Luminescence properties of defects in GaN

Luminescence properties of defects in GaN

Michael A. Reshchikov and Hadis Morko?

Citation: Journal of Applied Physics 97, 061301 (2005); doi: 10.1063/1.1868059

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APPLIED PHYSICS REVIEWS

Luminescence properties of defects in GaN

Michael A.Reshchikov a ?and Hadis Morko?

Department of Electrical Engineering and Physics Department,Virginia Commonwealth University,Richmond,Virginia 23284

?Received 13July 2004;accepted 18January 2005;published online 15March 2005?

Gallium nitride ?GaN ?and its allied binaries InN and AIN as well as their ternary compounds have gained an unprecedented attention due to their wide-ranging applications encompassing green,blue,violet,and ultraviolet ?UV ?emitters and detectors ?in photon ranges inaccessible by other semiconductors ?and high-power ampli?ers.However,even the best of the three binaries,GaN,contains many structural and point defects caused to a large extent by lattice and stacking mismatch with substrates.These defects notably affect the electrical and optical properties of the host material and can seriously degrade the performance and reliability of devices made based on these nitride semiconductors.Even though GaN broke the long-standing paradigm that high density of dislocations precludes acceptable device performance,point defects have taken the center stage as they exacerbate efforts to increase the ef?ciency of emitters,increase laser operation lifetime,and lead to anomalies in electronic devices.The point defects include native isolated defects ?vacancies,interstitial,and antisites ?,intentional or unintentional impurities,as well as complexes involving different combinations of the isolated defects.Further improvements in device performance and longevity hinge on an in-depth understanding of point defects and their reduction.In this review a comprehensive and critical analysis of point defects in GaN,particularly their manifestation in luminescence,is presented.In addition to a comprehensive analysis of native point defects,the signatures of intentionally and unintentionally introduced impurities are addressed.The review discusses in detail the characteristics and the origin of the major luminescence bands including the ultraviolet,blue,green,yellow,and red bands in undoped GaN.The effects of important group-II impurities,such as Zn and Mg on the photoluminescence of GaN,are treated in detail.Similarly,but to a lesser extent,the effects of other impurities,such as C,Si,H,O,Be,Mn,Cd,etc.,on the luminescence properties of GaN are also reviewed.Further,atypical luminescence lines which are tentatively attributed to the surface and structural defects are discussed.The effect of surfaces and surface preparation,particularly wet and dry etching,exposure to UV light in vacuum or controlled gas ambient,annealing,and ion implantation on the characteristics of the defect-related emissions is described.?2005American Institute of Physics .?DOI:10.1063/1.1868059?

TABLE OF CONTENTS

I.INTRODUCTION............................3II.FORMATION AND ENERGY LEVELS OF

POINT DEFECTS IN GaN....................5A.Theoretical approach ....................5B.Native point defects .....................61.Vacancies ...........................6a.Gallium vacancy....................7b.Nitrogen vacancy...................7c.Divacancy.........................72.Interstitials and antisite defects ..........7a.Gallium interstitial..................7b.Nitrogen interstitial..................7c.Gallium antisite....................8d.Nitrogen antisite....................8C.Impurities .............................81.Shallow donors ......................

8

2.Substitutional acceptors ................8

3.Isoelectronic impurities ................9

4.Hydrogen ab505386ddccda38366baf5fplexes .............................

91.Shallow donor—gallium vacancy

complexes ...........................102.Shallow acceptor—nitrogen vacancy

complexes ...........................103.Hydrogen-related complexes ............104.Other complexes .....................11E.Role of dislocations in the point defect

formation ..............................

11III.LUMINESCENCE METHODS................

12A.Steady-state photoluminescence ............

121.Recombination statistics ...............122.Effect of temperature on PL intensity .....133.Estimates of quantum ef?ciency .........144.Effect of excitation intensity on PL

intensity ............................

14

JOURNAL OF APPLIED PHYSICS 97,061301?2005?

0021-8979/2005/97?6?/061301/95/$22.50

?2005American Institute of Physics

97,

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5.Estimates of acceptor concentration in

n-type GaN (15)

B.Time-resolved luminescence (15)

C.Vibrational properties of deep-level defects..16

D.Photoluminescence excitation spectra (17)

E.Spatially and depth-resolved

cathodoluminescence (18)

F.Optically detected magnetic resonance (18)

IV.LUMINESCENCE RELATED TO POINT

DEFECTS IN UNDOPED GaN (18)

A.Yellow luminescence band (19)

1.Effect of temperature (20)

2.Effect of excitation intensity (22)

3.Effect of hydrostatic pressure (22)

4.Effect of electron irradiation (23)

5.Time-resolved PL (23)

6.Resonant excitation (25)

7.Vibrational model of the YL (26)

ab505386ddccda38366baf5fparison with the positron

annihilation results (26)

9.ODMR on the YL (27)

10.Effect of doping on the YL (27)

B.Yellow and green luminescence in

high-purity GaN (28)

1.Effect of excitation intensity (29)

2.Resonant excitation (30)

3.Time-resolved PL (31)

4.Effect of temperature (33)

C.Ultraviolet?shallow DAP?band (34)

1.Steady-state PL (34)

2.Time-resolved PL (36)

3.ODMR and identi?cation of the shallow

acceptor (37)

D.Blue luminescence band (38)

1.Steady-state PL (38)

2.Time-resolved PL (40)

3.Spatially and depth-resolved

cathodoluminescence (40)

4.Origin of the BL band in undoped GaN (40)

E.Red luminescence band (41)

F.Red and green luminescence bands in

Ga-rich GaN grown by MBE (42)

1.Effect of excitation intensity (42)

2.Effect of temperature (43)

3.Time-resolved PL (44)

4.Resonant excitation of the GL2and RL2

bands (45)

5.Origin and model of the GL2and RL2

bands (45)

G.Other broad bands in undoped GaN (46)

H.Characteristics and identi?cation of

radiative defects in undoped GaN (47)

V.INTENTIONALLY INTRODUCED IMPURITIES AND NATIVE DEFECTS (48)

A.Luminescence in Zn-doped GaN (48)

1.Blue luminescence band (49)

a.Effect of temperature (49)

b.Effect of excitation intensity (50)

c.Time-resolved PL (51)

d.Resonant excitation and vibrational

properties (51)

e.ODMR and defect identi?cation (52)

2.Green,yellow,and red luminescence

bands (52)

B.Luminescence in Mg-doped GaN (52)

1.Ultraviolet luminescence band in lightly

Mg-doped GaN (53)

2.Effect of potential?uctuations on PL (54)

3.UVL and BL bands in compensated and

heavily Mg-doped GaN (56)

a.Effects of growth conditions and

annealing (56)

b.Effect of excitation intensity (57)

c.Effect of temperature (58)

d.Time-resolved PL (60)

e.Effect of hydrostatic pressure (60)

f.Effect of electron irradiation (60)

g.Optically detected magnetic resonance..61

h.DLTS,positron annihilation,and the

infrared spectra (61)

4.Yellow and red luminescence bands (62)

5.Luminescence in GaN:Mg codoped with

shallow donors (62)

6.Identi?cation of defects in Mg-doped

GaN (62)

C.Luminescence in GaN doped with other

impurities (62)

1.Doping with shallow donors (62)

a.Silicon doping (62)

b.Oxygen doping (63)

c.Selenium doping (63)

d.Germanium doping (63)

2.Doping with acceptors (63)

a.Carbon doping (63)

b.Beryllium doping (64)

c.Calcium doping (64)

d.Cadmium doping (65)

e.Manganese doping (65)

f.Other acceptors in GaN (65)

3.Doping with isoelectronic impurities (65)

a.Arsenic doping (65)

b.Phosphorus doping (66)

4.Radiative defects introduced by

irradiation (66)

5.Transition and rare-earth elements (67)

a.Transition metals (67)

b.Rare-earth elements (67)

VI.DEFECT-RELATED LUMINESCENCE IN

CUBIC GaN (67)

A.Undoped material (67)

1.Exciton emission (67)

2.Shallow DAP band (67)

3.Deep defects (68)

B.Doped material (68)

1.Carbon doping (68)

2.Magnesium doping (69)

3.Silicon doping (69)

VII.EXCITONS BOUND TO POINT DEFECTS (69)

061301-2M.A.Reshchikov and H.Morko?J.Appl.Phys.97,061301?2005?

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A.Free excitons (69)

B.Bound excitons (71)

1.Excitons bound to shallow donors (71)

2.Excitons bound to acceptors (73)

3.Haynes rule in GaN (74)

VIII.UNUSUAL LUMINESCENCE LINES IN

GaN (75)

A.Y i lines (75)

1.Effects of sample treatments and

experimental conditions on the Y i lines (76)

a.Effect of hot wet chemical etching (76)

b.Effect of photoelectrochemical

etching (77)

c.Evolution of PL and memory effect (77)

d.Effect of excitation intensity (77)

e.Effect of temperature (77)

2.Characteristics of the Y i lines (78)

a.The3.45-eV line?Y1? (78)

b.The3.42-eV line?Y2? (79)

c.The3.38-eV line?Y3? (79)

d.The3.35-eV line?Y4? (79)

e.The3.34-eV line?Y5? (79)

f.The3.32-eV line?Y6? (79)

g.The3.21-eV line?Y7? (80)

h.The3.08-,2.85-,2.80-and2.66-eV

lines?Y8–Y11? (80)

3.Y i lines and structural defects (80)

a.Atomic force microscopy (80)

b.X-ray diffraction (80)

c.Transmission electron microscopy (81)

B.Oil-related3.31-and3.36-eV lines (81)

C.Identi?cation of the Y i lines (82)

IX.UNSTABLE LUMINESCENCE FROM

DEFECTS (82)

A.Unstable luminescence bands (82)

1.Blue band from the etched GaN surface..83

2.Blue and yellow unstable bands (83)

B.Manifestation of surface states in

photoluminescence (85)

1.Band bending at the surface of GaN (85)

2.Effect of UV illumination on PL (86)

3.Effect of ambient on intensity and shape

of PL bands (86)

4.Effect of passivation on PL (87)

X.SUMMARY (88)

I.INTRODUCTION

Gallium nitride and its alloys with InN and AIN have emerged as important semiconductor materials with applica-tions to green,blue,and ultraviolet portions of the spectrum as emitters and detectors and as high-power/temperature ra-dio frequency electronic devices.However,further improve-ments in device performance hinge on understanding and reduction of extended and point defects.The lack of native substrates makes the fabrication of ef?cient and reliable de-vices particularly dif?cult,which is typi?ed by dislocation densities in the range of109–1010cm?2on sapphire sub-strates unless special precautions are taken.Isolated point defects and defects related to dislocations are responsible for a variety of ailments in devices.In detectors,they manifest themselves as excess dark current,noise,and reduced re-sponsivity.In light-emitting devices,they reduce radiative ef?ciency and operation lifetime.Furthermore,the point de-fects and complexes are generally the culprits for parasitic current paths.Moreover,they decrease the gain and increase the noise—particularly the low-frequency noise—in elec-tronic devices,increase the threshold current,the slope ef?-ciency and operation lifetime of lasers,and are source of instability particularly in devices relying on charge control and high electric?elds such as?eld-effect transistors.

