Heterodimensional charge-carrier confinement in stacked submonolayer InAs in GaAs

Charge-carrier confinement in nanoscale In-rich agglomerations within a lateral InGaAs quantum well (QW) formed from stacked submonolayers (SMLs) of InAs in GaAs is studied. Low-temperature photoluminescence (PL) and magneto-PL clearly demonstrate strong vertical and weak lateral confinement, yielding two-dimensional (2D) excitons. In contrast, high-temperature (400 K) magneto-PL reveals excited states that fit a Fock-Darwin spectrum, characteristic of a zero-dimensional (0D) system in a magnetic field. This paradox is resolved by concluding that the system is heterodimensional: the light electrons extend over several In-rich agglomerations and see only the lateral InGaAs QW, i.e., are 2D, while the heavier holes are confined within the In-rich agglomerations, i.e., are 0D. This description is supported by single-particle effective-mass and eight-band $k·p$ calculations. We suggest that the heterodimensional nature of nanoscale SML inclusions is fundamental to the ability of respective optoelectronic devices to operate efficiently and at high speed.

Figure 1

(a) The successive deposition of 0.5 ML of InAs (green) followed by a few MLs of GaAs (yellow) should, naively, build up a stack of submonolayer InAs islands (b). (c) A cross-sectional scanning-tunneling-microscopy image, taken at $V=\pm 2.9$ V, $I=80$ pA, showing that, in reality, partial vertical alignment and In segregation leads to highly nonuniform In-rich agglomerations in an InGaAs quantum well. The green dashed lines are guides to the eye.

Figure 2

Low-temperature (2 K) zero-field normalized PL from the three SML (GaAs spacers of 1.5, 2.0, and 2.5 MLs) and the QW samples. The inset shows linewidth dependence on the stack height of the SML samples (or QW thickness, indicated by the circle).

Figure 3

Low-temperature (2 K) magneto-PL. (a) PL peak energy in Faraday geometry. The crossover from the low- to the high-field regime is indicated by an arrow for each sample. Inset: Individual PL spectra for the three samples at $B=15$ T. (b) In Voigt geometry the PL energy is quadratic in $B$ to the highest fields, demonstrating strong vertical confinement. Inset: Dependence of the diamagnetic shift coefficient $\mathrm{\Gamma }$ on the square of the stack height in the Voigt geometry.

Figure 4

PL linewidth dependence on $B$. (a) In Voigt geometry, little dependence is seen due to strong vertical confinement (small Bohr radii). (b) In Faraday geometry, the nonmonotonic variation in linewidth with $B$ is the result of two disorder length scales.

Figure 5

A schematic representation of the two disorder length scales ${\chi }_1$ and ${\chi }_2$ present in the SML samples. Ellipses illustrate exciton sizes at $B=0$ (solid line) and $B>>0$ (dashed line). Applying a magnetic field squeezes the exciton so it only sees the smaller ${\chi }_1$, which is most likely due to QW thickness. Adapted from Ref. [17].

Figure 6

(a) High-temperature (400 K) magnetic-field dependence of the PL peaks (Faraday geometry) for sample C. The solid lines are fits to a Fock-Darwin spectrum with Landau-level index $n$ and orbital angular momentum $l$. The confinement energy $\hslash {\omega }_0$ derived from the fits is found to be $\sim 9$ meV for all samples. The (red) dashed lines show the best attempt at a Landau-Level fit. (b) 400-K 17-T spectrum (thick line) with fitted peaks (thin lines), for sample C. (c) Low-temperature (2 K) magnetic-field dependence of the PL peaks (Faraday geometry) for the QW sample. The solid lines are Landau level fits while the (red) dashed lines are a best-attempt Fock-Darwin fit. (d) 15-T 300-K PL spectra for the QW sample, showing a strong dependence on excitation laser power.

Figure 7

Room-temperature time-resolved PL measured at the PL peak wavelength for sample A (black, measured at 1029 nm) and the QW sample (green, measured at 986 nm). Intensity-weighted average carrier lifetimes ${\tau }_{\text{av}}$ are indicated by the arrows, showing the SML carrier lifetime is approximately an order of magnitude shorter.

Figure 8

Temperature dependence of PL peak energy. (a) For sample A and the QW at various laser powers. The solid lines are Varshni [24] fits of the highest laser powers, 400 and 350 mW for the QW and SML sample, respectively. (b) The same data as (a) but focused on 0–50 K to highlight the S-shaped dependence on temperature at lower powers.

Figure 9

Effective mass calculations. (a) Schematic representation of the modeled system as a 5-nm, spherical ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ QD in a 13-nm-high ${\mathrm{In}}_y{\mathrm{Ga}}_{1-y}\mathrm{As}$ QW. (b) Calculated electron and hole confined states for $x=0.50$ and $y=0.15$. The hole is confined by the QD, but the lowest confined electron state is bound by the QW.

Figure 10

Effective-mass calculation of electron e and hole h confinement for 5-nm, spherical ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ QDs in a 13-nm ${\mathrm{In}}_y{\mathrm{Ga}}_{1-y}\mathrm{As}$ QW, with varying In content. The shaded regions are defined by the calculation, while the solid lines are guides to the eye indicating the approximate positions of the phase boundaries. The heterodimensional phase (green, 2D electrons and 0D holes) occupies the most likely regions of the parameter space.

Figure 11

Color contour plots of electron and hole wave functions in a 14-nm ${\mathrm{In}}_{0.25}{\mathrm{Ga}}_{0.75}\mathrm{As}$ QW with (a) no QDs, (b) an array of QDs with $x\le 0.5$, and (c) an array of QDs with $x\le 0.75$. The In composition is maximum in the center of each dot and follows a Gaussian profile across the array. The left-hand panel shows the morphology of the structure, while the middle and right-hand panels show the electron and hole wave functions, respectively.