Fighting Broken Symmetry with Doping: Toward Polar Resonant Tunneling Diodes with Symmetric Characteristics

Jimy Encomendero, Vladimir Protasenko, Farhan Rana, Debdeep Jena, and Huili Grace Xing

Phys. Rev. Applied 13, 034048 – Published 19 March 2020

Abstract

The recent demonstration of resonant tunneling transport in nitride semiconductors has led to an invigorated effort to harness this quantum transport regime for practical applications. In polar semiconductors, however, the interplay between fixed polarization charges and mobile free carriers leads to asymmetric transport characteristics. Here, we investigate the possibility of using degenerately doped contact layers to screen the built-in polarization fields and recover symmetric resonant injection. Thanks to a high doping density, negative differential conductance is observed under both bias polarities of $Ga N$ / $Al N$ resonant tunneling diodes (RTDs). Moreover, our analytical model reveals a lower bound for the minimum resonant-tunneling voltage achieved via uniform doping, owing to the dopant solubility limit. Charge storage dynamics is also studied by impedance measurements, showing that at close-to-equilibrium conditions, polar RTDs behave effectively as parallel-plate capacitors. These mechanisms are completely reproduced by our analytical model, providing a theoretical framework useful in the design and analysis of polar resonant-tunneling devices.

Received 4 September 2019
Revised 20 February 2020
Accepted 27 February 2020

DOI:https://doi.org/10.1103/PhysRevApplied.13.034048

Physics Subject Headings (PhySH)

Capacitance Electric polarization Quantum transport

Diodes Doped semiconductors III-V semiconductors Nitrides

Tunnel diode resonance

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jimy Encomendero ^1,*, Vladimir Protasenko¹, Farhan Rana¹, Debdeep Jena^1,2,3,†, and Huili Grace Xing^1,2,3,‡

¹School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA
²Department of Materials Science and Engineering, Cornell University, Ithaca, New York 14853, USA
³Kavli Institute at Cornell for Nanoscale Science, Cornell University, Ithaca, New York 14853, USA

^*jje64@cornell.edu
^†djena@cornell.edu
^‡grace.xing@cornell.edu

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Vol. 13, Iss. 3 — March 2020

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Figure 1
$Ga N$ / $Al N$ double-barrier RTD heterostructures. (a) Schematic representation of the complete device structure grown by molecular beam epitaxy on single-crystal n-type $Ga N$ substrates. Two device designs with varying doping concentration $N_{d}$ are synthesized and fabricated. (b) The equilibrium conduction-band energy profile of each sample is calculated by solving Poisson and Schrödinger equations self-consistently. As a result of the redistribution of free carriers, the conduction band profile and internal electric fields are modulated resulting in a shift in the energies of the resonant levels inside the well. (c) The electric field profile for the RTD structure featuring a doping density $N_{d}^{+} = 1 \times 10^{19} {cm}^{- 3}$ is also obtained from numerical calculations. The various layer thicknesses are also indicated: $t_{d}$ is the extension of the collector depletion region, $t_{s}$ is the thickness of the collector spacer, and $t_{b}$ and $t_{w}$ represent the thickness of the tunneling barriers and width of the quantum well, respectively.
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Figure 2
Current-voltage (J-V) characteristics of $Ga N$ / $Al N$ RTDs with different contact doping concentrations measured at cryogenic and room temperatures. (a),(b) When the doping level at the contacts is increased from $N_{d}^{+} = 1 \times 10^{19} {cm}^{- 3}$ to $N_{d}^{+ +} = 4 \times 10^{19} {cm}^{- 3}$ , the energy of the lowest resonant level is reduced, resulting in a lower peak voltage under forward bias. Within the region of NDC, plotted with dotted lines, parasitic oscillations are measured due to the RTD gain, which produces the chair-like feature. The peak and valley currents are the maximum and minimum currents that delimit the NDC region. (b) Under cryogenic conditions, the reduction of the thermal current component results in an increased peak-to-valley current ratio (PVCR), which is measured at 1.88 (1.63) for the RTD structure with the lower (higher) doping level. (c),(d) Logarithmic plots of the same data displayed in (a),(b), which reveal the exponential modulation of the tunneling current under nonequilibrium conditions. (d) Multiple resonant tunneling features, indicated by the arrows, are observed under forward and reverse bias. The origin of these features is explained in Fig. 3.
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Figure 3
Under cryogenic temperatures ( $T = 80 K$ ), various resonant tunneling features are observed in the J-V characteristics of $Ga N$ / $Al N$ RTDs. (a) The differential conductance reveals multiple peaks, indicated by the arrows, which correspond to the resonant alignment between the electron reservoirs in the contacts and the resonant levels within the well. (b) The voltages required to attain these resonances are strongly dependent on the doping concentration at the contacts. The experimentally measured resonant voltages are displayed as a function of the doping concentration, showing a good quantitative agreement with theoretical calculations. The experimental data points shown as circles were taken from Ref. [22]. (c)–(e) To elucidate the origin of the conductance peaks, we calculate the RTD band diagrams for each of the resonant configurations for $N_{d}^{+ +} = 4 \times 10^{19} {cm}^{- 3}$ , under forward- and reverse-bias conditions.
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Figure 4
III-nitride RTD capacitance measured under close-to-equilibrium conditions for the two RTD designs with different contact doping concentrations $N_{d}^{+}$ and $N_{d}^{+ +}$ . Employing our analytical model for polar RTDs, we also compute the theoretical RTD capacitance, given by Eq. (3), for the structure shown in Fig. 1, while varying the doping concentration between $1 \times 10^{19}$ and $9 \times 10^{19} {cm}^{- 3}$ (blue curves). The agreement between the experimental and theoretical results reveals that polar RTDs behave effectively as parallel-plate capacitors when the population of the resonant level is negligible. The inset depicts a general polar RTD structure, which shows the various layer thicknesses employed to calculate the effective parallel-plate distance $t_{cap} = t_{d} + t_{s} + 2 t_{b} + t_{w} + t_{c}$ and RTD capacitance $C_{RTD} = ϵ_{s} / t_{cap}$ .
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