Investigación de propiedades conductoras dependientes del tamaño en nanocables de Si individuales

Las imágenes actuales de Si NW con el sesgo de muestra de - 1,5 V con el mismo diámetro de 190 nm pero diferentes longitudes de a 350 millas náuticas, b 600 nm, c 800 nm y d 960 nm, respectivamente. Los perfiles actuales a lo largo de las líneas marcadas en a - d están trazados en e y f presenta las corrientes promediadas de los nanocables ( I _av ) en función de la longitud de NW. Las curvas del perfil en e se desplazan verticalmente como guía

Para verificar la inferencia anterior, se registraron curvas de corriente-voltaje (I – V) en Si NW individuales para investigar la barrera de Schottky en el contacto de la punta de metal / nanocable de Si. En la Fig. 6a se presentan las curvas I – V típicas en los Si NW con la misma longitud de 350 nm pero diferentes diámetros y en la Fig. 6b, respectivamente, las curvas de Si NW con el mismo diámetro de 190 nm pero diferentes longitudes. Todas las curvas I-V exhiben corrientes más grandes en la región de voltaje de muestra negativo, de acuerdo con las curvas I-V típicas con el contacto Schottky entre la punta de metal y el semiconductor tipo n. Como las curvas I-V exhiben buenas características de semiconductores de metal, indica que el efecto de la capa de oxígeno sobre la conductancia no es serio y, por lo tanto, se asume mínimo en la siguiente discusión. Mientras tanto, los resultados muestran que los nanocables más pequeños y más cortos exhiben una conductancia más grande que los más grandes y más largos, muy en consonancia con los resultados obtenidos a partir de las imágenes actuales. Para los análisis cuantitativos, se adopta un modelo de emisión termoiónica bien conocido para un contacto metal-semiconductor [58, 59]. En este modelo, las características I – V de un contacto Schottky con un semiconductor de tipo n en presencia de resistencia en serie se pueden aproximar como [59]:

Curvas I-V típicas en Si NW con la misma longitud de 350 nm pero diferentes diámetros ( a ) y el mismo diámetro de 190 nm pero diferentes longitudes ( b ). El recuadro en a muestra un resultado de ajuste típico de Si NW con un diámetro de 190 nm y una longitud de 350 nm. c y d representan las alturas de barrera de Schottky obtenidas a partir de los resultados del ajuste en función del diámetro y la longitud de NW, respectivamente

donde n es el factor ideal y R _S es la resistencia en serie. yo _S es la corriente de saturación, que se puede expresar mediante:

donde A es el área de contacto, A * es la constante de Richardson y φ _B es la altura de la barrera de Schottky (SBH) entre la punta de metal y el nanoalambre de Si. Así, SBH se puede obtener con la fórmula:

Las curvas I – V de la Fig. 6 ayb pueden ajustarse bien con la Ec. (1), y una línea de ajuste típica en la región delantera se muestra en el recuadro de la Fig. 6a. Para obtener los valores SBH de la corriente de saturación, se supone que la constante de Richardson efectiva A * es aproximadamente igual a la del silicio a granel, es decir, 112 A cm ^{- 2} K ^{- 2} para silicio de tipo n [59]. Se supone que el área de contacto es 2 × 10 ^{- 11} cm ² tomando el radio de la punta recubierta de Cr / Pt como 25 nm. Los valores de SBH se obtienen en aproximadamente 322, 359 y 377 meV para los Si NW con la misma longitud de 350 nm y diferentes diámetros de 190, 260 y 350 nm, respectivamente. Para Si NW con el mismo diámetro de 190 nm y diferentes longitudes de 350, 600, 800 y 960 nm, los valores de SBH son 322, 425, 473 y 495 meV, correspondientemente. A modo de comparación, la curva I – V típica se midió en el mismo tipo de oblea de Si, como se muestra en el archivo adicional 1:Figura S3 (a). Muestra claramente que la conductancia de la oblea de Si es mucho menor que la de los NW producidos. La corriente detectable solo se puede medir con voltajes de polarización altos (- 4 ~ - 10 V). Después de ajustar las curvas I – V con el modelo de emisión termoiónica anterior (archivo adicional 1:Figura S3 (b)), se obtuvo un valor SBH de 0,60 eV para el Si a granel. Obviously, all of the measured SBH values for Si NWs with different diameters and lengths are smaller than that of the bulk Si. Similar Schottky barrier lowering in nanowires has been reported by different groups on different types of nanowires, which was attributed to the carrier recombination in depletion region [46, 60], barrier inhomogeneity and Joule heating effect [48], or image potential lowering [47]. In our case, the barrier lowering can be also attributed to the large density of surface states induced image potential lowering and carrier charging in depletion region.

