phys. stat. sol. (b) 215, 109 (1999)

Subject classification: 71.55.Cn; 78.30.Am; S5

Zeeman Effect of Lyman Transitions:Electronic Raman Spectrum of Boron Acceptorsin Diamond

Hyunjung Kim1� 2� (a), R. Vogelgesang (a), A. K. Ramdas (a), S. Rodriguez(a), M. Grimsditch (b), and T. R. Anthony (c)

(a) Department of Physics, Purdue University, West Lafayette, IN 47907-1396, USA

(b) Argonne National Laboratory, Argonne, IL 60439, USA

(c) GE Corporate Research and Development, Schenectady, NY 12309, USA

(Received May 3, 1999)

Substitutional boron impurities in diamond exhibit characteristic Lyman transitions, originating inthe lower 1s�p3=2�: G8 ground state and terminating in its spin±orbit split 1s�p1=2�: G7 counterpart.In addition to the Lyman spectrum observed in the infrared having p-like final states, the1s�p3=2� ! 1s�p1=2� transition (D0) appears as an electronic Raman line. We have investigated theZeeman effect of the D0 Raman line for magnetic field B along different crystallographic direc-tions, for a variety of scattering geometries. The Zeeman components for B jj �001�, correspondingto pseudo-angular momentum change of 0; �2 (�1), with incident light polarized perpendicular(parallel) to B, occur with relative intensities proportional to the squares of the Luttinger para-meters, taking account of thermal depopulation effects. In addition, Raman transitions within the1s�p3=2) Zeeman multiplet, i.e. Raman electron-paramagnetic-resonance (EPR) lines, are observed.Measurements yield g-factors for the orbital and spin contributions to the Zeeman energy and areg1 � ÿ0:39� 0:04 and g2 � ÿ2:04� 0:10, respectively, which characterize the G8 and G7 multiplets.

1. Introduction

While the importance of the incorporation of substitutional shallow acceptors and do-nors in diamond as an elemental wide band gap semiconductor has been recognized,only boron has been so far successfully introduced in man-made diamonds [1]. All thesame, spectroscopic investigations of the energy levels of holes bound to boron impuri-ties have been extremely fruitful. Lyman spectra in the infrared [2, 3], electronic Ra-man effect [4, 5], and cathodoluminescence [6, 7] in the ultra-violet have revealed thenature of the bound states on the one hand and that of the underlying electronic bandstructure on the other [8, 9].

In the present paper, we report how the Zeeman effect of the electronic Raman linecorresponding to the transition between the 1s�p3=2� : G8 and its spin±orbit split counter-part 1s�p1=2� : G7, i.e. the D0 line, provides a microscopic characterization of the G5 � G6

ground state manifold of the boron acceptor. In addition, the investigation has revealeda Raman line at �77 cmÿ1, presumably associated with an as yet unidentified acceptor.

Hyunjung Kim et al.: Zeeman Effect of Lyman Transitions 109

1) Corresponding author: Tel.: 1-765-494-3020; Fax: 1-765-494-0706;e-mail: hjk@physics.purdue.edu

2) Present address: Advanced Photon Source, Argonne National Laboratory, Argonne,IL 60439, USA.

2. Experimental Results and Interpretation

With a magnetic field B applied along �001�, the �Td site symmetry of the acceptor trans-forms into �S4; as a consequence, 1s�p3=2�: G8, i.e. the J � 3=2 state, splits into the 3

2,12,

ÿ 12, and ÿ 3

2 angular momentum states belonging to the G5, G8, G7, and G6 irreduciblerepresentations of S4, respectively. Similarly, the J � 1=2 state, 1s�p1=2�: G7, resolves intothe G8�12� and G7�ÿ 1

2� sublevels in �S4. This decomposition under B jj �001� is displayed inFig. 1. The selection rules for Raman transitions between the J � 3=2 �M � 3

2 ;12 ; ÿ 1

2 ; ÿ 32�

and J � 1=2 �m � 12 ; ÿ 1

2� manifolds are: d � mÿM � 0;�2 or d � �1; the eight tran-sitions into which the D0 line splits are labeled 1, 2, 3, 4 and 10, 20, 30, 40, respectively.Using the polarizability tensors in Table IV of Ref. [5], the relative intensities of theeight Zeeman components can be readily stated in terms of the Luttinger parametersg2 and g3 which characterize the p3=2 and the p1=2 valence bands.

