Materials Science and Engineering B54 (1998) 149–152

Artificial neural network prediction of the band gap and meltingpoint of binary and ternary compound semiconductors

Zhang Zhaochun *, Peng Ruiwu, Chen NianyiShanghai institute of Metallurgy, Chinese Academy of Sciences, 865 Changning Road, Shanghai 200050, PR China

Received 9 September 1997; accepted 2 February 1998

Abstract

In this paper, an artificial neural network trained by experimental data has been used to predict the values of the band gap andmelting point of III–V, II–VI binary and I–III–VI2, II–IV–V2 ternary compound semiconductors. The calculated results werein good agreement with the experimental ones. © 1998 Elsevier Science S.A. All rights reserved.

Keywords: III–V, II–VI, I–III–VI2, II–IV–V2; Band gap; Melting point; Artificial neural network

1. Introduction

III–V and II–VI binary compounds are importantsemiconductors for microwave, optoelectron and in-frared devices, while I–III–VI2 and II–IV–V2 ternarycompounds are largely developed as non-linear opticaldevices and solar cell materials. The band gap (Eg)and melting point (TM) of these compounds are twoessential parameters determining their properties. Al-though these are measured experimentally and manystudies have been carried out on the relationship be-tween the band gap and chemical component of thesecompounds [1–3], an artificial neuron network (ANN)has not yet been used to predict them. In this paper,as another example of an ANN application in semi-conductor materials [4–6], and as a preliminary studyon combining ANN with a database and a knowledgebase, in order to create an expert system for the opti-mization of the design of compound semiconductors,the values of Eg and TM of some III–V, II–VI binaryand I–III–VI2, II–IV–V2 ternary compounds werecalculated by trained ANN and the predicted resultsare reported.

2. Calculation

An ANN has many interconnected processing ele-ments (neurons) [5,7]. It is a powerful tool for extract-ing hidden and useful information directly from a vastamount of experimental data, and especially useful forresolving some problems of non-linear and compli-cated systems.

The ANN of this paper was composed of threelayers: an input layer, a hidden layer and an outputlayer. Fig. 1 shows such a typical three-layered neuralnetwork.

In Fig. 1, m, p and q are the neurons of input,hidden and output layer, respectively. Ak is the kthinput pattern and Yk the kth objective output pattern.The wij and 6jt are the weight factors.

As ANN is working, each neuron of the hiddenlayer takes weighted inputs from the neurons of theinput layer and forms the sum. Then, a net input isobtained by adding an internal threshold value (u) tothe sum (sj)

sj= %m

i=1

wijai+uj i=1,2,…,m ; j=1,2,…,p

Finally, a sigmoid or symmetric tangent hyperbolicfunction f(sj) is used to transform the net input intoan output signal (bj)* Corresponding author.

0921-5107/98/$19.00 © 1998 Elsevier Science S.A. All rights reserved.

PII S0921-5107(98)00157-3

Z. Zhaochun et al. / Materials Science and Engineering B54 (1998) 149–152150

Fig. 1. Structural diagram of an ANN.

Table 1The predicted and experimental values of Eg and TM of GaAs, CdS,AgInS2 and CdSiAs2

TM (K)Compounds Eg (ev, 300 K)

Pred. Exp. Pred. Exp.

1.42GaAs 14591.21 15132.40CdS 16932.50 17481.87 12011.82 1118–1138 [18]AgInS2

1.49CdSiAs2 1.55 1163 \1123 [15]

optimizing process was used to determine the numberof hidden neurons. The transfer function of the inputlayer was linear and that of the hidden and outputlayers was a symmetric tangent hyperbolic (tan H)function. All ANNs were developed on a 586microcomputer.

3. Results

3.1. AIIIBV and AIIBVI binary compounds

The training set for ANN was composed of eightIII–V and eight II–VI compounds, which includedAlP, AlAs, AlSb, GaP, GaSb, InP, InAs, InSb, ZnS,ZnSe, ZnTe, CdSe, CdTe, HgS, HgSe and HgTe. GaAsand CdS were randomly chosen as the predicted set.According to the rule of crystalline chemistry of semi-conductors, covalent bonds and ionic bonds coexist inthe structure of III–V and II–VI compounds [9]. Thisiono-covalent bond energy directly determines thephysical properties of them. The basic atomic parame-ters affecting the iono-covalent bond energy mainlyinclude electronegativity, atomic number and radius.Born exponent is an important parameter determiningphysical properties of ionic crystals [10]. Thus, themean atomic number

Z( =12(ZA+ZB),

difference of electronegativity in the Pauling scale ofvalues (DX= �XA−XB�), lattice constant (a) and meanBorn exponent

n̄=12(nA+nB)

of these binary compounds were used as the inputs andthe band gap [11,12] and melting point [13,14] as theoutput. By using a leave-one-out method, the values ofEg and TM of GaAs and CdS were predicted by trainedANNs, as shown in Table 1.

