The luminescence of the excitonic molecules in uniaxially stressed Ge

Journal of Luminescence 24/25 (1981) 393-396 North -Holland Publishing Company

393

THE LUIiflNESCENCE OF TIlE EXCITONIC MOLECULES IN UNIAXIALLY STRESSED GE I.V.Kukushkin, V.D.Kulakovskii ~nd V.B.Timofeev Institute of Solid State Physics Academy of Sciences of the USSR 142432 Chernogolovka USSR

In the emission spectra of uniaxially compressed Ge the excitonic molecules (EM) have been discovered with the binding energy ~O,3 meV. The EM destroy under a magnetic field aligned spins of electrons and hole in free excitons (FE). The spin aligned FE

gas has been found to demonstrate the quantum statistical behavior. 1, EM in Ge are analogous of the positronium ones and due to that have a very small binding energy L~ 4—’O.1R (H is the excitonic Ryd— berg). As far as the binding energy of the electron—hole pairs in the electron—hole liquid (EHL) is significantly higher (~—O.5 H) the p~’tial fraction of EM is turned out extremely low even near the gas — EHL phase boundary. It’ a known the EHL binding energy strongly decreases with the lifting the valence and conduction band degeneracy (for example with use of an uniaxial stress of crystals)

where—as that of EM d.oes not. Recently Kukushkin et al. (1980) have found that the EM and EHL binding energies become comparable in pure Ge crystals highly compressed along the direction close to the <100> axis (Ge<—lOO>). Under conditions the densities FE 11N in a gas phasesuch become comparable as well at ofsufficiently flFE andlow EM temperatures and high excitation levels. The EM radiative decay in Ge being an indirect process is accompanied by the creation of photon, phonon and FE. It is revealed in the emission spectra by appearance of the new well resolved line H (Figure 1). The spectra were obtained under dc excitation with use

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9~’~

ICE

M

of an 4 Wt YAG laser. Fig.l. The behaviour of

FE

the FE and EM emission spectra of the pure

Lret un

stressed Ge <~l0O>( Pou 250 MPa) on the tempera-

for the curture; dc 2excitation,w = ves to 3 and 5 W/cin2 = 25 1W/cm for the curve 14• TFE = = 1.9K, 2.4K and 3K for the curves 1 to3 , respectively. The inset

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9 the d~pendence of

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~1

lnfT /2 IM/IFE] on used for determination

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of the EM binding energy.

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The halfwidth of the H-line is of order ~R even at T—.O because the recoil exciton takes away some kinetic energy. Here in and H are reduced and translational FE masses, respectively. Besides the line shape analysis the molecular origin of the H—line is confirmed by its temperature dependence (Fig.l), square dependence of its intensity on the FE one and its behavior under condition of the impact ionization in an electric field. (Kukushkin et al. (1980)). The most reliable experimental method of the EM binding energy determination in indirect gap semiconductors with a long FE life time is the thermodynamic one based on Saha equation. It follows that

~-‘ T_3/2n~~expL~/kT 0.06 value The ratio meV IM/IFE or~O.lR.This ~Nfound (see Fig.l) from theis temperature value turned is approximately out in dependence Ge <—100> threeof times equal the intensity to O.27~ higher than the use between of a variational method. It’s possible one thatcalculated the pair with interaction FE via deformation phonons slightly modifies the EM stability.

It is interesting to compare the shape of EM emission lines in unia— xially compressed Si and Ge in the dimensionless energy scale (in units of corresponding R) without use of any adjustable parameters. ________________________ Fig.2 illustrates the fitting of the emission spectra of FE and EM for Si — Ge<(r,/6 -o--S, and Ge recorded at the same ratios T=1,5~K T~?K IN/ICE and kT/R. The coincidance of

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—~

2

FE

~

these spectra indicates the insensiti— vity of the H-line shape to the ener— gy spectrum anisotropy difference. 2. Due to the small binding energy EM are a convenient model for investiga— tions of molecular properties in a magnetic field H. So both the paramag— netic

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and diamagnetic

shift

ene—

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q25

the paramagnetic

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split

rgies for FE become comparable with at H=l—2T. Under such conditions the EM stability becomes doubtfull. Note, term should be taken

into account only if the spin relaxa— tion time V 5j5 shorter than the FE life time’Z~g. Therefore it is not essen— tial in the case of the stressed Si <100>, where ‘C~>2~ . Kulakovskii et al. (1979) have found in the investi—

‘Rexc

Fig.2. The fitting of the emission spectra for FE and EM in pure Si and Ge recorded at the same ra— tios IN/IFS and kT/R. Si — pulsed (10 nsec) 2, laser, W’-~ Cu — vapour Ge — do YAG—laser, W— 310~ W/cm 25 W/cm2.

gation of EM in Si as well that the diamagnetic term very weekly disturbs the EM stability dispite their large ‘~C~<’~~ the influen— size. In. The the Fig.3 case ofshows Ge unlike Si ce of a magnetic field on the EM sta— bility in Ge <~—lOO>. It’s seen that the H line intensity drops with an

growth of H and becomes negligible at H>1.2T whereas that of the FE line increases. The observed destru— ction of EM Art Ge under such a small H due to the simultaneous contribution of both the diamagnetic and paramagnetic terms. Indeed, in Ge n in the excited spin states strongly decreases when the paramagnetic

splittings

g~ 8)’1H become more than kT. (g~ are g—

1. 1. Kiskusltkin t’t at / Excitouic too lecult’s in un/axial/v stressed Ge

395

factors electron (hole) and Jt~isBohrofmagneton). This imme—

FE

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diately leads to the destroying of EM in the case g~~-4 HI> ~ since the spin aligne’d excitons cannot form the bound molecular state. This fact is well known from the calculations of the hydrogen molecule stability.

