Gas Source Techniques for Molecular Beam Epitaxy of Highly Mismatched Ge Alloys

Abstract

Ge and its alloys are attractive candidates for a laser compatible with silicon integrated circuits. Dilute germanium carbide (Ge_1−xC_x) offers a particularly interesting prospect. By using a precursor gas with a Ge₄C core, C can be preferentially incorporated in substitutional sites, suppressing interstitial and C cluster defects. We present a method of reproducible and upscalable gas synthesis of tetrakis(germyl)methane, or (H₃Ge)₄C, followed by the design of a hybrid gas/solid-source molecular beam epitaxy system and subsequent growth of defect-free Ge_1−xC_x by molecular beam epitaxy (MBE). Secondary ion mass spectroscopy, transmission electron microscopy and contactless electroreflectance confirm the presence of carbon with very high crystal quality resulting in a decrease in the direct bandgap energy. This technique has broad applicability to growth of highly mismatched alloys by MBE.

1. Introduction

Ge and its alloys have kindled great interest for faster field effect and tunneling transistors, and even more interest as the possible “holy grail” CMOS-compatible laser [1,2,3,4,5,6]. Tensile Ge and optically pumped Ge_1−xSn_x lasers have been demonstrated, but these showed very high thresholds due to adverse band structures [3,4,6]. Dilute germanium carbide (Ge_1−xC_x) with x ≈ 0.01 has recently been predicted to show a strongly direct bandgap and favorable band alignments, with optical emission expected to rival that of III–V semiconductors [7]. However, past growth of Ge_1−xC_x using typical crystal growth techniques produced graphitic clusters and numerous carbon–carbon point defects [8,9,10,11].

Ge_1−xC_x is a highly mismatched alloy (HMA). C atoms are much smaller and more electronegative than their Ge host, analogous to N in GaAs. This has unusual effects on the band structure of the alloy. In particular, the virtual crystal approximation fails to predict semiconductor properties such as bandgap and band alignment. For example, one might expect alloying Ge with diamond (or GaAs with GaN) to increase the bandgap, but it instead decreases. This is often explained through a mechanism known as band anticrossing, in which C (or N) introduces an uncharged (isoelectronic) but localized impurity state above the conduction band edge [12]. The localized state hybridizes with the conduction band states and pushes them lower into the bandgap. Remarkably, the interaction is significantly stronger at the direct bandgap at Γ (k = 0) than in the indirect valleys in Ge, which leads to the creation of a direct bandgap from two indirect bandgap materials.

Highly mismatched alloys (HMA) are, by definition, far from thermodynamic equilibrium and can be challenging to grow without segregation or other defects. For example, the bulk solubility of N in GaAs is only 10¹⁴ cm⁻³, and C in Ge may be as low as 10⁸ cm⁻³ [13]. However, molecular beam epitaxy (MBE) is generally a kinetically limited process that can bypass thermodynamic limits and can incorporate several percent of the mismatched element [9,14]. Even so, HMAs must avoid high energy processes such as sputtering, implantation, and plasma ions to prevent segregation and formation of point defects [15]. Furthermore, Ge_1−xC_x growth must avoid carbon–carbon bonds, which create midgap traps [16]. Therefore, successful growth of Ge_1−xC_x must prevent C from remaining exposed on or segregating to the growth surface, leading to C clusters. Figure 1 shows the growth process using the chosen precursor gas method of tetrakis(germyl)methane (4GeMe).

In this work, we present techniques for MBE of Ge_1−xC_x without detectable carbon–carbon defects. Part 2 describes the synthesis of our carbon precursor gas source, 4GeMe, including modifications to the previous reports of the synthesis. Undesirable carbon–carbon bonds are avoided using a carbon precursor based on a Ge₄C core, in which each carbon atom is already fully surrounded by Ge [17,18]. This is distinct from the more common methylgermanes with Ge surrounded by multiple C atoms. Part 3 describes the hybrid gas source/solid source MBE system used for growth, and the techniques used. Part 4 describes our growth results. The pre-engineering of the desired final crystal structure by a priori precursor design is applicable to a range of material problems, and increases the value of epitaxy.

