Temperature-dependent ultrafast hot carrier dynamics in the dilute bismide alloy GaSb_1−xBi_x (x ≾ 0.4%) Free

The hot carrier solar cell (HCSC) proposed in 1982 by Ross and Nozik is a promising idea for third-generation photovoltaic devices.¹ In traditional p–n junction solar cells, the power conversion efficiency (PCE) is restricted by the Shockley–Queisser limit.² The reported fundamental energy loss mechanisms in the PCE in solar cells are (i) Carnot loss, (ii) subbandgap loss, (iii) emission loss, (iv) Boltzman loss, and (v) carrier thermalization (or relaxation) loss.³ Of these loss mechanisms, carrier thermalization loss contributes more than half of the total energy loss in semiconductors with bandgaps of less than 1.5 eV. GaSb is a low bandgap material (≈0.72 eV at 300 K), whose bandgap is further reduced by Bi incorporation (∼30 meV/%Bi).⁴ Hence, carrier thermalization loss may dominate the overall energy loss in GaSbBi. In principle, HCSCs are designed to prevent carrier thermalization loss by increasing the carrier relaxation time from subpicoseconds to nanoseconds so that, before they thermalize, the extraction of the excess energy of the “hot carriers” for power generation is made possible. In the past, GaSb has already shown potential in thermoelectric and thermophotovoltaic energy conversion technologies.^5,6

In the last few decades, the consistent research effort on dilute III–V-bismide semiconductor systems has yielded several practically important pieces of knowledge about these materials, which are useful in the field of optoelectronic devices.^7–11 The incorporation of a small amount of Bi in the host III–V system perturbs the regular lattice arrangement of the host, resulting in a large bandgap reduction.¹² Additionally, the spin–orbit band in these materials moves downward with increasing Bi incorporation, leading to a large spin–orbit splitting energy,¹³ providing photonic devices that are more thermally stable and less vulnerable to Auger losses than general InP-based devices used for optical communication.^14,15 In recent years, despite several difficulties related to growth, several research groups across the globe have successfully grown high-quality III–V-bismide epilayers with a high content of Bi.^16,17 Growing higher Bi-containing epilayers is of practical importance, as it has been observed in the past¹⁸ that for ∼10% Bi in GaAsBi, the spin–orbit splitting energy is higher than the bandgap (⁠ $Δ SO> E g$⁠), which shows the potential application of this material in telecom lasers.¹⁹ 

Very few reports on ultrafast carrier dynamics in the GaSbBi system are available. However, due to the interesting band structure (side L valley threshold is only 85 meV from the Γ valley at 300 K),²⁰ some reports are available on the GaSb system. Snow et al. studied carrier relaxation in bulk GaSb using picosecond time-resolved photoluminescence (TRPL) at low temperatures.²¹ They attributed the rapid carrier cooling to electron relaxation within the L valleys. Due to the large mass of L-valley electrons in GaSb,²¹ they also reported that for higher carrier density (>10¹⁹cm⁻³), radiative recombination dominates at low temperatures (4 K); however, at high temperatures, “Auger” recombination dominates.²² Pelouch and Schlie also studied the ultrafast carrier dynamics in GaSb using optical transmission-correlation spectroscopy and attributed the faster component to phonon scattering with a lifetime of 2–2.5 ps.²³ Recently, Yi Zhang et al. investigated hot carrier relaxation with different excitation energies and suggested that when the excitation energy is higher than the side L-valley threshold, the intervalley scattering (IVS) mechanism dominates hot carrier cooling and is not greatly affected by the strength of the Fröhlich coupling due to weak polarization of GaSb.²⁴ In addition, some reports are available on the study of carrier dynamics in GaSbBi and InGaSbBi quantum wells (QWs) by TRPL and transient reflectivity for high Bi content (∼10%–11%), and it was observed that the exciton lifetime decreases with the increase in QW width.^25,26 Additionally, in InGaSbBi, the estimated linear dispersion variation parameter significantly decreased from Δτ ≈ 20 to 10 ps/meV with increasing Bi content, suggesting the increasing role of the nonradiative recombination processes with Bi incorporation in these QWs.²⁶ Additionally, recently, Tristan et al.²⁷ studied the optical properties of GaSbBi epilayers using TRPL and observed that with the increase in Bi content in the epilayer (from 5.8% to 8% Bi), the photoluminescence (PL) decay time increases due to the increasing clustering effect. However, no reports are available on the temperature-dependent ultrafast dynamics of hot carriers in dilute GaSb_1−xBi_x systems (x < 0.5%).