It is customary to bring a variety of techniques to probe the optical and electrical signatures associated with point de-fects.Luminescence is a very strong tool for detection and identi?cation of point defects in semiconductors,especially in wide-band-gap varieties where application of electrical characterization is limited because of large activation ener-gies that are beyond the reach of thermal means.In spite of considerable progress made in the last decade in light-emitting and electronic devices based on GaN,understanding and identi?cation of point defects remain surprisingly enig-matic.One of the reasons is a vast number of controversial results in the literature.Therefore,a critical review of the state of understanding of point defects,particularly the issues dealing with their manifestation in luminescence experi-ments,is very timely.Even though the optical properties of GaN have been reviewed by Monemar,1–4only a small frac-tion of those reviews concerned themselves with defect-associated luminescence in GaN.It should also be noted that a brief review of point defects and their optical properties in GaN can be found in earlier reviews and books prepared as part of the general properties of GaN.5–13In many original works and reviews,analysis of the luminescence is limited to excitonic emission,a?eld which is well understood,leaving out an earnest discussion of point defects in GaN which still remain unidenti?ed.Traditionally by point defects one means native defects,impurities,and complexes with the size com-parable to the nearest atomic distance.Besides point defects, the crystal lattice may contain extended defects,such as dis-locations,clusters,domains,voids,etc.The latter commonly do not contribute to the luminescence,although may signi?-cantly affect the optical and electronic properties of the ma-terial by trapping carriers or gettering the point defects.

In order to illustrate the myriad of optical transitions that could be and have been observed in the luminescence spectra of GaN associated with defects,we present a table summa-rizing them?Table I?as well as a?gure?Fig.1?showing a schematic description of the related transitions and energy positions within the gap of the defect levels we are about to discuss in detail throughout the review.In addition to the luminescence energy-band positions,Table I tabulates their nomenclature and provides brief comments and references to the sections of this review where these lines and bands are discussed in detail.The energy position of the luminescence lines and bands may depend on strain in thin GaN layers, temperature,and excitation intensity.Therefore,in Table I

a?Electronic mail:mreshchi@ab505386ddccda38366baf5f

061301-3M.A.Reshchikov and H.Morko?J.Appl.Phys.97,061301?2005?

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TABLE I.List of main luminescence lines and bands in GaN. Maximum

position

?eV?Nomenclature Doping Comments Reference to the text

?pages?

3.478FE,X A Undoped69–71

3.471DBE,D0X A Undoped,Si A few close lines71–75

3.466ABE,A0X A Undoped,Mg Best FWHM?0.1meV73–75

3.44–3.46TES Undoped Plethora of lines71–72

3.455ABE Zn A weaker peak at3.39eV49,71–72

3.45–3.46Y1Undoped Correlates with inversion domains75–82

3.41–3.42Y2Undoped75–82

3.397Be e-A type64

3.387FE-LO Undoped69–71

3.38DBE-LO Undoped71–73

3.38Be DAP type64

3.37–3.38Y3Undoped75–82

3.375ABE–LO Undoped73–74

3.364ABE-LO Zn49,71–72

3.35–3.36Y4Undoped75–82

3.34Y5Undoped75–82

3.30–3.32Y6Undoped75–82

3.295FE-2LO Undoped69–71

3.288DBE-2LO Undoped71–75

3.283ABE-2LO Undoped71–75

3.28UVL Undoped e-A type34–37

3.272ABE-2LO Zn49,71–72

3.27DBE DBE in cubic GaN67–68

3.26UVL Undoped,Si DAP type19,34–37,47–48,63

3.1–3.26UVL Mg e-A and DAP53,54,56–62

3.21–3.23Y7Undoped75–82

3.16Shallow DAP in cubic GaN67–68

3.08Y8Undoped80

3.08C In cubic GaN68–69

3.0–3.05BL C Broad63–64

2.9–

3.0BL Undoped,Fe Broad,unstable intensity83–84

2.9BL P Broad,with?ne structure66

2.88BL Undoped Broad,with?ne structure19,38–41,47–48

2.88BL Zn Broad,with?ne structure48–52

2.86Y9Undoped80

2.8Y10Undoped80

2.8BL Cd Broad,with?ne structure64–65

2.7–2.8BL Mg Broad,large shifts56–62

2.6–2.8BL Undoped Broad,surface related83

2.68Y11Undoped80

2.6GL As Broad,with?ne structure65–66

2.6GL Zn Broad48,52

2.56AL Undoped Broad47

2.51GL3Undoped Broad47

2.5Ca Broad64

2.4–2.5Mg–O Broad62

2.48GL Undoped Broad29–34

2.43Hg Broad65

2.36GL2Undoped Broad19,42–48

2.2–2.3YL Undoped,C Broad19–34,47–48,63

1.9–

2.1C Broad,in cubic GaN68–69

1.8–

2.0RL Undoped Broad19,41,47–48

1.85RL2Undoped Broad19,42–48

1.8Zn Broad48,52

1.7–1.8Mg Broad62

1.66Undoped Broad42

1.64C Broad63–64

1.3?Fe?Sharp67

1.27Mn Broad65

1.193?Ti,Cr??Sharp67

0.95Undoped Sharp,irradiation induced66

0.85–0.88Undoped Sharp,irradiation induced66

061301-4M.A.Reshchikov and H.Morko?J.Appl.Phys.97,061301?2005?

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we give the energy positions corresponding to the strain-free GaN at low temperatures and excitation intensities.In the case of dispersion in the reported data for a particular lumi-nescence band,we give the most commonly observed energy position.In Fig.1,the positions of the energy levels are shown in scale,whereas the radiative transitions,depicted by the arrows,correspond to the zero-phonon line,which has higher photon energy than the maximum of the broad lumi-nescence band due to the Stokes shift.

The arrangement of this review is as follows:in Sec.II the theoretical predictions from the ?rst-principles calcula-tions regarding the formation probability and energy levels of main point defects in GaN are reviewed.Although the accuracy of the predictions may not be suf?ciently high,these efforts as a minimum provide a ?rst-order idea on what kind of defects we may expect in GaN while undertaking the task of analyzing the luminescence data.Section III presents basics of the luminescence methods employed.In Sec.IV ,the properties of the main luminescence bands in uninten-tionally doped GaN are reviewed.The plethora of data pub-lished in literature are classi?ed and analyzed,particularly dealing with the notorious yellow luminescence in undoped GaN.The results of different works are often controversial and need careful analysis.In this section,we present some previously unpublished data obtained in our laboratory in order to assist the reader to better formulate a model for a complete picture.

Luminescence from defects intentionally introduced in GaN ?by doping,postgrowth implantation,or by irradiation damage ?is analyzed in Sec.V .Among the numerous impu-rities we give particular attention to magnesium and zinc since these two impurities are of paramount importance for GaN-based devices and the published luminescence proper-ties of GaN doped with Zn and Mg are very controversial.Impurities,such as transition metals and rare-earth elements,are reviewed very brie?y,being beyond the scope of the theme of this review since the luminescence properties of semiconductors doped with these impurities are almost inde-pendent of the host material,being determined mostly by internal transitions associated with these elements but modi-?ed some by the crystal ?eld of the host material.Section VI

brie?y reviews luminescence from the other metastable phase of GaN—zinc-blende or cubic GaN.This crystal poly-type is not well developed and not widely used.Conse-quently,much less space is devoted to defects in cubic GaN.

We also brie?y review the near-band-edge luminescence related to recombination of excitons in GaN in Sec.VII,in part for completeness and in part to distinguish the typical excitonic lines from the unusual luminescence lines appear-ing in the same energy range.The properties of the unusual luminescence lines,inclusive of those that are now attributed to artifacts mistakenly reported in the literature as being re-lated to GaN,are discussed in Sec.VIII.In some cases,the luminescence in GaN evolves under ultraviolet illumination.The changes may be quite large and they are usually detected on time scales ranging from a few seconds to several hours.These changes may be due to metastability of point defects or some light-induced changes at or near the surface of GaN.In this vein,unstable luminescence and the effect of different ambient on luminescence are presented in Sec.IX.Finally,Sec.X brings this comprehensive review to a close with a brief summary.

II.FORMATION AND ENERGY LEVELS OF POINT DEFECTS IN GaN

In this section,the salient features of theoretical calcula-tions that may help to identify luminescence bands in un-doped and doped GaN are reviewed.In early studies,Jenkins and Dow,14based on an empirical tight-binding theory,have estimated the energy levels of vacancies and antisites in GaN.In the past decade since then,ab initio computational methods signi?cantly improved the accuracy of predictions of the defect energy levels in GaN.Neugebauer and Van de Walle,15–17and Boguslawski et al.,18have estimated not only the energy levels of the main point defects in GaN but also their formation energies and possible range of concentra-tions.Thereafter many theoretical groups employed and de-veloped the ?rst-principles calculations germane to nitrides for improved predictions and exploring the likelihood of for-mation of numerous point and structural defects in this material.19–24

A.Theoretical approach

The concentration c of a point defect in the semiconduc-tor formed at a temperature T under thermodynamic equilib-rium conditions is determined by its formation energy E f as

c =N sites exp

?

S f k ?E f

kT

?

,?1?

where N sites is the concentration of sites in the lattice where the particular defect can be incorporated ?N sites ?4.4?1022cm ?3for the substitutional defects in GaN ?and S f is the formation entropy,which is about 6k .19,20When the de-fects or their constituents are impurities,Eq.?1?gives an upper limit of their possible concentrations on the assump-tion that the impurities are abundantly available during the growth.Although the growth is a nonequilibrium process,at suf?ciently high growth or annealing temperatures the con-ditions may be approximated as in equilibrium.Equation ?1

?

FIG.1.Radiative transitions associated with major doping impurities ?see Sec.V ?and unintentionally introduced defects ?Sec.IV ?in GaN.For the V Ga O N complex,two charge states are shown ?Sec.IV B ?.Transitions re-sulting in the GL2and RL2bands are assumed to be internal and the related defect levels are unknown ?Sec.IV F ?.

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shows that E f is the key parameter for estimating likelihood of defect formation.Obviously,the defects with high forma-tion energies have less probability to form.

The formation energy can be calculated in the formalism of Zhang and Northrup25as

E f?q,E F?=E tot?q??E bulk tot??i n i?i+qE F,?2?where E tot?q?is the total energy of a supercell containing one defect in the charge state q,E bulk

tot is the total energy of the defect-free supercell,n i is the number of atoms of type i in this supercell,?i is the chemical potential of atoms of type i, E F?the Fermi level?is the electron chemical potential with respect to the valence-band maximum.The chemical poten-tials for Ga and N are usually considered for extreme growth or annealing conditions:?Ga=?Ga?bulk?for the Ga-rich case

and?N=?N

2for the N-rich case.Note that these values are

not independent in that?Ga+?N=?GaN.The formation en-ergy of the charged defects depends on the charge and the Fermi level at the time of defect formation?during growth or annealing?.As can be seen from Eq.?2?,the formation en-ergy of the positively?negatively?charged defects increases

?decreases?as the Fermi level moves from the valence-band maximum towards the conduction band.The slope of this variation is proportional to the charge state of the defect.The energy at which the levels corresponding to different charge states intersect determines the ionization level of the defect. Note that the calculations of the total energy may in general give an error of up to a few tenths of eV,and a variety of corrections is often used to improve the accuracy.The details on the?rst-principles calculations used for defects in GaN can be found in the recent review by Van de Walle and Neugebauer.26

The above approach enables one to calculate not only the formation energies and positions of the defect levels but also the binding and dissociation energies of complex de-fects,local modes of vibrations,and migration barriers or diffusivity of point defects.Any agreement between different groups,using slightly different approaches,increases con?-dence in the reliability of the results.

B.Native point defects

Native defects are always present in semiconductors and notably affect the electrical and optical properties of the host material.They are often formed as compensation sources when dopants are introduced,or as a result of nonstoichio-metric growth or annealing.The isolated native defects take the form of vacancies,interstitials,and ab505386ddccda38366baf5fplex defects formed through interaction of isolated native defects, and combinations of native defects and impurities are con-sidered in Sec.II D.

