Enlarged wells as probes to study superlattices

Superlattices and Microstructures, Vol. 1, No. 3, 1985

201

ENLARGED WELLS AS PROBES TO STUDY SUPERLATTICES

A. Chomette, B. Deveaud, 3.Y. Emery, A. Regreny Centre National d'Etudes des T~l~communications (LAB/ICM) 22301 LANNION FRANCE (Received 13 August 19g~ by ff.D. Dow) Within GaAs/Gal_xAlx As MBE grown superlattices (SL), a few GaAs wells have been purposely enlarged. Calculations show that enlarged wells introduce localized states in the SL band gap : the distance between such a localized state and the bottom of the SL conduction band (or the top ol the SL valence band) depends on the SL period and the enlarged well size. Luminescence and photoluminescence excitation results obtained on samples with different periods and enlarged well sizes are in good agreement with calculations. Once characterized, enlarged wells serve as probes in the study of SL optical and electrical properties. As examples, they were used to observe one monolayer size fluctuations and vertical transport by luminescence in GaAs/Gal_xAlxAS superlattices.

1 - INTRODUCTION Although small period superlattices (SL) have been at the origin of most studies on superstructures and heterostructures in lll-V semiconductors [l]~ they are far less well-known than quantum wells or heterojunctions [2]. The main reason is the c r i t i c a l part played by interfaces and ternary compound quality when the layer width decreases. Molecular beam epitaxy (MBE) remains the dominant technique for the growth of such structures. The quality of GaAs/Gat_xAlxAs superlattices can be substantially improved by adjusting the substrate temperature and the group V/Ill flux ratio [3]. This improvement is characterized by photoluminescence and excitation spectra : intensity, separation and width of luminescence peaks and in particular of excitonic peaks are good criteria of sample quality. In the present work, a number of undoped GaAs/Ga0.7AI0.3As superlattices were grown by MBE with equal well and barrier widths ranging from 3 nm to 7 nm. In part of the samples, three monolayers enlarged wells (EW) have been purposely introduced, the mean distance between two EWs being long enough (about 140 nm) to prevent any coupling between them. Those EWs were introduced as probes to study optical and transport properties o[ SLs : as a matter of fact, as is shown in § 2~ they create localized levels in the SL band gap, binding energies of which depend on the SL period and on the enlargement. In § 3, photoluminescence (PL) and photoluminescence excitation (PLE) results are presented in agreement with calculated levels. We present in § 4 an application of EWs introduction to the study of carrier motion along the growth axis (vertical transport) in SLs.

0749-6036/85/030201 + 0 4 $02.00/0

Our samples were grown in a home modified MBE 500 Riber system. Details of the growth process and of PL and PLE experimental conditions have been described elsewhere [#]. 2 - ENLARGED WELL

LEVELS

EW bound state energies can be calculated within a quasi periodical Kronig-Penney (KP) model [5], but this model does not provide precise enough wave functions in the EW neighbourhood. The model used in the present work is of the same type but non periodical : the sample is modelized by a series of N Gal_xAlxAS barriers (thickness LB, height V) and N-I GaAs wells (thickness L z e x c e p t the central well which is an EW of thickness LZ'). Wave functions I J, k~. > are built from plane waves : IJ, ÷k~ >

[ -7-g--

+

exp (i + k ~ . ~) C}(z)

+

where S, ka. and p are the sample surface, the wave and position vectors in the (x-y) plane and j the wave function label. [n the z direction, perpendicular to the layer% (j(z) reads • (j(z)

= a I exp(i kj z) + b!j exp(- i kj z)

in wells (l

l, 2, ... N-I)

and (j(z) = c!j exp(Kj z) + d I exp (- Kj z) in barriers (l = l, 2, ... N), w i t h K = '2¢~'~lsJ ¢"2Jm 2~ (progressive plane waves) and kj = d~ (evanescent plane waves), Ei being the j level energy and m 1 and m~the 'GaAs and Ga I xAlxAs effective masses. ~j(z) and its first derivative are continuous •

Z

.

.

-

© 1985 Academic Press Inc. (London) Limited

202

Superlattices and Microstructures, VoL 1, No. 3, 1985 [ ~j (z) l2

200' LZ=3nm

x=0.3

Bottom of conduction

>-

b~nd

Xai = 0.3

L z =3nm

Ls= 3rim

10-2

EW: ÷ 3 monolclyers

(.9 w z

+ 1 monolayer

IJJ

..~

150

/'

~/

. . . . . . . . . . . . . . . . . . .

