High density hot excitons in stressed pure silicon

~iSolid State Communlcatlone, Vol. 69, No. 2, pp. 159-162, 1989. ~rlnted in Great Britain.

0038-1098/89 $3.00 + .00 Pergamon Press plc

HIGH DENSITY NOT EXCITONS IN STRESSED PURE SILICON A. Uddin, H. Nakata and g. Otsuka Department of Physics, College of General Education, Usaka University, Toyonaka, Osaka 560, Japan. (Received 25 October 1988 by W. Sasaki)

We observe an unknown p h o t o l u m i n e s c e n c e peak from a uniaxtally s t r e s s e d pure s i l i c o n u n d e r e x t r e m e l y high e x c i t a t i o n in t i m e - r e s o l v e d measurements. The peak is splitting to the higher energy side from the freeexciton peak (TO/LO phonon replica) with stress. The peak intensity becomes s t r o n g e r as wall as l i f e t i m e s h o r t e n s with s t r e s s , while the f r e e e x c i t o n peak i n t e n s i t y d e c r e a s e s . We s p e c u l a t e the unknown peak may be due to the r e c o m b i n a t i o n of the cold e l e c t r o n and t h e l i g h t hole in the hot e x c i t o n . We a l s o o b s e r v e t h a t t h e g e n e r a t i o n r a t e of e x c i t o n s exp o n e n t i a l l y decreases with stress.

t i m e - r e s o l v e d measurements of the FE l u m i n e s cence. No change of the e x c l t o n peak p o s i t i o n was observed f o r d i f f e r e n t d e l a y times. These i n d i c a t e d h i g h l y homogeneous stress c o n d i t i o n s of our sample. Throughout the i n v e s t i g a t i o n the sample was in the same s e t t i n g . F i g u r e l ( a ) shows t y p i c a l luminescence spectra f o r S1 [ 2 ; t ] at 2 K. In t i m e - r e s o l v e d measurements we observe an unknown peak S as shown in Fig. l ( a ) . The peak p o s i t i o n s of TO and LO phonon r e p l i c a of " h o t f r e e - e x c i t o n (hFE) luminescence" in the spectrum ' I ' almost c o i n c l d e w i t h the r e s p e c t i v e peak p o s i t i o n s in the spectrum ' I I ' . Under s t r e s s t h e r e e x i s t two types of e x c l t o n s , c o l d e x c i t o n s and hot excztons. There are three kinds of hot e x c i t o n s : The hot e l e c t r o n in the upper four v a l l e y s of the c o n d u c t i o n band and the heavy and l i g h t holes in the valence hand of = j = ± 1 / 2 and = j = ± 3/2, r e s p e c t i v e l y , form two k i n d s of hot exc i t o n s . Another k i n d of hot excltons is formed by the cold e l e c t r o n in the lower two v a l l e y s of the conduction hand and the l i g h t h o l e . A c o l d e l e c t r o n and a heavy hole form a cold e x c i t o n , or an e x c z t o n in the o r d i n a r y sense. At zero stress there is no S peak. With stress the S peak comes out on the higher energy side of the FE (TO/LO) peak, as shown in Fig.1(b). The hFE peak positions of TO and LO phonon replica are not sensitive to stress. At zero stress, the FE and EHL peak energies appear at 1.097 and 1.083 eV, respectively. The separation of these two emission lines gives the binding energy of ENL.5 The separation of the FE and ENL peak decreases with stress. This indicates that the binding energy of the EBL decreases with stress. The EHL peak totally disappears at high stress, indlcatzng that EHL is not stable in the high stress limit. This appears inconsistent with Ref.5. The electron-hole liquid may, however, be shoen stable with inhomogeneous stress even in the high stress limit. We have measured the luminescence i n t e n s i t y of FE and EHL w i t h s t r e s s a t 2 K as shown i n

After a long time investigation of freeexcitons (FE) and electron-hole liquld (ENL)1-5 in indirect-gap semiconductors, there still remains much to be explained. The present studies have been made to investigate FE and ENL in pure silicon by photolumlnescence (PL) measurements. The sample was excited over a wide range of e x c i t a t i o n power with effective unzaxzal stress along <100> dlrectlon. This stress decreases the conduction- and valenceband degeneracies and gives rise to a system u s u a l l y denoted by Si [ 2 ; 1 ] , where the numerals in the square bracket indlcate the band edge degeneracies. The unstressed case may be denoted by Si [6;2]. The band structure of this system is well known. 6 In this letter we report the stress dependent FE and EHL luminescence intensztles as well as their peak energy. We observe a strong stress dependence of both FE and EHL decay processes and their relative luminescence Intensities at 2 Z. We observe an unknown PL peak in tlme-resolved measurements by using a 5 HW dye laser. This unknown peak is sphtting to the higher energy side from the FE (TO/LO phonon replica) peak with stress. We used a sample of s i n g l e - c r y s t a l pure s i l i c o n in t h i s study. The sample dimension was 1xlx3.5 me3. The i m p u r i t y concentration was c a l culated by photolumlnescence measurements, using the method of T a j i m a 7, to y i e l d 3x1011 c=-3 boron. For s t a t i o n a r y measurements, the sample was e x c i t e d by an Ar + l a s e r of 200 mW at X = 514.5 nm. The Ar + l a s e r beam was m e c h a n i c a l l y chopped at 200 Hz. For t i m e - r e s o l v e d measurements, the sample was e x c i t e d by a dye l a s e r at A = 590 nm w i t h a pulse w i d t h of 10 ns. The luminescence was d e t e c t e d by a Ge-PIN p h o t o d i o d e , cooled a t 77 K, with a response time of 0.2 ~ s. Stress homogeneity was checked by A ~ laser PL measurements of t h e FE l u m i n e s c e n c e . No broadening of the e z c i t o n peak was observed with s t r e s s . S t r e s s homogeneity was also checked by 159