The experimental results on the Zeeman effect of the D0 Raman transition are dis-played in Figs. 2 and 3 for a natural type-IIb diamond cooled to 5 K. The spectra wereexcited with the 6471 �A Kr� laser line and recorded in a right angle scattering geome-try with a CCD-based triple grating spectrometer. The experiments were performedwith B jj �001�, with the incident light along x0 jj �110� and the scattered light alongz jj �001�. In Fig. 2, the incident light is polarized along y0 jj ��110�, whereas in Fig. 3 it ispolarized along z. In both spectra the scattered radiation was not analyzed. The polar-ization configurations in Fig. 2 allow the appearance of transitions for d � 0;�2 labeledas 1, 2, 3, and 4 in Fig. 1; in Fig. 3 the selection rule d � �1 permits the transitions 10,

110 Hyunjung Kim et al.

Fig. 1. Energy level structure andthe selection rules for the 1s�p3=2�:G8 ! 1s�p1=2�: G7, i.e. D0 transitionas well as those for the Ramanelectron-paramagnetic-resonance(EPR) transition with a magneticfield (B) applied along �001�. �Td

and S4 are the double groups cor-responding to the site symmetriesof the substitutional boron accep-tor for B = 0 and B jj �001�, respec-tively. The selection rules for Ra-man scattering are d � 0;�2 (solidlines) or d � �1 (dashed lines);the eight transitions into which theD0 line splits are labeled 1, 2, 3, 4and 10, 20, 30, 40, respectively. TheRaman-EPR transitions E1 and E2(DM � �2) and E10 and E20(DM � �1) are indicated withthick solid lines

20, 30, and 40 displayed in Fig. 1. Clearly the Zeeman effect of the D0 line is unmistak-able. Even though the four Zeeman components of the D0 line are expected to beobserved for the polarization configuration employed in Fig. 2, only two strong outercomponents (1 and 4) are observed. The relative intensities for I1 : I2 : I3 : I4 are6�g2

2 � g23� : 2g2

2 : 2g22 : 6�g2

2 � g23� and those for I10 : I20 : I30 : I40 are 3g2

3 : 9g23 : 9g2

3 : 3g23. As

has been shown in Ref. [5], g2 is at least an order of magnitude smaller than g3 andhence the absence of lines 2 and 3 in Fig. 2 is not surprising; the relative intensity oflines 1 and 4, expected to be equal, reflects the thermal populations of the 1s�p3=2)Zeeman multiplet for a given magnetic field and temperature. Similar thermal popula-tion effects influence the relative intensities of 10, 20, 30, and 40 in Fig. 3. We draw atten-tion to the fact that the energy of 10 is slightly smaller than that of 1, whereas 40 occursat a somewhat higher energy than does 4; the energy difference in both cases is pro-duced by the Zeeman splitting of the G7 doublet.

Raman spectra recorded as a function of temperature (magnetic field) at a fixedmagnetic field (temperature) show easily observed thermal depopulation effects in therelative intensities of the Zeeman components of D0 and Raman-EPR transitions. Athigher fields or lower temperatures, the holes preferentially occupy the lower states inthe G8 multiplet, thus favoring the higher energy components. Such effects are useful inordering the sublevels of G8.

