The effect of electrode shape on Schottky barrier and electric field distribution of flexible ZnO photodiode

In this study, the effect of electrode shape difference on the height of the Schottky barrier and the electric field in flexible photodiodes (PDs) has been investigated. For this purpose, three different electrode designs were prepared on three flexible FR4 layers that were coated with Zinc Oxide (ZnO). The printing circuit board (PCB) method was used to create these copper electrodes. The asymmetry of the PD electrodes and the difference in the height of the Schottky barrier has led to the creation of self-powered PDs. The effect of the amount and shape of the distribution of internal electric fields generated in the PDs and its effect on the parameters of the PDs has been investigated with the help of simulations performed in COMSOL software. The photocurrent of the sample with circular and rectangular electrodes was equal to 470 µA in 15 V bias, which was twice as good as a sample with an interdigitated MSM structure. Also, this sample had the best response time among these three samples, which was equal to 440 ms.


Experimental
To prepare the samples, ZnO was coated on the FR4 fiberglass substrate using an RF Sputtering at ambient temperature. The FR4 fiberglass was a flexible substrate with a thickness of 0.15 mm.
ZnO disk with a diameter of 2 in. (99.99%) was used as the target, and the target-substrate distance was 10 cm. During the deposition, the sputtering power was set at 150 W, and the Argon pressure was 20 (mTorr). The deposition time was 1945 s, and the thickness of the ZnO layer deposited on the fiberglass substrate was about 700 nm. The electrodes were printed on the samples using the PCB method. To apply this method, we plotted the shape of the electrodes using Protel software, and the negatives of the design were prepared.
Then the negatives were inserted into the PCB machine for printing. These printed electrodes are made of copper with a thickness equal to 35 µm. In this method, hundreds of samples with different electrode shapes can be prepared at the same time. The structure of these PDs was MSM, where the electrodes were provided in different geometric shapes (Fig. 1).
The ZnO layer crystalline properties and its morphology were obtained using the X-ray-Diffraction (XRD) (Fig. 2) and the Scanning Electron Microscope (SEM) (Fig. 3).
SEM images of ZnO's thin layer with the fiberglass substrate show the ZnO layer's porosity (Fig. 3). As can be seen, the porous layer is well-formed. A porous layer is used since other studies have shown that porosity can benefit detector parameters [28][29][30][31] .  www.nature.com/scientificreports/ The work of porous ZnO in the PD can show that the porous vacant in the ZnO layer trap neutral oxygen and increase the response rate due to the neutral oxygen implanted in the grain boundaries in a porous ZnO 32 . The high UV photoelectric response can also be attributed to the high specific surface area. The optoelectronic response performance of ZnO nanomaterials is usually based on their surface state, which causes the upward band to bend close to the surface and trap holes 30,37 . In the dark condition, oxygen molecules absorb ZnO nanomaterials' surface and deplete electrons, creating a thin depletion layer with low electrical conductivity. Electron-hole pairs are created by UV illumination. The holes move to the ZnO surface due to the bending band and discharge of the adsorbed oxygen molecules, leading to the aggregation of electron concentrations and increasing the electrical conductivity. This particular structure increases absorption. This specific surface area also causes response quickly to the applied light illuminated to the ZnO surface.
In other words, the effect of oxygen is that it captures free electrons in dark conditions and trap holes in illumination, increasing the life cycle of photogenerated carriers and improving the photoelectric response performance of ZnO porous films 30 .