3.2. AIBIII C2VI and AIIBIVC2

V ternary compounds

For ternary compounds, the training set for ANNwas composed of 17 I–III–VI2 and 12 II–IV–V2 com-

bj= f(sj) j=1,2,…,p

Similarly, the input (Lt) and output (Ct) of a neuron ofthe output layer follow as

Lt= %p

j=1

6jtbj+gt j=1,2,…,p ; t=1,2,…,q

Ct= f(Lt) t=1,2,…,q

In which gt is the internal threshold.In this paper, the back-propagation algorithm (BP)

[8] was used for all the training work. The trainingprocedure is as follows. First, a set of examples oftraining data composed of input pattern (Ak) and ob-jective output pattern (Yk) is provided to ANN. Then,the weights and threshold values are iteratively adjustedaccording to the deviation of the neural output (Ck)from the objective one (Yk). The adjusted values of wij,6jt, u and g are given by the relations

D wij=bekj ak

i Duj=bekj (0BbB1)

D6jt=adkt bk

j Dgt=adkt (0BaB1)

Where a and b are learning coefficients. The e jk and dt

k

are represented in the form

dkt = (Yk

t −Ckt )Ck

t (1−Ckt )

ekj =

� %q

t=1

dkt 6jt

nbj(1−bj)

This procedure is repeated until the outputs match theobjective ones within a desired level of precision, or thenumber of learning times amounts to a desired limit.Finally, the trained ANN can be used to predict theoutput pattern of samples which are not included in thetraining set.

In the ANN calculation, the number of neurons ofthe input and output layers corresponded to the num-bers of the input and output patterns. A trial-and-error

Z. Zhaochun et al. / Materials Science and Engineering B54 (1998) 149–152 151

pounds, which included CuAlS2, CuGaS2, CuInS2,CuAlSe2, CuGaSe2, CuInSe2, CuAlTe2, CuGaTe2,CuInTe2, AgAlS2, AgGaS2, AgAlSe2, AgGaSe2,AgInSe2, AgAlTe2, AgGaTe2, AgInTe2, ZnSiP2, Zn-SiAs2, ZnGeP2, ZnGeAs2, ZnSnP2, ZnSnAs2, ZnSnSb2,CdSiP2, CdGeP2, CdGeAs2, CdSnP2 and CdSnAs2.However, when the values of TM were predicted, thenumber of trained samples was decreased to 24 due tothe lack of TM data of CuAlTe2, AgAlS2, AgAlSe2,AgAlTe2 and ZnSnSb2. AgInS2 and CdSiAs2 were cho-sen randomly as the predicted set. Similarly, the aver-age atomic number

Z( =14(2ZC+ZA+ZB),

difference of electronegativity in the Pauling scale ofvalues (DX= �2XC−XA−XB�), value of u [15] and av-erage Born exponent

n̄=14(2nC+nA+nB)

were used as the inputs, and the band gap [16,17] andmelting point [15,18] as the outputs. By using a leave-one-out method, the values of Eg and TM of AgInS2

and CdSiAs2 were predicted. The results are also shownin Table 1.

In Ref. [16], the calculated values of Eg of 21 ternarycompounds, most of which have not been synthesized,are given. Using ANN, we predicted their Eg values, asshown in Table 2.

4. Discussion and conclusion

Analysis of the data in Tables 1 and 2 reveals thatthe predicted values of Eg and TM are in good agree-ment with the experimental and calculated ones. Com-pared with other empirical methods, ANN only usesbasic atomic or structural parameters as the inputs. Ifenough samples have been collected, ANN can fit orpredict the values of target function. In calculation,ANNs needs neither to found a mathematical modelnor to draw into adjustable empirical parameters be-cause of the difference of composition and structure.The weights play a part in the transmitting feature, thatis, the network continuously acquires and stores knowl-edge through learning. Thus, the complex relationshipbetween the input and output features is recorded in theform of a weight matrix, and a non-linear mappingfrom input to output pattern is completed. However, asshown in Table 2, although the band gap of 21 ternarycompounds can be predicted by a trained ANN, thelarge deviation of the predicted values was observedfrom the calculated ones for several compounds, suchas CuTlTe2 and HgSiAs2, especially CdGeSb2 andHgGeAs2. It could be due to the overfitting of ANN.

