Spin dynamics of charged excitons in ultrathin (In,Al)(Sb,As)/AlAs and Al(Sb,As)/AlAs quantum wells with an indirect band gap

The charged exciton recombination and their spin dynamics are studied in ultrathin InSb- and AlSb-based quantum wells (QWs) surrounded by an AlAs matrix characterized by an indirect band gap. Strong material intermixing was observed that results in the QWs being composed of a quaternary ${\mathrm{In}}_x{\mathrm{Al}}_{1-x}{\mathrm{Sb}}_y{\mathrm{As}}_{1-y}$ or a ternary ${\mathrm{AlSb}}_y{\mathrm{As}}_{1-y}$ alloy. The band alignment in these QWs is identified as type I for (In,Al)(Sb,As)/AlAs and type II for Al(Sb,As)/AlAs. The magnetic-field-induced circular polarization of the photoluminescence $P_c$ is studied as function of the field strength. The observed nonmonotonic behavior of the $P_c$ dynamics at high magnetic fields is provided by the interplay of negative and positive trions, contributing to the emission. To interpret the experiment, we have developed a kinetic equation model which accounts for the dynamics of the trion spin states and the redistribution of trions between these states as a result of spin relaxation. The model is in quantitative agreement with the experiment and allows us to determine trion radiative lifetimes on the order of hundreds of microseconds, holes in the trion spin-relaxation times also in the hundreds of $\mu \mathrm{s}$ range, electrons in the trion spin-relaxation times of hundreds of ns, and heavy-hole $g$ factors of about $+3.5$ for the structures studied.

Figure 1

TEM and chemical mapping in cross-section STEM images, obtained by the EDAX technique. From top to bottom: (Ga,Al)(Sb,As)/AlAs, Al(Sb,As)/AlAs, and (In,Al)(Sb,As)/AlAs QW heterostructures. The distribution of elements is depicted by colors: Ga orange, Al yellow, As green, Sb red, and In blue.

Figure 2

Segregation profiles in interdiffused QWs with a nominal amount $N=0.25$ ML of deposited material (shown by cyan) along the QW growth axis, calculated by using Eqs. (1) with segregation coefficients in AlAs for indium $R_{\text{In}}=0.77$ and antimony $R_{\text{Sb}}=0.80$, and taking into account that gallium atoms do not segregate into AlAs, for (a) In and Sb in (In,Al)(Sb,As)/AlAs, (b) Sb in Al(Sb,As)/AlAs, and (c) Ga and Sb in (Ga,Al)(Sb,As)/AlAs QW heterostructures. Band diagrams of the interdiffused QWs calculated for these segregation profiles in the envelope function approximation within the eight-band $\mathbf{k}·\mathbf{p}$ model for electrons and holes, taking into account elastic strain in the heterostructures, using the nextnano$++$ simulation suite, for (d) (In,Al)(Sb,As)/AlAs, (f) Al(Sb,As)/AlAs, and (e) (Ga,Al)(Sb,As)/AlAs. $X_{xy}$ are the conduction band minima (magenta); the valence band has heavy hole character (black).

Figure 3

Normalized time-integrated photoluminescence spectra of the (In,Al)(Sb,As)/AlAs (red) and Al(Sb,As)/AlAs (green) QWs. Additionally, for comparison, we show the spectrum of the (Ga,Al)(Sb,As)/AlAs QW (sample S1) (dashed blue) studied in Ref. [25]. The pulse repetition rate of the excitation laser is 100 kHz. $T=5$ K.

Figure 4

Energy shift of the PL band maximum in the studied structures as function of excitation density. $T=1.8$ K. Solid lines give the dependence according to $E_{\text{max}}\left(P_{\mathrm{ex}}\right)-E_{\text{max}}\left(P_0\right)=(U_e+U_h)ln(P_{\text{ex}}/P_0)+b{(P_{\text{ex}}/P_0)}^{1/3}$ meV with $P_0={10}^{-3}$ W/${\mathrm{cm}}^2$: (a) (In,Al)(Sb,As)/AlAs, (b) Al(Sb,As)/AlAs. Insets show schematically the QW band structures. The $\mathrm{\Gamma }$ and X valleys of the conduction band are presented by black and green (and blue) colors, respectively. The red arrows mark the optical transitions.

