COMSOL Multiphysics is used for simulation modeling and calculation in this work. We mainly use the electric field, circuit, and magnetic field functions in the low-frequency electromagnetic field (AC/DC) module.

The optrode device used for the simulation models is based on the prototype that we described in 2016 (He Zhang et al., 2016), and its layout design is shown in Figure 1B. We have designed four different shielding measures on this basis and compared them with no shielding measure in the recording electrode potential to evaluate their shielding effects. Considering the non-uniform optrode structure, we divided it into two representative regions. One is the metal wire region, and the other is the μLED structure region. Then we selected a cross-section in each region to perform the 2D simulation.

The metal wire region mainly consists of the metal traces of the μLED and recording electrodes, in which the only interference source is the anode metal trace. The μLED structure region is the formation area of the PN junction. It includes the P-type and N-type gallium nitride (GaN) layer in addition to the metal traces. Since the GaN epitaxial wafers that we used have a structure with the P-type layer on the top and the N-type layer on the bottom, the P-type layer is also an interference source that cannot be ignored in the μLED structure region apart from the anode metal and the N-type layer mentioned in literature (Kim et al., 2016). Based on the interference source analysis, we constructed the 2D modeling of the metal wire region and the μLED structure region shown in Figure 1C. The wiring-above-anode is mainly designed to cope with the interference from anode wire, and the widening-cathode is for the N-GaN interference. The first three shielding methods are double-layer metal structures. There only needs to change the original metal layer shape, and no extra process flow is added. The last one is a three-layer metal structure, requiring an additional metal deposition process. The main difference between the models is that the P-GaN and N-GaN layers exist in the μLED structure region, resulting in that the shielding layer cannot cover the light-emitting area of the μLED.

We have also constructed 3D optrode models to reflect the electric field distribution more accurately in the 3D space. All the shielding schemes are the same as 2D modeling. The 3D model of no-shielding optrode is especially shown in Figure 1A, designed according to the actual device size (6,000 × 500 × 5 μm³). And the top view of other shielding schemes is shown in Figure 1E. The 3D modeling has both the characteristics of the metal wire region and the μLED structure region. A light window needs to be left above the light-emitting area in the shielding layer. All the electric field simulation models are set in an infinite air environment in order to simulate the real electric field distribution (Supplementary Figure S1).

In the electrical simulation, the potential is most commonly used to assess the magnitude of EMI according to the literature (Kim et al., 2016) (Ji et al., 2020; Kim et al., 2020). We did both static analyses (DC analysis) to observe the electrode potential when the μLED at the maximum input and transient analyses (time-domain analysis) to record the waveform reflecting the electrode potential varied with the μLED input voltage. In terms of material, the electrodes, leads, and shield are provided as metal, the rest of the shank is provided as insulator, and the shank is surrounded by air. These materials need to set the electrical conductivity (δ) and relative permittivity (ε), as shown in table 1.

In the static simulation, a 3 V DC voltage is applied to the anode metal, and the N-type GaN layer was applied with 10 mV according to literature (Kim et al., 2016). Considering that the P-type layer is connected to the anode metal, we also assume it to be 3 V following the worst case. In the transient simulation, pulse signals are separately applied to the anode (3 V, 1 Hz), P-type GaN (3 V, 1 Hz), and N-type GaN (10 mV, 1 Hz). The cathode metal and the shielding layer are always grounded during all the simulations. The recording electrodes are set to be no current flowing in, assuming that the amplifier connected with the electrode is ideal. These models are calculated through FEM, and the meshing of a 3D model is shown in Figure 2A.

To verify the simulation results, we designed and manufactured simplified optrode devices with corresponding shielding methods for in vitro tests. Considering that electromagnetic interference is mainly involved in our research and the anode metal is the key interference source, whether the μLED is conductive can be ignored. So we designed simplified optrode devices to reduce the process complexity and shorten the verification time. Only the metal traces of the μLED and the recording electrodes are retained. There is no P-type and N-type GaN layer in the μLED structure region so that we can tape out on the silicon wafers grown with SiO₂ rapidly. The simplified device can also exclude the influence of other noise sources in optrode, such as the noise-induced by the photovoltaic effect (Packer et al., 2013). We only fabricated the first four kinds of devices corresponding to the electrical field simulations, considering that the whole-shielding-layer scheme needs extra process steps which means higher cost, more difficult process and lower yield. Actually, the comparison of four kinds of devices is enough to illustrate our point of view.