2. Synthesis of 4GeMe

The choice of carbon precursor gas was motivated by the possibility of depositing carbon fully surrounded by Ge atoms, greatly reducing the risk of forming undesirable carbon–carbon bonds at the surface. Thermal dehydrogenation of the tetra-substituted E₄C core in (H₃E)₄C (E = Si, Ge; see Figure 1) precursors was reported for Si_1−x−yGe_xC_y alloys with bandgaps larger or smaller than Si_1−xGe_x [18,19,20,21,22,23,24,25,26]. The authors noted that these systems demonstrated a non-typical elongated Si–C and Ge–C bond length of 7% (1.89 Å (β-SiC)) and 5% (2.05 Å), respectively. This resulted in (i) the stretching of the E–C bonds to possibly reduce lattice strain and (ii) novel heteroatomic tetrels. E₄C compounds with a Ge₄C core could enable growth of dilute germanium carbide semiconductors with fully substitutional (sp³) carbon in a diamond lattice. This could yield lasers and modulators that are compatible with conventional silicon chip fabrication [20,26,27,28,29,30,31,32,33].

The modified techniques presented here led to a high purity, reproducible, and up-scalable synthetic route to the family of germyl methanes including (Cl₂BrGe)₄C, (1), (H₃Ge)₂CH₂, (2), (H₃Ge)₃CH, (3), and (H₃Ge)₄C, the desired precursor (4GeMe, 4). We confirm by multiple techniques that the correct nuclear magnetic resonance (NMR) spectra are different from published reports. All manipulations were carried out under ultrahigh purity nitrogen or argon gas using Schlenk-line and glovebox techniques. Toluene and diethyl ether were dried over a copper-based catalyst and 4 Å molecular sieve columns (Innovative Technology, Newburyport, MA, USA). GeCl₂•dioxane, squalene, benzyltrimethyl ammonium chloride, C₆H₅CH₂N(Cl)(CH₃)₃, and 4N grade CBr₄, all anhydrous compounds from Sigma-Aldrich, were used as received. LiAlH₄ (anhydrous, Sigma-Aldrich, St. Louis, MO, USA), was recrystallized from diethyl ether.

2.1. Synthesis Procedures

The first step of synthesis was similar to [18], producing (Cl₂BrGe)₄C (1) as follows. A Schlenk flask was charged with a 0.24 g (0.73 mmol) of CBr₄, 8 mL of toluene and a stir bar resulting in a clear and colorless solution. A separate flask was charged with 0.6 g (2.8 mmol) of GeCl₂.dioxane, 15–20 mL of toluene and a stir bar resulting in a colloidal white suspension. The solution of CBr₄ was slowly added to the latter via a stainless steel cannula. The mixture was then stirred for 2–12 h at room temperature resulting in a white cloudy solution. The reaction was then heated slowly to 80 °C, held at 80 °C for two hours, then filtered hot, resulting in a clear, colorless solution via a filter cannula. (Yield: 95%, or 85% scaled up five-fold.) All volatiles were evacuated off resulting in long thin white needles. Crystals of 1 were dissolved in dimethylformamide (DMF) and confirmed via electrospray mass spectroscopy (ESMS) in the positive-ion mode. The following ions were observed in positive-ion mode, (m/z): CCl₁₁Ge₄⁺ (691), CBrCl₁₀Ge₄⁺ (737), CBr₂C_l9Ge₄⁺ (781), CBr₃C_l8Ge₄⁺ (825), and CBr₄C_l7Ge₄⁺ (870).

