Micro-PL analysis of high current density resonant tunneling diodes for THz applications

There is a lack of efficient high-speed technology able to satisfy the ever-growing wireless data-demand.^1,2 As a consequence, the THz frequency range (0.1–10 THz)³ has attracted considerable interest as it offers the wide bandwidth required for high data-rate communications. Resonant tunneling diodes (RTDs) have been demonstrated to be the fastest solid-state device with oscillation near 2THz⁴ with highly attractive characteristics: tunability, compact dimensions, and room temperature operation.⁵ 

As for all quantum-effect devices,⁶ the RTD performance is critically dependent on crystal purity and heterointerface perfection. We previously demonstrated how ∼80% of the parasitic valley current is associated with non-thermal inelastic scattering,⁷ and as a consequence, the RTD output power is limited by crystal-related imperfections.

RTDs are composed of a single double-barrier QW generally grown by molecular beam epitaxy (MBE) or metal-organic vapor-phase epitaxy (MOVPE); despite the outstanding precision offered by these technologies, wafer characterization remains a difficult process, leading to knowledge barriers in epitaxial process optimization. X-ray diffraction characterization provides limited information compared to a periodic QW superlattice,⁸ while photoluminescence techniques are uninformative at room temperature.⁹ 

The electrical and physical characterization of these structures is, therefore, important to improve upon the reproducibility and support device engineering and commercialization. We previously proposed a nondestructive characterization scheme based on low-temperature photoluminescence spectroscopy (PL) in combination with high-resolution x-ray diffraction (HD-XRD), improved by the inclusion of a buried undoped “copy” QW.⁸ Critical information on the band offset has subsequently been obtained by applying photoluminescence excitation spectroscopy (PLE) with the additional benefit of an overall improvement in the repeatability of the realized epitaxial structure.¹⁰ It is important to note that several important nondestructive characterization techniques perform significant spatial-measurement averaging of a sample. Given the mesoscopic nature of RTDs, the relevance of these techniques is questionable or can be improved upon.

In this paper, we investigate the use of micro-PL to evaluate structural perfection on different length scales (higher and lower than the exciton radius) in two high current density RTD structures with highly strained QWs growth by MOVPE. The PL spot size is progressively reduced, reaching the typical RTD mesa-size (a few square micrometers). This is accomplished by employing windows (holes) of a reducing area on a chromium photolithography mask mounted on top of the wafer. We observed PL line shape differences between low and high strain-budget samples, highlighting the presence of long-range structural disorder associated with the strain relaxation process. The I-V characteristics of RTDs fabricated from these wafers are analyzed as a function of mesa-size, with the low strain-budget sample showing poor scaling of both peak and valley current with the area, in line with our nondestructive measurements of structural imperfection. This direct correlation of variation in micro-PL line shapes and variation of the static I–V characteristics indicate that care is needed in using macroscopic LT-PL for epitaxial wafer validation and that micro-PL provides a powerful technique in assessing the quality of RTD epitaxial materials.

Structures were grown using a Thomas Swan 7 × 2 robot-loaded close-coupled showerhead (CCS), metal-organic vapor phase (MOVPE) reactor. The group III precursors were trimethylaluminium (TMA), trimethylgallium (TMG), and trimethylindium (TMI), while the group V precursors were arsine (AsH₃) and phosphine (PH₃). A 300 nm InP buffer was deposited at 580 °C on Fe doped InP (001) offcut by 0.1° toward (111). The rest of structures were grown at 595 °C. 200 nm of AlInAs was grown to getter oxygen and improve the AlAs barrier symmetry, while 25 nm of InGaAs was grown to aid the nucleation of AlInAs. A CP21 wet etch profiler and Hall measurements were used to calibrate the doping concentrations, and the layer compositions were calibrated using a Bruker D8 Discovery.

After the InP buffer, the overgrowth continues with 200 nm undoped In_0.53Ga_0.47As. 400 nm highly n-doped In_0.53Ga_0.47As (2 × 10¹⁹ cm⁻³ Si) is then grown for the lower contact. A 20 nm n-doped In_0.53Ga_0.47As (3 × 10¹⁸ cm⁻³ Si) emitter layer is then deposited, followed by a 2 nm In_0.53Ga_0.47As spacer layer. An InGaAs quantum well is formed between two 1.1 nm AlAs barriers. On the collector side, a 20 nm In_0.53Ga_0.47As spacer layer is grown with a 25 nm In_0.53Ga_0.47As (3 × 10¹⁸ cm⁻³ Si) collector layer. The epitaxy is terminated with 15 nm n-doped In_0.53Ga_0.47As (2 × 10¹⁹ cm⁻³ Si) and 8 nm In_0.80Ga_0.20As (2 × 10¹⁹ cm⁻³ Si). The two samples analyzed in this paper differ only by the QW characteristics, the first one has 12 ML of InGaAs with a mole fraction of 85%, the second one has 16 ML with a mole fraction of 80%, samples will be denoted as sample “A” and “B,” respectively.