Table 2The calculated and predicted values of Eg of 21 ternary compounds

Compounds Eg (ev, 300 K)

Pred. (ANN) Cal. [18]

ZnSiSb2 1.07 0.9ZnGeSb2 0.85 0.5

1.18CdSiSb2 0.8CdGeSb2 1.03 0.2

2.17MgGeP2 2.11.56MgSnP2 1.8

MgSiAs2 2.08 2.01.60MgGeAs2 1.6

1.2MgSnAs2 0.931.39MgSiSb2 1.4

MgSeSb2 0.91.200.62 0.6MgSnSb2

1.58HgSiP2 1.61.36HgGeP2 1.2

HgSnP2 0.87 0.80.71.24HgSiAs2

1.08HgGeAs2 0.2CuTlTe2 0.42 0.9

1.1AgTlS2 1.110.63AgTlSe2 0.7

0.60.51AgTlTe2

An approach preventing ANN from overfitting is toemploy more input features than we used. In such acase, it usually couples with the increase of the numberof the weights and, hence, that of trained samples. Onthe other hand, the correlation between the input fea-tures and the output ones might become more compli-cated with the increase of the number of input features.In order to optimize ANN and improve predictedresults, it is reasonable to minimize the overfitting ofANN by selecting suitable input features and assem-bling enough trained samples.

Using a trained ANN, the band gap and meltingpoint of both III–V, II–VI binary compounds andI–III–VI2, II–IV–V2 ternary compound semiconduc-tors can be predicted satisfactorily. However, it is nec-essary to optimize ANN as much as possible, otherwisea large deviation of the predicted values from theobjective ones might arise.

References

[1] A.K. Vijh, J. Phys. Chem. Solids 29 (1968) 2233.[2] W.B. Pearson, Can. J. Chem. 37 (1957) 1191.[3] R.H. Bube, Photoconductivity of Solids, Wiley, New York,

1960.[4] W. Wei, Y. Liuming, W. Guangyu, P. Ruiwu, J. Appl. Phys. 78

(1995) 897.[5] W. Wei, Y. Liuming, P. Ruiwu, C. Nanyi, Z. Jingwei, Mater.

Sci. Eng. B31 (1995) 305.

Z. Zhaochun et al. / Materials Science and Engineering B54 (1998) 149–152152

[6] Z. Zhaochun, P. Ruiwu, in: Proc. of 7th China-Japan Sympo-sium on Science and Technology of Crystal Growth and Mate-rial, Shanghai, China, 1996, p. 118.

[7] R.P. Lippman, IEEE Trans. Acoust. Speech Signal Process. 3(1987) 4.

[8] J.J. Hopfield, Proc. Natl. Acad. Sci. USA 79 (1982) 2554; 81(1984) 3088.

[9] J.P. Suchet, Chemical Physical of Semiconductors, Van Nos-trand, London, 1965.

[10] L.C. Pauling, The Nature of the Chemical Bond, Cornell, Ithaca,1960.

[11] H.C. Casey Jr., M.B. Panish, Heterostructure Lasers, Part B,Academic Press, New York, 1986.

[12] S. Ignatowicz, K. Andrzej, Semiconducting Thin Films of AIIBVI

Compounds, Ellis Horwood, New York, 1990.[13] B.W. Wessels, G.Y. Chin, Advances in Electronic Materials,

American Society for Metals, OH, 1986.[14] S.J. Moss, A. Ledwith, The Chemstry of the Semiconductor

Industry, Blackie, Glasgow, 1987.[15] A. Zunger, Appl. Phys. Lett. 50 (1987) 164.[16] J.E. Jeffe, A. Zunger, Phys. Rev. B29 (1984) 1882.[17] Y. Shizhong, Y. Shuren, K. Changhe, The Application of Semi-

conductor Materials, Press of Engineering Industry, Bejing,1986.

[18] H. Matsushita, S. Endo, T. Irie, Jpn. J. Appl. Phys. 30 (1991)1181.

.