Figure 5

Schematic illustration highlighting the effect of material composition and composition fluctuations on the QW energy spectrum. Two types of fluctuations, short-range and long-range, are responsible for the Urbach tails and linewidths, respectively, as shown in Ref. [31].

Figure 6

Normalized PL intensity as function of temperature measured for (In,Al)(Sb,As)/AlAs, Al(Sb,As)/AlAs, (In,Al)As/AlAs [24], and GaAs/AlAs [21] thin indirect band gap QWs.

Figure 7

Low-temperature (1.8 K) time-integrated PL spectra of the ultrathin QWs measured at magnetic fields 0 T (dashed black line) and 8 T (solid red line) in the Faraday geometry ($\mathbf{B}\parallel z$): (a) (In,Al)(Sb,As)/AlAs, (b) Al(Sb,As)/AlAs.

Figure 8

Recombination dynamics measured at the PL maximum in longitudinal magnetic fields of $B=0$ (dashed black line) and 8 T (solid red line). (a) (In,Al)(Sb,As)/AlAs QW dynamics recorded at 2.00 eV. The solid line is a monoexponential fit with ${\tau }_r^{\mathrm{InSb}}=0.35\pm 0.02$ ms (b) Al(Sb,As)/AlAs QW dynamics recorded at 1.93 eV. The solid line is a monoexponential fit with ${\tau }_r^{\text{AlSb}}=0.38\pm 0.02$ ms. The laser pulse repetition rate is 400 Hz. The laser pulse ends at 10 ns. $T=1.8$ K.

Figure 9

Time-integrated PL spectra of the ultrathin QWs measured in Faraday geometry ($\mathbf{B}\parallel z$) at a magnetic field of 4 T in ${\sigma }^{+}$ and ${\sigma }^{-}$ polarization for $T=1.8$ K. The pulse repetition rate is 2 kHz and the emission is integrated over the temporal range of $0-0.5$ ms: (a) (In,Al)(Sb,As)/AlAs, (b) Al(Sb,As)/AlAs.

Figure 10

Magnetic field dependence of the polarization degree measured at the maximum of the time-integrated PL of $\theta =0^{\circ }$, ${15}^{\circ }$, ${30}^{\circ }$, and ${45}^{\circ }$. (a) (In,Al)(Sb,As)/AlAs QWs, (b) Al(Sb,As)/AlAs QWs. The solid lines show the results of model calculations for $\theta =0^{\circ }$ using the parameters given in text.

Figure 11

Temperature dependence of the polarization degree measured at the maximum of the time-integrated PL for $\theta =0^{\circ }$. $B=7$ T. (a) (In,Al)(Sb,As)/AlAs QWs, (b) Al(Sb,As)/AlAs QWs.

Figure 12

Dynamics of the circular polarization degree at the maximum of the time-integrated PL line measured at $T=1.8$ K for $B=8$ T in the Faraday geometry: (a) (In,Al)(Sb,As)/AlAs QWs and (b) Al(Sb,As)/AlAs QWs. The solid lines show the model calculation results with the parameters given in the text.

Figure 13

Scheme of the exciton spin structure in magnetic field, applied in the Faraday geometry, $\mathbf{B}\parallel z$. The case of positive $g_e$ and $g_{\text{hh}}$ with $g_{\text{hh}}>g_e$ is shown. The labels $++,--,-+$, and $+-$ correspond, respectively, to the exciton states with spin projection $+2$, $-2$, $+1$, and $-1$. The blue lines show the optically dark (spin-forbidden) states. The red lines show the bright (spin-allowed) states that result in ${\sigma }^{+}$ (solid line) or ${\sigma }^{-}$ (dashed line) polarized emission. The arrows indicate electron (hole) spin-flip processes increasing (dash-dotted) and decreasing (solid) the carrier energy, respectively.

