X-Ray Diffraction Analysis of III-V Superlattices: Characterization, Simulation and Fitting

X-Ray Diffraction Analysis of III-V Superlattices: Characterization, Simulation and Fitting Enlong Liu Xiangyu Wu Abstract Three samples of III-V semiconductor superlattice (SL) are investigated by X-ray diffraction (XRD). The XRD curves exhibit a number of features indicative of SL properties, including zero-order diffraction peak of both SL and the layer between SL and substrate, and a series of satellite peaks. Detailed models for each sample are established to simulate XRD results and by fitting simulation curves with experimental ones, the composition and period of each layer in SL is derived, which is nearly in consistent with the results given by theoretical calculation and the measurement by Transmission Electron Microscopy (TEM). XRD turns out to be a simple, reliable and fast characterization method for SL researches. 1 Introduction III-V semiconductor superlattice (SL) has numerous applications in electronic [1 3] and optoelectronic [4,5] devices after its electronic structure was fully understood [6] and the deposition methods become mature. Its heterostructure is also a model to understanding the growth mechanism and interfaces of semiconductor alloys in different ways, such as Chemical Vapour Deposition (CVD) and Molecular Beam Epitaxy (MBE). However, a little fluctuation in growth environment like temperature and the different properties at interfaces may cause a huge deviation in composition and period of SL structure and hence the device behaviours. For example, the composition of In 0.53 Ga 0.47 As grown by MBE turns out to be In 0.6 Ga 0.4 As in real sample. As the request of real-time monitoring of the growth progress, a fast and reliable way to characterize the deposited SL is needed. Transmission Electron Microscopy (TEM) is widely used in measuring the period of SL. But the composition of SL can not be read from TEM figures and preparing samples for TEM measurement is destructive to origin samples and the most time-consuming part in a series of experiments. X-Ray Diffraction (XRD) has been used to investigate crystal properties in powders for a long time and to analyse thin film [7,8], III-nitrides [9] and SL in recent years by applying the concept of X-Ray Reflectivity (XRR) [7,10], since the structure of SL is like the amplification of crystal planes, leading to periodicity in rocking curves. These X-Ray rocking curves provide information on strain, layer thickness, compositions and diffusion profiles in the structure assessment of SL [11]. Unlike that of TEM, the sample of XRD is easy to prepare. The measurements can be completed in situ during SL deposition onto wafer and take less time than TEM. Because of its non-destructive and highly efficient microstructural characterization, XRD has already been These two authors contributed equally to this report. 1

used to study several kinds of SL structures, such as InGaAs/GaAs [12] and InGaAs/InP [13]. However, these works assumed that the SL layers in sample are in the definite composition and thickness under ideal processing conditions, which is obviously not the case. And their works mostly concentrated on the strain in SL layer and the growth mechanism. In our project, we used XRD to study SLs with more complex structures and analysed the rocking curves based on theoretical calculations and models with parameters optimized by simulations and fittings. This report will first introduce the relative theory of XRD and its application in SL, then the characterization, simulation and fitting of three samples are summarized. At last, we will compare the results from XRD to those from TEM to verify the reliability of XRD measurement in SL studies. 2 XRD 2.1 Principle Scattering theory describes the interaction between light and matter. Particles can absorb light and be excited into an higher energy level, and then relax to the ground state by reemission of light, this phenomenon is called scattering. The scattering process can change the direction and frequency of light. Different scattering mechanisms are shown in Fig.1. In Rayleigh scattering, the frequency of light is not changed, while in Raman scattering, frequency is increased (anti-stokes scattering) or decreased (stokes scattering). Raman scattering is very useful in analysing molecular structure. But in XRD crystal analysis, Rayleigh scattering is detected, Raman scattering only decreases the intensity of XRD signal. The most important the- Figure 1: Band diagrams for Raman and Rayleigh scattering ory for XRD is the Bragg s Law. William Lawrence Bragg and William Henry Bragg observed that when X-ray strikes crystals, the reflected X-ray with produce special patterns. At certain wavelength and incident angel, a strong reflection peak was observed. This phenomenon was described by Bragg s law. As shown in Fig.2, two beams with identical wavelength and phase approach a crystalline solid and are scattered off by two different atoms within it. The lower beam traverses an extra length of 2d sin Θ. Constructive interference occurs when this length is equal to an integer multiple of the wavelength of the radiation. In the famous Bragg s equation, nλ = 2d sin Θ (1) λ is the wavelength of incident beam, Θ is the incident angle, n is an integer, d is the distance between the two atom plane. When this equation is satisfied, constructive interference will 2

