(1972) zpl temp dep (jpcs) 5 (1972) 1265

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    J. Phys. C : Solid State Phys. , Vol.5, 1972. Print ed in G reat Britain

    The temperature dependence of vibronic spectra inirradiated silicon

    A P G H A R E , G DAVIES and A T C O L L I N SWhea tstone Physics Laboratory, Kings College, Strand. Londo n W C2

    MS received 3 February 1972

    Abstract. Crucible grown and high purity floating zone silicon specimens have been irradiatedat room temperature with y rays. High resolution cathodoluminescence spectra of thevibronic b and s with zero p ho no n lines at 0.717, 0,724, 0.790, 0.795, 0.898 and 0,969 eVare given. The widths a nd energies of these lines, and the intensities of the 0.790, 0.795 and0,969 eV lines relative to the to tal intensities of their associated bands, are given in thetemperature range 25 to 75K . These data are discussed in terms of the theory of linear andquadratic electron-phonon coupling in the ad iabatic approximation, using Debye spectraof coupled phonons and, for the 0,790,0,795and 0,969 eV lines, densities of coupled ph ono nsderived from the emission band shapes. The theory gives a selfconsistency between thespectral band shapes and the widths and energiesof the zero phonon lines, but does notsatisfactorily fit the temperature dependence of the intensitiesof the zero phonon lines.It is not know n w hether the failure of the theory is due to a Jahn-Teller effect(no absorptionat the centres has been d etected),or to the coupling by the electron-phonon interaction ofelectronic states whose energies are not greatly separated compared with the phononenergies involved

    1. Introduction

    Luminescence spectra fromy, neu tron and electron irradiated silicon have been reportedby several work ers. After irradiation, all specimens will ap pa ren tly show a luminescenceba nd w ith a zero ph ono n line at 0.969 eV (Yukhnevitch 1965, Yukhnevitch and T kachev1966). Crucible grown specimens also show luminescence from a b and with zero ph ononlines at 0.790 and 0.795 eV (Spry and Compton 1965, Yukhnevitchet a1 1967). Thedependence of this system on the crucible grown origin of the specimens suggests theoptical centre involved is at least partly d ue to o xygen. This is confirmed by the annea lingbehaviour of the band, which closely follows that of theK or G-15 EP R spectrum(Joh nson and C om pto n 1971, Almeleh a nd Goldstein 1966). The annealing behaviourof the 0.969 eV band is similar to th at of the divacancy (John son an d C om pto n 1971,W atkins and Corbe tt 1965).

    In this paper we report high resolution cathodoluminescence spectra from cruciblegrown silicon, and from floating zone purified silicon, after room temperaturey irradia-tion. The emission band shapes and their temp eratu re dependence ar e repo rted over the

    range 25 to 75 K. These results are discussed in terms of the theory of vibronic spectrain the adiabatic approxim ation.

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    1266 A P G Hare. G Davies and A T Collins

    2. Experimental

    Before irradiation, the crucible grown silicon used in this work has a resistivity of0.5 R m and contains abou t 2 x loz4 m - 3 oxygen impurities, whereas the floating zonepurified silicon has a resistivity of 8R m and contains less than 10 m-3 oxygen.Rad iation dam age centres were created by exposing the samples to a total dose oflo8 ra dof y radiation in the spent fuel pond at AERE Harwell. The luminescence was excited bya 50kV electron beam with a mean b eam current of 50 pA . The luminescence wascollected from the excited face of the specimen an d ana lysed by a Spex 1702 m on o-chr om ator fitted with a 600 groove mm - grating blazed at 1.6 pm, and a P bS detectorcooled to solid CO, temperature. The electron beam was electronically chopped atabo ut 70 Hz and the alternating signal at the P bS detector was recovered using phasesensitive detection. Chopping the electron beam has two important advantages overchop ping the luminescence. Firstly the stray radiation from the heated tungsten filamentof the electron gun, which has a maximum infrared emission in the wavelength region

    being studied, does not give rise to an alternating signal at the detector. Secondly, fora given mean photon flux entering the spectrometer the heating of the sample by theelectron beam is halved.

