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Combinatorial design of semiconductor chemistry for bandgap engineering: “virtual” combinatorial experimentation
Applied Surface Science 223 (2004) 148–158
Combinatorial design of semiconductor chemistry for bandgap engineering: ‘‘virtual’’ combinatorial experimentation Changwon Suh, Krishna Rajan* Department of Materials Science and Engineering, Combinatorial Materials Science and Materials Informatics Laboratory, Rensselaer Polytechnic Institute, Troy, NY, USA
Abstract The objective of this paper is to show how one may design combinatorial libraries a priori by integrating data mining techniques with physically robust multivariate data. It is shown that large datasets can be developed from relatively small amounts of experimental and theoretically based information. This involves a process of strategically selecting appropriate physical based parameters that can be analyzed in a multivariate manner. In this paper we identify for the first time the bandgap and lattice parameters of nearly 200 stoichiometries of new and yet to be synthesized compound chalcopyrite semiconductors. The robustness of this ‘‘virtual’’ combinatorial experimentation approach is demonstrated by comparison to band gap predictions from theoretical studies on a range of compositions for a selected quaternary compound semiconductor. # 2003 Elsevier B.V. All rights reserved. JEL classification: 71.55.Cn; 71.55.Eq; 71.55.Gs Keywords: Semiconductor compounds; Crystallographic databases; Crystal stoichiometry
1. Introduction The field of ‘‘bandgap engineering’’ is in fact one of the earliest examples of combinatorial design of materials. The recognition that by matching lattice parameters of different covalently bonded semiconductors, one can engineer the bandgap of epitaxial heterostructures has been one of the success stories in integrating fundamental physics into device engineering. However, the strategy of what materials one may work with is limited to relatively few and the ‘‘discovery’’ of new materials with more complex chemistries is still a slow
*
Corresponding author. E-mail address: [email protected] (K. Rajan). URL: http://www.rpi.edu/rajank/materialsdiscovery.
process. Clearly high throughput experimentation techniques offer some exciting possibilities for developing such new materials. In this paper we wish to outline the use of a statistically based strategy combined with the appropriate understanding of key physical parameters to show how we can develop a computational screening tool prior to conducting combinatorial experiments. We propose the idea of ‘‘virtual’’ combinatorial libraries, which lay a map of suggested chemical combinations, likely to give the desired properties one is seeking. Using chalcopyrite semiconductors as a testbed, we show how such a library can be built. The formalisms of the mathematical foundations are described in Appendix A but suffice it to say that a judicious use of multivariate statistics tools serves as the means to manipulate and process the incoming data.
0169-4332/$ – see front matter # 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0169-4332(03)00918-8
C. Suh, K. Rajan / Applied Surface Science 223 (2004) 148–158
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Table 2 Descriptors for elements in virtual combinatorial library
2. Building the input for the combinatorial library The strategy of the work was as follows. We first identify a set of descriptors or parameters associated with our ‘‘raw’’ materials (i.e. elements). These descriptors need not be related themselves except for the fact that they each describe some physical characteristic that may be relevant to our desired property (e.g. bandgap). The choice of which and how many descriptors is in itself a subject of another paper, suffice it to say, we chose descriptors describing electronic and crystal structure level parameters. We focused on the combination of elements of I–III–VI compounds and II–IV–V compounds (see Table 1). Hence Table 1 outlines our ‘‘combinatorial chemical space’’ that forms the foundation of this study. For each of these selected elements, we chose five descriptors: valency, atomic number, melting point, electronegativity and pseudopotential radii (Table 2). The database was expanded to compounds from elements by first identifying in the reported literature, experimental/theoretical information on bandgaps of known I–III–VI and II–IV–V. The chemistries of these compounds helped define a strategy for deriving a new set of values for the same descriptors used for the elements. The parameterization of these descriptors for compounds was based using a relatively simple strategy originally proposed by Villars et al. which involved a linear weighting model [7]. The formulations are given below: For the binary system such as AxBy with x y and x þ y ¼ 1, the atomic parameters become: Average valence electron number, Nv ¼ xðNv ÞA þ yðNv ÞB . Average atomic number, Zavg ¼ xZA þ yZB . Average melting point, MPavg ¼ xMPA þ yMPB . Table 1 Combinatorial array of elements used in building our virtual array of I–III–VI and II–IV–V compounds I
II
III
IV
V
VI
Cu Ag Au
Zn Cd Hg
B Al Ga In Tl
C Si Ge Sn Pb
N P As Sb Bi
O S Se Te Po
Element
EN
AN
MP
PR
V
Be Mg Cu Ag Au Zn Cd Hg B Al Ga In Tl C Si Ge Sn Pb N P As Sb Bi O S Se Te Po
1.45 1.31 1.08 1.07 1.19 1.44 1.4 1.49 1.9 1.64 1.7 1.63 1.69 2.37 1.98 1.99 1.88 1.92 2.85 2.32 2.27 2.14 2.14 3.32 2.65 2.54 2.38 2.4
4 12 29 47 79 30 48 80 5 13 31 49 81 6 14 32 50 82 7 15 33 51 83 8 16 34 52 84
1562 922 1358 1235 1338 692.7 594.3 234.3 2365 933.5 302.9 429.8 577 3800 1687 1211 505.1 600.7 63.15 317.3 1089 903.9 544.6 54.36 388.4 494 722.7 527
1.08 2.03 2.04 2.375 2.66 1.88 2.215 2.41 0.795 1.675 1.695 2.05 2.235 0.64 1.42 1.56 1.88 2.09 0.54 1.24 1.415 1.765 1.997 0.465 1.1 1.285 1.67 1.9
2 2 11 11 11 12 12 12 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6
EN: electronegativity; AN: atomic number; MP: melting point; PR: pseudopotential radii; V: valency.
¼ Weighted electronegativity differences, DX 2xðXA XB Þ. Weighted differences of Zunger’s pseudopotential ¼ 2xfðrsA þ rpA Þ ðrsB þ rpB Þg. radii sums, DR For ternary compounds as if AxByCz if x y z and x þ y þ z ¼ 1, then: Average valence electron number, Nv ¼ xðNv ÞA þ yðNv ÞB þ zðNv ÞC . Average atomic number, Zavg ¼ xZA þ yZB þ zZC . Average melting point, MPavg ¼ xMPA þ yMPB þ zMPC . ¼ Weighted electronegativity differences, DX 2xðXA XB Þ þ 2xðXA XC Þ þ 2yðXB XC Þ. Weighted differences of Zunger’s pseudopoten ¼ 2xfðrsA þ rpA Þ ðrsB þ rpB Þg þ tial radii sums, DR A A 2xfðrs þ rp Þ ðrsC þ rpC Þg þ 2yfðrsB þ rpB ÞðrsC þ rpC Þg.
