Nonlinear UV absorption properties of bulk 4H-SiC Free

The dependence of optical response in SiC on both material and varying stimulus is readily available in the literature. Optical wavelength dependence α(λ) under both pulsed¹ and CW radiation has been documented.² Dependence of optical absorption on temperature α(T) has likewise been reported.³ Limited exploration of intensity-dependent optical absorption above the band gap has also been undertaken.⁴ 

This paper presents the intensity-dependent absorption α(I) above the band gap, a hitherto unexplored dependence of optical response, but one of importance to the wide-bandgap semiconductor industry for both production and device applications. It has implications for patterning, drilling, or ablating using UV lasers and optimizing and controlling behavior in intrinsically activated optoelectronics such as photoconductive switches and photodetectors. In the absence of thermal stimulus or applied electric fields, three mechanisms are expected to play a significant role in the absorption behavior: inter-band absorption, trap-assisted recombination, and free carrier absorption (FCA). Of these, the least explored in indirect bandgap, high purity semi-insulating (HPSI) materials are traps.

Traps are present throughout the gap, but in HPSI materials deep level traps have the highest density. These are also the most easily observed; shallow traps may be indistinguishable from the band edge in deep level transient spectroscopy (DLTS), while still facilitating Shockley-Read-Hall recombination. Experiments with GaAs have shown that optical excitation of electrons in deep traps is negligible in its contribution to overall absorption.⁵ The available literature documents the inverse scaling of bulk recombination lifetime with trap concentration having significant densities (n > 10¹³cm⁻³).^6,7 The great majority of this work concerns n-type SiC, while none addresses HPSI material.^8–12 These studies indicate bulk lifetimes of typically 0.1–3 μs, where the usual Z_1/2 and EH_6/7 traps dominate deep level transient spectroscopy (DLTS) results; these document concentrations in the 10¹³–10¹⁴cm⁻³ range.^10,13 Nowhere in the current literature can be found a similar study of HPSI 4H-SiC, whose recombination lifetime is very short. The HPSI SiC materials investigated here were previously characterized under 3.49 eV pulsed laser excitation, wherein the bulk recombination lifetimes were found to be 3 ns and 500 ps.¹⁴ Using the empirical relationship $τbulk(ns)=1.6⋅1016Nz1|2 (cm−3)$⁠, this trap density is estimated to be on the order of 10¹⁶cm⁻³, significantly higher than densities found in n-type samples in the literature.⁶ This high trap concentration also results in orders of magnitude higher resistivity, differentiating it from lower trap density (and lower resistivity) materials.^14,15

Pulsed laser excitation allows high-intensity optical excitation and insight into fast absorption processes unobservable through CW. Here, by pairing UV absorption experiments with numerical modeling, an advantage is gained over traditional pump-probe experiments (where the probe is typically VIS-IR), which means all optical stimulation is above band-gap and no extrapolation of absorption cross section is necessary.

Three samples from a single wafer of 490 μm thick HPSI 4H-SiC manufactured by Cree were treated per the procedure described below. The samples' origination in the same wafer ensures a high degree of consistency among them but at the cost of some degree of repeatability, since one sample was processed and tested under each condition. Hence, the experimental data are self-consistent, but some difference is expected if the same process were repeated using samples from a different wafer. The first was tested as-grown: previously characterized with a carrier recombination lifetime of 3 ns.¹⁴ The second was annealed at 1850 °C for 100 min and cooled at −30 °C per minute to prevent quenching; recombination lifetime here was shown to be 100 ns.¹⁶ The third was electron irradiated for 3.5 h at a density of 2 × 10¹⁸cm⁻²; bulk recombination lifetime is 500 ps.¹⁴ All samples were thinned (see Table I for a summary of their properties).

Initially, low power spectroscopy was performed on the as-grown sample to attain its wavelength dependent absorption α(λ); measured transmitted and reflected signals were processed using a Beer-Lambert equation accounting for two internal reflections [Ref. 5, p. 94].

where d is sample depth, α is absorption coefficient (cm⁻¹), R_m is measured ratio of reflected over incident energy, and T_m is ratio of transmitted to incident. Since annealing and irradiation affect the concentration of primarily mid-gap states without shifting the gap itself, the near-gap and below-gap absorption spectroscopy performed on the other two samples would appear nearly identical to the as-grown spectroscopic result shown (cf. Figure 1). The obtained result (cf. Figure 1) is consistent with the limited literature exploring these properties in the nominally semi-insulating samples² (note that higher absorption values are typically obtained in n-type samples, which prevail in the literature^1,3,17).