/"

r, f",

+ 3 monoloyers

II

10-3 I

/

~

1 i

'

I

i I 1 1 I I

I

] ./

~

i i

e

'

I

t I

I

,

t~

'~tl I

I i

t;•

I I

,,

, i l ,, I I I

I

,,

+ 6 monolQyers . . . . . . . . . . . . . . . . . . . . .

100 0

,/~" 3

U

10

1'5

LB [nm)

('l i i I I

10-¢ FIGURE 1 : V a r i a t i o n s of t h e b o t t o m of the SL c o n d u c t i o n band and of t h e bound s t a t e s due to l, 3 and 6 m o n o l a y e r s e n l a r g e d w e l l s i n t r o d u c e d inside t h e SL, v e r s u s the b a r r i e r w i d t h LB, all o t h e r p a r a m e t e r s b eing k e p t c o n s t a n t (well width L Z : 3 nm, A I c o n c e n t r a t i o n x : 0,30, number of SL periods b e t w e e n t w o EWs N = 22)

a t each i n t e r f a c e and ~j(z) vanishes at both ends of the f i n i t e sample, Tlie set of linear equations thus obtained has solutions only for peculiar values of el, which are the eigenergies when k t : 0. C a l c u l a t i o n s f o r e l e c t r o n s and holes only d i f f e r in the values of e f f e c t i v e masses and b a r r i e r heights (g5 % of G a A s - G a l _ x A l x A s band gap d i f f e rence f o r e l e c t r o n s , 15 % for holes). N u m e r i c a l solutions are in q u i t e good a g r e e m e n t w i t h those of the quasi p e r i o d i c a l KP model [5]. Only one bound s t a t e is found in the SL band gap when LZ' LZ is not too large which is the case in our samp l e s . Due to the f i n i t e size of the sample, the SL c o n d u c t i o n (or valence) band in k z is modelized by N - l levels. The states of i n t e r e s t are the t w o dimensional subband associated w i t h the e l e c t r o n (or hole) bound s t a t e ( z - w a v e [ u n c t i o n ~ l ( z ) , energy e l ) and the b o t t o n of the SL c o n d u c t i o n band (or top of the SL valence band) ( z - w a v e f u n c t i o n ~2(z), energy ~2)" On Fig. 1 are presented the v a r i a t i o n s of ~2 and c I ( t h r e e values of e n l a r g e m e n t : l , 3 and 6 monolayers) versus the b a r r i e r w i d t h LB, the w e l l w i d t h L Z being kept c o n s t a n t and equal to 3 nm. Three areas can be discerned on Fig. 1 : L B < 6 nm, 6 nm < L B < l0 nm and L B > l0 nm. In the f i r s t area, the coupling between wells is strong so we have a genuine SL (non negligible miniband w i d t h ) and the bound s t a t e energies vary w i t h the coupling strength d e t e r m i n e d by L B . In the t h i r d one~ the coupling is negligible and the energy levels are those of M u l t i - Q u a n t u m Wells. The second area corresponds to an i n t e r m e d i a t e case : the coupling between n o r m a l wells

! I

I)l

I b /

l

lO-S

FIGURE 2 : P r o b a b i l i t i e s to find an e l e c t r o n at p o i n t z when i t belongs to level I ([~l(Z)l 2 continuous line) or to level 2 ([~2(z)l 2 d o t t e d line). The SL p o t e n t i a l is inserted to show w h e r e the barriers and wells are l o c a t e d . The sample has an inversion s y m m e t r y about the enlarged well and only one half of the f u n c t i o n s is represented.

is weak and we have still a SL ; it is w e a k e r for the EWs, because of the p e r t u r b a t i o n due to the e n l a r g e m e n t , so the bound s t a t e levels have t h e i r isolated quantum w e l l values. Once obtained the eigenenergies, n o r m a lized z-value functions (~i(z)) are c a l c u l a t e d f r o m the preceding linear set of "equations. On fig. 2 the v a r i a t i o n s o f l ( l ( Z ) i 2 and l(2(z){ 2 ( t h a t is to say the p r o b a b i l i t i e s to find the e l e c t r o n in z when it belongs to level t or level 2) are depicted. As the sample is s y m m e t r i c a l , the wave functions are odd or even when the origin is set at the c e n t e r o5 the sample. For the b o t t o m of the SL conduction band (i.e (2(z)) t w o d i f f e r e n c e s can be noted w i t h regard to the corresponding wave f u n c t i o n obtained in a regular periodical SL : edges e f f e c t and EW e f f e c t . Edges e f f e c t is quite u r ~ a n t inasmuch as, when matrix elements coupling I t , ~s. > and 12, ~'j. > are needed, the c o n t r i b u t i o n of the edge+s area is zero since the localized f u n c t i o n I I , ka_ > vanishes here. The EW e f f e c t is easy to explain : ( l ( Z ) and (a(z), eigenfunctions of the same h a m i l t o n i a n , are ~ orthogona] so, when in the SL bands, c a r r i e r s are p a r t l y driven out of the EW neighbourhood in order to ensure t h a t or t h o g o n a l i z a t i o n .

