Influence of Surface States on Electronic Band Structure and Electron Density in InAs Nanowires and InAs Shell Nanowires

Semiconductor nanowires are recently of special interest due to the strong electron confinement in their one-dimensional structure, which, in turn, implies easily tunable transport properties of charge carriers. This is especially important for use of nanowires in electrical sensing devices as well as field-effect transistors. High surface-to-volume ratio typical for nanowires leads to strong dependence of their electrical properties on surface states. The quantum confinement of the charge carriers in nanowires might be even more strengthened due to manufacturing shell nanowires via the chemical etching of a core in core-shell structures [1]. The higher confinement in the shell nanowires in comparison to typical nanowires implies also higher surface-to-volume ratio, thus even stronger impact of surface states on electronic band structure and electron population of the shell structures.    

Here, we report on a theoretical study of impact of surface states on the electron band structure and electron density in intrinsic cylindrical InAs nanowires and InAs shell nanowires (Fig., inset). For the calculation of the electron conductivity, we describe the density of the surface states as a function of energy by the U-type dependence with the minimum corresponding to the neutrality level at the surface. We assume that in accordance with the experimental data for surface of bulk InAs presented in [2] the neutrality level is located about 160 meV above the conduction band edge. We calculate the band structure of the conduction band by the self-consistent solution of Poisson and Schroedinger equations in cylindrical coordinate system where the Schroedinger equation is solved for the envelope functions within the effective mass approach.

We show that for both nanowires and shell nanowires the conduction band bending and electron density in the nanowires are strongly affected by the charged surface states at both low and room temperature. Due to the location of the neutrality level above the conduction band edge the conduction band in both nanowires and shell nanowires is bent downwards at the surface giving rise to the formation of the electron accumulation channel at the surface (Fig., inset). The conduction band bending increases with increase of total density of surface states and for the density exceeding 10¹² cm^-2 the band profile remains almost without changing. Then, Fermi level at the surface in both types of structures is pinned in the vicinity of the neutrality level. The electron density in both nanowires and shell nanowires increases with increase in the total surface states density due to the donor-type states delivering electrons in the structures. The electron density reaches its maximum value for the surface states density above 10¹² cm^-2.  The figure displays that for the total density of surface states above 10¹² cm^-2 intrinsic nanowires and shell nanowires show significant two-dimensional electron density which increases with the external nanowire radius. Donor-type states of the internal surface in shell nanowires introduce additional electrons into the structure volume, thus increasing their two-dimensional electron density in comparison with conventional nanowires, This does not hold only for shell structures with the shell thickness below 15 nm which are less populated then the nanowires due to the strong electron confinement. The study delivers criteria for development of a building block for tube-like electrical devices.

Fig.:  Two-dimensional electron density vs external radius InAs nanowires (symbols) shell nanowires (solid line) with the shell thickness of 10, 20 and 30 nm at 300 K and the total surface states density above 10¹² cm^-2; inset: sketch of InAs nanowire and shell nanowire and their band structure.

[1] T. Rieger et al. Nano Lett. 12, 5559 (2012).  

[2] H. Hasegawa and T. Sawada, J. Vac Sci. Technol. 21, 457 (1982).