The partial manufacturing process of the simplified optrode is shown in Figure 2B, and the detailed processes are as follows: 1) cleaning silicon wafers with silicon dioxide on the upper surface; 2) spinning coating photoresist (AZ4340) at 4,000 revolutions per second; transferring the patterns of μLED metal traces from the mask to the substrate by lithography; 3) metal deposition of Cr/Au/Cr with 5/100/5 nm thickness; 4) metal lift-off to get the patterned metal traces of the μLED; 5) depositing SiO2 with 100 nm thickness by PECVD; 6) repeating the above steps (2–5) to obtain the metal traces of the recording electrodes; 7) etching SiO₂ to expose the electrode areas and the back-end pads. After all the processes are completed, we diced the wafer to release the optrode shank and welded the shank to the PCB by gold wire bonding, then applied UV glue to the welding area to complete the optrode package.

Based on the packaged optrode devices, we constructed the test system to verify the shielding effect (Figure 2C). Given that we usually care about the interference near the spike frequency, the signal generator is used to apply a sinusoidal voltage (3 V, 2 kHz) to the μLED’s metal traces. A multi-channel neuron data recording system (HTRP-128, Blackrock Microsystems, United States) is used to record the interference potential on the electrodes. The two instruments need to be connected to the same ground wire, and the entire test system requires a well-shielded environment. We have designed two kinds of interfaces to connect the optrode and the multi-channel recorder. One is used for all types of optrodes, and the other is designed for wiring-above-anode and whole-shielding-layer to make the shielding layer above the anode ungrounded. The test was carried out in the air. We selected three devices of each type to test the interference potential on the electrodes. The experimental and simulation results are analyzed from multiple perspectives, including logical analysis, circuit modeling, derivation of equations, and FEM.

The 2D electrostatic field simulation results are shown in Figure 3A, and the potential distribution on the 2D section is visually represented. Compared with no shielding measure, it can be clearly seen that no matter which shielding measure is adopted, the potential of the recording electrode area is significantly reduced in the metal wire region. We can also see that the whole-shielding-layer has the best shielding effect, the combined-shielding is the second, and the wiring-above-anode is the worst.

While in the μLED structure region, the potential distribution results are much different from the metal wire region. First of all, a significantly lower potential distribution can be seen in the case of no shielding measure. We had assumed that the 10 mV voltage applied with the N-type layer is an interference source according to (Kim et al., 2016), but it is more like a shielding layer actually, pulling down the recording electrode potential. Secondly, the shielding effect of wiring-above-anode is extremely poor. It is designed for the μLED anode metal, and it does not have too much shielding effect on the N-type layer interference. What makes it worse is that the shielding layer cannot block the P-type interference. This also results in that the combined-shielding have a similar effect with the widening-cathode. Finally, the shielding effect of the whole-shielding-layer becomes worse. Due to the existence of the light-emitting area, the interference source below cannot be completely covered.

These differences can be observed from the time-domain simulation results more clearly, as shown in Figures 3C,D. In the time-domain analysis, a sine pulse signal of 1 Hz is inputted to the interference sources, represented with the blue line in Figures 3C–E for the anode and the black line in Figures 3D,E for the N-type layer. And then the recording electrodes potential which changes over time can be outputted in the software. Since there are eight electrodes in total, the average potential of these electrodes is used to represent the magnitude of interference. We can see that all the average potential changes with the excitation signal synchronously in both 2D simulation results. Furthermore, in the metal wire region, the effects of different shielding schemes are consistent with the electrostatic simulation results according to the numerical range of the average potential. The whole-shielding-layer has the lowest potential, the combined-shielding is slightly higher, and the wiring-above-anode is two orders of magnitude higher than them. While in the μLED structure region, the result is clearly different from the metal wire region, just as reflected in the electrostatic field simulation results. And it can be further seen that the combined-shielding has the best shielding effect, the widening-cathode and the whole-shielding-layer are almost the same, and the wiring-above-anode is the worst.

The huge differences in the 2D electric field simulation indicate that a single 2D simulation is not enough to represent the true spatial potential distribution in a non-uniform optrode device. Thus the 3D simulation is necessary. The 3D electrostatic field simulation results are shown in Figure 3B. It can be observed that the 3D potential distribution has both the characteristics of the metal wire region and the μLED structure region. For all the shielding measures, the shielding effect is the same order as the 2D metal wire region. While the electrode potential of no shielding measure is much lower, and the wiring-above-anode has little shielding effect, which is similar to the μLED structure region.