occur, leading to Bragg peaks. Thicker material with more atom planes will produce narrower and stronger peaks. The basic scattering unit of a crystal is its unit cell. Figure 2: Schematic drawing of Bragg s Law As shown in Fig.3(a), XRD consists of a X-ray tube which produces X-ray source, a plane for specimen and a detector which collects the scattered X-ray signal. In Fig.3(b), ω is the angle between the emitter and substrate. 2Θ tunes the angle between emitter and detector. Ψ represents the vertical rotation of substrate plane, while Φ is the horizontal rotation of the substrate plane. At last, the x y z coordinates control the position of the specimen. (a) Figure 3: Structure of XRD system: (a) Schematic drawing of the XRD machine; (b) Explanation for different parameters in XRD measurement (b) Two commonly used scan methods are ω-scan and ω 2θ coupled scan, shown in Fig.4(a) and (c). In a ω scan, 2θ is fixed. In a coupled scan, ω and θ move simultaneously with the relationship ω = 2θ + offset. The triple axis diffractometer observes all peaks within a certain range like Fig.4(d), while ω scan only observe one special diffraction peak as in Fig.4(c). With ω scan, we can measure tilt independent of strain (dilation) and get defect information for each individual layer, but tilt and strain could not be independently resolved using a single doubleaxis rocking curve. A single coupled scan can resolve differences in the d-spacing values of the crystallographic planes (d-spacing corresponds to mismatch, composition, relaxation). A common strategy is to collect an ω 2θ scan, identify peak positions, then collect the rocking curve for each diffraction peak. 2.2 Superlattice Diffraction The greatest use of XRD in industry is the characterization of epitaxial structures on compound semiconductors. The composition of ternaries, mismatch of quaternaries, mis-orientation, layer thickness, tilt, relaxation, indications of strain, curvature and stress, and area homogeneity have important influence on the performance of III-V and II-VI semiconductors. With XRD, 3

(a) (b) (c) (d) Figure 4: (a) Schematic drawing for ω scan; (b) Curve of Si by XRD ω scan ; (c) Schematic drawing for ω 2θ scan ; (d) Curve of SiGe double layer by XRD ω 2θ coupled scan we can analyse all these parameters in a cheap, fast, non-destructive way. Of all these parameters, mismatch is the most important one, because it gives information not only about the strain, but also about the lattice constant and composition, which is further linked with the energy bandgap. For the same reason, layer thickness is also very important, due to quantum size effect. So in Rocking curve, we can always visualize two peaks or more, which is caused by tilt or mismatch between the substrate and superlattice epitaxial layers. Diffraction will also occur between different interfaces, so many small peaks will also be observed which gives information about the different layer thickness. As shown in Fig.5, according to Bragg s law, constructive diffraction will happen when θ and d satisfies certain condition, λ = 2d hkl sin θ (2) where d is the inter-plane distance, θ is the Bragg angle. In crystal, the basic diffraction unit is unit cell. For III-V semiconductor crystal with blende cubic structure (cubic crystal), we also have 1 = h2 + k 2 + l 2 a 2 (3) d 2 hkl For (004) plane used in the test, we have d 004 = a 4 (4), in which a is the lattice constant. Combine these equations, we can get the relation between wavelength of X-ray and lattice constant as follow: λ = a sin θ (5) 2 According to this equation, lattice constant a can be calculated, which gives information about mismatch. Moreover, Vegard s Law [14] gives out a Inx Ga 1 x As = xa InAs + (1 x)a GaAs (6), with which the composition of the SL can be calculated. To extract the composition information from XRD curves is one of our main targets. The second target is to extract the thickness of each layer in the SL structure and verify results with TEM image. According to Eq.(1), we get the expressions for two neighbouring Bragg peaks, Nλ = 2Λ sin θ n (7) (N 1)λ = 2Λ sin θ n 1 (8) 4

