However, these results are not accordance with the increment of qB in the printed SBDs, because the qB is theoretically inverse proportional to the work function of the Ag electrode. As previous reports, it is exemplified that the work function of AgNP is higher than that of bulk Ag metal from both theoretical and experimental results. Therefore, the increment of work function strongly indicates that AgNPs exist on the Ag electrode surface contacting to the p-Si, in which the existence of AgNPs is also implied from surface roughness. Furthermore, free electrons possessed by a metal nanoparticle should be depleted easier than bulk metal. The supply of electron to the outer AgNPs on the Ag electrode surface cannot keep up with the demand for conduction if electron mobility is limited in the sub-nanometer to micrometer scale in the printed Ag electrodes. Thus, the increment of barrier height can be expressed qualitatively by the depletion of the electrons at the Ag/p-Si interface due to the existence of AgNPs on the Ag electrode surface. Considering Schottky barrier diode, the charge transfer occurs between metal and semiconductor, and then a depletion contact is formed at the interface of metal/semiconductor contact. For contacts on semiconductors, the depletion-layer width, W is given by where , bi, q, and Nd are permittivity of semiconductor, builtin potential, electronic charge and doping density of semiconductor, respectively. Using built-in potential , Schottky barrier height, B is given by