Strong band gap reduction in highly mismatched alloy InAlBiAs grown by molecular beam epitaxy

Dilute bismuthides (also called bismides) are a type of highly mismatched alloy (HMA) in which a small amount of bismuth is incorporated into a conventional III-V semiconductor causing the host bandgap to be reduced significantly. The localized Bi impurity level is located near the valence band of host matrix, causing the split and upward shift of the valence band. A large bandgap reduction therefore occurs, which is often described by the valence band anticrossing (VBAC).¹ A bandgap reduction around 88 meV/%Bi was observed in GaBiAs² and around 56 meV/%Bi in InGaBiAs.³ In addition to the large bandgap reduction from Bi incorporation, spin-orbit splitting increases with Bi content, which could become larger than the bandgap. The dilute bismuthides have been shown to have great potential in applications like infrared lasers,⁴ photodetectors,⁵ and solar energy conversion.^6,7 These materials are difficult to synthesize due to a miscibility gap. They are, therefore, primarily studied in the dilute range and even this requires specific growth conditions. Molecular beam epitaxy (MBE) growth, being kinetically driven and far from equilibrium, is a great tool to overcome the miscibility gap issue.

The MBE growth window for dilute bismuthides is narrow. Bismuth incorporation depends strongly on the growth temperature. Bi concentration increases as growth temperature decreases.^8,9 Bi incorporation is also very sensitive to arsenic flux. Bi% decreases with increasing As$2$ flux. Group III atoms bond preferentially with As rather than Bi, and therefore excess As atoms arriving during growth hinder the Bi incorporation.⁸ Dilute bismuthides are grown with As:III flux near stoichiometric instead of the traditional large As overpressure.² However, low As flux could result in group III (e.g., Ga) droplets. Careful control of III:Bi:As$2$ flux ratio is necessary to incorporate Bi without Bi or III droplets. It has been reported that when growing with As$4$ instead of As$2$⁠, the As flux does not show significant impact on the amount of Bi incorporated,^10,11 and a growth temperature lower than 330 $°$C does not affect the amount of Bi incorporated into the film.¹² 

In this paper, we study the MBE growth and characterization of InAlBiAs. We have proposed to use InAlBiAs as the graded funnel barrier for a novel upconversion nanostructure previously,⁶ exploiting the flexibility in band engineering of dilute bismuthides. More generally, Al-containing dilute bismuthides allow more flexibility in band engineering in these materials. We first studied the $InAlBiAs$ with In and Al composition close to that of InAlAs latticed-matched to InP.

$InxAl1−xBiyAs1−y$ thin films were grown on 500 $μ$m (001) InP Fe-doped substrates at 300 $°$C by MBE (OSEMI Nextgen) equipped with In, Al, and Bi, and a valved arsenic cracker effusion cells. The oxide on InP was removed by heating the substrate over 565 $°$C for a very short amount of time under As overpressure until clear Reflection High Energy Electron Diffraction (RHEED) pattern was observed. The substrate temperature was monitored using band edge thermometry, but it is worth noting that this technique is somewhat difficult at 300 $°$C, so the actual growth temperature fluctuates approximately 5 $°$C. The In/Al beam equivalent pressure (BEP) ratio was chosen to be close to In$0.52$Al$0.48$As latticed matched to InP. There is a slight variation of group III composition from sample to sample because of the growth sensitivity. As$4$ overpressure of $4×10−6$ Torr was used during the growth based on previous reports of the MBE growth conditions of bismuthides.^10,11 A growth rate of 0.6 $μ$m/h were used for all samples. The Bi flux was varied to change the amount of Bi incorporated into the film.

In situ RHEED pattern was monitored during the growth, and streaky RHEED patterns were observed for all samples. Rutherford backscattering spectrometry (RBS) and high-resolution X-ray diffraction (HR-XRD) with reciprocal space mapping (RSM) were used for structural characterization. RBS is especially useful for determining the composition, and channeling RBS can help us to study the crystal quality of materials. For the RBS in this work, a National Electrostatics MAS 1700 pelletron tandem ion accelerator (5SDH) was used to generate a 30 nA beam of 4.7 MeV He++ through a $2×2$ mm aperture, integrated to $Q=21$ uC total charge per spectrum. A high beam energy of 4.7 MeV is used so that Bi signal is isolated, and it will not cause degradation of the samples since ions simply deposit deeper. Charles Evans analytical end station equipped with an Ortec ion detector (solid angle 3.6 msr) at 165$°$ scattering angle for RBS and a two-axis goniometer for channeling analysis was used. HR-XRD was conducted via a PANalytical XPert PRO materials research diffractometer with Cu K$α$ radiation.

