonics, which is composed of a 1.5-turn spiral inductor connected in series with the output port and a MIM capacitor of 30 μm × 40 µm in size shunting the output of HEMT. The MIM capacitor employs a 140 nm-thick SiO 2 layer deposited by electron-beam evaporation as its intermetal dielectric layer. Figure 3h shows the circuit layout for circuit simulations, which combines S-parameters of the passive impedance matching networks obtained from the EM simulations and the measured S-parameters of the HEMT on PI/SU8/ CNF. The simulation results shown in Fig. 3i indicate that the flexible microwave amplifier can achieve a peak small-signal gain of 6.69 dB at 5.3 GHz.
The amplifier fabrication process flow is shown in Fig. 4a. An extended schematic illustration of the process flow is shown in Supplementary Fig. 10. The amplifier fabrication began with picking up a rigid HEMT from a diced array of HEMTs ( Supplementary Fig. 4b). The Si substrate of the HEMT was    Fig. 4 Fabrication process and images of fMIC amplifier on a CNF substrate. a Schematic illustration of fabrication process flow for amplifier on CNF substrate. A membrane AlGaN/GaN HEMT on PDMS stamp was transfer printed on a PI/PMMA/Si temporary substrate followed by PI encapsulation. After opening via holes on the PI, a first layer of metal was deposited and patterned to form the inductors' spiral metal lines, the bottom electrode of MIM capacitor, and the ground plane. A stack of Ti/SiO 2 /Ti/Au was subsequently deposited to form the dielectric and top electrode of MIM capacitor, followed by casting of another layer of PI. After opening via holes on the PI at specific connection sites, a second layer of metal (for interconnect) was deposited and patterned. The completed membrane amplifier was picked up using a PDMS stamp after dissolving the sacrificial PMMA layer. The amplifier was then attached to a flexible CNF substrate with spin-cast SU8 as an adhesive layer. After UV light exposure for SU8 curing, the PDMS stamp was detached and the amplifier was fixed to the CNF substrate. b An optical microscope image of an amplifier on a temporary Si substrate. The scale bar is 0.4 mm. c A photograph of an amplifier on a PDMS stamp. The inset is a magnified view of the amplifier. The scale bar is 5 mm. d An optical microscope image of an amplifier on a CNF substrate under microwave measurements. The scale bar is 0.5 mm. e A magnified microscopic view of the active region of the membrane AlGaN/GaN HEMT that is integrated in the amplifier. The scale bar is 20 µm. removed with XeF 2 etching, leaving a membrane-form HEMT. The HEMT was then transfer printed to a temporary Si-handling substrate coated with a spin-cast PI layer and polymethylmethacrylate (PMMA) layer. The PMMA layer acts as a sacrificial layer and the PI as an adhesive layer. The input and output impedance matching networks were then fabricated on the Si temporary substrate. To minimize microwave propagation loss in the passive components, a thick metal stack (Ti/Cu/Ti/Au: 10/900/10/100 nm) was used for both layers of the metal paths of inductors, capacitor, and interconnects. A stack of Ti/SiO 2 /Ti/Au (10/140/ 10/100 nm) was deposited in one step to form the MIM dielectric layer and the top electrode layer of the MIM capacitors for a precise control of the capacitance value of the MIM capacitor 8 . Via holes through an insulation layer (PI:~1.5 μm thick) were formed by reactive ion etching (RIE) and an interconnected metal was formed to connect the two layers of the metal paths, completing the fabrication of the amplifier on the temporary Si substrate. The PMMA sacrificial layer was then dissolved in hot acetone to release the amplifier (Si substrate can be reused) and the amplifier was transfer printed to a SU8-coasted CNF substrate to complete the entire fabrication process. As most of the above fabrication procedures were carried out on a rigid Si substrate, all the conventional MMIC fabrication techniques can be directly adopted here.
