Quantum confinement and band offsets in amorphous silicon quantum wells

Quantum wells (QWs) are nanostructures consisting of alternating layers of a low and high band-gap semiconductor. The band gap of QWs can be tuned by changing the thickness of the low band-gap layer, due to quantum confinement effects. Although this principle is well established for crystalline materials, there is still controversy for QWs fabricated from amorphous materials: How strong are the confinement effects in amorphous QWs, where, because of the disorder, the carriers are localized to start with? We prepare an atomistic model of QWs based on a-Si:H to gain insight into this problem. The electronic structure of our atomistic QWs model is described with first-principles density functional theory, allowing us to study the confinement effects directly. We find that the quantum confinement effect is rather weak, compared to experimental results on a similar system.

Figure 1

DOS of bulk a-Si:H (gray line) calculated with the HSE06 functional. The DOS is smoothened with a spline (black line). The valence and conduction band edges are fitted with a square root function (red lines). The range of data used for fitting is indicated with red points.

Figure 2

DOS of a-Si:H slabs in vacuum compared to bulk. All curves were smoothened with a spline and aligned at the core potential of a silicon atom.

Figure 3

Band gaps of c-Si and a-Si:H slabs in vacuum as a function of slab thickness. Data points at 50 Å represent bulk values.

Figure 4

Charge density of four band edge states in bulk a-Si:H. In the top panel the charge density is averaged in the $x$ and $z$ direction. The bottom panel shows cuts through the 3 dimensional charge density along lines (parallel to the $y$-axis) that pass through the maximum value.

Figure 5

DOS of a-Si:H in the QW model compared to bulk. Both curves are smoothened with a spline. The alignment along the energy axis is arbitrary.

Figure 6

Local DOS (in ${10}^{21}$ ${\mathrm{cm}}^{-3}{\mathrm{eV}}^{-1})$ along the $y\mathrm{axis}$. The silicon cell is repeated in order to see both interfaces more clearly. Interfaces are marked by vertical lines. The band gap is centered around 6 eV.

Figure 7

DOS of bulk silicon and nitride in the QWs model. The colored curves result from smoothing the calculated DOS (gray lines) with splines. The curves are calculated from site-projected DOS summed in slabs 8 Å wide.

Figure 8

Band diagram of the a-Si:H/a-SiN:H quantum well (black color). Band gaps of a-Si:H and a-SiN:H determined from bulk cells (gray color). All values are in electron volts. Note that adding the offset values to the a-Si:H band gap does not give the band gap of a-SiN:H precisely. This is due to round-off errors.