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Si-Ge STRAINED LAYER SUPERLATTICES

H. Brugger, G. Abstreiter

To cite this version:

H. Brugger, G. Abstreiter. Si-Ge STRAINED LAYER SUPERLATTICES. Journal de Physique

Colloques, 1987, 48 (C5), pp.C5-321-C5-327. �10.1051/jphyscol:1987569�. �jpa-00226773�

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Colloque C5, suppl6ment au noll, Tome 48, novembre 1987

Si-Ge STRAINED LAYER SUPERLATTICES

H. BRUGGER and G. ABSTREITER

Physik-Department E16, Technische Universitat Miinchen, D-8046 Garching, F.R.G.

Abstract

We report on growth and properties of Si/SiGe s t r a i n e d layer s u p e r l a t t i c e s . C r i t i c a l thicknesses and relaxation processes in s i n g l e layers a r e studied with Raman spec- troscopy, LEED, and TEM. Phonon Raman s c a t t e r i n g i s used t o determine built-in s t r a i n and period length of s u p e r l a t t i c e s . Transport measurements show mobility enhancement in s e l e c t i v e l y doped samples. The ordering of e l e c t r o n i c bands due t o s t r a i n y i e l d s t o two-dimensional electron gases i n Si.

Introduction

The proposal of periodic one-dimensional potential s t r u c t u r e s by Esaki and Tsu / I / has i n i t i a t e d a vast amount of research a c t i v i t i e s on semiconductor s u p e r l a t t i c e s . The a r t i f i c i a l periodicity perturbs t h e band s t r u c t u r e of the host material giving r i s e t o narrow subbands i n t h e conduction and valence band. Their energies a r e strongly affected by t h e thickness of individual layers resulting i n a change of e f f e c t i v e gap energy. T h i s o f f e r s t h e p o s s i b i l i t y of t a i l o r i n g the electronic and optical properties. Specific s c i e n t i f i c and technological i n t e r e s t on strained-layer s u p e r l a t t i c e s (SLS) has developed during t h e past few years. For t h i n layers t h e l a t t i c e mismatch of t h e two semiconductors involved can be accommodated by e l a s t i c deformation. The corresponding s t r a i n influences d r a s t i c a l l y the band line-up and a c t s a s an additional parameter in band-gap engineering.

The combination of Si and Ge i s very a t t r a c t i v e due t o the interesting possi- b i l i t y of t h e occurrence of a direct-gap s u p e r l a t t i c e made of indirect-gap host materials. The band-gap conversion was f i r s t discussed by Gnutzmann and Clausecker /2/ a s a r e s u l t of Brillouin-zone folding. The new s u p e r l a t t i c e periodicity is a l s o reflected in t h e phonon properties a s demonstrated by Brugger e t a l . /3,4/ f o r Si/Ge SLS.

The progress in Si-MBE made i t possible t o grow high-quality pseudomorphic multilayer s t r u c t u r e s Si/SixGel-x i n t h e e n t i r e range of a l l o y compositions /5,6/.

S i , Ge, and SiXGel-, a l l o y s have i n d i r e c t band gaps, which were studied by optical absorption measurements /7/. There exists a 1 arge l a t t i c e mismatch between pure Si and Ge of about 4%. The l a t t i c e constant can be adjusted l i n e a r l y with composition x between t h e values of the pure semiconductors. The fundamental band gap of bulk S i ~ G e l - ~ ranges from 0.66 t o 1.12 eV and l i e s i n t h e i n t e r e s t i n g range of optical f i b e r communication (1.3

-

1.55 pm). The p o s s i b i l i t y of monolithic integration cif optoelectronic components on Si-ICs i s a very stimulating prospective.

In t h i s paper we f i r s t discuss the growth properties of lattice-mismatched SixGe1,, overlayers on GaAs. Raman spectroscopy and LEED i s used t o determine the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987569

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C5-322 JOURNAL DE PHYSIQUE

c r i t i c a l thickness hc of sing1 e layers necessary t o design appropriate commensurably grown SLS. The phonon s t r u c t u r e is d r a s t i c a l l y influenced both by the built-in s t r a i n and t h e a r t i f i c i a l period.