Zeeman Effect of Lyman Transitions: Electronic Raman Spectrum 111

Fig. 2. Zeeman effect of the D0

Raman transition in a naturaltype-IIb diamond cooled to 5 K.The spectra were excited with the6471 �A Kr� laser line and re-corded in a right angle scatteringgeometry with a CCD-based triplegrating spectrometer. The experi-ments were performed withB jj �001�, the incident light beingalong x0 jj �110� and the scatteredlight along z jj �001�. The incidentlight is polarized along y0 jj ��110�and the scattered radiation notanalyzed. The Zeeman compo-nents are labeled according toFig. 1

Another interesting observation is the appearance of a new peak identified with anarrow in Figs. 2 and 3. It is distinctly noticeable at the higher magnetic fields. We attri-bute it to transitions within the Zeeman multiplet of the 1s�p3=2), i.e. to Raman electronparamagnetic resonance (Raman-EPR). The spacings between the Zeeman sublevelsincrease with increasing magnetic field, finally allowing a Raman-EPR line to appear inthe spectral range recorded. The selection rules for the Raman transitions in which theinitial and final states belong to the same manifold for B � 0 are DM � �1 and �2except between states which are each other's time-reversal conjugates. We recall thatG8��Td� is equivalent to its complex conjugate but cannot be made equivalent to a realrepresentation, i.e. it is of type ªcº according to the Frobenius criterion (see, e. g. [10]).Thus, referring to Fig. 1, the Raman transitions � 1

2! � 12 and � 3

2! � 32 are forbidden

within the 1s�p3=2) multiplet.In the course of the above experiments, an intriguing result was obtained: a new

electronic line at �77 cmÿ1 observed at zero field, exhibits no splitting in the spectrashown in Fig. 2, but appears as a Zeeman doublet in Fig. 3. Clearly the polarizationcharacteristics for its Zeeman components are not the same as for those of D0. Theintensity of this transition is not proportional to the boron concentration, thus sugges-tive of the presence of another acceptor.

112 Hyunjung Kim et al.

Fig. 3. Zeeman effect of the D0

Raman transition with the incidentlight polarized along z, the otherexperimental conditions being thesame as in Fig. 2. The Zeemancomponents are labeled accordingto Fig. 1

The effective mass Hamiltonian for the G5 � G6 ground state of the acceptor in theabsence of spin±orbit interaction and in the absence of an applied magnetic field isgiven by D�ÿir� ÿ �e2=E0r� where D(k) is given in Eq. (4) of Ref. [5]. In order toobtain the g-factors one diagonalizes the perturbation

H0 � ÿ 23 D0I � S� mB�g1I� g2S� � B ; �1�

where g1 and g2 are g-factors associated with the orbital and spin degeneracies of theG5 � G6 multiplet, D0 is the spin±orbit splitting of the 1s level, mB is the Bohr magnetonand B is the applied magnetic field. By virtue of the Wigner-Eckart theorem, we canexpress g1I� g2S by gJ as long as only matrix elements within the G5 � G6 multiplet arecalculated. The energy eigenvalues are ÿ 1

3 D0 � g3=2mBBM, M � 32 ;

12 ;ÿ 1

2 ;ÿ 32 for J � 3

2 and23 D0 � g1=2mBBm, m � 1

2 ;ÿ 12 for J � 1

2. Here g3=2 � 13 �2g1 � g2� and g1=2 � 1

3 �4g1 ÿ g2�.The positions of the Zeeman components of the D0 line and those of the electronic

Raman line at �77 cmÿ1 are shown in Fig. 4 as a function of magnetic field. Measure-ments yield g3=2 � ÿ0:94� 0:02 and g1=2 � 0:16� 0:05 leading to g1 � ÿ0:39� 0:04 andg2 � ÿ2:04� 0:10 characterizing D0. The ordering of the levels in Fig. 1 is consistentwith the convention that the spin g-factor of the hole is negative.

Acknowledgements The authors acknowledge support from the National ScienceFoundation Grant No. DMR 98-00858 at Purdue and from the U.S. Department of En-ergy, BES Material Sciences (Grant No. W-31-109-ENG-38) at Argonne National La-boratory.

Zeeman Effect of Lyman Transitions: Electronic Raman Spectrum 113

Fig. 4. The positions of the Zee-man components of D0 and thoseof the electronic Raman line at�77 cmÿ1 (inset) as a function ofmagnetic field, B jj �001�

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114 Hyunjung Kim et al.: Zeeman Effect of Lyman Transitions