In addition to this, in the SEM image, the electrodes and the ZnO layer exist together, which means the electrodes are well arranged on the substrate (Fig. 3a).  www.nature.com/scientificreports/ Samples 1 and 2 have a special photovoltaic property in 0 V bias due to the electrodes' asymmetry, and both specimens can be called self-powered PDs 15 . To explanation this, the height of the Schottky barrier was calculated 24 . In general, in a Schottky contact, if the E 00 < < K B T, the thermionic emission overcomes the junction electronic transport process without tunneling, where K B is the constant of Boltzmann, T is absolute temperature, │ E 00 │ is the energy-dependent on the probability of tunneling [38][39][40][41] . E 00 can be calculated using Eq. (1): where q is the elementary charge, ћ is the reduced Plank constant, N is the carrier density, m * is the effective mass, and ε s is the relative dielectric permittivity. In this work, m e = 0.27 m 0 , and ε s = 8.3 for ZnO, and the carrier concentration N is about 9.3 × 10 16 cm -3 . E 00 is about 2.2 meV for the ZnO films, much smaller than the thermal energy K B T at room temperature (26 meV). Thus, the current passing through the Schottky barrier can be described as follows: www.nature.com/scientificreports/ where K B is the Boltzman constant, T is the absolute temperature, n is the ideality factor, A is the junction area, A * is the Richardson constant (A * = 4пm * q 2 /h 3 ), ɸ B is the barrier height, h is the Plank constant, and I 0 is the reverse saturation current 24 . The flow passing through the Schottky barrier's height is obtained in a metal-semiconductor contact Eq. (2). Equation (2) can also be rewritten as follows: After calculating I 0 for each connection, the value of I 0 is placed in Eq. (3), and the height of the Schottky barrier ɸ B for each metal-semiconductor connection is obtained. For each of the PDs, the Schottky barrier's height was obtained corresponding to each one and is given in Table 1. The value of I 0 was obtained for each electrode-ZnO connection using MATLAB software from diagram of. Figure 7 shows a view of MATLAB software and the calculation of I 0 . P 2 in Fig. 7 is Ln(I 0 ).
Based on the energy band theory, the energy band diagrams for samples 1,2 under both dark and UV light illuminated conditions are analyzed and illustrated in Fig. 8a and b,c, respectively. In the dark, the Fermi energy levels (E F ) of ZnO and the electrode are equal. According to the theory calculations [43][44][45] , the width of the depletion region on the Cu (big)-ZnO interface must be greater than the width of the depletion region on the Cu (small)-ZnO interface. Under ultraviolet light, electron-hole pairs are generated on ZnO's surface, as exhibited in Fig. 8b. The electrons in the conduction band (E c ) tend to flow away from the metal-semiconductor interfaces, and the holes in the valence band (E v ) move towards the contact. Collected and trapped holes create a local potential in the interface so that the effective height of the Schottky barrier decreases due to the difference in the width of depletion region between Cu (big)-ZnO and Cu (small)-ZnO, and asymmetric distribution of electric potential in ZnO film can induce the difference in separation and transfer of carrier. Since the number of collected and trapped holes in the two interfaces, which reduces the height of the Schottky barrier between two electrodes of Cu (big)-ZnO and Cu (small)-ZnO, which because the number of holes in The Cu (big) -ZnO interface is larger, so the Schottky barrier height reduction is greater (Fig. 8c) 46 . As a result, typical photovoltaic specifications can be seen in asymmetric MSM PDs at a bias voltage of 0 V (samples 1,2). It is worth noting that the change in the height of the barrier is highly dependent on ZnO's electrical properties and the Cu electrodes' structure, which can determine the local potential 16  www.nature.com/scientificreports/ When a bias voltage is applied between two electrodes, an electric field is created and causes the charge carriers to move, which leads to the production of current. The difference in the electrodes' shape leads to the difference in the electric field's shape and amount. As a result, the dark current (Fig. 4a), photocurrent (Fig. 4b) and response time (Fig. 5) also vary. To show the influence of an electric field in the organization of electric charges, the electric displacement field is defined 51 :   www.nature.com/scientificreports/ where ε 0 is the vacuum permittivity, ε r is the relative (dielectric) permittivity, and E is the electric field. The question arises that we do not have the values ε 0 and ε r . What should we do? The answer is that since ε 0 and ε r are related to the material, and all three of our samples are the same material, therefore ε 0 and ε r are the same for all three of our samples, And because our work is comparative, the amount does not matter to us. Based on Eq. (5), the difference in E leads to the difference in D. We used COMSOL Multiphysics software to obtain the electric displacement field, electric field, and total electric energy. As mentioned, the amount of current caused by charge carriers' movement is directly related to the electric field (E) and the electric displacement field (D).
The electric field and electric displacement field simulation results at 15 V bias and total electric energy are given for all three samples (Fig. 9). Electric current results from electric charge movement around a circuit, but to move an electric charge from one electrode to another, there needs to be a force to create the work to move the electric charge. The total electric energy is defined: J is the total electric energy, V is the voltage, and C is the electric charge. The total electric energy at the same voltage for these samples was as follows (Fig. 9c,f,i):  www.nature.com/scientificreports/ As seen in Fig. 9, The order of the maximum of the E (V/m) and the D (C/m 2 ) at bias 15 V are as follows: In the dark, the issue of the Schottky barrier and local potential difference is not raised. In Table 1, dark current (µA) at bias 15 V: In general, current means the movement of charge carriers regardless of what is due. According to the statements, the greater the electric displacement field that causes the carriers to move, the greater the current.