We can draw the same conclusions from the 3D time-domain result (Figure 3E). The wiring-above-anode is a little lower than no shielding measure in average potential, and they are close to the input voltage of the N-type layer. Although the average potential is consistent with the 2D metal wire region in order, it is different in the numerical range. This can be reflected in Figure 3F, in which we chose the peak value of the time-domain curves to compare the 2D and 3D results. We can further see that the 3D potential values are all between the metal wire region and the μLED structure region for each shielding measure. This is because the 3D simulation can be regarded as the synthesis of many 2D simulations, and it proves that the 3D simulation is more reasonable to be used in the optrode EMI analysis.

In the fabrication of the optrode, there are some important parameters that may influence the effect of the shielding layer. One is the process parameters, such as the thickness of the deposited metal layer and the center distance between the μLED metal layer and the electrode metal layer, which actually represents the thickness of the insulating layer between the two metal layers. The other is the layout design parameters, such as the width of the cathode, the width of the anode, and the edge-to-edge distance between the anode and the electrode region. Based on the 2D widening-cathode model, we have evaluated the impact of these parameters in detail and the result is shown in Figure 4.

In order to get a better shielding effect, the optrode needs to be designed with larger W₀ and D₁, smaller W₁, T, and D₀. But the precondition is to ensure the feasibility of the process, suitable device size, and stable device performance. Furthermore, we define the ratio of the average potential to these parameters as the significance to the shielding effect. We can see that D₀ (its “significance” is about 10 mV/μm) should be given priority compared with T (0.5 mV/μm) between the two process parameters. Similarly, the W₀ (110 μV/μm) is much more important than D₁ (24 μV/μm) and W₁ (56 μV/μm) during layout parameters.

A packaged optrode is shown in Figure 5A. We tested more than three times for each selected device, and the data recorded by the multi-channel system is averaged. The result is shown in Figure 5B. The recorded potential is reduced in the order of without shielding, wiring-above-anode, widening-cathode, and combined-shielding, proving the effectiveness of our designed shielding layers. We can also see the shielding effect by comparing the same optrode with different interfaces (Figure 5C). The average potential is obviously dropped after the shielding layer above the anode is grounded. There is no significant difference in potential values for the same type of device. Therefore, we averaged the values for each type and compared them with the 3D simulation result, as shown in Figure 5D. It is obvious that the variation trend of the experimental results is consistent with the simulation results under different shielding methods. This shows that the simulation results are effective for qualitative analysis. We can know whether the designed shielding methods are effective and which kind of shielding has a better effect through the simulation results.

Although the experimental and simulation results have the same trend, they are not consistent in quantity. In order to explain this difference, we constructed different circuit models corresponding to the simulation environment and the actual test environment. And firstly we found that the electrode potential observed in the existing simulation model is not the real interference potential on the recording electrode but the spatial potential at the location where the recording electrode is. The spatial potential (V_r) is dependent on the distance from the interference source, as shown in Figure 6A. It is related to the amplitude of the noise source (V_s) but has nothing to do with the frequency, which is not in coincidence with reality. While the real electrode interference is a kind of coupled voltage due to the distributed capacitance between the recording electrode and the μLED anode, as shown in Figure 6B. The larger the equivalent capacitance (C₁) is, the greater the coupled voltage (V_n) is. And it will become higher as the frequency (ω) increases. This relationship can be expressed as Eq. 1. V n = V s ⋅ Z 1 j ω C 1 + Z (1) where Z can be replaced by Z_a (a coupling capacitor between the electrode and the ground) in the air, and can be replaced by Z_p [a first-order R-C model of the electrode-electrolyte interface (Nathan and Jafari, 2015)] in the phosphate buffer saline (PBS). The shielding layer can just lower the V_n by reducing C₁, which can be reduced to zero under ideal circumstances.