I t i s demonstrated t h a t Raman s c a t t e r i n g i s an easy tool t o determine quantita- t i v e l y t h e s t r e s s i n s i d e t h e layers and the period length of SLS. These parameters a r e necessary i n model 1 ing band 1 ine-up and subband s t r u c t u r e in the s u p e r l a t t i c e . The appearance of two-dimensional electron systems i n s i d e the Si-layers, a s observed by Shubnikov-de Haas and cyclotron-resonance experiments /8/, can be explained con- s i s t e n t l y using the s t r a i n - e f f e c t s on t h e band structure. The modification of the e l e c t r o n i c band s t r u c t u r e of u l t r a t h i n Si/Ge SLS y i e l d s t o new optical t r a n s i t i o n s i n t h e energy range below t h e Si band gap /9,10/.

C r i t i c a l thickness and relaxation

SLS can be grown e p i t a x i a l l y on a s u b s t r a t e o r on an appropriate buffer layer under adequate conditions. To achieve good electronic and optical q u a l i t y , t h e a c t i v e regions should be f r e e of crystal defects l i k e m i s f i t dislocations. This i s only possible i f the individual l a y e r thickness and the overall dimension of asymmetrical- l y s t r a i n e d SLS remain below c r i t i c a l values which depend on the l a t t i c e mismatch.

We b r i e f l y report on systematic studies of c r i t i c a l thicknesses of SixGe1-, layers on GaAs (110) and Ge (110) surfaces. The difference i n l a t t i c e constant between t h e overlayer and the s u b s t r a t e can be l i n e a r l y varied i n t h e range from nearly perfect l a t t i c e matching (Ge) t o about 4% ( S i ) . The l a t t i c e mismatch i s e l a s t i c a l l y accom- modated (biaxial s t r e s s ) up t o a c r i t i c a l thickness hc which depends strongly on x.

hc i s plotted versus l a t t i c e mismatch f i n Fig. 1, a s determined by Raman s c a t t e r i n g and LEED. The i n t e n s i t y of t h e LO-phonon i n polar semiconductors, which is forbidden i n f i r s t - o r d e r Raman back-scattering from (110) surfaces, turns out t o be very sen- s i t i v e t o the creation of m i s f i t dislocations close t o t h e interface. The LO-inten- s i t y is proportional t o t h e square of t h e e l e c t r i c f i e l d and consequently d i r e c t l y related t o the band bending in GaAs close t o t h e interface. This l i g h t s c a t t e r i n g technique, which i s called electric-field-induced Raman s c a t t e r i n g (EFIRS), i s described i n more d e t a i l in-Ref. /117. EFIRS appeak t o 6 e an excellent optical tool

lattice mismatch f

(%I

~$zzQ

0 LEED

\

\ Raman

\ (EFlRS t

silicon fraction x

Fig. 1: C r i t i c a l thickness of mismatched SixGel-x over- layers on (110) GaAs

Fig. 2: High resolution TEM micrograph o f a x e d Si0.tjGeo film on (110) GaAs. Misfit dislocations a r e indicated by arrows.

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tions /12,13/ as we1 1 as t o determine c r i t i c a l thicknesses of GaAs/SixGel -x mis- matched systems /14/. The experimental values of hc a r e given by f u l l dots i n Fig.1.

Due t o the absorption of l i s h t c r i t i c a l thicknesses in S i ~ G e i - ~ ..

. ,.

can onlv be detected i f h c < 200

1

0 r . x Z 0.4.

-

Low enerav electron d i f f r a c t i o n (LEED) has been used t o a e t information about the change

2

the l a t e r a l surface l a t t i c e constant. This is"observed as a s h i f t of t h e LEED-spots, which can be determined e a s i l y t o an accuracy of about 0.3% by analyzing the data with a vidicon camera /15/. LEED-measurements yield information about hc from x

2

0.2 up t o x = 1 provided t h a t t h e overlayer i s of good c r y s t a l l i n e quality. The corresponding hc-values a r e given by open c i r c l e s in Fig. 1.

The c r i t i c a l layer thickness of l a t t i c e mismatched overlayzrs has been c a l - culated f o r example by van der Merwe on t h e basis of a balance between i n t e r f a c i a l energy (EI % f ) and areal s t r a i n energy density associated with a film of thickness h (EH % hf2) /16/. Such theoretical predictions a r e given by the solid line. The equilibrium theory r e s u l t s in rather low values of h c compared t o the experimental points. A reason f o r t h i s underestimation i s probably the neglection of an activation b a r r i e r f o r the generation of m i s f i t dislocations in v.d. Merwe's theory.

