spectroscopie de dÉfauts - luminescence ithe …spectroscopy, particularly luminescence, in the...

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SPECTROSCOPIE DE DÉFAUTS - LUMINESCENCEITHE ANALYSIS OF WIDE BAND GAP

SEMICONDUCTORS BY OPTICALSPECTROSCOPY

P. Dean

To cite this version:P. Dean. SPECTROSCOPIE DE DÉFAUTS - LUMINESCENCE ITHE ANALYSIS OF WIDE BANDGAP SEMICONDUCTORS BY OPTICAL SPECTROSCOPY. Journal de Physique Colloques, 1974,35 (C3), pp.C3-127-C3-143. �10.1051/jphyscol:1974319�. �jpa-00215567�

https://hal.archives-ouvertes.fr/jpa-00215567

https://hal.archives-ouvertes.fr

SPECTROSCOPIE DE DEFA UTS - LUMINESCENCE I.

THE ANALYSIS OF WIDE BAND GAP SEMICONDUCTORS BY OPTICAL SPECTROSCOPY

P. J. DEAN

Royal Radar Establishment, Malvern, Worcs, England

RCumB. - A la suite d'une brke recapitulation des nombreuses techniques optiques signifi- cative~ et de leurs avantages pour I'analyse des impuretes, le texte principal met I'accent sur la spectroscopie d'absorption et de luminescence. L'auteur examine les conditions requises pour la meilleure exploitation possible de la methode. L'anaIyse a basse tem+rature utilisant les cristaux semiconductcurs assez bien purifib nkssites par beaucoup de dispositifs electroniques modernes. L'analyse courante peut dire rapide et non destructrice et particulikrement appropriee a la detection et la reconnaissance (luminescence) ou a 1'Cvaluation quantitative (absorption) de certains types d'impuretes, souvent celles qui sont les plus interessantes dans les dispositifs Clectriques et optiques. Des exemples sont donnes, surtout pour Gap et GaAs, des nombreuses techniques possibles pour relier les caracteristiques importantes des spectres optiques aux diffkrents types d'impuretes donneurs, accepteurs et pieges isoelectroniques, et de leur extension a I'identification d'espkces chimiques.

Abstract. - Following a brief summary of the wide variety of relevant optical techniques and their advantages in impurity analysis, thc main text emphasises absorption and luminescence spectroscopy. Attention is given to the conditions required for greatest exploitation of the method, analysis at low temperatures using the relatively refined semiconducting crystals needed in many current electronic devices. Routine analyses can be swift and non-destructive, particularly suited to the detection and recognition (iuminescence) or the quantitative estimation (absorption) of certain types of impurity, often just the ones of greatest general interest in electrical and optical devices. Examples are given, mainly in Gap and GaAs, of the variety of techniques available to link key features in the optical spectra with the different classes of impurity, donors, acceptors and isoelectronic traps, and their extension to the identification of chemical species.

I. Introduction. - . Most semiconductor devices depend for their operation on the presence of the right impurities in correct positions in the crystal lattice. For convenience we can define the related impurity or defect-dominated properties as extrinsic. A variety of analytical techniques exist to determine the composition of solids, including atomic absorption and emission spectroscopy, mass spectroscopy, X-ray fluorescence, proton back scattering and activation analysis. Surfaces can be charac- terised by several specific techniques. These can typi- cally provide sensitivities

1 ppma , or 4-5 x l o t 6 atoms in 1 cm3

of a typical solid. Several of the techniques become very difficult when we seek the ubiquitous elements B, C, 0, Mg, Al, Si, S, Fe and Cu. Unfortunately, these elements are most likely to dominate the properties of refined material, they include many of the persis- tent, inadvertently present impurities. We are concerned here with a very important commercial field. Semiconductors and the devices made from them represent a world market currently estimated at - 20 billion per annum !

The demands on analysis depend very much on the device. In semiconductors, light emitting diodes

(LEDs) are formed from pn junctions with quite heavy doping to provide the desired high bulk conductivity, certainly in the 10'' cm-3 range and often 2 lo1* ~ r n - ~ , especially for the direct gap variety. One might then think that an analytical sensitivity of - 1 ppma is quite sufficient. However, the operation of these devices, particularly the indirect gap variety, depends upon the control of the impurity- induced recombination of minority carriers injected through the pn junction. For an efficient device, the carriers must recombine in a particular manner, through transitions at the advertently present recombination centre, the luminescence activator. Unfor- tunately, the available concentration of suitable centres is often quite low, particularly for centres with deep levels which produce light at energies well below the semiconductor band gap EB. Red G a p : Zn, 0 famps provide a good example; the maximum available concentration of the Zn,,-0, luminescence activator is - 1016 cm-3 [I]. Thus we need sensitivities of 5 0.2 ppma for the analytical control of such LEDs. Solid state microwave sources operating at 10 GHz require n-type material with carrier concentrations in the low lo1' cm-3 range, which can only be provided by advertent doping in the materials used, for example GaAs. The electron mobility must

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C3-128 P. J. DEAN

be high, so the compensation level should be low. Impurity control in solid state microwave amplifiers is still more stringent at a given operating frequency. As far as we know, the presence of shallow compensating acceptors as v~el! as deep trapping levels of any type is cnt~rely deleterious to the operation of these devices. We therefore need very good quality semiconductor material, whose properties must be defined through analysis at sensitivities ,$ 0.02 ppma (- lo1* cin-9).

it is natural to seek analysis of semiconductor material using the properties basic to the operation of the device itself. Right from the beginning, semiconductors were analysed through electrical measurements. As is well known, combination of measurements of the Hall effect and conductivity provides the concentration and mobility of the majority carriers. At an appropriate temperature, the concentration is essentially N,-N, in an n-type crystal and the mobility can be measured at a temperature where it is dominated by ionized impurity scattering.

Conveniently, 300 K is suficient for nearly complete ionization of the relevant shallow donors, ED 5 0.1 eV white the compensation level can be estimated from the impurity-limited mobility measured at 77 K. Use of the Brooks-Herring analysis of carrier scattering at ionized impurities in the derivation of the total concentration of ionized impurities from measurements of carrier mobility at 77 K have been discussed by Wolfe, Stillman and Dimmock [2] for n-type GaAs. While this information is very important, it is limited and the technique has the following disadvantages.

a) It is relatively slow, requiring special specimen preparation. Thus, good quality contacts have to be prepared and the desired material properties may be influenced in subtle, often unrecognised ways by the necessary contact preparation treatments. The micro Hg probe represents a considerable advance here for certain semiconductors, particularly since solid state pressure contacts may well irreversibly damage the semiconductor surface. These electrical trarisport properties of epitaxial layers can only be measured on substrates of relatively high resistiility, an inappropriate form for most devices. Schottky barrier capacitance can provide the profile of ND- N,, in an epitaxial iaycr on a conducting substrate, but it is an even slower analytical technique, usually requiring the deposition of a special Au surface layer.

b) As usually performed, electrical measurements provide no evidence of the identity of the donors or the compensating acceptors. As is well known,. such information can be obtained from a study of electrical transport throughout a wider temperature range containing the onset of thermal ionization of the majority donors. These analyses are extremely tedious, to such an extent that, they are not usually performed on a routine basis: The results can be dificult to

interpret, because the effective donor or acceptor ionization energy is significantly dependent on the total (donor and acceptor) impurity concentration in the usual concentration range of device relevance. Often, many subtle eflects must be considered before impurities can be recognised reliably from activation energies derived from the temperature-dependence of elcctrical transport propcrties. Thus, Neumark [3 ] in a recent analysis of impurity activation energies for the shallow Zn acceptor in Gap notes that the effect of screening by impurity ions as well as by free carriers must be considered. The screening results in a reduction with increase in temperature of the effective activation energy obtained from Hall data, needed to account for the experimental results on Gap : Zn. The activation energy is reduced by 50 % when the screening parameter

where a, is the radius of the unperturbed acceptor. This occurs for I N,-N, I in the low lo t8 cm-3 range, where we shall see that certain types of optical spectra (particularly d-a pair spectra [4]) remain only weakly perturbed, providing impurity identification and estimates of E, still free from significant corrections associated with the impurity concentration. It is impossible to recognise in the electrical transport data the simultaneous presence of two donors whose ionization energies do not differ by more than, say 25 % at equal concentrations. Recognition of the presence of a minor donor at concentrations say 5 10 % of the major is very dimcult unless their ionization energies differ widely. Even the hard won data taken over a wide temperature range provide no information on the nature of the compensating acceptors, since there is no dependence on E,.