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Collectively this new database forms our known or ‘‘training set’’ onto which we can apply our data analysis tools.
3. Results and analysis For this study we applied a technique known as partial least squares (PLS) to serve as a predictive tool based on our training data. PLS is a multivariate predictive technique with distinct advantages over the classical multiple regression and principal component regression approaches. The use of partial least squares techniques is well established in many fields such as psychology, chemometrics, process control, biology and economics. The advantages of PLS over multiple linear regression include its handling of collinearity, missing variables, robustness with respect to coefficients. In PLS, the collinear data matrix is transformed into a latent structural matrix with orthogonal vectors. It can fit data with fewer components than other modeling approaches. PLS has the desirable property in that the precision
of the model parameters improves with the increasing number of relevant variables and observations. The mathematical formulations underlying the PLS calculations are described in Appendix A, but the computational procedure involves eigenvalue calculations of the data matrix which permit one to identify the maximum covariance between disparate datasets. Before we can apply the technique to a set of unknown compounds, it was first tested on our training data. Figs. 1 and 2 demonstrate the robustness of the analysis using the training dataset (Table 3). Based on these results, we embarked on completing our analysis of property prediction for over 200 compounds based on our initial combinatorial input of elements outlined in Table 1. The results are given in Table 4. It should be noted that the deviation from PLS derived results from the first principles LDA calculations simply reflects the differences that exist between experimental and theoretical studies. Our data mining analysis relied heavily on the experimental data and hence the difference, however the data trends match well.
Fig. 1. 4LV PLS results for I–III–VI chalcopyrite compounds.
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Fig. 2. 3LV PLS results for II–IV–V chalcopyrite compounds.
Fig. 3. Comparison of theoretically derived calculations with PLS derived results.
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Table 3 Chalcopyrite compounds data table (training set) Type
Compound
Experimental mini-Theoretical band mal band gap energy (eV) gap energy (eV)
Nature of band gapa
Lattice constant ˚) (A
c/a ratio
Reference
I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 II–IV–V2 II–IV–V2 II–IV–V2 II–IV–V2 II–IV–V2
CuAlS2 CuAlSe2 CuAlTe2 CuGaS2 CuGaSe2 CuGaTe2 CuInS2 CuInSe2 CuInTe2 AgAlS2 AgAlSe2 AgAlTe2 AgGaS2 AgGaSe2 AgGaTe2 AgInS2 AgInSe2 AgInTe2 ZnSiP2 ZnSiAs2 ZnGaP2 ZnGaAs2 CdSiP2
3.49 2.67 2.06 2.43 1.68 1.0–1.24 1.53 1.04 1.06 3.13 2.55 2.27 2.64 1.8 1.32 1.87 1.24 0.95 2.07 1.74 2.05 1.15 2.2–2.45
d d
5.31, 5.34, 5.333 5.606 5.964 5.347–5.356 5.59–5.614 5.994 5.517–5.523 5.773–5.784 6.167 5.695, 5.720 5.956, 5.986 6.296 5.743–5.757 5.973, 5.985 6.283 5.816, 5.872 6.090–6.109 6.406 5.399 5.61 5.465 5.672 5.678
1.96, 1.958 1.954 1.975 1.959 1.966 1.987 2.016 2.008 2 1.802, 1.772 1.805, 1.793 1.878 1.786–1.789 1.823, 1.793 1.897 1.92–1.91 1.916–1.919 1.962 1.933 1.94 1.965 1.966 1.836
[1–3] [1–3] [1,2] [1,2,4] [1,2,4] [1,2,4] [1,2,4] [1,2,4] [1,2,4] [1,2] [1,2] [1,2] [1,2,4] [1,2,4] [1,2,4] [1,2,4] [1,2,4] [1,2,4] [1,2,4] [1,5,6] [1,5,6] [1,2,5] [1,5,6]
II–IV–V2 II–IV–V2 II–IV–V2 II–IV–V2 II–IV–V2
CdSiAs2 CdGaP2 CdGaAs2 CdSnP2 CdSnAs2
1.55 1.72 0.57 1.17 0.26
5.885 5.74 5.942–5.945 5.9 6.094
1.849 1.878 1.888 1.951 1.956
[1,2,5] [1,2,5] [1,2,5] [1,6] [1,6]
a
3.4 2.7 0.92 0.20 0.43 0.01 0.01 0.18
(LDA) (LDA) (LDA) (LDA) (LDA) (LDA)
1.02 (LDA) 0.17 (LDA) 0.17 (LDA) 0.35 (LDA) 0.10 (LDA) 0.21 (LDA) 1.22 (LDA) 0.91 (LDA) 1.16 (LDA) 0.13 (LDA) 1.16 (FLAPW), 1.19 (LDA) 0.42 (LDA) 0.75 (LDA) () 0.44 (LDA) 0.03 (FLAPW) () 0.72 (FLAPW)
pd pd, d (th) pd, I (th) d pd d d d
Nature of bandgap: d—direct; pd—pseudo-direct; th—theoretical; I—indirect.