Figure2shows the calculated formation energies for all isolated native point defects in GaN as a function of the Fermi level in all stable charge states.The transition levels so calculated for the native defects are illustrated in Fig.3.The slope of each line in Fig.2represents a charge of the defect. For each charge state only the segment giving the lowest overall energy is shown.The changes in slope of the lines represent the energy level of the defect?Fig.3?that can be

measured experimentally.It is clear from Fig.2that self-

interstitial and antisite defects have very high formation en-

ergies and thus are unlikely to occur in GaN during growth at

least in n-type GaN.Gallium and nitrogen vacancies may be

abundant in n-and p-type GaN,respectively.It must be

noted,however,that electron irradiation or ion implantation

can create the defects which have high formation energy in

large concentrations.

1.Vacancies

Similar to the case of GaAs,27vacancies in GaN are

multiply charged defects,and several defect levels may ap-

pear in the energy gap?Fig.3?.A gallium vacancy?V Ga?may be the dominant native defect in n-type GaN,whereas the

nitrogen vacancy?V N?may be abundantly formed in p

-type FIG.2.Formation energies as a function of Fermi level for native point defects in GaN.Ga-rich conditions are assumed.The zero of Fermi level corresponds to the top of the valence band.Only segments corresponding to the lowest-energy charge states are shown.Adapted with permission from Limpijumnong and Van de Walle,Phys.Rev.B69,035207?2004?.Copy-right?2004?by the American Physical

Society.

FIG.3.Transition levels for native defects in GaN,determined from forma-tion energies displayed in Fig.2.Adapted with permission from Limpijum-nong and Van de Walle,Phys.Rev.B69,035207?2004?.Copyright?2004?by the American Physical Society.

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GaN.Evidently N-rich conditions favor formation of V Ga, while in the Ga-rich case the formation of V Ga is facilitated.

a.Gallium vacancy.The gallium vacancy has relatively low formation energy in n-type GaN when the Fermi level is close to the conduction band.Being an acceptorlike defect, the V Ga acts as a compensating center.The2?/3?,?/2?, and0/?transition levels of V Ga are estimated at1.10,0.64, and0.25eV,respectively?Fig.3?.21Slightly larger values of the ionization energies?about1.5,1.0,and0.5eV,respec-tively?have been reported by other authors.22,28However, the formation energies of V Ga3?are consistently low when the Fermi level is close to the conduction band.In n-type GaN the Ga vacancy is completely?lled with electrons,and cap-ture of a photogenerated hole,e.g.,during photolumines-cence measurements,may lead to radiative transition of an electron from the conduction band or from a shallow donor level to the3?/2?level of V Ga.The calculated migration barrier for V Ga3?is relatively low:1.9eV.21Therefore,the Ga vacancies are mobile in a wide range of temperatures typi-cally used during growth or thermal annealing.It is likely that they migrate and form complexes with more stable de-fects.

b.Nitrogen vacancy.Early calculations predicted the en-

ergy levels of the nitrogen vacancy to be close to or inside

the conduction band.14,15,18In fact,owing to these early cal-

culations,the n-type conductivity in undoped GaN has for a

considerable period of time been attributed to V N,14an attri-

bution which is still in circulation.However,the?rst-

principles calculations showed that V N might be formed in

detectable concentrations in n-type GaN only under Ga-rich

conditions.15,18In this scenario,an electron from the reso-

nance0/?state would autoionize to the bottom of the con-

duction band,where it would form an effective-masslike

state bound by the Coulomb tail of the vacancy potential.15,18

Thus V N acts as a donor.There is only one transition level for

V N in the gap which is the3+/+state situated at about

0.5±0.2eV above the valence-band maximum?Fig.3?.21,29

The2+charge state is unstable,and transition from+to3

+charge state causes a large lattice relaxation.21,24,29The

migration barrier for the charge states3+and+is estimated

at2.6and4.3eV,respectively.21Similar to the case of V Ga,

the relatively low migration barriers?at least for V N3+?could pave the way for the formation of complexes between V N

and more stable defects during high-temperature growth or

annealing,especially in p-type GaN where the3+state may

dominate.

c.Divacancy.A divacancy?V Ga V N?has relatively high formation energy in GaN and is unlikely to form in large concentrations?Fig.4?.This particular defect,if formed,is expected to produce at least two deep levels in the energy gap of GaN and behaves as a double acceptor in n-type and as a double donor in p-type GaN.22

2.Interstitials and antisite defects

Formation of interstitial and antisite defects is often con-sidered to have a low probability in GaN due to the small lattice constant of GaN and the large size mismatch between Ga and N atoms.30However,under certain conditions some of these defects may form but in very small concentrations.

a.Gallium interstitial.The large size of the Ga atom leads to high formation energies of the Ga interstitial?Ga i?and associated fairly large lattice relaxations.Only the octahedral site is stable for Ga i.21Although in n-type or under N-rich conditions the formation of Ga i is improbable in thermody-namic equilibrium,it may form under electron irradiation in GaN or under conditions used for p-type growth?Fig.2?. Similar to V N,Ga i is a donor with the resonance+/0state in the conduction band and a3+/+state deep in the band gap ?Fig.3?.18,21The3+/+energy level is predicted at about2.5 eV above the valence band.21A metastable behavior is pos-sible for the3+state.21The migration barrier for Ga i is esti-mated as approximately0.9eV,21in agreement with the ex-perimental results of Chow et al.31who have discovered the mobile Ga i in irradiated GaN at temperatures below room temperature?Sec.V C4?.Note that the optically detected electron-paramagnetic-resonance?ODEPR?experiments in Ref.31apparently detected the2+charge state of Ga i,which was predicted to be unstable.21It is possible that the meta-stable2+state could be activated by optical excitation.21 High mobility of Ga i even at room temperature implies that Ga i is trapped by some other defect?s?and does not exist in GaN as an isolated defect in equilibrium.

b.Nitrogen interstitial.The nitrogen interstitial?N i?forms a N–N bond.15,18,21,24It has a high formation energy, especially in Ga-rich conditions?Fig.2?.Up to four stable levels corresponding to different charge states of N i can be formed in the energy gap?Fig.3?.21The N–N bond distance monotonically decreases with an increasing charge of N i, approaching the bond distance in a N2molecule in the case of N i3+.15,21Note that the two N atoms share one N site in apparently equal relation.The highest stable level??/0?is expected at about2eV above the valence-band maximum.21 Therefore,in n-type GaN,N i will act as a simple acceptor. However,the formation energy of this defect is too high

in FIG.4.Calculated formation energies and ionization levels for the defects in GaN in the Ga-rich case.The dashed lines correspond to isolated point defects and the solid lines to defect complexes,respectively.Reprinted with permission from Mattila and Nieminen,Phys.Rev.B55,9571?1997?. Copyright?1997?by the American Physical Society.

061301-7M.A.Reshchikov and H.Morko?J.Appl.Phys.97,061301?2005?

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GaN grown under equilibrium Ga-rich conditions.The mi-gration barrier for N i is only about1.5eV for the?and 3+charge states,21so that diffusion of nitrogen interstitials is likely to occur in GaN at temperatures slightly above room temperature.

c.Gallium antisite.The gallium antisite?Ga N?introduces a few deep levels in GaN?Fig.3?.18,21The4+/3+level of Ga N is expected at about0.9eV above the valence ban

d.21 Therefore,in p-type GaN this native defect may be respon-sible for signi?cant compensation if the Ga-rich conditions are ab505386ddccda38366baf5frge outward lattice relaxation around the Ga N has been noted by several theorists.18,23

d.Nitrogen antisit

e.The nitrogen antisite?N Ga?appar-ently introduces three21or perhaps even four32deep levels in the energy gap of GaN?Fig.3?.It can behave as a compen-sating double donor in p-type GaN or an acceptor in n-type GaN.The formation energy of N Ga is very high regardless of the position of the Fermi level,especially under Ga-rich con-ditions?Fig.2?.It should be pointed out that Mattila et al.32 predicted a reasonably low formation energy of N Ga3?in strongly n-type GaN grown under N-rich conditions.

The neutral N Ga defect may exhibit a metastable behav-

ior,similar to its analog in GaAs which is known as the EL2 defect.33,34Mattila et al.32and Gorczyca et al.23predicted that the neutral N Ga defect can transform into V Ga N i defect in cubic GaN.

C.Impurities

Generally,C,Si,and Ge on the Ga sites and O,S,and Se on the N sites are considered as shallow donors in GaN, whereas Be,Mg,Ca,Zn,and Cd on the Ga sites and C,Si, and Ge on the N sites could potentially give rise to relatively shallow acceptors in this semiconductor.Below we brie?y review the formation energies and energy levels calculated from?rst principles and by using the effective-mass method. While the former could predict which defect is easier to form,the latter could provide a much better accuracy in de-termining the ionization energy.

1.Shallow donors

Wang and Chen35calculated the energy levels of substi-tutional shallow donors in GaN in the effective-mass ap-proximation accounting for such effects as mass anisotropy, central-cell potential correction,and the conduction-band-edge wave function of the host material.They deduced the following donor ionization energies in wurtzite GaN:34.0, 30.8,and31.1meV for C,Si,and Ge on the Ga site,and 32.4,29.5,and29.5meV for O,S,and Se on the N sites. Boguslawski and Bernholc20considered substitutional C,Si, and Ge impurities in wurtzite GaN in the framework of?rst-principles calculations.They have found that formation en-ergies of Si Ga and Ge Ga donors are reasonably small?0.9and 2.3eV,respectively,for Ga-rich conditions?,while formation of C Ga donor has a low probability.In various theoretical investigations the formation energy of neutral C Ga has been estimated as4–4.7eV for the N-rich case and5.7–6.5eV for the Ga-rich case.20,23,36Neugebauer and Van de Walle17and Mattila and Nieminen22have obtained small formation ener-gies for O N and Si Ga donors?both below2eV in the Ga-rich case?.With decreasing the Fermi level,the formation energy of the shallow donors linearly decreases?Fig.5?,so we may expect an even easier formation of the substitutional shallow donors in high-resistivity or p-type GaN if these impurities are present in the growth environment.

2.Substitutional acceptors

Ionization energies of the main substitutional acceptors in wurtzite and also zinc-blende GaN have been calculated in the effective-mass approximation by Mireles and Ulloa37and Wang and Chen,38the results of which are presented in Table II.

As tabulated in Table II,the main candidates for the shallow acceptors are Be Ga,Mg Ga,C N,and Si N.P?d?r39con-cluded from the analysis of the electronegativity differences between the acceptor atoms and the host atoms that the ion-ization energy of Be Ga is the smallest among the likely ac-ceptors and is only slightly greater than the effective-mass value estimated by the same author as85meV.In the order of increasing ionization energies,the other Ga-substitutional acceptors are Mg,Zn,Cd,and Hg,as follows from the

elec-FIG.5.Calculated formation energies as a function of Fermi level for shal-low donors and acceptors in GaN grown in the most favorable for these dopants conditions?except for Si Ga which should have even lower formation energy in Ga-rich conditions?.Solid lines—Ga-rich case,dashed lines—N-rich case.The zero of Fermi level corresponds to the top of the valence band.The data for Ca,Zn,Mg,and Be are taken from Ref.30,C—from Ref.36,and O and Si—from Ref.53with kind permission from the authors. TABLE II.Calculated acceptor ionization energies?in meV?for wurtzite

?wz?and zinc-blende?zb?GaN.

Acceptor

E A?wz?

?Ref.38?

E A?wz?

?Ref.37?

E A?zb?

?Ref.38?

E A?zb?

?Ref.37?Be Ga187204183133

Mg Ga224215220139

Ca Ga302259297162

Zn Ga364331357178

Cd Ga625620

C N152230143147

Si N224203220132

Ge N281276

061301-8M.A.Reshchikov and H.Morko?J.Appl.Phys.97,061301?2005?

