Structures of an asymmetrically coupled double-well superlattice by

SCIENCE IN CHINA (Series A)

VOI. 40 NO. 9

September 1997

Structures of an asymmetrically coupled double-well superlattice by double-crystal X-ray diffraction MA Wenquan

(%*el,ZHUANG Yan (E g),WANG Yutian (£3E!) and JIANG Desheng

(?I@%)

(National Research Center for Optoelectronic Technology, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China) Received April 4, 1997

Abstract An asymmetrically coupled ( GaAs/AlAs/GaAs/AlAs )/GaAs ( 001 ) double-well supperlattice is studied by HRDCD (high resolution double-crystal X-ray diffractometry) . The intensity of satellite peaks is modulated by wave packet of different sublayers. In the course of simulation, the satellite peaks in the vicinity of the node points of wave packet are very informative for precise determination of sublayer thickness and for improving accuracy. Keywords:

superlattice, simulation, wave pocket method, node point.

The structural characteristics of superlattice are the most important and fundamental parameters because the physical and device properties depend on them. Therefore great enthusiasm and efforts have been devoted to precise characterization of superlattices. High resolution double-crystal X-ray diffraction (HRDCD) plays an indispensable role in determining the structure of superlattice precisely due to its high resolution and nondestructiveness, and almost no additional sample preparation is needed. At present, the HRDCD method is widely accepted and prevalent. The usual process is to obtain the structural parameters by fitting the experimental results according to X-ray dynamic or kinematical theories. Although many papers have reported the superlattice including 2 sublayers in one period, investigations on superlattice including 4 sublayers in one period are still rare because the contribution of different sublayers to diffraction pattern intermingles and results in a complicated so-called

"

satellite-peak modulation phenomenon", and thus it is much

more difficult to analyze and simulate. In this paper, we investigate an asymmetric GaAs/AlAs/GaAs/AlAs double-well superlattice. The experimental curve is simulated by X-ray dynamic theory[1v21 which is regarded as more precise than kinematical theory due to its consideration of interactions between the incident and the reflected waves. But its physical image is not so direct. However, a "wave packet method" based on kinematical theory[3s41,which is considered to have clear physical image, may be employed to explain the complicated satellite-peak modulation phenomenon as well. It is also found that the satellite peaks in the vicinity of "node points of wave packet" are especially beneficial to precise determination of sublayer thickness and to the enchancement of the accuracy of simulation. The sample is a 20-period asymmetric GaAs/AlAs/GaAs/AlAs

double-well superlattice

which is grown on a semi-insulating GaAs substrate of (001) orientation by molecular beam epitaxy (MBE) . The respective thicknesses of wells and barriers are deliberately designed asymmet-

No. 9

STRUCTURES O F ASYMMETRICALLY COUPLED WUBLE-WELL SUPERLATTICE

1005

ric. It has been reported[" that such a structure forms type- I -type- fl mixed double quantum wells in which free carrier scattering is the dominant sacttering mechanism and the carrier concentration can be adjusted within a relatively wide range. The precise determination of different sublayers is very crucial. The HRDCD experiment is carried out by a Rigaku SLX-1A diffractometer whose X-ray generator is RU-200BH. The copper target is used and X-ray wavelength is 0.154 051 nm. The Ge (004) asymmetric diffraction monochomator is employed as the first crystal. The measurement is completed by 8 / 2 8 scan mode and the resolution of rotation angle B is 0.001". The voltage and current of X-ray tube are 50 kV and 150 mA, respectively. In order to improve the accuracy of measurement, the step scan mode is used. According to the dynamic theory, the total reflective amplitude of (OOh) diffraction for an N-layer heterostructure Rh, N,T is

R ~ , N -, T - [ R ~ , N + R ~ , N - I , T ( T ~ , N T ~ , T - R ~ , N R ~ , N )( 1I) / ( ~ Rh,N and Th,N are reflective and transmissive amplitude of the N t h layer for ( OOh) diffrac-

where tion, respectively, and

Rh Th

(2) (3)

