Shallow donors in GaN: A magnetic double resonance investigation

Solid State Co~u~tio~,

Vol. 99, No. 5,

PII soo38-1098(96po193-7

SHALLOW DONORS IN GaN: A MAGNETIC

DOUBLE RESONANCE

I~ESTIGATION

G. Denninger, *’ R . Beerhalter,’ D. Reiser,’ K. Maier,b J. Schneider,b T. ~tchpro~’

and K, Hiramatsu’

’ 2. Physikalisches Institut, Universitiit Stuttgart, Pfaffenwaldring 57, D-70550 Stuttgart, Germany ’ Fraunhofer Institut fur Angewandte Festkorperphysik, TullastraBe 72, D-79108 Freiburg, Germany ’ Department of Electronics, School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 46801, Japan (Received 16 January 1996; accepted in revved

form20

march 1996 by J. Kuizl)

The residual shallow donor in GaN is investigated by electron spin

resonance and the Overhauser shift double resonanCe technique. From the resolved quadrupolar splitting, we determine the electric field gradients at the Ga and the N site. The hyperfine interaction, as determined simultaneously from the Overhauser shift and the Knight shift, supports a delocalized donor wavefunction with an effective Bohr radius of 20-30A. Copyright 0 1996 Elsevier Science Ltd Keywords: A. ~~conductors, D. electronic states, D. spin dynamics, E. electron parama~eti~ resonance, E. nuclear resonances.

Gallium nitride (GaN) and related III-V ternary alloys as Al,Gal_XN and Ga,In,,N are direct-bandgap se~~onductors which have considerable potential for optoelectronic devices o~rating in the visibleto-ultraviolet spectral region. This was envisioned already decades ago. However, useful applications of III-V nitride semiconductors still demand solutions for such elementary questions as n-type or p-type conductivity control. In this Communication, we will concentrate on the properties of shallow donors in GaN investigated by magnetic double-r~onan~ methods. The growth of GaN layers, on sapphire ((r-A&OS) substrates, can be achieved by various vapour phase epitaxial techniques. In general, such as-grown, nominally undoped GaN layers exhibit a pronounced n-type conductivity. The microscopic identity of the shallow donors is presently still under debate. Nitrogen vacancies and oxygen contaminations have been discussed [l], but recent investigations favour group IV impu~ties on Ga positions. The residual shallow donors in kxagonul GaN have recently been studied [“L-S] by electron spin resonance (ESR). Complementary data have further been obtained by optically detected magnetic resonance (ODMR) via photoluminescence [3-81. The ESR

* Author to whom correspondence

should be sent.

of shallow donors in the cubic modification of GaN, as stabilized by epitaxial growth on a (00 1) silicon substrate, was also observed 191. In this Communication, we will concentrate exclusively on doubleresonance expe~ments of the Overhauser shift type [13-161. This ESR-NMR method is applicable for motional- and/or exchange-narrowed ESR lines. The Overhauser shift measures the average hyperfine interaction complementary to the Knight shift and is especially advantageous in ~miconductors. In some experiments the Overhauser shift has been investigated either by the dependence of the ESR-line position on microwave power or on temperature. Murakami et al. [17] relied on the dominance of the hyperfine interaction at the In site in InP and interpreted their results as originating only from the In sublattice. Carlos et al. [4] observed the temperature dependence of the ESR-position in GaN and interpreted it in terms of interaction with the Ga sublattice alone. We show in our results that a double-resonance investigation is both necessary and advantageous: (i) the contribution of the individual nuclear species can be separated. (ii) the Dynamic Nuclear Polarization (DNP) enhan~ents are considerable and can be determined for all the isotopes.

