Quantitative Method to Determine Planar Defect Frequency in InAs

Article pubs.acs.org/crystal

Quantitative Method to Determine Planar Defect Frequency in InAs Nanowires by High Resolution X‑ray Diffraction Ziyang Liu,*,†,‡ Clement Merckling,† Matty Caymax,† Rita Rooyackers,† Nadine Collaert,† Aaron Thean,† Olivier Richard,† Hugo Bender,† Wilfried Vandervorst,†,§ and Marc Heyns†,‡ †

imec, Kapeldreef 75, 3001 Leuven, Belgium Department of Materials Engineering and §Department of Physics and Astronomy, KULeuven, 3001 Leuven, Belgium

‡

S Supporting Information *

ABSTRACT: The ongoing study of {111} planar defects (PDs) in III−V nanowires (NWs) entails a fast and quantitative characterization method beyond transmission electron microscopy (TEM). We report here a simple and reliable method to calculate the PD frequency in InAs NWs using a lab X-ray diffractometer. The fact that the PD distribution is location independent and irrelevant to the NWs diameter in catalyst-free InAs NWs epitaxy makes PD frequency global calculation possible. We demonstrated that the PDs follow a geometric distribution in NWs. As a consequence, applying a 1D disordered layers diffraction model, we relate the diffraction peak angle directly to the PD frequency. The calculated PD frequency values are in good agreement with that extracted from high resolution TEM analysis. As an example, we applied this method to study the influence of growth temperature on PD frequencies in the frame of a 2D nucleation model.

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INTRODUCTION Semiconductor nanowires (NWs) are expected to have wide applications, especially in the field of electronics, optics, energy, and sensing.1−5 Among them, III−V NWs are of great interest due to the intrinsic properties of III−V semiconductors, such as high carrier mobility and direct bandgap from visible to infrared spectrum. III−V NWs can be grown vertically on Si(111) substrate using bottom-up growth methods.6,7 Thanks to the small footprint of NW on Si, most of the defects caused by large lattice misfit are confined near the interface with no threading part. With a further reduced diameter, it is even possible to totally eliminate the misfit dislocations,8 which leads to a great progress for integration of III−V semiconductors on Si. Moreover, the vertical geometry of III−V NWs is naturally suitable to fabricate the vertical gate-all-around devices, which will provide the best electrostatic control of the gate over the channel and save space in integrated circuits.1,9 However, there are some important issues unsolved in III−V NW growth, among which a striking one is the polytypism: a variety of crystal structures can coexist in III−V NWs, making them unique from their bulk counterparts.10,11 This is closely related to the high density of stacking faults or twins in NWs.12 For convenience and avoiding confusion, we refer to them as planar defects (PDs) indiscriminately. In the bulk form, III−V lattice adopts cubic (3C) structure, which consists of “ABCABC...” stacking in the [111] direction, where the letters A, B, and C denote one of three possible stacking positions of an (111) atomic bilayer. Because of PDs, this stacking sequence can be altered, and other crystalline phases are introduced, © XXXX American Chemical Society

which are called polytypes. The extreme case with stacking sequence transformed into an “ABABAB...” form, which actually is the form of a hexagonal (2H) lattice, corresponds to 100% PDs inserted in a 3C crystal. Taking the average of these two ends, that is, one PD in every two bilayers, a 4H polytype is obtained, with an “ABCBABCB...” stacking sequence. Because the faulted layers (e.g., “BA” in an ”ABABC” stacking) follow hexagonal sequence locally, we can describe them as hexagonal segments, and their frequency as hexagonality in this Article. In this sense, the hexagonality of 4H structure is 50%, while 2H is 100%. The lattice structures of the three polytypes (3C, 4H, and 2H) are schematically shown in Figure 1. Unfortunately, in most cases, PDs are not regularly distributed in NWs and continuous pure polytype segments are hardly observed.12,13 These random defects have negative impacts on electrical and optical properties of NWs.14,15 Thanks to the recent intense study of crystal structure engineering in vapor−liquid−solid (VLS) NW growth, it is now possible to control III−V NW crystalline phase by tuning growth parameters and the NW diameter.12,16,17 Based on these works, it has been confirmed experimentally that 2H phase III− V NWs have properties different from their 3C counterparts, thus opening up new opportunities to fabricate novel NW devices.18−21 Despite of these efforts, the VLS technique is not Received: April 9, 2015 Revised: June 12, 2015

A

DOI: 10.1021/acs.cgd.5b00489 Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

Article

frequency by XRD. At last, applying this method, we discuss the influence of growth temperature on the PD frequencies in the scope of classic nucleation model.