InP’s bandgap is 1.34 eV at room temperature, and In$0.52$Al$0.48$As’s bandgap is 1.47 eV. Therefore, absorption based methods like spectrophotometry are not able to provide bandgap information of $InAlBiAs$ since the thick substrate will start to absorb at a lower energy. Furthermore, since small amounts of Bi will reduce the bandgap to be closer still to the InP bandgap, photoluminescence from the film will be impossible to distinguish from the substrate peak. Spectroscopic ellipsometry was, therefore, used to characterize the $InAlBiAs$ bandgap. Ellipsometry measures the change in the polarization state of light reflected from the surface of a sample. It can be used to characterize sample thickness, optical constants, surface and interfacial roughness, etc. A variable angle spectroscopic ellipsometer (VASE; J.A.Woollam) at the Institute of Energy Conversion at the University of Delaware was used. The measurements were taken with an incident light wavelength from 265 to 1400 nm with a step size of 5 nm, at incident angles of 68$°$⁠, 73$°$⁠, and 78$°$⁠. We extracted the physical properties of the $InAlBiAs$ layer from the ellipsometry measurements using the model described as follows. Tabulated optical constants were used for the InP substrate layer (WVASE32). The parametric model, developed at the J. A. Woollam Co., Inc. by Craig Herzinger and Blaine Johs,¹³ is very useful for analyzing dielectric and semiconducting materials that have complicated critical point structures and was therefore used for $InAlBiAs$ films. The model uses parameterized functions to describe the critical point structures. Each critical point structure is composed of 4 polynomials with a total of 12 parameters. Parameters from an established InAlAs parametric model were used as initial values for $InAlBiAs$⁠. The In$0.52$Al$0.48$As parametric model was tested on In$0.52$Al$0.48$As grown on InP and was able to fit the reference sample very well. The Bruggeman effective medium approximation (EMA) was used to describe the surface roughness. The layer thicknesses determined by the ellipsometry agree very well with the values given by HR-XRD.

The calculations of Bi interstitials in the dilute $In0.5Al0.5BixAs1−x$ alloy were based on the density functional theory^14,15 within the generalized gradient approximation¹⁶ and the screened hybrid functional of Heyd, Scuseria, and Ernzerhof (HSE06)^17,18 as implemented in the VASP code.^19,20 The interactions between the valence electrons and the ionic core are treated within the projector-augmented wave (PAW) method.^21,22 We first generated In$0.5$Al$0.5$As using the special quasirandom structure method²³ for a supercell with 64 atoms. Then, we replaced one As atom with one Bi atom, resulting in a $In0.5Al0.5BixAs1−x$ dilute alloy with $x=3.12$%. All the supercell calculations used a 2 × 2 × 2 mesh of k-points for integrations over the Brillouin zone and a cutoff of 350 eV for the planewave basis set. The effect of spin-orbit coupling, which is especially strong for the Bi-containing compounds, was included.

Additionally, the VBAC model was applied to the experimentally obtained bandgap of $InAlBiAs$ with Bi% less than 3%. In the model, the new valence band edge energy with Bi incorporation $EM+$ for $InxAl1−xBiyAs1−y$is expressed as

where $EM$ is the energy of the matrix (InAlAs) valence band edge, $EBi$ is the energy of the Bi impurity state, and $β$ describes the interaction strength between the matrix VB and the Bi impurity state that depends on both group III composition and Bi%.³ $β$ is described as a linear function of In composition: $ax+b$⁠, where a and b are parameters obtained from fitting the bandgaps determined by ellipsometry.

