Microscale Schottky superlubric generator with high direct-current density and ultralong life

Miniaturized or microscale generators that can effectively convert weak and random mechanical energy into electricity have significant potential to provide solutions for the power supply problem of distributed devices. However, owing to the common occurrence of friction and wear, all such generators developed so far have failed to simultaneously achieve sufficiently high current density and sufficiently long lifetime, which are crucial for real-world applications. To address this issue, we invent a microscale Schottky superlubric generator (S-SLG), such that the sliding contact between microsized graphite flakes and n-type silicon is in a structural superlubric state (an ultra-low friction and wearless state). The S-SLG not only generates high current (~210 Am−2) and power (~7 Wm−2) densities, but also achieves a long lifetime of at least 5,000 cycles, while maintaining stable high electrical current density (~119 Am−2). No current decay and wear are observed during the experiment, indicating that the actual persistence of the S-SLG is enduring or virtually unlimited. By excluding the mechanism of friction-induced excitation in the S-SLG, we further demonstrate an electronic drift process during relative sliding using a quasi-static semiconductor finite element simulation. Our work may guide and accelerate the future use of S-SLGs in real-world applications.


The fabrication process of graphite mesa with Au film and n-Si
In order to get graphite flake, we firstly fabricated square graphite mesa arrays with Au film on highly ordered pyrolytic graphite (HOPG, ZYB grade (Brucker) 1 ). In the fabrication process as shown in Supplementary Fig. 1a, we firstly spun on a double layer photoresist LOR 1A (100 nm)/ZEP (400 nm) on the fresh cleavage surface of the HOPG (i), and then removed the photoresist of the mesa array area by electron beam lithography (ii). Secondly, we grew the Au array film with thickness of 100nm through electron beam evaporation (includes the 10nm Cr as adhesion layer) (iii) and lift-off (iv) process. Lastly, we used metal as a mask to obtain graphite mesa with Au film by reactive ion etching (oxygen ions) process (v), where the etching depth is 2.5 μm.
In order to show the effect of the fabricated graphite mesa with Au film, we carried out a series of characterizations, where the optical images of fabricated graphite mesa with Au film validated by optical microscopy (HiRox KH-3000) are shown in Supplementary Fig. 1b, the brighter area in the images is the protruding mesa. And the three-dimensional white light interference image of graphite mesa with Au film is shown in Supplementary Fig. 1c, where the bottom image is a sectional view of a graphite mesa, the height of the graphite mesa is 2.6 μm. For the fabrication of n-Si, we used electron beam evaporation to deposit a layer of 100nm Al on one side of a 4-inch, 200um thick, double-polished silicon wafer with a <100> crystal plane, then used the wafer scriber to cut into small pieces of 1cm 1cm size, soaked the each piece in BOE (Buffered oxide etch) solution for 15 minutes to remove the oxide layer on the surface of n-Si, and finally cleaned with acetone, alcohol, and deionized water, encapsulate with vacuum.

The transfer process of graphite flake
In order to form the S-SLG structure shown in Fig. 1a, we transferred graphite flake with single crystal superlubric interface to the n-Si surface, and the specific process is shown in Supplementary Fig. 2, where the left side of each figure is schematic diagram, and the right side is optical microscope observation. Firstly, we used a tungsten microtip controlled by a micromanipulator (Kleindiek MM3A) to attach the Au film of graphite mesa fabricated in Supplementary Section 0, as shown in Supplementary Fig. 2a, and applied a shear stress by the micromanipulator until they split a short distance from their vertical direction, as shown in Supplementary Fig. 2b. Secondly, we removed the microtip to observe whether the sheared graphite flake undergoes self-recovery motion (SRM) 2 to determine whether it has a single crystal superlubric interface 3 , as shown in Supplementary Fig. 2c. Lastly, we re-attached the graphite flake which has SRM property with a microtip and split it out completely, as shown in Supplementary Figs. 2d and e, after that, we removed the dangling graphite flake dragged by the microtip, and placed it slowly by micromanipulator on the atomically smooth fabricated n-Si surface in Section 0, at this time, since the adsorption force of the graphite flake and n-Si is larger than that of the microtip and graphite flake, the graphite flake will remain on the n-Si surface, as shown in Supplementary Fig. 2f, which formed the S-SLG structure shown in Fig. 1a. Since the interface of the finally transferred graphite flake was not exposed during the whole fabrication process in Supplementary Section 0, it would not be contaminated.

The work function measurement of n-Si and HOPG
The work function of n-Si and HOPG was measured with the AFM tip coated Au   Furthermore, the work function of Al is 4.28 eV. Therefore, the ohmic contact ( ) will be formed between the bottom Al electrode and n-Si of S-SLG.

