Surface passivation method for semiconductor nanostructures

A common problem in modeling the electronic structure of quantum dots is the construction of a passivating agent, which can be used to render the surface of the dot electronically inert. We demonstrate that fictitious, “hydrogenlike” pseudoatoms may be used for surface passivation for II-IV and III-V semiconductor nanostructures. Using pseudopotentials constructed within density functional theory, we provide a recipe for the construction of these passivating atoms and provide physically motived criteria for obtaining an optimal passivation. To establish the validity of this approach, we apply our procedure to passivate GaAs quantum dots.

Figure 1

Ionic potentials for hydrogen and fictitious hydrogens ${\mathrm{H}}^{*}$ with a nuclear change $Z$ of 0.75 and 1.25. The pseudopotentials were generated using a radius cutoff of 1.5 a.u.

Figure 2

Calculated charge density $\left(\mid \psi {\left(\mathbf{r}\right)}^2\mid \right)$ for ${\mathrm{Si}}_{130}{\mathrm{H}}_{98}$: (a) HOMO and (b) LUMO.

Figure 3

(Color online) HOMO-LUMO gap of ZnSe and GaAs quantum dots, $E_g$, as a function of fractional charge $\eta$. Surface II (or III) and VI (or V) atoms of each dot are rebonded with fictitious hydrogens ${\mathrm{H}}^{*}$ with nuclear charges of $1+\eta$ and $1-\eta$, respectively. The maximum gap for the same value $\eta$ for different dot sizes.

Figure 4

Calculated charge density for ${\mathrm{Ga}}_{65}{\mathrm{As}}_{65}{\mathrm{H}}_{98}^{*}$: (a) HOMO and (b) LUMO. Ga, As, and fictitious hydrogen atoms are represented by large dark circles, large gray circles, and small circles, respectively.

Figure 5

Calculated contour plots of valence charge density for (a) ${\mathrm{Si}}_{130}{\mathrm{H}}_{98}$ and (b) ${\mathrm{Ga}}_{65}{\mathrm{As}}_{65}{\mathrm{H}}_{98}^{*}$ quantum dots.

Figure 6

HOMO-LUMO gap $E_g$ as a function of the GaAs dot diameter $D$. The horizontal dashed line indicates the calculated gap for bulk GaAs in the zinc blende structure.

Figure 7

Calculated DOS’s of GaAs quantum dots with surface passivation, comparing with bulk. A Gaussian function of 0.05 eV was used for finite broadening. Calculations for bulk were done with a $12\times 12\times 8$ Monkhorst-Pack $k$-point mesh (Ref. 11) and an energy cutoff of $\sim 25\mathrm{Ry}$.

Figure 8

Calculated charge density for ${\mathrm{Ga}}_{65}{\mathrm{As}}_{65}{\mathrm{H}}_{98}^{*}$ with levels located at (a) 7.93 eV (b) 6.37 eV below the “valence band” edge (HOMO). Ga, As, and fictitious hydrogen atoms are represented by large dark circles, large gray circles, and small circles, respectively.

Figure 9

Calculated DOS’s of passivated GaAs quantum dots: (a) Ga-centered ${\mathrm{Ga}}_{19}{\mathrm{As}}_{16}{\mathrm{H}}_{36}^{*}$; (b) As-centered ${\mathrm{Ga}}_{19}{\mathrm{As}}_{16}{\mathrm{H}}_{36}^{*}$; (c) Ga-As bond centered ${\mathrm{Ga}}_{19}{\mathrm{As}}_{19}{\mathrm{H}}_{42}^{*}$.