The transmittance and therefore the absorption outside the values shown in Figure 1 are beyond the diagnostics resolution and are not shown.

The high optical intensity setup consists of a frequency-tripled Nd:YAG laser outputting at 355 nm wavelength with an FWHM of 7 ns operating at 10 Hz (Quanta-Ray Pro-270). Wavelengths above the UV are filtered with UG-11 glass, and a sample of the beam is split off for measuring the incident beam intensity/energy; standard 355 nm laserline mirrors were used for beam-steering (cf. Figure 2). Each photodiode was isolated from stray reflections and scattering from the laser beam and from ambient light. The angle of incidence was kept at 15°, so that the reflected beam could be used for reflectance measurements, while maintaining a near-normal incidence. Unevenness in the laser spatial profile is compensated by scraping the beam profile to the size of the photodiode's active area, ensuring each photodiode senses the same spatial profile.

An incident, reflected, and transmitted data point was measured with 3 custom photodiodes at each energy from 80 single shots integrated and noise-corrected with laser energy at each shot within ±5% of the nominal energy. Each sample was tested with light incident on each (c-plane) face over a range of energies, and no significant change in reflectivity was observed with respect to either orientation or intensity. From this, it is reasonable to conclude the imaginary-refractive-index-altering higher order nonlinear effects (χ⁽ⁿ⁾) do not play a significant role in the absorption behavior observed.

The effective absorption coefficient in the as-grown sample decreases linearly at low energies and then changes rapidly at around 11 mJ·cm⁻², suggesting bleaching. The irradiated sample appears to exhibit bleaching from the onset at low energy. The longer recombination lifetime annealed sample shows the opposite trend, increasing its absorption with increasing incident energy.

Two-photon absorption has typically been found to be about four orders of magnitude weaker than single photon processes in wide bandgap semiconductors; it is accordingly neglected here.¹⁸ At its simplest, the laser absorption process may be described as a two energy level problem with absorption, spontaneous emission, radiationless transitions, etc. between the valence and conduction band energy levels. While portions of the complicated observed experimental behavior, cf. Fig. 4, could be reproduced with a two-level model by assuming different recombination rates for the different materials, cf. Table I, it took as a minimum a four-level model to capture the detailed features (see Fig. 3).

In the finite difference time domain (FDTD) model, three processes (inter-band, FCA, and deep level trapping) and four levels (valence v, trap t, conduction c, and above-valley conduction ce) were considered (cf. Figure 3). Assuming a light beam propagating in positive x-direction yields two general equations describing the light intensity and population change in the space/time domains. First, the intensity change $∂I∂t=cn(∂I∂x−aI)$⁠, wherein the spatial light intensity change propagates at the effective speed of light c/n through the medium, with the light's continued absorption described by the differential absorption coefficient, a; and second, $∂n∂t=∂I∂x1Ephoton−nτ$⁠, wherein the rate of change in energy level population, $∂n∂t$⁠, is equal to the influx of optically excited population and removal by relaxation with the time constant, τ. Expanding to the processes accounted for here, the time and space dependent equations describe (1c) light intensity attenuation with time and penetration depth; (1d) differential absorption coefficient as a sum of interband absorption and FCA; (1e) time rate of change in valence band population; (1f) time rate of change in trap population; (1g) time rate of change in conduction valley population; and (1h) time rate of change in above-valley conduction band population

where C₁—ratio of conduction-to-trap vs. conduction-to-valence relaxation probability; B₁₂ and B₂₃—absorption cross section (fitted parameters) relating band population with a; n_v, n_c, and n_ce—valence, conduction valley, and above-valley conduction band population densities, respectively; $Eλ=hcλ$ photon energy; and τ₃₂, τ₂₁, and τ_t—recombination lifetimes.

Since the deep trap recombination lifetime, τ_t, is much longer than the laser pulse (100 s of nanoseconds), it is treated here as a conduction-band-depleting mechanism that shuts off when the total trap density of states is saturated. In modeling of longer timescale processes, the electron-occupied traps would undergo hole capture and release electrons to empty valence band states (Table II).