347

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SHALLOW DONORS IN GaN

Vol. 99, No. 5

(iii) the individual spin lattice relaxation rates of the coupled nuclei can be determined. (iv) in the case of single crystals, the resolved nuclear quadrupole splittings allow the direct determination of the electric field gradients (EFG) at the nuclear positions. We finally mention that the ESR data on GaN are very similar to those for n-type zinc oxide (ZnO) [ 11, 121, which also crystallizes in the hexagonal wurtzite structure and has a comparable bandgap [E,(ZnO) = 3.2eV vs E,(GaN) = 3.4eV, at 300 K]. The GaN-sample investigated in this study was a 220~pm-thick free-standing platelet. Its face was perpendicular to the hexagonal c-axis of GaN. This sample was originally grown on a (000 I)-oriented sapphire (o-A1203) substrate by hydride vapour phase epitaxy. Details of the preparation have been given before [lo]. The concentration of neutral shallow donors was estimated from the ESR results to be 5 x 10’6cm-3 (at 5 K). The ESR-spectrum of this sample, as recorded on a Bruker 300 ESP X-band (9.5 GHz) spectrometer is shown in the insert of Fig. 1. A rather narrow line, ABpp M 0.5 mT at 5 K with Lorentzian lineshape is observed, as expected for delocalized electrons in the conduction band or in a shallow impurity band of semiconductors (CESR: conduction electron spin resonance). The linewidth of an isolated shallow donor with an effective Bohr radius of x 27 A is dominated by the hyperfine interaction with the 69Ga, 7’Ga and i4N nuclei. A simulation by Monte-Carlo methods yields an expected linewidth of x lo-20mT and a Gaussian lineshape. Thus, there is appreciable motional or exchange narrowing by a factor of M 50. The g-factor of the ESR-signal in Fig. 1 exhibits a weak anisotropy with respect to the angle between B. and the c-axis, with 811= 1.9503 f 0.0001)

gl = 1.9483 f 0.0001.

The effective electron spin relaxation times rl (longitudinal spin relaxation time) and 71 (transversal spin relaxation time) can be estimated from the linewidth ABpp % 0.5 mT (5 K) and from the saturation behaviour (see below): 7; g 9.9 ns and rl 2 50 ,us. The hyperfine interaction (hfi) between conduction electrons or electrons with sufficient exchange interaction and the nuclear moments is averaged, if the spin correlation time 7, of the electronic spin at a particular nuclear position is short compared to the characteristic time scale h/A (A: hfi energy). The most prominent consequences for the ESR and NMR properties are:

F

s

-5

E

6

-10

-15

-20

-25t ' j ' j .' 1 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 RF-frequency (MHz)

Fig. 1. Overhauser shift in GaN, T = 8 K, 20mW microwave power. The quadrupolar interaction is resolved for all the isotopes. 1,c, h denotes low, central and high transition. Insert: Electron spin resonance line of GaN, T = 5 K, B. 11c. The fit is the sum of two Lorentzians AB = 0.304 mT and AB = 0.86 mT, with 14% dispersion contribution. (i) the NMR-frequency is shifted compared to the value of the bare nuclei by an amount o( A - (S,), where (SJ is the average z-component of the electronic spin polarization. This paramagnetic shift is well known in metals as the Knight shift. (ii) the ESR-frequency is shifted oc A - (I,) by the coupling to the nuclei, (I,) denotes the average nuclear spin polarization. This shift is known as the Overhauser shift. (iii) at a sufhciently high concentration of either conduction electrons or donors the nuclear spinlattice relaxation is dominated by the hti. (iv) saturation of the ESR transition(s) results in an enhancement of the nuclear spin polarization (ZJ. This phenomenon is called Dynamic Nuclear Polarization (DNP) or Overhauser effect. The basic idea of an Overhauser shift experiment is to record the ESR line position as a function of a swept radiofrequency field. Figure 1 shows an overview result for GaN: all the relevant isotopes shift the ESR line as can be clearly seen from the plot of the ESR position vs RF from 1 to 6MHz (microwave power: ? 20mW, RF-power: E 1OmW). Due to the rather long nuclear relaxation times (up to a few hundred seconds in GaN at 5 K), the general appearance of an Overhauser shift signal is a step-like decrease at the NMR transition followed by a slow

relaxation towards equilibrium. This can be seen very clearly at &! 1.1 MHz for the two transitions of 14N (I = 1, Am, 1 + 0, Am, 0 + -1). Both isotopes of Ga (69Ga, Z = 3/2,60.1% abundance; 7’Ga, Z = 312, 39.9% abundance) result in 3 shift peaks each (indicated in Fig. l), due to the resolved quadrupole splitting. The shift signal due to 14N is much larger than anticipated from the atomic values of the hfi and a detailed investigation reveals important parameters: Fig. 2 shows two sets of data for 2.52 mW and 10 mW splitting of microwave power. The quadrupole Av,, = 20.89 kHz is resolved and the effect of DNP with increasing microwave power is clearly visible. From the theory of the quadrupolar interaction (see, e.g. the treatment in Abragam [18]), the line splitting is Auss = “Q(Z - 4). The electric field gradient V,, (z along the crystallographic c axis) is connected to the electric quadrupole moment eQ and VQby v

= vQ’h’21’(2Z I,? 3eQ

- 1) (1)

’