    The temperature of the sample was controlled over the range 24to 100 K using anAir Pro du cts AC-3L-110 Cryotip refrigerator w ith hydrogen as working gas, andover the range 5 to 30 K using a liquid helium cryostat fitted with a drip-feed valve.The magnitude of the beam heating was determined by mounting a thermocoupledirectly on one sample and measuring the difference between the sample and mounttemperatures as a function of beam current.

    The response function of the spectrometer and detector was determined by recordingthe spectrum from a strip tungsten filament lamp. Long-wavelength-pass filters wereused to eliminate unwanted orders of diffraction. The temperature of the filament wasmeasured with an optical pyrometer and the black body spectrum calculated afterapplying the correction factor for tungsten (Ro berts an d M iller 1960). Allowance w asalso made for the transmission characteristics of the filters which were measured on aspectro photom eter. T he experimental emission spe ctra were all corrected for the responseof the measuring system and transformed from a linear wavelength to a linear energyscale.

    3. Results and discussion

    3.1. T h e emission spectra

    Figure 1 shows a typical emission obtained at 26K from a sample of crucible grown,irradiated silicon. After irradiation the intrinsic luminescence (Deanet a1 1967) is onlyvery weakly observed. It does no t interfere with the present m easure me nt, The 0.969 eVzero pho non line is at the head of a ba nd stretching to 0.8 eV. Th e shar p structure between0.969 eV an d 0.905 eV will be shown to arise from one phonon vibronic transitionsassociated w ith the 0.969 eV line. Th e sh arp line at 0.897 eV is ano the r zero ph on on line,and not a localized mode replica of the 0.969eV line. This is seen on studying thetemperature dependence of the two lines( 53.2), for a ha rmo nic local mod e will give anemission line of the same width as the zero phonon line. At low temperatures the widthof the 0.897 eV line is seen to be gre ater tha n t hat of the 0.969 eV line. If a local m ode

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    Tem pera ture dependence of vibronic spectra in irradiated silicon 1267

    pho non is involved it must, therefore, be an har mo nic, so that it may be inhomogeneou slybroadened thro ugh coupling to lattice strains and homogeneously broadened by lifetimebroadening. The lifetime broadening will increase with temperature as alternativechannels for the decay of the local mode are created by the excitation of lattice modes.

    I I

    0.65 0.75 0.85 0.95Photon energy C e V )

    Figure 1. Cathodoluminescence spectrum from; irradiated crucible grown silicon. taken at26 K. Inset is an electron ic energy level diagra m for the lower energy em ission (discussed in5 3.1).

    In practice, the width of the 0,897eV line increases slightly less than the 0.969 eV line(figure2), showing that bo th a re zero ph on on lines. Spectral features at 0.88,0.86,0.8.5 eVare o ne p ho no n replicas of the 0.897 eV line (cf the structure below the 0.969 eV line).The emission between 0.969 and0.80 eV is thus mainly composed of two vibronic bandswith zero p ho no n lines at 0.897 an d 0.969 eV. These lines have always been observedin the same ratio of 1: 11, and so presumably occur at the same centre. Two further linesa t 0.900 an d 0.825 eV do n ot fit into this sche me.