The bulk lifetime and annealing processing of the annealed sample suggest its deep trap density on the order of 10¹⁴cm⁻³.¹³ The available density of states for 4H-SiC is usually calculated as 2.1 × 10¹⁹cm⁻³ [Ref. 19, p. 22], but near the band edge, the effective density of states (density of available states) should be lower, as the states accessible for interband absorption is photon-energy-limited; Galeckas found the peak carrier density in a similar experiment to be 7 × 10¹⁸cm⁻³, similar to the n₀ value used.²⁰ In the as-grown and annealed case, trap densities of states were assumed to be approximately equal, since their bulk recombination lifetimes are quite low. In optimizing simulation variables to fit experimental data (cf. Figure 4), the absorption cross sections (B₁₂ and B₂₃) and density of states (n₀) were found first in the annealed case (the simplest since trap-assisted recombination is irrelevant here). Then, the irradiated case was modeled to find the best trapping coefficient C₁. Finally, holding all values constant except the experimentally derived τ₂₁ and τ₃₂, the as-grown case was fitted.

Published studies focused on FCA measures absorption behavior in doped samples, whereas FCA in HPSI materials has not. In the absence of relevant FCA information, it remains unknown how FCA relaxation time and absorption cross section compare to interband relaxation times. The parameters chosen here were set under the assumption that FCA relaxation lifetimes are roughly equal to interband relaxation times and that their sum is close to τ_bulk. Since the sample is semi-insulating, Burstein-Moss shift or other band-modification as a result of increasing conduction band occupation was assumed to be negligible. Stimulated emission is also excluded since it should only begin to play a substantial role at intensities where more significant bleaching occurs. Finally, due to the small observation solid angle, spontaneous emission, being isotropic, is also excluded from the considerations.

The effective absorption of a physical sample with specific dimensions is determined by the modeled transmittance through the sample, while the differential absorption in space is fitted by cross section parameters B₁₂ and B₂₃. Hence, the cross sections determine the absorption coefficient in aggregate. This is most easily observed in comparing measurements to simulation values at low energy (cf. Figure 4), where the effective absorption coefficient of the as-grown sample, 129 cm⁻¹, matches within the 7% value of a ∼ n₀·B₁₂ in the low energy limit (cf. Eq. (1h)) with n_c ∼ 0 cm⁻³. The measured divergent lifetime-dependent absorption trends suggest that conduction band population plays a significant role in the intensity dependence of absorption, meaning the role of FCA must be non-negligible above band gap. Consistently, the simulated best fit of all data emerges when B₂₃ ≈ 3·B₁₂. Physically, this is intuitive when the material is visualized as a lattice of Bohr atoms; electrons in a higher energy state further from the nucleus should have larger absorption cross section (represented by B here). It should be noted that the behavior at pulse energies below the experimentally tested were simulated using the above parameters. In the as-grown and annealed samples, these indicate a convergence of absorption coefficient toward the α value suggested in the CW experiments.

It is noted that the distinct properties of HPSI material may limit the applicability of these results to n- or p-type materials. In more heavily doped materials, trap density has repeatedly been established and related empirically to recombination lifetime. The model implemented here corroborates this trend, however, suggesting a high deep trap density not previously noted in the literature, but which is consistent with the empirical relation between bulk recombination lifetime and deep trap density [Ref. 19, p. 174]. One may consider expanding the investigation to doped SiC and paired with DLTS to further verify the influence trap and recombination lifetime have on α(I) under intrinsic optical excitation.

The intensity dependent absorption coefficient and the role of bulk recombination lifetime in the nonlinear absorption behavior of 4H-SiC have been studied. Bulk samples of 4H-SiC were found to display an intensity-dependent above bandgap absorption chiefly governed by their respective recombination lifetimes of 0.5 ns, 3 ns, and 100 ns. A semi-empirical 1D FDTD model based on a four energy level scheme was developed that yielded the main features of the experimentally observed nonlinear absorption. Assuming fewer than four levels would not produce reasonable results, and using more than four levels would simply increase the number of a-priori unknown parameters without contributing more specifics to the discussion. The observed is consistent with free carrier absorption and deep-level trapping playing dominant roles in nonlinear absorption of light under pulsed stimulation above the band gap in 4H-SiC.

The work was supported in part from by the Office of Naval Research under Grant No. N00014-15-1-2650 and by AFOSR Grant No. FA95501010106, “Collaborative Research on Novel High Power Sources and Physics of Ionospheric Modification.”