RBS was used to identify both the group III and group V elements composition in the $InxAl1−xBiyAs1−y$ samples. Figure 1 shows the randomly oriented RBS spectrum as well as the simulation of $In0.56Al0.44Bi0.02As0.98$⁠, where the individual contributions of In, Al, As, P, and Bi are also shown. As shown in Fig. 1, the Bi channel (around 1300) is clearly separated from the others, and the concentration can, therefore, be easily determined by fitting the experimental data. To further study the crystalline quality of the film and how Bi atoms are incorporated, aligned RBS measurements have been done in comparison to randomly oriented measurements. The axial channeling is aligned to the normal axis of the sample surface, which is [001]. In Fig. 2, significantly lower intensity of the aligned spectrum than the randomly oriented data indicates overall good crystallinity of the $InxAl1−xBiyAs1−y$ film.

Equation (2) is used to make a first-order estimate of on-lattice fraction of Bi atoms,²⁴ 

where $χBi$ is the ratio of the $χBi$ intensity in the aligned RBS spectrum to the Bi intensity in the randomly oriented spectrum. $χhost$ is that of a “host” atom species, and In is selected in our calculations. From this, it is estimated that $∼$89% Bi atoms are incorporated substitutionally, while only $∼$11% Bi atoms occupy the interstitial sites. Also, $χBi$ remains relatively stable of $∼$0.25, which indicates minimal Bi% gradient across the film. For arsenic, the RBS survey shows that $∼$99% of As atoms are substitutional, indicating Bi atoms form more interstitials than As.

The relation between the Bi% measured by RBS and Bi BEP used for the growth is shown in Fig. 3. More Bi is incorporated in the film with higher Bi flux, until around BEP of $2×10−8$ Torr where Bi% saturates around 3% under the given growth condition.

A $ω−2θ$ scan on the (004) plane was performed on all the samples. Figure 4 shows the $ω−2θ$ scans for three InAlBiAs samples with Bi% from 2% to 3.2%. The sharp and intense peak at 63.3382$°$ corresponds to the InP substrate. The less intense peak to the left of the substrate peak corresponds to the $InAlBiAs$ layer. Clear fringes could be observed for each composition, even for the highest Bi% of 3.2%, indicating that smooth interfaces are achieved. This agrees with the observed streaky RHEED pattern throughout the growth.

RSM on the (224) plane was performed on the sample with the highest amount of Bi, which is the most likely to relax. The result is shown in Fig. 5, and a line which indicates that a fully strained film is drawn as a guide to the eye. The $InAlBiAs$ peak falls along this vertical line, indicating that the 200 nm film is fully strained to the substrate. This is consistent with the previous report on InGaBiAs that the layer could remain fully strained to the substrate with a thickness far exceeding the critical thickness.⁸ 

We tested four different local configurations for the substitutional Bi in the $In0.5Al0.5Bi0.0312As0.9688$ alloy, varying the number of In/Al nearest neighbors. We find that Bi prefers a site coordinated with four Al atoms. We attribute this to the size effect, since the Al–Bi bond length (2.75Å) is much shorter than In–Bi (2.91Å) in the zincblende structure. For the Bi interstitial in the dilute $In0.5Al0.5Bi0.0312As0.9688$ alloy, we find that the total energy for a given charge state varies by less than 0.1 eV for different configurations where the extra Bi occupies the tetrahedral interstitial site. The formation energy of interstitial Bi for the different charge states is calculated using the chemical potential of Bi as the energy per Bi in the dilute $InAlBiAs$ alloy.²⁵ Our results show that the Bi interstitial in dilute InAlAsBi alloys displays an amphoteric behavior, as shown in Fig. 6. It is stable in the 3+ charge state for the Fermi level below 0.6 eV, neutral for the Fermi level between 0.6 and 1.1 eV, and 1$−$ charge state for the Fermi level 1.1 eV above the valence band. This is consistent with the (qualitative) semi-insulating behavior of our films as determined from Hall effect measurements. These deep states provide an opportunity for device engineering in those applications where short carrier lifetime is desirable.

We note that the predicted formation energy of Bi interstitials is somewhat high (⁠$>1$ eV), indicating that their presence in the film is likely due to kinetics during the growth. Compared to As interstitial, we find that Bi has an energy barrier for migration that is at least 1 eV higher. A recent report indicates that the As interstitial is highly mobile in GaAs, with migration barrier less than 0.5 eV.²⁶ This would make the As interstitial highly unstable during growth (or even at room temperature). This explains why significantly fewer As interstitials than Bi are observed in RBS measurements.

