Magnetotunneling Spectroscopy of Dilute Ga(AsN) Quantum Wells

We use magnetotunneling spectroscopy to explore the admixing of the extended GaAs conduction band states with the localized N-impurity states in dilute ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}}_{1-y}{\mathrm{N}}_y$ quantum wells. In our resonant tunneling diodes, electrons can tunnel into the N-induced $E_{-}$ and $E_{+}$ subbands in a ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}}_{1-y}{\mathrm{N}}_y$ quantum well layer, leading to resonant peaks in the current-voltage characteristics. By varying the magnetic field applied perpendicular to the current direction, we can tune an electron to tunnel into a given $k$ state of the well; since the applied voltage tunes the energy, we can map out the form of the energy-momentum dispersion curves of $E_{-}$ and $E_{+}$. The data reveal that for a small N content ($\sim 0.1\%$) the $E_{-}$ and $E_{+}$ subbands are highly nonparabolic and that the heavy effective mass $E_{+}$ states have a significant $\Gamma$-conduction band character even at $k=0$.

Figure 1

$I(V)$ curves at $T=4.2\mathrm{K}$ incorporating ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}}_{1-y}{\mathrm{N}}_y$ layers with $y=0$ and $0.08\%$. The dashed line is the $I(V)$ under illumination for the sample with $y=0.08\%$. The insets sketch the conduction band profile at zero bias for a diode with and without $N$. When $y$ is increased from 0 to $0.08\%$, the lowest quasibound state of the QW, $E_0$, splits into two bound states, $E_{0-}$ and $E_{0+}$. In addition, N introduces localized states with energies below the GaAs conduction band edge.

Figure 2

$I(V)$ curves at $T=4.2\mathrm{K}$ for RTDs incorporating a ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}}_{1-y}{\mathrm{N}}_y$ layer with $y=0.08\%$, 0.43, 0.93, and $1.55\%$. The inset shows the dependence of the threshold voltage $V_{\mathrm{t}\mathrm{h}}$ on $y$.

Figure 3

(a) $I(V)$ curves under illumination at $T=4.2\mathrm{K}$ and various $B$ for a RTD with $y=0.08\%$. $B$ is increased from 1 to 11 T by steps of 0.5 T. For clarity, the curves are displaced along the vertical axis. The double step decrease of $I(V)$ marked by asterisks on one of the high-field curves arises from the instability in the current due to the strong negative differential conductance. The left inset is a sketch of the magnetotunneling experiment. (b) $I(V)$ curves with $B$ in the range 0 to 7.5 T. Dotted lines are guides to the eye and show resonances $E_{0-}$, $E_{0+}$, and $E^{*}$. (c) Differential conductance, $dI/dV$, plot for $B=0\mathrm{T}$.

Figure 4

(a) Voltage position of current peaks $E_{0-}$, $E_{0+}$, and $E^{*}$ in $I(V)$ as a function of $B$ (top axis) and of $k=esB/\hslash$ (bottom axis). (b) Energy–wave-vector dispersion curves for bulk ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}}_{1-y}{\mathrm{N}}_y$. (c) Energy–wave-vector dispersion curves for a ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}}_{1-y}{\mathrm{N}}_y$ QW (continuous lines) and for a GaAs QW (dotted lines). The energies are measured relative to the minimum of the GaAs conduction band and the N content is equal to $0.08\%$.