We determine V,, = (0.594 f 0.003) x 1020Vm-2 at the 14N position. Similarly the quadrupole splittings of 69Ga and 7’Ga can be analysed and yield field gradients V,, = (6.44 f 0.03) x 10%Vm-’ c9Ga) and V,, = (6.47 f 0.03) x 1020Vm-2 (71Ga). Within the experimental error, the field gradient is independent of the Ga isotope. The ratio of the electric field gradients v,,(Ga)/V,,(N) = 10.82 f 0.07. For a quantitative analysis of the DNP, a series of measurements with varying microwave power has been conducted for all the relevant nuclear transitions. The shift increases with increasing microwave power, due to the DNP. Quantitatively, from a model

-5 ’

-40

-30

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SHALLOW DONORS IN GaN

Vol. 99, No. 5

-20

I I 0 10 -10 RF-frequency Offset (kHz)

Fig. 2. 14N Overhauser and 10 mW microwave fit to a model including monoexponential build

20

30

of rate equations for the Overhauser effect [19], we expect AB, = ABk(l + V-s), where ABL is the Overhauser shift in thermal equilibrium, V is DNP enhancement and s is the ESR saturation parameter. The dependence of s on microwave-power can be evaluated directly from the Bloch equations as

The expected linear relation of AB,, vs s is shown in Fig. 3 for both 69Ga and 71Ga central transitions. Similar plots are obtained for both 14N transitions. The slope determines the DNP enhancement I/ and the axis-offset the thermal equilibrium value AB:. The results, extrapolated to complete NMR saturation are summarized in Table 1. A further consequence of the averaged hfi is the paramagnetic shift of the NMR position by the average polarization (SJ of the electrons. In metals this is the Knight shift, proportional to the Pauli susceptibility and thus nearly independent of temperature. If the electrons do not form a Fermi system, as is the case in lightly doped semiconductors, this shift is termed paramagnetic shift and is expected to vary with l/T. Since (Sz) can be directly manipulated by ESR saturation [(SJ = (Si) - (1 -s)], this shift is directly accessible in our experiment. The NMR-line position, corrected for different B. fields due to the Overhauser shift is shown in Fig. 4 vs ESR saturation for the Ga central transition and the two 14N transitions. The slope yields directly the paramagnetic shift. Note that this procedure makes no assumption on the chemical shift and is the most direct way to measure the NMR shifts induced by the electronic spin. The relative shifts are (152 f 70) ppm for 7’Ga

I

40

shift, T = 8 K for 2.52 mW power. Offset: 1100 kHz. The a Lorentzian lineshape and a up is shown by the solid lines.

Microwave-saturation s Fig. 3. Overhauser, + # c) - 4 transition.

T = 8K,

for 69Ga and 71Ga,

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SHALLOW DONORS IN GaN

350

Table 1. V: dynamic nuclear polarization enhancement. AB&: Overhauser shift in thermal equilibrium at temperature T. D = ABk/Bo: relative Overhauser shift (in ppm). V/ Vmax: relative dynamic nuclear polarization

V ABL(nT) D = ABkIBe (ppm) VI vlnax

69Ga, central T=8K

“Ga, central T=8K

‘IGa, central T=5K

14N, low T=SK

63.9 f 223 f 0.624 f 0.023 f

104.5 f 15.7 294f44 0.821 f 0.12 0.049 f 0.008

257.8 f 38 256 & 38 0.714 f 0.11 0.12 f 0.02

22.7 f 793 * 2.21 f 0.0025 f

9.6 33 0.094 0.004

and (259 f 70) ppm for 69Ga. Within the experimental error, both shifts are equal. The same procedure applied to both transitions of 14N as shown in Fig. 5 and we deduce a paramagnetic shift of (5 10 f 75) ppm and (644 f 95) ppm. Again both are equal within experimental error, the average is (557 f 85) ppm. Interpreting these shifts as the average hyperhne interaction over all the nuclei connected to the donor wavefunction (see discussion below), the ratio between N and Ga hfi is (2.8 f 1.4), showing a stronger hfi at the N site than at the Ga site. The corresponding ratio of the Overhauser shift D is (2.8 f 0.9) (see Table 1). Both results are independent and confirm a significant hyperfine interaction at the N site. The results of the Overhauser shift, particularly the resolved quadrupole splitting, clearly show, that the observed ESR-signal is an intrinsic signal of GaN and not a defect related to either the substrate or the buffer layer. From the DNP, we conclude that the ESR signal is either motionally or exchange narrowed and originates either from conduction electrons and/ or donors forming a donor band. The large size of the paramagnetic shift, the NMR saturation behaviour, the temperature dependence of the ESR linewidth and the nonexponential relaxation of the coupled nuclei can only be explained if we assume a donor wavefunction spread out considerably in space. Therefore we discuss our results in a model of a shallow donor in the Effective-Mass-Theory (EMT). The wavefunction of a shallow donor in the EMT is hydrogen 1 - s like