We used ultrafast pump–probe transient reflectivity (PPTR) to study the temperature-dependent hot carrier dynamics in GaSb_1−xBi_x epilayers with x = 0%, 0.2%, and 0.4% grown by liquid-phase epitaxy (LPE) using Pb as the growth solvent.^28,29 We discuss the mechanism behind the cooling of hot carriers and their temperature dependence. We present the possible origin of the increased relaxation time at higher temperatures. We observed that the ultrafast carrier dynamics in GaSb_1−xBi_x are influenced by the presence of dilute amounts of Bi (<0.5%) in the host GaSb system.

GaSb_1−xBi_x epilayers were grown on ⟨100⟩-oriented GaSb substrates using LPE, wherein Pb was used as a solvent. 5 N pure Pb (Alfa Aesar) was used as a source of solvent material, and 6 N pure Bi granules (Azelis France) were used as a source of Bi. A single-crystal undoped GaSb wafer served as the source of Ga and Sb. Details of the growth are discussed elsewhere.³⁰ In the present work, we used GaSb_1−xBi_x epilayers with x = 0%, ≈0.2%, and ≈0.4%. The Bi content in the epilayer was determined using high-resolution x-ray diffraction spectroscopy. The carrier concentration of these epilayers was estimated using CV measurements,³⁰ and the thickness of the epilayers was measured by cross-sectional scanning electron microscopy (SEM). The thickness of the epilayer is in the range of 5–6 μm, as measured by cross-sectional scanning electron microscopy (SEM). The epilayers were strain-relaxed due to sufficient thickness. Details of the samples are presented in Table I. Photoluminescence (PL) measurements were performed at low temperatures (10 K), and the PL spectra, shown in Fig. S1 in the supplementary material, indicate that the bandgap decreases with increasing Bi concentration. Raman spectroscopy was performed on the epilayers to identify the Bi-induced changes in the phonon modes. In all the samples, GaSb-based TO and LO modes at ∼227 and ∼233 cm⁻¹ are the dominant modes.³¹ These LO and TO modes are not significantly shifted in GaSbBi epilayers compared to GaSb. This is consistent with earlier reports³²—even at very high Bi concentrations (∼10%), the shift in Raman modes was reported to be very small, ≈1 cm⁻¹.

The ultrafast carrier dynamics were studied using a degenerate (λ = 800 nm) pump–probe technique in the reflection geometry using ≈100 fs-long pulses at a repetition rate of 80 MHz from a mode-locked Ti:sapphire laser. The pump beam was chopped at a frequency of 50 kHz using a photoelastic modulator. The spot diameter of the pump beam was ∼25 μm, and the average pump fluence used for all the measurements was ≈0.2 mJ/cm². The intensity change in the reflected probe was recorded using a photodiode and a lock-in amplifier. Temperature-dependent measurements were performed at different temperatures in the range of 6.6–300 K using an ultralow vibration closed cycle refrigerator. The temperature of the sample was monitored using a Si diode sensor and a Lakeshore 340 model controller. The normalized PPTR signal of the GaSb_(1−x)Bi_x epilayer with x ≈ 0.4% for different temperatures is presented in Fig. S2 in the supplementary material.