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EXPERIMENTAL SECTION

InAs NWs were grown on Si(111) substrates by a MOVPE system. Two kinds of catalyst-free growth methods were used. The first one is conventional SAG, where NWs are grown by the aid of patterned holes in an oxide mask.7 Another method is called nonpatterned (NP) growth here because it does not need prepatterning, similar to the reported “self-catalyzed” approach.31 Details about growth can be found in the Supporting Information. The diameter of NWs grown by SAG varies from 140 to 400 nm depending on the patterned oxide template size and the growth conditions, while the diameter of NWs grown by NP method is much smaller (∼30 nm) and uniform. The sample information is shown in Table 1. It should be noticed that for the comparison of NP and SAG methods, A and C had the same set of growth parameters during the growth step, and B and D had another set. InAs NWs were characterized by an FEI NOVA200 scanning electron microscope (SEM). Crystal structure was analyzed by a Tecnai F30S TEM working under 300 kV. For NWs by SAG, a spinon-carbon and electron beam Pt layer were first deposited as a capping layer, then the slices for TEM inspection were prepared by focused ion beam at 30 kV and milling finished at 5 kV. NP-grown NWs were prepared in a different way: the samples were rinsed in ethanol for a 10 min ultrasonic bath, droplets of the solution containing NWs were then deposited on a lacey carbon copper grid for inspection. All images were taken along 3C ⟨110⟩ zone axis in order to reveal the (111) PDs. HR-XRD was done on a PANalytical X’pert PRO diffractometer, equipped with a Cu Kα radiation source. A Ge(220) four-bounce monochromator and an analyzer were used to achieve the triple-axis high resolution geometry.

Figure 1. Schematic lattice chains of 3C, 4H, and 2H polytypes. H and C denote atomic bilayer occupying hexagonal and cubic site, respectively. dcc, dhc, and dhh are the (111) interplanar distances corresponding to cubic-to-cubic, hexagonal-to-cubic, and hexagonal-tohexagonal interactions.

suitable for large scale NW device fabrication due to the problems such as metal impurities and random NWs placement on the wafer surface. This is not the case for selective area growth (SAG), which is considered as a more integrationfriendly approach. However, it brings more challenges in controlling the crystalline phase of III−V NWs. To the best of our knowledge, InP NW is the only demonstrated one in the III−V NW family that could be grown in a pure crystalline phase using SAG, though only achieved on InP(111) A substrates.15,22,23 Meanwhile, the PD formation mechanism is still under study.24−26 To address the application and theoretical understanding needs, detailed analysis on PD distribution and crystalline phase in III−V NWs is the key. Therefore, an efficient quantitative method for NWs crystalline phase analysis is required. Up to now, to explore crystal structure information in NWs, the method is largely limited to high resolution transmission electron microscopy (HR-TEM). This destructive method needs a complex sample preparation procedure and thus is time-consuming. Another concern is its representativeness, owing to the limited volume it probes. In this respect, high resolution X-ray diffraction (HR-XRD) offers a great option. Till now, some attempts were made with synchrotron X-ray source, but the direct comparison of XRD results with TEM data is still missing.27−30 Besides, there is no quantitative method reported for standard X-ray diffractometer. In this context, we propose in this study a fast method to determine the PD frequencies in InAs NWs quantitatively using a laboratory diffractometer. Catalyst-free InAs NWs grown by metal−organic vapor phase epitaxy (MOVPE) system were used as a model experimental system. The HR-TEM study confirms that PDs follow a geometric distribution in InAs NWs. Consequently the average interplanar distance in 1D disordered layers was obtained, making it possible to calculate the PD