The advent of optoelectronic semiconductor devices, particularly LEDs naturally re-emphasises the possi- bility of material analyses using optical spectroscopy, the subject of this talk. We shall see that the optical techniques complement the traditional electrical ones. They are particularly suited to the detection and recognition of impurities. The simultaneous presence of several different donors and acceptors can be recognised in a single measurement. The characteristics of certain types of optical spectra, such as the d-a pair spectra already mentioned, which depend only on the low radius electronic ground states of the impurity centres, are less sensitive to the obscuring effects of interimpurity interactions than the results obtained from electrical analyses. The relative concentrations of impurities of a given type, which produce generically similar spectra, can be estimated readily from most types of optical spectra. Luminescence spectra, a main feature of this talk, provide only an order .of magnitude indication or perhaps set a limiting value for the absolute concentration of the impurity centres. The absolute concentration can be estimated from a variety of types of optical absorp-

THE ANALYSIS OF WIDE BAND GAP SEMICONDUCTORS (3-129

tion spectra, which often depend on the preparation of the impurity or defect centre in a prescribed electronic state. However, the optical absorption technique requires initial calibration in most cases, usually performed by comparison with the electrical data. Certain optical techniques can provide absolute concentration information, for example photocapacitance. However, this technique again requires preparation of some type of electrical contact. Photocapaci- tnnce is particularly useful for the characterisation of the deep centres which often limit the performance of semiconductor devices and which, for a variety of reasons, may not produce detectable luminescence or significant optical absorption. Such techniques lie outside the scope of this talk. My objective today is to provide a quick survey of the exploitation of optical spectroscopy, particularly luminescence, in the detection and recognition of some of the most obvious impurities in semiconductors. I will emphasise spectra connected with donors, acceptors and some neutral centres such as point defect isoelectronic traps and certain d-a associates.

2. Main text. - (Fig. 1) Summarises the classes of electronic spectra. I should say immediately that another optical technique exists, ~lamelq impurity plto~oiz absorption spectroscu~~y. This technique can have sensitivity down to 1 ppma for certain important impurities, particularly those whose mass is significantly less than the host atom replaced or which are bound interstitially with large force constants. Like some of the electronic spectra discussed here, phonon spectroscopy can provide information not only on the concentration of these impurities (also requires calibration) but particularly on the lattice site and state of association of the impurity. However, it is worth noting here that in favourable cases equivalent information can be obtained from the structured

ELECTRONIC SPECTRA I N SEMICO!dOUCTORS --

1 !NZR!Ns!C-!L!ru?!s-AIIFiiNDAt!k"!11?L-EoG5

(a) D I R E C T TYPE, \k = kplOt

(b) IND IRELT TYPE, i 3 .* k7,0t

2 EXIR!Y~!C_~!MP~R!I!I?~LAIE:~!~-F:A~!RE_Z

(a ] I NTRA-CENTRE TRANS I T I OWS

(b) FREE-TO-BOUND TRANSIT13NS

( c ) INTER- IMPLRITY TRANS lP lONS

( d ) BOUNO EXCITONS

(e) 8O3ND PHONONS

sidebands which occur in the electronic spectra of iznpurities. An example of this will be provided later in the talk. Impurity phonon absorption spectroscopy has tlie particular advantage that the relationship between the energy of the impurity mode and the normal modes of the host lattice can be predicted with a considerable degree of confidence. However, many detailed effects remain obscure and the strength of the absorption depends upon a dynamic charge parameter which is not wcll correlated with the presence of static excess charge at the impurity and seems best determined by empirical means. This type of impurity phorion spectroscopy, involving wave-lengths 2 5 p and frequently 2 10 p, has been reviewed elsewhere [ 5 ] and is outside the scope of this talk. We should simply note that only certain impurities can be detected in a sensitive manner from the phonon spectra, just as only certain types of impurity provide readily detected electronic spectra in semiconductors. It is useful that the selection (sensitivity) criteria are quite different, so that these two optical analytical techniques are often complementary. The electronic spectra often provide appreciably higher levels of concentration sensitivity because they are obtained in an energy range covered by much more sensitive optical detectors, the near infra-red, visible or ultraviolet, and are less subject to obscuring effects of absorption from intrinsic lattice vibrations or from electronic transitions due to weakly bound or free electronic particles. We can say that the electronic spectra provide considerable information about the vibrational states of the impurity and also of the host lattice, briefly illustrated later in the talk. The reverse is not usually true except in certain very special cases, for exarnple the LO phonon bound at a neutral donor or acceptor [6].

(Fig. 2) Contains an energy level scheme for several donors and acceptors in Gap, and certain transitions between them and the valence and conduction bands.

FIG. 2. - Schematic optical transitions involving shallow and Fro. 1 . -- A listing of types of electronic spectra in semi- deep donors and acceptors. Important centres in GaP have

conductors. been selected for illustration.

C3- 130 P. J. DEAN

An intra-centre recombination is shown for the deep donor 0. Bound exciton transitions do not appear, otherwise the major generic types of impurity-induced electronic transitions are shown. The ionization energies of the relevant impurity centres are often small, less than 200-300 meV. They act as carrier trapping rather than recombination centres at 300 K, a necessary consequence of the fact that many are deliberately added to provide controlled electrical conductivity in electronic devices which must operate at room temperature. Thus S is a typical shallow donor, ED - 104 meV and Zn is a typical shallow acceptor, E, - 64 meV in G a p [7]. Because of this and in order to minimise spectral broadening effects due to phonon interactions it is necessary to record electronic spectra below 77 K, often at He'temperatures. Liquid nitrogen temperature spectra are usually adequate for the impurity phonon analysis technique already mentioned. However, we shall see that the techniques for recording optical spectra a t He temperatures are trivial nowadays and should discourage no-one. High spectral resolution is essential to take full advantage of the technique.

(Fig. 3) Reviews the information which can be obtained from electronic spectra.

DIVIDENDS FROM ELECTRONIC SPECTRA

I PRESENCE OF MANY IMPURITIES REVEALE3 - HIGH SENSITIVITY AND OFTEN SPECIFICITY

2 SPECIFICITY - APPEARANCE OF CHARACTERISTIC SPECTRAL ENERGY, OFTEN e OR h BINDING ENERGY AT IMPURITY

3 SPECIFICITY - TYPE OF I'IPURITY THROUGH DETAILED PROPERTIES OF TRANSITION. SOMETIMES EVEN TYPE OF SUBSTITUTIONAL SITE EG I N AB ZINCBLENDE MATERIAL

(Fig. 4) Compares several optical techniques-need for contacts, sensitivity and ability to measure concentration. Sensitivity may well be much better than 1 ppma.

(Fig. 5) Shows the equations for cross-section in optical absorption. The term [C] is given by

where (Ecff/E)2 is the local field correction between the average macroscopic field of the photon E and the local field Ecff at the impurity central cell. It is - 1 for an extended state in a covalent centre, but may be much larger for a deep state. The Lorenz

1 form, valid for extreme localisation is - (n2 + 2)2,

9 which is - 20 for a typical 111-V compound semi-

B A S I C E Q U A T I O N S FOR CROSS-SECTIONS

I M P U R I T Y E L E C T R O N I C A B S O R P T I O N PER CENTRE

[adu = , n = R E F R A C T I V E l h O E X

f - O S C I L L A T O R STRENGTH; - : FOR I S O L A T E D INTRA-CENTRE T R A N S I T I O N , OFTEN << I FOR B A N D - I M P U R I T Y T R A N S I T I O N , E S P E C I A L L Y FOR

I N D I R E C T SEMICONDUCTOR

f - f E X x N , f E X D E F I N E D / M O L OF SEMICONDUCTOR (O.CO25 I N C d S )

N I S NUMBER OF MOLS COVERED BY e - h OVERLAP (- 1 0 0 0 I N CdS)

DETJ!LEp_BfiLAt44E, RELATES L I F E T I M E I AND f

4 CONCENTRATION OF IMPURITY, USUALLY ORDER OF MAGNITUDE, 2 SOMETIMES WITH PRECISION I = 4 . 5 A / n f , >, I S WAVELENGTH

FIG. 3. - Information provided by extrinsic electronic spectra FIG. 5. - The use of optical spectra for the determination of in semiconductors. concentrations.