    The pair of zero pho no n lines at 0.790,0.795 eV thermalize in a way closely describableby the Boltzmann relation

    where I , , I, are the intensities of the 0.795, 0.790 eV lines. Go od fits are o btained withE = 4 m e V, r = 1 as observed by Jones and Compton (1971),or with the spectro-scopically observed E = 5.2meV and r rv 0.5. At 24K the 0.790eV line is dominant.The structure between0.80 and 0.72 eV is therefore predominantly due to one ph ono n

    vibronic transitions associated with this line. Further lines are seen at 0.717, 0.722 and0.724 eV, apparently always with the 0.790, 0.795 eV d oublet. The stronge st, at 0.717 eV,

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    1268 A P G Hare, G Davies and A T Collins

    and the sec ond stronge st, at 0.724 eV, have a separa tion of 7.1 meV, which is differentfrom the 0.790, 0.795 eV splitting (5.2 meV). Th e in tensity ratio of the 0.717, 0.724 eVlines is Z,,,/Z,,, = 2.7 It 0.1 at 25 K, and is relatively temp erature indepe nden t,indicating that the splitting occurs in the final states of the transitions. These facts aresufficient to show that the 0.717, 0.724 eV lines are not local mode replicas of the 0.790,

    0.795 eV lines .A weak line is observed at 0 .722 eV, 5.2 meV from the 0.717 eV line. These

    I I ,

    0 50 100 0 50 100Temperature lo

    Figure 2. Measured and calculated full widths at half heights of zero phonon lines at( a ) x 0.790, 0 0,795 eV, ( b ) 0,969 eV, (e) 0.898 eV, (6, 0 0,717, x 0,724 eV. I n ( a ) and( b ) the lines a re calculated using thep ( w ) shown in figure 6 and Debye spectra with cut offenergies 22 and 15 meV respectively give closely simila r lines. In(c) and (4 he calculationuses Debye spectra with cut off energies of16 meV.

    figures are consistent with an energy level scheme as in the inset of figure1. The sharp0.759 eV line is a zero ph on on line of a no the r centre: on ann ealing its strength increaseswhile th e emission show n in figure 1 disapp ears.

    The emission between 0.80 and 0.61 eV is thus mainly associated with two pairs ofzero p ho no n lines at 0.790, 0.795 eV and 0.717, 0.724 eV. This emission has not beenobserved in the floating zone purified silicon, which further substantiates the belief thatit originates from an oxygen containing complex (Jo hns on and Co mp ton 1971).

    3.2. Tempera ture effects

    The widths an d peak energies of the prom inent zero ph on on lines are shown as a functionof temperature in figures 2 and3. The full lines through the experimental points have

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    Tempe rature dependence of vibronic spectra in irradiated silicon 1269

    Temperature ( K )

    Figure 3. Measured and calculated energies of the zero phonon lines at(a ) 0.790 and0.795 eV, (b )0.969 eV, (c) 0.898 eV, (40 .7 17 and 0,724 eV. In(a ) and (b) he lines are calcu-lated using the p(w) shown in figure 6, and Debye sp ectra with cutoff energies of 22 meV

    an d 15 meV give closely similar lines. In(c) an d (4 he calculation uses Debye spe ctra withcut off energies of 16 meV.

    c,

    Figure 4. Measured a nd calculated ratios of the integrated transition p robabilities of thezero phonon lines relative to their total associated band probabilities for(a ) the 0.790,0.795 eV b and, (b ) he 0.969 eV b and . In( a ) th e su m of the 0,7 90 and 0 .795 eV lines has beenused. The accurately fitting lines are calculated with Debye spectra with cut off energies22 and 15 meV respectively. Th e badly fitting lines are calculated from thep(w) in figure 6.

    L11

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    1270 A P G Hare, G Davies and A T Collins

    been calculated as described in0 3.4. The total intensities of the emission bands decreasereversibly with increasing tem per atur e above 25K. By 100 K the in tegrated intensitiesof the ban ds associa ted with the 0,969 eV an d 0.790, 0.795 eV lines are respectively4 %and 2% of their values at 25 K . In ad diti on , the fraction of the em ission in the zerophonon lines decreases as shown in figure4. Previously, Jones and Compton (1971)have rep orted the temp erature depen denc e of the width of the 0.790 an d 0.969 eV lines.Ou r da ta are in agreement.