The second synthesis step produced multiple germyl methane groups (H₃Ge)₂CH₂, (2), (H₃Ge)₃CH, (3), and (H₃Ge)₄C (4GeMe, 4). A Schlenk flask was charged with 0.412 g (0.455 mmol) of compound 1, 0.104 g (2.735 mmol) of LiAlH₄, 0.015 g (0.064 mmol) of C₆H₅CH₂N(Cl)(CH₃)₃, 15–20 mL of squalene and a large magnetic stir bar. The cloudy white mixture was stirred for 5 days at room temperature resulting in a light cream color. The reaction was heated for 2 h at 80 °C and then distilled for 12 h into a flask at −196 °C until a pale green color was seen (yields: 35%). This resulted in 4GeMe. A further distillation of the pale green compound at 80 °C for another 12 h into a separate flask at −196 °C resulted in a mixture of compounds 2 and 3. To further increase the purity of 4GeMe, a four trap-to-trap distillation apparatus connected via high vacuum tubing was used to separate the distillates at various temperatures: (i) −45 °C, least volatile 4GeMe; (ii) −78 °C, compound 3; (iii) −116 °C, compound 2; and (iv) −196 °C for any unidentified side products. C₆D₆ (δ, ppm): 2: GeH₃, t, 3.64; CH, sept, −0.20; 3: GeH₃, d, 3.84; CH, quint, −0.60; 4GeMe: GeH₃, s, 3.34.

2.2. Synthesis Results and Discussion

Electrospray mass spectra (ESMS) in positive ion mode were recorded on a Micromass Quattro-LC triple quadrupole mass spectrometer with 100 °C source temperature, 125 °C desolvation temperature, 2.5 kV capillary voltage, and 20–55 V cone voltage [34]. The samples were introduced by direct infusion with a Harvard syringe pump at 10 μL/min. Gas Phase FT-IR was carried out on a Bruker Tensor 27 (Bruker, Billerica, MA, USA) spectrometer using a Pike Tech 10 cm gas cell with KBr windows. 1D and 2D NMR were carried out for ¹H, and ¹³C{¹H} using 2D homonuclear correlation spectroscopy (COSY) [35], and ¹³C-HMBC [36,37] on either a Bruker Avance III HD 400 (Bruker, Billerica, MA, USA) 400 MHz or a Varian DirectDrive 600 (Varian/Agilent, Santa Clara, CA, USA) 600 MHz spectrometer with C₆D₆ (δ (ppm): ¹H, 7.15; ¹³C, 128.0) and CDCl₃ (δ (ppm): ¹H, 7.26; ¹³C, 77.36) standards in an airtight J-tap NMR tube.

The initial synthesis step is readily achieved as the commercially available GeCl₂•dioxane undergoes a germylene insertion when reacted with carbon tetrabromide: GeCl₂•dioxane + CBr₄ → (Cl₂BrGe)₄C (1) in a solution of toluene [18,19]. Previous reports indicated an initial reaction time of two hours at a 2.2 mmolar scale at room temperature with 79% yield [19]. In this work, a time study showed that slowly stirring for 8–12 h leads to almost complete conversion with 95% yield at a 2.2 mmolar scale, and 85% yield at a five-fold scale (see

Table 1. Yields of (Cl₂BrGe)₄C (1) and 4GeMe (4).

Compound	Yields
(Cl2BrGe)4C	79% a	95% b	85% c
(H3Ge)4C	0 d	0 e	0 f	35% g

^a Repeated literature synthesis [18]: 2.2 mmol, rt, 2 h; ^b 2.2 mmol, rt, 8–12 h; ^c Five-fold increase of [b]; ^d repeated literature synthesis [18]: LiAlH₄, rt, 3d, then distillation at 60 °C for 8 h; ^e LiAlH₄, rt/40/50 °C, 2d/3d/5d, then distillation at 40/60/80 °C for 6/8/12 h; ^f LiAlH₄, rt, 3d, then distillation at 190–220 °C for 8–24 h; ^g LiAlH₄, rt, 3–5d, heat for 2 h at 80 °C, then distillation at 80 °C for 8–12 h.

).

Additionally, if stringent air-free conditions and freshly distilled and degassed solvents are used, after filtering hot, pure large white needles grow immediately upon slow evacuation of all volatiles. This procedure eliminated the need for recrystallization. The ¹³C spectrum showed no carbon peaks, as expected, as no traces of the starting material CBr₄ (C₆D₆, δ (ppm): s, −29.71) [38,39] or residual solvent peaks (toluene, C₆D₆, δ (ppm): CH₃, 21.10; C(i) 137.91; CH(o) 129.33; CH(m) 128.56; CH(p) 125.68) were detected [40]. We believe the increase in reaction time and slow evacuation of volatiles promotes complete germylene insertion without decomposition.