The uniqueness of the fMIC fabrication is that area-consuming passive components in the amplifier were integrated on an inexpensive CNF substrate and not on an epitaxial substrate (Fig. 1b). The fabrication method is drastically different from thinning down III-V-based rigid MMIC chip to obtain bendable MMIC 21,31 (Fig. 1a). The fMIC method makes much greater use of epitaxial substrate materials and thus significantly reduces material cost.
As manufacturing microwave transistors requires high-cost fabrication processes such as electron-beam lithography, ohmic contact metal, and high-temperature annealing, the increase in active transistors' density in the proposed approach leads to substantial reduction of processing cost per transistors as well, which is also the most important reason to employ larger semiconductor wafers in the semiconductor industry 59 . After transfer-printing membrane HEMT on temporary Si substrate, we fabricated the rest of the passive components using conventional low-cost photolithography systems with large feature sizes (e.g., at level of microns). The combined yet sensible use of high-cost processes for fabricating high density of transistors on epitaxial semiconductor wafer and low-cost processes for fabricating large-area passive components on temporary substrate at different fMIC fabrication stages enable a cheaper and faster fabrication process than conventional flexible MMIC approaches (see Supplementary Note 2 for detailed discussion). The conventional fabrication process and the reduced use of epitaxial materials together render the fabrication cost-effective. Only a very small piece of native epitaxial substrate was used for the HEMT fabrication, which has maximized the use of the epitaxial material. Figure 4b-d show optical images of the amplifier before dissolving the PMMA sacrificial layer (on temporary Si substrate), after being picked up on PDMS stamp and sitting on CNF substrate during on-wafer microwave measurements, respectively. Figure 4e shows a microscopic image of the HEMT integrated in the amplifier. The flexible amplifier has a compact size of 1.4 mm × 2.4 mm, which is comparable to a rigid AlGaN/GaN HEMT-based MMIC chip 60 . As shown in Fig. 4d, 92.6% of the fMIC amplifier area was occupied by passive components and only the remaining 7.4% of the area was used by the HEMT, for which the G-S-G pads of the HEMT still account for the majority HEMT area (see Supplementary Fig. 4).
Small-signal characterizations of flexible microwave amplifier. The small-signal microwave performances of the amplifier were characterized on flat (Fig. 5a) and bent surfaces with bending radii of R = 38.5 mm (Fig. 5d) and R = 28.5 mm (Fig. 5g). Figure 5b, e, h present the measured small-signal gain as a function of frequency under flat and bent radii of 38.5 mm and 28.5 mm, respectively. To measure the small-signal gain values, the HEMT in the amplifier was biased at 10 V for V DS and the V GS was swept from −0.8 V to 0.2 V with a 0.1 V step. As the V GS was increased, the small-signal gain values increased until peak-gain values were reached at 5.51, 5.37, and 5.29 dB at V GS of 0.2 V under the three mechanical conditions. It was noted that the peak-gain frequency under the three conditions also shifted to lower frequencies (5.62, 5.60, and 5.58 GHz, respectively) as the bias was increased. To clearly illustrate the trend of the peak-gain shift, Fig. 5c, f, i plot the extracted peak-gain values and the peak-gain frequencies from Fig. 5b, e, h, respectively, as a function of V GS . As the V GS increased from −0.8 V to 0.2 V, the monitored drain current of the HEMT in the fMIC also increased ( Supplementary Fig. 11) and so did the transconductance of the HEMT ( Supplementary  Fig. 7b), which led to the increase in the RF gain values of the HEMT (Eq. (1)) and the small-signal power gain of the amplifier. Shifting of the peak-gain frequency was also observed. The maximum small-signal gain curves obtained at V GS of 0.2 V under flat and bent conditions were compared in Fig. 5j. Overall, the small-signal gain changes were minimal due to bending, showing the mechanical bendability and robustness of the amplifier against bending. Supplementary Table 5 summarizes simulated and measured gain values of the amplifier at the interested frequencies and peak-gain frequency shifting values.