PPTR spectra for GaSb_1−xBi_x epilayers with x = 0% (undoped GaSb), 0.2%, and 0.4%, are shown in Figs. 1(a) and 1(b) for 6.6 and 300 K, respectively. The PPTR signals for all three samples show an impulsive positive transient with a fast decay (≈0.8–2 ps) at low temperature (6.6 K), followed by a relatively slower (≈10–30 ps) decay process. The PPTR signal also shows a sharp peak at zero delay time, possibly due to the coherent artifact.³³ As shown in Fig. 1(b), at room temperature, the PPTR signal shows a different behavior compared to low temperatures; the initial positive transient quickly decays (≈4–5 ps), and a transient with negative amplitude emerges similar to what was reported for GaSbBi QWs.²⁵ To analyze these complicated PPTR dynamics, we modeled the experimental data using two independent exponential relaxation processes: (i) a fast relaxation, which gives a transient with positive amplitude, and (ii) a slow relaxation process, which has a positive amplitude at low temperatures and changes sign at high temperatures ≿100 K. τ₁ and τ₂ are the characteristic decay times associated with the fast and slow relaxation processes, respectively, and A₁ and A₂ are the corresponding amplitudes.

Figures 1(a) and 1(b) show the best fit to the data along with different transient processes for the undoped GaSb sample at 6.6 K and 0.4% Bi-containing GaSbBi epilayer at 300 K, respectively, which shows the effectiveness of this approach in fitting the experimental data. From the fitting, the initial fast decay time at 6.6 K is obtained as τ₁≈ 1.8 ± 0.06 and ≈0.8 ± 0.04 ps for the GaSb_1−xBi_x epilayers with x = 0% and 0.4%, respectively, and it is attributed to the initial cooling time of the hot carriers. Similarly, a slower decay time at 6.6 K is obtained as τ₂≈ 30 ± 0.9 and ≈10.5 ± 0.2 ps for the GaSb_1−xBi_x epilayers with x = 0% and 0.4%, respectively. The slower decay time is comparable to the reported low-temperature (4 K) data of GaSb.²² The evolution of both τ₁ and τ₂ at 6.6 K with Bi content, x in the GaSb_1−xBi_x epilayers, is presented in Fig. 2, and it shows that the dilute amounts of Bi in the epilayer increase the relaxation rate of both slow and fast processes. τ₁ is associated with the initial thermalization of hot carriers to the band edge, which is affected by carrier–phonon scattering. Due to the higher carrier density in GaSbBi epilayers compared to the GaSb epilayer (shown in Table I), the carrier–phonon scattering is enhanced in GaSbBi epilayers, resulting in the reduction of τ₁ in GaSbBi epilayers. In the present work, as the probe energy is higher than the bandgap energy, the observed slower decay time τ₂ is affected by both band-to-band radiative and other intravalley relaxation processes: $1 τ 2= 1 τ r+ 1 τ I$⁠, where $τ r$ and $τ I$ are the radiative and intravalley nonradiative mechanisms, respectively. At low temperatures, $τ r≫ τ I$⁠; therefore, $τ 2$ is dominated by $τ r$⁠. Hence, this leads to shorter values of τ₂ at low temperatures. It has been observed in the past that in the case of polar semiconductors, the radiative rate is increased with an increase in carrier density, which eventually results in a shorter lifetime.³⁴ This may be the reason for the observed reduction in τ₂ in GaSbBi epilayers compared to the GaSb epilayer. This observation of a shorter decay time in Bi-incorporated samples agrees with other reports on other Bi-containing III–V semiconductors.³⁵ 