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F i g . 2 . At zero s t r e s s the EHL peak i n t e n s i t y i s s t r o n g e r than the BE peak. We a l s o observe t h r e e weak peaks o f bound e x c i t o n s BI , B2 and B3.8 These peaks are very s e n s i t i v e to s t r e s s and t o t a l l y d i s a p p e a r a t 22 HPa s t r e s s . The EHL peak intensity exponentially decreases with stress and becomes z e r o a t 157 MPa s t r e s s . A l i t t l e background l u m i n e s c e n c e r e m a z n s . The s p e c t r a l f u l l w i d t h a t h a l f maximum (FWHN) of t h e EXL peak d e c r e a s e s w i t h s t r e s s i n a g r e e m e n t w i t h Ref.5. This z n d i c a t e s a l a r g e l y reduced d e n s i t y at high s t r e s s . We have measured the l i f e t i m e of EHL in d i f f e r e n t s t r e s s e s . The d e c a y time c o n s t a n t s of the EHL luminescence are measured over a r a n g e o f s t r e s s 0-180 HPa u s i n g t h e t i m e r e s o l v e d t e c h n i q u e . All of t h e s e d e c a y c u r v e s a r e e x p o n e n t i a l and show a marked i n c r e a s e in l z f e t i a e with i n c r e a s i n g s t r e s s . The e l o n g a t i o n of l i f e t i m e zs d i r e c t l y r e l a t e d to the d e c r e a s e in e-h p a i r d e n s i t y in EHL. The F£ peak i n t e n s i t y becomes s t r o n g e r with s t r e s s , g i v i n g a maximum value a t 55 HPa s t r e s s . This may be due to the e v a p o r a t i o n of e x c i t o n s from EHL. A f t e r t h a t the FE peak i n t e n s i t y exp o n e n t i a l l y d e c r e a s e s with s t r e s s u n t i l a r o u n d 135 HPa and then i t becomes almost c o n s t a n t with s t r e s s . This constancy of the FE peak i n t e n s i t y say be due to the t r a n s f e r of e l e c t r o n s zn t h e e x c i t o n s y s t e m from t h e u p p e r f o u r v a l l e y s to the lower two v a l l e y s of t h e c o n d u c t i o n band,

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Fzg. 1 (a) Unknoen PL peak ' S ' z n spectrum ' I I ' xs from t z m e - r e s o l v e d measurements a t a d e l a y tzme o f 2 . 5 ~ s. E x c z t a t z o n zs made by a dye l a s e r . The spectrum ' I ' zs f r o m PL m e a s u r e m e n t s , e x c i t e d by Ar + l a s e r o f 200 mW. The S peak zs around 6 =eV hzgher energy szde of FE(TO/LO) zn spectrum ' I ' . (b) Peak energzes of v a r i o u s peaks o b s e r v e d zn Ar + l a s e r PL m e a s u r e m e n t s a r e p l o t t e d as a f u n c t z o n of s t r e s s . The s e p a r a t i o n of FE and EHL peaks tends to become c o n s t a n t a t hzgh s t r e s s l z m z t .

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Vol. 69, No. 2

the upper v a l l e y and the lower v a l l e y at 135 NPa stress. No phonons are a v a i l a b l e f o r i n t e r v a l l e y t r a n s i t i o n below 135 MPa. Above 135 MPa the hot e x c i t o n can r e l a x to the cold e x c i t o n by e m i t t i n g an i n t e r v a l l e y TA phonon. Wagner et e l . 10 suggest t h a t the decay of EHL in a uniaxzally <100> s t r e s s e d Si i s governed by the e v a p o r a t i o n of f r e e e x c i t o n s because of the l a r g e r e d u c t i o n of the binding energy of EHL. Auger recombinat i o n is dominant f o r <111> stress as well as f o r zero stress on account of the much higher binding energy than for <100> s t r e s s . The gradient of the EHL luminescence decrease is higher than that of FE. The s t r e s s d e p e n d e n t p h o t o l u m i n e s cence i n t e n s i t i e s of EHL and FE can be expressed e m p i r i c a l l y as