T E C H N I Q U E AND Q U A N T I T A T I V E A S P E C T

Q T - Q U A N T I T A T I V E , Q L - Q U A L I T A T I V E

FIG. 4. - A comparison of various optical analytical techniques.

TECHN l QUE

OPT l C A L A B S O R P T I O N

L U M l NESCENCE

RAMAN SCATTERING

P H O T O C O N D U C T I V I T Y / PHOTOCAPACITANCE

S E N S I T I V I T Y

V A R I A B L E , E S P E C I A L L Y I F h O T I N T R A - C E N T X E

V A R I A B L E , E X C E L L E N T I N FAVOURABLE CASES

REASONABLE I N SPECIAL CASES

GENERALLY REASONABLE

CONTACTS

N 0 (BUT S H A P I N G )

NO

N 0

YES

CONCENTRATION*

QT (NEEDS C A L I B R A T I O N ESPEC I A L L Y I F NOT I N T R A - C E N T R E )

Q L (APPROX FROM L I N E W I D T H S A N D K I N E T I C S )

Q L / Q T (ABSOLUTE FOR BOUND PHONON)

QT CAPAC I TANCE)

I

THE ANALYSIS O F WIDE BAND GAP SEMICONDUCTORS C3-131

conductor. With this form, the relation for the optical cross-section is known as the Smakula formula, ,widely used in the study of colour centres in ionic crystals [9]. Note the giant oscillator strength of Rashba and Gurgenishvili, specifically relevant for the absorption of weakly bound excitons [lo]. The total oscillator strength of the absorption at an isolated centre, say a donor is calculable for a given form of interaction potential. For example :

16 n2 e2 h ,,, (hv - E , ) ~ ' ~ f=-- ED - --

3 m * c hv3

for a deep. donor where a 6-function potential may be used [I I]. The features seen most easily in optical absorption are the transitions from the ground state to the bound excited states, which occur an energy slightly lower than required for optical ionization of the donor. Unfortunately, the fractional oscillator strength of these transitions is very low for very deep states, and the dominant delta function impurity- electron interaction may well exhibit no bound excited states. Another problem for a deep centre is that much of the oscillator strength may be contained in phonon sidebands, which are less likely to show well resolved, easily measured structure [12]. On the other hand, a shallow donor, whose states are well represented by a long range Coulomb potential shows relatively strong interbound state transitions and a relatively much weaker photoionization continuum. We show later the readily detected data typical for shallow donors in GaAs.

(Fig. 6) Shows the simple ,experimental equipment needed for photoluminescence or optical absorption. We have already noted that the samples must be mounted in a low temperature cryostat. For the study of lun~inescence from relatively inefficient activators, where strong optical pumping with a focussed laser beam is highly advantageous, as well as for measurements at the lowest temperatures, it is essential to immerse the sample directly in liquid refrigerant. If slightly higher temperatures, 2 6-10 K and weaker

M A G N E T !

FILTER PHOTO-

MULTlPLlEil

, M E R C U R Y ARC OR

ARGON ION LASER

FIG. 6. - A schematic view of a typical apparatus for optical analysis, neglecting the cryostat needed for the essential low

temperature studies.

optical pumping can be tolerated, then very simple and cheap means exist [I31 whereby temperatures stable to - f 0.5 K can be readily attained, granted a supply of liquid He.

(Fig. 7) In luminescence, particularly, the properties of the sample may be examined in detail across the surface (limited by beam focus, readily down to - 100 p) and in depth (limited by the ambipolar carrier diffusion length - 1 p). Profile information can be obtained from luminescence studies of suitably step-etched samples. Angle-lapping, often used for electrical profiles [14], is not very appropriate for photoluminescence analysis under strongly absorbed exciting light. Work damage often has a strongly deleterious effect on the intensity and spectral form (influence of strain [15]) of luminescence originating close to the semiconductor surface. Photoconductivity may be used as well. As we will see, this enhances the signal from transitions to relatively shallow excited states of the impurity, whereas thermalisation ensures the dominance of the deepest excited states in luminescence spectra.

>I:LCT~C'?A?P SLIT

31SP?RS13U - 4 A U l r n ~ - 3 5 nrvirrn;

. . . . . --.+::.-..: 1 - ..

&PA-TFh 'ILlCR

SPC' SIZE

'I -= 211~

FIG. 7. - A second schematic view of the experimental equipment, ernphasising the spatial resolution and scanning readily

attained using focussed laser excitation of photoluminescence.

(Fig. 8) Shows the optical absorption of thin, chemi- cally polished layers of epitaxially grown GaAs [15A]. The intrinsic exciton absorption predominates. Traces of impurity absorption also occur, despite the small layer thickness (10 p and 2 p) and the low impurity concentration, N , - N , - I O l 4 ~ m - ~ . The theory of

FIG. 8. - The absorption spectra of thin vpe layers of GaAs, after separation of the substrate (from ref. [lSA]).

C3-132 P. J. DEAN

Rashba and Gurgenishvili predicts f - lo6 f,, for excitons bound to neutral donors in GaAs. This results in f - 4 and T = 1.8 ns for radiative recombination, close to the observed value [16].

(Fig. 9) Interband intrinsic electronic absorption is generally some lo3 weaker in an indirect gap semiconductor like Gap. Impurity-assisted absorption is also usually proportionately weaker. However, given an appropriate form of electron-impurity interaction, it is possible to obtain impurity-induced absorption with large oscillator strength. Thus, for the well known isoelectronic trap N in Gap, the wave-function of the electron bound to this neutral centre contains a large admixture of components associated with the conduction band from the direct gap at the zone centre. The

strong absorption is consistent with expectation for a shallow bound electron state in the central field of a 8-function potential well [17]. The oscillator strength exceeds 0.1, and the N-induced absorption changes the room temperature body colour of thin slices of Gap from honey brown to red at modest impurity concentrations - 1018 ~ m - ~ . This is the basic reason why N is such an effective activator for green luminescence in Gap. The greater absorption near the bandgap corresponds through detailed balance to a greatly enhanced probability for green band-edge luminescence. The N concentration can be determined from low temperature optical absorption at the sharp bound exciton no-phonon line down to < lo'* ~ r n - ~ in a sample 1 mm thick. This concentration can be

FIG. 9. - A portion of the absorption edge of undoped Gap (intrinsic spectrum) and of Gap containing 7 x 1018 cm-3 isoelectronic Np (only 1.5 x 1018 cm-3 according to ref. [19]) (extrinsic spectrum).

THE ANALYSIS O F WIDE BAND GAP SEMICONDUCTORS C3-133

measured absolutely from optical spectra using the oscillator strength determined from the lifetime observed for the allowed electronic transition, relating absorption and luminescence by detailed balance [18]. However, recent charged particle activation analyses for N in G a p have provided a significant correction to the oscillator strength [19]. A much more dramatic discrepancy between separately measured values of s and f'for donor bound excitons in G a p : S and Si : As led to the recognition of the dominance of non- radiative (Auger) recombinations of excitons bound to centres containing additional weakly bound electronic particles [20] in indirect semiconductors.