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tronegativity difference between these impurities and Ga atom.39Park and Chadi29examined the atomic and electronic structures of substitutional Be,Mg,and C acceptors in GaN through?rst-principles calculations and concluded that these impurities would give effective-mass states in GaN,not AX states.The calculated formation energies of some of these substitutional acceptors are shown in Fig.5.The formation energies of Mg Ga and Be Ga and their ionization energies are the lowest.One problem for Be,however,is that the atom is too small and can incorporate ef?ciently on the interstitial site,where it acts as a double donor.30,40–42Therefore,among the group-II impurities,Mg and Be are the most promising p-type dopants for GaN,and Be appears to be the best can-didate,provided that the conditions that suppress formation of Be i donors can be established.This is technologically challenging to say the least.The formation energies of ac-ceptors from group-IV impurities,such as Si N and Ge N,are relatively high,so that formation of these acceptors is un-likely in GaN under equilibrium conditions.20,30The forma-

tion energy of C N could be suf?ciently low in Ga-rich conditions.19,20,23,36,43However,the C N acceptor might be compensated by interstitial C when the Fermi level is close to the conduction band.36Note also that the formation ener-gies of the acceptors decrease with increasing Fermi level,so that we may expect ef?cient formation of C N and Si N accep-tors in undoped or n-type doped GaN when these impurities are present in the growth environment.

Neugebauer and Van de Walle30also examined the for-mation energies of acceptors from group-I impurities,such as K Ga,Na Ga,and Li Ga.They predicted that these acceptors have relatively high formation energies and large ionization energies,and are therefore not likely to be candidates for successful p-type dopants.Moreover,the formation energies of the Na and Li interstitials are much lower in p-type GaN, so that these alkali impurities would rather behave as single donors.30

3.Isoelectronic impurities

Arsenic and phosphorus could substitute nitrogen atoms in GaN to form isovalent defects,As N and P N.In silicon, germanium,and most of III-V semiconductors isovalent im-purities do not introduce deep energy levels in the band gap. However,the theory predicts formation of deep gap states by isovalent impurities in GaN,similar to the situation in II-VI compounds,due to large size mismatch of the isovalent at-oms in GaN.44,45The?rst-principles calculations have shown that the As N and P N defects may exist in neutral,+,and 2+charge states in GaN.Mattila and Zunger45predicted the 2?/?and+/0energy levels of As N to be0.24and0.41eV above the valence-band maximum,and those of P N to be 0.09and0.22eV,respectively.45Van de Walle and Neugebauer46obtained the values for the same as0.11and 0.31eV for the2?/?and+/0levels of As N,respectively. The formation energy of As N is quite large,and under the most favorable conditions?Ga rich and Fermi level above 2.3eV?,the?rst-principles calculations predict the formation energy of As N of about4.5eV.In p-type GaN,and/or in N-rich conditions,formation of As Ga antisite-type defect is much more likely.46This defect is a double donor with the 2+/0level at about2.5eV above the valence-band maxi-

mum.In addition,the formation energy is very small when

the Fermi level is close to the valence band.46Therefore,the

presence of As can cause signi?cant compensation during

growth of p-type GaN.

4.Hydrogen

Monatomic interstitial hydrogen is predicted to exist in

two charge states in GaN:H+and H?,whereas the H0state is

unstable?Fig.6?.47–49H+prefers the N antibonding site,

whereas for H?the Ga antibonding site is the most energeti-

cally stable.H+is expected to be mobile even at room tem-

perature due to a small migration barrier?about0.7eV?,

while H?has a very limited mobility in GaN due to a very

large migration barrier?about3.4eV?.47It follows from Fig.

6that the solubility of H is considerably higher under p-type

conditions?where it exists as H+?than under n-type condi-tions?where it is H??.The value of the negative-U effect ?transition of H?into H+?is extremely high??2.4eV?,larger than in any other semiconductor.47In contrast with Si or

GaAs,the H2molecule has low stability and high formation

energy in GaN.47Since hydrogen is abundantly present in

most of GaN growth processes,such as metal-organic

chemical-vapor deposition?MOCVD?,hydrate vapor-phase

epitaxy?HVPE?,and ammonia-based molecular-beam epi-

taxy?MBE?,and easily migrates,especially in p type,it

should form stable complexes with other defects in GaN,

playing an important role in the material properties?see Sec.

II D3?.

ab505386ddccda38366baf5fplexes

From the results of calculations presented in Sec.II B

we expect that none of the simple native defects could exist

in GaN in substantial concentrations.However,complexes

between native defects and impurities,including hydrogen,

are expected to be the dominant unintentionally introduced

defects.

FIG.6.Calculated formation energy of interstitial hydrogen in wurtzite GaN as a function of Fermi level.E F=0corresponds to the valence-band maximum,and formation energies are referenced to the energy of a H2 molecule.Reprinted with permission from Van de Walle,Phys.Status Solidi B235,89?2003?.

061301-9M.A.Reshchikov and H.Morko?J.Appl.Phys.97,061301?2005?

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1.Shallow donor—gallium vacancy complexes

The gallium vacancy is the dominant native defect in n-type?in particular,undoped?GaN because the formation energy of V Ga is low in this case?Fig.2?.However,as noted in Sec.II B1,V Ga could easily diffuse even at moderate temperatures of growth or thermal annealing and would readily form complexes with other defects.It should be un-derscored that formation of complexes is driven by electro-static forces.The impurities that are most likely to form stable complexes with V Ga are donors.A negatively charged acceptor?the charge of V Ga is3-in n-type GaN?and a posi-tively charged donor are attracted to each other.According to the calculations of Neugebauer and Van de Walle,17V Ga O N and V Ga Si Ga complexes act as double acceptors in GaN,and their?/2?energy levels?at1.1and0.9eV,respectively?are close to the2?/3?transition level of the isolated V Ga?at1.1 eV?.The electronic structure of Ga vacancy dominates the electronic structure of the V Ga-shallow donor complexes, very similar to the situation in n-type GaAs.50–52Formation

of the V Ga O N complex is even more favorable than formation of isolated V Ga.17Similar results have been obtained by Mat-tila and Nieminen,22who compared the formation energies of the isolated V Ga and the V Ga O N complex for different posi-tions of the Fermi level?Fig.4?.The V Ga O N complex has a binding energy of?1.8eV,as compared to?0.23eV for the V Ga Si Ga complex.17This indicates that the V Ga O N com-plex is much more stable and it may be the dominant com-pensating acceptor in n-type GaN.The V Ga C N complex has a low formation energy,but is unstable in n-type GaN because both constituents are acceptors and repeal each other.17,36 2.Shallow acceptor—nitrogen vacancy

complexes

The situation with N vacancy and shallow acceptors in p-type GaN is essentially the same as for the Ga vacancy, and shallow donors in n-type GaN.N vacancy,V N,being a mobile and dominant compensating donor in p-type GaN, would be attracted by negatively charged acceptors during growth and cooling down or thermal annealing.The binding energy for a neutral Mg Ga V N complex is about0.5eV,29,53 although Gorczyca et al.54obtained a value of2.8eV.The formation energy of the Mg Ga V N complex is signi?cantly lower than the sum of the formation energies of the isolated Mg Ga and V N.54Park and Chadi29assumed that the Mg Ga V N complex is responsible for the persistent photoconductivity in GaN:Mg55and attributed the bistability to the neutral and 2+states of this complex.Van de Walle et al.53argued that the relatively low binding energy of the Mg Ga V N complex prevents abundant formation of these complexes in p-type GaN in thermal equilibrium.However,their formation can be enhanced by kinetically driven processes on the sample surface during growth.It is not clear where in the band gap the energy level of Mg Ga V N is.Kaufmann et al.56assumed that Mg Ga V N is a deep donor with an energy level at about 0.4eV below the conduction band.Park and Chadi29esti-mated the energy level of?Mg Ga V N?2+at about0.7eV above the valence band,while Gorczyca et al.54obtained an energy level much closer to the valence band.Note that in the latter report the energy level of V N was also much lower than that

obtained in Refs.29and53.Similar to the Mg Ga V N com-

plexes in GaN:Mg,the Be Ga V N complexes are expected to

form in Be-doped GaN.57

Lee and Chang58examined the possibility of formation

of Mg i V N complexes in p-type GaN.While incorporation of

the isolated Mg i is unlikely in GaN due to large atomic ra-

dius of Mg,formation of the Mg i V N complexes has low

enough formation energy when the Fermi level is close to the

valence band.58The charge state of the Mg i V N complex is3+

in this case,and therefore it can ef?ciently compensate Mg Ga

acceptors.58The energy level of the Mg i V N complex?or even

three close levels?is about2.8eV above the valence-band

maximum.Similar results have been obtained by Gorczyca

et al.54Therefore,Mg i V N might be the compensating donor

in p-type GaN:Mg,apparently not Mg Ga V N.The energy level

of the compensating donor has been determined in the pho-

toluminescence study of Kaufmann et al.56at about0.4eV

below the conduction band.Note that the Mg i V N complex

could be formed only under Ga-rich conditions and when the

Fermi level is very close to the valence band.58This means

that passivation with hydrogen or N-rich conditions would

prevent formation of this compensating donor.Lee and

Chang58also assumed that hydrogen passivation can stabi-

lize formation of the Mg i V N complex at higher positions of

the Fermi level.However,this conclusion is somewhat

questionable.54

3.Hydrogen-related complexes

As is commonly the case with other semiconductors,hy-

drogen readily forms complexes with defects in GaN also.In

addition,the formation energies of the hydrogenated defects

are often relatively lower.In n-type GaN,hydrogen atoms

could be bound to a Ga vacancy,in as many con?guration as

four,to form complexes such as?V Ga H?2?,?V Ga H2??,?V Ga H3?0,and?V Ga H4?+.59The?rst three complexes are ac-ceptors,whereas the last one is a single donor.The formation

energies of the V Ga H n complexes are shown in Fig.7.With

the exception of the?V Ga H4?+complex,the

hydrogenated FIG.7.Calculated formation energies of hydrogenated Ga vacancies in GaN as a function of Fermi energy.The formation energies of the isolated vacancy?V Ga3??,of interstitial H+and H?,and of the Si donor are also in-cluded.Reprinted with permission from Van de Walle,Phys.Rev.B56, 10020?1997?.Copyright?1997?by the American Physical Society.

061301-10M.A.Reshchikov and H.Morko?J.Appl.Phys.97,061301?2005?

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vacancies have lower formation energies than the isolated V Ga,which points to the importance of these complexes in GaN.The calculated energy levels of the?V Ga H?2?and ?V Ga H2??complexes?at about 1.0eV above the valence band?are close to that of the isolated V Ga,while the level of

?V Ga H3?0is near the valence-band maximum.59It must be pointed out that in n-type GaN,formation of complexes with several H atoms,such as?V Ga H3?0and?V Ga H4?+,is unlikely since in n-type GaN the isolated hydrogen atom exists as H?which would be repelled from the negatively charged Ga vacancy.59Dissociation of the V Ga H n complexes is unlikely due to the large associated binding energies.59Therefore, once formed during growth in the presence of hydrogen, these complexes cannot dissociate during postgrowth ther-mal annealing.

In p-type GaN,hydrogen passivates the dominant accep-tor?Mg Ga?,as well as the dominant compensating donor ?V N?.47,59In the case of Mg,the electrically neutral Mg–H complex has a binding energy of0.7eV,with the H atom located in an antibonding site behind the N neighbor of the acceptor.47During postgrowth annealing,the Mg–H complex dissociates,and H diffuses either to the surface or to the extended defects.47Similarly,in Be-doped GaN,the Be–H complexes may form with a binding energy of1.81eV and a dissociation energy of2.51eV.40A postgrowth annealing would also be required to remove the hydrogen from Be acceptors.

