Improving carrier mobility of polycrystalline Ge by Sn doping

To improve the performance of electronic devices, extensive research efforts have recently focused on the effect of incorporating Sn into Ge. In the present work, we investigate how Sn composition x (0 ≤ x ≤ 0.12) and deposition temperature Td (50 ≤ Td ≤ 200 °C) of the Ge1−xSnx precursor affect subsequent solid-phase crystallization. Upon incorporating 3.2% Sn, which is slightly above the solubility limit of Sn in Ge, the crystal grain size increases and the grain-boundary barrier decreases, which increases the hole mobility from 80 to 250 cm2/V s. Furthermore, at Td = 125 °C, the hole mobility reaches 380 cm2/V s, which is tentatively attributed to the formation of a dense amorphous GeSn precursor. This is the highest hole mobility for semiconductor thin films on insulators formed below 500 °C. These results thus demonstrate the usefulness of Sn doping of polycrystalline Ge and the importance of temperature while incorporating Sn. These findings make it possible to fabricate advanced Ge-based devices including high-speed thin-film transistors.


Results
The as-deposited Ge 1−x Sn x layers, which are precursors for SPC, were analyzed by using x-ray reflectivity (XRR) and Raman spectroscopy. Figure 1(a) shows that, with increasing T d , the atomic density of both precursors Ge and Ge 0.97 Sn 0.03 (corresponding to x = 3.2%) increases and asymptotically approaches that of crystals. In addition, for low T d (≤100 °C), Sn doping allows the atomic density of the precursor approach that of the crystals. Figure 1(b) shows that Ge 0.97 Sn 0.03 samples with T d = 50, 100, and 150 °C exhibit broad peaks near 270 cm −1 , corresponding to amorphous (a-) Ge. The sample with T d = 200 °C exhibits a sharp peak near 300 cm −1 , corresponding to crystalline (c-) Ge, in addition to an a-Ge peak. In this study, clear peaks corresponding to Sn-Sn or Ge-Sn vibrational modes 38 were not observed because of the low x and/or the measurement condition of the Raman system. Figure 1(c) shows that the atomic density of the precursor with T d = 50 and 125 °C increases with increasing initial Sn concentration x. Over the entire x range 0 ≤ x < 0.05, the atomic density for T d = 125 °C exceeds that for T d = 50 °C and is equivalent to that of crystalline GeSn. Figure 1(d) shows the x dependence of Raman spectra at T d = 125 °C. The samples with x = 0.4%-4.5% exhibit the a-Ge peak, whereas the sample with x = 12% exhibits both the crystalline Ge peak and the a-Ge peak. The study using transmission electron microscopy confirmed that the Ge layer with T d = 125 °C is completely amorphous and contained no crystals. The crystallinity, defined as the ratio of the Raman peak intensity of c-Ge to that of a-Ge 11 , was found to be 56% for the Ge 0.97 Sn 0.03 sample with T d = 200 °C [ Fig. 1(b)] and 69% for the Ge 0.88 Sn 0.12 sample with T d = 125 °C [ Fig. 1(d)]. These results indicate that crystalline nuclei start to form in the a-Ge 1−x Sn x layer for x = 3.2% at T d > 150 °C and x > 4.5% at T d = 125 °C. This behavior is consistent with the previous reports that the crystallization of a-Ge 1−x Sn x is facilitated by increasing x 41-43 and T d 11 . Thus, these optical studies reveal that both x and T d strongly influence the atomic density and crystalline state in the precursor layer.
The samples were then annealed for 5 h to induce SPC at a growth temperature T g = 450 °C. Figures 2(a-j) show the crystal-orientation maps obtained by electron backscattering diffraction (EBSD), which indicate that the grain size dramatically varies with both x and T d . Figure 2(i) shows that, with respect to T d , the grain size evolves differently for Ge and GeSn. For Ge, the grain size increases with increasing T d and then begins to decrease. As a result, the grain size peaks around 100 ≤ T d ≤ 150 °C. Conversely, the grain size of Ge 0.97 Sn 0.03 decreases with increasing T d . Note that the grain size of Ge 0.97 Sn 0.03 greatly exceeds that of Ge when the substrate is not heated (T d = 50 °C). Figure 2(j) shows that, for both T d = 50 and 125 °C, the grain size of Ge 1−x Sn x strongly depends on x and peaks at x = 1.6%. For all samples containing Sn (x > 0), the grain size is larger at T d = 50 °C than at T d = 125 °C. The maximum grain size is approximately 7 µm, which is the largest grain size among semiconductor layers formed by SPC. We investigate the origin of this evolution in grain size from the perspective of substitutional Sn concentration y in SPC-GeSn. Since the lattice constant of Ge 1−y Sn y depends on y, y can be determined from the Ge-Ge peak position in the Raman spectrum 34,38 . We therefore determine y from the Raman spectra by using the following equation proposed by Lin et al. 34 : where Δω(y) is the difference between the shift in the Ge-Ge peak of Ge 1−y Sn y [ω(y)] and that