2

T=1,5K

M

2

3. Thus in Ge <—-100> at H

= 2~4T there is an unique possibility for an optical excitation of the quasiequilibrium spin 1 aligned FE gas of the high den— 3 sity. It’s naturally to expect that such system in Ge should 4 or even demonstrate the than moreHebright qu— I antuin behavior ________________________ spin aligned hydrogen (Hf). So, 707 70~ 709 710 7/1 hu)meV do Boer parameter 11= ~~/~ 4 and Fig.3. The behavior of the EM emi— 0.55 for Hf. Here for 6 and are is equal to 0.14 He 6 65 ssion line in Ge <—100) under stag— the energy and radius of a pa— netic field. H=0,O.4T,O.8T and ii’ interaction. Determining ~ l.2T for the curves 1 to 4, respec— and 6 for FE by a simple scal— tively. ing of the hydrogen values one

-I F-

~

f_ast

FE obtaines the value for the ~ spin Note aligned that

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0,5 -

_____ ____________________________

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Pig.4. The LA—phonon assisted FE emission spectra recorded at the bath texnperatures2.l5K and 1.75K and different dQ excitation le— vels: W in W/czn~ are equal to 5 and 60; 4 and 40 for the curves 1 and 1’, 2 and 2’, respectively. The approximation of the FE line shape in terms of Boltzman and Bose—Einstein distributions are shown by squares and circles, respectively. The inset repre— sents the full spectra at 1.75K.

no is ~>0.45 gas—liquid expected (Nosanow, in phase the l977)~ system transition with Fig.4 the represents emission line the change shape of riseFEof the FE density. At with low nFE the line shape is in agg— reement with that calculated with use of Boltzman distribution of PE~I(E)—~’.exp(—E/kT) where E is counted off the low energy edge of the FE—line. With an increase of the excitation level at fixed bath temperature T 6 the FE—line narrows. This fact indicates the devia— tion of the FE distribution from the classical one and ne— cessity to take into account the quantum (boson) nature of FE. In the case of an ideal bo— so gas of FE its emission line shape is described by the exore— ssion I(E)—~f(E) where f(E~ = = ~xp (E+ JP4FCD/kT —lt~ is Bose— Einstein distributidi function, J~tisthe chemical potential (J~~Fe~O) of FE bound with their density as 23/2] ~ =[Dii

fr-.

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3’)c,

Isii/iishl,is,

si

(II

/Z5(

/i55Ii/(

/5555/55 51/55

1/? Il//fSLVfs/// S

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As it follows from these expres—

sions in the range of I~vn~<2kT the line FE narrows with the de—

crease of I±4FEI. allows to determine n~ This from fact the FE-li— ne shape analysis.

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-~

Fig.5 shows the experimental de— ~ ,

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.

-

~-T~2n~ pendencies of the FE line half width )~omits intensity (which

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JJ,T8=1,75K

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;

- -~

~

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~—

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is proportional to Tflr~) at two bath temperatures 6 =1.75K and 2.15K. Note that the temperature of a FE system TeE is slightly higher than that of bath even at the lowest used excitation level: T~:F=2,1K and 3.1K at T~=1.75K andbroadening 2.15K, respectively, The 11— ne at the highest ex-

citation level seems to be due to the increase of TCE It f ci— lows from the analysis of the narrowest FE line shape at both investigated temperatures that J°/~=—0.l9 meT. The limit for ~ is obviously associated with a FE condensation into EHL. The HIlL emission line L is well seen in the emission spectra at the highest excitation levels (see 3 at The T F6 FE =3.1K and 2.1K, inset at Fig.2l). densities are respectively. equal to n~6=2.8 i~’~and 1.2 lO’~ cuC It’s naturally to suppoze that the so dense FE gas is not ideal. Indeed, the dimensionless parameter nu~characterizing the deviation of the system from the ideal one reaches in our case -~ 0.1 even at the choice of the scattering length l1~=2iJ 6’ , where Lig is Bohr radius of FE. Thus, the value nG~ for FE system under consi4. The emission line of nonideal FE strogas deration is only two times less than that in the case of the is be broadenen. It’s possible this is the main reason nglyexpected nonidealto liquid of He why our attempts to receive the FE line half—width smaller than 3K were unsuccessfull although we can further decrease the liquid chemical potential by use of the higher deformations (up to 500 MPa). Up to now there is no theretical discription of the nonideal FE gas line shape. However f or the first approximation one can assume that the minimal observe~)‘ is equal to the energy parameter of the nonideal gas fl=4iiti c~ 9n/M. It is interesting to note that under such assumption it has been found that sZ~is indeed equal to&sg Pig.5. The dependence of the FE line half—width on its intensity, Dots are experimental points, dashed lines represent the cal— culated dependencies for the ideal FE Bose—gas. The dot—dash— ed lines show ~ in the case of Boltzman distribution under con— dit ion TFG =T~’.

Shortly, the attractive interaction between spin aligned FE at large distances seems to be sufficient only to form very we&kly bound EHL rather than EM. Due to repulsive short range interaction such FE gas of a high density demonstrates the quantum behavior in accordance with Bose—Einstein statistic. Thus the FE system under consideration is a new nontrivial quantum object. ~akushkin I.V. ,V.D.KulaHovskii,V.B.Timofeev (l980)Pisma ZhETF~,3O4. Kulakovskii V.D.,A.V.Malyavkin,Y.B.Timofeev (1979) ZhETF ~, 752. Nosanow L.N.(1977) Quantum Fluids and Solids eds S,B.Triclcey, E.D.Adamns,J.W.Dufty, Plenum Press, N.Y.—London, p.279.