(Fig. 10) We must have high quality crystals to exploit optical spectroscopy fully in the detection and measurement of impurities in semiconductors. We need sharp spectra for identification, but the no- phonon lines are very sensitive to the macroscopic state of the crystal. For example, inhomogeneous

CRYSTAL REQUIREMENTS FOR D E T A I L E D R E C O C K I T I O N

I M P U R I T Y L E V E L MUST BE LARCE ENOUGH FOR D E T E C T I O N BUT S U F F I C I E N T L Y SMALL TO A V O I D STRONG I N T E R - I M P U R I T Y - I N T E R A C T I O N S AND PLASMA S C R E E N I N G ( F O R CENTRES. W I T H

E X C E S S C H A R G E C A R R I E R S )

FOR FREE E X C I T O N , HANA'iURA SHOWS THAT B I N D I N G ENERGY

WHERE a I S THE DONOR BOHR R A D I U S

FOR €:/Ex = 0 . 9 ; N 3 / N y ' 0 . 5

N, D E F I N E D FOR MOTT I N S U L A T O R - * M E T A L T R A N S I T I O N

s~n~m-p~gng~w!~c I N A D D I T I O N I N T R A - I M P U R I T Y T R A N S I T I O N S

FOR BOUND EXC I T O N

FIG. 10. - The conccntration broadening of optical no-phonon lines

strain broadens the spectral lines, and they split into clearly resolved subcomponents in the uniform strain fields often inadvertently present [15]. These effects are particularly noticeable in zincblende scmiconduc- tors, where they are dominated by splitting of the F , valence band. Typical deformation potentials which relate stress and strain are a few eV, and splittings of - 10 meV may occur for stresses - l kbar (10 kg. mrK2) . Indirect gap zincblende semiconductors contain extra effects due to the removal of the degeneracy of electron states derived from equivalent conduction band valleys under stresses of appropriate symmetry. This sensitivity of the optical spectra may be turned to advantage in enabling the inhomogeneity of the built-in strain to be probed across the surface of a semiconductor slice.

The spectra are also sensitive to free carrier screening of the interaction between the impurity and the electronic particle. The screening of free carriers is usually described in the Debye approximation, with the Debye screening radius ( ~ k T j 4 ne2 IZ)' '~. Bound states whose unperturbed radii are large compared with this radius cannot exist. We are concerned with shifts and broadening~ of spectral lines at temperatures and concentrations where no free carriers occur, unlike the screening problem in electrical transport studics [3]. Hanamura has shown that the dominant effect on free or bound exciton lines is screening due to the dielectric effect of neutral donors, which predominate when m,* < m: and therefore ED < LA. Note that the screening criteria depend upon the cube of the Bohr radius. For a hydrogenic centre, this means that the sensitivity to such screening effects of the states of principal quantum number n is proportional to n6, a large effect ! This is the reason that broadened but barely shifted optical no-phonon lines occur under doping conditions where electrical data show strong deviations from the dilute concentration limit. As already mentioned, electrical transport in p-type Gap : Zn gives EL - 0.5 E: near N,-ND= 1018 ~ m - ~ , when strongly broadened but essentially unshifted no-phonon lines from recombinations at d-a pairs of separation - 20 A can still be recognised [3], [4].

Stark broadening also occurs due to interaction between a bound cxciton, say and a nearby ionized impurity of either sign (the energy shift is proportional to I Ze 12).

(Fig. 11) According to Hanamura [21], the Stark interaction lowers the bound state peak energy by an

amount 4 - Nz , 4 1 3 a: EcK compared with the value (4; ,

given from' screenilqg alone and causes an asymmetric line profile with a low energy tail varying like (AE)-'I4. The effect has been analyscd in n-type CdS and is strong in the high conccntration region of metallic impurity conduction [22]. At the present, its contribution to the structured low energy wing often seen for bound excitons at intermediate impurity concentrations in G a p [23] is a matter of conjecture. Stark broadening of donor photoexcitation spectra in GaAs, illustrated later, has a generically similar origin.

(Fig. 12) The recognition of impurities in optical spectra comes largely from their characteristically different transition energies. This is a particularly powerful method when the spectra show sharp lines so that differences between closely similar impurities of a given type can be recognised clearly. Not all electronic transitions give sharp no-phonon lines, as indicated.

(Fig. 13) Given the presence of sharp no-phonon lines, we can recognise the generic nature of the transition not only from the spectral form (transition energy, strength of phonon cooperation) but also from certain perturbation spectra. Most useful, I believe, are the perturbations (line splittings and shifts) produced in a

P. J. DEAN

WAVELENGTH 1 A I 4950 4900 4850 4800

1

H Z O .1%0 TR,\%SIT ONS g VALUE

FIG. 13. - Representations of neutral and ionized donors and acceptors, the states formed by the capture of excitons and their behaviour in a magnetic field. The indicated magnetic splittings apply for exciton binding to neutral donors or acceptors in a wurtzite semiconductor, where both upper (U) and lower (L)

states are Kramers doublets (from ref. [24]). PHOTON ENERGY lev1

FIG. 11. - The luminescence of excitons at neutral CI donors in CdS for various concentrations of neiltral donors (from gu = gh cos 0, where 6 is the angle between and H,

ref. [22]). due to the hole, assuming the two electrons are in an antisymmetric spin state.

magnetic field. Again, we need no contacts to the sample, but unfortunately a rather large magnetic field. A line splitting of - 0.8 meV or - 6.5 cm-' requires 35 kG at g = 2, a typical value. We analyse the magnetic effects in terms of the magnetic splittings of the upper and lower states between which the electronic transitions occur. I take the example of an exciton bound to a neutral donor in a wurtzite semiconductor, where :

g , = 2, and is isotropic, due to the electron

The upper state is a Kramers doublet because the 4-fold valence band characteristic of the zincblende- semiconductor is split by the axial crystal field of the wurtzite lattice structure [24].

(Fig. 14) A simple but very revealing Zeeman spectrum results, illustrated for point defect N substitutional donors in 6 HSiC [25]. We see that the g, = 0 when 0 = 900, as predicted, and the spectrum is a simple doublet whose splitting gives g, directly. The larger outer splitting I g, + g, I also disappears

CHARACTERISTIC ENERGIES I N OPT ICAL SPECTRA OF DIFFERENT TYPES OF IMPURITY

* NO-PHONON L I N E S ARE SHARP(S) , MODERATELY BROAD (ME) OR BROAD(B) AS INDICATED

FIG. 12. - Characteristic energies for various types of extrinsic electronic spectra in semiconductors, neglecting phonon interactions.

PHOTON ENERGY

C.E WHERE C I S 3 /4 , 8/9, - - FOR HYDROGENIC CENTRE 0 ,A

E - E + k~ g D,A

2 E - (EA + E ~ ) + e / c r D A + f ( r o A ) 4

E - C.E g x D ,A

(C I S SOMETIMES - 0 . 1 - 'HAYNES R U L E ' )

E - ( E l + ED,A) + f y r l D p A )

Eg - ( E + I , )

i 4 I

( E l , - EM B I N D I N G OF e OR h TO POINT CHARGE I F E l I S LARGE)

l MPURITY TYPE

DONOR (D) OR ACCEPTOR ( A )

l SOELECTRON l C TRAP ( I ) (MORE GENERALLY, NEUTRAL TRAP)

TRANSIT13N"

INTERNAL (S)

FREE-TO-BOUVD(B)

D-A P A l R ( S OR B)

BOUND EXC ITON (S )

I -D,A P A I R (ME) BOUND E X C ITON(S)

THE ANALYSIS OF VITDE BAND GAP SEMiCONDUCrORS C3-135

FIG. 14. - Fan and rotational Zeeman diagrams for an exciton bound to one of the three crystallographically inequivalent donors in (~urtzite) 6 H Sic. These Zeeman data indicate g, -- 2.0 (P), gh - 3.2 (5). Here, g h is defined as 3 X tize

value in Fig. 15.

when 8 = 00, but for a different reason. The intensity of the corresponding transitions contains a term [1 - / cosd 11 [24]. The splitting of the remaining doublet yields ] g, - g, I .

