Band structure of segmented semiconductor nanowires

We have calculated the band structures for strained segmented nanowires involving all combinations of AlN, GaN, InN, AlP, GaP, AlAs, GaAs, InP, InAs, AlSb, GaSb, and InSb, as a function of segment length. This was done for two different growth directions of the wires, [100] and [111]. Both the $\Gamma$ and the $X$ conduction-band minima were included in the calculations as well as the valence bands. Short segments behave like strained quantum wells and our results thus include strained quantum wells as a subset. We find all material combinations that give metallic segments due to a negative band gap and we find all the band alignments that may occur. We identify those structures which show spontaneous charge separation as well as those which are suitable for the optical generation of polarized exciton gases, with their rich phase diagram, theoretically predicted to include superfluids and supersolids. Some device related ideas are presented. Due to the amount of data (several hundreds of diagrams) most of our results are presented as a webpage.

Figure 1

(Color online) (a) A drawing of a segmented wire with a square cross section, oriented along the [001] direction, in this paper being defined as the $z$ direction. The dashed line indicates the $yz$ plane in which was used for the calculations shown in Figs. 2, 3, 5, 6. (b) A drawing of a segmented wire having a hexagonal cross section, oriented along the [111] direction.

Figure 2

(Color online) (a) A surface plot of $e_{xx}+e_{yy}+e_{zz}$ in a [001] oriented wire in the $yz$ plane indicated in Fig. 1a consisting of an InAs segment in InP. The length of the InAs segment is 50 and the width of the wire is 100. The InAs segment is under hydrostatic pressure which is largest at the center of the segment and smallest at the surface of the segment. The InP is under tension close to the segment but is under weak compression further out before equilibrium is established. (b) A surface plot of $e_{xx}$ in the wire. This strain tensor component has only weak variation across the wire. (c) A surface plot of $e_{zz}$ in the wire. The behavior is quite complex and very different from that of $e_{xx}$.

Figure 3

(Color online) (a) A surface plot of the conduction-band minimum for a [001] oriented wire in the $yz$ plane defined in Fig. 1a, consisting of an InP wire with an InAs segment. The length of the InAs segment is 50 and the width of the wire is 100. (b) A surface plot of the valence-band maximum for the same wire.

Figure 4

(Color online) The band edges in an InAs/InP wire plotted along the [001] direction and through the center of the wire. The wire is the same as in Fig. 3. The length of the InAs segment was varied from 2 to 100, where the width of the wire (along the $x$ direction) was 100. The blue trace is the $\Gamma$ conduction band, black traces are the $X$ conduction bands, and red traces are the valence bands.

Figure 5

(Color online) (a) A surface plot of $e_{xx}+e_{yy}+e_{zz}$ in a [001] oriented wire in the plane indicated in Fig. 1a, consisting of an InAs wire with an InP segment. The length of the InP segment is 50 and the width of the wire is 100. The InP segment is under hydrostatic tension which is largest at the center of the segment and smallest at the surface of the segment. The InAs is under compression close to the segment and then is under weak tension further out before equilibrium is established. (b) A surface plot of $e_{xx}$ in the wire. This strain tensor component has only a weak variation across the wire. (c) A surface plot of $e_{zz}$ in the wire. The behavior is quite complex and very different from that of $e_{xx}$.

Figure 6

(Color online) (a) A surface plot of the conduction-band minimum for a [001] oriented wire defined in Fig. 1a consisting of an InAs wire with an InP segment. The length of the InP segment is 50 and the width of the wire is 100. (b) A surface plot of the valence-band maximum for the same wire.

Figure 7

(Color online) The band edges in a [001] oriented wire consisting of InAs with an InP segment. The plots are along the center of the wire. The length of the InP segment was varied from 2 to 100, where the width of the wire (along the $x$ direction) was 100. The blue trace is the $\Gamma$ conduction band, black traces are the $X$ conduction bands, and red traces are the valence bands.

Figure 8

(Color online) Surface plots of the band edges in a wire consisting of a heterostructure of InAs and InP. The wire is oriented along the [001] direction. InAs is to the left of the interface.

Figure 9

(Color online) The band edges in a [111] oriented InP wire with an InAs segment. The plot is through the center of the wire. The length of the InAs segment was varied from 2 to 100, where the width of the wire (along the $x$ direction) was 100. The blue trace is the $\Gamma$ conduction band, black traces are the $X$ conduction bands, and red traces are the valence bands.

Figure 10

(Color online) Different band offsets that may occur at a segment. The letters s (for segment) or b (for barrier) indicate which material has the lowest energy conduction-band minimum. Type I-s is a normal quantum well, confining both electrons and holes to the segment. Type II-s confines electrons to the segment and holes to the wire or barrier. Type III-s is metallic and the conduction-band minimum of the segment is below the valence-band maximum of the barrier, giving rise to transfer of electrons to the segment and holes to the barrier. The inverted structures may also occur denoted by type I-b, type II-b, and type III-b.

Figure 11

(Color online) The band structure of [111] oriented wires consisting of an InP segment in GaAs. Blue trace is the $\Gamma$ conduction band, black traces are the $X$ conduction bands, and red traces are the valence bands.

Figure 12

(Color online) The band structure of [111] oriented wires consisting of an InAs segment in InSb. For short segments we have a negative band gap in the InAs. For longer segments the InAs conduction-band minimum is below the valence-band maximum of the InSb. As a result electrons will accumulate in the InAs segment and holes in the InSb barrier. The blue trace is the $\Gamma$ conduction band, black traces are the $X$ conduction bands, and red traces are the valence bands.

Figure 13

(Color online) The band structure of [111] oriented wires consisting of an InSb segment in InAs. The blue trace is the $\Gamma$ conduction band, black traces are the $X$ conduction bands, and red traces are the valence bands.

Figure 14

(Color online) Overview of the band structure of segmented wires oriented along the [001] direction where the segment length is 2 and the wire width is 100. Such short segments behave like strained two-dimensional layers. The blue trace is the $\Gamma$ conduction band, black traces are the $X$ conduction bands, and red traces are the valence bands.

Figure 15

(Color online) Overview of the band structure of segmented wires oriented along the [111] direction where the segment length is 2 and the wire width is 100. Such short segments behave like strained two-dimensional layers. The blue trace is the $\Gamma$ conduction band, black traces are the $X$ conduction bands, and red traces are the valence bands.

Figure 16

(Color online) Overview of the band structure of segmented nitride wires, where the segment length is 2 and the wire width is 100. Such short segments behave like strained two-dimensional layers. Blue trace is the $\Gamma$ conduction band, black traces are the $X$ conduction bands, and red traces are the valence bands.

Figure 17

(Color online) (a) A drawing of a dipole gas in a wire. (b) It is possible to separate the electron and hole gases by using a spacer layer. (c) Periodic arrays of dipole gases can be contemplated. (d) Schematic of electrically contacting a wire device using negative gap semiconductors for the contacting regions.

Figure 18

(Color online) Band structure of [001] oriented wires consisting of a segment of InSb in InP. Short segments have a negative band gap with a Fermi level close to the conduction band of InP, assuming that the Fermi level is between the valence-band maximum and the conduction-band minimum. Blue trace is the $\Gamma$ conduction band, black traces are the $X$ conduction bands, and red traces are the valence bands.