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RESULTS The 2θ−ω scans near the 3C InAs (111) position are shown in Figure 2a, in which dashed lines indicate the diffraction angles of ideal polytypes. All diffraction curves were calibrated by aligning Si(111) substrate peaks to its theoretical value of 28.443°. For SAG samples, two distinct peaks are observed. One is at a larger angle and matches the normal (111) diffraction of 3C InAs. The other locates in an intermediate position between pure 2H InAs (0002) and 3C InAs (111) peaks. It should be noted that these peak positions are not impacted by the NW length and density if the same growth condition is applied. The details are shown in the Supporting Information. A wide range 2θ−ω scan of sample C has also been taken as shown in Figure 2b. The “abnormal” peaks indicated by the red arrows are on the left side of the 3C peaks (blue arrows) and the distance between them increases with the diffraction order. The diffraction order of the “abnormal” peaks follows a linear relationship with sin θ/λ (Figure 2c), where θ is its Bragg angle and λ = 1.5406 Å is the wavelength of X-ray. This indicates that the peak series corresponds to a lattice having a larger interplanar spacing in the [111] direction compared with the relaxed 3C lattice. Nevertheless, the peak

Table 1. Sample Description and Growth Parameters ID

growth method

growth temperature (°C)

TBAs/TMIn molar flow rates (μmol/min)

typical diameter (nm)

typical length (nm)

NW density (μm−2)

A B C D E

NP NP SAG SAG SAG

565 565 565 565 605

370/1 31/1 370/1 31/1 31/0.5

35 30 200−350 140−200 200−400

4708 1904 233−1857 1373−2655 157−314

3.47 7.95

B



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Figure 2. (a) HR-XRD 2θ−ω scan results around InAs (111) Bragg reflection. SAG samples are plotted in dotted lines, NP grown samples in solid lines. The curve color implies samples grown under different growth conditions (black, 565 °C, V/III ratio of 370; red, 565 °C, V/III ratio of 31; blue, 605 °C, V/III ratio of 62). The peak positions of ideal polytypes (2H, 4H, and 3C) are shown in dashed lines. (b) Peaks corresponding to 3C (111), (222), and (333) diffractions are plotted separately from a large range XRD 2θ−ω scan. Red and blue arrows indicate the InAs mixed-phase peaks and 3C peaks in different orders, respectively. (c) Linear fitting of diffraction order n as a function of sin(θ)/λ, where θ is the Bragg angle of InAs mixed-phase peak. Lattice parameter extracted from the slope is c = 7.013 Å.

shift is not likely caused by strain, since InAs NWs are fully relaxed from the early stage of the growth on the Si substrate due to their small footprint.32,33 Therefore, the shifted peaks are linked to certain crystal structures with larger lattice parameters in [111] direction. In order to figure out the origin of this double peak phenomena, sample morphology was examined as shown in Figure 3a. Apart from NWs, irregular blocks, which are the byproducts of the growth, are occasionally observed in all samples. TEM analyses of the irregular blocks show that they are nearly free of any PDs (Figure 3b). The HR-TEM picture and its fast Fourier transform pattern (Figure 3c,d) further reveal that these blocks are composed of pure 3C phase. Moreover, further analysis of SEM pictures shows that the relative intensity of the XRD peak of the 3C phase increases with estimated volume ratio of irregular blocks (see Supporting Information). However, as typical HR-TEM pictures of NWs in Figure 4 show (the local maxima of HR-TEM pictures were highlighted by dots,34 based on which the stacking sequence was analyzed and labeled), (111) PDs in parallel with the growth front are randomly distributed throughout the NWs, i.e., crystalline phase is mixed in NWs. As shown in Table 2, the interplanar distance of 4H and 2H polytype InAs are larger than that of 3C InAs.35 Therefore, it can be concluded that the 3C peak in XRD is related to the irregular grown 3C blocks, while the shifted peaks are caused by the mixed-phase NWs. We notice that similar conclusion was reached in local probe XRD using a focused synchrotron beam.30 In that sense, we will focus on the latter kind of peaks and term them as “mixedphase peak” in the following paragraphs. A fact worth mentioning is the uniform PD distribution throughout a sample. For each single wire analyzed, different

