Electron paramagnetic resonance and optically-detected magnetic resonance of donors in AlxGa1-xAs

Journal of Electronic Materials, Vol. 20, No. 1, 1991

Electron Paramagnetic Resonance and Optically-Detected Magnetic Resonance of Donors in AIxGal_xAS

T. A. KENNEDY and E. GLASER

Navel Research Laboratory, Washington, DC 20375

The Electron Paramagnetic Resonance (EPR) and Optically-Detected Magnetic Reso- nance (ODMR) work on Si-donors in AlxGal_~As is reviewed in the context of the shallow-deep bistability (DX) problem. Three donor states are important. Little work has been published on donors tied to the F-minimum. However, there are many results for X-donors. In A1As/GaAs heterostructures, well-resolved spectra reveal a donor state comprised of independent X= and Xy valleys with the Xz valley unpopulated due to the hetero-epitaxial strain. As A1 mole fraction decreases, intervaltey coupling is evident from the line positions and linewidths. The published attempts to observe and identify the deep (relaxed) state are inconclusive. Some suggestions for future work are pre- sented.

Key words: AIGaAs, electron paramagnetic resonance, donors, DX centers

INTRODUCTION

Donors in Al~Gal_xAs are presently being studied intensely because they exhibit properties which de- part strongly from hydrogenic effective mass theory. These properties limit devices formed from Al~Gal_xAs and heighten scientific interest in the nature of the donors. Two major experimental man- ifestations of deep-center behavior are a large Stokes shift and persistent photoconductivity at low temperature. Thus donors in AI~Gal_~As have a shallow-deep instability. Electron Paramagnetic Reso- nance (EPR) and Optically-Detected Magnetic Resonance (ODMR) experiments have been applied to this problem in order to determine the atomic structure and symmetry of the donors. In this paper, we review the magnetic resonance efforts to elucidate the shallow and deep properties of donors in AlxGal_~As.

The paper is organized as follows. A description of the techniques, possible areas of application, and early results are given in the next section. Much has been learned about the shallow donor state associated with the X-minimum. These results have been divided into two sections: the first on AlAs/ GaAs host material and the second on alloy depen- dences and Alo.4Gao.6As/GaAs host material. At- tempts to observe resonance of the deep state are described in the next section. A summary and dis- cussion of future work comprise the last section.

TECHNIQUES AND EARLY WORK

The magnetic resonance experiments are based upon the absorption of a microwave quantum at the energy of the Zeeman splitting of an unpaired electron spin. Due to the weak coupling of the spin to other degrees of freedom, the resonance is very sensitive to the atomic structure and symmetry of the environment of the electron. The symmetry is re- flected in the position of the resonance which is de-

(Received October 3, 1989)

0361-5235/1991/1401-4955.00�9 AIME

scribed by the g-value. Hyperfine interactions produce line broadening and, potentially, line splitting. EPR has provided a wealth of information on the donors in other semiconductors such as Si. 1

Both EPR and ODMR are valuable for the study of donors in Al~Gal_~As. EPR can be performed in the cold dark and thus probe the true ground state of the system. Photo-excited EPR tests long-lived excited states. Since the absorption is in the microwave range, EPR requires fairly large samples and/ or large donor concentrations. ODMR studies the donor in the excited (occupied) state of a distant do- nor-acceptor pair (DAP). 2 For example, the process might involve the donor and a shallow acceptor:

D ~ ~ § (1)

In practice, the donor ODMR has been observed on both shallow and deep recombination processes de- pending on the starting material and experimental conditions. 3-5 ODMR has the advantage of great sensitivity and can study moderate concentrations of donors in thin epitaxial layers.