To examine the stability of the Ge–C core, crystals of 1 were dissolved in a solution of DMF, and ESMS clearly showed that the sp³ hybridized carbon cluster core remained intact even after ionization (see Figure 2). In the positive ion mode, several cluster species were characterized by their isotope pattern [18,19,34,41,42]. The clusters retained the mass of the core Ge₄C with several halides (m/z = CCl₁₁Ge₄⁺ (691), CBrCl₁₀Ge₄⁺ (737), CBr₂Cl₉Ge₄⁺ (781), CBr₃Cl₈Ge₄⁺ (825), and CBr₄Cl₇Ge₄⁺ (870)), thus supporting the stability of compound 1. Such multi metal-chalcogenide clusters, with partial oxidation caused by the electric ESMS field, is a common phenomenon when being ionized [41,42]. However, evidence of the intact core was unexpected as the Ge–Cl (356 kJ/mol) and Ge–Br (276 kJ/mol) have stronger bond dissociation energies than the Ge–C (255 kJ/mol) bond. Hence, one might expect the weaker Ge–C bonds to break apart first and fewer intact polyanions of compound 1 to be detected in the ESMS, but this did not occur [43,44,45]. This is a key point for epitaxial semiconductor growth using 4GeMe, since it suggests the C–Ge bonds can remain intact when the molecule adsorbs onto a Ge surface, especially if the strong halide bonds are replaced by weakly bonded hydrogen to create 4GeMe.

These results confirmed that the tetrasubstituted sp³ hybridized carbon core in 1 remains intact and could be reduced to produce the target compound, (H₃Ge)₄C, containing weaker Ge–H (290 kJ/mol vs. Ge–Cl 356 kJ/mol) bonds. In addition, this supports our hypothesis that it may be feasible that upon thermal dehydrogenation of the latter compound—4GeMe—the Ge₄C carbon core will remain intact. Moreover, the central carbon atom is also sterically protected by the bulky germanium atoms as in compound 1 (covalent radii: C = 0.77 Å, Ge = 1.22 Å) [43] (see Figure 2) thus assisting in driving the dissociation of the stronger Ge–H bonds [18]. Indeed, this is the case for hydrogermolysis reactions where the stronger terminal Ge–H bond in R₃Ge–H (R = Ph, Me) is cleaved at slightly elevated temperatures in preference to the weaker Ge–C bonds forming a Ge–Ge bond (256 kJ/mol) in R₃Ge–GeR’₃ (R = Ph, R’ = Et, Bu, Ph; R = Me, R’ = Bu) [34,46,47]. Hence, we proceeded in attempting to reproduce the syntheses of (H₃Ge)₄C by utilizing lithium aluminium hydride to hydrogenate 4GeMe.

Several initial attempts at the reaction of 1 with anhydrous LiAlH₄ at the suggested [18] ambient temperatures for 3 days in a solvent with a high boiling point, such as squalene, followed by distillation (60 °C) were unsuccessful. At low temperatures, the synthesis did not proceed, and only a grey-white mixture was seen. Stirring for 1–10 days at higher temperatures from 60 to 220 °C was also not successful. An increase in temperatures concomitantly with longer reaction times instead led to the decomposition of the reaction mixture to unidentifiable dark brown-black solutions and precipitates (see Table 1 for more details).

A breakthrough was reached after numerous temperature vs. time reaction conditions were monitored over a period of five to ten days consecutively. As the reaction was stirred for a minimum of two days to a maximum of five days (neither increasing the yield of the target compound (H₃Ge)₄C (4GeMe)), the color changed from a dark grey-white suspension to a pale cream color. At this stage, the reaction was heated over several hours to 80 °C and held there for 2 h. The reaction mixture was then distilled into a −196 °C trap for eight to twelve hours until a mint green color was seen.

