Impact of alloy disorder on the band structure of compressively strained GaBi${}_x$As${}_{1-x}$

The incorporation of bismuth (Bi) in GaAs results in a large reduction of the band gap energy ($E_g$) accompanied with a large increase in the spin-orbit splitting energy (${△}_{SO}$), leading to the condition that ${△}_{SO}>E_g$, which is anticipated to reduce hot-hole producing Auger recombination losses whereby the energy and momentum of a recombining electron-hole pair are given to a second hole which is excited into the spin-orbit band. We theoretically investigate the electronic structure of experimentally grown GaBi${}_x$As${}_{1-x}$ samples on (100) GaAs substrates by directly comparing our data with room temperature photomodulated reflectance (PR) measurements. Our atomistic theoretical calculations, in agreement with the PR measurements, confirm that $E_g$ is equal to ${△}_{SO}$ for $\mathit{\text{x}}\approx$ 9$\%$. We then theoretically probe the inhomogeneous broadening of the interband transition energies as a function of the alloy disorder. The broadening associated with spin-split-off transitions arises from conventional alloy effects, while the behavior of the heavy-hole transitions can be well described using a valence band-anticrossing model. We show that for the samples containing 8.5$\%$ and 10.4$\%$ Bi the difficulty in identifying a clear light-hole-related transition energy from the measured PR data is due to the significant broadening of the host matrix light-hole states as a result of the presence of a large number of Bi resonant states in the same energy range and disorder in the alloy. We further provide quantitative estimates of the impact of supercell size and the assumed random distribution of Bi atoms on the interband transition energies in GaBi${}_x$As${}_{1-x}$. Our calculations support a type-I band alignment at the GaBi${}_x$As${}_{1-x}$/GaAs interface, consistent with recent experimental findings.

Figure 1

Room temperature photoreflectance (PR) spectra for the four compressively strained GaBi${}_x$As${}_{1-x}$ samples, in the region of the fundamental band gap highlighting the $E_g^{E_{v1}}=E_{c1}-E_{v1}$ and $E_g^{E_{v2}}=E_{c1}-E_{v2}$ transitions. The black circles are from measured values and the red lines are the fits obtained by Eq. (3). The green bars are the calculated GaAs HH+LH $\Gamma$-character plots for the alloy valence band states, computed from 8000 atom supercell calculations. The values of the HH- and LH-related transition energies are selected from the $\Gamma$ character plots as the energies with the highest HH and LH $\Gamma$ character projections, respectively. The dashed lines are a guide to the eye and indicate the PR fitting transition energies.

Figure 2

Room temperature photoreflectance (PR) spectra for the four compressively strained GaBi${}_x$As${}_{1-x}$ samples in the region of the spin-orbit-split-off transition ($E_g^{E_{SO}}=E_{c1}-E_{SO}$). The black dots are from measured values and the red lines are the fits described by Eq. (3). The green bars are the calculated GaAs SO $\Gamma$-character plots for the alloy valence band states, computed from 8000 atom supercell calculations. The upper arrows in each panel indicate the PR fitting energies and the lower arrows mark the calculated energies from the $\Gamma$-character plots. The prominent feature around 1.77 eV in the PR spectra is due to the SO-related transition from the GaAs substrate.

Figure 3

Plot of the room temperature transition energies, $E_g^{E_{v1}}$, $E_g^{E_{v2}}$, and $E_g^{E_{SO}}$, obtained from fitting the PR spectra (black solid lines) and calculated from the atomistic simulations (broken red lines). The values are directly extracted from Figs. 1 and 2.

Figure 4

Comparison of the experimental and theoretical values of the energy gap $E_g$ and spin-orbit-splitting energy ${\Delta }_{SO}$ obtained from the results of Fig. 3. The values of the Bi composition where $E_g={\Delta }_{SO}$ obtained from theory and experiment are also shown.

Figure 5

For each Bi composition of the experimentally grown samples, we calculate and plot combined HH and LH $\Gamma$ character for three alloy supercells consisting of 1000, 4096, and 8000 atoms. For the same Bi composition, a larger alloy supercell will have more Bi atoms and therefore an increased number of pair and cluster configurations. This is reflected by the wider $\Gamma$-character distribution for larger supercells. The significant overestimation of the alloy VBE energy in 1000 atom supercell calculations for 8.5$\%$ and 10.4$\%$ samples is due to artificially enhanced cell-to-cell interaction of pair and cluster states in the structures considered.

Figure 6

For each of the four Bi compositions, we consider four random distributions of Bi atoms in the supercell, labeled as RD1, RD2, RD3, and RD4. Each random distribution introduces different pair and cluster states and therefore exhibits different broadening of the combined HH and LH $\Gamma$ character. The calculated data are shown for 8000 atom supercell calculations. We also specify the values of individual HH and LH contributions in the few highest energy bars of the plot as (HH,LH). If (,LH) or (HH,) is mentioned for a particular bar, that indicates that HH or LH contribution in that bar is less than 0.1$\%$. The zero of energy is taken in all cases at the GaAs valence band maximum.

Figure 7

The Bi composition dependent shifts in the band edge energies $E_{c1}$, $E_{v1}$, and $E_{v2}$ of the GaBi${}_x$As${}_{1-x}$ alloy are shown, obtained from the compressively strained and free-standing 8000 atom supercell calculations at low temperature. The strain shifts the lowest conduction band edge to higher energy, reducing its slope from 28 meV per $\%$ Bi to 15 meV per $\%$ Bi. The splitting between the two highest valence band edges is also increased due to compressive biaxial strain.