InN: Breaking the limits of solid-state electronics

The speed and complexity of Si CMOS digital logic circuits have been steadily increasing by shrinking the size of Si MOSFET transistors, but it has already reached the end limits of miniaturization. Further progress, essential for higher performance and complexity electronics, may be realized by replacing the n-type MOSFET transistor channel with a III–V semiconductor providing a significant increase in the electron velocity.¹ Similarly, there is increasing interest in using THz frequencies in ultra-high-speed information and communication systems, such as in wireless communications, or in infra-red imaging systems and spectroscopy detection.^2,3 At present, quantum cascade lasers are being developed as the THz electromagnetic wave emitters. The functionality of these optical devices is based on the electron–phonon interaction in the semiconductor lattice, and thus, they can operate only at low temperatures, making them less practical for applications.^3,4 Therefore, a new approach for the THz microwave source based solely on the electron transport is desired. Until now, the highest transistor switching speed of ∼0.7 THz has been obtained by using InAs as a channel material,⁵ defining the THz frequency gap between the electronic and optical devices.³ 

The speed performance of transistors is dependent on the carrier transit time τ in the channel along the gate, as the cut-off frequency f_T is defined as 1/(2πτ). The carrier transit time is given as τ = L_G/v, where v is the electron drift velocity along the channel and L_G is the gate length.⁶ Consequently, v is the most important material parameter, defining the switching speed of electronic devices. The crystal structure, which is specific for every semiconductor material, is the main variable determining the maximal v.⁷ According to theoretical calculations, InN provides the highest steady-state electron drift velocity among all semiconductors, with a value of ∼5–6 × 10⁷ cm s⁻¹.^8–11 Consequently, assuming L_G = 20 nm, f_T of an InN-channel transistor could ideally reach about 4 THz. Moreover, low effective mass of electrons in InN may lead to non-stationary dynamics along ultra-short L_G values, increasing f_T beyond its steady-state value.^8–10,12 Graphene might be seen as a 2D alternative to the InN semiconductor due to extremely high electron mobility and a comparable electron velocity of about 5 × 10⁷ cm s⁻¹ (Ref. 13). However, graphene is a metallic system, i.e., transistors cannot be pinched-off, limiting its application in electronics.¹³ In contrast, InN, with a reasonably small energy bandgap between the valence and free electron quantum states (which is the main asset of semiconductors), promises full digital and analog capabilities.¹⁴ 

However, up to present, there is no experimental verification of expected steady-state v or any demonstration of an InN-based microwave transistor. The main reason for this lies in the immature stage of the InN crystal growth and lack of a suitable substrate. InN belongs to the group of nitride semiconductors, and thus, readily available GaN templates or substrates might be seen as a natural choice. However, there is a direct relation between the lattice misfit and the critical thickness of the grown layer beyond which it relaxes.¹⁵ Therefore, the huge misfit (about 11%) between InN and the underlying GaN leads to almost immediate InN relaxation, as the growth is initiated.^14,16,17 Consequently, a large number of dislocations are generated at the GaN/InN interface, propagating into the grown InN layer.^14,16 Electron scattering on crystal imperfections limits the electron mobility and the electric field-induced velocity acceleration.¹⁸ Moreover, crystal dislocations can lead to a premature electric field-induced breakdown.¹⁹ Therefore, in order to improve the crystalline quality, a thick InN film must be grown, allowing for device-quality electron mobilities above 1000 cm² s⁻¹ V⁻¹ (Refs. 14 and 18). At room temperature, state-of-the-art InN layers, grown by molecular-beam epitaxy (MBE), have demonstrated an electron mobility of ∼1500 cm² s⁻¹ V⁻¹ for an InN layer thickness of 500 nm, while for a higher InN thickness of 5 µm, the electron mobility reached a value of 3010 cm² s⁻¹ V⁻¹.^20,21 However, in the case of InN-channel transistors, the channel thickness must be kept well below a few tens of nm in order to allow for the gate electrostatic control over the current flow. Therefore, the first attempts in demonstrating InN-channel transistors suffered from poor material quality.^22–24 On the other hand, before technical aspects of the thin film InN growth are solved, experimental verification of record v in thick InN layers remained a challenging but manageable goal. We pioneered this type of InN characterization in our previous work.¹⁹ 