The N vacancy in p-type GaN may also be passivated by hydrogen during the growth to form the?V N H?2+complex with the binding energy of1.56eV.59The formation energy of the?V N H?2+complex is lower than the formation of the isolated H+and V N when the Fermi level is low in the gap.59 The V N H complexes can be formed only during growth as diffusion of H+towards V N is highly unlikely in p-type GaN since they repel each other.Formation of the?V N H2?+com-plex is also possible,while the?V N H3?0complex is unstable.60The V N H complex is expected to have a2+/0 transition level at about2.5eV above the valence band and a 0/2?level close to the conduction band,60while earlier cal-culations predicted the0/+transition level of V N H to be near or in resonance with the conduction band.59Both V N3+and ?V N H?2+could be formed in abundance in p-type GaN and compensate the dominant acceptor.Note that the hydrogen-ated vacancies may lose their hydrogen after the sample is grown,either during cooling down or during postgrowth an-nealing,and V N3+could also migrate during high-temperature annealing.21

4.Other complexes

The other element,in addition to H,that is unintention-ally present in any growth systems is O which must be dealt with.While O is a ubiquitous problem for all semiconduc-tors,O in GaN takes on a new dimension.The O atom in N site is a shallow donor in GaN and it might hamper attempts to obtain p-type material in addition to causing undesirable background donors.The formation energy of the Mg Ga O N complexes is very low.54Therefore,these complexes can readily form in Mg-doped GaN when oxygen is present in the growth environment.Gorczyca et al.54predicted that for-mation of these complexes would result in semi-insulating

GaN,since both O N and Mg Ga levels would be pushed out of

the energy gap.However,the relatively low binding energy

of the Mg Ga O N complex?0.6eV?is unfavorable for the com-

plex formation,unless the kinetically driven processes on the

surface result in the preferential incorporation of Mg Ga O N.53

In Be-doped GaN,Be Ga O N complex could be formed,

which is neutral.40,41Moreover,the Be Ga O N Be Ga complex

could be formed with the0/?transition level at0.14eV

above the valence-band maximum.40Along with the forma-

tion of Be i2+donors,the?Be Ga Be i?+donor complexes might form in Be-doped GaN which end up compensating the Be

acceptor.40However,the postgrowth annealing at tempera-

tures above600°C should result in dissociation of these

complexes.40

E.Role of dislocations in the point defect formation

Due to large lattice mismatch,heteroepitaxy of GaN on

sapphire substrates results in?lms containing threading dis-

locations with the densities from?108to?1010cm?2,de-

pending on growth method and conditions,and whether dis-

location reducing methods are employed.The situation is not

much different if other substrates with seemingly smaller lat-

tice mismatches are used.These dislocations are mainly par-

allel to the c axis,and their Burgers vectors are equal to a ?edge-type?,c?screw-type?,or a+c?mixed-type?.The?rst-principles calculations enable comparison of formation ener-gies and structures of different types of dislocations and point defects that can be trapped by the stress?elds associ-ated with the dislocations.

In contrast to the earlier prediction that threading dislo-

cations are electrically inactive in GaN,61later calculations

indicated that various types of dislocations may introduce

numerous energy levels in the gap.62–64In particular,thread-

ing dislocations are expected to behave as deep donors in

n-type material and deep acceptors in p type.62Under Ga-

rich conditions dislocations decorated with Ga vacancies

have the lowest formation energy in n-type GaN,while in

N-rich conditions dislocations decorated with Ga vacancies

have the lowest formation energy in p-type GaN.62,65To a

?rst extent these results are consistent with the experimental

?ndings from a scanning-capacitance microscopy study,in-

dicating the presence of negatively charged dislocations in

n-type GaN.66Note that deep donors in n-type material and

deep acceptors in p-type material usually do not contribute to

luminescence,67therefore dislocations are not expected to

manifest themselves in luminescence experiments,unless

point defects are trapped at them due to the large stress?elds

near dislocations.

The behavior of point defects trapped at threading-edge

dislocations in GaN was examined by Elsner et al.68First-

principles calculations indicated that V Ga and its complexes

with one or more O N have very low formation energies at

different positions near the threading-edge dislocations.The

results indicate that the formation energies of V Ga,O N,and

their complexes at different sites near the threading-edge dis-

location are much lower than the formation energies of the

corresponding defects in the bulk.Energy levels of the de-

061301-11M.A.Reshchikov and H.Morko?J.Appl.Phys.97,061301?2005?

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fects trapped at dislocations generally shift as compared to the point defects in bulk,however,the shift is not large.68In short,the stress?eld of threading-edge dislocations is likely to trap Ga vacancies,oxygen,and their complexes.A variety of the V Ga-containing complexes may form acceptorlike de-fect levels in the lower half of the band gap and therefore be responsible for some transitions observed in luminescence experiments.Note that a similar situation might take place in p-type GaN,where the dislocations may trap V N and V N-related complexes.

III.LUMINESCENCE METHODS

Photoluminescence?PL?and cathodoluminescence?CL?have been the most widely used experimental methods ap-plied to investigations of GaN.Defects in GaN have been studied by analyzing the steady-state PL?SSPL?,time-resolved PL?TRPL?,and PL excitation?PLE?spectra.Opti-cally detected magnetic resonance?ODMR?,a variant of the PL technique,along with the positron annihilation method has been extensively used for identi?cation of point defects in GaN.

A.Steady-state photoluminescence

The SSPL spectroscopy is widely used for qualitative analysis of GaN and its ab505386ddccda38366baf5fmonly,the SSPL is gen-erated in GaN by illuminating it with a He–Cd laser?325 nm?beam with optical power levels of up to approximately 60mW.In investigating defects,however,special precaution must be taken to employ a suf?ciently low excitation density since the defect-related PL often saturates at power densities of the order of10?2–10?1W/cm2.Failure to do so would very likely cause skewing of the PL spectrum in favor of excitonic emission at higher excitation densities,giving the false impression about the relative strength of defect-induced transitions.Similarly,focusing the laser beam and using small slit widths of a monochromator for the entire PL spec-trum would also distort the PL in favor of excitonic transi-tions.In such a case,the chromatic dispersion of lenses used to collect the PL,as well as the different effective sizes of the emission spots for the ultraviolet?UV?and visible emission attributed,in particular,to photon-recycling process,69may lead to a marked,but arti?cial,enhancement of the UV?near band edge?over the visible part in the PL spectrum?mainly defect-related?.

Qualitative terms,such as“very intense PL that con?rms high quality of the material,”are omnipresent in the litera-ture regarding GaN.However,there have been very few at-tempts to estimate the absolute value of the PL intensity or its quantum ef?ciency?QE?for a quantitative analysis.Al-though the direct measurement of the QE is not straightfor-ward,attempts have been made to estimate this important parameter for GaN.70,67G?ldner et al.70simultaneously de-tected the calorimetric absorption?measure of nonradiative recombination which results in heating of the sample?,trans-mission,re?ection,and excitation power,and reported the QE to be below20%for thin GaN layers grown by MOCVD on sapphire and up to75%for bulk GaN crystal grown by HVPE.An indirect method based on quantitative analysis of the competition of radiative and nonradiative recombination

channels was suggested by Reshchikov and Korotkov,67and

is presented in Sec.III A3.

Quantitative studies of point defects in GaN by PL have

rarely been undertaken.Often,qualitative estimations of the

acceptor concentration in n-type GaN were made by compar-

ing the ratios between the defect and near-band-edge emis-

sion intensities.71,72However,this ratio is shown to depend

not only on the defect concentration but also on the experi-

mental conditions,in particular,on the excitation

intensity,67,73,74as was mentioned above.Temperature depen-

dence of the defect-related PL intensity in GaN has often

been used to determine the nature of a given optical transi-

tion.For example,the donor-acceptor-pair?DAP?transitions

have been distinguished from the conduction-band-acceptor ?e-A?transitions by the thermal behavior of PL.75–77How-ever,the thermal behavior of PL may be complicated by a

competition between several recombination channels as is

shown below using a simple phenomenological approach.67 1.Recombination statistics

Let us now consider an n-type semiconductor containing

several radiative acceptors A i with concentrations N A

i

.The electron-hole pairs are excited with a generation rate G?cm?3s?1?.The concentration of the photogenerated holes in the valence band is p,the concentration of equilibrium ?n0?and photogenerated??n?free electrons is n=n0+?n.Af-ter optical excitation,the holes are captured by acceptors at the rate C pi N A

i

?p,where C

pi

?cm3s?1?is the hole-capture co-ef?cient for the i th acceptor and N A

i

?is the concentration of ionized acceptors of type i.A competing process is the for-mation of excitons with the rate C ex np,where the coef?cient C ex describes the ef?ciency of the exciton formation.In ad-dition to radiative processes,some of the holes recombine nonradiatively.For simplicity,the nonradiative recombina-tion rate can be introduced as C ps N S?p,where C ps and N S?are the average hole-capture coef?cient and the concentration of the nonradiative centers,respectively.Thus,in general,the hole-capture rate can be expressed as C i N i?p,where C i=C ex, C pi,or C ps and N i?=n,N A

i

?,or N

S

?for excitons,radiative ac-ceptors,and nonradiative defects,respectively.

At elevated temperatures,the bound holes may return to

the valence band as a result of thermal activation or exciton

dissociation.The probability of this process,Q i?s?1?,is pro-portional to exp??E i/kT?,where E i is the thermal activation energy for the radiative acceptors?E A

i

?,nonradiative centers ?E S?,or the exciton dissociation energy?E ex?.Taking into account all these processes?Fig.8?,the detailed balance equation for the hole concentration in the valence band in steady state in the case of N recombination channels can be written in the form

?p

?t=G?

?

i=1

N

C i N i?p+?i=1

N

Q i N i0=0,?3?

where N i0=N A

i

0,N

S

0,and N

ex

is the concentration of holes bound to radiative acceptors,nonradiative centers,or form-ing excitons,respectively.At suf?ciently low excitation in-

061301-12M.A.Reshchikov and H.Morko?J.Appl.Phys.97,061301?2005?

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tensities,N i 0?N i ?

?N i ,the steady-state equation for the con-centration of holes bound to the i th defect can be written as

?N i

0?t =C i N i p ?N i 0?R i

?Q i N i 0=0,?4?

where the second term describes recombination via the i th

channel and the parameter ?R i characterizes the recombina-tion lifetime ?in general case it may evolve in time in tran-sient processes ?.

The capture rates are usually much faster than recombi-nation rates.As a result,the ef?ciency of each of the recom-bination channels is proportional to the rate of capture of the minority carriers ?holes in n -type GaN ?.Therefore,in the low-temperature limit,where both the thermal release of the bound holes and the exciton dissociation are negligible,the QE of each recombination channel,?i ?0?,is given by the ratio of hole-capture rate for a speci?c recombination chan-nel to the total escape rate of holes from the valence band

?i ?0?=

C i N i p

?j =1N

C j N j p =

C i N i

?j =1

N

C j N j .?5?

With the above assumptions,an expression for the intensity

of PL via each defect can be determined as 67

I i PL =

N i 0?R i =?i G =?i

*1+?1??i *??R i

Q i G ,?6?

where

?i *=?i ?0??

1??

j i

N

?j ?0??Rj Q j

1+?Rj Q j

?

?1

,?7?

and ?i is the QE of the i th channel accounting for dissocia-tion of excitons and thermal escape of holes from the defects to the valence band.