From fitting the transient reflectivity data for the samples at 300 K, the initial fast decay is obtained as ≈4.6 ± 0.2 and ≈4.1 ± 0.1 ps for the GaSb_1−xBi_x epilayers with x = 0% and 0.4%, respectively. It has been observed in the past that in the case of GaSb epilayers for near band edge excitation at room temperature (300 K), the initial fast transient decay observed is in the range of 1.5–2.2 ps.²³ The origin was attributed to the thermalization of hot carriers generally observed in a bulk semiconductor with a low phononic bandgap.^36,24 When the excitation pump energy is higher than the band edge energy and even higher than the lower side (L) valley threshold energy,²⁰ the excited carriers scatter to the L valley of the conduction band via IVS [as shown schematically in Fig. 4(a)]. Since the effective mass of carriers and density of states are higher in the L valley than that in the Γ valley,³⁷ the scattering of carriers back to the Γ valley slows down. Hence, this increases the initial carrier relaxation time (τ₁) by a factor of ≈1.5–2 compared to the resonant excitation case.²⁴ 

In Fig. 1(b), we observe a negative amplitude (A₂) associated with a slower decay process in the PPTR signal at 300 K. The relaxation time (τ₂) obtained from the fitting, linked with the slower decay process, is ≈345–450 ps at 300 K, while τ₂ at low temperature (≈6.6 K) is ≈10–30 ps. The amplitude of the slower process changes sign when going from low to high temperature, and the decay time becomes longer at higher temperatures, indicating that another mechanism is affecting the slower transient process. Hence, we measured the temperature-dependent PPTR on undoped and 0.4% Bi-doped epilayer samples to understand the dynamics of the fast and slow decay processes. Figure 3 shows the 2D color map of the PPTR signal for the GaSb_0.996Bi_0.004 epilayer. The map shows that the PPTR signal consists of two regions separated by the black dotted line. Below cryogenic temperatures (≥100 K), the slow decay process of the PPTR signal has a relaxation time of <60 ps, but at higher temperatures, the PPTR signal becomes negative and takes a longer time (≾450 ps) to relax, which suggests that the slower decay process is influenced by another mechanism at higher temperatures.

The transient reflectivity of the GaSb_1−xBi_x epilayers at temperatures below ≈100 K is very similar to what was observed at 6.6 K. Figure 4(a) shows the schematic band structure of GaSbBi with different optical transitions below and above ≈100 K to understand the hot carrier relaxation dynamics. The low-temperature bandgap, E_g, of GaSb_0.996Bi_0.004 is ≈0.8 eV, and the energy difference between the heavy hole and spin–orbit spin-off band value, $Δ SO$⁠, is ≈0.76 eV.³⁸ Below ≈100 K, an optical pulse (pump pulse) is absorbed and creates electron–hole pairs in the valence band [heavy (HH)/light hole (LH) band] and conduction band (CB) states, as shown in Fig. 4(a). As a result, a dense population of nonequilibrium carriers (“hot electrons”) occupy the higher energy states of CB. This initial distribution of carriers differs from a “Fermi-Dirac distribution,” as they cannot be assigned to a single temperature. These photoexcited hot carriers are quickly scattered (on a femtosecond time scale) to the L valley due to their large mass and higher density of states, and they start to cool down to lattice temperature through phonon emission [as shown schematically in Fig. 4(a)], which has also been reported in the past for GaSb.^21,22,37 After cooling, carriers are scattered back to the energetically favorable Γ valley and finally relax to the CB edge of the Γ valley. This process usually takes a few ps and is the mechanism behind fast decay. Again, once these carriers cool and occupy the unoccupied states near the CB edge, leading to band filling, electrons start recombining with holes in the valence band, giving rise to a slower decay process. Figure 5(a) shows that the fast decay (τ₁) in both undoped and 0.4% Bi-containing epilayers increases with increasing temperature, which may be due to the lowering of the CB edges with temperature, which eventually increases the “hot carrier” cooling time.