The slight degradation of the small-signal power gain of the amplifier and the observed shifting of the peak-gain frequencies when the amplifier was bent were a result of the degraded RF performance of the HEMT in the amplifier (see Fig. 3g), as well as by the slight impedance mismatch between the input/output matching networks and HEMT in the amplifier circuit. The input and output impedance values of the HEMT could be slightly changed as its bias was changed. Previous studies 6 have also shown that inductance value of spiral inductors and capacitance value of the MIM capacitor can be altered under certain degrees of mechanical deformation. These changes led to the shifting of impedance matching in the amplifier and thus gain degradation, which was qualitatively verified by simulations (see Supplementary Note 6, Supplementary Table 6, and Supplementary Figs. 12 and 13 for details). According to the reported trend 55,56 , it is expected that as the bending radius of the amplifier is further increased, the performance of the HEMT and therefore the amplifier performance will continue to degrade until a mechanical failure occurs when the limit of the tensile strain of GaN is reached.
Large-signal characterizations of flexible microwave amplifier. Although the amplifier circuit was designed using the small-signal S-parameters of the HEMT, large-signal microwave characteristics of the amplifier circuit were characterized to estimate the RF power handling capabilities of the fMIC for continuous-wave mode operation. Supplementary Fig. 14 shows the measurement setup for large-signal microwave characterization of the amplifier. The microwave loss in cables, bias tee, and connectors in the measurement setup was calibrated. A microwave signal generator was used to sweep the input power level at 5.5 GHz, the designed center frequency. The initial bias of the HEMT in the amplifier was fixed at V GS of 0.2 V and V DS of 10 V. Figure 5k (flat) plots the output microwave power (P OUT ), the large-signal power gain (Gain), and the power-added efficiency (PAE) of the amplifier as a function of input microwave power (P IN ). Figure 5k shows that the amplifier can achieve a peak PAE of 4.7% at P IN of 5.76 dBm without bending. The corresponding P OUT at the peak PAE was 9.75 dBm (9.44 mW) and the concurrent gain was 3.99 dB with a gain compression of 2.25 dB from the small-signal gain of 6.24 dB at 5.5 GHz. The P OUT at −1 dB gain compression point (P OUT | −1 dB ) was 7.76 dBm (5.97 mW) and P OUT | −3 dB was 10.3 dBm (i.e., 10.64 ± 0.19 mW). To our knowledge, this is the first report of a flexible microwave amplifier that can output microwave power larger than 10 mW beyond 5 GHz. Supplementary Table 7 compares the various parameters of the amplifier with that of a SiGe BiCMOS power amplifier on thinned Si substrate 23 , illustrating the various performance advantages of the HEMT fMIC amplifier.
The large-signal microwave performance of the amplifier under mechanical bending (R = 38.5 mm, Fig. 5d) was further characterized and the results are shown in Fig. 5l. A peak PAE of 4.04% was measured along with P OUT of 9.35 dBm (8.61 mW) and gain of 3.59 dB. The P OUT | −1 dB and P OUT | −3 dB were 7.98 dBm (6.28 mW) and 9.85 dBm (9.66 mW), respectively. The slightly larger P OUT | −1 dB under bending condition compared with the flat condition was due to a larger P IN . These results indicated that the amplifier is mechanically reliable for microwave power amplification. Furthermore, based on the measured parameters shown above, the temperature distribution of the HEMT in the amplifier was analyzed using simulations. The detailed simulations are shown in Supplementary Fig. 15. The highest temperature of the HEMT experienced during large-signal operation was estimated to be around 184°C. According to the reported thermal reliability of GaN HEMTs (Supplementary Table 1), the amplifier is also considered thermally reliable.