The spatial potential and the coupled voltage are completely two different concepts. Under the same conditions, the former is much larger than the latter, which partly explains why the simulation result (whole-shielding with 550 μV is the best) in Figure 3 is much higher than the background noise (lower than 20 μV) of common neural recording systems. But there is a positive correlation between them. It is not difficult to understand that the higher the spatial potential is at a point, the greater the coupled voltage will be when a recording electrode is located there. To better illustrate this point, we studied the relationship between the width of cathode metal (W₁), the width of anode shielding metal (W₂), the spatial potential (U₀), and the coupling capacitance (C₀) which can represent the coupled voltage according to Eq. 1, based on the widening-cathode and the wiring-above-anode methods in 2D electric field simulation. It can be clearly seen from Figure 7 that there is a positive correlation between the spatial potential and the coupling capacitance. It means that when the shielding layer is widened, the spatial potential will decrease, and the coupling capacitance will become smaller, resulting in a lower coupled voltage. The result indicates that it is feasible to evaluate the effects of various shielding schemes by observing the spatial potential of the electrode area in software simulation, but it can only be qualitatively analyzed and cannot be quantified.

Another factor that causes the difference between the experimental and the simulation results is the interference from the outside of the optrode shank, such as the welding pads at the stern, the PCB, and the interface with the amplifier. These interferences can be represented as a coupling capacitor (C₂) in Figure 6C. The presence of C₂ will result in an increase in V_n, and there will be a lower limit for reducing V_n by shielding layer, which indicates why the experiment result is so high in Figure 4D. The relationship can be expressed as Eq. 2. V n = V s ⋅ Z a 1 j ω ( C 1 + C 2 ) + Z a (2) And these interferences can be reduced by a more reasonable back-end package and interface design. For example, we have designed a new PCB with a whole-shielding layer that can reduce the interference by more than 400 times (Figure 6D).

From the above analysis, it is not difficult to see the shortcomings of the current simulation model, that is, only qualitative analysis can be performed. Thus we constructed a quantitative simulation model according to Figure 6E. Here we firstly connect the recording electrode to an R-C model using the software’s circuit function, where the resistance (R) and the capacitance (C) can be obtained by the electrochemical impedance test of the electrodes. And secondly, we have considered the PBS environment by which the optrode is surrounded. This kind of conductive solution is difficult to use specific material to represent in the software. But considering that the solution is connected to the ground through a reference electrode, we can also simplify it to be a grounded R-C model which is applied to the model boundary. What’s different is that the resistance (R) and the capacitance (C) should be obtained from the reference electrode impedance, which is much smaller than the recording electrode.

The new quantitative simulation model is used to analyze the electric field interference in no-shielding and widening-cathode optrode, and the frequency-domain simulation result is shown in Figure 6F. It can be seen that the electrode potential is higher with the frequency increases, which is consistent with reality. When it is at 1 kHz, the interference potential under no shielding is about 70 μV, which is the same order with the amplitude of a spike. With widening-cathode shielding, the potential is reduced to about 20 μV, enough to meet the actual needs if the model parameters are reasonable. In addition, the time-domain simulation result (Supplementary Figure S2) shows that noise spikes appear on the recording electrodes when the input signal is flipped, which is similar to the actual situation. It also demonstrates the shielding effect of widening-cathode method. These results only show the feasibility of quantitative analysis to electric field interference in optrode, but the specific parameters and components of the simulation model still need to be perfected and its reliability needs to be verified by actual test using the new designed device with a more reasonable package and connection.

We not only analyzed the EMI inside the optrode caused by electrical field, but also considered the possible interference caused by magnetic field. As the term EMI describes, the interference of the electric field and magnetic field often exists at the same time under the action of the varied excitation signal. The magnetic field simulation results (Supplementary Figure S3) show that the magnetic field interference is much smaller than the electrical field interference. This may be due to the small footprint of the optrode device. According to our coil model, the potential at the ends of the induction coil (V_out) is related to the maximum magnetic flux in the coil (Ф), and the magnetic flux is a function of the magnetic field strength (B) and the area enclosed by the induction coil (S), namely: ø = BS (3)

Considering that the magnetic field strength (B) is proportional to the current passing through the excitation coil (I), when the input voltage is constant, the magnetic field strength is inversely proportional to the resistance of the input circuit (R). Thus we can derive that when the device footprint is scaled down by L times, the resistance (R) will increase by L times, the area (S) will be reduced by L² times, and the magnetic flux (Ф) will be reduced by L³ times. This means that the magnetic flux will drastically decrease as the device footprint shrinks. Therefore, the magnetic field interference can be ignored compared with the electric field interference for the small footprint optrode we designed.