Apart from the c r i t i c a l thickness hc of s i n g l e layers t h e r e e x i s t s another c r i t i c a l length ~ S L S which a r i s e s from t h e overall thickness of asymmetrically strained s u p e r l a t t i c e s , even i f the individual layers (1,2) a r e thinner than hcl y 2 .

h s ~

i s found t o be determined approximately by the weighted average s t r a i n in the whoge s t r u c t u r e ,171. Exoerimental values of hqr

---

9 from Si/Ge SLS a r e discussed in Ref. / l o / .

To g e t information on t h e type of m i s f i t dislocations we have studied strained overlayers w i t h thicknesses above hc by transmission electron microscopy (TEM1/18/.

Fig. 2 shows the lattice-image of a GaAs (llO)/Si0.5Ge0.5 heterojunction. The film thickness of t h e a l l o y layer i s well above the c r i t i c a l value hc. The Si0.5Ge0.5 overlayer is of good c r y s t a l qua1 i t y . Additional (1 11) planes, however, appear 1n- s i d e t h e film. This corresponds t o a 600 mixed dislocation with s l i p vector para1

-

l e l <'110> lying in a 1111) plane. The s t r a i g h t dislocation l i n e s stop a t the i n t e r f a c e a s marked by arrows. Due t o the l a t t i c e m i s f i t a high number of dangling bond s t a t e s along the dislocation 1 ines a r e generated close t o the 'nterface.

The expected density increases with l a r g e r m i s f i t f up t o 7.4 x l o t 3 cm-2 i n the case of pure Si on GaAs (1 10).

The growth of several SixGel-x films with d i f f e r e n t compositions on GaAs (110) has a l s o been studied by phonon Raman spectroscopy. Typical spectra of thin

Si0.5Ge0.5 films a r e shown in Fig. 3. The mismatch i s about 2%. The spectra were measured i n s i t u , during growth. The corresponding thickness of the overlayer i s given in Angstroem. SixGel- alloys show a three-mode behaviour /19/. The evolution of these modes can be clearfy seen i n Fig. 4. The optical phonon of the GaAs-sub- s t r a t e i s attenuated due t o increasing 1 i g h t absorption with growing overlayer thickness.There i s a c h a r a c t e r i s t i c s h i f t in frequency f o r commensurate, i .e.

e l a s t i c a l l y strained layers. The relaxation process appears a s a continuous s h i f t i n phonon energies up t o the values of unstrained material indicated by arrows. The

;Eil

relaxation i s a gradual process completed f o r film thicknesses l a r g e r than in t h e case of Si0 5Ge0.5. There i s , however, some evidence f o r a small residual s t r a i n even f o r l a r g e film thicknesses h >> h c /20/. Raman scattering a1 lows a quantitative determination of b u i l t - i n s t r a i n or corresponding s t r e s s . I t averages the s t r a i n d i s t r i b u t i o n over the layer thickness and t h e area 07 the used l a s e r spot.

Systematic investigations of t h e strain-induced s h i f t of phonon frequencies of SixGel-x a1 loy layers a r e shown i n Fig. 4 f o r 0 < x < 0.8. All three modes of the a1 loy f i lms decrease monotonically with increasing x. The downward s h i f t i s charac- t e r i s t i c of t e n s i l e biaxial s t r a i n E = (a

-

ao)/ao with a and a. being the in- plane l a t t i c e constant under s t r a i n and t h e i n t r i n s i c l a t t i c e constant of the film, respectively. The Si-Ge related mode vibration shows a nearly l i n e a r behaviour with s t r a i n . The frequency s h i f t can be used t o measure b u i l t - i n s t r a i n s quantitatively.

A l i n e a r f i t t o the experimental values yields AW = -(8.82 c m - I ) ~ ( % ) f o r films under t e n s i l e biaxial s t r a i n grown on (110)-surfaces, The s h i f t has opposite sign and i s nearly twice a s large a s f o r SixGel-x under biaxial compression grown on (100) Si surfaces as determined by Cerdeira e t a l . /21/.