Low-temperature PL was performed in a closed-cycle helium cryostat, with the sample at a temperature of 13 K. A frequency-doubled neodymium-doped yttrium-vanadium-oxide (Nd:YVO4) laser at 532 nm was used to excite the sample. The PL signal was filtered by a double-grating Bentham DMc150 monochromator and detected by an InGaAs trans-impedance photodetector. Measurements were conducted using a laser power density of ∼0.5 mWcm⁻² with the photomask varying the excitation/detection spot size. The mask is a common commercial 3 × 3 × 0.006 in. chrome/quarts photolithography mask, positioned with the chrome absorber in contact with the sample. The designed pattern has 19 different holes, with dimensions providing areas from 100 to 10 μm² (step of 10 μm²) and from 9 to 1 μm² (step of 1 μm²). Each element in the pattern is separated by 300 μm to avoid PL-contribution from more than one source.

Diffraction effects are expected considering small apertures, extending the excited area beyond aperture edges. The photomask with the chrome absorber has the task to limit both the excitation and detection region; consequently, unwanted lateral PL emissions from the surrounding area are blocked by the chrome absorber.

We have shown that PL mapping using a ∼100–300 μm² excitation area¹¹ of the entire wafer surface showed a uniform spectral response for both designs, confirming uniform macroscopic properties. However, for high-current-density THz RTDs, much smaller regions of the sample are scanned.

At the current stage, we cannot scan the exact same spot on the sample decreasing the aperture dimensions as the mask is pressed on the sample, and holes are distributed on an area ≤0.5 cm². However, micro-PL variations are observed scanning multiple regions of the wafer, highlighting that these disorders are equally distributed on a macro scale (entire wafer), but additionally, randomly distributed on a microscale.

Figure 1(a) shows a schematic of the band-profile and the material system, with lines indicating the first two quasi-bound states (e₁ and e₂) in the QW conduction band, and the first heavy hole state (hh₁) in the valence band. Red arrows indicate the optical transition detectable in PL. The bulk transition is due to the lattice-match (LM)-InGaAs bulk bandgap, the type-II transition is generated by the recombination of electrons in the bulk conduction band with the heavy hole state in the QW, the type-I transition is due to the optical transition between the quasi-bound states in the active region, from e₁ to hh₁.

Figure 1(b) shows a not-to-scale schematic of the RTD active-region, with black lines highlighting the heterointerface roughness between the AlAs barrier and the InGaAs well. Vertical black dashed-lines indicate the thickness in ML units, while horizontal arrows indicate the monolayer fluctuation in the well thickness, designated as XML in gray, the –1 ML in dark red, and the +1 ML in green. Figure 1(b) schematically shows the impact of these growth imperfections on PL spectra; the interface roughness (length scale ≪ exciton) creates broadened peaks (increase in σ), while the ML fluctuation creates separate features (length scale ≫ exciton), leading to an overall broad PL spectrum.¹² 

The distribution of the peaks on the energy axis is highlighted at the top of the figure. Colored ellipses indicate QW excitons [radius ∼ 10 nm (Ref. 13)], which act as our probe, highlighting the length-scale of these structural imperfections.¹⁴ Figure 1(c) shows a representative wafer slice where the ML-islands are highlighted using the same color coding from Fig. 1(b). As a point of reference, a scanning cathodoluminescence (CL) study on the GaAs/AlGaAs material system showed the ad-extension of these islands to be >2 μm².¹⁵ For the InGaAs/InP material system under high strain conditions ([In] ≥ 80%), similar results were observed by scanning tunneling microscopy (STM)¹⁶ and atomic force microscopy (AFM).¹⁷ Typical RTD mesa sizes vary with application, ranging from 25 μm² for Sub-THz oscillators¹⁸ to ∼1 μm² for high Jpeak structures for high-frequency operation.^5,19 For such structures, the device/mesa dimensions are comparable with the expected extension of ML-islands.

Figures 2(a) and 2(b) show the experimental low-temperature PL spectra from sample A and sample B, respectively. Data are normalized and shifted in amplitude, and the curves are disposed in decreasing order starting from the top 100 μm² holes.