14N high T=8K 3.4 120 0.33 0.004

30.8 f 4.6 664f99 1.85 f 0.28 0.0034 f 0.0006

concentration No 2 5 x lOI crn3. The mean distance between donors is 271 A, approximately 10 times a,#. If I?0 were considerably lower or if a,H were smaller, no exchange narrowing of the donor ESR would result and ENDOR would be applicable. In the case of isolated shallow electron centres in AgCl this was shown experimentally [23]. ENDOR experiments demonstrated, that the individual hfi of a nucleus cy can be written as A, - IcP(a)12,where A, is an amplification factor and @(a) is the envelope wavefunction. Thus, contrary to the situation in systems where the electrons form a Fermi system, the nuclei in the sample are not equivalent with respect to the hyperfine interaction. The standard interpretation of the Fermicontact hfi in terms of the square of the wavefunction at the nuclear position is no longer valid, but has to be replaced by an average over the envelope wavefunction a(o). A detailed discussion will be given elsewhere. However, the electric field gradients V,, as determined by the Overhauser shift should be identical to the V,,

BDGa and “Ga Paramagnetic 5.0 , , I ,

shift

14N Paramagnetic

shift

6.0

v b)

The effective “Bohr radius” a,# depends only on the effective mass m* and the dielectric constant E, aejy = a0 - E/m*. Experimental values of m* are (0.2 f 0.02) [20], (0.236 f 0.005) [21], calculations by the local density approximation predict rni = 0.20, rn; = 0.22 [22]. E is slightly anisotropic with E; = 10.4, ~1 =09.5 [20]. Thus from EMT,0 we expect an aefl % 26.5A. Even with a,8 E 26.544 most of the donors are isolated from each other at the

c 0.0

L-----J 0.0 0.2

1

0.4

0.6

0.6

1.0

30

’ 1J

0.2 0.4 0.6 0.6 1.0 Microwave saturation s

Fig. 4. Frequency position of the NMR position vs ESR saturation s. T = 8 K. Left side: 69Ga offset: 3743 kI-& 7’Ga, offset: 4675 kHz. Right side: ldN transitions, (a) offset = 1108 kHz, (b) offset: 1088 kHz.

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SHALLOW DONORS IN GaN

at unperturbed nuclear positions since the donor wavefunction is delocalised. The value V,, = (6.45 f 0.005) x 10n’ V mm2(Ga site) is in good agreement with NMR magic angle spinning results in GaN powder (V,, = 6.75 x 10” V me2) [24]. To our knowledge, the N-site V,, = (0.594 f 0.003) x 102’ Vmm2 has not been determined by other methods. Both values should be interpreted by a bandstructure calculation of GaN, their ratio depends on the ionicity of the bond. The main advantage of the Overhauser shift technique is the high sensitivity of the double resonance scheme, which allows the investigation of small single crystals, epitaxial layers and thin films, unsuitable for NMR experiments. The microscopic nature of the donor could be identified, if the hfi of the central nucleus could be determined experimentally. In the present experiments, a search for Si was unsuccessful, robably due to the low natural abundance (4.6% for B Si). A successful experiment would demand samples intentionally doped with, e.g. isotopically enriched 29Si and/or larger single crystals. ENDOR type experiments on the other hand would require much lower concentrations of the donors. This in turn would broaden the ESR line by over an order of magnitude and we expect standard ESR/ENDOR experiments not to be feasible with present samples. In summary, we have determined the Overhauser shift, the paramagnetic shift (Knight shift) and the Dynamic Nuclear Polarization resulting from the coupling of the shallow donor in GaN to the nuclei of the lattice. From the resolved quadrupolar splitting, both electric field gradients at the Ga and N site have been determined with high precision. The hyperfine interaction at the N-site is stronger than expected from atomic values. The combined Overhauser shift and Knight shift data can be explained by a ddonor wavefunction with aefl in the range of 20-30A. The high sensitivity of the double resonance scheme is decisive for these investigations and extensions to thin epitaxial layers and higher frequency experiments are presently under way.

2. 3. 4. 5. 6.

7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. :;: 21.

Acknowledgement-One the Volkswagen-Stiftung

of the authors (J.S.) thanks for financial support.

22. 23.

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