Table 4 Virtual chalcopyrite compounds data table (test set) Compound
Predicted band gap energy (eV) by PLS
CuBO2 CuBS2 CuBSe2 CuBTe2 CuBPo2 CuAlO2 CuAlPo2 CuGaO2 CaGaPo2 CuInO2 CuInPo2 CuTlO2
0.0807 4.1354 3.5699 3.0768 0.0308 1.0101 0.8986 1.8999 1.7884 2.4383 2.3269 3.4319
Theoretical band gap energy (eV)
Nature of band gapa
Predicted lattice constant by PLS 4.5981 5.511 5.8313 6.1312 6.2737 4.4194 6.095 4.4333 6.1089 4.5688 6.2445 4.7973
Lattice ˚) constant (A
c/a ratio
Reference
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Table 4 (Continued ) Compound
Predicted band gap energy (eV) by PLS
CuTlS2 CuTlSe2 CuTlTe2 CuTlPo2 AgBO2 AgBS2 AgBSe2 AgBTe2 AgBPo2 AgAlO2 AgAlPo2 AgGaO2 AgGaPo2 AgInO2 AgInPo2 AgTlO2 AgTlS2 AgTlSe2 AgTlTe2 AgTlPo2 AuBO2 AuBS2 AuBSe2 AuBTe2 AuBPo2 AuAlO2 AuAlS2 AuAlSe2 AuAlTe2 AuAlPo2 AuGaO2 AuGaS2 AuGaSe2 AuGaTe2 AuGaPo2 AuInO2 AuInS2 AuInSe2 AuInTe2 AuInPo2 AuTiO2 AuTiS2 AuTiSe2 AuTlTe2 AuTlPo2 ZnCN2 ZnCP2 ZnCAs2 Zn0.5C0.5As Zn0.5C0.5Sb ZnCBi2 ZnSiN2
0.7842 0.2187 0.2744 3.3205 0.0058 4.2103 3.6448 3.1517 0.1056 0.9352 0.8237 1.825 1.7135 2.3634 2.252 3.357 0.8591 0.2936 0.1995 3.2456 0.7492 4.9653 4.3998 3.9067 0.8606 0.1802 4.0359 3.4704 2.9773 0.0688 1.07 3.1461 2.5806 2.0876 0.9585 1.6084 2.6077 2.0422 1.5491 1.497 2.602 1.6141 1.0486 0.5555 2.4906 6.006 2.8996 2.0704 2.0704 0.4855 1.104 5.4655
Theoretical band gap energy (eV)
Nature of band gapa
0.9
1.1 0.71 0.6
Metallic
Predicted lattice constant by PLS
Lattice ˚) constant (A
c/a ratio
Reference
5.7102 6.0305 6.3305 6.4729 4.9227 5.8356 6.1559 6.4558 6.5983 4.744 6.4196 4.7579 6.4335 4.8934 6.5691 5.1219 6.0348 6.3551 6.6551 6.7975 5.5635 6.4764 6.7967 7.0967 7.2391 5.3848 6.2977 6.618 6.918 7.0604 5.3987 6.3116 6.6319 6.9319 7.0743 5.5343 6.4472 6.7675 7.0675 7.2099 5.7627 6.6756 6.9959 7.2959 7.4383 5.6714 5.3842 5.5793 5.5793 5.6206 5.9146 5.6631
5.58 5.832 6.299
2.001 1.995
[2] [2] [2]
5.882
[2]
6.529
[2]
5.044 5.384
[8] [8]
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Table 4 (Continued ) Compound
Predicted band gap energy (eV) by PLS
Zn0.5Si0.5P Zn0.5Si0.5As ZnStSb2 Zn0.5Si0.5Sb ZnSiBi2 ZnGeN2 Zn0.5Ge0.5P Zn0.5Ge0.5As ZnGeSb2 ZnGeBi2 ZnSnN2 ZnSnP2 Zn0.5Sn0.5P ZnSnAs2 Zn0.5Sn0.5As ZnSnSb2 ZnSnBi2 ZnPbN2 ZnPbP2 ZnPbAs2 ZnPbSb2 ZnPbBi2 CdCN2 CdCP2 Cd0.5C0.5P CdCAs2 Cd0.5C0.5As CdCSb2 Cd0.5C0.5Sb CdCBi2 CdSiN2 Cd0.5Si0.5P Cd0.5Si0.5As CdSiSb2 CdSiBi2 CdGeN2 Cd0.5Ge0.5P Cd0.5Ge0.5As CdGeSb2 CdGeBi2 CdSnN2 Cd0.5Sn0.5P CdSnSb2 CdSnBi2 CdPbN2 CdPbP2 CdPbAs2 CdPbSb2 CdPbBi2 HgCN2 HgCP2 HgCAs2
2.3591 1.5299 0.055 0.055 1.6445 4.9757 1.8692 1.04 0.5449 2.1344 4.4468 1.3403 1.3404 0.5112 0.5112 1.0738 2.6633 3.7358 0.6293 0.1998 1.7848 3.3743 5.8097 2.7032 2.7032 1.8741 1.8741 0.2891 0.2891 1.3004 5.2692 2.1627 1.336 0.2514 1.18409 4.7793 1.6729 0.8437 0.7412 2.3308 4.2504 1.144 1.2701 2.8596 3.5394 0.433 0.3962 1.9811 3.5706 4.5586 1.4522 0.623
Theoretical band gap energy (eV)
Nature of band gapa
Predicted lattice constant by PLS
Lattice ˚) constant (A
1.56 (GW) 0.68 (GW) 0.9
d md
5.262 5.483 6.077 5.962
[9] [8] [2] [8]
1.15 (GW) 0.23 (GW) 0.5
I md
5.382 5.597 6.111
[9] [9] [2]
1.70 (GW)
I
0.79 (GW)
md
5.3759 5.571 5.6125 5.6123 5.9063 5.7709 5.4837 5.6789 5.7202 6.0141 5.8719 5.5847 5.5847 5.7799 5.7799 5.8212 6.1151 6.0915 5.8043 5.9994 6.0407 6.3347 5.9651 5.6779 5.6779 5.8731 5.8731 5.9143 5.9143 6.2083 5.9568 5.6696 5.8648 5.9061 6.2 6.0646 5.7774 5.9726 6.0139 6.3078 6.1657 5.8785 6.1149 6.4089 6.3852 6.098 6.2931 6.3344 6.6284 6.2613 5.9741 6.1693
1.22 (GW) 0.8
0.33 (GW) 0.2
0.80 (FLAPW)
d Metallic
5.651 5.688 5.851 5.87 6.275
c/a ratio
2 2 2
Reference
[1,2] [9] [1,2] [9] [1]
4.973
[8]
5.201
[8]
5.62
[8]
5.378 5.61 6.344
[9] [8] [2]
5.523 5.755 6.383
[9] [8] [2]
5.797 6.479
[8] [6]
C. Suh, K. Rajan / Applied Surface Science 223 (2004) 148–158
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Table 4 (Continued ) Compound
Predicted band gap energy (eV) by PLS
HgCSb2 HgCBi2 HgSiN2 HgSiP2 HgSiAs2 HgSiSb2 HgSiBi2 HgGeN2 HgGeP2 HgGeAs2 HgGeSb2 HgGeBi2 HgSnN2 HgSnP2 HgSnAs2 HgSnSb2 HgSnBi2 HgPbN2 HgPbP2 HgPbAs2 HgPbSb2 HgPbBi2 BeCN2 BeCP2 BeCAs2 BeCSb2 Be0.5C0.5Sb BeCBi2 BeSiN2 Be0.5Si0.5P Be0.5Si0.5As BeSiSb2 Be0.5Si0.5Sb BeSiBi2 BeGeN2 Be0.5Ge0.5P BeGeAs2 Be0.5Ge0.5As BeGeSb2 Be0.5Ge0.5Sb BeGeBi2 BeSnN2 BeSnP2 Be0.5Sn0.5P BeSnAs2 Be0.5Sn0.5As BeSnSb2 Be0.5Sn0.5Sb BeSnBi2 BePbN2 BePbP2 BePbAs2
0.9619 2.5514 4.0181 0.9117 0.0825 1.5024 3.0919 3.5283 0.4218 0.4074 1.9923 3.5818 2.9994 0.1071 0.9362 2.5212 4.1107 2.2884 0.8181 1.6472 3.2322 4.8217 6.6467 3.5403 2.7111 1.1262 1.1262 0.4633 6.1062 2.9998 2.1706 0.5857 0.5857 1.0038 5.6164 2.5099 1.6808 1.6808 0.0958 0.0958 1.4937 5.0875 1.981 1.981 1.1519 1.1519 0.4331 0.4331 2.0226 4.3765 1.27 0.4409
