Structural, electrical, and magneto-optical characterization of paramagnetic GaMnAs quantum wells

The growth of GaMnAs by molecular beam epitaxy is typically performed at low substrate temperatures $(\sim 250°\mathrm{C})$ and high As overpressures, leading to the incorporation of excess As and Mn interstitials, which quench optical signals such as photoluminescence (PL). We report on optical-quality ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}∕{\mathrm{Al}}_{0.4}{\mathrm{Ga}}_{0.6}\mathrm{As}$ quantum wells (QWs) with $x<0.2\%$ grown at a substrate temperature of $400°\mathrm{C}$. Electrical and structural measurements demonstrate that this elevated temperature reduces As defects while allowing the substitutional incorporation of Mn into Ga sites. From a combination of Hall and secondary ion mass spectroscopy measurements we estimate that at least 70%–90% of the Mn incorporates substitutionally in all samples studied. The incorporation behavior shows both a substrate temperature and QW width dependence. The low defect density of these heterostructures, compared to typical lower-temperature-grown GaMnAs, enables the observation of both polarization-resolved PL and coherent electron spin dynamics, from which the conduction-band exchange parameter is extracted. No evidence of long-range Mn spin coupling is observed, whereas negative effective Curie temperatures indicate spin heating due to photoexcitation. Light Mn doping maximizes the electron spin lifetime, indicating the importance of the Dyakonov-Perel decoherence mechanism in these structures. PL spectra reveal a low-energy peak from shallow donors, which, because of the paramagnetic behavior of its PL polarization, we ascribe to Mn interstitials.

Figure 1

(a) Schematic of sample layer structure and conduction-band energy along the growth axis $\widehat{z}$. (b) Mn concentration profile measured by SIMS for four $7.5\text{−}\mathrm{nm}$ QWs with varying Mn-doping level (Mn effusion cell temperatures marked in the figure) and (c) for QWs with the same Mn-doping level but varying substrate temperatures (marked in the figure). The uncalibrated Al SIMS signal (plotted as black lines) serves as a marker for the QW region.

Figure 2

Beam energy test for preferential Mn sputtering (knock-on). (a) and (b) show AFM images of the sample morphology in the center of SIMS craters formed by a $2\text{−}\mathrm{keV}$ and $8\text{−}\mathrm{keV}$ ${\mathrm{Cs}}^{+}$ beam, respectively. (c) AFM image of the bare sample surface. (d) The Mn profiles in sample C measured at two different beam energies as labeled. Solid lines are exponential fits to the Mn profile tail below the QW.

Figure 3

(a) Percentage of $x$ as calculated from SIMS data (see text) as a function of the inverse Mn effusion cell temperature. Four quantum well sample sets of different well width are shown. (b) Percentage of $x$ versus quantum well width. Lines connect samples grown with the same Mn cell temperature, which is labeled in the figure.

Figure 4

The room-temperature two-dimensional hole density (p2D) per hour (h) of Mn shutter time as a function the inverse Mn source temperature. Three sample sets grown at $400°\mathrm{C}$ are plotted, and the data are fit to an exponential thermal activation (Arrhenius) equation, plotted as a line.

Figure 5

The two-dimensional hole density (p2D) as a function of inverse sample temperature for $500\text{−}\mathrm{nm}$-thick bulk GaMnAs (a)–(c) and for $7.5\text{−}\mathrm{nm}$-thick GaMnAs QWs (d)–(f). Exponential thermal activation (Arrhenius) fits are plotted as lines over the temperature range used for fitting.

Figure 6

The activation energy $\left(E_a\right)$ for holes as a function of Mn concentration in bulk and QW samples extracted from Arrhenius fits—e.g., Fig. 5. The $110\text{−}\mathrm{meV}$ activation energy for an isolated ${\mathrm{Mn}}^{2+}$ ion in GaAs is plotted as a dashed line for reference.

Figure 7

The fraction of substitutional Mn $({\mathit{Mn}}_{\mathit{Ga}}∕\mathit{Mn})$ as a function of $x$, estimated assuming no surface depletion and full thermal activation of both ${\mathrm{Mn}}_{\mathit{Ga}}$-doped holes and ${\mathrm{Mn}}_i$-doped electrons. The minimum fraction of substitutional Mn (dashed line, $2∕3$) for $p$-type GaMnAs is plotted.