Earlier, we reported 500-nm thick InN films grown by MBE that exhibited a density of 7.2 × 10⁸ and 5.6 × 10¹⁰ cm⁻² for screw and edge dislocations, respectively, with the electron mobility of 1040 cm² s⁻¹ V⁻¹ at room temperature.¹⁸ A high purity crystal was grown by using a nitrogen plasma source without hydrogen-containing gases (NH₃).²⁵ Our specific test structures consisted of planar two-terminal resistors formed by a plasma etching and Ohmic contact formation. Etching was performed down to the high-resistivity GaN layer, so that the height (h) of the resistors was defined by the InN thickness. We applied 10-ns long voltage pulses and extracted current (I)–voltage (V) characteristics. Consequently, v could be calculated as v = I/qnhw, where q is the electron charge, n is the electron concentration, and w is the resistor width.¹⁹ Pulsed probing was necessary to eliminate the self-heating effect and possible burnout of the InN structure.²⁶ Still, a 10-ns time scale could be considered long enough to reach the steady-state electron drift condition.⁸ Promising v ∼ 2.5 × 10⁷ cm s⁻¹ was extracted in this way when a premature InN breakdown appeared at ∼22 kV cm⁻¹ regardless of the resistor length.¹⁹ The obtained v value was about twice as high compared to conventional GaN-based structures²⁷ but was still clearly lower than theoretical expectations for InN.^8–11 In the present work, we extract v in further optimized high-quality InN layers. Unexpected outcomes are obtained suggesting a need for a revision of fundamental properties of InN. We show that InN is the best far-reaching candidate for advancing ultra-fast electronics beyond any prior expectations.

Analogous to our previous report, MBE is used for the growth of the GaN/InN (0001) samples demonstrating In-polarity at the surface, while pulse-operated resistors were implemented for v extractions. This time, however, the InN growth recipe was optimized for a lower number of dislocations, while the InN thickness was increased up to 775 nm.¹⁸ The InN surface morphology was studied by scanning electron microscopy (SEM), while the crystalline quality was assessed by high-resolution x-ray diffraction (HRXRD).^19,28 Before processing a series of 8-µm long and 4-µm wide resistors, the electron mobility and concentration in the InN layer were determined by Hall effect measurements.²⁹ The fabricated InN test structures were subject to 10-ns long voltage pulses; microwave probes and impedance matching of the pulse generator with the load were implemented to minimize reflections of the incident waves. A two-channel oscilloscope was used to record the voltage drop V₂ − V₁ along a nominal resistor R_m, providing assessment of the current as (V₂ − V₁)/R_m. The electric field applied on the InN test structure was calculated as V₁/L, with L being the length of the InN test resistor and V₁ being the incident voltage.

Figure 1 shows the SEM view of the surface of the grown InN film. A compact InN film consisting of large coalesced InN grains was evident, with a reduced density of dislocations that originate at the grain coalescence boundaries.

Figure 2 illustrates the results of HRXRD scans recorded in (a) symmetric 2θ/ω mode and (b) rocking curve mode The positions of 2θ/ω maxima correspond to the lattice parameters c of perfectly stoichiometric InN and GaN compounds, even though some marginal strain in InN was still present. On the other hand, the full width at half maximum of the (0002) InN rocking curve, in combination with the (10-11) rocking curve (not shown), indicates the density of 7.2 × 10⁸ and 4.6 × 10¹⁰ cm⁻² for screw and edge dislocations, respectively. This is by about 20% less edge dislocations than in our previous study, although a thinner InN sample was used in that case.

The high-quality InN structural properties were also confirmed by conductivity and Hall effect measurements, as shown in Fig. 3, down to 20 K. At room temperature, the electron mobility and carrier concentration reached 1940 cm² s⁻¹ V⁻¹ and 7.9 × 10¹⁷ cm⁻³, respectively. The weak dependence of the electron mobility on temperature indicated that the electron scattering was still dominated by dislocations generated at the GaN/InN interface, and not by phonons of the vibrating InN lattice.³⁰ 