Theoretical band gap energy (eV)
Nature of band gapa
1.6 0.7
1.2 0.2
0.8
8.2, 4.22 (LDA)
3.60 (LDA) 1.68 (GW) 1.19 (GW)
1.16 (GW)
pd
I I
I
0.53 (GW)
0.98 (GW)
I
0.45 (GW)
I
Predicted lattice constant by PLS 6.2106 6.5045 6.2531 5.9659 6.161 6.2023 6.4963 6.3609 6.0737 6.2688 6.3101 6.6041 6.4619 6.1747 6.3699 6.4112 6.7051 6.6814 6.3942 6.5894 6.6307 6.9246 5.1124 4.8252 5.0204 5.0617 5.0617 5.3556 5.1041 4.8169 5.0121 5.0534 5.0534 5.3473 5.212 4.9248 5.1199 5.1199 5.1612 5.1612 5.4551 5.313 5.0258 5.0258 5.2209 5.2209 5.2622 5.2622 5.5562 5.5325 5.2453 5.4405
Lattice ˚) constant (A
c/a ratio
Reference
5.74 5.926
[2] [2]
5.78 5.966
[2] [2]
5.909
[2]
3.847, 3.71
[2,10]
5.207
[8]
4.1 5.086 5.305
[10] [9] [9]
5.608
[8]
5.17
[9]
5.397
[9]
5.723
[8]
5.465
[9]
5.664
[9]
5.902
[8]
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Table 4 (Continued ) Compound
Predicted band gap energy (eV) by PLS
BePbSb2 BePbBi2 MgCN2 MgCP2 MgCAs2 Mg0.5C0.5As MgCSb2 Mg0.5C0.5Sb MgCBi2 MgSiN2 MgSiP2
1.1441 2.7336 7.1467 4.0403 3.2111 3.2111 1.6262 1.6262 0.367 6.6062 3.4998
Mg0.5Si0.5P MgSiAs2 Mg0.5Si0.5As MgSiSb2 MgSiBi2 MgGeN2 MgGeP2 Mg0.5Ge0.5P MgGeAs2 Mg0.5Ge0.5As
3.4998 2.6706 2.6706 1.0857 0.5038 6.1164 3.0099 3.0099 2.1807 2.1807
MgGeSb2 MgGeBi2 MgSnN2 MgSnP2 Mg0.5Sn0.5P MgSnAs2 Mg0.5Sn0.5As MgSnSb2 MgSnBi2 MgPbN2 MgPbP2 MgPbAs2 MgPbSb2 MgPbBi2 MgSeSb2
0.5958 0.9937 5.5875 2.481 2.481 1.6519 1.6519 0.0669 1.5226 4.8765 1.77 0.9409 0.6441 2.2336 0.428.6
a
Theoretical band gap energy (eV)
Nature of band gapa
5.4817 5.7757 5.6459 5.3587 5.5539 5.5539 5.5952 5.5952 5.8891 5.6376 5.3504
2.83 (LDA)
3.36 1.16 1.47 1.93 2 0.93 1.4
(LDA) (FLAPW), (LDA) (GW) (GW)
2.1 1.13 (GW) 1.6
Predicted lattice constant by PLS
md pd md
pd I Semimetallic
1.8 1.2 0.6
0.9
5.3504 5.5456 5.5456 5.5869 5.8808 5.7455 5.4583 5.4583 5.6534 5.6534 5.6947 5.9887 5.8465 5.5593 5.5593 5.7544 5.7544 5.7957 6.0897 6.066 5.7788 5.974 6.0152 6.3092 5.6871
Lattice ˚) constant (A
c/a ratio
Reference
4.11
[10]
5.109
[8]
5.527
[8]
4.44 5.64, 5.72 1.769 (experimental) 5.276 5.804 5.502 6.221
[10] [2,6,10]
5.656 5.411 5.841 5.644
[2] [9] [2] [9]
5.774 5.679 5.958 5.902 6.374
[2] [8] [2] [8] [2]
6.258
[2]
[9] [2] [9] [2]
Nature of bandgap: d—direct; pd—pseudo-direct; md—marginally indirect (<0.1 eV); I—indirect.
While this new database shows promise, the ultimate challenge is to develop a validation test for some of these predictions. Despite the large amount of work in the computational materials science literature, there are relatively few simulation studies, which have been developed solely for the purpose of exploring new compounds. For the class of materials studied here, we are fortunate to have one such study, namely that by Samanta et al. which has predicted band gaps for a selection of composition
of alloys of the compound AgGaxIn1xSe2 [11]. This compound is actually a quaternary, but we used a linear interpolation from our training dataset for AgInSe2 and AgGaSe2 ternaries. Fig. 3 shows that our predicted values as derived from the PLS calculations correspond remarkably well with the theoretical predictions. This encouraging result provides further confidence in the value of our virtual combinatorial library as a design tool for synthesizing new chemistries.
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4. Conclusions This paper has demonstrated an a priori approach to develop combinatorial libraries, which can serve as an effective screening tool to guide combinatorial experimentation. The application to designing and tailoring chemistries of compound semiconductors is just one Appendix A. Procedures of PLS for bandgap energy
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example of the use of this approach to materials design in general. By integrating this approach to larger datasets, even more robust and reliable predictions of materials behavior can be made. Hence virtual combinatorial libraries can also serve as a way to develop more targeted experimental strategies for materials design and development.
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Appendix A. (Continued )
Acknowledgements The authors gratefully acknowledge support from the National Science Foundation International Materials Institute Program for the Combinatorial Sciences and Material Informatics Collaboratory: CoSMICIMI; grant # DMR 0231291. References [1] A. Zunger, Appl. Phys. Lett. 50 (3) (1987) 164. [2] J.E. Jaffe, A. Zunget, Phys. Rev. B 29 (4) (1984) 1882. [3] O. Madelung (Ed.), Semiconductors other than group IV elements and III–V compounds, Data in Science and Technology, Springer, Berlin, 1992.