Friction and current measurements of AFM system
The friction and current measurements of the graphite/n-Si heterostructures were performed under an ambient atmosphere. The experimental set-up included a commercial NTEGRA upright AFM (NT-MDT), a 100 μm XYZ piezoelectric displacement platform, a high numerical aperture objective lens ( 100 (Mitutoyu)) and visualized conductive AFM tip (ACCESS-NC-GG(Appnano)). Fig. 1a shows the schematic of the experimental set-up. We accurately pressed the AFM tip on the Au cap of the graphite flake through the optical microscope and piezoelectric displacement platform. The AFM tip was calibrated in situ by the Sader method 6,7 for the normal direction force and the diamagnetic levitation spring system 8 for the lateral direction force. The bottom Al film of the n-Si is grounded through the iron stage, and the conductive AFM tip is also grounded by connecting a precision ammeter, which can accurately measure the current through AFM tip in the sliding process.

Calibration of AFM tip
Take the friction measurement in Fig. 1d as an example, the normal force was applied by using the AFM cantilever, which can be written as , 3 where is the optical lever sensitivity, is the normal spring constant, and is optical detector signal. The lever sensitivity is measured by performing a standard force curve measurement as shown in Supplementary Fig. 4a where is the optical lever sensitivity, is the lateral spring constant of diamagnetic levitation system 8 , and is measured frictional optical detector signal 8 .
The 3.05 10 N/m was calibrated by using high-speed CCD to detect the vibration frequency of the levitate graphite sheet and precision balance to measure its mass 8 . The optical lever sensitivity was measured by using the AFM tip to drag the levitate graphite sheet and measure its force curve as shown in Supplementary Fig. 4b, we tested 122 times, and 12 of them are drawn in the figure, and we obtained its average slope 4.58 pA/μm through linear fitting. Therefore, we calculated the lateral force coefficient / 6.66 nN/pA.

Noise current measurement of AFM system
In order to detect the noise of AFM (NT-MDT) current measurement system, we adopted the same structure as in Fig. 1a, used the AFM tip static contact the graphite flake, and the measured noise current is shown in Supplementary Fig. 5a, where the x-axis is 256 data points collected in each cycle (the frequency is 1Hz), and the yaxis corresponds to the time of each cycle. We further averaged the 256 data points of each cycle to obtain the relationship between the average noise current , and time as shown in Supplementary Fig. 5b. It can be seen that the noise current is basically maintained at the order of 1pA, which is much smaller than the measured current in Fig. 1, and illustrates the reliability of the measured current. Relationship between the average noise current , and time .

Current decay caused by graphite flake delamination
The graphite flake contains many incommensurate interfaces, which has probability of delamination during the sliding process, resulting in relative sliding between inner layers, and we analyzed its influence on S-SLG through an interesting experimental phenomenon. A total of four processes occurred:    Supplementary Fig. 6d, while the measured current in Supplementary Fig. 6e was also close to 0 and the measured friction suddenly increased to ~3 μN, which indicates the low current and high friction stress characteristics of AFM tip/n-Si ordinary S-G.
The above experiments proove that the current generation of S-SLG is completely caused by the relative sliding at the graphite/n-Si interface rather than the relative sliding between the inner layer of the graphite flake.

Open-circuit voltage and power measurement
The

Noise current and voltage measurement
In order to detect the noise current and voltage measurement of the above system, we adopted the same structure as Supplementary Fig. 7a

The open-circuit voltage and short-circuit current waveform under different normal force
The tungsten probe was controlled by the micromanipulator to apply different

The I-V characteristics of graphite/n-Si interface under different normal force
In order to verify the Schottky contact formed by the graphite flake and n-Si and explain the weak normal force correlation in Fig. 2b, we used the same system as shown in Supplementary Fig. 7a, replaced the electrometer with the KEITHLEY 2400 digital source meter, and measured the current-voltage (I-V) curves under different normal forrce as shown in Supplementary Fig. 9a (the positive direction of the bias voltage is applied to the graphite flake relative to n-Si, and the sacn speed is 0.096 V/s), the one-way conduction characteristic shows that a Schottky junction is formed between the graphite flake and n-Si ( ), in which the forward conductivity is better for larger normal force. Subsequently, we used the thermionic emission model * We first focus on the inverse part ( 0), the current | | is very small, that is, where * 1 exp is effective current. The relationship between * and is shown in Supplementary Fig. 9b, which showed exponential relationship

The open-circuit voltage measured by null method
As a double check, we further used the null method 9  We gradually changed the bias voltage from 150 mV to 200 mV at intervals of 50 mV to obtain the output current as shown in Supplementary Fig. 10c. We obtained the average current under different bias voltages as shown in Supplementary  Fig. 10d (blue scatter points), and fit by cubic spline (red line). We obtained the opencircuit voltage corresponding to the output current equal to zero is 138.5 mV, which is consistent to the result in Fig. 2 and confirms the accuracy of the measurement.