2.Effect of temperature on PL intensity

It is evident from Eqs.?6?and ?7?that the temperature

dependence of the PL intensity in n -type GaN is largely de-termined by exciton dissociation and thermal escape of holes from the defects to the valence band.Although the exact expressions for the exciton dissociation can also be derived,78it is much easier to account for the contribution of the exciton dissociation into the defect-related PL ?the term ?R ex Q ex ?by taking the temperature dependence of the inte-grated exciton emission intensity from the experiment.67

The probability of thermal activation of holes from an acceptor,Q A i can be obtained from a detailed balance as

Q A i =C pi g ?1N V exp ??E A i kT ?

?8?

with

N V =2

?m h kT

2??2?

3/2

?9?

and

C pi =?pi ?p =?pi

?

8kT

?m h

,?10?

where g is the degeneracy factor of the acceptor level,N V is

the density of states in the valence band,m h is the effective mass of the holes in the valence band,?p is the hole thermal velocity,and ?pi is,by de?nition,the hole-capture cross sec-tion of the i th acceptor.An analysis of Eqs.?6?and ?8?shows that the temperature dependence of PL intensity for the i th acceptor involves a region of thermal quenching with an ac-tivation energy E A i at temperatures T satisfying the condition

?1??i *??R i Q i ?1.Variation of the parameter ?i *

in the region of thermal quenching of PL related to i th acceptor can be ignored if the quenching regions for different defects do not overlap signi?cantly.Parameters E A i and C pi ?or ?pi ?can be obtained by ?tting Eq.?6?to the experimental dependence of the PL intensity in the region of thermal quenching of the PL band related to the i th acceptor.Note that the value of E A i calculated from the ?t to the experimental data using Eq.?6?is somewhat different from the ionization energy obtained from the slope of the Arrhenius plot of I PL ?T ?1?due to the temperature dependence of N V and C pi .The temperature de-pendence of the acceptor energy level may also lead to some discrepancy between the value of E A i at temperatures of PL quenching and the value of E A i ?T =0?obtained from the low-temperature spectroscopy.

An analysis of Eqs.?6?–?8?also indicates that the inte-grated PL intensity for the given recombination channel at a given temperature depends on the quenching state of the rest of the recombination channels.Therefore,several

increases

FIG.8.Schematic of the main transitions in n -type GaN in conditions of PL.Electron-hole pairs ??n =p ?are created with the rate G by optical exci-tation.The photogenerated holes are captured by radiative acceptors ?one acceptor level A i is shown ?,nonradiative defects ?S ?,and form excitons ?Ex ?.The level for excitons is conventional,meaning only that some energy is required to dissociate the excitons.The solid and dotted lines show the transitions of electrons and holes,respectively.Optical transitions are shown by the straight solid lines;recombination of holes at nonradiative centers with free electrons is shown with a dashed line.Rates for all the transitions are noted.

061301-13M.A.Reshchikov and H.Morko?J.Appl.Phys.97,061301?2005?

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of the PL intensity are expected in the form of intensity steps corresponding to thermal quenching of other PL bands.An example of the calculated temperature dependencies of PL intensity related to three radiative recombination channels is shown in Fig.9.The increase in PL intensity in the region of thermal quenching of a particular recombination channel is associated with the redistribution of the released holes among all unquenched channels.The complete quenching of the i th channel results in the stepwise increase of the PL intensity from other recombination channels R i times,if the overlap of the quenching regions can be neglected.A simple expression for R i can be obtained from Eqs.?6?and ?7?

R i ?1+

?i ?0?

1?

?j

?j ?0?

,?11?

where the summation is taken over the recombination chan-nels which have been thermally quenched prior to the quenching of the i th channel.

Besides the above analysis of the PL intensity,the tem-perature dependencies of the PL band line shape and peak position can sometimes provide useful information on the nature of transitions and the type of a defect.The effect of temperature on the PL spectrum related to a deep-level defect is discussed in Sec.III D.The PL bands caused by DAP recombination are expected to shift to higher photon energies ?blueshift ?with increasing temperature due to thermal escape of electrons from long-lived distant pairs contributing at the low-energy side of a PL band due to weaker Coulomb interaction.79,80However,one should be careful with the in-terpretation of the shift since defects with strong electron-phonon coupling often exhibit a blueshift owing to the par-ticulars of their adiabatic potentials.81Moreover,the PL bands from DAPs with relatively deep donors and acceptors may exhibit red or blueshift with temperature,depending on the excitation conditions.80,82

3.Estimates of quantum ef?ciency

The QE of PL can be estimated from the temperature dependence of the PL intensity using Eq.?11?.The relative values of ?i ?0?can be obtained at low temperatures as the integrated PL intensities for all the PL bands.67The absolute value of ?i ?0?can be calculated from the value of the step-wise increase in PL intensity for any band,which is related to the thermal quenching of the i th channel

?i ?0?=

?

1

R i ?1

+?j

I j PL ?0?I i

PL ?

?1

,?12?

where the summation is taken over the channels quenched prior to quenching of the i th channel.

The internal QEs estimated by this method in undoped GaN layers agree well with the values obtained by direct measurement of the laser and PL power levels with correc-tion for re?ection and the geometry of the PL collection setup.67In this review,we give the values of the QEs for different GaN samples calibrated by using the same standard,whenever the data allow.

4.Effect of excitation intensity on PL intensity

High and even moderate excitation power levels could saturate the defect-related PL since the defect concentration and lifetime are ?nite.Let us now consider the case when thermalization of the holes trapped by the i th acceptor is negligible and assume that only the i th acceptor is subject to saturation by nonequilibrium holes in the considered excita-tion range.Then,from the steady-state rate equations similar to Eqs.?3?and ?4?one can obtain an expression for the PL intensity related to the i th acceptor as 67

I i PL =

N i

0?R i =12?G +N i ?i ?R i

??

12??

G +

N i

?i ?R i

?

2

?

4GN i

?R i

,?13?

which for the case of low QE of the i th channel ??i ?1?simpli?es to

I i PL ?

G G ?R i N i

+1?i

.

?14?

For low-excitation rates ?G ?R i ?i ?N i ?,the I i PL ?G ?depen-dence is linear and at high excitation rates it is expected to

saturate at the value of N i ?R i

?1

.Instead of complete saturation,a square-root dependence of the PL intensity is often ob-served for defects in GaN at excitation densities above the range of 10?2–1W/cm 2.67,74,83

The square-root dependence of the defect-related PL in-tensity as a function of the excitation power is expected at high-excitation densities when the concentrations of photo-excited carriers ??n and p ?exceed the free-electron concen-tration in dark ?n 0?.67,74However,the excitation density nec-essary to inject ?n ,p ?1018-cm ?3nonequilibrium carriers ?typical concentration of free electrons in GaN at room tem-perature ?,is about 105W/cm 2,84which is much higher than that commonly used in defect-related PL studies.One of

the

FIG.9.Calculated temperature dependencies of the PL QE for three radia-tive recombination channels in GaN:excitonic ?ex ?and via two acceptors

?A 1and A 2?.The dependences were calculated using Eqs.?6?–?10?with the following parameters:?ex ?0?=0.2;?A 1?0?=0.2;?A 2?0?=0.08;?R ex Q ex =250exp ??10meV/kT ?,?R 1=10?5s,?R 2=5?10?5s,C p 1=10?6cm 3s ?1,C p 2=4?10?7cm 3s ?1,E A 1=0.34eV,E A 2=0.8eV.Reprinted with permis-sion from Reshchikov and Korotkov,Phys.Rev.B 64,115205?2001?.Copyright ?2001?by the American Physical Society.

061301-14M.A.Reshchikov and H.Morko?J.Appl.Phys.97,061301?2005?

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reasons for the square-root dependence of the defect-related PL at moderate excitation powers is recombination through nonradiative donors that may be present in GaN in relatively high concentrations,particularly near the surface.67Another possibility is the reabsorption of the UV emission by deep-level defects,which is known as photon recycling.

5.Estimates of acceptor concentration in n-type GaN

Once the hole-capture coef?cients C pi are evaluated for different acceptors?Sec.IV H for defects in undoped GaN?, the ratio between the concentrations of each acceptor can be determined from an analysis of the low-temperature PL spec-trum.This is a simple and effective method for estimating the relative concentrations of unintentional acceptors in n-type GaN,and one that could be widely employed for a sample characterization.Indeed,all that is necessary is the ability to measure the PL spectrum at suf?ciently low tem-peratures and excitation intensities85followed by?nding the integrated intensity for each band in relative units.Then,the ratio between the concentrations of the i th and j th acceptors can be found as67

N A

i N A

j =

I i PL

I j PL

C pj

C pi

.?15?

To determine the absolute values of the acceptor concentra-tions,the concentration of one of the acceptors should be found independently by?tting the dependence of the PL in-tensity on excitation intensity,as described in Sec.III A4.

B.Time-resolved luminescence

By measuring the PL intensity at a given photon energy as a function of time delay after an excitation pulse,valuable insight can be garnered about the recombination mecha-nisms.A full emission spectrum can also be measured at different decay times.A spectral analysis helps to distinguish the overlapped PL bands and investigate the evolution of the PL band shape and its shift with time.

The luminescence decay in GaN is often nonexponential, especially at low temperatures.The most plausible cause for the nonexponential decay of PL is the DAP recombination. When an electron bound to a donor recombines with a pho-togenerated hole bound to an acceptor,the radiative recom-bination rate W is not constant but depends exponentially on the separation,R,between the donor and acceptor

involved,79,86

W?R?=W max exp??2R a D ?.?16?

where W max is the transition probability in the limit R→0 and a D is the Bohr radius for a more weakly bound particle ?an electron on the shallow donor in GaN?.It is evident from Eq.?16?that the lifetime of the bound hole,?=W?1,is much

longer for distant pairs than for close ones.This results in an increase of the instantaneous lifetime of the measured PL with the time delay.The transient PL depends on the details of the spatial distribution of pairs.Thomas et al.79obtained the following expression for the PL intensity decay in the case of a random distribution of DAP:

I?t??N exp?4?N?0??e?W?R?t?1?R2dR

?

??0?W?R?e?W?R?t R2dR,?17?

where N is the concentration of the majority constituent in DAPs.Equation?17?combined with Eq.?16?describes well the nonexponential decay of low-temperature PL in undoped GaN.76,87

From simple reasoning,we expect an increase of W max with increasing ionization energy of an acceptor E A due to increasing localization of the bound hole.Indeed,the maxi-mum rate of the DAP transitions in the effective-mass ap-proximation upon neglecting many-body effects is given by80,88

W max=64A?a A a D

?3,?18?

where the parameter A depends on the optical properties of the semiconductor and on the photon energy???A?s?1??4.5?108???eV?for GaN?,and a A is the Bohr radius for the bound hole given by89

a A=

?

?2m

h

E A

.?19?

Although the effective-mass approximation may not be a good choice for deep-level defects,it nevertheless provides surprisingly good results.88,90

Note that potential?uctuations,typically present in highly compensated and/or heavily doped semiconductors as a result of the random charge distribution,91also result in a nonexponential PL decay.This is due to localization of car-riers in potential wells,very similar in nature to their local-ization on spatially separated donors and acceptors.The problem of the potential?uctuations is discussed in more detail in Sec.V B2.

With increasing time delay,PL bands originating from the DAP-type transitions,especially those involving deep donors,are expected to shift to lower energies.79,80This ef-fect is caused by a faster recombination in close pairs,which contribute to the high-energy side of the band due to a stron-ger Coulomb interaction.The deeper the donor,the larger the shift is expected,but it still remains below the value of ion-ization energy of the donor.80The absence of a noticeable shift of a PL band with the time delay may indicate that shallow donors are involved.