of the c-Ge wafer (ω Ge ), a is a constant of 82 cm −1 34 , and Δω strain is the shift due to strain. In general, the Ge-Ge peak of Ge [ω(0)] on a glass substrate shifts to the lower wavenumber than ω Ge because of the strain induced by the difference between the thermal expansion coefficients of Ge and the glass substrate 14,44 . Assuming that the thermal strain of Ge 1−y Sn y is the same as that of Ge because y is low (<5%), Eq. (1) may be rewritten as strain Ge Ge Therefore, we estimate y from Raman spectra, of which examples are shown in the inset of Fig. 3(a). Figure 3(a) shows that y decreases with increasing T d . This suggests that higher T d makes Sn precipitate, as estimated from the difference between x (=3.2%) and y. This result is likely caused by enhanced surface migration of Sn during precursor deposition. Figure 3(b) shows that y increases with increasing x, which is accompanied by Sn precipitation for x > 1.6%. This behavior can be explained from the perspective of the solid solubility of Sn in Ge (1-2%) 37 . It is well known that y exceeds the solid solubility for GeSn thin films grown in a non-equilibrium system including SPC [41][42][43] . The relationship between y and growth temperature in this study is approximately consistent with the previous reports. Considering that c-Sn facilitates Ge nucleation 42 , the decrease in grain size at higher T d and for x > 1.6% [ Fig. 2(i,j)] is attributed to the promotion of Ge nucleation because of Sn precipitation. In contrast, when Sn does not precipitate (x ≤ 1.6%), the grain size increases with increasing x [ Fig. 2(j)]. The mechanism leading to this result remains unclear, but it may possibly be due to Sn doping weakening the amorphous bonds in Ge, which could enhance the lateral growth of crystals.
We used Hall-effect measurements to evaluate the electrical properties of the SPC-Ge 1−x Sn x layers. All samples showed p-type conduction, similar to conventional undoped poly-GeSn 45,46 . This is because the vacancy in Ge provides shallow acceptor levels that generate holes at room temperature 47 . Figure 4(a) shows that Ge 0.97 Sn 0.03 samples have lower hole concentration p than Ge samples for all T d . Figure 4(b) shows that Ge 0.97 Sn 0.03 has higher hole mobility μ p than Ge for all T d , whereas Ge 0.97 Sn 0.03 has smaller grains than Ge for T d > 75 °C [ Fig. 2(i)]. Figure 4(c,d) show that the electrical properties of Ge 1−x Sn x are influenced by x, T d , and T g . Figure 4(c) shows that Sn doping effectively lowers p, except for the samples with x = 4.5% and T d = 125 °C. When T g = 450 °C and x > 0, the samples with T d = 50 °C exhibit lower p than the samples with T d = 125 °C. In particular, the sample with T d = 50 °C and x = 4.5% exhibits the lowest p of 1.4 × 10 17 cm −3 , which is the minimum p among poly-Ge(Sn). For T d = 125 °C, higher T g leads to lower p. This behavior is common in poly-Ge, which suggests that vacancies can be reduced by high-temperature annealing 14,30 . Figure 4(d) shows that, for all three samples, μ p increases  with increasing x and peaks at x = 3.2%. The reason why both p and μ p increase and decrease at x = 4.5% is likely because of the decrease in crystalline quality caused by significant Sn precipitation, as suggested by Figs 2(j) and 3(b). The samples with T d = 125 °C exhibit significantly higher μ p than the sample with T d = 50 °C. Furthermore, the higher T g provides a higher hole mobility μ p . Consequently, the sample with x = 3.2%, T d = 125 °C, and T g = 475 °C exhibits the maximum μ p of 380 cm 2 /V s.
Considering that grain-boundary scattering is one factor behind decreased mobility, the hole mobility of Ge approaches the trend of grain size in Fig. 2(i). In contrast, the hole mobility of Ge 0.97 Sn 0.03 does not follow this trend. These results suggest that μ p of GeSn is strongly influenced by factors other than grain size. According to the carrier conduction model proposed by Seto for polycrystalline semiconductors 9 , the carrier mobility limited by grain-boundary scattering can be determined by using where µ is the carrier mobility, E B is the energy barrier of the grain-boundary, T is the absolute temperature, L is the grain size, m * is the effective mass, and k is the Boltzmann constant. Figure 5(a) shows that the Arrhenius plot of µT 1/2 makes almost-downward-sloping straight lines for all x; however, the lines are slightly curved at high temperatures (1000/T < 4) for x = 0-3.2%. The trap-state density Q t in the grain boundaries can be determined by using 8 where N is the carrier concentration, ε is the dielectric permittivity, and q is the elementary charge. Figure 5(b) shows that E B and Q t determined by the slope of µT 1/2 at low temperatures (1000/T > 4) depend on x. Note that the minimum values of E B and Q t are obtained for the highest μ p sample with x = 3.2% at T d = 125 °C.