The dependence of SBH values on nanowires’ diameter and length is plotted in Fig. 6 c and d respectively, and it can be found that the SBH increases obviously with the increasing of both nanowires’ diameter and length. In addition, the same measurements were done on Si NWs with different diameters of 260 and 350 nm for all lengths, and the I–V curves are shown in Additional file 1:Figure S4 a and b, respectively. The obtained diameter-dependent SBH values from curve fitting for all lengths are listed in Table 1 and plotted in Additional file 1:Figure S5. The results show that the SBH values increase with increased diameter for all lengths, and also increase with increased length for all diameters. Therefore, the results obtained from the I–V curves analyses suggest that the Schottky barrier lowering is more significant for the nanowires with smaller diameters and shorter lengths. On the other hand, the ideal factor n and series resistances R s of Si NWs with different diameters and lengths can also be obtained from the fitting results, as listed in Table 1. The results show that n is much larger than 1 for all nanowires (2.8 ~ 9.4), indicating that the contact between the tip and nanowire is not ideal metal-semiconductor contact, probably due to the existence of oxide layer. On the other hand, the R s increases with increased diameter as well as increased length. For example, R _S increases from 6.1 to 21.6 MΩ as the diameter increases from 190 to 350 nm for the same length of 350 nm and increases from 6.1 to 32.3 MΩ for the length from 350 to 960 nm with the same diameter of 190 nm. The increase of R s with increased length is reasonable, while that increase with increased diameter is out of expectation. There is no good explanation for it at present, which may because that the series resistance is not simply the resistance of nanowire and the effective tip-nanowire contact area is not exactly equal to the nanowire’s sectional area. Nevertheless, the series resistances of Si NWs did be much smaller than the contact resistances, therefore the conductance of Si NWs should be dominated by the SBH determined contact resistance.

The origin of the size-dependent SBH is not very clear yet. The mechanism explanation for similar diameter dependence of SBH has been supposed in several literatures [45,46,47,48, 60]. For example, Leonard et al. interpreted this effect with the point of electron-hole recombination in depletion region [60]. As the recombination time decreased as the nanowire diameter was reduced, current density increased with decreasing nanowire diameter. Yoon et al. explained the diameter-dependent SBH using the presence of interface states [47]. Mao et al. attributed its origin to barrier inhomogeneity and Joule heating effect [48]. In our case, the Si NWs are made by the MACE method, so there inevitably exist an amount of defects on the surface and a reformed thin oxygen layer, resulting in a large density of surface states. Actually, from the enlarged SEM images and AFM observation, the top surface of Si NWs is very rough, further increasing the density of surface states. We think the presence of surface (or interface) states should be the main cause of the diameter dependence of SBH. According to previous literatures [47, 61, 62], the SBH lowering was interpreted by charged interface states. By adopting the cylindrical coaxial capacitor model used in reference [47], interface state–induced carrier transfer will form two opposite charged layers (metal and semiconductor contact surface) which generates an electric field opposite to the built-in electric field and lowers the barrier potential. As the surface state density increases with decreased nanowire diameter, smaller SBH is obtained on nanowires with a smaller diameter. Why the values of SBH related to the nanowire length is not clear yet. As the MACE time increased, the surface disorder or roughness increases correspondingly. Different changes in the surface microstructures may introduce different changes of SBH values, which need further investigations to work it out. Anyway, whatever the origin of size dependence of conductive properties, the size-dependent SBH lowering could result in higher conductance, which should be beneficial for practical applications.

EFM Measurements on Single Si NWs

To further verify the size-dependent SBH results of Si NWs obtained by CAFM, the EFM measurements were performed on the same samples and the EFM phase shift was measured as a function of applied DC bias. In previous literatures [63, 64], the relation between phase shift and electrostatic force has already been established, where the tip-sample system is roughly treated as a plane capacitor. When a bias is applied between the tip and the sample, the capacitive electrostatic force gradient would cause a phase shift. At a lifted height where the Van de Waals force can be ignored, the electrostatic force acted on the tip can be expressed as [63]:

donde C , V _EFM y V _CPD are the capacitance, applied DC voltage and contact potential difference (CPD) between the sample and tip, respectively. V _CPD can be written as (φ _sample − φ _tip )/e when the bias voltage V _EFM was applied to the sample in our experiments. The phase shift detected by EFM is proportional to the gradient of the electrostatic force, which can be written as:

where Q is the quality factor, k is the spring constant of the probe and z is the distance between tip and top of Si NW.

De la ecuación. (5), it can be seen that the EFM phase shift should be equal to zero at V _EFM = V _CPD . Therefore, V _CPD can be achieved from the EFM measurements. The ΔΦ ~V _EFM curves measured at a lift height of 100 nm on the individual Si NWs with different diameters and lengths are shown in Fig. 7 a and b as the scattered dots, respectively. By using Eq. (5), the ΔΦ ~V _EFM curves can be fitted well, shown as the solid lines in Fig. 7 a and b. From the fitting parameters, the values of V _CPD can be obtained, as presented in Fig. 7 c and d as a function of diameter and length respectively. The results show that the CPD values increase with increased diameter and increased length. Similar CPD results have been reported in a previous work performed by Kelvin probe force microscopy on ZnO NWs, in which the absolute value of CPD between ZnO nanowire and Pt/Ir tip also increased with increased diameter [65]. As diagrammed in Additional file 1:Figure S6, the value of SBH roughly equals to qV _CPD plus E _n (=E _C − E _F ). As E _n is a constant for all Si NWs made from the same material, the size dependence of V _CPD well represents the size dependence of SBH. Therefore, from the EFM results, it can be suggested that, the SBH values increase with the increasing of NWs’ diameter and length, well consistent with the results achieved by CAFM measurements. Similarly, the EFM measurements are performed on all series of Si NWs, and the diameter-dependent V _CPD values at different lengths are shown in Additional file 1:Figure S7(a) and (b) respectively, which exhibit same diameter dependence as that obtained by CAFM.

∆Φ ~ V curves measured by EFM on individual Si NWs with a different diameters of 190, 260, and 350 nm (length = 350 nm) and b different lengths of 350, 600, 800, and 960 nm (diameter = 190 nm). c y d present the V _CPD values obtained by curve fitting as a function of NWs’ diameter and length. The curves in a y b are vertically shifted for guidance