Figure 8

(Color) Time-resolved electron spin dynamics in $d=7.5\mathrm{nm}$ GaMnAs QWs. (a) An example of KR data (points) together with fit (line). (b) ${\nu }_L$ as a function of $B$ for different $x$ values (solid points); larger points indicate increasing $x$. Open data points are for the $x=0$ sample. Red lines in (b) are fits to Eq. (4).

Figure 9

(Color) The transverse electron spin lifetime $\left(T_2^{*}\right)$ at $T=5\mathrm{K}$ versus the percentage of Mn for four quantum well sample sets of varies width. The plotted values of $T_2^{*}$ are the mean values from $0\text{to}8\mathrm{T}$, and the error bars represent the standard deviations.

Figure 10

(Color) Temperature dependence of ${\nu }_L$ for $7.5\text{−}\mathrm{nm}$ quantum wells. (a) The effect of increasing $T$ on the $B$ dependence of ${\nu }_L$ for the sample with $x\sim 0.007\%$ (solid points) and for the $x=0$ sample (open points). (b) $T$ dependence of ${\nu }_L$ at constant $B$ for the $x\sim 0.007\%$ sample. Red lines in (a) and (b) are fits to Eq. (4).

Figure 11

(Color) $g_e$ as a function of $d$. Black points are from control $(x=0)$ samples of this study; red circles and squares are from Refs. 6, 12, respectively. Lines guide the eye.

Figure 12

$\Delta E$ as a function of $B$ at $T=5\mathrm{K}$ for QWs with (solid circles) and without Mn doping (open circles); larger points indicate increasing $x$. Fits to Eq. (4) are shown as lines.

Figure 13

(Color) $\Delta E$ for the sample with $d=5\mathrm{nm}$ and $x\sim 0.032\%$ at various temperatures. Fits to Eq. (4) are shown as lines.

Figure 14

(Color) $x{N}_0\alpha$ as a function of $x$ from fits shown in Fig. 12; error bars are the size of the points. Linear fits are shown for each sample set of constant $d$.

Figure 15

(Color) The effect of confinement on $s\text{−}d$ exchange coupling. (a) $N_0\alpha$ extracted from fits in Fig. 14 and plotted as a function of $d$. (b) $N_0\alpha$ as a function of electron kinetic energy for GaMnAs.

Figure 16

(Color) PL plotted as a function of emission energy for a set of $7.5\text{−}\mathrm{nm}$ QWs with varying Mn doping; the samples are excited with $1\mathrm{W}∕{\mathrm{cm}}^2$ at $1.722\mathrm{eV}$. Samples with $x>0.13\%$ showed no PL.

Figure 17

(Color) Polarization-resolved PL for QWs of varying $d$ and $x$ at $T=5\mathrm{K}$. Two-Gaussian fits to the data are shown as black lines, and the higher-energy Gausssian is attributed to the heavy-hole exciton in the QW. The excitation enregy is set to $1.722\mathrm{eV}$ for (a)–(f) and $2.149\mathrm{eV}$ for (g) and (h).

Figure 18

(Color) Polarized emission splitting $\left(\Delta E_{\mathit{PL}}\right)$ as a function of $B$ at $T=5\mathrm{K}$ for QWs of varying $d$ and $x$. Data from QWs with $x=0$ are shown as open circles, while data from QWs with $x\sim 0.013\%$ in (a), $x\sim 0.007\%$ in (b), $x\sim 0.004\%$ in (c), and $x\sim 0.0025\%$ in (d) are shown as solid circles. Fits to $\Delta E_{\mathit{PL}}$ for $\mid B\mid <2\mathrm{T}$ appear as blue lines.

Figure 19

PL polarization spectra for a $7.5\text{−}\mathrm{nm}$ GaMnAs QW with an $1.72\text{−}\mathrm{eV}$ excitation at $1.0\mathrm{mW}$ (a) near the QW emission peaks $(\sim 1.6\mathrm{eV})$ and (b) at the bulk Mn-acceptor line for GaMnAs $(\sim 1.4\mathrm{eV})$, which results from unintentional Mn doping in the $300\text{−}\mathrm{nm}$-thick GaAs buffer layer. The spectra are plotted as a function of emission energy for different magnetic fields from $-8$ to $+8\mathrm{T}$ at $1\text{−}\mathrm{T}$ intervals. (c) The PL polarization integrated over a single emission peak as a function of $B$ for the high-energy ($\sim 1.57\mathrm{eV}$ at $\mathrm{T}=5\mathrm{K}$, open circles) and low-energy ($\sim 1.55\mathrm{eV}$ at several temperatures, solid symbols) peaks and (d) for the bulk Mn-acceptor line peak plotted for several temperatures.