Effect of hydrostatic pressure on the fragmented conduction band structure of dilute Ga(AsN) alloys

We show that the combined use of magneto-tunneling spectroscopy and hydrostatic pressure $P$ provides a powerful means of probing and strongly modifying the fragmented conduction band structure of dilute $\mathrm{Ga}{\mathrm{As}}_{1-y}{\mathrm{N}}_y$ quantum well layers. We demonstrate the strong effect of pressure on the $\mathrm{Ga}{\mathrm{As}}_{1-y}{\mathrm{N}}_y$ states over a wide range of energies and $k$ vectors not accessible in previous optical investigations of interband transitions around $k=0$. Also, we report a large pressure coefficient for the effective mass, $m$, of the conduction electrons, $\partial m∕\partial P\approx 3\times {10}^{-3}{m}_e{\mathrm{kbar}}^{-1}$, nearly an order of magnitude larger than that found in GaAs ($\partial m∕\partial P=4\times {10}^{-4}{m}_e{\mathrm{kbar}}^{-1}$, where $m_e$ is the electron mass in vacuum).

Figure 1

Schematic band diagram of our RTDs and of the geometry of our magneto-tunneling experiment. The magnetic field $B$ is applied perpendicular to the direction of current $z$. Varying the intensity of $B$ allows us to tune an electron to tunnel into a $k$-vector state of the $\mathrm{Ga}{\mathrm{As}}_{1-y}{\mathrm{N}}_y$ QW, while the applied voltage $V$ tunes the energy $\epsilon$.

Figure 2

(a) $I\left(V\right)$ at $T=4.2\mathrm{K}$ for a $\mathrm{Ga}{\mathrm{As}}_{1-y}{\mathrm{N}}_y$ RTD $(y=0.2\%;w=10\mathrm{nm})$ at different values of $B$ and $P$. (b) Differential conductance, $G\left(V\right)=dI∕dV$, plots at $B=0\mathrm{T}$ and different $P$. For clarity, the curves are displaced along the vertical axis.

Figure 3

(Color online) Color and contour line plots of $G\left(V\right)$ as a function of energy $\epsilon$ $(\sim V)$ and $k$ vector $(\sim B)$ as derived from our magneto-tunneling experiment on a $\mathrm{Ga}{\mathrm{As}}_{1-y}{\mathrm{N}}_y$ RTD $(y=0.2\%;w=10\mathrm{nm})$. The vertical scale does not correspond to an absolute energy scale. Plots (a)–(d) correspond to $P=1\text{bar}$, $3.9\mathrm{kbar}$, $6.4\mathrm{kbar}$, and $9.3\mathrm{kbar}$, respectively. The full dot and the arrows indicate energy and $k$ vector $k^{*}$ values of anticrossing in the $\epsilon \left(k\right)$ curves. The value of $k^{*}$ is considerably smaller than the size of the Brillouin zone $k_{\mathrm{BZ}}$, i.e., $k^{*}∕k_{\mathrm{BZ}}\sim 0.1$.

Figure 4

(Color online) $P$ dependence of the ratios $k^{*}\left(P\right)∕k^{*}\left(0\right)$, ${\Delta }_G\left(P\right)∕{\Delta }_G\left(0\right)$, and $m\left(P\right)∕m\left(0\right)$ as derived from our magneto-tunneling measurements on a $\mathrm{Ga}{\mathrm{As}}_{1-y}{\mathrm{N}}_y$ RTD $(y=0.2\%;w=10\mathrm{nm})$. The three ratios are labeled as $r$ in the vertical axis. The curves represent the $P$ dependence of the three ratios calculated using a two-level BAC model for bulk $\mathrm{Ga}{\mathrm{As}}_{1-y}{\mathrm{N}}_y$. The $P$ dependences of $k^{*}$ and ${\Delta }_G$ are shown in the inset.