A combination of clear liquid and waxy product, as expected [18,19], was collected along with a white precipitate. A gas phase FT-IR of the products showed positive indications of the target compound, 4GeMe, as the spectrum clearly showed the vibrational hydride, GeH₃, at 2075 cm⁻¹ (vs., GeH str) and 839 cm⁻¹ (m, GeH₃, sym def), along with CH vibrations at 3032 cm⁻¹ (vw, CH str). This suggested that there were mixed products in the sample, possibly including partially hydrogenated compounds such as (H₃Ge)₂CH₂, (2) and (H₃Ge)₃CH, (3), along with the fully hydrogenated target compound, (H₃Ge)₄C, (4GeMe).

Thus, a ¹H NMR of the sample was taken in an airtight J-tap tube in C₆D₆ (see Figure 3). This showed several unidentified products, possibly including partially hydrogenated compounds and decomposition species. Nevertheless, the spectrum clearly shows peaks that are readily assigned to compound 2 (GeH₃, t, 3.64 ppm; CH, sept, −0.20 ppm) and compound 3 (GeH₃, d, 3.84 ppm; CH, dect., −0.60 ppm), in good agreement with [18]. However, the ¹H singlet (GeH₃) reported to be 4.07 ppm for 4GeMe was instead found at 3.34 ppm. This disparity may explain why other attempts to reproduce the synthesis technique in Ref. [18] were elusive. Extensive 2D experiments, below, were repeated to confirm that the GeH₃ shifts are at 3.34 ppm rather than the reported 4.07 ppm [18,19].

The 2D COSY spectrum in Figure 4A shows that the ¹H resonance signal at 3.84 ppm (green) correlates to the decatet at −0.60 ppm (green) and the resonance signal at 3.64 ppm (blue) correlates to septet at −0.20 ppm (blue), confirming that, indeed, compounds 2 and 3 exist, respectively. Also, the signal at 3.34 ppm correlates to no other signal, as expected for a singlet peak. In other words, all H atoms are in equivalent chemical environments, which is strong evidence for the desired target 4, (H₃Ge)₄C.

In Figure 4B, 2D HMBC correlates the resonance signal of the central carbon atom core with the resonance of the proton through C–Ge–H bonding. This would be detected if, indeed, a proton is two bonds away from carbon, hence confirming the hydrogenation product and stability of the compound in C₆D₆ at room temperature conditions. Compounds 2 (blue *), 3 (green *), and 4GeMe (yellow *) correlate a proton triplet at 3.63 ppm to the carbon signal at 220.55 ppm in compound 2, (H₃Ge)₂CH₂; a proton doublet at 3.83 ppm to the carbon signal at 211.92 ppm in compound 3, (H₃Ge)₃CH; and a proton singlet at 3.342 ppm to the carbon signal at 67.37 ppm in compound 4GeMe, (H₃Ge)₄C. Hence, this reaction pathway was clearly a one-pot synthesis for all three of these compounds.

Fractional distillation was used to separate the products, keeping 2 and 3 as these have been shown to dramatically improve the growth of germanium on silicon wafers [31,48,49,50]. Thus, a four trap-to-trap distillation apparatus connected via high vacuum tubing collected the distillates from the reaction vessel at various temperatures: (i) −45 °C for the least volatile 4GeMe; (ii) −78 °C for 3; (iii) −116 °C for 2; and (iv) −196 °C for any unidentified side products. Compounds 2 and 3 were isolated at said temperatures as seen via NMR, as previously discussed. However, in the first trap, we were able to isolate 4GeMe free of contaminants (see Figure 5) except for the partially hydrogenated (H₃Ge)₂CBr₂ species. For this compound, ¹H singlet at 2.114 ppm correlated with ¹³C signal at 21.4 ppm in HMBC spectrum [51]. Although not 100% pure, this is a significant improvement from the previous sample (refer to Figure 3), and the remaining background compound is not expected to interfere with semiconductor growth [17].