It is also worth noting that the calculated bandgap of In$0.5$Al$0.5$As is 1.29 eV, while the calculated bandgap is 1.19 eV for the dilute $In0.5Al0.5Bi0.0312As0.9688$ alloy. The lattice parameter changes by less than 0.4% upon introduction of 3.12% of Bi into the In$0.5$Al$0.5$As. Therefore, the calculated bandgap reduction is about 32 meV/%Bi assuming a linear reduction as a function of Bi%. This provides a reasonable comparison to our experimental measurements and the VBAC study on the bandgap reduction in $InAlBiAs$⁠.

Four $InAlBiAs$ samples with the same composition (⁠$In0.54Al0.46Bi0.024As0.976$⁠) but different layer thicknesses (50, 100, 200, and 300 nm) were grown to perform multisample analysis to obtain the $InAlBiAs$ parametric model values. Examples of the $InAlBiAs$ raw ellipsometry spectrum along with the model fit are shown in Fig. 7. Bandgaps of $InAlBiAs$ were extracted from the model and plotted as a function of Bi concentration in Fig. 8. Bi reduces the bandgap strongly by $∼113$ meV/% Bi if one naively assumes a linear fit through all the points. This value is very large compared to the 57 meV/% Bi reduction in InGaBiAs³ and 88 meV/% Bi in GaBiAs.² 

The result is presented in Fig. 8, where each scattered point corresponds to the experimental result of an individual sample, and each colored solid line indicates the bandgap calculated from VBAC model for different In%. The experimental values agree well with the VBAC calculation in the low Bi% range, while the measured bandgap for InAlBiAs with $∼$3% Bi deviates from the VBAC prediction. Although the interaction parameter $β$ in the VBAC model is a fitting parameter, other values did not give physically meaningful fits. It is possible that Bi-related alloy disorder like Bi clusters within the sample affect the band structure strongly; this is not captured by the VBAC model. More sophisticated theoretical modeling is needed to understand the effect. This deviation from the VBAC theory was also observed in $InGaBiAs$ with Bi% $≥$ 5%.²⁷ If we only consider the range with Bi% $<$ 3%, the bandgap reduction is around 47 meV/%Bi.

From ellipsometry, other critical points energies are also obtained. Figure 9 shows how critical points $E0$ (⁠$Eg$⁠)and $E0+Δ0$ change with Bi%. The critical point energies of In$x$Al$1−x$As are calculated using the reported composition-dependent expression.²⁸ The result suggests that $E0+Δ0$ energy is less affected by the incorporation of Bi compared to $E0$⁠, which is consistent with studies on GaBiAs and $InGaBiAs$⁠. The optical constants of $In0.54Al0.46BixAs1−x$ are plotted in Fig. 10.

The growth and characterization of the Al-containing dilute bismuthide InAlBiAs is demonstrated. Samples were grown by MBE at low growth temperature and low As$4$ overpressure on the InP substrate resulting in films containing up to 3.2% Bi%. The valence band anticrossing theory was applied to describe the bandgap change with Bi%. The bandgaps determined by spectroscopic ellipsometry agree with the VBAC fairly well up to 2.4% Bi composition in $InAlBiAs$⁠. The bandgap reduction was shown to be around 47 meV/%Bi in this low Bi% range. For the samples with $≥$3% Bi%, the experimentally determined bandgaps deviate significantly from the VBAC, which might be caused by effects such as bismuth clustering in the samples with high Bi%. This could strongly impact the valence band but is not captured by the VBAC model used here. Further investigation of the model and optimization of the $InAlBiAs$ crystal quality, including mitigating Bi clustering, are needed. Additionally, because the observed Bi interstitials are kinetically trapped, optimization of growth conditions to reduce their concentration would be useful in applications for which deep states are undesirable.

The authors would like to thank support from the W. M. Keck Foundation for this project. Parts of this work were carried out by the Characterization Facility, University of Minnesota, which receives partial support from the National Science Foundation (NSF) through the MRSEC program. The authors would like to acknowledge Rutgers University for conducting some of the RBS measurements. A.J. was supported by the NSF Early Career Award under Grant No. DMR-1652994. The DFT calculations were carried out using the Extreme Science and Engineering Discovery Environment (XSEDE) supercomputer facilities, supported by the NSF under Grant No. ACI-1053575, and the Information Technologies (IT) resources at the University of Delaware, specifically the high-performance computing resources.