    3.3. Discussion of th e low temperature spectral shapes

    The shap es of the spec tra indicate that the electronic orb itals involved a t the centres arelocalized within a very few ato m ic distances of the centres. This is seen on com parisonwith the bound exciton recombination luminescence from neu trat dono rs and acceptorsin silicon (Dean et a1 1967). The re the em ission occursin the photon range -1.0 to- .2 eV, with the involvement of transverse optic phonons very similar to those thatconserve momentum in intrinsic emission. These bound excitons may be pictured as ahole at the valence band maximum and an electron at the conduction band minima atk = (0.82,0,0) (D um ke 1960). Although the 0.969, and 0.790 eV transitions do couple totransverse acoustic pho no ns of this wavevector (energy 19 meV : Solbrig 1970), there isclearly no sim ple selection of pho no ns occ urring (figure1).It is ap pro pr iate , therefore, todiscuss the shape of the spectra in terms of a point defect, quasimolecular, approach,rather than through perturbed band states.

    The existence of vibronic, as opposed to electronic, spectra is due to electron-phononcoupling. The exact shape of the spectrum is determined by the nature of the coupling.Th us an electron-phonon interaction tha t is linear in the lattice displacement gives adifferent spectral shape from a strong qu ad ra tic interaction (eg Kiel 1965), while linearcoupling itself may be of totally symm etric form (eg Ma rad ud in 1966) or give Jahn-Tellerdistortions (eg Longuet-Higginset a1 1958).

    Absorption lines at 0.790,0*795and 0 96 9 eV have not been observed in this work, orin any other, so that the na ture of the coupling cannot be determined by comparing theabsorption and emission spectra. Instead we note that the widths of the zero phononlines (figure 2) increase by typically2 meV between0 and 75 K. This is the sam e magnitude(relative to the Ra man energy) as observed over the sa me tempe rature range (relative tothe D ebye temperature) at vibronic centres in diam ond (Davies 1970 and unpublishedcalculations), for which the quadratic coupling terms are small.

    We canno t exclude the existence of a Jahn-Teller coupling, although the emission

    spectra do not show double peaked phonon assisted bands. In the remainder of thispape r we will investigate how closely the d at a may be described using the theories basedon the adiabatic a pproximation (eg M ara dud in 1966). On e reason for doing this is thatat both the centres providing the luminescencein figure 1 there are electronic levelswhose energy separation is not large com pared with the energies of the coupled pho nons.Th us the 0.969 and 0.898 eV lines have a se paration only 9 % larger tha n the R ama nenergy of silicon (D olling an d Cowley 1966, Solbrig 1970), andso, if the initial state ofthe transitions is the same, the final states have this separation. The inset in figure1shows a very similar spacing between some of the levels. The coupling of the nearbyelectronic states by the electron-phonon interaction break s down the validity of theadiabatic approximation, and although no detailed theory of the effect exists, we mayexpect that the standa rd adiabatic approximation would be on the point of breakdownwhen the electronic states have a separation of just larger than the phonon energies

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    Temperature dependenceof vibronic spectra in irra diated silicon 1271

    involved. These emission band s may, therefore, provide an example of the beh aviourofvibronic bands on the point of breakdown of the adiabatic approximation by this effect.

    Using the adiabatic approximation it is possibleto write analytical expressions forthe shap e of the spectrum (eg Pryce 1965, M arad udin 1966). Th e transition proba bilityfor the transition at a frequencyv is

    CO

    W V )= 1 y(v) (1)n = O

    where the transition probability of an n-fold phonon process Wn(v)has a relative inte-grated strength

    S"dv Wn(v)= ex p ( - S ) .-c n!