(Fig. 15) Similar effects can occur in a zincblende semiconductor. We consider an axial donor where the degeneracy of the valence band is lifted locally in the crystal field of the axial centre. My example is a Li- related donor in Gap 1261. Now, there is a compli- cation in that the donor has a < 1 1 1 > type symmetry axis, but at s given crystal setting H cannot lie along, or be perpendicular to eadz of the 4 sets of crystallographically equivalent < 111 > directions. Although the Zeenlan spectra are now more complex, analysis of the spectrum delilies the syn~metry axis in a way familiar in electron spin resonallce spectroscopy. Again, the g-values of the electron and hole can be obtained very directly from these Zeeman spectra,

PHOTON ENERGY eV

FIG. 15. - Z w m n splittings of an exciton bound to an axial donor in Gap, attributed to interstitial Li. Data are given for the three prillcipal symmetry directions of magnetic field relative to the crystal axes, repeated for N / < 111 > from a second crystal with narrower magnetic subcomponents. The data differ slightly from reference [26] which contains a rninor

nun~erical error and the resultant fit is improved overall.

here g, = 2.00, g, = 0.89 [26]. The Roth three-band theory 1271 provides a fair estimate of the reduction in electron g-value below the free electron value of 2.0 in narrow direct gi-p semiconductors like GaAs [28] and InSb 1271. However, rather small changes in the absolute g-vatues typical between different centres in a given semiconductor have not received much theoretical exploitation. The extent to which a given set of g-values conforms to existing knowledge provides a powerful check on the validity of a given assignment for an impurity-related electronic transition arid empirical trends have been noted which sharpen such fitting criteria 171, 1291.

(Fig. 16) Amonpt the relatively covalentiy bonded semiconductors, there has been a considerable amount of work on magnetic analysis of impurity bound exciton spectra in Gap. I show a collection of data

ii . NfllRSI' 5ap . 9) L I D i ,;i iSa.OR . m I SO'ROPIC J

Sb -50 . E1 VLRY

P il Id+lL"'ill SPLII'I9GI lW s""*riSY

III,SCrROP>C :PRY &NISO'R3PIC P !m-C) W 3 : 1

' j .Rt I tciAl lON,l i I F F I C V S u:,% :, 6' AXlnL C i N r a i S

FIG. 16. - Scl~ematic representations of the J-J coupling schemes and the Zeeman splittings of excitons bound to J = 0 centres in a 7incblende semiconductor, arranged with progressive reduction in site symmetry from left to right. The examples

listed all occur in Gap.

for excitons bound to a variety of neutral centres; isoelectronic point defects or isoelectrollic associates. Here, there is a simplification in that there is no free spin in the lower state, which contains no exciton so that J = 0, g , = 0. However, J-J coupling allows two or three upper (exciton) states for a point defect, split by the electron-hole exchange interaction. The splitting of the lower energy, B or J = 2 exciton state in the cubic field for a T, impurity site may be negligible, as for the iV exciton [30], or readily detected, as for the Bi exciton [31]. Its presence contributes a large anisotropy to the magnetic splittings of line B until the Zeeman splittings % E,,-EB,, 0.28 meV for the Bi exciton. The magnetic splittings of an exciton bound to an axial, C,,, isoelectronic trap are complex due to the type of orientationaf effect already noted for the Li donor exciton. Again, the symmetry axis can be readily defined from the magnetic data. The Li,-Li,,-0, [32] centre has been chosen for the example rather than the centre of similar type studied earlier [33], Cd,,-O,, because more of the theoretically predicted subcomponents were detected for the Li-related centre. Exciton binding to a centre of still lower symmetry,

C3-136 P. J. DEAN

possibly C,, with a large crystal field splitting, causes the re-appearance of a simple, isotropic Zeeman spectrum. There are at least two candidates for the C,, symmetry Sbp-Sbp associate in the luminescence of Gap : Sb, one shallow exciton near 2.326 eV with just the expected pair of states J = 0 and J = 1 and a much deeper bound exciton with no-phonon components near 2.29 eV, including a second unexpected pair splitting like J = 0 and J = 1 bound excitons [34]. Since then, a number of bound exciton doublets with similar magnetic properties have been seen in Gap [35] as well as excitons bound to neutral axial acceptors containing holes with quenched orbital angular momenta both in Gap [34] and GaAs : Cu 1361. In all these spectra, it seems important that the hole rather than the electron should interact strongly with the impurity ; for example the N, (Np-N,) bound excitons [37] split more like a minor perturbation of the behaviour of an exciton bound to isolated N, than like the simple model for Sb,-Sb, given in figure 16.

(Fig. 17) As a simple example of information available in the phonon sidebands of an electronic transition, I show the luminescence of N in Gap [38]. The form of most of the structure down to the strong peak labelled A-LO is very similar to the one phonon density of states of the perfect Gap lattice. This distribution has been calculated using the lattice vibrational dispersion curves determined from inelastic neutron scattering 1391. When examined in detail, the broader replicas due to acoustical phonon-assisted transitions show many of the slope discontinuities known as van Hove singularities. At lower transition energies, a

FIG. 17. - The luminescence of excitons at the N p isoelectronic trap in Gap, showing the two no-phonon lines A and B resulting from J-Jcoupiing (Fig. 16) and the form of the phonon sideband incIuding the local mode overtone replica A-2 LOC, of energy

121.8 meV (from ref. [38]).

well defined peak appears, caused by an overtone of a symmetrical local mode vibration involving The fundamental is weak because of symmetry considera- tions. The energy of the local mode W,,, is closely approximated by the simple expression

where k is a force constant, here essentially that of the Ga-P bond 1371, the M, are the masses of a Ga and N atom and a is a factor which is empirically - 1.3 -, 2 for a number of local modes in 111-V semiconductors [S]. The presence and behaviour on isotopic substitution of this local mode provides the best possible evidence for association of the spectrum with N,. Generally, as the localisation energy of the exciton increases, that is the centre becomes a deep trap, the proportional strength of the local mode effects increases. In addition, the general strength of the coupling to all types of phonon increases. For a more complex centre, say an axial defect, the fundamental local mode vibrations can also give strong spectral satellites. These effects arc well documented in the exciton luminescence of the axial centre Li,Li,,-0, in Gap, where true local modes, gap modes and in-band .resonance modes of Li and 0 all appear [32].

(Fig. 18) I believe a good case has been made for the role of optical spectroscopy in the quantitative estimation of impurities in semiconductors and for the recognition of particular impurities through analysis of the generic transitions they induce. I now turn to a brief survey of very recent work on the recognition of different donors and, particularly acceptors in GaAs through optical spectra. Personally, I have found it amazing that our studies and applica- tions interests in GaAs have been carried as far as they have without anyone being able to identify convincingly the residual impurities which control the electrical properties of refined GaAs. This is particu-

FIG. 1%. - The energies of free to bound bands reported in the edge luminescence of relatively lightly doped GaAs, and the chemical assignments where given. The first two columns contain recent data reported in reference 1421, obtained from RRE (vpe) and STL (lpe) GaAs. The remaining data was extracted from references [41a]-[41m]. 5 denotes an electrical

measurement.

THE ANALYSIS OF WIDE BAND GAP SEMICONDUCTORS C3-137

larly remarkable for the acceptors, where the chemical shifts are much larger than for the donors, as I shall show. I mentioned before that the concentrations of these acceptors are poorly controlled at a level where they give significant compensation in typical GaAs X-band microwave devices, a very uncomfortable situation. Of course, people have previously attempted to identify acceptors in GaAs, many using photo- luminesfence [MI. They correctly anticipated that the technique should work particularly well for acceptor recognition. Unfortunately, until recently there has been no concerted body of work capable of providing a definitive link between spectral effects and chemical species. Much of the earlier work was performed with material of inadequate purity. Some recent workers avoided this problem, but established the nature of their acceptor impurities by allegedly reasonable guesswork. 1 show that this produced a very confused literature, particularly for the more common acceptors C, Si, Zn. As you will guess, I believe we have now removed this confusion through the data shown in columns I and I1 of figure 18.

(Fig. 19) Shows the generic form of the acceptor and donor bound exciton spectra. as well as the free to bound and donor-acceptor pair spectra and the intrinsic exciton luminescence of a typical direct gap semiconductor such as GaAs. The whole effect is

EX-N CENTRE EX-N ACCtPTOri 9;- t (DEEP) j? (SrlALL<?Wl

FIG. 19. - A schematic representation of the low temperature edge luminescence of a refined, direct gap semiconductor such as GaAs. The <( twoelectron >) replicas 2e for the Ex-NDONOR lines are displaced nearly 314 ED below the parent lines for the hydrogenic shallow donors characteristic of GaAs, while the corresponding displacements for the acceptor (( two-hole ))

satcllies, 2h bear a more cornplcx relationship with En (ref. [421 and 1471). Here N means neutral, not nitrogen.

usually known as the edge luminescence, although some restrict this term to cover only the F ---t B and D-A pair components, not mutually resolved in this representation. I will describe these latter spectra and the exciton spectra separately. Particularly note the satellite labelled 2h from the principal bound exciton doublet labelled Ex-N acceptor. I will show that this satellite provides valuable confirmation for the exis- tence of the divers acceptor species to be discussed 1.121.