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C5-324 JOURNAL DE PHYSIQUE

We have a1 so studied t h e phonon behaviour of u l t r a s h o r t period superlattices.

They were grown using MBE a t a s u b s t r a t e temperature of 450° C and c o n s i s t of 15 periods of several monolayers Si and Ge. Spectra of samples w i t h d i f f e r e n t period length d = d i + d ~ , a r e shown i n Fig. 5. The periodicity along t h e growth direction causes a ~ r i 7 l o u i n - z o n e folding and t h e appearance of new gaps i n the phonon spectra Doublet modes observed below 100 cm-1 correspond t o folded LA modes. The dispersion curve of these modes can be measured /4/ and analyzed with a layered e l a s t i c con- tinuum model /24/. The energetic positions of t h e back-folded modes s h i f t t o higher values with decreasing period length d a s c l e a r l y seen i n Fig. 5. By comparing t h e frequencies with calculated energies t h i s can be used t o determine accurately the period of s u p e r l a t t i c e s /3/.

The peaks a t higher energies (> 200 cm-1) in the spectra correspond t o optical phonons i n t h e SLS. The dispersion curves of Si and tie do not overlap in frequency.

Therefore confined modes i n each layer a r e expected (phonon quantum we1 1 s). They show up a s shoulders i n t h e Si and Ge phonon peaks a s indicated by arrows. F i r s t order Raman spectra of pure Si and pure Ge e x h i b i t a s i n g l e peak a t 525 cm-1 and a t 305 cm-1, respectively. The strain-induced s h i f t in energy of t h e Si-phonon is l a r g e r i n samples 4/11 and 3/9 which were grown on a Ge(ll0) buffer l a y e r compared with sample 6/11 grown on a Si0.25Ge0.75 buffer layer. In this case a l s o t h e energy of t h e Ge-phonon is shifted t o higher energy in these layers. Caused by the f i n i t e penetration depth a l s o the phonon s t r u c t u r e of t h e buffer layer i s seen (denoted by P). In addition, an i n t e r f a c e mode ( I F ) i s observed i n between t h e S i and Ge modes.

The Raman spectra d i r e c t l y prove t h e p o s s i b i l i t y of growing high quality Si/Ge SLS w i t h sharp i n t e r f a c e s and individual layer thicknesses of only a fev! monolayers.

F i r s t experiments i n d i c a t e new optical t r a n s i t i o n s i n t h e energy range of about 0.7

-

0.9 eV /lo/. Such energ'ies a r e expected f o r t h e fundamental gap of these SLS with staggered band line-up making optical t r a n s i t i o n s i n d i r e c t in real space.

GaAs (110) / Sio,Geo,

-

200 Energy 300 Shift LOO (cm-I) 500

lattice mismatch f

(%I

Si

-

content

x

Fig. 4: Frequency difference bet- ween phonon peak positions i n s t r a i n e d and relaxed samples of t h e same composition. SixGel-x was grown on (I 10) 6aAs a t Tq = 410°C.

The spectra were taken a Tm

-

80 K.

Fig. 3: Raman spectra of s i n g l e -0.5 films on GaAs

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studied in Si/Sir~.gGe0,5 SLS grown on Si sub- strates. In such samples the sign of the s t r a i n in the SiGe alloy layers i s reversed.

The arrangement i s shown in Fig. 6. Two types of buffer layers have been used. Superlattices grown on Si a r e asymmetrically strained. This can be seen directly in the corresponding Raman spectrum shown in Fig. 6. The Si phonon mode of the 60

8

thick layers appears a t the energy as expected for unstrained bulk Si (64.5 rneV). The three SiGe related modes on the other hand are shifted upwards due t o biaxial compressive strain. Using a

Si0.75Geo buffer layer leads to a smaller s h i f t of t i e alloy modes. In addition, the Si mode i s shifted downwards by about 1 meV f o r t h i s sample. This shows the strain sym- metrization in SLS grown on an Sioa7 Ge0.25 buffer layer, whose l a t t i c e spacing fiies j u s t in between those of Si and Sio.5Geo 5.

The strain distribution has a strong influence on the conduction band offset, which i s re- flected directly in the transport properties of selectively doped sampl es

.