203

Superlattices and Microstructures, Vol. 1, No. 3, 1985

1.60

1.55

1.65

7/7 W r-~SL

5/5

W,

5

ENERGY (eV)

I

i

,SL

o

>)Z LIJ I-Z

enlargments of 1, 2, 3, 6 and 10 monolayers, the probabilities to find the bound electron inside the EW are respectively found to be 35 %, 5g %, 7 1 % , g6 % and 93 %. At last when the SL period increases, the enlargement being kept constant, the localization is found to increase. In conclusion of this paragraph, when introduced inside a regular SL, EWs create bound states, the binding energy and the localization of which ban be adjusted by a judicious choice of the set of parameters (Lz~ LB, LZ', x). 3 - LUMINESCENCE EXPERIMENTS

3/3

W ,

,SL

We have p e r f o r m e d PL and PLE experiments on our samples in order to v e r i f y the calculations presented in § 2. Fig. 3 shows the luminescence spectra of four quasi symetrical (L 7 = L R) SLs with periods ranging from 6 to 1/4~ nm, igside which three monolayed EWs have been introduced, the mean distance b e t w e e n two EWs being kept c o n s t a n t and equal to 140 nm. For each sample, two peaks appear on fig. 3 and correspond to heavy-hole excitonic r e c o m b i n a tion in the EW and the SL. The peaks a t t r i b u t i o n has been confirmed by PLE e x p e r i m e n t s in which corresponding light-hole exciton peaks have also been found. We checked that the SL excitonic peaks w e r e at the same energies than in c o r r e s ponding unperturbed SLs : the respective intensities of these peaks will be the subject of § 4. Table 1

i

0.80

i

i

i

i

0,15 0.13 WAVELENGTH (~m)

FIGURE 3 : C o m p a r i s o n of the luminescence s p e c t r a obtained using the same excitation conditions (6470, IW cm-2) in [our d i f f e r e n t perturbed s u p e r l a t t i c e s t r u c t u r e s . 4 SIs (see Tab. 1 for c h a r a c t e r i s t i c s ) are each perturbed by introduction of a 3 monolayers wider well (0~gSrrn) each 140 nm: (one over ten wells in the 7/7 SL and one over 23 wells in the 3/3 SL). Exciton recombination is observed both in the SL and in the enlarged wells (W) in all cases. The intensity ratio b e t w e e n the twopeatcs ( I W / I s L ) increases as the SL period d e c r e a s e s as a consequence of more efficient p h o t o c a r r i e r s motion in the g r o w t h direction. As far as the bound state [unction ( [ ( z ) is concerned, one can check on fig. 2 that it is localized near the EW but that this localization is weaker than in a classical quantum well. Furthermore the localization increases with the size of the enlargement : when all other parameters are identical to those in fig. 2, with

Sample

7/7

5/5

4/a

3/3

Lz(nm)

6.55

4.9

4.25

2.54

LB(nm)

6.27

4.9

4.25

2.83

x

0.2g

0.2g

0.26

0.285

Eexp(meV)

10

16.g

20.g

20

Ecalc(meV)

11.6

17.4

16.g

19.6

In Tab. l distances between EW peaks and SL peaks (E exp) are compared to t heor et i cal distances calculated using the model of § 2 (Ecalc - Ebe + Ebb where Ebe is the electronic EW binding energy and Ebh the heavy hole one). Calculations were performed using X-rays determined parameters [6] for SLs (also reported in Tab. l). In three cases (7/7, 5/5 and 3/3) the agreement is good and the observed discrepancy can probably be explained, besides the precision of the model and of the luminescence experiments, by the d i f f e r e n c e of exciton binding energy in SLs and EWs. As, in l i t t e r a t u r e , no result is available on this subject, it remains a m a t t e r of f u t u r e work. The discrepancy is greater for the f o u r t h sample (4/4) and another explanation must be invoked in this case. The luminescence peaks o[ this sample are larger than those of the other samples, which reveals a less good quality. Moreover, we have shown elsewhere [7] that monolayer interface steps, inherent in the growth process, induce [luctuations of