    S , the Huang -Rhys factor, may be experimentally determined from the transitionprobability of the zero ph ono n line and tha t of the full band :

    The transition probability of an n phonon process is the (n - 1)th convolution of th e

    00

    0.60 0.70 0.80Photon energy (eV)

    Figure 5. (a) xperimental spectrum m easured at 26K of the 0.969 eV and 0.898 eV bands(dotted curve). Subtraction of the assumed0498 eV band leaves the broken curve. Thecalculated fit is shown by the full curve and the emission involving one phonon by thechain curve. Inset is the difference of the me asured (d otted curv e) an d calculated (full curve)spectra. (b ) Spec trum of the 0.790, 0.795 eV a nd 0.717, 0.724 eV bands as meas ured a t24 K (dotted curve). The arro wed feature at 0.759 eV is an extra zero pho non line. The cal-culated spectrum is shown by the full curve. Inset is the difference of the measured andcalculated spectra.

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    1272 A P G Hare, G Davies and A T Collins

    one ph onon process Wl(v).Thus W,(v) and S define the spectrum. If a , W,(v) s guessedand S measured, a spectrum may be calculated and compared with experiment. Suc-cessive iterations enable a suitableWl(v) o be obtained tha t fits the spectrum . The resultsof the calculation are presented here in terms ofa weighted frequency distributionp ( w )which is related to W,(v) by (Maradudin 1966):

    P ( V - vo)( v - v 0 l 2

    W,(v) constant x exp ( - S ) {n(v - vo) + 13 (4)

    where

    and v o is the zero ph onon frequency.Before comp aring the calculated and experimental spectra it is necessary to allow for

    the effects of crystal perturbations, which broaden the observed spectrum. This, and

    (to a good approx imation) the thermal b roadening of the spectrum discussed below,may be allowed for by taking a convolutionof the calculated spectrum w ith the observedzero phonon line.

    Taking first the band associated with the 0.969 eV line, we note that because the0.898 eV line has an integrated intensity 9% of the 0.969 eV line it makes an appreciablecontribution to the emission below 0.90 eV.If it is assumed that the 0.898 eV line hasexactly the sam e pho non coupling a s the 0.969 eV line, subtracting the assumed 0.898 eVcontribution gives the approx imate shape to the 0.969 eV band shown in figure5a . The

    5

    Figure 6 . Densities of coupled phonon states for the0,969 eV band (full curve) and the0.790, 0,795 eV band (broken curve) compared with the phonon energy times the perfectlattice density of phono n states (chain curve).

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    Temperature dependence of vibronic spectra in irradiated silicon 1273

    Huang-Rhys factor for the0.969 eV line is then found to be S 2.06 at 26 K. Afterperforming the iterative computations described above, the experimental spectrum offigure 5a may be fitted quite well, as shown by the solid line, using the derivedp(w)shown in figure6.

    Unfortunately the0.717 eV line has an obviously different pho no n coupling from the0.790 eV line (figure1).The calculated fit to the band (figure5b) is selfconsistent, in thatthe Huang-Rhys factor used (S - 2.35) in calculating the spectral shape is also thatwhich is obtained from equation3 using the area enclosed under the calculated curvein the numerator of the right hand side of equation3. However, the p(w)used in thecalculation (figure6 ) cannot be claimed to be unique, alth oug h the energies of the peaksin th e p(w)must be correct, In performing the calculation, both linesin the 0*790,0.795eVdoublet have been assumed to have the same phonon couplingso that the observedspec trum is the sum of two shifted bands of different strengths.

    3.4. Analysis of the tem perature dependence

    Tem perature changes in the emission spectra may arise through electronic or vibrationaleffects. O ne simple electronic effect is the ch ange in charge state of a cen tre, due to itsionization, for example. Another example is the redistribution of electrons among theenergy levels of the centre. Both exam ples may result in the app earan ce of new ba nds orthe quenching of the luminescence. Electronic temperature effects are thus generallycharacterized by changes in the emission intensity. The rapid fall-off in emission from25 to 100 K (53.2) is, therefore, prob ably electronic in origin, but since both the0.969 and0.790, 0.795 eV bands fall off at comparative rates it is unlikely that the cause is eitherof the examples ab ove, since this wo uld require very similar electronic energy band s a tthese two d issimilar centres. It is possible th at othe r defects in the crystals are involved,but detailed studies of the decrease in emission have not been made.