Successful experiments on mobility enhancements have been reported f o r two-dimensional electron and hole gases /8,22/.

Hal 1 mobility, Shubnikov-de Haas osci l- 1 ations, and cyclotron resonance were studied with a series of symmetrically strained Si/Si0,5Ge0,5 superlattices. The samples are doped selectively with Sb by secondary im- plantation /25/. The position of the Sb doping spike was varied with respect t o the Si/SiGe 1 ayer sequence. The temperature dependence of the mobility and the measured peak value a t T = 20 K i s shown in Fig. 7.

Enhanced mobilities are observed when the Sb-dopants are situated inside the SiGe layers. These samples show a monotonic in- crease of the mobility with decreasing tem- perature and saturation a t low temperatures.

These observations have been explained by the formation of 2D electron gases i n the Si layers which are spatially separated from the charged donor impurity atoms. The two- dimensional behaviour of the carriers and the confinement i n Si has been further con- firmed by the angular dependence of the Shubnikov-de Haas effect and by cyclotron resonance experiments. A s t r a i n induced lowering of the Si conduction band was sug- gested on the basis of these experiments /23/. Careful measurements with selectively doped superlattices grown directly on Si indicate that the conduction band edges are approximately equal when Si i s un- strained /26/. Built-in tensile strain in the Si layers can lower the two-fold degenerate conduction band minima (heavy

Tm.77 K i10~0011aIO110 WGe

0 100 200 300 LOO 500

Energy Shift (cm-1) Fig. 5: Raman spectra of Si/Ge SLS

Fig. 6: Schematic diagram of the -structure and phonon spectra of Si/SiGe SLS

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C5-326 JOURNAL DE PHYSIQUE mass normal t o t h e (IOU) layer planes) by a few

p H i 1 0 3 ~ 2 1 SI / SlGe /

hundred meV, which favours electron confinement II ,,

in the Si layers. The valence band edge i s - tT= ZOKI always much higher i n the SiGe o r Ge layers.

The band o f f s e t s have been confirmed theoretic- a1 l y by self-consistent subband calculations /27/ and by band s t r u c t u r e calculations /28,29,! N-

The s i t u a t i o n can be summarized i n t h e follow- ing way: For unstrained Si and compressively

32

o 5 0 A

strained SiGe t h e conduction band o f f s e t i s posltton of

very small throughout the whole range of com-

5

sb dopant

positions. W i t h increasing t e n s i l e s t r a i n rn present i n the Si l a y e r s a staggered band 0 I 1000

line-up appears w i t h t h e conduction band edge

,

much lower in Si. This i s shown schematically in Fig. 8.

<

I Vs 82

F i r s t applications of Si/SiGe SLS Vs 83

appeared already i n t h e l i t e r a t u r e . The

e f f e c t of band gap narrowing due t o s t r a i n / vs 75

has been used f o r waveguide avalanche photo- 10 loo 1000

detectors with separate absorption and multip-

l i c a t i o n s a s discussed by Luryi e t a1

.

/30/. TEMPERATURE (K) The successful fabrication of n-channel

MODFETs was recently reported by DB'mbkes e t

a l . /31/, which was achieved by s e l e c t i v e Fig. 7 : Temperature dependence Sb-doping of a Si/Si 0-5GeoS5 heterostructure of mobility

a s discussed above. There is a l s o f i r s t doped SLS

C'

I Si 1SiGe1 Si [SiGel Si I

cb I I I

E

I I I I I I

l l l l l l

vb

u ,

I , I I I I I

Fig. 8: Real-space energy diagram of a strained-layer s u p e r l a t t i c e

evidence f o r new optical t r a n s i t i o n s i n u l t r a s h o r t period SiIGe s u p e r l a t t i c e s /9,10/. A c l e a r experimental manifestation of t h e t r a n s i t i o n from i n d i r e c t gap t o d i r e c t gap semiconductor in such novel s t r a i n e d layer s u p e r l a t t i c e s i s , however, s t i l l lacking.

Acknowledgements

We thank E. Kasper, H.J. Herzog, and H. Jorke f o r providing part of the samples and f o r many stimulating discussions. We a r e a l s o grateful t o J . Mazur, H. Oppolzer, and H. Cerva f o r performing the TEM-experiments.

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