The AlxGal_xAs alloy system provides three can- didates for donor studies (See Fig. 1). First, there is the donor tied to the F-minimum which is lowest at small Al-mole fraction (x). The effective mass is very small for F electrons and thus the effective Bohr radius is large (-100/k). Many samples are suffi- ciently heavily-doped that the donors form an im- purity band. EPR of GaAs has been reported with a g-value of 0.5228. 6 Polarization ODMR experiments of conduction electrons found g -- -0.44 for GaAs varying smoothly to +0.6 for AlxGal_xAs with x = 0.36. Second, there is the deep (relaxed) state of the donor which is lowest at intermediate and high Al-mole fractions. There is presently no magnetic resonance observation clearly assigned to this state. Third, there is the donor tied to the X-minimum which is either lowest or nearly degenerate with the relaxed state at the highest mole fractions. The anisotropic effective mass for X is moderately heavy

49 �84

50 K e n n e d y a n d G l a s e r

2./. I 1 I I

2.2 F L -

-~ 2.0

w 12 = . "DX uJ

t . '~ - - - - HYDROGENIC LEVELS

1.6 ~.'" CONDUCTION BANDS

1.4 J i I J 0 0.2 0 .4 0.6 0.8 1.0

A l A s MOLE FRACTION x

Fig. 1 - - Conduction band minima and donor states in ALGal_~s. The effective-mass donor levels associated with the F and X minima are shown as dotted lines and the deep s tate (DX) of the donor is shown as a dashed line. Figure courtesy of P. Mooney.

( r n t = 0.19 mo and mz = 1.1 mo) 8 and thus the effective Bohr radius is - 1 5 / L Isolated donors can be studied at least with ODMR. Most of the published results have concerned X-donors.

The EPR of X-donors was first observed and iden- tified in single crystals of AlxGal_xAs grown from a Ga solution. 9 The isotropic single line observed at 20 and 27 K has a g-value of 1.963 and linewidths of 4.0 and 2.6 mT in samples with x from 0.68 to 0.84. Although no intentional dopants were added, the samples contained Si and were n-type. Since the carrier concentration correlated with the strength of the EPR signal, the spectrum was assigned to the Si donors.

Soon after the work on solution-grown crystals, anisotropic EPR of the X-donor was observed in AlxGal_xAs grown by liquid phase epitaxy on GaAs substrates. 1~ The anisotropy is axial about the growth direction and increases with Al-mole fraction in samples with x from 0.55 to 0.8. Recent ODMR data which demonstrate this effect is shown in Fig. 2.11 From the similarity of the EPR data to X-ray double crystal diffractometry on the same system, the anisotropy was assigned to "valley repopulation" among the X minima caused by the hetero-epitaxial

1 0 1 1 strain of Al~Gal_~As on GaAs. '

THE EFFECTIVE MASS STATE IN AIAs:Si /GaAs

To gain an understanding of the donor state associated with the X-minimum, it is helpful to begin with pure AlAs on GaAs. For this case, there are no alloy effects and little, if any, interaction between the X and L bands. The heteroepitaxial strain is at its maximum, 1.4 x 10-3.12 Angular studies in both the (110) and (001) planes have revealed the complete symmetry of the donor state. 13 An ordering of the important interactions is then possible

~A

_A <~ >

6 4 [ - ' ' ' ' E1 ] 0 ] '

1,960[- O > Eo o l ]

1

54 - 521

1.950

4 8 �9 - x = 0 . 5 0 X~ k "

46 \ Y

42 I I I I I I I

-20 0 2o 4 0 60 s o ioo ( d e g )

Fig. 2 - - Donor g-values as a function of the angle between the applied magnetic field (B) and the [001] direction for two AlxGal_~As layers. The solid l ines are fit to the data. The inset shows the experimental geometry.

using the magnetic resonance data with appropri- ate theory.

The Si-related ODMR exhibits tetragonal symmetry about the [001] growth direction (See Fig. 3). Consistent with the early EPR studies, there is only one line in the (110) which shifts from g = 1.945 for B II [110] to 1.978 for B It [001]. However, two lines appear for most directions in the (001). For B 6[ [100], these have g-values of 1.917 and 1.976. For

r -

e

z

d

z I .U (5 z < T O

- - I I I I I I I

(1T0) / / ~

/00,/ 1

830 840 850 860 870 880 890 900 910 MAGNETIC FIELD (mT)

Fig. 3 - - ODMR spectra obtained for the Si-doped A1As/GaAs heterostructure with B in the (110) and (001) planes. These results demonstrate the te t ragonal symmetry about the [001] direction of the shallow donor state. Vertical bars indicate g = 1.94.