(Fig. 20) Contains the characteristic temperature dependence of the F -. B and D-A pair spectra over the temperature range in which appreciable therrnali-

RRE SP2Rb

FIG. 20. - The evolution of the free-to-bound band F-B from the donor acceptor pair band P with increasing temperature in vpe GaAs, which contains only one residual shallow acceptor, Zn. Since the donors are energetically indistinguishable, the edge lutninescence contains just one pair and one frce-to-

bound luminescence band (from work leading to ref. 1421).

sation of the shallow donors (ED - 6 meV) commences. 'The free to bound, F 4 B transitions predominate at T 2 15 K in GaAs, the exact temperature depending somewhat on the optical pumping rate. The spectra to be reported here were obtained using relatively low densities of photoexcitation. At this temperature, when kT - ED/4, the majority of the electrons secom- bine from the bottom of the valence band rather than when trapped out on the shallow donors. I believe that in the absence of structure due to transitions at discrete D-A pairs, and short of using the more complicated technique of time-resolved spectroscopy, the EA values are best obtained from analyses of the F -+ B band. The positions and shapes of the F + B bands are less subject to details of the observational technique. However, these bands are best studied at the lowest temperatures at which the D-A pair bands remain negligible, using dilutely doped samples. Both of these precautions are intended to minimise spectral broadening.

(Fig. 21) Summarises F - - B spectra from a series ofjudiciously acceptor doped GaAs, as well as showing typical spectra for undoped, refined vpe and lpe GaAs. From these data, the quite distinct set of dominant residual acceptors in the latter material can be determined with some confidence 1421. We find that vpe GaAs from a variety of laboratories contains Zn as the principal acceptor impurity, while lpe GaAs is usually

P. J. DEAN

FIG. 21. - A comparison of the cdgc lumincsccnce of a set of refined GaAs lightly backdoped with the indicated acceptors, made at 15 K where the free-to-bound components arc seen in near-isolation (Fig. 20). The vpe material always tcnds to show the Zn band, while undoped Ipe GaAs shows bands due to C, Si and Ge (?). The relative strength of the C band shown here underestimatcs the relative concentration of C acceptors since this shallow Iumincscence band undergoes significant preferential thermal ionization at 15 K (from work leading to

ref. [42]).

dominantly contaminated by C acceptors, although the acceptors Si and, we believe Ge are also usually significant. The ionization energies of the acceptors Si and Cd are closely similar, hard to separate by this technique. However, we are aided by the chemical fact that Cd is not an inadvertent acceptor species in refined GaAs, unlike Si (for lpe material), while Si and Cd can be differentiated in high quality material through their disparate (( two-hole )) satellites (2h in Fig. 19).

(Fig. 22) Our confidence in these results is enor- mously increased by corroboration from bound exciton data, where the linewidths are much smaller (- 0.1 + 0.2 meV cf 2 + 3 meV) and our ability to distinguish different acceptors is greatly enhanced. This is so if we determine the shifts in the (( two-hole >> satellites, in which the acceptor is left in an orbital excited state after recombination of the exciton [43]. These (( two-hole )> shifts, which represent the relevant excitation energies of the acceptors, are strongly affected by the acceptor chemical shifts, almost as much as the free to bound bands. In the principal acceptor bound exciton lines, the neutral acceptor to which the exciton is bound is left in its ground state after the transition. The positions of these lines vary

'7 , , . T T -1' r i - - 7 1 7 :- ----,--7

17 Mg 11

I; ! I Zn I

1: II Cd 111 C I -

Si .I 1 : - . Ge J : i l i l I !. I P ~ 6

7 . "Fe

b l -.+-i . ++-I ,.-: -;. :--1 , , , . . 1.18 1.19 eV i.5C 1.51

: bound exc~ton spectrum 1.5K Il; free to bound transition peak 5K

FIG. 22. - The energies of the broad free-to-bound bands and cc two-hole u satellites (to the left) of the cxciton-neutral acceptor bound exciton components (right) in thc edge photoluminescence of refined GaAs, lightly back-doped with the indicated shallow acceptors. The lowcr two rows illustrate spectra typical of undoped GaAs of state of the art purity (from

work leading to rcf. [42]).

hardly a t all with E,. This contrasts strongly with expectation from Haynes' rule, established to describe such bound excitonsfor donorsand acceptors in Si [43a], corroborated in a modified form recently in G a p [26] and for shallow donors in CdS [44]. We see that the highest energy principal acceptor bound exciton doublet occurs for the deepest acceptor. Ge. This means that the exciton localisation energy has actually decreased with increase in E,, the antithesis of Haynes' rule ! We met this situation before in comparing optical spectra of the acceptors Zn and Cd in InP [45], another 111-V direct gap semiconductor closely similar to GaAs. The doublet structure of the acceptor bound excitons arises from J-J coupling, we believe between the electron and holes, the hole-hole splitting being somewhat larger. I will not discuss this aspect further here.

(Fig. 23) We have compared our spectra with the s -+ p photoexcitation spectra measured by Kirkman and Stradling [46] for the acceptors C and Zn in GaAs

15 EXCITON

L l I Z L I J

0 2 ~ 5 4 2 z ? O n

Ln '

S BINDING ENERGY

FIG. 23. - Relationship between 1s and 2s binding energies of shallow acceptors in GaAs, including the theoretical datum T for a hydrogenic acceptor (ref. [47]). The relevant experimentally observed transitions are indicated in the'inset, where BE and TH denote bound exciton and two-hole transitions. The transitions Is -t 2p appear in infrared photoexcitation (ref. [46]),

(from ref. [42]).

THE ANALYSIS OF WIDE BAND GAP SEMICONDUCTORS C3-139

and with effective mass variational calculations of Lipari and Baldereschi [47j. The relevant effective mass levels, their classification scheme and the bound exciton transitions we observe are illustrated. It is clear that the excited state responsible for the e two hole )) satellites is 2S,,,, an even parity state. Know- ledge of the IS binding energies determined from the F -. B spectra enables us to calculate the binding energies of the 2s states. These lie on a smooth curve, interestingly independent of whether the acceptor is on the Ga or As lattice site. The curve extrapolates back to the theoretical (effective mass) point T. The good- ness of this agreement between the theoretical and experimental spectra makes it quite clear that the levels ail arise at T, symmetry, point defect acceptors.

(Fig. 24) I n contrast to the valence band, the conduction band in GaAs is simple, non-degenerate and nearly spherical. The donor photoexcitation spectra have been studied in the far infra-red near 250 )i, using Fourier Transform spectroscopy. The levels follow a scheme very similar to the H atom. In particular, the p excited states split linearly in a magnetic field according to expectation for an orbital effect, AEH = ekHlm* c with m" = 0.066 5 mo [48j. It is convenient to record photoconductivity spectra, where the two step photo-therrnal ionization process ensures that structure due to transitions to high excited states becomes favoured if the temperature is suitably

Ga As

T - i . 4 6 . K

to) H = OkG

( i s - Continuum)

/ i 1 - L - I -- . - I- .- Id.& J

20 a,, bC 80 100 170

FREQUENCY (cm-'1

Frc. 24. - Shallow donor photoexcitation spectra of refined GaAs measured through low temperature photoconductivity at (n ) zero and (h) a small magnetic field. The Is-np transitions are very sensitive to field because of the large orbital g-factor

of the low mass rl electrons in GaAs (from ref. (481).

adjusted. As we noted earlier, peaks due to interbound state transitions are strong compared with the structure due to direct photo-ionization for a shallow Coulombically bound centre. These lines become narrower and the s -+ p lines appreciably stronger as H increases.

{Fig. 25) It is convenient to examine the 1s -, 2p- transition in more detail, since a combination of linear and quadratic Zeeman and diamagnetic effects ensures little sensitivity to H near 15 kG [48). The quadratic Zeeman shift depends on the square of the magnetic quantum number m, causing an uneven spacing of transition 1s -+ 2p0 between Is -+ 2p- and 1s -, 2p'.