[4] S.N. Rashkeev, W.R.L. Lambrecht, Phys. Rev. B 63 (2001) 165–212. [5] S.N. Rashkeev, S. Limpijumnong, W.R.L. Lambrecht, Phys. Rev. B 59 (4) (1999) 2737. [6] A. Continenza, S. Massidda, A.J. Freeman, Phys. Rev. B 46 (16) (1992) 10070. [7] P. Villars, et al., J. Less-common Met. 132 (1987) 289. [8] T. Wang, N. Moll, K. Cho, J.D. Joannopoulos, Phys. Rev. Lett. 82 (16) (1999) 3304. [9] T. Wang, N. Moll, K. Cho, J.D. Joannopoulos, Phys. Rev. B 63 (2000) 035306. [10] A.G. Petulthov, W.R.L. Lambrecht, B. Segall, Phys. Rev. B 49 (7) (1994) 4549. [11] L.K. Samanta, D.K. Ghosh, G.C. Bhar, Phys. Rev. B 33 (6) (1986) 4145.
Combinatorial design of semiconductor chemistry for bandgap engineering: ‘‘virtual’’ combinatorial experimentation Changwon Suh, Krishna Rajan* Department of Materials Science and Engineering, Combinatorial Materials Science and Materials Informatics Laboratory, Rensselaer Polytechnic Institute, Troy, NY, USA
Abstract The objective of this paper is to show how one may design combinatorial libraries a priori by integrating data mining techniques with physically robust multivariate data. It is shown that large datasets can be developed from relatively small amounts of experimental and theoretically based information. This involves a process of strategically selecting appropriate physical based parameters that can be analyzed in a multivariate manner. In this paper we identify for the first time the bandgap and lattice parameters of nearly 200 stoichiometries of new and yet to be synthesized compound chalcopyrite semiconductors. The robustness of this ‘‘virtual’’ combinatorial experimentation approach is demonstrated by comparison to band gap predictions from theoretical studies on a range of compositions for a selected quaternary compound semiconductor. # 2003 Elsevier B.V. All rights reserved. JEL classification: 71.55.Cn; 71.55.Eq; 71.55.Gs Keywords: Semiconductor compounds; Crystallographic databases; Crystal stoichiometry
1. Introduction The field of ‘‘bandgap engineering’’ is in fact one of the earliest examples of combinatorial design of materials. The recognition that by matching lattice parameters of different covalently bonded semiconductors, one can engineer the bandgap of epitaxial heterostructures has been one of the success stories in integrating fundamental physics into device engineering. However, the strategy of what materials one may work with is limited to relatively few and the ‘‘discovery’’ of new materials with more complex chemistries is still a slow
*
Corresponding author. E-mail address: [email protected] (K. Rajan). URL: http://www.rpi.edu/rajank/materialsdiscovery.
process. Clearly high throughput experimentation techniques offer some exciting possibilities for developing such new materials. In this paper we wish to outline the use of a statistically based strategy combined with the appropriate understanding of key physical parameters to show how we can develop a computational screening tool prior to conducting combinatorial experiments. We propose the idea of ‘‘virtual’’ combinatorial libraries, which lay a map of suggested chemical combinations, likely to give the desired properties one is seeking. Using chalcopyrite semiconductors as a testbed, we show how such a library can be built. The formalisms of the mathematical foundations are described in Appendix A but suffice it to say that a judicious use of multivariate statistics tools serves as the means to manipulate and process the incoming data.
0169-4332/$ – see front matter # 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0169-4332(03)00918-8
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Table 2 Descriptors for elements in virtual combinatorial library
2. Building the input for the combinatorial library The strategy of the work was as follows. We first identify a set of descriptors or parameters associated with our ‘‘raw’’ materials (i.e. elements). These descriptors need not be related themselves except for the fact that they each describe some physical characteristic that may be relevant to our desired property (e.g. bandgap). The choice of which and how many descriptors is in itself a subject of another paper, suffice it to say, we chose descriptors describing electronic and crystal structure level parameters. We focused on the combination of elements of I–III–VI compounds and II–IV–V compounds (see Table 1). Hence Table 1 outlines our ‘‘combinatorial chemical space’’ that forms the foundation of this study. For each of these selected elements, we chose five descriptors: valency, atomic number, melting point, electronegativity and pseudopotential radii (Table 2). The database was expanded to compounds from elements by first identifying in the reported literature, experimental/theoretical information on bandgaps of known I–III–VI and II–IV–V. The chemistries of these compounds helped define a strategy for deriving a new set of values for the same descriptors used for the elements. The parameterization of these descriptors for compounds was based using a relatively simple strategy originally proposed by Villars et al. which involved a linear weighting model [7]. The formulations are given below: For the binary system such as AxBy with x y and x þ y ¼ 1, the atomic parameters become: Average valence electron number, Nv ¼ xðNv ÞA þ yðNv ÞB . Average atomic number, Zavg ¼ xZA þ yZB . Average melting point, MPavg ¼ xMPA þ yMPB . Table 1 Combinatorial array of elements used in building our virtual array of I–III–VI and II–IV–V compounds I
II
III
IV
V
VI
Cu Ag Au
Zn Cd Hg
B Al Ga In Tl
C Si Ge Sn Pb
N P As Sb Bi
O S Se Te Po
Element
EN
AN
MP
PR
V
Be Mg Cu Ag Au Zn Cd Hg B Al Ga In Tl C Si Ge Sn Pb N P As Sb Bi O S Se Te Po
1.45 1.31 1.08 1.07 1.19 1.44 1.4 1.49 1.9 1.64 1.7 1.63 1.69 2.37 1.98 1.99 1.88 1.92 2.85 2.32 2.27 2.14 2.14 3.32 2.65 2.54 2.38 2.4
4 12 29 47 79 30 48 80 5 13 31 49 81 6 14 32 50 82 7 15 33 51 83 8 16 34 52 84
1562 922 1358 1235 1338 692.7 594.3 234.3 2365 933.5 302.9 429.8 577 3800 1687 1211 505.1 600.7 63.15 317.3 1089 903.9 544.6 54.36 388.4 494 722.7 527
1.08 2.03 2.04 2.375 2.66 1.88 2.215 2.41 0.795 1.675 1.695 2.05 2.235 0.64 1.42 1.56 1.88 2.09 0.54 1.24 1.415 1.765 1.997 0.465 1.1 1.285 1.67 1.9
2 2 11 11 11 12 12 12 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6
EN: electronegativity; AN: atomic number; MP: melting point; PR: pseudopotential radii; V: valency.
¼ Weighted electronegativity differences, DX 2xðXA XB Þ. Weighted differences of Zunger’s pseudopotential ¼ 2xfðrsA þ rpA Þ ðrsB þ rpB Þg. radii sums, DR For ternary compounds as if AxByCz if x y z and x þ y þ z ¼ 1, then: Average valence electron number, Nv ¼ xðNv ÞA þ yðNv ÞB þ zðNv ÞC . Average atomic number, Zavg ¼ xZA þ yZB þ zZC . Average melting point, MPavg ¼ xMPA þ yMPB þ zMPC . ¼ Weighted electronegativity differences, DX 2xðXA XB Þ þ 2xðXA XC Þ þ 2yðXB XC Þ. Weighted differences of Zunger’s pseudopoten ¼ 2xfðrsA þ rpA Þ ðrsB þ rpB Þg þ tial radii sums, DR A A 2xfðrs þ rp Þ ðrsC þ rpC Þg þ 2yfðrsB þ rpB ÞðrsC þ rpC Þg.