Electron Paramagnetic Resonance of Donors in Al=Ga~_~As

[ool]

X z i

/

i I ',, ]

\ [1 lo]

[o 1 o]

Fig. 4 - - Schematic diagram of the conduction band constant energy ellipsoids about the X-point minima in momentum space for the AlxGal xAs/GaAs samples with high x. The dashed ellipsoids indicate that these valleys lie higher in energy due to the heteroepitaxial stress along the [001] (growth) axis.

B ]l [110], the g-value is within error equal to the value for the same direction when measured in the (110). Complete rotation patterns have been obtained and confirm the tetragonal symmetry. 14

In the effective mass theory of donors in semiconductors, the symmetry of the donor states is deter- mined by the symmetry of the lowest conduction band. is The present data can be readily associated with the strain-split X minima (See Fig. 4). Each ellipsoid can be characterized by a g-value with the field parallel to the long axis (g II) and a g-value with the field along the short axes (g ~ ). Strain raises the energy of Xz which is completely depopulated at the measurement temperature of 1.6 K. The single line in the (110) arises from the degenerate Xx and Xy valleys. In the (001) these valleys are split reveal- ing the perpendicular and parallel single-valley g- values with the field in the [100]. Identical results are obtained for B II [010].

The Si shallow donor state in A1As/GaAs can be described by ordering the physical interactions by their energy (See Table I). The binding energy of the effective mass state is approximately 40 meV. 16 Because of the symmetry of the X minimum with

Table I. Energies of the Si Effective Mass State in AlxGal-xAs/GaAs.

E n e r g y in E n e r g y in Interaction A1As/GaAs Alo 4Gao sAs/GaAs

EM Binding Energy 40 meV 40 meV Strain Splitting 15 meV 6 meV Intervalley (Spin Orbit) <15 meV -6 meV hv, kT 0.1 meV 0.1 meV Alloy Disorder Splitting 0 Small Interband (X-L) Small Small

51

respect to the Group III lattice site, donors on this site (including Si) do not have a valley-orbit interaction (central cell effect). 16'17 With a deformation potential of 5 eV, is the Xz is raised above the Xx and Xy valleys by 15 meV. Spin orbit, or any interaction which couples the X valleys, must be much smaller than 15 meV. The microwave quantum and kT are the order of 0.1 meV.

With strain removing the Xz valley, the Si donor state consists of independent Xx and Xy valleys.

THE E F F E C T I V E M A S S STATE F O R x >- 0.4

The resonance associated with the X-minimum has been studied by both ODMR and EPR down to a mole fraction of 0.4. Here the X band is nearly degenerate with both the L and F bands and DX shallow-deep instability properties are readily observed. The shallow state associated with the X-minimum is found to be quite different in Alo.4Gao.sAs/GaAs from the independent valley state in A1As/GaAs.

The splittings and anisotropies observed for AlAs/ GaAs decrease with decreasing Al-mole fraction. For example, the splitting with B II [100] vanishes for x = 0.41 (See Fig. 5). The ODMR results from NRL are summarized in Fig. 6.13 Other ODMR results 19 and EPR results 2~ are in agreement with the NRL results. The anisotropy in the (110) is still detect- able for x = 0.41. Generally one can conclude that

c- Z3

Z

_..,I

z LU (3 Z <: -1- (,.)

830 840 850 860 870 880 890 900 910 MAGNETIC FIELD (mT)

Fig. 5 - - ODMR spectra obtained for several AlxGal_.As/GaAs samples with B H [100]. The splitting between the two resonances observed for the A1As/GaAs sample decreases with decreasing Al mole fraction. Vertical bars indicate g = 1.94.