Figure 3. (a) Characteristic tilted view SEM picture of an irregular block (shown in red) coexisting with NWs. (b) TEM picture of a block, taken in ⟨110⟩ zone axis, shows there is nearly no planar defects inside. (c) HR-TEM picture and (d) its fast Fourier transform identifies that the block is composed of pure 3C phase.

positions (bottom, center, and top) were studied, and the hexagonalities were found to be similar. Figure 4f illustrates the hexagonalities from the bottom to the top in a 4.1 μm NW grown by NP method. The variation is within 8%, which is the largest value we observed. For the SAG NWs, whose length is shorter than 1 μm, the hexagonality variation within one wire is even less (within 3.4%). Besides, in each sample, the difference C



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Table 3. Summary of Hexagonality Extracted from TEM Analyses and Calculated from the XRD Model

A B C D E

Figure 4. (a−e) Typical HR-TEM pictures corresponding to InAs NWs in samples A−E (see Table 1 for details). The local maxima in contrast range are highlighted by spots, and stacking sequence is shown by ABC notation. (f) A low resolution TEM picture of sample A, which shows one 4.1 μm long single InAs NW grown by NP method. Insets are the HRTEM pictures taken at top, middle, and bottom of this NW, with the corresponding PD frequencies marked above.

InAs 3C InAs 4H InAs 2H

(111)/(000l) interplanar distance c/p (Å)

(111)/(000l) 2θ (deg)

10.4923

3.4974

25.447

14.0171

3.5043

25.396

7.0250

3.5125

25.336

hexagonality (TEM)

mixed-phase peak 2θ (deg)

hexagonality (XRD)

849 262 910 199 981

56.9% 76.7% 59% 76.9% 93.3%

25.389 25.368 25.393 25.360 25.345

54.6% 73.0% 51% 79.8% 92.6%

Figure 5. Distribution of the 3C segment thickness (in atomic bilayer numbers) in NWs grown under different V/III ratios (black, V/III = 370; red, V/III = 31). Linear fitting indicates that the frequency of 3C segment follows an exponential relationship with its thickness.

which in total 1759 and 461 atomic bilayers are counted, respectively. The clear linear trend indicates that the segment thickness frequency is in simple exponential form (p(k) = BAk, where A and B are fitting parameters). If the Poissonian nucleation process is assumed, for each atomic bilayer ready to form at growth front, there are two possibilities: occupying a cubic site or hexagonal one. The probabilities of the two events are respectively pc and ph, where pc + ph = 1 and ph equals hexagonality. The probability of forming a k-bilayer 3C segment is equal to pkc ph (k = 0, 1, 2, 3...), which agrees with the observed exponential relationship. Therefore, the PD follows a geometric distribution, similar to what has been reported in VLS grown NWs.36 With these statistic results, in order to understand how the distribution of PDs impacts the diffraction peak, it is necessary to analyze the interplanar distances within a polytypic crystal. Along the close-packed [111]/[0001] direction, neighboring bilayers interact in three possible ways: cubic-to-cubic, hexagonal-to-cubic, and hexagonal-to-hexagonal. If we only consider the first nearest neighbor interactions, there are in total three kinds of interplanar distances defined by them: dcc, dhc, and dhh. It is obvious that they are equal to the (111) interplanar distance in 3C, 4H, and 2H structures, respectively, as shown in Figure 1. This assumption has been confirmed in the 6H SiC case, where dcc and dhc is similar to the interplanar distance derived from the lattice parameters of 3C and 4H type SiC, respectively.37 The probabilities of different interplanar distances can be calculated based on ph. To explore all stacking sequences, we have enumerated them arbitrarily from a hexagonal layer. In each k-bilayer 3C segment confined by hexagonal layers, there are k − 1 cubic-to-cubic and two cubic-to-hexagonal interactions. The hexagonal-to-hexagonal interaction only happens when another hexagonal layer follows the first one,

Table 2. Lattice Parameters and (111)/(000l) 2θ Bragg Diffraction Angles for the Different InAs Polytypesa lattice parameter c(å)

bilayer numbers counted in TEM

a

Lattice parameter values are taken from the work of Kriegner et al.35 p stands for the periodicity of the polytype, i.e., p = 2 for 2H, 3 for 3C, and 4 for 4H.