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Collectively this new database forms our known or ‘‘training set’’ onto which we can apply our data analysis tools.
3. Results and analysis For this study we applied a technique known as partial least squares (PLS) to serve as a predictive tool based on our training data. PLS is a multivariate predictive technique with distinct advantages over the classical multiple regression and principal component regression approaches. The use of partial least squares techniques is well established in many fields such as psychology, chemometrics, process control, biology and economics. The advantages of PLS over multiple linear regression include its handling of collinearity, missing variables, robustness with respect to coefficients. In PLS, the collinear data matrix is transformed into a latent structural matrix with orthogonal vectors. It can fit data with fewer components than other modeling approaches. PLS has the desirable property in that the precision
of the model parameters improves with the increasing number of relevant variables and observations. The mathematical formulations underlying the PLS calculations are described in Appendix A, but the computational procedure involves eigenvalue calculations of the data matrix which permit one to identify the maximum covariance between disparate datasets. Before we can apply the technique to a set of unknown compounds, it was first tested on our training data. Figs. 1 and 2 demonstrate the robustness of the analysis using the training dataset (Table 3). Based on these results, we embarked on completing our analysis of property prediction for over 200 compounds based on our initial combinatorial input of elements outlined in Table 1. The results are given in Table 4. It should be noted that the deviation from PLS derived results from the first principles LDA calculations simply reflects the differences that exist between experimental and theoretical studies. Our data mining analysis relied heavily on the experimental data and hence the difference, however the data trends match well.
Fig. 1. 4LV PLS results for I–III–VI chalcopyrite compounds.
C. Suh, K. Rajan / Applied Surface Science 223 (2004) 148–158
Fig. 2. 3LV PLS results for II–IV–V chalcopyrite compounds.
Fig. 3. Comparison of theoretically derived calculations with PLS derived results.
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Table 3 Chalcopyrite compounds data table (training set) Type
Compound
Experimental mini-Theoretical band mal band gap energy (eV) gap energy (eV)
Nature of band gapa
Lattice constant ˚) (A
c/a ratio
Reference
I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 I–III–V12 II–IV–V2 II–IV–V2 II–IV–V2 II–IV–V2 II–IV–V2
CuAlS2 CuAlSe2 CuAlTe2 CuGaS2 CuGaSe2 CuGaTe2 CuInS2 CuInSe2 CuInTe2 AgAlS2 AgAlSe2 AgAlTe2 AgGaS2 AgGaSe2 AgGaTe2 AgInS2 AgInSe2 AgInTe2 ZnSiP2 ZnSiAs2 ZnGaP2 ZnGaAs2 CdSiP2
3.49 2.67 2.06 2.43 1.68 1.0–1.24 1.53 1.04 1.06 3.13 2.55 2.27 2.64 1.8 1.32 1.87 1.24 0.95 2.07 1.74 2.05 1.15 2.2–2.45
d d
5.31, 5.34, 5.333 5.606 5.964 5.347–5.356 5.59–5.614 5.994 5.517–5.523 5.773–5.784 6.167 5.695, 5.720 5.956, 5.986 6.296 5.743–5.757 5.973, 5.985 6.283 5.816, 5.872 6.090–6.109 6.406 5.399 5.61 5.465 5.672 5.678
1.96, 1.958 1.954 1.975 1.959 1.966 1.987 2.016 2.008 2 1.802, 1.772 1.805, 1.793 1.878 1.786–1.789 1.823, 1.793 1.897 1.92–1.91 1.916–1.919 1.962 1.933 1.94 1.965 1.966 1.836
[1–3] [1–3] [1,2] [1,2,4] [1,2,4] [1,2,4] [1,2,4] [1,2,4] [1,2,4] [1,2] [1,2] [1,2] [1,2,4] [1,2,4] [1,2,4] [1,2,4] [1,2,4] [1,2,4] [1,2,4] [1,5,6] [1,5,6] [1,2,5] [1,5,6]
II–IV–V2 II–IV–V2 II–IV–V2 II–IV–V2 II–IV–V2
CdSiAs2 CdGaP2 CdGaAs2 CdSnP2 CdSnAs2
1.55 1.72 0.57 1.17 0.26
5.885 5.74 5.942–5.945 5.9 6.094
1.849 1.878 1.888 1.951 1.956
[1,2,5] [1,2,5] [1,2,5] [1,6] [1,6]
a
3.4 2.7 0.92 0.20 0.43 0.01 0.01 0.18
(LDA) (LDA) (LDA) (LDA) (LDA) (LDA)
1.02 (LDA) 0.17 (LDA) 0.17 (LDA) 0.35 (LDA) 0.10 (LDA) 0.21 (LDA) 1.22 (LDA) 0.91 (LDA) 1.16 (LDA) 0.13 (LDA) 1.16 (FLAPW), 1.19 (LDA) 0.42 (LDA) 0.75 (LDA) () 0.44 (LDA) 0.03 (FLAPW) () 0.72 (FLAPW)
pd pd, d (th) pd, I (th) d pd d d d
Nature of bandgap: d—direct; pd—pseudo-direct; th—theoretical; I—indirect.
