Workfunction Polarization or Entrapment

Bond contraction deepens the interatomic potential well and enhances the charge density in the relaxed surface region. The locally confined electrons near the 

The total number of electrons Ng of a nanosolid conserves. At the lower end of the size limit of a spherical or semispherical dot (/f 1 nm, t = 3), the average bond length is around 80 % of that in the bulk, and hence, the O will reduce from the original value by 30 % (Ep shifts up by 0.8 — 1), according to Eq. (16.12). 

The 1 of Na particles around 0.4—2.0 nm size varies inversely with the size R and lowered from the bulk value of 2.75 to 2.25 eV (by 18 %) [94]. Carbon nanotubes have a 1 of 4.6-4.8 eV at the tips, which is 0.2-0.4 eV lower than that of carbon (graphite) bulk. A small fraction of the nanotubes have a I value of 5.6 eV. This discrepancy results from the metallic and semiconductive characteristics of the nanotubes. The average of porous Si increases as the crystalline size decreases because of etching the impurity Si-H, Si-O, and Si-H-O bonds at the surface [95]. 

Amorphous carbon (a-C) films have a uniquely intrinsic stress ( 12 GPa) that is almost one order of magnitude higher than those found in other amorphous materials such as fl-Si, a-Ge, or metals ( 1 GPa) [98]. Applying pressiue to a material, one can modify its electronic properties, e.g., band structure, resistivity, work function, due to the stress [99]. Poa et al. [98, 100] found a correlation between the stress and the threshold field for electron emission, as shown in Fig. 16.14. 

The mechanism for the external pressure lowered is different from that of the intrinsic stress though the effects are the same. The intrinsic compressive stress increases the charge density and raises the resistivity because of the entrapment, whereas the external stress pumps the N(E) up and raises the conductivity by polarization. This mechanism is in accordance with observations that the resistivity of an as-grown nanostructure increases with the inverse of solid size but, under stretching, the electrical conductivity remains comparable to that of bulk copper [106, 107]. 

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