The contact area calculation of AFM tip/n-Si ordinary S-G
For AFM tip/n-Si ordinary S-G, the DMT model 10 can best approximate the contact between the AFM tip and the hard poorly adhesive material. According to the DMT model 10 , the contact area is given by: where is AFM tip radius, is the normal force applied to the AFM tip, γ is the energy of adhesion, the term 2 can be considered as an additional load, which is determined by the "pull-off" force in the force curve, and is the reduced Young's modulus given as 4.49 μN, and in order to obtain the "pull-off" force, we performed a force curve measurement as shown in Supplementary Fig. 11, there is a negative valley (the black dashed box area) of retraction process, the illustration is the partial zoom, which the valley value is the adhesion "pull-off" force 2 65.9 nN, therefore, we calculated 343.52 nm through Eq. (8). Through the above analysis, we conclude that the "pull-off" force is much smaller than the normal force applied to AFM tip (2 ≪ ), which can be ignored in Eq. is the maximum friction shear stress of the contact region, and is the measured friction force.

Surface characterization method of tribological experiment
In order to verify the contact between the graphite flakes and n-Si in the S-SLG is in the state of structural superlubricity (SSL), we conducted a series of tribological tests as shown in Fig .3. Here, we show the specific process and method of the experiment.
The first step is characterized the two sliding interfaces, for graphite flake surface, we used the method described in Supplementary  For the second step, we used the lateral force measurement system of AFM (NT-MDT) to measure the relationship between friction force and normal force with displacement amplitude of 2 μm and speed of 4 μm/s, where each point was tested 40 times. Then we fitted the corresponding friction coefficient (Fig. 3c), and measured the friction force of 6,000 cycles sliding process with displacement amplitude 4μm and speed 8μm/s under a normal force of 23.8 μN (Fig. 3d).
For the third step, we performed some characterizations on the two interfaces after 6,000 sliding cycles. For the slided n-Si surface, we firstly used Asylum Research Cypher S AFM in tapping mode to perform a larger range morphological characterization and found the position of the graphite flake as shown in Supplementary   Fig. 12, that is, located the sliding region (the yellow dashed frame), and further characterized the small sliding region of n-Si through the positioning function of AFM, to judge whether there is any observable damage on slided n-Si surface (Fig. 3e).  Supplementary Fig. 14d), and then used the micromanipulator to stick the small glue drop with the graphite flake ( Supplementary Fig. 14e). The Supplementary   Fig. 14f is the microscope observation of the sticking process.

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Step 3: When the small glue drop is solidified and bonding, the bonding force between the small glue drop and the graphite flake will be larger than the van der Waals adsorption force between the graphite flake and n-Si, so we could lift the graphite flake by the micromanipulator (Supplementary Fig. 14g). After the above process, we flipped 180 degree of microtip to observe the slided interface of graphite flake by optical microscope as shown in Supplementary Fig. 14h, where the illustration in the upper left corner is a partial enlarged view (the region within the yellow dashed frame). Furthermore, we performed the Raman characterization on the flipped slided graphite flake interface (Fig. 3f), to judge whether there is any observable damage from whether there is a D peak (1350 cm ).

The graphite defects resolution estimation of Raman measurement
Due to the limitations of Raman equipment, the measured results have a certain degree of noise. Therefore, we cannot observe D peaks (1350 cm ) below the noise level. And the defect density of graphite can be obtained according to the intensity ratio of D peak (1350 cm ) and G peak (1580 cm ) , which 13 where 0.022. According to the Raman results in Fig. 3f, we can obtain that the maximum value of / is around 0.0597, and the defect density is around 7.84 10 , which is the graphite defects resolution of our Raman measurement. If the density of the defect is less than this low value, we cannot distinguish based on the currently Raman measurement.

The tunnelling probability of electron through Schottky barrier in S-SLG
According to the principle of tunneling effect 13 , for a certain distributed potential barrier , the electron with lower energy than the height of the barrier has a probability to tunnel the barrier, and the corresponding probability is , 2 * ℏ , 14 Where * 1.08 is effective electron mass, is the inertial mass of electrons, ℏ is the Planck constant, 0.0287 eV is the upper limit of friction energy generated by the interaction of each dangling bond with silicon atoms, which is calculated in Discussion on the mechanism of S-SLG Section in manuscript, and where and are the electron mobility and diffusion coefficient respectively. The and are the hole mobility and diffusion coefficient respectively.

