Resonant Zener tunnelling via zero-dimensional states in a narrow gap diode

Abstract

Interband tunnelling of carriers through a forbidden energy gap, known as Zener tunnelling, is a phenomenon of fundamental and technological interest. Its experimental observation in the Esaki p-n semiconductor diode has led to the first demonstration and exploitation of quantum tunnelling in a condensed matter system. Here we demonstrate a new type of Zener tunnelling that involves the resonant transmission of electrons through zero-dimensional (0D) states. In our devices, a narrow quantum well of the mid-infrared (MIR) alloy In(AsN) is placed in the intrinsic (i) layer of a p-i-n diode. The incorporation of nitrogen in the quantum well creates 0D states that are localized on nanometer lengthscales. These levels provide intermediate states that act as "stepping stones" for electrons tunnelling across the diode and give rise to a negative differential resistance (NDR) that is weakly dependent on temperature. These electron transport properties have potential for the development of nanometre-scale non-linear components for electronics and MIR photonics.

Figure 1. Resonant tunnelling diodes based on the narrow-gap In(AsN).

(a) Energy band diagram of a p-i-n In(AsN)/(InAl)As resonant tunnelling diode (RTD) at thermal equilibrium. The black dotted lines indicate the Fermi energy and the lowest quasi-bound electron state E₁ of the In(AsN) QW. Inset: Sketch of the p-i-n diode with the In(AsN) QW in the intrinsic (i) layer, and substitutional and interstitial N-atoms in InAs. (b) Current-voltage I(V) curve at T = 2 K for an In(AsN) RTD with mesa diameter d = 100 μm showing a strong peak D. Inset: dI(V)/dV curve showing a weak resonant feature E₁.

Figure 2. Temperature dependence of resonant Zener tunneling.

(a) Current-voltage I(V) characteristics at temperatures T from 15 K to 300 K of In(AsN) (top) and InAs (bottom) RTDs with mesa diameter d = 200 μm. (b) Bias dependence of the activation energy E_a describing the dependence of the current I on temperature, i.e. I = I₀exp(−E_a/k_BT). Inset: Electron diffusion and tunnelling. (c) I(V) characteristics of the In(AsN) RTD at T = 15 K, 220 K and 296 K after subtraction of the diffusion current.

Figure 3. Magneto-tunnelling spectroscopy of zero dimensional states.

(a) Current-voltage I(V) curves at magnetic fields B_x = 0, 2, 4, 6, 8, 10, 12, 14 T, applied perpendicular to the direction z of the current for an In(AsN) RTD with mesa diameter d = 100 μm (T = 2 K). (b) Measured (dots) and calculated (lines) dependence of the normalized current I(B_x)/I(0). The model shown in the two panels is for a Coulomb (left) and an harmonic (right) potential U(x, y). In each panel, different curves correspond to different sizes λ₀ of the electronic wavefunction.

Figure 4. Resonant Zener tunnelling in magnetic field parallel to the direction of current.

(a) Current-voltage I(V) curves at magnetic fields B_z = 0, 2, 4, 6, 8, 10, 12, 14 T, applied parallel to the direction z of the current for an In(AsN) RTD with mesa diameter d = 100 μm (T = 2 K). (b,c) Differential conductance dI(V)/dV curves versus B_z in the bias region of electron tunnelling into the first subband, E₁, of the In(AsN) (b) and InAs (c) QW for B_z = 0, 4, 6, 8, 10, and 14 T. The insets show the dI(V)/dV curves at small applied biases (T = 2 K).

Figure 5. Resonant Zener tunnelling via zero dimensional states.

Calculated profile of the conduction band edge at applied biases V = 0 V (continuous line) and V = 0.05 V, 0.1 V (dashed lines). The arrow sketches tunnelling of electrons from the n-emitter layer into localized states of the In(AsN) layer (shaded rectangle). Insets: Profile of both the conduction and valence band edges under the same bias conditions illustrated in the main panels.