In both series of spectra, we observe a peak at 0.8 eV associated with the LM-InGaAs bulk peak; at higher energy, the spectra are broad due to the three type-I transitions as explained in Fig. 1(b).

Structures have different QW characteristics but with similar type-I transition energies.

Figure 2(a) shows that with reducing hole area, essentially identical spectra are obtained. The dominance of the bulk transition is observed to reduce with reducing holes size, but down to a 4 μm² hole size the contribution of X, +1 ML and –1 ML type-I PL transitions remains almost unchanged. PL intensity is equally distributed between the type-I peaks. For the smallest holes used, small changes in the intensity of the X, +1 ML and –1 ML type-I PL transitions are observed. Figure 2(b) shows that the dominance of the bulk transition is again observed to reduce with the reducing mask size, but quite different PL spectra (different contributions of X, +1 ML and –1 ML type-I transitions) are obtained for all hole sizes. Sample B shows a peak at ∼0.85 eV associated with the –1 ML QW thickness. This peak is also persistent reducing the hole size, indicating a predominant distribution of the –1 ML island.

The length scale of a long-range disorder (≫exciton) is, therefore, observed to be quite different in these two samples. For sample A, this is ∼4 μm² as Fig. 2(a) shows PL line shape differences for mask holes < 4 μm² holes. For sample B, the length scale is ∼>100 μm², as there are clear line shape differences observed in Fig. 2(b) for mask holes < 100 μm².

We previously demonstrated that other structural variations like the thickness of the barriers (AlAs ML fluctuation) and in the [In] mole fraction are not higher than ±0.5 ML and ±1%, respectively; the impact of these imperfections on the transition energy is not higher than 0.1 meV for barriers and 7 meV for [In].¹⁰ The observed variation in Fig. 2 is not in the peak position but in the peak intensity, consistent with variations observed in well-width fluctuation; consequently, we excluded these other structural variations from the analysis.

The growth conditions for two samples were nominally identical, and therefore, these differences in PL (and hence structural uniformity) are attributed to the structural design itself. The active regions are highly strained, which is known to lead to corrugation of the growth plane prior to defect formation.²⁰ For the coherent growth of strained structures without the formation of dislocations, the limit has often been described in terms of the critical thickness, defined as the maximum achievable thickness of a material X pseudomorphically grown on material Y.²¹ One of the more realistic limits was modeled using a mechanical equilibrium approach by Matthews and Blakeslee (M&B).²⁰ This model was investigated for the AlAs/InGaAs/InP material system²² to design highly strained QWs and for the optimization of the intrinsic resonator efficiency in high-current-density RTD designs.

Figure 3 is obtained by solving recurrent equation (5) of M&B using the InP substrate as the unstrained lattice constant. According to the M&B model, 5.04 ML of InAs can be uniformly grown on an InP substrate before strain relaxation occurs through misfit dislocations. The InGaAs critical thickness is plotted varying the In molar fraction x, and the region of defect-free coherent growth is represented in green in Fig. 3.²³ The yellow regions are then obtained adding the critical thickness of a single tensile AlAs barrier of varying thickness, and InGaAs introduces a compressive stress that can be compensated by tensile AlAs. The worst-case scenario is assumed where only the first barrier matters in the relaxation scheme. The red zone will, thus, exceed this limitation, where growth may be possible, with the risk of introducing increasing numbers of defects.

The dots of Fig. 3 indicate the position of the analyzed structures on the graph, and both are in the yellow region. Sample B is close to the limit indicated by the 4 ML barrier line, but this limit is exceeded if we consider the +1 ML fluctuation.

During the growth process, the InGaAs is deposited on the first AlAs barrier, this barrier alone has to balance the QW 16-ML stress until the second barrier is complete, and for highly mismatched design, imperfections are more likely to occur.^24,25 This relative thick stack of MLs is more exposed to strain-induced relaxation due to nucleation of dislocation²⁶ leading to the formation of islands.^27,28

Figure 4 plots the I–V characteristics obtained from sample A and sample B with an RTD mesa area of 2.4 μm². Devices were fabricated in the same fabrication run under the same conditions to eliminate other possible sources of discrepancies and focus the analysis only on the crystal quality. Details about the fabrication process are reported elsewhere.¹⁹ Measurements were conducted in the third quadrant to minimize self-heating and prevent catastrophic failure.⁷ The peak and valley voltages and currents are indicated in Fig. 4 by labels and colored dots. Device performances are in line with our previous predictions. Sample A shows the highest current peak and higher intrinsic resonator efficiency,²² and the narrow well reduces the electron transit time increasing the peak current. The resonant condition is reached faster in sample B thanks to the wider well that moves the first quasi-bound state to lower energy, and in sample A the effect of a narrow well is partially compensated with a higher molar fraction that reduces the e₁ and increases the e₂ level. As a consequence, the peak voltage is similar to sample B. Valley voltage differences are expected to be related to the position of the second quasi-bound state.