3. Growth System and Techniques

With the desired 4GeMe precursor in hand, we turned to epitaxial growth. For MBE of Ge_1−xC_x, we designed a gas delivery system attached to an Intevac Mod Gen II MBE to perform hybrid gas-source/solid-source growth, particularly of Group IV materials. The growth chamber is pumped by a corrosive-rated Pfeiffer 1200 °C turbomolecular pump as well as an ion pump. A substrate manipulator capable of reaching 1200 °C for desorbing suboxides from silicon wafers was installed, although the growths presented here were performed on GaAs substrates. A Staib reflection high energy electron diffraction (RHEED) gun with a differential pumping option allows operation at high chamber pressures, although differential pumping has not been found to be necessary in growths to date. The MBE has a background pressure of 6 × 10⁻¹⁰ Torr without liquid nitrogen (LN2), and <1 × 10⁻¹⁰ Torr with LN2.

The gas delivery system in Figure 6 was designed to allow maximum flexibility in the growth of different materials, with digermane, trisilane, and additional ports for custom precursor gases such as (H₃Ge)₄C or dopants. Gas pressures are measured using Baratron gauges (MKS, Orland Park, IL, USA) for true gas pressure independent of species. Also, unlike thermocouple or Pirani gauges with hot (80–120 °C) wires, Baratrons operate at low ambient temperatures that avoid precracking of any delicate precursors (e.g., SnD₄). The gas flow is accurately and precisely controlled to extremely low flow rates through either Horiba Z500 (Horiba, Boulder, CO, USA) digital mass flow controllers or computer-controlled leak valves. A residual gas analyzer (RGA) allows in situ sampling of the precursor gases within the gas cabinet, as well as leak checking, before opening to the MBE chamber. Four capacitive manometers provide a true measure of pressure independent of gas species [52]. Gases are delivered to the growth chamber by either a cold injector or hot injector, allowing the freedom to use multiple gases simultaneously, including gases that require pre-cracking prior to their arrival at the wafer surface and those that do not. The gas delivery system was designed with minimal dead space to reduce memory effects and increase gas switching speeds. All valves and mass flow controllers (MFCs) are under computer control, and every gas inlet has at least two paths to each MBE gas injector line.

Initial gas-source growths of Ge using digermane showed that the gas utilization was very weak, with <0.1% incorporation. We determined the original cold gas injector nozzle was too far from the surface of the wafer, leading to significant overspray. We replaced the injector with a single 6 mm outer diameter stainless steel tube ending 10 cm from the wafer center. In addition, the majority of the precursor gas that failed to adhere to the wafer surface subsequently condensed on the nearby MBE cryoshroud, which is cooled by liquid nitrogen and has a significantly larger surface area. Although this eliminated the typical memory effect seen in gas source growths, it also prevented any opportunity for additional adsorption attempts of gas molecules with the wafer surface. Therefore, the LN₂ was turned off for gas source growths and was found to be unnecessary due to the low background pressure in the MBE chamber.

4. Growth Method

In order to provide carrier confinement and optical transparency at the relevant wavelengths near the Ge band edge, growth was performed on GaAs(100) substrates. The initial III–V buffer growth was completed on a GaAs(100) wafer in a Veeco Gen 930 III–V MBE chamber (Veeco, St. Paul, MN, USA), which is attached under ultrahigh vacuum (UHV) to the hybrid source MBE mentioned above. The native oxide was desorbed under As beam equivalent pressure (BEP) of 1 × 10⁻⁵ Torr, then a clean epitaxial surface was grown with a 100 nm GaAs buffer, a 50 nm AlAs layer as a back barrier, and another 20 nm of GaAs. Sample flatness was confirmed by a streaky RHEED pattern. The sample was then transferred under UHV to the hybrid source MBE chamber.

As mentioned above, carbon–carbon bonds must be prevented from forming during Ge_1−xC_x growth to avoid midgap trap states [16]. Common carbon sources for epitaxial growth, such as CBr₄, metalorganics, and plasmas, all deposit bare C atoms on the Ge surface, and these atoms ride the growth front until they meet other C atoms and incorporate as carbon clusters [10,53,54,55]. Worse yet, hyperthermal C and hot graphite evaporate directly as large clusters of carbon atoms (C₈ and larger) [10], forming unavoidable defects in Ge. In contrast, by using (H₃Ge)₄C, the carbon atom is fully surrounded by Ge, with no C–H bonds and no direct way for C to bond to a surface. Even if two (H₃Ge)₄C molecules land side by side, the C atoms are no closer than third-nearest neighbors, which is a known stable crystal structure [56].