    Th e temperature effects of electron-phonon coupling show up pred ominan tly in thespectral distrib ution of the emission rather than its intensity-linear an d qu ad rat icelectron-phonon coupling leave the integrated transition probability of a band un-changed (Maradudin1966). The tempera ture depend ence of the Huang-Rhys factor is

    and is particularly noticeable by a weakening of the zero phonon line. Using standardassump tions concerning the magnitude of the qua dra tic electron-phonon coupling

    relative to the linear coupling, the widthr of a zero ph on on line may be written in termsof p(w)as

    r = a , dw{p(w)}2n(w){n(w)l} ( 6 )sTh e energy of the zero pho no n line changes by

    Q = a2 dw p(w){n(w)+ t }J (7 )and

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    1274 A P G Hare, G Davies and A T Collins

    In a dditio n to these effects we must allow for the effects of crystal inhomo geneities andlattice thermal e xpansion . Usually the width o f a zero phon on line is dom inated , at lowtemperature (whenr --t 0),by crystal inhomo geneities. At finite temperature, the observedlineshape is the convolution of the inhomogeneous broadening (which we assume istemperature indepen dent) and the lorentzian phon on broadening (equation6). The

    low tempera ture lineshapes in the present specimens are of 'bi-lorentzian' form:I (v) = { b + ( V - , ) ' > - ~

    The convolution of this with a lorentzian has been given analytically (Davies1970).Using this tabulation, equation6 may be fitted to the data. The rmal exp ansion gives anenergy shift to the bands. The shift cannot be calculated since the hydrostatic straincoupling of the bands is unknown, but through the Gruneisen law it is closely propor-tional to Q equation 7 Imbusch et a1 1964). The temperature range of the present dataonly covers the range where the expansion coefficientis increasingly negative (Dollingand Cowley 1966). he measured shifts of all the zero phonon lines are proportional tothe enthalpy of silicon, calculated from the d at a of Pea rlman an d K eesom(1952).

    Fits of equation s5,6,7 o the d at a are given in figures2,3,4 sing the p ( w )of figure 6and also using Debye spectra(p(w) cc w 3 , aradudin 1966). The fits to the widths andenergies of the 0.790, .795 and 0.969 V lines using the p(w) derived from the em issionspectra are very good. However the fits to the intensities of the zero phonon lines arepoo r (figure4). In making the fit, equ ations3 and 5 have been written asI, = I ,k exp ( - S) ,where I, and I, are the integrated transition probabilities of the zero phonon lines andthe full band. The co nstant in equation5 for S has been fixed using the m easured valuesat low temperature. The constantk has been treated as a best fit pa ram ete r: ideally itwould have the valuek = 1.) The intensities of the zero phonon lines may be closelydescribed by Deb ye spectra forp(w),with maximum energies of -20 meV. This energy

    is a very plausible value, considering the energy of the m ajor pe ak in thep ( w )of figure 6.However, in this case the D ebye appro xim ation is misleadingly accurate, and evidentlyits use in parameterizing the temperature dependence of zero phonon lines can hide aninadequacy in the theory.

    The success in fitting the widths a nd shifts, but not the intensities, of the zero ph ono nlines is probably due to the weighting ofr an d R (equations 6 and 7) to a smallrange of low values ofw. In contrast, S (equation 5) depends on the entire spectrum andconsequ ently may be far more affected by failureof the theory. It is interesting to noteth at a less detailed application of the same theory as used here to theF+ centre in Ca O(which shows a Jahn-Teller effect) also gives goo d fits to the width and energy, but notintensity, of the zero ph ono n line (Escribe and Hug hes1971).