Figure 14

Schematic illustration of the spatial separation of photogenerated charge carriers in a QW with strong energy dispersion of the electron (blue circles) and hole (red circles) states. Insets show the fine structure of positively and negatively charged trion spin states, undergoing the Zeeman splitting. The thick (thin) arrows correspond to dominating (suppressed) optical transitions in emission.

Figure 15

Schematic illustration of energy states that undergo the Zeeman splitting of negatively (a)–(d) and positively (e)–(h) charged trions composed of electrons and heavy holes covering different combinations of $g$ factors: (a) and (e) $g_e>0$, $g_{\text{hh}}>0$, (b) and (f) $g_e<0$, $g_{\text{hh}}>0$, (c) and (g) $g_e<0$, $g_{\text{hh}}<0$, (e) and (h) $g_e>0$, $g_{\text{hh}}<0$. The thick solid (thin dashed) arrows relate to dominating (suppressed) optical transitions in emission.

Figure 16

Magnetic field dependence of the PL circular polarization degree calculated in case of $g_e>0$ and $g_{\text{hh}}>0$ for (a) $T^{+}$ with ${\tau }_{se}=$ 0.1, 0.01, and 0.001 ms and (b) $T^{-}$ with ${\tau }_{\text{sh}}=0.1$ ms, $g_{\text{hh}}=1$, 2, and 4. We assume in the calculations $T=1.8$ K and ${\tau }_r=1$ ms.

Figure 17

Dynamics of the circular polarization degree calculated in case of $g_e>0$ and $g_{\text{hh}}>0$ for the PL of (a) $T^{+}$ with ${\tau }_{\text{se}}=$ 0.1, 0.01, and 0.001 ms and (b) $T^{-}$ with ${\tau }_{\text{sh}}=$ 0.1, 0.01, and 0.001 ms in a magnetic field of 10 T. We assume in the calculations $T=1.8$ K and ${\tau }_r=1$ ms.

Figure 18

Magnetic-field dependence of $P_c$ calculated for a set of different ratios of ${\tau }_{\text{se}}/{\tau }_{\text{sh}}$ and $N_{T^{+}}/N_{T^{-}}$ at $T=1.8$ K: (a) $g_e=2$ and $g_{\text{hh}}=1$, $N_{T^{+}}/N_{T^{-}}=1$, ${\tau }_{\text{se}}/{\tau }_{\text{sh}}$ = 0.01, 0.1, 1, 10, 100. (b) $g_e=2$ and $g_{\text{hh}}=4$, $N_{T^{+}}/N_{T^{-}}=1$, ${\tau }_{\text{se}}/{\tau }_{sh}$ = 0.01, 0.1, 1, 10, 100. (c) $g_e=2$ and $g_{\text{hh}}=1$, ${\tau }_{\text{se}}/{\tau }_{\text{sh}}$ = 10, $N_{T^{+}}/N_{T^{-}}=0.2,0.5,1,2,5$. (d) $g_e=2$ and $g_{\text{hh}}=4$, ${\tau }_{\text{se}}/{\tau }_{\text{sh}}$ = 10, $N_{T^{+}}/N_{T^{-}}=0.2,0.5,1,2,5$.

Figure 19

Dynamics of $P_c$ calculated for a set of different ratios of ${\tau }_{\text{se}}/{\tau }_{\text{sh}}$ = 0.01, 0.1, 1, 10, 100, and $N_{T^{+}}/N_{T^{-}}=1$ at $T=1.8$ K: (a) $g_e=2$ and $g_{\text{hh}}=1$, $B=2$ T. (b) $g_e=2$ and $g_{\text{hh}}=4$, $B=2$ T. (c) $g_e=2$ and $g_{\text{hh}}=1$, $B=10$ T. (d) $g_e=2$ and $g_{\text{hh}}=1$, $B=10$ T.

Figure 20

Calculation of $P_c$ for $g_e=2$ and $g_{\text{hh}}=-4$. $T=1.8$ K for a set of different ratios ${\tau }_{\text{se}}/{\tau }_{\text{sh}}$= 0.01, 0.1, 1, 10, 100, and $N_{T^{+}}/N_{T^{-}}=1$: (a) magnetic field dependence, (b) dynamics at $B=10$ T.