A' 420 I-

I /'

"OF GUAS 4 ) f ~ s - 3 ~ , m = + i l I A

too - I f' I -

'E 9or 2 I g aor-

0 5 rO tJ 20 25 30 33 40

MAGNETIC FIELD ( k G 1

FIG. 25. - The magnetic fan diagram for two shallow donor photoexcitation lines in GaAs. Thc lines show targe parama- gnetic splittings and diamagnetic shifts consistent with a near hydrogenic centre with low electron mass (from ref. I481).

(Fig. 26) The dominant factor in setting the asymmetric shape of the sharp neutral donor inter-bound state absorption lines in typical closely compensated, refined GaAs is inhomogeneous broadening due to the Stark effect from ionized impurities. The effects of those few ionized centres nearest to a given neutral donor predominate. Superficially, the theory is similar to that described above for bound exciton spectra [21], but it has been considerably extended by Larson (49). The local electrlc field is assumed uniform at each neutral donor, while the variations between donor sites due to the statistics of the relative distribution of: neighbouring ionized centrcs produce the inhomogeneous line broadening. For dilutely doped, relatively weakly compensated GaAs, and low magnetic fields the broadening is dominated by a quadrupolar interaction of a neutral donor in the local gradient of the electric field. For significant compensation, as for the samples illustrated here, and particularly at high magnetic fields - 55 kC, when the quadrupoie

C3-140 P. J. DEAN

Sample I Sample 2

I

a.

PHOTON ENERGY

FIG. 26. - The experimental lineshapes (circles) and theoretical fits (lines) to the Is-2p- magnetic subcomponent of shallow donor photoexcitation spectra in GaAs. The reduction of the inhomogeneous line broadening arises from the decrease in electric polarizability of the donor states in the magnetic field and a consequent reduction in the quadratic Stark effect (from

ref. 1491).

moments of the Is and 2p' states are equal and oppo- site, the quadrupolar contribution is quenched and the broadening is dominated by the quadratic Stark effect, i. e. the interaction of the electrostatic field of the charged centres with the induced dipole moment of the neutral donor. In total, for a transition between the ith and jth donor states, the local energy Ahvij is given by

where the E, are the energies of the unperturbed states, the Q, are quadrupole moments, the F, are components of the electric field parallel and perpendicular to the magnetic field which defines the direction z and the coefficients C represent directional averages of the electrostatic interaction for the quadratic Stark effect and contain the polarizability of the neutral donors. The detailed evaluation of lineshape using this primary equation is complicated by the treatment of the spatial statistics of the electric field. Besides affecting the linewidths, the internal electric field couples the 2s and 2p0 donor states, breaking the parity selection rule against Is -+ 2s photoexcitation 1501. The reduction of linewidth with field due to the quenching of the quadrupolar component is clearly shown in figure 26. Vapour phase epitaxial sample 1 is doped ,near I O l 4 cm-3 with -- 90 % compensation, sample 2 is doped near 3 x lOI4 ~ r n - ~ with -- 70 % compensation.

(Fig. 27) These effects conspire to make it convenient to examine the very small chemical shifts for donors in GaAs from the 1s -t 2p- photocxcitation peaks at fields 15 -+ 20 k c . i show some spectra obtained recently by Stradling et a/. [51], in which several donor species have been identified through studies of appro-

FIG. 27. - The Is-2p- magnetic subcomponents of shallow donor photoexcitation spectra from several refined, sometimes back-doped single crystals of GaAs. Line A remains unidentified though S is an obvious candidate according to expcrience with other 111-V semiconductors (updated from ref. [51 1, partly with

information from S.~ILLMAN G. E. (private communication).

priately doped samples. The total spread in chemical shift is < 1 cm-' or - 0.1 meV. appreciably smaller than reported in an early study on inadequately refined GaAs 1521. These small chemical shifts are a direct consequence of the small contact interaction between the donor core and the electron wavefunction even in the Is ground state, where a, -- 100 A.

(Fig. 28) Is intended to show that by no means all is known about the optical spectra in GaAs, even for those few major impurities discussed in this talk. The band labelled Si ? is a characteristic of Si-doped Ipe GaAs and is associated with the well-known 0.1 eV deep acceptor upon which the efficient operation of heavily Si-doped GaAs LEDs depends [53]. Despite

FIG;. 28. - The edge photoluminescencc of an Ipe GaAs : Si single crystal showing structure near 1.49 eV associated with the - 35 mcV shallow Si acceptor, and the broader features of hv < 1.40 eV associated with the 0.1 eV acceptor characteristic of this type of material. The identity of this deeper

acceptor remains unknown (from work leading to ref. [42]).

THE ANALYSIS O F WIDE BAND GAP SEMICONDUmORS C3-141

this device interest, the exact nature of the Si-related centre responsible for this band is unknown. Note that the strength of LO phonon coupling is about 100 times larger than in the doublet (F -t B and D-A pair) associated with the isolated Si,, acceptor, discussed above. Coupling to acoustical phonons is also strong for the lower energy band, to the extent that the F -t B and D-A pair contributions, which presumably exist, cannot be separated. The Si ? spectrum is superficially similar to that reported by Cho and Hayashi [54] from molecular beam epitaxial GaAs : Si. However, these authors found it specific to material prepared under As-excess conditions, which is inconsistent with the usual findings for the 0.1 eV acceptor in GaAs : Si, namely that it is seen in Ipe material, but not for melt grown or vpe crystals [55]. On the other hand, like the mbe but unlike previous reports of Ipe GaAs : Si, the spectrum in figure 28 was obtained at a relatively low concentration of Si, NA-ND - 1 x lot3 ~ m - ~ . It has been suggested that this 0.1 eV acceptor is connected with the simple associate Sic,-Si,, [56]. However, this associate is a (molecular) isoelectronic centre, not an acceptor. Further, this particular isoelectronic centre is not expected to possess a bound state, since EA + ED is only - 40 meV for Si in GaAs. Impurity phonon studies indicate that GaAs : Si contains much more complex Si associates, in addition to this simple form (NEWMAN, R., private communication and reference [5]).

The behav~our of Si in GaAs is further complicated by the presence of an even broader photoluminescence band peaking near 1.18 eV at 77 K, exceptionally

strong in heavily Si-doped vpe GaAs [55]. It is not clear whether this is the same as the peak reported near 1.22 eV in mbe GaAs [54] at 80 K for a total Si concentration 2 5 x 10" ~ m - ~ . A 40 meV shift in such a broad band could readily result fortuitously from differences in recording conditions in uncorrected photoluminescence spectra. The vpe work suggested that this band involves a Si associate containing some unknown impurity, while the mbe work confirmed that this band is very strong in heavily-doped GaAs : Si grown under As-rich conditions. Evidently, much additional work will be needed to establish the centres responsible for even the dominant photoluminescence of GaAs : Si. A close interaction between photoluminescence and impurity phonon spectroscopy should yield dividends in this difficult task, given that the photoluminescence spectra are devoid of helpful detail.

Ackno-dedgments. - Explicit citations for some of the data presented in this talk are contained in the figure captions. The author is glad to acknowledge collaboration with several co-workers in connection with the remaining, major fraction of the data, including R. L. Hartman, C. H. Henry, D. G. Thomas, and A. M. White. Particular thanks are due to A. M. White for the very recent work on acceptors in GaAs. As ever, I am grateful to the many skilled crystal growers with whom I have had the fortune to collabo- rate. Their skill forms the essential basis of any improvement in our understanding of the physics of impurities in semiconductors.

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4911. [26] DEAN, P. J., Lun~itlesce?~ce of Crystals, Mo!ecl+les and Sol~r-

lions (Plenum, New York), 1973, p. 538. [27] ROTH, L. M., LAX, R. and ZWERDI.ING, S., Phys. Rev.

114 (1959) 90. [28] W I I I I ~ , A. M., HINCHI.IFFE, I., D J A N , P. J. and GKEENE,

P. D., Solid Store Comm~ot. 10 (1972) 497.

C3-142 P. J. DEAN

[29] DEAN, P. J., FAULKNER, R. A. and KIMURA, S., Phys. Rev. B 2 (1970) 4062.

