Magnetophonon oscillations in the negative differential conductance of dilute nitride $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{N}}_x$ submicron diodes

We study the nonlinear electron dynamics that occurs in the dilute nitride alloy Ga(AsN) when, in high applied electric fields, conduction electrons gain sufficient energy to approach the energy of the localized N level. This process leads to a strong negative differential conductance (NDC) effect. In a quantizing magnetic field, we observe that the threshold electric field for NDC is resonantly modulated when electrons can relax energy by inter-Landau-level transitions involving the emission of a longitudinal optical phonon. This unusual manifestation of magnetophonon resonance reveals that the mechanism giving rise to NDC is an inherently fast $(<{10}^{-12}\mathrm{s})$ process of relevance for terahertz electronics.

Figure 1

(Color online) (a) Energy–wave-vector dispersion relation $\epsilon \left(k\right)$ for the hybridized subbands of $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{N}}_x$ $(x=0.1\%)$, calculated from a two-level band-anticrossing model. The lines describe the $\epsilon \left(k\right)$ curve for GaAs and the energy position of the N level $(T=4.2\mathrm{K})$. (b) Schematic of our device. The arrows indicate the orientation of the current $I$ and electric $\left(\mathbf{F}\right)$ and magnetic fields $\left(\mathbf{B}\right)$. (c) Current-voltage characteristics $I\left(V\right)$ of our device at $4.2\mathrm{K}$ and $\mathbf{B}=0$. The continuous line is the calculated $I\left(V\right)$ curve which includes the contribution of current due to free carriers (dashed line) and injected space charge (dotted line).

Figure 2

Current-voltage characteristics $I\left(V\right)$ of our device at $4.2\mathrm{K}$ and various $B$. The magnetic field is increased from $0\text{to}23\mathrm{T}$ in steps of $1\mathrm{T}$. The dashed line is a guide to the eye showing the bias shift of the peak in $I\left(V\right)$ induced by $B$. The inset shows magnified $I\left(V\right)$ curves with $B$ increased from $9\text{to}23\mathrm{T}$.

Figure 3

(a) Magnetic field dependence of the critical field $F_T$ for NDC in $I\left(V\right)$. The line is a guide to the eye. The error on $F_T$ is within the size of the data points. (b) Magnetic field dependence of the longitudinal magnetoresistance measured under various applied biases $V$. (c) Plot of $-d^{2}R∕d{B}^2$ versus $B$ at $V=0.10\mathrm{V}$.

Figure 4

Plot of $N$ vs $1∕B$ for $F_T$ (circles), for the magnetoresistance in $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{N}}_x$ $(x=0.1\%)$ (stars), and in an all-GaAs diode (dots). Data for GaAs are from Ref. 25. The continuous and dashed lines represent the curve $N=(m_e^{*}{\omega }_{\mathit{LO}}∕e)B^{-1}$ with $m_e^{*}=0.13m_e$ and $m_e^{*}=0.07m_e$, respectively. The inset shows the dependence of $m_e^{*}$ on $V$ for $\mathrm{Ga}{\mathrm{As}}_{1-x}{\mathrm{N}}_x$.