Disposal of flexible microwave amplifier. Although rigid-chipand the rigid-board-based MICs are not easily disposed of and prone to electronic waste, flexible CNF substrate-based electronics have been shown to be biodegradable 10,61 , a significant benefit over other flexible host substrates such as polyethylene terephthalate and PI. In the demonstrated amplifier, a simple calculation showed that the CNF substrate accounted for~92% weight of the amplifier. As an alternative approach to biodegradation via fungi 10 to the disposal of the CNF-based fMIC circuit, disposition via incineration was attempted. As shown in Fig. 6, the CNF-based amplifier burst into flames instantly when ignited by a candle and turned into ashes after~7 s, which is similar to that of other wood-based devices 62,63 . Although a detailed analysis was unable to be performed during incineration, it is expected that the major composition of the gas produced was carbon dioxide considering the highest possible temperature (>1100 K) of a candle flame 64 . The easy disposal of the amplifier indicates the green feature of fMIC approach, which could be environmentally significant if such fMIC is massively produced in the future.

Discussion
In summary, we have demonstrated a viable approach to producing cost-effective, easy-to-implement, green, flexible microwave amplification circuits that may address many microwave/ wireless applications. With a minimal addition of a new tool for transfer printing, the demonstrated approach is ready for adoption into large-scale manufacturing. Despite that GaN HEMT was specifically used in the demonstration, the approach can be applied to other semiconductor materials as long as the same principles apply. It is noted that further reduction of the active transistor size by minimizing their connecting pads is readily feasible. Research on flexible amplifiers toward higher power and/ or higher frequency, which requires overcoming greater challenges of heat dissipation and reduction of parasitics than what is revealed herein and on other transistor-containing microwave circuits represents important directions of explorations in the future.

Methods
Preparation of CNF substrate. The tetramethylpiperidine-1-oxy-oxidized CNFs suspension was mixed at 0.9% weight percent using a mechanical mixer (Brookfield, Model L692) and further homogenized by sonication (Fisher Scientific, Model CL-334). Subsequently, the suspension was filtered with a hydrophilic polytetrafluoroethylene membrane (pore size: 0.1 μm, Omnipore membrane filter, model JVWP14225, Millipore Corporation, USA) under air pressure (1 MPa). Following filtration, wet CNF films were placed between a filter paper and a metal plate for further drying with a 10 kg weight on top of metal plate to achieve a flat and smooth surface for the CNF paper. The dried CNF paper was coated with biobased epoxy resin (SUPER SAP® ONE, Hayward, CA) and sandwiched between two vacuum bagging films under vacuum for 24 h to cure.
Fabrication of AlGaN/GaN HEMT array on Si and membrane HEMT. The AlGaN/GaN heterostructure was grown on a 1 mm-thick Si (111) substrate using a metal organic chemical vapor deposition system. The detailed AlGaN/GaN HEMT layer structure is illustrated in Supplementary Fig. 1  NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-16957-4 ARTICLE cycle duration: 120 s) and membrane HEMT was obtained on PDMS stamp (see schematic illustration in Supplementary Fig. 1).  Fig. 5). After 5 min UV exposure (5.5 W/cm 2 ) to cure the SU8, the PDMS stamp was retracted and the membrane HEMT was fixed on the CNF substrate (see Supplementary Fig. 2a). To characterize the HEMT, the PECVD oxide protection layer can be stripped off using a buffered oxide etchant (BOE, 6 : 1).