Figure 5: Drawing for the mechanism of extracting mismatch and composition from XRD. Combine these two equations, the equation for thickness calculation can be derived as below, λ = 2Λ(sin θ n sin θ n 1 ) (9) 2 sin θ n 2 sin θ n 1 = 1 (10) λ Λ. To eliminate errors, the final and most important equation is derived by averaging over the positions of satellite peaks of order n: 2 sin θ n 2 sin θ SL λ = ± n Λ, where Λ is the thickness of SL period, λ CuKα = 0.15405nm is the wavelength of incident X-ray, θ n is the n th-order peak in rocking curve, θ SL is the zero-order peak. (11) (a) Figure 6: Schemes indicating the calculation of layer thickness: (a) Example of XRD rocking curves [13] ; (b) X-ray diffraction in SL structure (b) 3 Results and Discussions 3.1 Sample Structure All three samples are deposited by MBE in different conditions, whose structures are shown in Fig.7. Every sample has a InP(001) substrate, which is 600 m thick, and a InAlAs buffer layer deposited on top of a Si wafer sequentially. The number of repeat unit in their superlattice (SL) is 5. The difference of the structure lies in SL materials. For sample 1 (S1) and sample 2 (S2), their SL layers are made of InP and InGaAs alternatively, and the thickness of each layer of SL in S2 is twice of that in S1, which is determined by the time of MBE deposition process. While the SL layers of sample 3 (S3) is made of InGaAs and InAlAs respectively, and the thickness of InGaAs is the same as that in S2, but for InAlAs all information is totally 5

unknown. Furthermore, the composition of both InAlAs buffer layer and repeat unit in SL are also needed to be determined. These samples can be used in XRD experiment directly instead of preparation like TEM samples. Figure 7: Schematic drawings for three samples: (a) S1; (b) S2; (c) S3 3.2 XRD Experiments Results XRD measurements are conducted on XPert Pro MRD machine made by PANalytical. We used double-axis ω 2θ mode in XRD measurement to characterize all three samples. The X-ray incident plane on the samples has been optimized by justifying Φ and Ψ offset to get maximum signal intensity. The incident angle range for measurement ω 4, and step size is 0.00004. The result curves for three samples are shown in Fig.8, with modification in amplitude and substrate peak offset for clear comparison. Figure 8: XRD curves for S1. S2 and S3 At the first glance of Fig.8, every curve has two big peaks and many satellite peaks, and the distance between satellite peaks in S2 is smaller than that in S1. These peaks contain all the information about the composition and thickness in buffer layer and SL layers in each sample. What we will do is to derive all the parameters of these samples from these XRD curves after identifying the peak belongings, calculating theoretically and simulating. At this stage, only 6

the greatest peak in each sample can be determined as the InP substrate peak, the others will be studied in the following section. 3.3 Curves Analysis and Simulation 3.3.1 Peaks Belonging XRD curves are quite complicated with many peaks and fringes as above. It can only be sure that the highest peak is the substrate peak, because substrate has the largest thickness and hence the highest diffraction intensity. XRD analysis is based on the understanding of XRD curves, without which it s impossible to do calculation or simulation. So in this section we first made a simulation of only the substrate and buffer layer to understand the buffer layer s contribution on total curve. Then we also made a simulation with only substrate and SL in order to exclude the contribution from buffer layer and analyse how SL influences the total curve. The simulation results are shown below in Fig.9. (a) (b) Figure 9: Separate simulation results: (a) InAlAs buffer layer simulation; (b) InGaAs/InP superlattice simulation The highest peak labelled by purple arrow appears in both simulations, meaning that this peak is produced by the substrate diffraction. This Bragg peak is decided by λ = a InP 2 sin(θ 7