Superlattices and Microstructures, VoL 1, No. 3, 1985

204 -+ I monolayer in the well size. Consequently the 3 monolayers EW contains 2 and 4 monolayers enlarged areas. As in the 4/4 sample the X rays measured parameters (L Z and L B) are larger than those aimed when the sample was grown (#,25 nm instead of 4 nm), contrary to what is found for the other samples, the number of 4 monolayers enlarged areas might be greater. The observed EW luminescence peak, larger than in other samples, might then correspond to two unresolved peaks due to 4 and 3 monolayers enlarged areas. As a matter of fact~ the value of Eex p (20,8 meV), extracted from the maximum of this peak, lies between Ecalc calculated with 3 monolayers EWs (16,8 meV) and Ecalc calculated with # monolayers EWs (23,2 meV). Further studies are necessary to precise this interpretation. 4 - APPLICATION TO VERTICAL TRANSPORT

EWs, once characterized, can be used in the study of SL properties. As a first example, one monolayer steps at interfaces, typical of the growth process, have been observed by luminescence. This is the subject of another paper in the same issue [7]. In this paragraph, a second example is briefly exposed : greater details can be found elsewhere [4]. In our samples, the mean distance between two EWs has been kept constant (~ 140 n m ) ; so the proportion (P) of EWs to regular wells decreases with the SL period. Table 2 Sample

P

R

717

1/10

0.7

5/5

ill4

4

4/4

I/IS

6

3/3

1/22

70

On Tab. 2 are reported the proportion P and the intensity ratio R of EW luminescence peak to SL luminescence peak for the four samples the spectra of which are represented on fig. 3. If photocarriers were to recombine where they are created9 the ratio R would be proportional to P. On the contrary R increases when the SL period and P decrease. Thus carriers photocreated in the SL move along the z axis and are trapped on the EW localized level and the lower the SL period the more efficient this transfer. We must point out that carriers do not move above the GaAIAs barriers since they are created at an energy lower than the GaAIAs gap energy. The ratio R is only slightly affected by laser power variations and temperature increase from 1 K to 100 K. Using the model of § 2, we calculated the SL and EW wave functions and, via the F e r m i golden rule, the m e a n trapping t i m e s of e l e c t r o n s and holes f r o m the SL conduction and valence first minibands onto the EW bound s t a t e s , assuming

ionized ~mpurtty scattering as the dominant perturbation in the range of temperature considered (l K to 100 K). Then these calculated times were compared to the mean trapping times derived from experimental values of ratio R and estimated values of carrier lifetimes in the SL and the EWs. To summarize our results and the discussion presented in [4], we can say that the agreement between calculated and experimental mean trapping times is satisfactory when the impurity concentrations are supposed to be 3 x 1015 cm -3 in GaAs and 5 x 1016 cm-3 in GaAIAs. The impurity c o n c e n t r a t i o n in GaAIAs is not known and might be higher, which would improve the a g r e e m e n t . At last the c a r r i e r c a p t u r e on 3 monolayers EW bound s t a t e s can be enhanced by a partial c a p t u r e via the 2 monolayers enlarged a r e a s which were mentioned in § 3 and which have levels n e a r e r the SL bound edges : in this cas% the a g r e e m e n t b e t w e e n calculated and e x p e r i m e n t a l t i m e s is quite good. 5 - CONCLUSION

Introduction of enlarged wells in a regular superlattice induces localized levels in the SL band gap. Photoluminescence and photoluminescence excitation experiments supply peaks in the places expected within the framework of a simple model. Enlarged wells thus provide a reference mark to study optical and transport properties of superlattices. An example has been presented • the vertical motion of carriers in the direction perpendicular to the layers. Another type of application is the creation of bound states, the binding energy and localization of which can be adjusted by a set of structural parameters (well and barrier widths, AI concentration, enlargement).

[l]

L. Esaki and l ~ , 61 (1970)

R. Tsu, IBM 3. Res. Dev.

[2]

L.L. Chang, 3. Vac. Sci. Technol. g l (2), (1983)

[3]

Ya Li Sun, W.T. Masselink, R. Fisher, M.V. Klein~ H. Morko~ and K.K. Bajoj J. Appl. Phys. _5.5 (10) (1984)

[4]

A. C h o m e t t e , B. Deveaud, 3.Y. Emery, A. Regreny and B. L a m b e r t , to be published

[5]

M. C o m b e s c o t and C. Benoit a la Guillaume Solid S t a t e C o m m . 39~ 651 (1981)

[6]

3. K e r v a r e c , M. Baudet, 3. Caulet, P. Auvray, 3.Y. Emery, and A. Regreny 3ourn. of Applied Cryst. 17, (1984)

[7]

B. Deveaud, 3.Y. Emery, A. Chomette, 13. Lambert and M. Baudet Single Monolayer Well Size Fluctuations in the Luminescence of GaAs/GaAIAs Superlattices, Same issue.