The simulation process
The whole quasi-static simulation process was divided into three steps: Step 1: Firstly, we simulated the electron and hole distribution when the Schottky diode was formed to reach static equilibrium (Δ 0) by the slider and stator. The mesh division is shown in Supplementary Fig. 16a, and the simulation result of electron concentration distribution is shown in Supplementary Fig. 15b. It can be seen that a depletion layer is produced in n-Si. We further made a cut line in the middle ( 0) to observe the distribution of energy band , electric field in the y direction , the logarithm of the electron concentration log and hole concentration log as shown in Supplementary Fig. 15c, where the orange dotted line is the location of the heterojunction interface, and the green region is the depletion layer, which penetrates primarily into the n-Si region, and the width of depletion in the p + -Si region can be neglected. It indicates that the space charge region in p + -Si is almost distributed at the interface, and the built-in electric field is also primarily distributing in n-Si region, which is similar to metal/semiconductor contact. Therefore, the above results illustrate the rationality of using heavily doped p + -Si as an equivalent metal. Step 2: After equilibrium, we moved the upper slider with a displacement of Δ 0.5μm with a contrived constraint that the electron distributions of both the slider and the stator would not change, as shown in Fig. 4a, and the carrier distribution had reached a non-equilibrium state. Step 3: We removed the constraint and started the transient simulation with the state of the step 2 as the initial condition, and the meshing is shown in Supplementary Fig. 16b, to simulate the transport process of carriers, electric potential distribution and related parameters (energy band distribution of cutline A B and A B ) over time.

The unbalance electric potential and electric field distribution
The

The estimation of unbalanced electron drift motion characteristic time
Based on the theory of static Schottky junction 5 , we can obtain the charge of the depletion layer , 22 where is the charge of electron, 10 cm is doping concentration of n-Si, 4 μm is the contact area in simulation model and is the depletion layer width.
According to Eq. (15) and considering the bias voltage applied to n-Si, we can obtain 2 , 23 where 11.7 is the relative permittivity of silicon, is the vacuum permittivity and 0.87 V is the contact potential difference, which is obtained from the band diagram in Supplementary Fig. 15c. Substituting Eq. (23) into Eq. (22) can obtain

. 24
It corresponds to the nature of capacitor, and the equivalent capacitance when 0 The dynamic process of depletion layer establishment and destruction of the continuous sliding can be regarded as the charging and discharging process of the equivalent capacitor , so we can obtain the characteristic time with series resistance of 10 kΩ as

The discussion and classification of all reported ordinary S-G
We can divide the all reported ordinary Schottky generators (S-Gs) into nano tip 9,14 (NT S-Gs), macro tip 9,14-17 (MT S-Gs) and surface contact [18][19][20][21][22][23] (SC S-Gs) according to its contact area. The corresponding parameters of various type reported ordinary S-Gs plotted in Fig. 5 are shown in the Supplementary Table. 1. Among them, a typical NT S-G is consist of a conductive AFM tip pressed against a smooth surface, which will generate high pressure of 1-10 Gpa due to the small contact area of 10-100 nm calculated by MDT model 10 , which cause high friction stress to excite a large number of electrons leading to a high current density of 10 -10 Am . Therefore, NT S-Gs are likely based on the friction excitation mechanism 9,14 . Due to the small contact area, the highest total current achieved by NT S-Gs is observed to be around 0.15 nA 14 , which is one order of magnitude smaller than S-SLG. Furthermore, the wear caused by high friction stress also makes the current of NT S-Gs completely decays during the first few cycles 14 , which the lifetime is three orders of magnitude shorter than that of S-SLG.
The MT S-Gs has a similar structure to NT S-Gs. The difference is that the radius of macro conductive tip is generally around 1 mm, and the contact area are typically 0.1-1 mm calculated by the Hertz model, which is much larger than NT S-Gs.
Therefore, MT S-Gs has lower pressure of 50-670 Mpa and current density of 3-214 Am .
The structure of SC S-Gs is different from that of NT-ordinary S-Gs and MT S-Gs, which is consist of a bulk metal material pressed against a smooth surface to form surface-to-surface contact, and the reported SC S-Gs are all in macroscale, so it has the larger contact area of 1-100 mm and lower pressure of 2 kPa -6MPa compared to NT S-Gs and MT S-Gs, but the wear is still inevitable as the operation cycle increases 18,19 , which indicates that the friction excitation mechanism cannot be excluded of reported SC S-Gs.
In conclusion, the above three types of ordinary S-Gs cannot achieve high current density and long lifetime simultaneously, that is, high current density means lower lifetime, and vice versa. But we exclude the friction excitation mechanism in our S-SLG because the low friction energy is not enough to excite electrons, so it is based on a completely new mechanism, and most likely the DLED mechanism. Therefore, S-SLG is not limited by the above contradictory, and our experimental results shows that it achieved almost unlimited lifetime while maintaining high current density.