52 Kennedy and Glaser

1.99

1.98

1 9 7

1.96

LU

J 1.95 >

1.94

1.93

1.92

1.91 0.0

i i

(1 To)

o [11o]

[] [ool]

I I I ) I

(ool)

�9 [11o]

�9 [lOOl []

[]

[]

[] �9

o

] T

I I I I I l L l I

0.2 0.4 0,6 0.8

A L U M I N U M M O L E F R A C T I O N (x)

Fig. 6 -- Compilation of the ODMR g-values as a function of the AlAs mole fraction (x) with B rotated in the (110) and (001) planes.

the decreased splittings and anisotropies indicate tha t the valleys are more coupled at low Al-mole fractions.

The linewidths of the resonance provide fur ther evidence tha t the character of the donor state is changing with Al-mole fraction. EPR and ODMR linewidth data for Si donors is summarized in Fig. 7. The linewidth may arise from a variety of sources.

18

16

14

12

~- 10 E m 8 <1

4

2

o o.o

1 [ I I I I 1 I I

� 9 A B • �9

� 9 ABI)

[] [] []

0 13

I I I I I I I I I

0.2 0.4 0.6 0.8 .0 ALUMINUM MOLE FRACTION (x)

Fig. 7 -- Plot of the ODMR (filled symbols) and EPR (open symbols) linewidths for Si donors in AlxGa~ ~As/GaAs heterostructures. Filled squares and circles: K-band data at 1.6 K (Ref. 11, 13). Filled triangles: X-band data at 1.6 K (Ref. 18). Open circles: X-band data at 6 K (Ref. 19). Open squares: X-band data at 20 K (Ref. 9).

Hyperfine interactions with the host atoms are probably the strongest contribution. These are very sensitive to the valley-orbit interaction and thus the chemical nature of the donor. In ODMR, donor-acceptor exchange interactions can produce linewidth but this mechanism has not been confirmed in AlxGa,_x/GaAs. In EPR, donor-donor interactions will affect the linewidth if the concentration is high enough. Strains from the random alloy do not seem to be important since the linewidth is not a maximum for x = 0.5. Some of the differences between linewidths measured under different conditions suggest which mechanisms are important. For example, the ODMR linewidths are broader than the EPR widths al though the EPR widths increase after photoexcitation. 21 Measurements at NRL and at IAF, Freiburg 21 show that the lindwidth increases with microwave frequency for Si-doped samples. Much more work needs to be done to unders tand these contributions. However, there is a t rend evident in the data of increasing linewidth with decreasing mole fraction.

The Si shallow donor state in Alo.4Gao.~As can be described by ordering its energies (See Table I). The effective mass energy is assumed not to change with mole fraction. Note tha t the g-value for B II [110] does not vary with alloy composition. The heteroepitaxial strain decreases to 6 meV, which can ac- count for the decreased anisotropy in the (110). However, the loss of splitting in the (001) implies an increased intervalley coupling to a value com- parable to the strain splitting. This interval ley coupling is believed to be spin-orbit interaction. The resonance parameters change smoothly through x = 0.5, which is believed to be the composition with the greatest alloy disorder (assuming randomness). There is also no evidence for L-X mixing, such as a change in the g-value toward what was observed for donors in Ge. 22

This shallow state in the region where the conduction bands cross shows evidence of intervalley coupling, which may also indicate some deepening from the effective mass level. Photo EPR experiments confirm that this state is the metastable state of the donor. 2~

THE PROBLEM OF R E S O N A N C E OF THE D E E P STATE

EPR is capable of elucidating the structure of the ground state of the donor if it is paramagnetic in the cold dark. The fact tha t there are no definitive observations of this resonance presents a puzzle. Some theoretical models predict that the ground state has negative-U character with double occupation and no paramagnetism. 23'24 This state is consistent with the lack of an EPR spectrum. However, a recent static susceptibility experiment indicates tha t the ground state is paramagnetic with S = 1/2. 25

The type of resonance expected for the deep state of DX can be inferred from other resonance results. Deep donors, such as the antisites in GaAs 26 and

Electron Paramagnetic Resonance of Donors in AlxGal-xAs 53

Al~Gal_~As ~'27 have g-values with small shifts from the free-electron value and linewidths of about 30 mT. Although the antisites have nuclear moments which lead to large central hyperfine interactions, the dominant Si isotope, 2SSi, is non-magnetic and thus the spectrum for DX would be dominated by a single line. The g-anisotropy due to any distortion from tetrahedral symmetry would probably be small compared to the linewidth.