    Using the p ( w ) obtained from the low temperature spectra, it should be possible tocalculate the shape of the spectra at high temperature. This would be done (to a goodapproxim ation a t not to o high a temperature) by simply using equation4 o obtain thepart of the spectrum involving the emission of one phonon,W,(v), and calculating thecorresponding part of the spectrum involving the absorption of a phonon from thelattice :

    I "'",, vo)l,abS(v)= W1(2v, - v) expThe total spectrum would then be generated using equations1 and 2, with the appro pri-

    ate high temperatu re value ofS . However, we have seen that the tem perature dependenceof S cannot be calculated from p(w)using the present theory, and so a fully selfconsistent

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    Temperature dependence of vibronic spectra in irradia ted silicon 1275

    fit to the spectra cann ot be ob tained.On a practical level, the fact that the vibronic ban dsoverlap creates further difficulties. However, if we again use the assumptions that the0.898 eV line has exactly the same shapeof ph on on assisted ban d as the 0.969 eV line,and that these bands always have relative strengths of1 : 1 1 , then the calculated hightemp erature spectra of figure7 bare obtained when themeasured values ofS are employed.The smoothing out of the features in the band, and the weakening of the0.95 eV peak,as the temp erature increases is similar to th at found experimentally (figure7a) .Howevera sha rp peak at0.933 eV (arrow ed in figure7 a ) s not reprod uced in the calculation. Thispeak has not been studied-it is possibly an oth er weak zero phono n line (the80Kspectrum in figure7 a requiring - 5 times higher gain than the25 K spectrum).

    Figure 7. (a) The m easured cathodoluminescence between 0.84 and 1.0 eV a t25 , 5580 K. ( b ) The spectra calculated at 25 , 55 and 80 K using the measured values of Sassuming the0.898 eV line has the same shape of phon on assisted band as the0.969 eVThe feature at 0.933 eV, arrowed in (a), is not reproduced in the calculation.

    an dandline.

    Finally, in figure 6 the calculatedp ( w )are compared with the p(w) that would resultfrom unweighted coupling of the transitions to all the lattice phonons. It is interestingto note that a peak at42 meV app ears in the 0.790 eV coup ling, and an inflexion occursat that energy in the 0.969eV coupling, corresponding to a sharp peak in the perfectcrystal density of phono n states (Dolling and Cowley 1966). This peak does no t derivefrom any m ajor symmetry direction (Solbrig1970).

    4. Summary

    Crucible grown and high purity floating zone purified silicon has been irradiated atroom temperature using y radiation. High resolution cathodoluminescence spectraof

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    1276 A P G Hare, G Davies and A T Collins

    the vibronic bands with zero ph on on lines at0.717,0.724,0.790,0.795,0498and 0.969 eVhave been given. The widths a nd energies of these lines, an d the intensities of the0.790,0.795 and 0.969 eV lines relative to the total intensities of their associated bands, havebeen given in the temp erature range25 to 75 K. An atte mp t to describe these da ta, usingthe simplest (adiaba tic app roxim ation ) theory of the band s is partly successful, but th eintensities of the zero ph ono n lines ca nn ot be fitted using the spectra of coupled p hon onsderived from the emission spectra. It is not yet known whether this failure is due to aJahn-Teller effect or to the co upling of electronic states whose separatio n is not m uchgreater tha n the energies of some of the ph on on s interacting with the transitions.

    Acknowledgments

    We wish to thank the Royal Society and the University of London Central ResearchFu nd for financial assistance, and CE Jones and E C Lightowlers for helpful discussions.One of us (APGH) is grateful to the SRC for a Research Studentship.

    Note added in proof: Recent measurements have confirmed that the peak at0.933 eV(figure 7a)does not occur at the same optical centre as the0.969 eV line-the ra tio of thestrengths of the lines is specimen dependent.

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    (Lon don: Oliver and Boyd)