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Double injection in graphene p-i-n structures
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Figures

Image of FIG. 1.

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FIG. 1.

Schematic view of the cross-sections of MGL p-i-n structures with chemically doped n- and p-contact regions (upper panel) and with such regions electrically induced by the side gate-voltages and (lower panel).

Image of FIG. 2.

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FIG. 2.

Qualitative view of band profiles of a GL p-i-n structure (a) at  = 0 and (b) at forward bias . Opaque and open circles correspond to electrons and holes, respectively. Wavy, straight, and dashed arrows correspond to the recombination in the i-region (assisted by optical phonon emission), tunneling at the contact, and thermionic leakage to the contact, respectively.

Image of FIG. 3.

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FIG. 3.

Fermi energy in the i-region as a function of the bias voltage for different values of parameter . Opaque squares correspond to electron (hole) Fermi energies at  = 0 calculated numerically in Sec. IV .

Image of FIG. 4.

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FIG. 4.

Conduction band bottom (valence band top) profiles in the i-region calculated for different bias voltages at  = 0.1 (upper panel) and  = 1.0 (lower panel) at  = 100. The extreme left and right markers (at ) show the positions of the Dirac point at p-i and i-n junctions. Insets show detailed behavior in close vicinities near the i-region edges.

Image of FIG. 5.

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FIG. 5.

Spatial distributions of the electron Fermi energy at  = 1 and  = 100 calculated for different values of bias voltage at . Inset shows dependences near the n-contact. Opaque circles correspond to data obtained using analytical model.

Image of FIG. 6.

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FIG. 6.

Spatial distributions of electron density at different bias voltages ( and ).

Image of FIG. 7.

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FIG. 7.

Spatial distributions of the electron Fermi energy at  = 1 and  = 100 calculated for different values of ratio and  = 250  mV at .

Image of FIG. 8.

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FIG. 8.

Coordinate dependences of normalized electron velocity calculated for  = 1.0 and  = 250 mV at different values of .

Image of FIG. 9.

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FIG. 9.

The normalized electron velocity versus coordinate for  = 1.0 and  = 250 mV at different values of normalized edge recombination velocity (left panel). Right panel shows details of the same dependences in close vicinity of the p-i interface.

Image of FIG. 10.

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FIG. 10.

Current-voltage characteristics for different values of parameter . Inset shows the current as a function of parameter calculated at  = 250 mV for  = 1.0.

Image of FIG. 11.

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FIG. 11.

Comparison of band edge profiles in structures with abrupt (solid line with markers, the same as in Fig. 4 ) and with smeared p-i and n-i junctions (without markers) at  = 500 mV for  = 1.0.

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/content/aip/journal/jap/113/24/10.1063/1.4812494
2013-06-28
2014-04-20

Abstract

We study the processes of the electron and hole injection (double injection) into the i-region of graphene-layer and multiple graphene-layer p-i-n structures at the forward bias voltages. The hydrodynamic equations governing the electron and hole transport in graphene coupled with the two-dimensional Poisson equation are employed. Using analytical and numerical solutions of the equations of the model, we calculate the band edge profile, the spatial distributions of the quasi-Fermi energies, carrier density and velocity, and the current-voltage characteristics. In particular, we demonstrated that the electron and hole collisions can strongly affect these distributions. The obtained results can be used for the realization and optimization of graphene-based injection terahertz and infrared lasers.

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Scitation: Double injection in graphene p-i-n structures
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/24/10.1063/1.4812494
10.1063/1.4812494
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