To fabricate HEMT on PI/SU8/CNF, a temporary Si substrate was prepared by spin-coating a layer of PMMA (PMMA 950 A2, 3000 r.p.m. 30 s, baked at 180°C for 3 min) as a sacrificial layer. Then PI was spin-cast (4000 r.p.m. 30 s) on the Si substrate twice and baked at 150°C for 4 min each time, followed by baking at 200°C for 30 min and 350°C for 3 h in nitrogen ambient (ibid). Then the PI was spin-cast (3000 r.p.m. 30 s) again and baked at 100°C for 45 s (partially cured), followed by contacting the membrane HEMT on a PDMS stamp with the partially cured PI. The membrane HEMT was printed on the PI/PMMA/Si substrate after 1 min by detaching the PDMS stamp followed by baking at 150°C for 4 min. The HEMT was then encapsulated by spin-casting a layer of PI on the HEMT. Using a layer of 100 nm-thick Cu as a hard mask, via holes were formed on the electrodes of HEMT using plasma to consecutively etch of PI (Unaxis 790, CF 4 /O 2 : 2/80 s.c.c.m., pressure: 75 mTorr, RF power: 100 W) and oxide (Unaxis 790, CF 4 /O 2 : 45/5 s.c.c.m, pressure: 40 mTorr, RF power: 100 W). After removing the Cu layer (Copper Etchant APS-100), the HEMT sitting on the PI/PMMA/Si structure was immersed in hot acetone (baked on hotplate at 200°C) for 2 h, to remove the PMMA layer and release the membrane HEMT (encapsulated in two PI layers) from the Si substrate. Finally, the membrane HEMT was printed on a CNF substrate coated with SU8, followed by UV curing (see Supplementary  Fig. 2b).
Fabrication of amplifier on CNF substrates. The fabrication process of amplifier consists of HEMT fabrication and passives fabrication. The HEMT fabrication completely resembled the procedures that were described above. After the via holes were opened on the electrodes of HEMT sitting a PI/PMMA/Si-handling substrate, a Ti/Cu/Ti/Au stack layer (10/900/10/100 nm) was deposited to form a ground plane, spiral metal lines of inductors, and bottom electrode of MIM capacitor. Next, Ti/SiO 2 (10/140 nm) and Ti/Au (10/100 nm) were deposited as the dielectric layer and top electrode of the MIM capacitor, respectively. A PI layer was spin-cast and cured as an insulation layer. Via holes through the PI layer were formed using RIE (Unaxis 790) with a copper hard mask (100 nm). Ti/Cu/Ti/Au (10/900/10/100 nm) was deposited as interconnect metal, followed by PI encapsulation. Via holes were formed to expose input and output coplanar G-S-G pads using RIE (Unaxis 790). The amplifier was released in hot acetone and then transfer printed to a SU8coated CNF substrate ( Fig. 4a and Supplementary Fig. 10).
RF measurements and analysis. Semiconductor parameter analyzers (HP 4155B and Keithley 4200-SCS) were used to measure DC characteristics of AlGaN/GaN HEMTs on different substrates. S-parameters of the HEMTs on different host substrates and that of the amplifier on CNF under different bending conditions were measured using a vector network analyzer (Agilent PNA E8364A), after finishing standard on-chip calibration using a short-open-load-thru (SOLT) calibration kit. The DC bias voltages were supplied by the HP 4155B. Large-signal continuous-wave microwave characteristics of the amplifier were measured using the measurement setup shown in Supplementary Fig. 14. The 5.5 GHz signal was generated using a microwave signal generator (HP 83592B). A DC power supply (Agilent E3631A) was used to provide DC biases for the amplifier through its input/output ports using bias tees (HP 11590B). G-S-G microwave probes (Infinity Probe, Cascade Microtech) were used for on-chip probing. The output RF signal was first attenuated with a microwave attenuator (MOD 20600-6, Omni Spectra), then sensed by a power sensor (HP 8481 A), and finally was read with a microwave power meter (Agilent EPM-442A).
EM properties of the metal pads on Si and CNF structures were simulated using CST microwave studio ® . The simulations of the small-signal microwave performance of the amplifier under flat and bent conditions performed through EM/circuit co-simulations of passive impedance matching networks and the measured S-parameters of the HEMT on PI/SU8/CNF substrates using Advanced Design System (Keysight).

Data availability
The experiment data that support the findings of this study are available from the corresponding author upon reasonable request.