The e₂ state is at higher energy in sample A due to the QW characteristic described before, and for this reason, the valley point requires higher bias with respect to sample B.

Despite the difference in the peak current, samples show an unexpected similar valley current. This undesired current is partially attributed to the thermal effect generated by the applied current. The current is higher in sample A; consequently, we expected sample B to have a much lower valley current with respect to the measured one. We, therefore, suspect that the structural non-uniformities highlighted by PL are also affecting the RTD device performance.

Figure 5(a) plots the peak and valley currents of three device fabrication runs from sample A with mesa areas of 1.2, 1.4, 1.6, 1.8, 2.0, 2.4, and 3 μm². Larger area test devices were shown to exhibit catastrophic failure. Figure 5(b) plots the same data for three device fabrication runs from sample B. For sample A, we observe a monotonic increase in both peak and valley current increasing the mesa area. For sample B, while the peak current increases in a monotonic correlation, the valley current varies significantly, with only a collective increasing trend being observed in increasing the device area. The variations observed between the three device fabrication runs are also significant, indicating reliability issues. Barrier and well heterointerface roughness has been shown to increase valley current due to electron scattering.²⁹ Using a step-by-step procedure of I–V measurement and etching, we previously demonstrated how the structural imperfections have a strong impact on the RTD valley current.⁷ 

Variation in the valley current characteristics is significant in sample B, showing poor area scalability and reproducibility as compared to sample A. Variations in the valley current are often attributed to errors in the fabrication process in the canon. However, our samples were fabricated side-by-side in multiple processing runs, where such errors would be detected early.

We note the observation in valley current variation is consistent with the micro-PL data in Fig. 2, where limited variation in the PL spectrum is observed for sample A and significant variations for sample B. Differences in the RTD characteristics due to island formation growth have been demonstrated in large area devices (≥100 μm²) through variations in charge accumulation, observed by combining PL and I-V measurements.³⁰ In sample B, we observe PL fluctuation from 100 to 10 μm² while stronger differences are observed approaching the 1 μm². Valley currents from mesas with these dimensions are observed to be quite different in three sets of devices [Fig. 5(b)]. Similar to a macro-PL scan, large devices are expected to cover multiple ML islands, and the I-V characteristics are obtained from the average electronic properties of the device area. By contrast, our comparatively small devices were fabricated on an area that is of a similar scale to a single ML island (XML, +1 ML, –1 ML) or parts thereof. Consequently, the local electronic properties may be expected to be different, affecting the valley current and consequently the scaling and reproducibility of the valley current.

We, therefore, note that in tackling the challenge of reducing the valley current in high-J RTDs for THz applications, the effect of long-range disorder in the epitaxial material requires removal, with micro-PL allowing a route to understanding its effect on valley current.

Figure 5(c) shows the theoretical maximum RF power P_RF,max ≈ $316ΔIΔV=316AΔJΔV$³¹ of the measured RTD devices as a function of the associated mesa area of sample A and sample B, respectively.

As plotted in Fig. 5(c), a linear trend characterizes sample A, meaning that both the available current density ΔJ and voltage swing ΔV of the devices are same. Moreover, the difference between the three sets of devices is negligible, indicating wafer structural uniformity and high yield.

On the other hand, sample B presents a highly non-linear oscillatory behavior due to the associated instability of the valley current and so ΔJ, which is caused by monolayers fluctuations in the QW and islands formation as previously discussed. In addition, the three sets of devices do not present the same trend. This is detrimental in terms of oscillator performance since the major contribution to the RF power of high-current density RTDs is provided by ΔJ, whose unpredictability and associated low reproducibility level inevitably lead to a large statistical deviation of output power performance.

We have reported the application of micro-PL to understand micro-scale uniformity of high-J InGaAs/AlAs/InP RTD structures for THz applications, not observable through standard macro-scale PL. Two similar samples are shown to exhibit different long-range disorders through the variation of their PL line shapes with the reducing excitation/detection area. Devices fabricated from these materials show poor valley current scaling and reproducibility, suggesting that the material variation is a critical factor in the device performance. The need for such characterization techniques to cast a light on material uniformity and future device design and epitaxial process development to minimize the valley current is highlighted.

This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie under Grant Agreement No. 765426 (TeraApps).