When using the 4GeMe molecule, the growth temperature has to be optimized so that the Ge–H bonds can thermally crack but the Ge–C bond does not. Solid-source Ge and digermane allow for high quality crystal growth at lower temperatures than the commonly used germane gas. However, if the growth is at too low of a temperature, crystal originated pits will form due to the formation of Ge vacancies. Conversely, too high of a growth temperature will break Ge–C bonds in the 4GeMe, and C atoms will be exposed to form undesirable C clusters.

The Group IV growth began with 10 nm of solid-source Ge grown at 400 °C (thermocouple) at a growth rate of 60 nm/h. For the remainder of the growth, the Ge shutter was left open. In order to maximize the 4GeMe incorporation efficiency, the ion pump remained off during the growth, and the gate valve was closed to the turbomolecular pump. The 4GeMe was then injected at a foreline pressure of 30 mTorr as measured on the capacitive manometer for 20 s, at which point the growth chamber pressure had risen to 5 × 10⁻⁵ Torr by ion gauge. The gate valve was left closed for an additional 40 s to allow the 4GeMe additional residence time in the chamber, while solid source Ge continued to deposit. Next, the gate valve was opened for 20 s to pump out the residual gases. This 4GeMe deposition was repeated for a total of 15 cycles (20 min), for a total of 20 nm of solid-source Ge growth. The substrate temperature was increased by 25 °C, then 50 nm of solid-source Ge was grown. This cycle was repeated a total of six times, with successively higher substrate temperatures up to 525 °C.

5. Experimental Results

Figure 7 shows the cross-sectional transmission electron microscopy of the Ge:C sample. The first several layers of Ge and Ge:C appear to have grown smoothly. The growth appears to turn rough above 475 °C. It is important to note that C clusters can act as Frank-Read sources, which would generate large dislocation networks, but analysis of the TEM shows no signs of dislocations. Figure 8 shows secondary ion mass spectroscopy (SIMS) performed on the sample by Evans Analytical Group, showing clear C incorporation. It appears that at the lower growth temperatures there is incomplete incorporation of the 4GeMe molecule. At 450 °C and above, the incorporation increases, suggesting more complete cracking and/or adsorption (sticking coefficient) of 4GeMe. The plateaus seen in Figure 8 are at approximately 0.03% and 0.05%. Due to the roughness of the sample and the limited resolution of SIMS, the C content is effectively averaged over the entire Ge and Ge_1−xC_x superlattice and does not directly measure the C in the quantum wells. Considering the thicknesses of the 20 nm Ge_1−xC_x wells and 50 nm Ge barrier layers, the 0.05% average is equivalent to approximately 0.2% C in the Ge_1−xC_x wells grown at T_sub ≥ 450 °C.

To look for subtle changes in the direct bandgap, contactless electroreflectance (CER) measurements were performed. Like photoreflectance (PR), CER modulates the built-in electric field in the sample, which changes the reflectance at energies corresponding to direct optical transitions such as the direct bandgap [57,58]. An important advantage of CER over PR spectroscopy is the elimination of problems with the modulation of the refractive index inside the sample which leads to an unwanted Fabry–Perot oscillation [59]. A strong direct bandgap transition followed by Franz–Keldysh oscillations (FKO) is visible in the CER spectrum of the Ge:C sample shown in Figure 9. The transition energy can be estimated from the analysis of FKO [60] as shown in the inset in Figure 9.

Despite the very small amount of C shown in SIMS, Figure 9 shows a decrease in the direct bandgap energy from 0.80 eV (Ge) to 0.776 eV, a difference of 24 meV. To the authors’ knowledge, this was the first demonstration of a decrease in direct bandgap in a Ge:C sample with no defects detectable by electron-dispersive X-ray spectroscopy in scanning transmission electron microscopy (STEM-EDX), nuclear reaction analysis Rutherford backscattering spectroscopy (NRA-RBS), or Raman spectroscopy [17]. It is noteworthy that a significant reduction in direct bandgap was achieved even though the carbon and defect concentrations were both below the detectable limits of these common techniques.