With increasing temperature,the electrons from shallow donors thermalize to the conduction band,and the DAP tran-sitions are gradually replaced by transitions from the conduc-tion band to the same acceptor?e-A transitions?.For the e-A transitions,the decay is commonly exponential and the char-acteristic radiative lifetime,?R,depends on the free-electron concentration n0,provided that n0??n.The electron-capture coef?cient for the acceptor C n can then be expressed as

061301-15M.A.Reshchikov and H.Morko?J.Appl.Phys.97,061301?2005?

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?R =

1C n n 0

.?20?

The electron-capture coef?cient in the effective-mass ap-proximation for a neutral defect can be approximately esti-mated as 80

C n =64?Aa A 3

.

?21?

In the transition temperature range where the decay gradually transforms from nonexponential to exponential,the average

or effective lifetime of PL,?R

*

,can be introduced.87It is de?ned as the time delay corresponding to the position of a maximum in the dependence t ?I PL ?t ?,where I PL ?t ?is the PL

intensity at time t .In the case of the DAP recombination,?R *

is the time of transition between the pairs,giving the largest contribution to the PL after pulse excitation.In the case of

the e-A transitions,?R

*

is the characteristic time of decay ?PL intensity decays as exp ??t /?R *

??.

In the temperature range where the SSPL intensity quenches,the lifetime of PL usually decreases with an acti-vation energy corresponding to thermalization of holes from an acceptor to the valence band.In general,the PL lifetime ??PL ?with allowance made for thermalization of holes can be expressed as 92

?PL ?1

=?R ?1+?q ?1=C n n 0+K exp ??

E A

kT

?

,?22?

where E A is the ionization energy of the acceptor,?q is the characteristic time of the hole escape to the valence band,and the coef?cient K depends on the hole-capture character-istics of the acceptor.

Similar to Eq.?10?for nonradiative capture of holes,we can de?ne the capture cross section for electrons,?n ,as

?n =C n v n ?1?C n

?8kT

?m n

?

?1/2

,?23?

where v n and m n are the velocity and effective mass of free electrons ?m n =0.22m 0for GaN ?Ref.93??.Note that whether C n and C p or ?n and ?p are temperature dependent or not is still an open question for defects in GaN.

C.Vibrational properties of deep-level defects

In contrast to the shallow defects,recombination of car-riers at deep-level defects usually results in broad PL bands due strong electron-phonon coupling.This mechanism can simply be illustrated as follows:For a deep acceptor,the hole wave function is localized at one of the bonds and its asym-metrical location would cause the atoms to shift from their ideal sites,as shown in Fig.10.After recombination of the bound hole with a free electron or electron at a spatially separated donor,the atoms would move to their original sites because all the bonds are restored and equivalent ?Fig.10?.The atomic relaxation causes vibration of the lattice,i.e.,emission of phonons.The radiative emission energy is re-duced by the energy released through phonon emission.In different recombination processes,the number of emitted phonons is different,which results in a broad PL band.

The measure of the electron-phonon coupling is the Huang–Rhys factor,S .94The larger the S ,the stronger the electron-phonon coupling is and the broader the PL band is.The so-called con?guration coordinate ?CC ?model 95–97is often used to illustrate and even quantitatively describe re-combination involving a localized carrier.The simplest one-dimensional CC diagram is illustrated in Fig.11.In this dia-gram,adiabatic potentials represent the total potential energy,including electron and nuclear,of the defect.The equilibrium positions of the ground and excited states are displaced according to the strength of the electron-phonon coupling.In the simplest case,the electronic state interacts with a single localized vibrational mode of frequency ?0.In general,the phonon frequencies in the ground and excited states may be different and are represented by the terms ?0

g and ?0e ,respectively.At low temperatures ?kT ???0e

?optical transitions take place from the zero vibrational level of the excited state,and the maximum of the emission ?E max ?cor-responds to the solid vertical line AB indicated in Fig.11.After emitting a photon,the system relaxes to the zero vibra-tional level of the ground state by emitting several phonons with energies ??0g in the crystal ?transition B →C ?.Probabil-ity of optical transition from the zero level of the excited state to the n vibrational level ?n =0,1,2,…?of the ground state is determined by the Poisson

distribution

FIG.10.Schematic representation of a recombination of the localized hole

with a free electron,resulting in emission of a photon and several

phonons.

FIG.11.An example of the CC diagram and resulting PL spectrum.

061301-16M.A.Reshchikov and H.Morko?J.Appl.Phys.97,061301?2005?

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W 0→n =e

?S S n

n !

.?24?

In the case of strong electron-phonon coupling ?S ?1?,S represents the mean number of the emitted phonons for each photon absorption or emission process.The larger the S ,the wider the band and the less resolved transitions correspond-ing to different vibration levels are.In general,the Huang–Rhys factor,S ,is different for absorption and emission,S ab and S em ,and yet in the one-dimensional CC approximation a simple relation between these values can be obtained

S ab S em =??0

e ??0

g .?25?

The full width at half maximum ?FWHM or W ?of the

PL band depends on temperature T and in the one-dimensional CC model W(T)is given by

W ?T ?=W ?0?

?coth

???0

e 2kT ?=

??8ln 2

S em ??0

g ?S ab

??coth ???0

e 2kT

?

.

?26?

At high temperatures,the bandwidth is proportional to T 1/2and at low temperatures it is temperature independent.Thus,it is possible to ?nd parameters W ?0?and ??0e from the tem-perature dependence of the FWHM of a PL band.Further,if the position of the zero-phonon line ?E 0?is known,one can

estimate the quantity ???0g S em ?with the accuracy of 12???0g

???0e ?:

??0g S em =?E 0?E max ?+12??0g ??E 0?E max ?+12??0e

,

?27?

and then ?nd parameters ??0g ,S em ,and S ab using Eqs.?25?and ?26?.

The temperature-related shift,?E em =E em ?T ??E em ?0?,of the broad PL band may have little or no correlation to the band-gap reduction.The following expression for ?E em is derived in the one-dimensional CC approximation for a de-fect with strong electron-phonon coupling 81

?E em =

?

?g 2??e

2

?e

2+

8?e

4?e 2??g

2

+

?e 2?

??

E abs ?E em

E em

?

kT .?28?

Thus,a shift to higher or lower energies can be observed for the broad PL bands with increasing temperature,depending on the particulars of the adiabatic potentials of the recombi-nation centers.

It is important to note that in the cases of e-A and DAP transitions involving shallow donors,the shapes of the adia-batic potentials are determined solely by the adiabatic char-acteristics of the acceptor since its wave function is more localized.Therefore,no difference in the shape of the PL band can be noted between the e-A and DAP transitions in the ?rst approximation.Only the positions of the PL bands would be shifted by the ionization energy of the donor.How-ever,this shift often remains unnoticed due to the large PL bandwidth and strong temperature dependence of the band position.

D.Photoluminescence excitation spectra

PLE spectrum for a particular PL band can be obtained by using a tunable laser or a broad band lamp combined with an additional monochromator as the excitation source.The monochromator dispersing the PL is set to a particular wave-length,which is usually at the maximum of the analyzed PL band,and the wavelength of the excitation source is varied in order to obtain the excitation spectrum.The PLE spectrum is expected to coincide with the absorption spectrum with the difference that in the latter case several different transitions may contribute and complicate the spectral analysis.Photo-ionization of a defect is an inverse process to the lumines-cence,and in n -type GaN it involves a transition of an elec-tron from an acceptor level to the conduction band,or to the excited state of the defect.In p -type GaN,we may expect a very similar photoionization of an electron from the valence band to a deep donor,followed by a recombination between this electron and a free hole.Note that the photoionization spectra measured by PLE,absorption,photocapacitance,or photoconductivity methods should have more or less similar shapes since the mechanism of the photoexcitation is the same in all the above cases.

Broad PL bands arising from deep-level defects with strong electron-phonon couplings usually result in broad bands in the PLE spectrum also.This is illustrated schemati-cally in Fig.12.At low temperatures,the system in the ground state ?represented by an acceptorlike defect ?lled with electrons in n -type GaN and the surrounding neighbor-ing atoms ?stays at zero level and oscillates.The energy pro-vided by the optical excitation source can bring the system to an excited state ?solid line CD in Fig.12?.The transition C →D in our example corresponds to a transition of an elec-tron from the acceptor level to the conduction band or to the excited state of the acceptor near the conduction band if any.The electron transition is much faster than the motion of atoms ?adiabatic approximation ?.Therefore,the transition is vertical in

the CC diagram.Depending on the phase of the

FIG.12.An example of the CC diagram and resulting PLE spectrum.

061301-17M.A.Reshchikov and H.Morko?

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zero-level oscillations,the system may be closer or farther

from the equilibrium point in the excited state?as shown by

the dashed lines on both sides of transition CD?.Therefore,

after numerous photoexcitation processes the absorption en-

ergy evolves into a broad band.In the case of a strong

electron-phonon coupling,which causes the minima of the

ground and excited states to be suf?ciently displaced,the

shape of the absorption band is nearly Gaussian.However,

for a weak electron-phonon coupling and small displacement

of the adiabatic potential minima the shape of the absorption

band is asymmetric with an abrupt edge near the zero-

phonon transition line,E0.After the excitation,the system

relaxes to its minimal energy position by emitting several

local or lattice phonons?transition D→A?.Then the system

stays at the zero level at low temperatures and after a period

of time?PL lifetime?it returns to the ground state by emis-

sion of a photon?A→B?and consequent emission of a few

phonons?B→C?.

For transitions of electrons from the defect level to the

conduction band the shape of the PLE or absorption spec-

trum may depart from the Gaussian shape and have an ex-

tended shoulder at the high-energy side due to the possible

transitions to the quasicontinuous states in the conduction

band.When the energy of the excitation becomes equal or

exceeds the band gap,transitions of electrons from the va-

lence band to the conduction band and subsequent nonradi-

ative capture of a hole by a deep acceptor?nonresonant ex-

citation of the acceptor?would give a step in the PLE

spectrum corresponding to the band-to-band absorption.The

relative contribution of the resonant and nonresonant transi-

tions in the PLE spectrum depends on the thickness of the

sample and speci?c values of the nonradiative and optical ?photoionization?capture cross sections for a particular ac-ceptor.The energy displacement of the emission and absorp-

tion maxima?Stokes shift?facilitates the measurement of the

PLE spectra.

The PLE spectra from deep-level defects,including con-

tributions from the resonant and nonresonant excitations,

have been studied in GaN?Refs.76and98–100?,and are

discussed in Secs.IV A6and IV B2.

E.Spatially and depth-resolved cathodoluminescence

CL is produced by absorption of high-energy electrons

and resultant spontaneous emission of light corresponding to

speci?c transitions in a semiconductor.It can be detected as

a CL spectrum or as a distribution of CL intensity over a

certain area of the semiconductor surface?CL image?.The

latter case is conveniently facilitated by a combination of a

scanning electron microscope and a luminescence collection

system.When an incident electron beam bombards the semi-

conductor under test,it?rst causes the emission of secondary

electrons from a thin surface layer which is on the order of

10nm causing that region to be positively charged.101The

secondary electrons also penetrate into the sample to some

depth which depends on the acceleration voltage?V b?.This negatively charged layer is much thicker than the positively charged surface layer from which the secondary electrons escaped.The electron penetration depth in GaN increases from about0.2to more than4μm as V b is increased from5

to35kV.102,103Note that the energy-loss depth pro?le maxi-

mizes at approximately30%of the penetration depth.104The

penetration depth increases with increasing V b,and the

electron-hole pair generation rate is proportional to the beam

power?E b I b?.The CL intensity is determined not only by the generation rate but also by the penetration depth through the

process of self-absorption,105surface recombination,compe-

tition of different recombination mechanisms,and migration

of charges with time.101,103

Depth-resolved CL experiments are usually conducted

under constant beam power or constant power-density con-

ditions.The penetration depth is varied by varying the accel-

erating voltage.Depth-dependent CL spectra can be taken

also from the edge of a cleaved sample.Since the radiated

area is about0.1–1?m2,depth pro?ling is especially condu-cive for thick layers or bulk samples since electrons cannot penetrate deeper than?5?m.