= E I E ~ ( CI Cz)/(C2(2 - C l E i ) , = CiCz(E1 - Ez)/(C2E2

-

CiEi),

C1.2 = exp( - i#1,2t 1, 4 =b

~

3

h

~

(6) (7) (8)

~

b =Y ~ / Y ~ , Z = sin(20B) A,,

(9)

Aw = 8 - 8, + ( E cos2a ~ + E / sin2a)taneBIt (E'~/)sinacosa, (10) where ~0 and are the 0th and h t h Fourier coefficients of polarizability, respectively; h is the X-ray wavelength (A = 0 . 1 5 4 051 nm) ; b is asymmetry factor, yo and yh are direction cosines of the incident and diffracted waves, respectively; OB is the kinematical Bragg angle; t is the thick-

xh

ness of N t h layer; a is the angle between crystal surface and reflection plane; strains perpendicular and parallel to the crystal surface, respectively.

E'

and

E /,'

are the

The period of superlattice is obtained according to the experimental curve:

where A 8 is the angular spacing between 2 satellite peaks. Keeping the period of superlattice constant, we fit the experimental results using X-ray dynamic theory. Although the thickness value of each sublayer can be obtained by simulation, the resolution and accuracy are still unsatisfactory. Alternatively, by using the "wave packet method" based on X-ray diffraction kinematical theory, which is regarded to have a more clear physical image, one may avoid the problems mentioned above.


1006

Vol. 40

The reflective amplitude of an N-period superlattice with four sublayers A, B, C, D in one period according to X-ray diffraction kinematical theory is

where

I' = I ,

+

I , = YZ,

I2

+

13,

+ ~ 2 +, Y: +

(13) Y;,

(14)

1 2 = 2 p A q B ~ ~ ~+( OB) @ A+ 2 q B q C c o ~ ( @fB DC) f ~ ~ ~ " C ~ D@C CO + SOD), ( 13

(15)

= 2 p A % ? C ~ ~ ~ (+ 2 Q B + QC) + ~ ~ B ~ D C @BO+S2 ( @ +~ @D)

+ 2 !PAVDcos(

+ 2 QB + 2 a C + DD)

(16) (17)

= A,Y,,

where re is the classical electron radius; Fj, V, and t, are the j t h layer structure factor, volume of the unit cell, and thickness, respectively. E ; and E ,// are the j th layer strains perpendicular and parallel to the surface. Other parameters coincide with that of the preceding in its represented meaning. I n e q . ( 2 1 ) , 'k; =

sin@.

Yi

is the wave packet of the j t h layer which is analogous to the

diffraction amplitude of a single eqitaxy layer. From eq. ( 1 2 ) , when

C Q= ~n ~the diffraction K,

I

intensity reaches the maximum and the corresponding angles are the positions of satellite peaks of superlattice, but it also can be seen that the diffraction intensity is modulated by different wave packets in one period in which intensity modulation phenomenon of satellite peaks appears. When @, = n n , i. e. PI = 0, the corresponding angles are called the "node points of the modulation wave for j t h sublayer". It is found that, in the vicinity of the node point, ?PIvaries very sensitively with A w , i. e. when @ ] + n ~ , the variation of the intensity I primarily comes from the variation of ?PI and other sublayer's modulation wave packets only contribute to I' slightly. Thus, if we choose the satellite peaks in the vicinity of the node points of j t h sublayer wave packet to simulate, the other sublayer' s effects on I ' can be nearly removed and an accurate thickness of j t h sublayer can be obtained. Similarly, the accurate parameters of other sublayers can also be obtained. In fig. 1, curves 1 and 2 represent the experimental X-ray rocking curve and the final simulation cune b y hynam~ctheory. The f\na\ .result lor GaAsl AlAs/ GaAs/ MAS layer tK~cknessin one period is

No. 9

STRUCTURES O F ASYMMETRICALLY COUPLED DOUBLE-WELL SUPERLATTICE

GaAs

AlAs

GaAs

AlAs

2 . 7 nm

1 0 . 7 nrn

7 . 8 nm

21.0 nm

Fig. 1 .