Table 4 Virtual chalcopyrite compounds data table (test set) Compound
Predicted band gap energy (eV) by PLS
CuBO2 CuBS2 CuBSe2 CuBTe2 CuBPo2 CuAlO2 CuAlPo2 CuGaO2 CaGaPo2 CuInO2 CuInPo2 CuTlO2
0.0807 4.1354 3.5699 3.0768 0.0308 1.0101 0.8986 1.8999 1.7884 2.4383 2.3269 3.4319
Theoretical band gap energy (eV)
Nature of band gapa
Predicted lattice constant by PLS 4.5981 5.511 5.8313 6.1312 6.2737 4.4194 6.095 4.4333 6.1089 4.5688 6.2445 4.7973
Lattice ˚) constant (A
c/a ratio
Reference
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Table 4 (Continued ) Compound
Predicted band gap energy (eV) by PLS
CuTlS2 CuTlSe2 CuTlTe2 CuTlPo2 AgBO2 AgBS2 AgBSe2 AgBTe2 AgBPo2 AgAlO2 AgAlPo2 AgGaO2 AgGaPo2 AgInO2 AgInPo2 AgTlO2 AgTlS2 AgTlSe2 AgTlTe2 AgTlPo2 AuBO2 AuBS2 AuBSe2 AuBTe2 AuBPo2 AuAlO2 AuAlS2 AuAlSe2 AuAlTe2 AuAlPo2 AuGaO2 AuGaS2 AuGaSe2 AuGaTe2 AuGaPo2 AuInO2 AuInS2 AuInSe2 AuInTe2 AuInPo2 AuTiO2 AuTiS2 AuTiSe2 AuTlTe2 AuTlPo2 ZnCN2 ZnCP2 ZnCAs2 Zn0.5C0.5As Zn0.5C0.5Sb ZnCBi2 ZnSiN2
0.7842 0.2187 0.2744 3.3205 0.0058 4.2103 3.6448 3.1517 0.1056 0.9352 0.8237 1.825 1.7135 2.3634 2.252 3.357 0.8591 0.2936 0.1995 3.2456 0.7492 4.9653 4.3998 3.9067 0.8606 0.1802 4.0359 3.4704 2.9773 0.0688 1.07 3.1461 2.5806 2.0876 0.9585 1.6084 2.6077 2.0422 1.5491 1.497 2.602 1.6141 1.0486 0.5555 2.4906 6.006 2.8996 2.0704 2.0704 0.4855 1.104 5.4655
Theoretical band gap energy (eV)
Nature of band gapa
0.9
1.1 0.71 0.6
Metallic
Predicted lattice constant by PLS
Lattice ˚) constant (A
c/a ratio
Reference
5.7102 6.0305 6.3305 6.4729 4.9227 5.8356 6.1559 6.4558 6.5983 4.744 6.4196 4.7579 6.4335 4.8934 6.5691 5.1219 6.0348 6.3551 6.6551 6.7975 5.5635 6.4764 6.7967 7.0967 7.2391 5.3848 6.2977 6.618 6.918 7.0604 5.3987 6.3116 6.6319 6.9319 7.0743 5.5343 6.4472 6.7675 7.0675 7.2099 5.7627 6.6756 6.9959 7.2959 7.4383 5.6714 5.3842 5.5793 5.5793 5.6206 5.9146 5.6631
5.58 5.832 6.299
2.001 1.995
[2] [2] [2]
5.882
[2]
6.529
[2]
5.044 5.384
[8] [8]
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Table 4 (Continued ) Compound
Predicted band gap energy (eV) by PLS
Zn0.5Si0.5P Zn0.5Si0.5As ZnStSb2 Zn0.5Si0.5Sb ZnSiBi2 ZnGeN2 Zn0.5Ge0.5P Zn0.5Ge0.5As ZnGeSb2 ZnGeBi2 ZnSnN2 ZnSnP2 Zn0.5Sn0.5P ZnSnAs2 Zn0.5Sn0.5As ZnSnSb2 ZnSnBi2 ZnPbN2 ZnPbP2 ZnPbAs2 ZnPbSb2 ZnPbBi2 CdCN2 CdCP2 Cd0.5C0.5P CdCAs2 Cd0.5C0.5As CdCSb2 Cd0.5C0.5Sb CdCBi2 CdSiN2 Cd0.5Si0.5P Cd0.5Si0.5As CdSiSb2 CdSiBi2 CdGeN2 Cd0.5Ge0.5P Cd0.5Ge0.5As CdGeSb2 CdGeBi2 CdSnN2 Cd0.5Sn0.5P CdSnSb2 CdSnBi2 CdPbN2 CdPbP2 CdPbAs2 CdPbSb2 CdPbBi2 HgCN2 HgCP2 HgCAs2
2.3591 1.5299 0.055 0.055 1.6445 4.9757 1.8692 1.04 0.5449 2.1344 4.4468 1.3403 1.3404 0.5112 0.5112 1.0738 2.6633 3.7358 0.6293 0.1998 1.7848 3.3743 5.8097 2.7032 2.7032 1.8741 1.8741 0.2891 0.2891 1.3004 5.2692 2.1627 1.336 0.2514 1.18409 4.7793 1.6729 0.8437 0.7412 2.3308 4.2504 1.144 1.2701 2.8596 3.5394 0.433 0.3962 1.9811 3.5706 4.5586 1.4522 0.623
Theoretical band gap energy (eV)
Nature of band gapa
Predicted lattice constant by PLS
Lattice ˚) constant (A
1.56 (GW) 0.68 (GW) 0.9
d md
5.262 5.483 6.077 5.962
[9] [8] [2] [8]
1.15 (GW) 0.23 (GW) 0.5
I md
5.382 5.597 6.111
[9] [9] [2]
1.70 (GW)
I
0.79 (GW)
md
5.3759 5.571 5.6125 5.6123 5.9063 5.7709 5.4837 5.6789 5.7202 6.0141 5.8719 5.5847 5.5847 5.7799 5.7799 5.8212 6.1151 6.0915 5.8043 5.9994 6.0407 6.3347 5.9651 5.6779 5.6779 5.8731 5.8731 5.9143 5.9143 6.2083 5.9568 5.6696 5.8648 5.9061 6.2 6.0646 5.7774 5.9726 6.0139 6.3078 6.1657 5.8785 6.1149 6.4089 6.3852 6.098 6.2931 6.3344 6.6284 6.2613 5.9741 6.1693
1.22 (GW) 0.8
0.33 (GW) 0.2
0.80 (FLAPW)
d Metallic
5.651 5.688 5.851 5.87 6.275
c/a ratio
2 2 2
Reference
[1,2] [9] [1,2] [9] [1]
4.973
[8]
5.201
[8]
5.62
[8]
5.378 5.61 6.344
[9] [8] [2]
5.523 5.755 6.383
[9] [8] [2]
5.797 6.479
[8] [6]
C. Suh, K. Rajan / Applied Surface Science 223 (2004) 148–158
155
Table 4 (Continued ) Compound
Predicted band gap energy (eV) by PLS
HgCSb2 HgCBi2 HgSiN2 HgSiP2 HgSiAs2 HgSiSb2 HgSiBi2 HgGeN2 HgGeP2 HgGeAs2 HgGeSb2 HgGeBi2 HgSnN2 HgSnP2 HgSnAs2 HgSnSb2 HgSnBi2 HgPbN2 HgPbP2 HgPbAs2 HgPbSb2 HgPbBi2 BeCN2 BeCP2 BeCAs2 BeCSb2 Be0.5C0.5Sb BeCBi2 BeSiN2 Be0.5Si0.5P Be0.5Si0.5As BeSiSb2 Be0.5Si0.5Sb BeSiBi2 BeGeN2 Be0.5Ge0.5P BeGeAs2 Be0.5Ge0.5As BeGeSb2 Be0.5Ge0.5Sb BeGeBi2 BeSnN2 BeSnP2 Be0.5Sn0.5P BeSnAs2 Be0.5Sn0.5As BeSnSb2 Be0.5Sn0.5Sb BeSnBi2 BePbN2 BePbP2 BePbAs2
0.9619 2.5514 4.0181 0.9117 0.0825 1.5024 3.0919 3.5283 0.4218 0.4074 1.9923 3.5818 2.9994 0.1071 0.9362 2.5212 4.1107 2.2884 0.8181 1.6472 3.2322 4.8217 6.6467 3.5403 2.7111 1.1262 1.1262 0.4633 6.1062 2.9998 2.1706 0.5857 0.5857 1.0038 5.6164 2.5099 1.6808 1.6808 0.0958 0.0958 1.4937 5.0875 1.981 1.981 1.1519 1.1519 0.4331 0.4331 2.0226 4.3765 1.27 0.4409