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where x is s t r e s s , A is the luminescence i n t e n s i t y of EHL at zero stress and p is a decay f a c t o r of 1.75xi0 "2 NPa -1. In Eq. (2), Bexp(qx) is the term f o r the increase of the FE peak i n t e n s i t y with stress due to the evaporation of excitons from EHL, where B is a constant to give the peak intensity at zero stress and q is a factor of 8.2x10 -3 Mpa-1. The term Cexp(-rx) in Eq. (3) is an exponential decrease of the FE peak intensity with stress after 55 NPa stress, where C is another constant and r is another decay factor of 7.3x10 -3 HPa -I. The decrease of FE luminescence with stress is not clear. We are speculating some probable reasons: (1) the capture rate of a free e l e c t r o n and a free hole to form an e x c i t o n may p o s s i b l y d e c r e a s e due t o t h e s i m p l i f i c a t i o n of band s t r u c t u r e , (2) the binding energy of excztons may decrease with stress due to the decrease in the d e n s i t y of states and the e f f e c t i v e mass of e l e c t r o n s and holes, (3) the generation rate of the f r e e electron and hole may decrease with stress, and (4) the non-radiative Auger recombination may enhance with stress. The exciton binding energy in Si at 2 K is 14.7 meV at zero stress.11 We have observed the i n t e n s i t y of the S line at 67, 112 and 180 MPa stresses as a function of e x c i t a t i o n l n t e n s ~ z y a t d delay time of 2.0 ~ s as shown in Fig.3. The maximum intensity of e x c i t a t i o n is 1MW. The S peak i n t e n s i t y becomes stronger with stress while the FE peak i n tensity d e c r e a s e s . The t h r e s h o l d e x c i t a t i o n power to o b s e r v e the S l i n e i n c r e a s e s w i t h stress. This we can see by e x t r a p o l a t i o n to the lower e x c i t a t i o n power as shown in F i g . 3 . At zero stress the l i f e t i m e of FE i s 0.97 p s which agrees with other authors' values. With increasing s t r e s s the l i f e t i m e of FE remains almost c o n s t a n t . The l i f e t i m e of the S l i n e , on the o t h e r hand, remarkably decreases from 1.32 p s at 67 HPa to 0.58 # s at 180 HPa.

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Fig.3. The r e l a t i o n of ' S ' peak i n t e n s i t y w i t h the e x c i t a t i o n power in t i m e - r e s o l v e d measurements at a delay time of 2.0 # s . The peak i n tensity i n c r e a s e s w i t h s t r e s s and becomes saturated at high excitation p o w e r . The t h r e s h o l d e x c i t a t i o n power to observe the 'S' peak seems to increase with stress.

Still we have no clear idea about the S peak. The splitting of the S peak from the FE peak with stress is comparable with the splitting of the valence bands, = = ± I / 2 and mj= ± 3/2, at k=0.12, 13 At 100 H~a, the splitting of valence bands is 4.95 meV (Ref.12) at ?7 K and the splitting of the S peak from the FE peak zs 5.6 meV at 2 K. So we are speculating thls peak to be the r e c o m b i n a t i o n of the cold electron and the light hole in the hot exczton. But the question is why holes can populate so much in the higher energy subband (mj = ± 3 / 2 ) of the valence band with stress. No doubt holes should have a tendency to populate in the lower energy subband (mj = ±I/2) of the valence band. Some authors have observed a similar type peak in III-V compounds under high excitation.14, 15 They explain it by the radiative recombination of Auger-excited holes In the spht-off valence band with free or shallowly bound conductionband electrons. Our observations also suggest that in silicon the Auger-excited holes in the stress split-off valence band may enhance their p o p u l a t i o n with stress. The special role of uniaxzal stress may thus find multzfold utility in non-equilibrium carrier kinetics studies zn semiconductors.

Acknowledgements- T. Ohyama and T. Tomaru are acknowledged f o r t h e i r valuable experimental assistance. The a u t h o r s a r e g r a t e f u l t o M. Takeshima f o r discussions.

References

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3. V.D.Kulakovskzz, Soy. Phys. S o l i d State, 20, 802(1978). 4. V.D.Kulakovskzz,imofeev,and V.H.Edel'shtezn, Soy. Phys. JETP, 47, 193(1978).

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5. P.L.Gourley, and J.P.Wolfe, Phys. Rev.B 24,5970(1981). 6. J.C.Henssl, and G.Feher, Phys. Rev. 129, 1041(1963). 7. M.Tajima, Appl. Phys. Lett. 32, 719(1978). 8. M.L.W.Thewalt, and J.A.Rostworoeski, Can. J. Phys.,5_]_,1898 (19?9). 9. A.D.Zdetsis, CheJ. Phys. 40, 345(1979). lO.J.Wagner, A.Forchel, W.Scheid, and R.Sauer, Solid State comBun. 42, 275(1982).

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ll.T.M.Rice, Solid State Physics. V01.32, edited by H.Ehrenreich, F.Seitz, and D.Turnbull (Academic Press, N.Y. 1977) P. 11. 12.Lucien D.Laude, Fred 8.Pollak, and H.Cardona, Phys. Rev.8,~,2623(1971). 13.J.Wagner, A.Forchol, and R.Sauer,'Solid State Commun. 38, 991(1981) 14.G.Benz and R.Conradt, Phys. Rsv. BI6, 843(1977). 15.M.Takeshima, Butsuri 37, 913(1982) (in Japanese).