The

1007

Experimental and simulated X-ray rocking rurves for (002) diffraction. 1, Experimental; 2, simulated

+ 4th satellite peaks and + 8th satellite peaks are almost extinct.

In fig. 2 curves 4 , 2 ,

3 , l represent wave packets of GaAs ( 2 . 7 nm) , AlAs ( 1 0 . 7 nm) , GaAs ( 7 . 8 nm) , AlAs (21.0 nm), respectively; 5 is wave packet when one period is regarded as one layer, i. e. the wave

Z~rhetil

Fig. 2.

Patterns of wavy packets of the GaAs(2.7 nni), AIAs( 1 0 . 7 nm). GaAs(7.8 nm). and AlAs (21 nm) sublayers together with patterns of the 1 period of superlattice, and the refined. 1, AIAs(21.0 nm); 2, AlAs ( 1 0 . 7 nm); 3, GaAs(7.8 nm)

;

4, GaAs(2.7 nm) ; 5, 1 period; 6, simulated.

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Vol. 40

packet of one superlattice period and curve 6 is the simulated curve by kinematical theory. The points A, A' and B, B' in fig. 2 are node points of AlAs (21 nm), AlAs ( 1 0 . 7 nm) wave packet, corresponding to the & 4th and 8th satellite peaks, respectively. If we adjust AlAs(21 nm) sublayer thickness with a deviation of only 0 . 1 nm from 21 nm, the resulting variation of simulat-

+

ed curve will be quite pronounced. Comparing simulated curve with experimental curve, we found that there is a good agreement between the two curves when the thickness of ALAS sublayer is 21 nm. Therefore it indicates that the thickness of the AlAs sublayer is 21 nm with 0 . 1 nm resolution. In the same way, the thicknesses of AlAs(l0.7 nm) and GaAs(7.8 nm) sublayers can also be decided. Because the extent of the wave packet of GaAs ( 2 . 7 nm) is very wide and there is only one node point in the range of measurement, the wave packet method cannot be used, but its thickness can be decided easily if considering that the thicknesses of AlAs(l0.7 n m ) , GaAs ( 7 . 8 nm), AlAs(21 nm) and 1 period are known and its resolution is also 0 . 1 nm. It is obvious that the agreement between simulated and experimental curves is nearly perfect; thus it is clear that the method we employed is reliable. In summary, a simulation of X-ray double crystal diffraction pattern of complicated superlattice structures based on dynamic theory and combining with wave packet method gives satisfactory results.

References 1 Vardanyan, D. M . , Manoukyan, H. M . , Petrosyan, H. M . . The dynamic theory of X-ray diffraction by the one-dimensional ideal superlattice, Acta Cryst. , 1985, A41 :212. 2 Tapfer, L. , La Rocca, G . C. , Lage. H. et al . , Strain relief process at highly strained semiconductor heterointerfaces studied by high X-ray diffraction, Applied Surface Science, 1992, 56-58: 650. 3 Speriosu. V. S . Kinematical X-ray diffraction in nonuniform crystalline films: strain and damage distribution in ion-implanted garnets, 1 . A p p l . Phys., 1981, 52(10):6094.

.

4 Speriosu, V. S . , Vreeland T . , J r . , X-ray rocking curve analysis of superlattices, J . Appl . Phys., 1984, 56(6) :1591. 5 Liu Wei, Jiang Desheng, Liu Kejian et a l . , Broadening of the excitonic linewidth due to scattering of two-dimensional free carriers, A p p l . Phys. L e t t . , 1995, 67(5) :31.