Some magnetic resonance experiments have been performed which address the deep state. EPR of AlxGal_xAs with x = 0.4 detected a very sharp line (0.8 mT) with g = 2.001 which could not be attrib- uted to the deep state. 2s Recent EPR work on a sim- ilar sample did not detect any signal which could be assigned to the deep state and the authors con- cluded that the line would have to have a width in excess of 120 mT to be undetectable. 2~ This linewidth seems too broad to be caused by ligand hyperfine interactions. Other workers report signals which might be due to the deep state. In EPR on Sn-doped samples, a 60 mT wide line was observed with g = 1.84. 29 And in ODMR (with the excitation light present), a 40 mT line was observed with g = 2.00. 4 Electron-nuclear double resonance (ENDOR) may be required to ascertain whether the defects responsible for these signals include a Si atom.

If the ground state is doubly occupied, there may be a spin triplet excited state which could be detected by ODMR. Many antisite defects exhibit such spectra, a~

Magnetic resonance of the ground state remains a problem of great interest.

SUMMARY AND POSSIBLE FUTURE WORK

The AlxGal_~As alloy system contains three donor states (See Fig. 1). A summary of the present status and possible future work for magnetic resonance follows.

Very little has been done on the donors tied to the F-minimum. There does not seem to be any obstacle to perform EPR or ODMR through a donor-accepter pair mechanism. Neither does there seem to be a strong motivation for studying resonance of the F donors to address the DX problem.

The donors tied to X are amenable to resonance studies and much has been learned. The hetero-epitaxial strain from the AlxGal_xAs/GaAs mismatch strongly affects the donor state. Independent valleys characterize A1As/GaAs samples. In the band- crossover region, the X-valleys are coupled. Some areas of study are incomplete, as evidenced in par- ticular by the linewidth data. The dependence on donor concentration needs to be studied and different chemical species explored.

Magnetic resonance studies of the deep state re- main a challenge. Any broad signal with g = 2.0 needs to be definitely assigned to Si (or other dop- ant species) to distinguish it from other deep levels. Magnetic circular dichroism (MCD) ODMR and ENDOR could be applied to this problem. Perhaps

EPR under different conditions of frequency, temperature and power would reveal the deep state.

We look forward to further results on this fasci- nating donor/alloy system.

ACKNOWLEDGEMENTS

We thank P. Mooney for providing Fig. 1. The work at NRL was supported in part by the Office of Naval Research.

R E F E R E N C E S 1. For reviews, see G. W. Ludwig and H. H. Woodbury, in Solid

State Physics, Vol. 13 (Academic Press, New York, 1962), p. 223, and G. Lancaster, Electron Spin Resonance in Semi- conductors (Plenum Press, New York, 1967).

2. For reviews, see B. C. Cavenett, Adv. Phys. 30, 475 (1981), and J. J. Davies, J. Cryst. Growth 72, 317 (1985).

3. T. A. Kennedy, R. Magno, E. Glaser and M. G. Spencer, in Defects in Electron. Mater., eds. M. Stavola, S. J. Pearton and G. Davies, Mat. Res. Soc. Symp. Proc. Vol. 104 (Mate- rials Research Society, Pittsburgh, 1988), p. 555.

4. E. A. Montie and J. C. M. Henning, J. Phys. C. 21, L311 (1988).

5. For a review, see T. A. Kennedy and E. Glaser, in Physics of DX Centers in GaAs Alloys, ed. J. C. Bourgoin, Solid State Phenomena Vol. 10 (Sci-Tech Publications, Vaduz, Liechten- stein, 1990), p. 53.