[3O] MERZ, J. L., FAULKNEK, R. A. and DEAN, P. J., PhyS. Rev. 188 (1969) 1228.

[31] DEAN, P. J. and FAULKNEK, R. A., Phys. Rev. 185 (1969) 1064.

[32] DEAN, P. J., Phys. Rev. B 4 (1971) 2596. [33] HENRY, C. H., DEAN, P. J. and CUTIIBERT, J. D., Phys.

Rev. 166 (1968) 754. [34] DEAN, P. J., FAULKNER, R. A. and SCHOSHEKR, E. G.,

Proceedings of the International Conference on the Physics of Semiconductors 1970 (US Atomic Energy Comm., Oak Ridgc, Tenn.) 1970, p. 286.

[35] DEAN, P. J., J. Lunt. 7 (1973) 51 and unpublished data, for example on Gap : Cu, Li.

[36] WILLMANN, F., BIMBERG, D. and BLATTE, M., Phys. Rev. B 7- (1973) 2473.

[37] THOMAS, D. G. and HOPFIELD, J. J., Phys. Rev. 150 (1966) 680.

[38] THOMAS, D. G., Proceedings of the International Confe- rence on the Physics of Semiconductors, Kyoto 1966, J. Phys. Soc. Japan 21 (1966) 265.

[39] YARNELL, J. L., WARREN, J. L., WENZEL, R. G. and DEAN, P. J., Proceedings of rite I~zternational Conference on Neutron Inelasric Scattering, Copenhagen (International Atoniic E-ergy Agency, Vienna 1968), 1968, p. 301.

[40] Some of this work has been reviewed by WILLIAMS, E. W. and BEBB, H. B., Semiconduc~ors and Semimetals (WILLARDSON, R. K. and BEER, A. C. Eds) (Academic Press, New York) 1972, tome 8, p. 321.

[41a] BKANTLEY, W. A., HWANG, C. J., DAWSON, L. R. and QUEISSER, H. J., Solid State Commun. 10 (1972) 1141.

[41 b] ROSSI, J. A., WOLFE, C. M. and DIMMOCK, J. O., Phys. Rev. Lerr. 25 (1970) 1614.

[41c] OZEKI, M., DAZAI, K . and RYUZAN, O., Jap. J. Appl. Phys. 11 (1972) 1049.

[41d] DINGLE, R., Phys. Rev. 184 (1969) 788. [41e] SHAH, J., LEITE, R. C. C. and GORDON, J. P., Phys.

Rev. 176 (1968) 938. [41fl WILLIAMS. E. and BEBB. H. B.. J. P ~ Y s . & Chem. Solids

[41j] KRESSEL, H. and HAWRYLO, F. E., J. Appl. Phys. 41 (1970) 1865.

[41k] HILL, D. E., J. Appl. Phys. 41 (1970) 1815. [411] R o s z ~ o c z ~ , F. E., EKMANIS, F., HAYASHI, I. and

SCHWAKTZ, B., J. Appl. Phys. 41 (1970) 264. [41m] CONSTANTINESCU, C. and P~TKBCU-PRAHOVA, I., J.

Phys. & Chem. Solids 28 (1967) 2397. [42] WHITE, A. M., DEAN, P. J., ASHEN, D. J., MULLIN, J. B.,

WEBH, M., DAY, B. and GREENE, P. D., J. Phys. C. 6 ( 1 973) L 243.

[43] This type of bound exciton satellite was first studied for donors in Gap, DEAN, P. J., CUTHBERT, J. D., THO- MAS, D. G. and LYNCH, R. T., Phys. Rev. Let!. 18 (1967) 122.

[43a] HAYNES J. R., Phys. Rev. Let!. 4 (1960) 361. [44] NASSAU, K., HENRY, C. H. and SHIEVER, J. W., Proceedings

of' the International Conference on the Physics of Semiconductors, 1970 (US Atomic Energy Cornm. Oak Ridge, Tenn.) 1970, p. 629.

[45] WHITE, A. M., DEAN, P. J., FAIRHURST, K. M., BARDSLEY, W., WILLIAMS, E. W. and DAY, B., Solid State Commun. 11 (1972) 1099.

(461 KIRKMAN, R. F. and STKADLING, R. A,, J. Phys. C. 6 (1973) L 324.

[47] LIPARI, N. 0. and BALDERESCHI, A., Phys. Rev. Letr. 25 (1970) 1660.

'[48] STILLMAN, G. E., WOLFE, C. M. and DIMMOCK, J. O., Solid State Commun. 7 (1969) 921.

[49] LARSON, D. M., Private communication. [50] STILLMAN, G. E., LARSON, D. M. and WOLFE, C. M.,

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reference [8] and STRADLING, R. A., EAVES, L., HOULT, R. A., MIURA, N., SIMMONDS, P. E., and BRADLEY, C. C., Gullium Arsenide and related compounds (The Inst. of Physics, Bristol), 1973, p. 65.

[52] SUMMERS, C. J., DINGLE, R. and HILL, D. E., Phys. Rev. B l(1970) 1603.

[53] Sce, for example, LADANY, I., J. Appl. Phys. 42 (1971) 654. [54] CHO, A. Y. and HAYASHI, I., Solid State Elect. 14 (1971)

* ? C . .

30 (1969) 1289. 1 L J .

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(Inst. of Physics, Bristol) 1973, p. 3. F . Z . , J . Appl. Phys. 39 (1968) 2006 ; [41i] SCHAIRER, W. and STATH, N., J. AppL Phys. 43 (1972) KRESSFL, H. and NELSON, H., J. Appl. Phys. 40 (1969)

447. 3720.

THE ANALYSIS OF WIDE BAND GAP SEMICONDUCTORS

DISCUSSION

Y. MARFAING. - May the Haynes' rule be extra- polated to deep centers ?

P. J. DEAN. - A variety of recent work has shown that the Haynes' rule is much more complex than has been supposed hitherto. The spectra of excitons bound to neutral donors and acceptors in Gap show that although AE,, aEA, ED, the straight lines repre- senting this trend do not pass near the point E,, = EDPA = 0. Unfortunately, luminescence of excitons bound to very deep centres such as the donor 0, or acceptor Sip has not been identified, so experimental extrapolation of Haynes' rule to very deep centres has not been obtained. The strength of the relevant no-phonon lines is predicted to be low for such luminescence, both because of strong electron-phonon interaction and particularly as a result of very strong Auger recombinations. The work on excitons bound to neutral acceptors in GaAs described in this talk, as well as some other experimental indications, suggests that extrapolation of Haynes' rule data obtained for nearly effective mass-like centres to centres with much larger binding energy is a very dangerous procedure. Hayne's plot is very puzzling for acceptors in GaAs (and InP). E,, is nearly independent of E, over the whole range of E,, we observe (roughly comparable to the range of central cell corrections observed for simple acceptors in Si and Gap). Indeed, (E,,),, < (E,,),,,

although (EA),, >>(E,),,! On the other hand, we know that E,, eventually increases with E, when the latter is very large, for example for (Sn),,. Thus, Hayne's rule curve is very non-linear (and even non-monotonic) in GaAs and InP and can only be determined empirically at present.

H. KRESSEL. - YOU show a value for the ionization energy of Si,, which is larger than the value reported by Williams some years ago. Is the difference due to a higher purity in your crystals ?

P. J. DEAN. - The Si data were obtained primarily from very lightly back-doped Ipe crystals. These crystals were grown by P. L). Greene at STL labs in a system which gave ( N D - N,) in the low loL3 range with no advertent doping. With progressive addition of Si, the material become p-type in the 10'4-10'6 range. The three'free-to bound'peaks in the edge luminescence transformed to a single band identical in spectral position to the central member of the original three. Similarly, though the undoped material showed two sharp two-hole bound exciton replicas, only one of these persisted in the Si-doped material (the two-hole replica of the Ge exciton is intrinsically ill-defined, we believe due to strong coupling of the relevant hole transition and the optical phonon). We clearly distinguish between Zn and Si in these optical data, and are certain that (EA),i > (E,),,

spectroscopie de dÉfauts - luminescence ithe …spectroscopy, particularly luminescence, in the...

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