Discussion
The hole mobility of SPC-Ge 1−x Sn x strongly depends on both x and T d : a maximum mobility of 380 cm 2 /V s occurs for the sample with x = 3.2%, T d = 125 °C, and T g = 475 °C [ Fig. 4(d)]. The reason is discussed as follows. According to Matthiessen's rule and Irvin's curve of poly-Ge with p on the order of 10 17 cm −3 1 , when μ p is less than about 250 cm 2 /V s, it is primarily limited by grain-boundary scattering as well as ordinary polycrystals. Conversely, when μ p exceeds 250 cm 2 /V s, impurity scattering influences μ p in addition to grain-boundary scattering. For T d = 50 °C, μ p increases from 80 to 250 cm 2 /V s because of Sn incorporation [ Fig. 4(d)], which is attributed to the reduction of grain-boundary scattering, because of increased grain size [ Fig. 2(j)] and likely because of the reduction of E B . By increasing T d to 125 °C, μ p increases for all x, reaching approximately 300 cm 2 /V s for x < 4.5%. We examined the effect of T d in our previous study on SPC-Ge 11 : substrate heating at appropriate temperature during precursor deposition (T d = 125 °C) reduces E B and dramatically enhances μ p . This is explained from the perspective of the atomic density of the amorphous precursor. Moreover, increasing T g to 475 °C further improves μ p for all x [ Fig. 4(d)]. This is likely due to the reduction of impurity scattering because of decreased p [ Fig. 4(c)], which corresponds to the reduction of vacancy-related defects 14,30 . Even for T d = 125 °C, μ p peaks at x = 3.2% [ Fig. 4(d)], although the grain size is relatively small [ Fig. 2(g)]. The high μ p is attributed to reduced impurity and grain-boundary scattering due to the decrease in p [ Fig. 4(c)] and E B [ Fig. 5(b)], respectively. The decrease in p is likely caused by Sn passivating the vacancy in Ge, as mentioned in previous studies 37,46 . Meanwhile, the SPC of a-GeSn progresses while sweeping Sn, which cannot be solid-solved, to the growth front 43 .
Considering that the reduction of E B is possibly due to Sn existing at the grain-boundary, the Sn may passivate dangling bonds and thereby reduce Q t and E B [ Fig. 5(b)]. Because excessively large x (>3.2%) deteriorates crystal  Fig. 4(d)] due to Sn precipitation, x should be slightly larger than the solubility limit. Therefore, the reduction of both E B and p, by controlling x and T d , leads to the maximum mobility of 380 cm 2 /V s. In conclusion, the precursor conditions of both the initial Sn concentration x and the deposition temperature T d strongly influence the crystalline quality and electrical properties of SPC-Ge 1−x Sn x . We obtain a grain size of approximately 7 μm for x = 1.6% and T d = 50 °C, which is the maximum value reported to date for semiconductor films formed by SPC. Conversely, the hole mobility μ p of GeSn reflects the energy barrier E B and the hole concentration p rather than the grain size. The sample with x = 3.2% and T d = 125 °C has E B = 4.1 meV and p = 2.1 × 10 17 cm −3 , resulting in μ p = 380 cm 2 /V s, which is the highest hole mobility among semiconductor layers formed on insulators at less than 500 °C. Since the performance of Ge-TFTs is limited by the properties of poly-Ge thin films, such high μ p and low p will directly improve the field effect mobility and leakage current in the Ge-TFTs. Thus, by controlling x and T d in the Ge 1−x Sn x precursor for SPC, an excellent semiconductor thin film forms at low temperature. The process developed herein is simple enough for practical fabrication of high-speed TFTs for advanced system-in-displays or three-dimensional integrated circuits.

Methods
Sample preparation. The Ge 1−x Sn x (0 ≤ x ≤ 0.12) precursors were deposited on SiO 2 glass substrates by using the Knudsen cells of a molecular beam deposition system (base pressure of 5 × 10 −7 Pa). The deposition rate of Ge was fixed at 1.0 nm/min, whereas that of Sn was adjusted to obtain the targeted GeSn composition. The deposition time was 100 min. The Ge and Sn source, manufactured by Furuuchi Chemical Corporation, had a purity of 99.999% and 99.9999%, respectively. The substrate temperature T d during the deposition ranged from 50 to 200 °C. Note that T d spontaneously rises from room temperature to 50-60 °C without heating the substrate because of the thermal energy radiated from the Knudsen cell, and the notation for this temperature is simplified as T d = 50 °C. The samples were then loaded into a conventional tube furnace in a N 2 atmosphere and annealed for 5 h at 450 or 475 °C to induce SPC.
Material characterization. Rutherford backscattering spectrometry was used to determine x in Ge 1−x Sn x to be 0, 0.4, 0.8, 1.6, 3.2, 4.5, and 12.0%. XRR was done by using a Rigaku SmartLab, and Raman spectroscopy was done by using a Photon Design RSM-310 with a laser wavelength of 532 nm. The EBSD analyses were done by using a JEOL JSM-7001F with a TSL OIM analysis attachment. The Hall effect was measured by using the Van der Pauw method with a Bio-Rad HL5500PC. The hole mobility and hole concentration were averaged over five measurements for each sample.