6. W. Duncan and E. E. Schneider, Phys. Lett. 7, 23 (1963). 7. C. Weisbuch and C. Hermann, Phys. Rev. B15, 816 (1977). 8. B. Rheinlander, H. Neumann, P. Fischer and G. Kuhn, Phys.

Status Solidi B49, K167 (1972). 9. R. Bottcher, S. Wartewig, R. Bindemann, G. Kuhn and P.

Fisher, Phys. Status Solidi B58, K23 (1973). 10. S. Wartewig, R. Bottcher and G. Kuhn, Phys. Status Solidi

B70, K23 (1975). 11. E. Glaser, T A. Kennedy and B. Molnar, in Shallow Impur-

ities in Semicond. 1988, ed. B. Monemar, Inst. Phys. Conf. Ser. 95 (Institute of Physics, Bristol and Philadelphia, 1989), p. 233.

12. M. C. Rowland and D. A. Smith, J. Cryst. Growth 38, 143 (1977).

13. E. Glaser, T. A. Kennedy, R. S. Sillmon and M. G. Spencer, Phys. Rev. B40, 3447 (1989).

14. T. A. Kennedy, E. R. Glaser, B. Molnar and M. G. Spencer, Int. Conf. on the Sci. and Tech. of Defect Control in Semi- cond., ed. K. Sumino (Elsevier, Amsterdam, to be published); and to be published.

15. W. Kohn and J. M. Luttinger, Phys. Rev. 98, 915 (1955). 16. T. N. Morgan, Phys. Rev. B34, 2664 (1986). 17. T. N. Morgan, Phys. Rev. Lett. 21,819 (1968). 18. P. Lefebvre, B. Gil, H. Mathieu and R. Planel, Phys. Rev.

B39, 5550 (1989). 19. J. C. M. Henning, E. A. Montie and J. P. M. Ansems, Proc.

15th Int. Conf. on Defects in Semicond., Mater. Sci. Forum, 38-41, ed. G. Ferenczi (Trans Tech, Aedermansdorf, 1989), p. 1085.

20. P. M. Mooney, W. Wilkening, U. Kaufmann and T. F. Kuech, Phys. Rev. B39, 5554 (1989).

21. W. Wilkening and P. M. Mooney, private commun. 22. G. Feher, D. K. Wilson and E. A. Gere, Phys. Rev. Lett. 3,

25 (1959). 23. D. J. Chadi and K. J. Chang, Phys. Rev. Lett. 61,873 (1988). 24. K. Khachaturyan, E. R. Weber and M. Kaminska, Proc. 15th

Int. Conf. on Defects in Semicond., Mat. Sci. Forum, 38-41, ed. G. Ferenczi (Trans Tech, Aedermansdorf, 1989), p. 1067.

25. K. A. Khachaturyan, D. D. Awschalom, J. R. Rozen and E. R. Weber, Phys. Rev. Lett. 63, 1311 (1989).

26. R. J. Wagner, J. J. Krebs, G. H. Stauss and A. M. White, Solid State Commun. 36, 15 (1980).

54 Kennedy and Glaser

27. M. Fockele, B. K. Meyer, J. M. Spaeth, M. Heuken and K. Heime, Phys. Rev. B40, 2001 (1989).

28. E. R. Weber, in Microscopic Identification of Defects in Semiconductors, Mater. Res. Soc. Syrup. Proc., vol. 46, eds. N. M. Johnson, S. G. Bishop and G. D. Watkins (Materials Research Society, Pittsburgh, 1985) p, 169.

29. H. J. vonBardeleben, J. C. Bourgoin, P. Basmaji and P. Gi- bart, Phys. Rev. B 40, 5892 (1989).

30. See, for example, N. D. Killoran, B. C. Cavenett, M. God- lewski, T. A. Kennedy and N. D. Wilsey, J. Phys. C15, L723 (1982); and K. P. O'Donnell, K. M. Lee and G. D. Watkins, Solid State Commun. 44, 1015 (1982).

Documents

Electron paramagnetic resonance and optically-detected magnetic resonance of donors in AlxGa1-xAs