Evidence for various higher-subband resonances and interferences in a GaAs/AlAs asymmetric quadruple-quantum-well superlattice analyzed from its photoluminescence properties

In this paper, we present evidence for the resonances between higher subbands in an asymmetric quadruple-quantum-well (AQQW) superlattice (SL) by photoluminescence (PL) spectra. Since each QW in an AQQW is separated by thin barriers, subband interferences can easily arise. As a result, various PL branches caused by the subband resonances are observed, including PL emissions from the higher-energy Γ states, the X state in a barrier with longitudinal optical phonon replica, and long-range Γ-X transfer with Γ-X mixing. However, in conventional QW systems, the PL emissions from higher-energy subbands and their interference have not been clearly observed yet; in our system, the interferences between higher-energy subbands can be observed through PL emission, since we achieved effective electron injection into the higher subbands under very thin barriers. From these observations, we exposed the existence of such interferences and transport processes.

Figure 1

Schematic illustration of potential profile of AQQW SL. Left and right sides correspond to $p$-cap side and $n$-substrate sides.

Figure 2

(a) Schematic illustrations of hole subband energy (below) and electron energy (above). Arrows indicate relaxation of electrons to Γ21 ground state and holes to hh21 ground state, and their radiative recombination corresponds to the PL emission under the flat-band condition. (b) Calculated wave-function profile and energy level of subbands. Heavy-hole subbands of hh31and hh41 are not shown. Barrier height is reduced due to space limitations.

Figure 3

Photoluminescence (PL) spectra vs reverse-bias voltage in the longer-wavelength region under 1-mW 532-nm laser excitation. Color represents logarithmic PL intensity ($\mathrm{base}=10$).

Figure 4

Hole subband energy fan chart based on QW2. Energy fan chart is calculated based on standard QW of QW2, since hh is initially gathered in QW2 under flat-band condition. In the QW2 base case, subband state in QW2 shows little or no energy change.

Figure 5

Schematic illustrations of Γ11-X11 resonance and wave-function (probability density) profiles at 0.3 V. Arrows indicate carrier transport. Thick lines with arrow indicate Γ-X mixing point. Thick dashed arrow indicates radiative recombination from Γ11-X11 mixed state to hh11. Dotted lines with arrows indicate radiative recombination from Γ21 at bias voltage lower than 0.3 V.

Figure 6

Schematic illustration of electron transport and resonances at each characteristic bias voltage.

Figure 7

Photoluminescence (PL) spectra vs reverse-bias voltage in shorter-wavelength region under 1-mW 532-nm laser excitation. Color represents logarithmic PL intensity ($\mathrm{base}=10$). The integration time of the cooled-CCD detector is ∼100 times longer than that for Fig. 3 to detect weak PL.

Figure 8

Electron subband energy fan chart based on QW1, since radiative recombination shown in Fig. 7 occurred with hh11 in QW1. Thick solid curves are Γ ground states in four QWs. Dotted lines are X subbands in the 11-ML barrier B1. Crossed thin lines indicate anticrossings. Higher-electron-energy states are not shown, since little or no electron occupation is expected due to relaxation to lower-energy states.

Figure 9

Current vs reverse-bias voltage characteristics (I-V curve) of sample under 1-mW laser excitation intensity. Inset shows detailed I-V curve below 4 V.

Figure 10

Schematic illustrations of Γ11-X11 resonance and wave-function profiles at 3.7 V. Large wave-function overlapping between Γ11 and X11 generates reappearance of X11-hh11 transition corresponding to PL emission at around 690 nm for a bias voltage at around 3.7 V. Thick black line with arrow indicates Γ-X mixing. Dashed arrow indicates space indirect transition from Γ11-X11 mixed state to hh1.

Figure 11

Electron subband energy fan chart at 1.7 V. Dotted lines with arrow indicate Γ21-X11 resonance. Thick black line with arrow indicates Γ-X mixing. Dashed arrow indicates space indirect transition from Γ21-X11 mixed state to hh1.

Figure 12

Schematic illustrations of carrier transfer and wave-function profiles at (a) 2.5 V, (b) 6.5 V. Dashed lines are LO-phonon replica energy.

Figure 13

Schematic illustrations of carrier transfer and wave-function profiles at 8.5 V. All ground Γ subband states contribute to electron escape to next AQQW period through X states in B1 barrier.