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Exact determination of electrical properties of wurtzite Al1−xInxN/(AlN)/GaN heterostructures (0.07 ≤ x ≤ 0.21) by means of a detailed charge balance equation

Published online by Cambridge University Press:  19 April 2010

Marcus Gonschorek*
Affiliation:
Institute of Condensed Matter Physics (ICMP), Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.
Jean-Francois Carlin
Affiliation:
Institute of Condensed Matter Physics (ICMP), Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.
Eric Feltin
Affiliation:
Institute of Condensed Matter Physics (ICMP), Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.
Marcel Py
Affiliation:
Institute of Condensed Matter Physics (ICMP), Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.
Nicolas Grandjean
Affiliation:
Institute of Condensed Matter Physics (ICMP), Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.
*
Corresponding author: M. Gonschorek Email: marcus.gonschorek@epfl.ch
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Abstract

This paper discusses the determination of key electrical parameters of AlInN/(AlN)/GaN heterostructures from capacitance–voltage (CV) measurements. These heterostructures gained recently importance since they allow for high electron mobility transistor (HEMT) devices with several remarkable records: densities of the 2D electron gas (2DEG) of 2.6 × 1013 cm−2 for lattice-matched (LM) heterostructures and barrier thickness of 14 nm, beyond 2 A/mm saturation currents, above 100 GHz operation for heterostructures grown on Si (111) with gate length of 0.1 µm. Despite these striking experimental results, a consistent determination of the most important electrical parameters, namely polarization sheet charge density, surface potential, and dielectric constant of the alloy are still missing. By setting up the correct charge balance equation, these parameters can unambiguously be determined. For instance, in the case of nearly LM Al0.85In0.15N these parameters amount to σAl0.85In0.15N/GaN ~ 3.7 × 1017 m−2, eΦS ~ 3 eV and ɛAl0.85In0.15N ~11.2, for the charge density, the surface barrier potential, and the dielectric constant, respectively.

Information

Type
Original Article
Copyright
Copyright © Cambridge University Press and the European Microwave Association 2010
Figure 0

Fig. 1. Critical thickness tcr expected for the onset of plastic relaxation via the formation of MDs for the Al1−xInxN alloy grown on GaN with a = 0.3182 nm. The lattice matched condition is met at x = 0.175, where epilayers could potentially be grown infinitely thick. In practice, tcr drops rapidly below 100 nm within a ±1% range from the LM condition.

Figure 1

Fig. 2. (a) Polarization charge density bound at the heterointerface of the ABN/GaN heterostructure grown on Ga-face GaN [14]. Positive sign indicates the presence of a 2DEG whereas for negative polarization charges a 2DHG is expected. (b) Band diagram for the balance equation model of an AlInN/AlN/GaN heterostructure. Note the signs of the polarization across both heterointerfaces, which have crucial importance.

Figure 2

Fig. 3. (a) Electrochemical CV of an Al0.85In0.15N/AlN/GaN heterostructure. The AlN interlayer thickness is 1.1 nm for all subfigures. During the measurement a ~1 nm thin layer at the AlInN surface is transformed into an oxide. Black curves are as measured and gray ones true CV considering the oxide. (b) Depletion voltages Vdepl as a function of AlInN thickness. Slope and offset are indicated. (c) 2DEG density as a function of the total barrier thickness dAlInN + dAlN : obtained by RT Hall measurement (RH) and integrated from the CV-curves in subfigure (a). The full line corresponds to equation (2) solved for n2d(dAlInN) together with the set of parameters (9) and (10).

Figure 3

Fig. 4. CV curves for an Al0.85In0.15N/AlN/GaN heterostructure with a fixed AlInN thickness of ~12.5 nm and various AlN interlayer thicknesses. Inset shows the depletion voltage for the respective interlayer thicknesses. The behavior is not linear as in Fig. 3(b). This is caused by thickness dependence of the surface potential and possibly due to a change in the static dielectric constant for these ultrathin layers. Local slope for thicker interlayers gives approximately the value expected for an AlN layer.

Figure 4

Fig. 5. (a) Depletion voltages Vdepl for 6 and 14 nm thick barriers as a function of the Al1−xInxN thickness for several compositions. Black and gray lines stand for the tensile and compressive regime, respectively. (b) 2DEG density (integrated from CV curve) at RT for 6, 9, 14, and 33 nm thick Al1−xInxN barriers on GaN epilayers (black squares). Blue lines correspond to fits using equation (2). A full line turning into a dashed line indicates that the critical thickness tcr, beyond which pseudomorphic AlInN layers are expected to relax, is reached for the respective composition.

Figure 5

Table 1. Critical thickness tcr for plastic relaxation, 2DEG densities deduced from C–V measurements for 6 and 14 nm thick barriers, band offset at the AlInN/AlN interface, surface potential, and bound interface sheet density for five different compositions in the nearly LM regime between 7 and 21%.

Figure 6

Fig. 6. (a) Lines correspond to spontaneous (—) and piezoelectric (…) polarization charges and the sum of both (——) at RT for an AlInN random alloy. 2DEG densities for 6 nm thick (gray squares), 14 nm thick (dark gray squares) AlInN barriers, and the extrapolated total bound. (b) Electric field across the AlInN barrier for 7, 12, and 14.5% indium calculated from equation (2) using the parameters from Table 1.