in hexagonality among NWs is negligible although their diameters can be varied especially in SAG samples due to the patterning geometries. For example, in sample C, the hexagonality of a 200 nm diameter NW is 59.8%, while that of a 350 nm one is 56.4%. This indicates that for each sample, only one global hexagonality value is enough to depict the PD frequency, as presented in Table 3. Once the growth condition was settled, the NWs grown by different methods have similar hexagonality (A vs C; B vs D), although there is a huge difference in NW diameters. In other words, NW hexagonalities are independent of their diameters ranging from 30 to 350 nm. We will go into detail about this statement later in the discussion section. In Figure 5, the natural logarithm of pure 3C segment frequency is plotted as a function of its thickness (i.e., the number of successive cubic bilayers it contains). The analysis includes samples grown under V/III ratio of 370 and 31 for D



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which means k = 0. Accordingly, the relative probabilities of three kinds of interplanar distances are ∞

pcc =

∑ ph pck (k − 1) k=2

phc = 2(1 − ph ) phh = ph

(1)

Because of the weight terms that account for interlayer interaction numbers, their sum does not equal 1. For 1D randomly disordered layers containing two different interplanar distances, the randomly distributed PDs have the effect of displacing the diffraction maxima to positions corresponding to the average lattice parameter.38 This argument can be extended to the three interplanar distances case as studied here (see Supporting Information). We can obtain the average interplanar distance along [111] direction from the relative probabilities in eq 1: d̅ =

Figure 7. HR-XRD 2θ−ω scan around 3C InAs (111) diffraction of InAs NW samples grown on Si(111) under a set of temperatures (492−604 °C) at V/III ratio of (a) 370 and (b) 31. The hexagonalities ph are derived by our method, and the temperature dependence of parameter ln(1/ph − 1) is plotted (c).

It is obvious that the mixed-phase peak shifts to smaller angles as the growth temperature increases, indicating that hexagonality increases with growth temperature. The exact hexagonality values were then obtained by the model (detailed values can be found in the Supporting Information). Assuming a circular nucleus shape, the energy barrier of 3C and 2H nuclei are

(dhhphh + dhcphc + dccpcc ) (phh + phc + pcc )

(2)

According to Bragg’s Law, its first order diffraction angle is ⎛ λ ⎞ θ = arcsin⎜ ⎟ ⎝ 2d ̅ ⎠

ΔG3*C =

(3)

The relationship between the hexagonality and the diffraction peak position 2θ is derived based on eqs 1, 2, and 3, as shown in Figure 6. The red line is the calculated result, while the blue

ΔG2*H =

πγ3C 2sc Δμ πγ2H 2sc

Δμ − σFsc

(4)

where γ3C and γ2H are the edge energy of 3C and 2H phase nuclei, respectively, sc is the area one molecule occupies, Δμ is the supersaturation, and σF is the extra interface energy caused by a PD. Because of the geometric distribution of PDs, 3C and 2H nucleation can be viewed as two independent events. If a steady state nucleation is assumed, their relative nucleation rates are ⎛ ΔG * ⎞ 3C ⎟ J3C = A3C exp⎜ − ⎝ kT ⎠ ⎛ ΔG * ⎞ 2H J2H = A 2H exp⎜ − ⎟ ⎝ kT ⎠ Figure 6. Two-theta dependence on NW hexagonality. The red line is the model developed in this study, and black square dots are the experimental results from HR-TEM (see Table 3 for detailed values). The parameters from pure polytype (3C, 4H, and 2H) InAs, on which the calculation relied, are shown in blue stars.