tilt). In Fig.9(a), the second highest peak labelled by green arrow only appears in the buffer layer simulation, meaning that this peak has nothing to do with SL and substrate, so it should be the InAlAs buffer layer peak, because the buffer layer has the second highest thickness, so the peak intensity is only next to the substrate peak. Many fringes are observed around buffer layer peak in Fig.8(a), which are caused by the constructive diffraction of reflection between the top surface and bottom surface of the buffer layer, the distance between these fringes is decided by the thickness of the buffer layer. These fringes are also observed in the circled area in the experimental curve, which have good consistence with the simulation. Fig.9(b) comes to the contribution from SL to total curve in. The most important peak is labelled by the red arrow. This peak is the 0-order peak of SL layer. This peak is formed by mismatch, reflecting the difference in the lattice constant of SL layer, this leads to difference in Bragg angles. If this peak appears at the left side of the substrate peak, it means that a InGaA > (a InP ) and SL layer is under compressive strain and vice versa. Misorientation can also influence this peak. The smaller peaks labelled by black arrows are satellite peaks formed by the constructive interracial diffraction of SL, which give information about SL layer thickness. If the uniformity of different SL layers are bad, these peaks will be broadened as an instruction of interlayer uniformity. Unfortunately, no numerical results of thickness variation can be extracted at present. Moreover, there are always three smaller peaks between every two neighbouring satellite peaks in the simulation curve. Its number N gives information about the number of SL period by N + 2. So three small peaks means the SL period is repeated by five times, which is coincided with our sample structures. 3.3.2 Theoretical Calculation S1 After analysing the source of all the peaks in XRD curve, the theoretical calculation of all the parameters can be carried out. For the sake of redundancy, we will only calculate S1 parameters in detail. The peaks labelled by the red arrows in Fig.10 are the fringes of the InAlAs buffer layer. According to Eq.(10), we get the buffer layer thickness of 117nm. SL period thickness is calculated with the angles labelled by blue arrows by using 2 sin θ 4 2 sin θ SL λ = ± 4 Λ (12), where θ 4 = 32.29795, θ SL = 31.67345, λ = 0.15405nm. And we get Λ 34.2nm. Also we notice that the even order peak is much weaker than the odd order peak, indicating that the thickness of the two layers in SL are quite similar. So we assume that the thickness of each layer is 17.1nm. From the deviation between the substrate peak and 0-order peak, the mismatch and composition of SL can be derived. Take θ s = 31.69545 and θ SL = 31.67345 into offset = θ s θ InP (13) and λ = a 2 sin(θ SL offset) (14) where θ InP = 31.668 is already known, this leads to a InGaAs = 5.874. According to Eq.(6) and lattice constant as a InAs = 6.058 and a GaAs = 5.623, the composition of InGaAs in SL is x = 0.577, i.e. its formula In 0.577 Ga 0.423 As/InP. 8

However, this calculation is based on a very simplified model, where the influence of refractive index isn t taken into consideration. And in the experiments, the contribution of misorientaion on the separation between 0-order peak and substrate peak fails to be eliminated, which might be important. Kinetic model should be used if the precise value from calculation is desired, though the value above is good enough to be used as initial for further simulation and fitting. Figure 10: Peak analysis for S1: Red arrows indicate the peaks originated from buffer layer; blue arrows show the different orders of peak originated from SL, the 2nd order peak disappears because of destructive interference S2 With the in-detail analysis for peak belongings in S1, it is natural to use the same methodology to study peaks in S2 curve. By splitting the whole sample structure into two part, substrate with buffer layer only and substrate with SL only, it is easy to find out which peak comes from where in S2 curve. The results are shown in Fig.11. The initial values for simulation of S2 come from two parts. The first one is from known conditions listed in Section 3.1, saying that the thickness of SL in S2 is twice as that in S1. Besides, as we assume the two layers in SL period are in same thickness, we can use 34, 2nm as the initial thickness for InGaAs layer, which is given out from 17.1nm multiplied directly by 2 in Table 1. On the other hand, the period of SL in S2 can be calculated using Equation after identifying the peaks in Fig. To minimize the error, the angle value of 1st order and 7th order of peak are used, leading to Λ = 70nm. Thus, the thickness of InP is 70 34.2 = 35.8nm. The other calculated results are listed in Table 1. S3 The curve of S3 is more complicated, but peak identification and calculation is nearly the same as that in S2. Based on what we knew for this sample, i.e. the thickness of InGaAs is the same as S2, it is easy to know its initial value as 34.2nm. According to Fig.12, the intensity of the even order of satellite peaks are still very high, indicating the different thickness of the two layers in one SL period. Furthermore, this SL period can also be calculated with Equation, which is 53.6nm. So the thickness of InAlAs is 53.6 34.2 = 19.4nm. The composition of InGaAs is given by using the angle value of 0 order peak and Equation. As for the composition of InAlAs in SL, there is no 0 order peak for this layer, meaning that it has the same lattice constant with the substrate InP. With Equation, the composition of InAlAs can be calculated as well, which is listed in Table 1. 9