In the case of GaSb_(1−x)Bi_x epilayers studied here, E_g is equal to the spin–orbit split energy (⁠ $Δ SO$⁠) at ≈100 K.³⁹ This resonance in energy leads to the anomalously large interband CHSH-Auger process [a conduction electron and a heavy hole recombine, and the energy released is used to excite into the spin-split-off band a hole from near the valence band (VB) maximum] in GaSb_(1−x)Bi_x, which eventually generates holes in the split-off valence band [as shown schematically in Fig. 4(b)].^40,41 This Auger process has a higher probability since momentum transfer and the activation energy are small. Hence, CHSH-Auger is the dominant intrinsic loss mechanism, and its contribution increases as n³, where n is the carrier density in the material.⁴² Again, this Auger process strongly depends on temperature, as the carrier density also increases with an increase in temperature. Here, the incorporation of Bi in GaSb increases the carrier density (shown in Table I), which eventually influences the CHSH-Auger process in GaSbBi epilayers. It has also been reported²² earlier that at higher temperatures (above ≈100 K), when GaSb is excited above E_g, radiative transition involving holes in the split-off valence band and thermalized electrons at the CB edge dominates. In the present work, we used an 800 nm (≈1.55 eV) pump, which is higher than the GaSb_(1−x)Bi_x bandgap; hence, the CHSH-Auger recombination process is relatively strong at higher temperatures (above ≈100 K). Figure 5(b) depicts that at higher temperatures, ≿100 K, the slower relaxation time is increased with an increase in temperature. Additionally, it can be seen in the inset of Fig. 3 that at 250 K, the slower decay process of the PPTR signal returns to the equilibrium value at approximately 400 ps, but with an increase in temperature, it takes an even longer time. Since the “Auger” process is dominant in both samples, the band edge electron and hole densities are not equal, which results in a reduced band-to-band recombination rate, and this, in turn, increases the time of the slower decay process at higher temperatures in both epilayers, as shown in Fig. 5(b).

Additionally, at higher temperatures (above ≈100 K), more electrons accumulate near the CB edge due to the addition of extra carriers (electrons) from the SO band since the pump energy is higher than the sum of E_g and $Δ SO$⁠. These carriers absorb the probe beam and escalate to higher energy states of the CB [as schematically shown in Fig. 4(b)], yielding the negative amplitude to the slower transient process. Figure 5(b) also shows that at higher temperatures (>150 K), the Bi-containing GaSbBi epilayer has lower values for slower decay (τ₂) compared to the undoped GaSb epilayer. As we already know, the incorporation of Bi in the III–V semiconductor creates a resonant state near the valence band edge of the host III–V system, which eventually reduces the bandgap of the material by pushing the valence band upward in energy, but at the same time, it increases the value of $Δ SO$ by pushing the split-off band deeper in energy.^43,44 This increase in $Δ SO$ reduces the Auger recombination compared to undoped samples. The Auger recombination increases the band-to-band recombination rate, eventually reducing the slower decay (τ₂) time in the GaSbBi epilayer compared to the undoped GaSb epilayer at higher temperatures.

In summary, the temperature-dependent carrier relaxation dynamics are studied in GaSb_1−xBi_x epilayers containing dilute amounts of Bi (x ≾ 0.4%). Increased carrier density due to Bi incorporation reduces both the fast and the slow decay time in GaSbBi epilayers compared to undoped GaSb epilayers. The slower decay process is affected by CHSH-Auger recombination at higher temperatures (>100 K), and the corresponding decay time increases with increasing temperature in the GaSb_1−xBi_x epilayers.

See the supplementary material for 10K PL (Fig. S1) data and temperature-dependent normalized PPTR signal (Fig. S2).

A.S.S. acknowledges the financial support received from IISER TVM under the academic research fellowship scheme. The authors thank Dr. Subhasis Das and Professor Sunanda Dhar for their helpful suggestions during the growth of the samples.

The authors have no conflicts to disclose.

Akant Sagar Sharma: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Writing – original draft (equal); Writing – review & editing (equal). S. J. Sreerag: Methodology (equal). R. N. Kini: Funding acquisition (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding authors upon reasonable request.