To obtain a CL image at a certain photon energy which

can be varied,the electron beam is scanned over an area of

up to0.1?0.1mm2.Such images may help identify the lu-

minescence bands and determine their spatial distribution

and relation to structural defects.

F.Optically detected magnetic resonance

Electron paramagnetic resonance?EPR?and its variant,

ODMR,provide information on the ground state and micro-

scopic origin of defects through obtaining the values and

angular dependencies of the Zeeman splitting?g tensor?and

interpretation of any hyper?ne ab505386ddccda38366baf5fpared to EPR,

ODMR relates the magnetic information to particular lumi-

nescence bands and assists their identi?cation.

The g value of the free electron is g e=2.0023.In the

?rst-order perturbation theory the deviation of the g value for

a particular center is given by?/?E,where?is the spin-

orbit interaction constant.106Usually donors show g values

smaller than free electrons,and acceptors have a positive g

shift.However,there are exceptions to this simple rule.107

Donors in GaN are typically characterized by g factors be-

tween1.949and1.962,showing a small anisotropy?g??g??0.003–0.006?.Acceptors are characterized by a relatively larger value and anisotropy of the g factor.108,109

IV.LUMINESCENCE RELATED TO POINT DEFECTS IN UNDOPED GaN

Typical low-temperature PL spectra from selected unin-tentionally doped GaN samples are shown in Fig.13.In addition to the near-band-edge emission due to bound and free exciton transitions and their phonon replicas,the PL spectrum from undoped GaN almost always contains a broad yellow luminescence?YL?band with a maximum at about 2.2eV?Fig.13?.The YL band is by far the most studied PL band in GaN.Despite this inordinate effort,it is still not clear how many and what kind of defects contribute to that broad emission band?see Sec.IV A?.In high-purity GaN grown by HVPE,the YL band is replaced by a green luminescence ?GL?band at about2.5eV under certain experimental

061301-18M.A.Reshchikov and H.Morko?J.Appl.Phys.97,061301?2005?

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conditions.110–114The GL band is attributed to another charge state of the defect 112responsible for the YL band,the details of which are discussed in Sec.IV B.

Another PL band,observed in undoped GaN at low tem-peratures,is known as the shallow DAP band.115This band is characterized by a relatively sharp peak at about 3.25–3.27eV followed by several replicas at energies which are mul-tiples of the LO phonon energy in GaN ?Fig.13?.The no-menclature chosen has its roots in the fact that at low tem-peratures that band is caused by transitions from the shallow donors to the shallow acceptors.At elevated temperatures,the DAP-type transitions are gradually replaced by the e-A transitions involving the same shallow acceptor.Since the shapes of the DAP and e-A bands are similar and these tran-sitions cannot always be delineated from each other,we will refer hereafter both the shallow DAP and e-A bands as the ultraviolet luminescence ?UVL ?band.Unlike the YL band,which remains nearly unchanged with increasing tempera-ture at least up to the room temperature,the UVL band quenches at temperatures above ?150K and typically can-not be detected at room temperature.Properties of the UVL band are examined in Sec.IV C.

In GaN layers grown by MOCVD or HVPE,another broad band,the blue luminescence ?BL ?band,is often ob-served in the low-temperature PL spectrum at about 2.9eV ?Fig.13?.This band begins to quench above 200K,and at low temperatures it exhibits a characteristic ?ne structure.116We present a detailed description of the BL band in Sec.IV D.

In undoped GaN grown by HVPE or MOCVD methods,a red luminescence ?RL ?band is sometimes observed at about 1.8eV ?Fig.13?,often as a shoulder to the YL band.In Sec.IV E,we present some data regarding the RL band in GaN.

Two broad bands,a green one at about 2.5eV and a red one at 1.9eV ,have been detected 99,117only in high-resistivity

GaN samples grown by MBE under extremely Ga-rich con-ditions.These bands exhibit properties very different from those of the RL band in GaN grown by MOCVD or HVPE and the GL band in GaN grown by HVPE.To avoid any confusion,these bands will be denoted hereafter as RL2and GL2bands,respectively ?Fig.13?.The properties of these bands are presented in Sec.IV F.

In some investigations,a few less common PL bands have been observed in the visible part of the spectrum,as discussed in Sec.IV G.The contribution of all the above-mentioned defect-related bands varies from sample to sample,and no clear correlation is yet established until present between the appearance of most of these bands and presence of particular defects in the GaN samples.

The defects discussed in Sec.IV are presumably point defects which are more or less uniformly distributed inside the GaN layer,i.e.,bulk defects.As has been shown,the surfaces also affect luminescence substantially.Some PL bands appear only after speci?c treatment of the GaN sur-face.We present a detailed description of such bands,in particular,the surface-related blue band,in Sec.IX A.PL from undoped GaN sometimes also contains sharp peaks that cannot be attributed to well-known exciton or defect-related transitions.These features are commonly assigned to mani-festation of structural ?extended ?defects.These unusual PL lines in undoped GaN are discussed in Sec.VIII.A.Yellow luminescence band

In most of the unintentionally and intentionally doped n -type GaN samples grown by the various techniques avail-able,the room-temperature PL spectrum contains a near-band-edge emission at about 3.42eV and the YL band peak-ing at 2.20–2.25eV ?Fig.14?.The YL band has been the topic of literally hundreds of publications.Only the investi-gations with meaningful contributions are discussed here.The YL band in GaN is always broad,nearly Gaussian with FWHM of about 350–450meV ,and structureless even at

the

FIG.13.PL spectra from undoped GaN at 15K.The spectra are plotted in logarithmic scale and displaced vertically for better

viewing.

FIG.14.Normalized room-temperature PL spectra of the MOCVD-grown sample ?mo76?and three representative MBE-grown GaN layers.All the spectra were measured in identical conditions with an excitation density of 0.1W/cm 2.Weak oscillations of intensity are caused by light interferences.

061301-19M.A.Reshchikov and H.Morko?J.Appl.Phys.97,061301?2005?

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lowest measurement temperatures.However,the exact posi-tion and shape of the YL band are sometimes sample depen-dent.Although a few attempts have so far been made to resolve two or more bands118–120or phonon-related?ne structure in the broad YL band,121,122we believe that the departure of the YL shape from Gaussian may be related to the particulars of the spectral response of the optical system used in some cases and to the interference effects in others.

There are several,albeit contradictory,results in the lit-erature concerning the origin of the YL band and the effects of doping on its intensity.In early experiments of Pankove and Hutchby12335elements were implanted in GaN and most of them resulted in appearance or enhancement of the YL band.From that investigation,one can glean the obvious that the YL is related not to a speci?c impurity but to some native defect introduced by the implantation damage.First-principle calculations predict that several V Ga-related defects may be responsible for YL in undoped GaN?Sec.II?.Posi-tron annihilation experiments strongly support the prediction of the theory that V Ga is abundantly formed in n-type GaN.124–133Substantial decrease and even disappearance of the YL with p-type doping also favors its assignment to a defect containing V Ga.123,134Ogino and Aoki98have found that Si and O doping do not affect the relative YL intensity, while doping with carbon enhanced this emission.These au-thors attributed the YL band to a complex involving a Ga vacancy and a C atom substituted for the nearest neighbor of the Ga sites.Several other experimental groups also attrib-uted the YL band to C impurity or a complex involving carbon.135–140The origin of the YL in undoped GaN is dis-cussed in more detail in Secs.IV A10and IV H after the main properties of this band are treated.

Not only the identity of the YL-related defect but also the type of transitions responsible for the YL,as well as the question of whether the related defects are located in depth or at the surface of GaN,have been the subject of spirited discussion for many years.In the earliest detailed study of YL,98the band was attributed to a radiative transition from a shallow donor to a deep acceptor,presumably the V Ga C N complex.The band shape,position,and activation energy of its thermal quenching have been explained consistently within a simple CC model with the acceptor level being lo-cated about0.86eV above the valence band.98The debates began some15years later when Glaser et al.141explained their ODMR results associated with this band using an alter-native model.This model is based on a two-stage process involving nonradiative capture of an electron by a deep double donor followed by radiative recombination between the electron at the deep donor and a hole at a shallow accep-tor.Although this model appears very improbable from basic PL reasoning?see Sec.III A?,it was seemingly con?rmed by a few experimental groups142and cited plentifully in many investigations devoted to YL in GaN.Other investigations making use of time-resolved PL,76,143,144photocapacitance and optical deep-level transient spectroscopy?DLTS?,145,146 Raman scattering,147,148hydrostatic pressure,149,150and PL excitation76did not support the model of Glaser et al.141 The questions on?i?whether YL originates from bulk or surface defects,?ii?what the depth distribution of the YL-related defects is,and?iii?whether YL is related to point or

structural defects have received extensive coverage.CL mea-

surements indicated that the YL band is enhanced with in-

creasing probe depth toward the substrate,151in accordance

with the observation of stronger YL near the GaN/sapphire

interface when the sample is illuminated from the front side

and the backside.152,153Etching experiments demonstrated

nearly independence of the YL intensity on depth into the

layer.154,155In contrast,photovoltage spectroscopy was used

to argue in favor of surface defects being responsible for the

YL band.156,157Both correlation158and anticorrelation159be-

tween YL and structural defects in GaN have been reported.

Slightly different positions and shapes of the YL in dif-

ferent investigations may in part be related to a lack of cor-

rection for the spectral response of measurement systems.A

point of interest is,however,that in one report different po-

sitions of the YL bands,obtained with the same setup,have

been cited.100Superposition of several unresolved bands may

affect the position and shape of the broad YL band.We ob-

served a small shift?up to50meV?between bands very

similar in shape?Fig.14?.The YL band in these samples did

not shift with increasing excitation power and its intensity

was nearly independent of temperature in the range of15–

300K.As it will be shown below,the slightly different po-

sitions of the YL band found in the literature can simply be

due to varying effects of structural defects on apparently the

same point defect.Although formation of defects with

slightly different spatial structure,various interactions be-

tween the point and structural defects,and even substantial

contributions of surface states,which are spread in energy,in

some samples cannot be ruled out without an extensive

study.Below we present the main properties of the YL band

in GaN that we believe will help shed some much needed

light to identify the defect?s?responsible for the YL band or

a set of unresolved YL bands in undoped GaN.

1.Effect of temperature

The effect of temperature on the intensity,shape,and

position of the YL band has been the topic of many

reports.67,76,98,137,143,152,160–165The temperature dependence

of the YL intensity,in comparison with the integrated PL

intensities of the exciton emission,inclusive of all the emis-

sions in the range of3.3–3.5eV and the BL band,is shown

in Fig.15.In the samples with high QE,a fast decrease of

the exciton band intensity at temperatures from15to about

60K is accompanied by the corresponding increase in the

defect-related PL intensities in agreement with Eqs.?6?and ?7?.In the temperature range of200–260K a quenching of the BL band in the sample with the highest QE is accompa-

nied by an increase in the intensity of the YL and exciton

bands?the latter is seen as a shoulder in Fig.15?.A similar

increase of the YL band intensity has been observed with

increasing temperature from10to about100K?Refs.161

and165?and is attributed to a trap of13.7meV below the

shallow donor.161It should be noted,however,that the ob-

served effect can be explained without invoking any traps.

Indeed,as shown in Sec.III A2,the quenching of the inte-

grated exciton emission with an activation energy of about

13meV?Ref.67?results in enhancement of other PL bands

061301-20M.A.Reshchikov and H.Morko?J.Appl.Phys.97,061301?2005?

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