Figure 11: Peak analysis for S2: Red arrows indicate the peaks originated from buffer layer; blue arrows show the different orders of peak originated from SL, the 2nd order peak disappears because of destructive interference Figure 12: Peak analysis for S3: Red arrows indicate the peaks originated from buffer layer; blue arrows show the different orders of peak originated from SL, the even order peaks appear at this time Table 1: Thickness and Composition of three samples given by theoretical calculation Sample S1 S2 Substrate-InP S3 600µm Layer-InAlAs 117nm Layer 1 InP Layer 2 InGaAs Substrate 126nm 17.1nm 17.1nm In-0.577 10 InP InGaAs 35.8nm 34.2nm In-0.572 135nm InGaAs InAlAs 34.2nm In-0.556 19.4nm In-0.52

Table 2: Thickness and Composition of three samples given by simulation and fitting Sample S1 S2 S3 Substrate-InP 600µm Layer-InAlAs 135nm, In-0.59 132nm, In-0.52 135nm, In-0.52 Layer 1 InP 17.9nm InP 36.0nm InGaAs Substrate Layer 2 InGaAs 29.7nm In-0.60 17.0nm InGaAs 34.5nm InAlAs 21.7nm In-0.60 In-0.60 In-0.52 3.3.3 Simulation results and discussions With all the initial values in thickness and composition for all three sample, we use simulation and fitting to finalize the accurate value of these parameters. The software packages named XPert Epitaxy and XPert Smoothfit provided by PANalytical are used for simulation and fitting respectively. The simulation curves and fitting results are discussed below. In Table 2 are listed all data derived from XRD curves under the analysis flow from theoretical calculation to simulation and fitting. It is clear that the thickness in each sample satisfies the relations we have already talked about in Section 3.1 and the composition for InGaAs in SL keeps constant for three samples, meaning that the deposition is stable for different sample processes. As mentioned above, the simulation curve for S3 is not quite identical with the experiment one, it needs further confirmation and modification after its comparison with TEM results, as well as the other two samples. Fig.13(a)-(c) show simulation curves compared with experimental curves of three samples after horizontal translation to the curves for better correspondence. As it is shown, all simulation curves are in consistent with experimental ones very well, indicating the great similarity of our established fitting models with the real samples. 4 Comparison with TEM Results Even though the composition and thickness of the samples are already got from XRD curves, it is necessary to verify them. To do so, TEM pictures are used, for the thickness of different layers can be read out directly. Fig. shows a series of TEM pictures for three samples. Fig.14(a)-(c) give out the thickness of InAlAs buffer layer, which is 137nm, 140nm and 136nm for S1, S2 and S3 respectively. Fig.14(d)-(f) show the layer thickness in SL part of all samples. For S1, its InP layer is 18nm thick and InGaAs is 16nm. In S2 the InP layer is 38nm and InGaAs layer is 33nm, both of which are nearly two times of those in S1. These data indicate the accuracy of MBE deposition process, so does the 32nm-InGaAs layer in S3, which is nearly the same as 33nm in S2. The totally unknown InAlAs layer in S3 is shown to be 20nm in thickness. The limitation of TEM is in its inability to get composition of different layers in each sample, which is the superiority of XRD. Listed in Table 3 are the data from TEM and XRD. The composition information can not be read from TEM figures, but is uniquely given by XRD curves. Though data of S1 and S2 11

