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El juicio de igualdad frente a la aplicación de la norma de forma

CAPÍTULO VI: LOS JUICIOS DE IGUALDAD UTILIZADOS EN LA

6.1. Examen de igualdad utilizado por la jurisprudencia de la Corte IDH

6.1.2 Casos analizados en función de la obligación estatal de garantía (igualdad

6.1.2.2 El juicio de igualdad frente a la aplicación de la norma de forma

Before evaluating the coupling effect between magnetic field and piezotronic effect, the ZnO NW array was first tested under magnetic field. The current-voltage (I-V) characteristics are

illustrated in Figure 5.3a. The rectifying property of the I-V curves indicated that a Schottky barrier was formed between ZnO NWs and Ag electrode. It can be observed that the peak currents of ZnO decreased from 3.0 µA to 2.1 µA as the external magnetic field increased from 0 to 180 Gauss (G). A part of the free electrons inside ZnO NWs were forced to move toward the surface of ZnO NWs due to Lorentz Force, hereby forcing a part of free electrons to gravitate toward the surface of ZnO NWs due to Lorentz Force caused by the magnetic field. According to oxygen-related electron-trap filling mechanism,32 the electrons were trapped by the surface defects or adsorbed by oxygen ions in air as presented in region I of Figure 5.3f, therefore, the number of free electrons was reduced , resulting in an increment of the resistance of ZnO NW. Besides, the electron accumulation at the ZnO NW surface generated a depletion region near the surface of ZnO NWs, which further increased the resistance of ZnO NWs. It should be noted that the peak current of ZnO is inversely proportional to the magnetic field strength, because the number of the trapped/accumulated electrons at the surface of ZnO NW become larger as the magnetic field strength increased, resulting in a decrement of the conductivity of NW. In order to

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investigate the coupling effect between piezotronic effect and magnetic field, the ZnO NW array was measured with stresses from 0.5 N to 1.5 N as indicated in Figure 5.3 b, c and d. It can be observed that the peak current significantly increased with an increment of the stress due to piezotronic effect. According to a previous report,33 potential barrier height modulation generally makes more significant contribution to current response than depletion layer modulation, therefore, we believe that the enhancement of the peak currents is mainly due to the strain- induced piezopotential inside ZnO NWs (region II of Figure 5.3f). When the force was applied to the NW, the NW was bent due to its randomly growing direction and then the strain-induced positive piezopotential was generated at the surface of ZnO NW which lowered the Schottky Barrier Height (SBH) between ZnO and Ag, resulting in a significant increment of the peak current. The magnitude of the piezopotential is dependent on the degree of mechanical deformation, thus highest peak current is gained at 1.5 N stress, and the peak currents with 1.5 N stress in both the absence and presence of magnetic field are at least one order of magnitude higher than that with 0 N stress. The piezotronic effect enhanced peak currents also decreased by applying a magnetic field. The magnetic-induced peak current differences (∆𝐼 = 𝐼𝐵− 𝐼0, where

𝐼𝐵 and 𝐼0 are the peak currents with and without magnetic field, respectively) of ZnO NWs with different magnetic field strength and stresses are summarized in Figure 5.3e, and it can be observed that the peak current differences are magnified as the magnetic field strength and stress increased. The absolute peak current difference (10.1 µA) with 1.5 N stress is 10 times larger than that (0.9 µA) with 0 N stress, which demonstrates that the piezo-magnetotronic effect can enlarge the magnetic-induced current response.

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Figure 5.3 I-V characteristics of ZnO NWs device under (a) 0 N (b) 0.5, (c) 1 and (d) 1.5 N stress. (e) The summary of the peak current difference of the device under various stresses. (f) Schematics of energy bands alignment and electron movement under magnetic field which is directed perpendicularly out of the screen.

To further demonstrate the piezo-magnetotronic coupling effect and improve the magnetic-induced current response, we designed further experiments by fabrication of the ZnO/Co3O4 core/shell NW array. Figure 5.4a illustrates the I-V curves of ZnO/Co3O4 NW array

in absence of stress under magnetic field. Compared to the I-V curves of ZnO device in Figure

5.3a, it can be observed that the magnetic-induced peak currents of ZnO/Co3O4 decreased from

9.9 µA to 4.8 µA as the magnetic field increased from 0 to 180 G. The absolute peak current difference (5.1 µA) is 5 times larger than that (0.9 µA) of ZnO because of the precipitation of Co3O4 and its rough surface, which created crystallographic defects at the ZnO/Co3O4 interface

due to the lattice mismatch between the two materials, and provided preferential adsorption site for oxygen molecules (region I of Figure 5.4f), compared to the smooth surface of ZnO NWs. The ZnO/Co3O4 NW array was then measured with different stresses from 0.5 N to 1.5 N

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the force was applied to the core/shell NWs, the core ZnO NWs were bent and the strain-induced positive piezopotential lowered the SBHs of ZnO/Co3O4 and Co3O4/Ag (region II of Figure 5.4f)

which resulted in a large increment of the peak current of ZnO/Co3O4 NW array. When it’s

measured under magnetic field, more electrons were forced by the magnetic field to move towards the surface resulting in a large decrement of peak currents. All the peak current differences of ZnO/Co3O4 NW array are summarized in Figure 5.4e, and it can be seen that the

absolute peak current difference (91.8 µA) of ZnO/Co3O4 NW are 9 times larger than that (10.1

µA) of ZnO NW array under the same conditions due to the significant increment of current the core/shell structure, which proves the core/shell heterostructure is capable of enhancement of the magnetic-induced current response.

Figure 5.4 I-V characteristics of ZnO/Co3O4 NWs device under (a) 0 N (b) 0.5, (c) 1 and (d) 1.5 N stress. (e) The

summary of the peak current difference of the device under various stresses. (f) Schematics of energy bands alignment and electron movement under magnetic field which is directed perpendicularly out of the screen.

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