6. Discussion

Bare C atoms on the surface can ride the growth front, which is a longstanding problem in this material system. When C atoms ride the surface, they incorporate into the growth when they meet additional C atoms and form C–C or larger carbon clusters. As shown in Figure 7, crystal quality is very high with no stacking faults or dislocations detected. Another confirmation of the crystal quality is the lack of detectable carbon clusters by HRTEM, Raman spectroscopy, and NRA-RBS [17]. Due to the lack of evidence of C clusters, it is believed that the C atoms are incorporating as part of the Ge₄C structure of the original (H₃Ge)₄C molecule. There was a distinct change in growth kinetics above 475 °C, which the authors attribute to chemisorption of the (H₃Ge)₄C leading to a H₂-passivated surface. Further growths are required to identify growth conditions for flat layers; however, SIMS suggests that 450 °C is needed for complete (H₃Ge)₄C incorporation while keeping below 475 °C for smooth growth.

The clear CER signal observed in Figure 9 shows very good crystallinity with a strong direct optical transition at the Γ point of the Brillouin zone. A decrease in the direct bandgap of 24 meV is consistent with theoretical predictions and very close to the photoreflectance results [17]. Additional growth with %C close to 1 at % should be performed to confirm the theoretical predictions for a direct bandgap and confirm the measured decrease in bandgap is due to C and not the Franz–Keldysh effect.

A 1:100 ratio for (H₃Ge)₄C Ge BEP was chosen in order to grow dilute Ge_1−xC_x with <1 at % C. Our initial growth assumed that the sensitivities would be similar, and choosing a BEP for (H₃Ge)₄C that was approximately one percent of Ge’s BEP would give a reasonable incorporation rate. However, when comparing relative sensitivity factors (R_g) for different atoms and molecules, assuming it can be approximated by the ratio of ionization cross sections at 150 eV [61], a Ge₂H₆ molecule is expected to have an R_g approximately double that of GeH. The R_g for Si(CH₃)₄ is nearly four times that of GeH [62]. We attribute the difference between (H₃Ge)₄C:Ge fluxes and C:Ge atomic mole fractions to the difference in R_g between our Ge source and (H₃Ge)₄C. Although the ionization cross section and sensitivity factor of (H₃Ge)₄C are unknown, a factor of 5 difference fits the trend for GeH₃, GeH₄, and Ge₂H₆.

Mass transport calculations are as follows. Molecular flow through 1.4 m of tubing with an inner diameter of 4.6 mm from the foreline to the delivery end of the gas injector, the gas conductivity of the gas delivery line is C_pipe,mol = $\overline{\mathit{c}}$πd³l⁻¹/12 = 2.6 mL/s [63]. For a foreline pressure of 30 mTorr, this corresponds to a flow of 7.8 × 10⁻⁵ Torr L·s⁻¹.

One of the challenges to producing direct bandgap GeSn and related alloys is the strain present in the materials. In order to turn Ge into a direct bandgap semiconductor, 1.4%–2% biaxial strain must be applied [2,64,65,66,67]. A direct bandgap GeSn laser was recently demonstrated, but that required >12% Sn [6]. To grow a direct bandgap, Ge_1−xC_x should require less than 1% C [7]. The People–Bean model [68] predicts a critical thickness of 1250 nm for 1% C Ge_1−xC_x on Ge, so strain does not limit Ge:C device design. This contrasts with GeSn, where it predicts 57 nm critical thickness. Even the more conservative Matthews–Blakeslee model predicts a Ge_1−xC_x critical thickness of 36 nm, which is more than enough thickness for quantum wells [69]. What little strain does exist in Ge:C is tensile, which contributes favorably, if negligibly, to a direct bandgap.

7. Conclusions

Through the use of specially designed precursor gases and a custom designed gas delivery system, molecular beam epitaxy is uniquely capable of growing HMAs like Ge_1−xC_x well into the miscibility gap. Taking advantage of kinetically-limited growth regimes, C can be effectively incorporated without defects. When incorporated substitutionally, contactless electroreflectance confirms a decrease in direct bandgap with very dilute amounts of C in Ge.