Theoretical band gap energy (eV)
Nature of band gapa
1.6 0.7
1.2 0.2
0.8
8.2, 4.22 (LDA)
3.60 (LDA) 1.68 (GW) 1.19 (GW)
1.16 (GW)
pd
I I
I
0.53 (GW)
0.98 (GW)
I
0.45 (GW)
I
Predicted lattice constant by PLS 6.2106 6.5045 6.2531 5.9659 6.161 6.2023 6.4963 6.3609 6.0737 6.2688 6.3101 6.6041 6.4619 6.1747 6.3699 6.4112 6.7051 6.6814 6.3942 6.5894 6.6307 6.9246 5.1124 4.8252 5.0204 5.0617 5.0617 5.3556 5.1041 4.8169 5.0121 5.0534 5.0534 5.3473 5.212 4.9248 5.1199 5.1199 5.1612 5.1612 5.4551 5.313 5.0258 5.0258 5.2209 5.2209 5.2622 5.2622 5.5562 5.5325 5.2453 5.4405
Lattice ˚) constant (A
c/a ratio
Reference
5.74 5.926
[2] [2]
5.78 5.966
[2] [2]
5.909
[2]
3.847, 3.71
[2,10]
5.207
[8]
4.1 5.086 5.305
[10] [9] [9]
5.608
[8]
5.17
[9]
5.397
[9]
5.723
[8]
5.465
[9]
5.664
[9]
5.902
[8]
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Table 4 (Continued ) Compound
Predicted band gap energy (eV) by PLS
BePbSb2 BePbBi2 MgCN2 MgCP2 MgCAs2 Mg0.5C0.5As MgCSb2 Mg0.5C0.5Sb MgCBi2 MgSiN2 MgSiP2
1.1441 2.7336 7.1467 4.0403 3.2111 3.2111 1.6262 1.6262 0.367 6.6062 3.4998
Mg0.5Si0.5P MgSiAs2 Mg0.5Si0.5As MgSiSb2 MgSiBi2 MgGeN2 MgGeP2 Mg0.5Ge0.5P MgGeAs2 Mg0.5Ge0.5As
3.4998 2.6706 2.6706 1.0857 0.5038 6.1164 3.0099 3.0099 2.1807 2.1807
MgGeSb2 MgGeBi2 MgSnN2 MgSnP2 Mg0.5Sn0.5P MgSnAs2 Mg0.5Sn0.5As MgSnSb2 MgSnBi2 MgPbN2 MgPbP2 MgPbAs2 MgPbSb2 MgPbBi2 MgSeSb2
0.5958 0.9937 5.5875 2.481 2.481 1.6519 1.6519 0.0669 1.5226 4.8765 1.77 0.9409 0.6441 2.2336 0.428.6
a
Theoretical band gap energy (eV)
Nature of band gapa
5.4817 5.7757 5.6459 5.3587 5.5539 5.5539 5.5952 5.5952 5.8891 5.6376 5.3504
2.83 (LDA)
3.36 1.16 1.47 1.93 2 0.93 1.4
(LDA) (FLAPW), (LDA) (GW) (GW)
2.1 1.13 (GW) 1.6
Predicted lattice constant by PLS
md pd md
pd I Semimetallic
1.8 1.2 0.6
0.9
5.3504 5.5456 5.5456 5.5869 5.8808 5.7455 5.4583 5.4583 5.6534 5.6534 5.6947 5.9887 5.8465 5.5593 5.5593 5.7544 5.7544 5.7957 6.0897 6.066 5.7788 5.974 6.0152 6.3092 5.6871
Lattice ˚) constant (A
c/a ratio
Reference
4.11
[10]
5.109
[8]
5.527
[8]
4.44 5.64, 5.72 1.769 (experimental) 5.276 5.804 5.502 6.221
[10] [2,6,10]
5.656 5.411 5.841 5.644
[2] [9] [2] [9]
5.774 5.679 5.958 5.902 6.374
[2] [8] [2] [8] [2]
6.258
[2]
[9] [2] [9] [2]
Nature of bandgap: d—direct; pd—pseudo-direct; md—marginally indirect (<0.1 eV); I—indirect.
While this new database shows promise, the ultimate challenge is to develop a validation test for some of these predictions. Despite the large amount of work in the computational materials science literature, there are relatively few simulation studies, which have been developed solely for the purpose of exploring new compounds. For the class of materials studied here, we are fortunate to have one such study, namely that by Samanta et al. which has predicted band gaps for a selection of composition
of alloys of the compound AgGaxIn1xSe2 [11]. This compound is actually a quaternary, but we used a linear interpolation from our training dataset for AgInSe2 and AgGaSe2 ternaries. Fig. 3 shows that our predicted values as derived from the PLS calculations correspond remarkably well with the theoretical predictions. This encouraging result provides further confidence in the value of our virtual combinatorial library as a design tool for synthesizing new chemistries.
C. Suh, K. Rajan / Applied Surface Science 223 (2004) 148–158
4. Conclusions This paper has demonstrated an a priori approach to develop combinatorial libraries, which can serve as an effective screening tool to guide combinatorial experimentation. The application to designing and tailoring chemistries of compound semiconductors is just one Appendix A. Procedures of PLS for bandgap energy
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example of the use of this approach to materials design in general. By integrating this approach to larger datasets, even more robust and reliable predictions of materials behavior can be made. Hence virtual combinatorial libraries can also serve as a way to develop more targeted experimental strategies for materials design and development.
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Appendix A. (Continued )
Acknowledgements The authors gratefully acknowledge support from the National Science Foundation International Materials Institute Program for the Combinatorial Sciences and Material Informatics Collaboratory: CoSMICIMI; grant # DMR 0231291. References [1] A. Zunger, Appl. Phys. Lett. 50 (3) (1987) 164. [2] J.E. Jaffe, A. Zunget, Phys. Rev. B 29 (4) (1984) 1882. [3] O. Madelung (Ed.), Semiconductors other than group IV elements and III–V compounds, Data in Science and Technology, Springer, Berlin, 1992.
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