Figure 4(a) shows typical voltage waveforms, recorded by an oscilloscope, along with a schematic of the measurement setup. In Fig. 4(b), the InN current density as a function of the electric field (E) intensity, along with the calculated drift velocity, is presented. Noteworthy is the linear increase of the current and corresponding drift velocity values up to unprecedented I ∼ 100 A/mm and ν ∼ 1 × 10⁸ cm s⁻¹ at E ∼ 48 kV cm⁻¹ when values nonlinearly hike. Prior to that, depending on the assumed band structure and nonparabolicity factor of the InN central valley, saturation of the electron velocity should normally appear at E ∼ 15–40 kV cm⁻¹ due to increased phonon scattering.^8–11,31 In our case, however, theoretical saturation seems to be shifted beyond the breakdown field, which along with enhanced material strength and decent electron mobility accounts for the observed record ν − E performance. Premature breakdown at E ∼ 48 kV cm⁻¹ was found to be mostly reversible, in agreement with earlier suggested interband trap-assisted tunneling along the InN/GaN interface.¹⁹ Consequently, despite the huge energy of the pulse applied to the resistor, temperature rise was not critical in our case, likely due to the short duration of the event. Nevertheless, our experimentally observed electron velocity is about twice as high as those predicted by any theory before.

A further increase in the breakdown field and saturation of ν could be expected in structures grown with a less defective interface. Therefore, study of alternative underlying layers for fewer misfits toward InN can be suggested in a first instance. This solution may provide a lower number of dislocations and decent mobility even in thin InN layers without premature breakdown. In respect to that growth on In-rich InAlN layers has been proposed recently,^32,33 first experimental verifications of InN/InAlN heterostructures are in progress.²⁸ Because of the anisotropy of InN,³⁴ testing of differently oriented resistors can also be suggested.

Nevertheless, our experimentally observed InN steady-state electron drift velocity of about 1 × 10⁸ cm s⁻¹ is by far the highest ever reported in any solid-state device, being about twice as high as what has been reported for graphene,¹³ In_0.8Ga_0.2As (ν ∼ 5.6 × 10⁷ cm s⁻¹),³⁵ or theoretically calculated for InN.^8–11 Discrepancy with the theoretical estimations calls for a revision on understanding the InN fundamental properties, likely related to the theoretical band structure of InN. A similar revision had taken place earlier after the optical bandgap of InN was modified from 1.9 eV to about 0.7 eV or less.^18,36

We note that apart from the InN/GaN interface, a high density of defects is present also at the InN surface causing Fermi level pinning in the conduction band, electron accumulation, and additional electron mobility degradation.^18,37 Thus, there might be some ambiguity in ν extraction because of the parallel conduction through the InN surface, bulk, and interface.^18,37 In our recent work, we analyzed Hall data of the thick InN film (identical to the present case) in combination with a 120-nm thick InN modeling conduction through both distorted regions.¹⁸ For the InN bulk (B) and surface/interface regions (I) at room temperature, we determined the electron mobility and concentration to be 2462 (1007) cm² s⁻¹ V⁻¹ and 4.9 × 10¹⁷ (3.7 × 10¹⁸) cm⁻³, respectively. Consequently, we can calculate the InN bulk electron velocity as ν_B = I_B/qn_Bh_Bw, where I_B = I/(1 + (n_Ih_Iμ_Ι)/(n_Bh_Bμ_Β)). Applying this approximation, we can estimate that our extracted ν, in respect to the InN bulk (real) value, has been underestimated by about 20%.

Finally, it should be mentioned that the steady-state electron velocity in GaN is only about one tenth of the value found in InN, but still, an f_T above 400 GHz has been achieved in short channel GaN-based transistors.^27,38 Consequently, taking into account a higher prospect for the electron non-stationary dynamics in InN,^8–10,12 a significant breakthrough of future InN-based communication and information systems in the THz frequency range can be expected. InN may finally close the frequency gap between the electronic and optical devices.

The work in Slovakia was supported by the Ministry of Education, Science, Research, and Sport of the Slovak Republic—VEGA (Grant No. 2/0012/18). The work in Greece was supported by the Hellenic Foundation for Research and Innovation (HFRI), project: EPINEET (Grant No. HFRI-FM17-3173). The collaboration between the two institutions was supported by the EU-H2020 Research and Innovation programme under Grant Agreement No. 654360 NFFA-Europe.