Electrically induced $n\text{−}i\text{−}p$ junctions in multiple graphene layer structures

The Fermi energies of electrons and holes and their densities in different graphene layers (GLs) in the $n$ and $p$ regions of the electrically induced $n\text{−}i\text{−}p$ junctions formed in multiple-GL structures are calculated both numerically and using a simplified analytical model. The reverse current associated with the injection of minority carriers through the $n$ and $p$ regions in the electrically induced $n\text{−}i\text{−}p$ junctions under the reverse bias is calculated as well. It is shown that in the electrically induced $n\text{−}i\text{−}p$ junctions with moderate numbers of GLs the reverse current can be substantially suppressed. Hence, multiple-GL structures with such $n\text{−}i\text{−}p$ junctions can be used in different electron and optoelectronic devices.

Figure 1

(Color online) Schematic view of (a) a multiple-GL structure and its band diagrams at (b) zero bias voltage $\left(V=0\right)$ and (c) at reverse bias (for GL with $k=1$). Arrows indicate the directions of propagation of injected electrons and holes as well as those thermogenerated and generated due to interband tunneling.

Figure 2

(Color online) The electron Fermi energy ${\mu }_k$ as a function of the GL index $k$ calculated for multiple-GL structures with different number of GLs $K$ for different gate voltages $V_g$ at $T=300\text{K}$ (upper panel) and $T=77\text{K}$ (lower panel).

Figure 3

(Color online) Voltage dependences of electron Fermi energies in some GLs in multiple-GL structure with different $K$ at $T=300\text{K}$.

Figure 4

(Color online) Electron density vs GL index in multiple-GL structures with different number of GLs ($K=10$ and $K=50$) at different temperatures and $V_g=1000\text{mV}$.

Figure 5

(Color online) Comparison of the ${\mu }_k$ vs $k$ dependences calculated for different temperatures using numerical and simplified analytical (solid line) models.

Figure 6

(Color online) Temperature dependence of reverse current (injection component, $J_i$) for multiple-GL structures with different number of GLs.