(5)

where A3C and A2H are the kinetic term, including the effect of attachment frequency, adatom density, and Zeldovich factor; k is the Boltzmann constant. The crystalline phase is assumed stable after the critical nuclei size is reached. Therefore, the hexagonality is equal to the proportion of the 2H nucleation rate to the total rate, which can be written

stars are the reference values of pure phase polytypes, on which the calculation is established. The experimental data from Table 3 are inserted as well in black dots. It is clear that the hexagonality values calculated by our model agree well with the experimental TEM results, thus a quantitative link between XRD diffraction angle and PD frequency is built.

ph =

■

J2H J3C + J2H

=

1

(

A exp

−ΔG3*C + ΔG2*H kT

)+1

(6)

where A = A3C/A2H and is temperature independent. Based on this Arrhenius-like equation, PD frequency and temperature can be linked if −ΔG3C * + ΔG2H * is assumed constant within the studied range. The value ln((1/ph) − 1) of these samples are plotted with reciprocal of the temperature in Figure 7c. The clear linear relationship between them is consistent with eq 6. We extract the value ΔG2H * − ΔG3C * from the slope of the linear fitting, which is 1.35 eV at V/III ratio of 31 and 1.42 eV at V/III

DISCUSSION We used this method to study the influence of temperature on hexagonality in the context of classical nucleation model.24 InAs NWs were grown under different temperatures at V/III ratios of 31 and 370, respectively. Their HR-XRD 2θ−ω scans were taken and are shown in Figure 7a,b. E



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layers with three distance elements. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.5b00489.

ratio of 370. These results are similar to the one obtained by Johansson et al. using the same model, while their study was based on HR-TEM picture analysis.39 This further confirms the effectiveness of our model. There is an interesting finding in HR-TEM study (Table 3) that hexagonality is not affected by NW diameter, which has already been noticed before.13,15 This is totally different from VLS growth in which NW diameter is considered as one of the main parameters to engineer defect density.16,40 A tentative explanation can be made based on the nucleation model. Equation 4 is applicable to both catalyst-free and VLS growth; however, different reference should be taken for the Δμ calculation (for simplicity, nuclei are assumed totally inside liquid droplets in VLS growth). In catalyst-free growth the supersaturation is the chemical potential difference between vapor phase and solid phase. It has been revealed that the strong dependence of PD frequency on NWs diameter in VLS growth is due to the Thomson−Gibbs effect in liquid catalyst, which introduces an additional positive term in the supersaturation equation inversely proportional to the metallic droplets (and NWs) radius.40 As a result, the value of −ΔG*3C + ΔG*2H would be decreased with decreasing radius, and PD frequency ph would increase. In contrast, the supersaturation in catalyst-free growth is the chemical potential difference between vapor phase and solid phase, and the former keeps constant irrespective of the diameter. Although the Thomson− Gibbs effect would also influence the chemical potential of solid phase, it is possible that the factor only takes effect at very small size. Therefore, the supersaturation as well as hexagonality in SAG is less dependent on NW diameter compared with VLS growth. It is worth mentioning that only two assumptions are made in the XRD model: (i) interaction is limited to the first nearest neighbors (i.e., 1D random disorder with three kinds of defined interplanar distance); (ii) the difference of interplanar distance among all possible interactions is very small. In principle, since III−V NWs are not the only system troubled by basal PDs,41 this model potentially has wider application as long as PDs globally follow a certain distribution. A possible refinement to this model is to consider higher order interplanar interactions. In addition, higher order of diffraction (e.g., (333)) is preferred to determine the lattice parameter more accurately if intensity could be guaranteed.

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Corresponding Author

*Phone: +32 016283300. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Z.L. and C.M. are grateful to Dr. Yves Mols for his support on the MOVPE tool. REFERENCES

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CONCLUSION In summary, we have done an in-depth analysis of PD distribution in catalyst-free InAs NWs grown on Si(111) substrate. A fast and nondestructive method using HR-XRD to determine PD frequency is developed accordingly. Accurate results that are comparable to HR-TEM analysis are demonstrated. This provides a promising characterization technique facilitating the understanding of the complex mechanism in III−V NW epitaxy. To give an example, the effect of growth temperature on hexagonality is studied using this method.

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AUTHOR INFORMATION

ASSOCIATED CONTENT

S Supporting Information *

Details of InAs NW epitaxy procedure, the impact of NW length and density on XRD peak position, relative volume of irregular blocks analysis, growth temperature-dependent nanowire hexagonality values, and deduction of equivalent lattice parameter equation corresponding to 1D randomly disordered F



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Quantitative Method to Determine Planar Defect Frequency in InAs

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