Figure 13: Comparison between simulation curves and experimental curves for (a) S1, (b) S2 and (c) S3 12

Figure 14: TEM pictures with thickness labels for three samples: (a) S1 buffer layer; (b) S2 buffer layer; (c) S3 buffer layer; (d) S1 SL layers; (e) S2 SL layers; (f) S3 SL layers. 13

Table 3: Comparison between results given by XRD and TEM Sample Part Material XRD TEM Error Layer InAlAs 135nm 137nm 2nm InP 17.9nm 18.0nm 0.1nm S1 SL 17.0nm 16.0nm +1.0nm InGaAs 0.6 NA NA Layer InAlAs 132nm 140nm 8nm InP 36.0nm 38.0nm 2nm S2 SL 34.5nm 33.0nm +1.5nm InGaAs 0.6 NA NA Layer InAlAs 135nm 136nm 1nm 29.7nm 32.0nm 2.3nm InGaAs S3 0.6 NA NA SL 21.7nm 20.0nm +1.7nm InAlAs 0.52 NA NA show a good consistency between XRD and TEM, data of S3 has relatively large error, which corresponds to the fact of deviation in simulation curve to experimental one in Fig.(c). It may come from the more complex structure of S3 with too many parameters and the imperfect simulation software algorithm. Besides, the interlayer between SL and buffer layer is not taken into consideration for all three samples, which may also be the source of error. The influence from the interlayer is being researched in the following work. All in all, it is obvious from the comparison that the errors are acceptable and within the permissible range, indicating that XRD characterization, simulation and fitting has high reliability in deriving the thickness of different layers and provides extra informations which can not be given by TEM, i.e. compositions. It makes XRD not only a complement for TEM, but a intact method for SL studies. 5 Conclusion We have carried out XRD studies on superlattice samples with different compositions and periods. Based on the information derived from XRD rocking curves, three models were established and simulated. The fitting results of all three models not only gave information which TEM could not, but also corresponded well with data already given by TEM figures, indicating the reliability and accuracy of XRD measurement in superlattice structures. With its nondestructive property and high efficiency in conducting experiments and results derivation, the applications of XRD in superlattice fields can be foreseen. 14

6 Acknowledgement The authors would like to thank Dr. Clement Merckling for the teaching, instruction and organization throughout the whole project, and Dr. Weiming Guo for his fruitful discussions and practical assistance, and the group leader Prof.Dr. M. Caymax. References [1] J. Tsai, et al., Applied Physics Letters 96, 063505 (2010). [2] J. Gu, et al., Electron Devices Meeting (IEDM), 2012 IEEE International (2012), pp. 23.7.1 23.7.4. [3] M. Sugiyama, et al., Optoelectronic and Microelectronic Materials Devices (COMMAD), 2012 Conference on (2012), pp. 125 126. [4] G. Scamarcio, et al., Science 276, 773 (1997). [5] M. Courel, J. Rimada, L. Hernández, Progress in Photovoltaics: Research and Applications 21, 276 (2013). [6] D. Smith, C. Mailhiot, Rev. Mod. Phys. 62, 173 (1990). [7] M. Birkholz, Thin film analysis by X-ray scattering (wiley-vch, 2006). [8] P. Fewster, Semiconductor Science and Technology 8, 1915 (1993). [9] M. Moram, M. Vickers, Reports on Progress in Physics 72, 036502 (2009). [10] D. Bowen, B. Tanner, High Resolution X-Ray Diffractometry And Topography (Taylor & Francis, 1998). [11] V. Speriosu, T. Jr.Vreeland, Journal of Applied Physics 56, 1591 (1984). [12] Z. Ming, et al., Applied Physics Letters 66, 165 (1995). [13] D. Cornet, R. LaPierre, D. Comedi, Y. Pusep, Journal of Applied Physics 100, 043518 (2006). [14] A. R. Denton, N. W. Ashcroft, Phys. Rev. A 43, 3161 (1991). 15