As a result, it can be seen that the simulation confirms our experimental data. Under illuminated, in addition to the electric field, the local electric potential, which is caused by the electrodes' asymmetry, is also involved. As a result, these two factors must be considered together. Our experimental results, the highest electric current under illuminated in sample 1, exceeded it in sample 3. As we learn from the basic concepts of electromagnetism, the electric field is more intense at the sharp points. As a result, the electric field's intensity in those areas is more intense can see in Fig. 9a,b; at the corners of the rectangular electrode, the density of electric field lines is higher. As a result of both the shape and the amount of electric field, as well as the asymmetry of the electrodes and the creation of a local potential difference, illuminated current (µA) at bias 15 V for PDs are: The local potential difference due to the electrodes' asymmetry creates an electric field that helps compensate for the smaller electric field amount in sample 1 compared to sample 3. As a result of these two factors, sample 1 surpass sample 3. In sample 2, because its field is much smaller than samples 1 and 3 (therefore, it has the lowest amount of dark current) and its local potential difference due to the electrodes' asymmetry could not compensate, so it is observed. Which also has the lowest amount of current under illuminated.
Also, the responsivity of a PD provides information related to the generation of a photocurrent per unit incident UV power on a PD. Moreover, the specific detectivity defines the information associated with the ability to detect a weak UV illumination by a PD. In general, the specific detectivity of a PD is related to its noise. The responsivity and specific detectivity were measured as follows 52 : where e is the absolute value of elementary charge and A o is the UV signal exposed area.
The responsivity for samples 1,2 and 3 in the wavelength 365 nm is equal to, respectively 1.2, 0.05 and 0.53 AW -1 at a bias voltage of 15 V. Also, specific detectivity for them in the same conditions is equal to, respectively 5.77 × 10 11 , 3.2 × 10 10 and 9.5 × 10 10 Jones. These data also show the superiority of sample 1 among other samples.
For response time, photogenerated carriers move faster with a drift speed due to the electric field, which improves the photon flow and causes higher response speeds. The point is that for the response time because there is illuminated, due to the Schottky barrier and the local potential difference is also involved, the response time (ms) at bias 5 V for these PDs is: In short, if only the difference between the Schottky barrier is considered, sample 2, sample 1, and finally sample 3, respectively, had the largest difference (using MATLAB software). If only the shape and amount of electric field are considered, the maximum value should be for sample 3, then sample 1, and finally sample 2 (with COMSOL multiphysics software). While both of these factors must be considered together, and when both are considered together, it can be seen that in sample 1, a difference in the Schottky barrier leads to local potential and thus to a local electric field. It can be prepared with the help of the main electric field and surpass the photocurrent of sample 1 from sample 3. In sample 2, because the electric field amount was much lower, this local electric field could not compensate for this shortage.

Conclusion
In this study, the effect of electrode shape on the parameters of flexible UV PDs based on porous ZnO on the fiberglass (Fr4) substrate was investigated. It was observed that the difference in the height of the Schottky barrier could be the basis for the creation of self-powered PDs. Also, the shape of the electrodes affects the amount and shape of the electric field created, which is the transfer factor of the charge carriers, which leads to a change in the output current of the PDs. Among these 3 PDs, which were fabricated simultaneously using RF sputtering and PCB techniques, sample 1 was the best in the current at 0 V (0.8 µA), the photocurrent (at 15 V = 470µA) and the response time (440 ms). From experimental data and information obtained from computing and simulation software (MATLAB and COMSOL Multiphysics), it can be concluded that the output currents of the PDs in illuminated are related to the difference of potentials and electric fields created. These samples are different www.nature.com/scientificreports/ in two ways: first, the difference in local potential due to the difference in the height of the Schottky barrier, and second, the difference in shape and amount of electric field due to the difference in the shape of the electrodes. Between these 3 PDs, sample 1 with two circular and rectangular electrodes showed the best performance under illuminated conditions (both at 0 V and in bias mode).