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Magnetoreflection studies of ion implanted bismuth
~
Solid State Communications, Vol.43,No.4, pp.233-237, Printed in Great Britain.
]982.
0038-I098/82/280233-05503.00/0 Pergamon Press Ltd.
MAGNETOREFLECTION STUDIES OF ION IMPLANTED BISMUTH C. Nicollni t, T.C. Chieu t*, G. Dresselhaus § and M.S. Dresselhaus t* Massachusetts Institute of Technology Cambridge, MA 02139
(Received
5 March 1982 by R.H. Silsbee)
The effect of the implantation of Sb ions on the electronic structure of the semimetal bismuth is studied by the magnetoreflectlon technique. The results show long electronic mean free paths and large implantatlon-lnduced increases in the band overlap and L-polnt band gap. These effects are opposite to those observed for Bi chemically doped with Sb. tation depth Rp. 7 Finally, because of the low melting point of bismuth (Tm = 271°C), it was expected that the lattice damage produced by the ion implantation could be readily annealed. Several arguments suggest that the magnetoreflection spectra from ion-lmplanted samples would be unsuitable for quantitative study. On the basis of Raman scattering studies of ion implanted graphite, 8 it was expected that the lattice damage caused by ion implantation would seriously degrade the mean free path so that the condition ahz >> I could no longer be satisfied. Because of the strong spaclal dependence of the profile for the implanted ions, it is expected that the contribution to the magnetoreflectlon spectrum from the ion rich region between Rp-- ARp and Rp + ~Rp would differ signiflcantly from that for both the region through which the ions pass before coming to rest (d < R p - ARp), and the region not significantly penetrated by ions (d > Rp + ~Rp). This variation in ion concentration within the skin depth is expected to result in a smearing out of the resonant structures. Finally, the total ion concentration within the optical skin depth is low (~ 400 ppm), so that if a uniform ion concentration were achieved, little effect on the magnetoreflection spectrum would be expected. The mmgnet oref lection results presented here for Sb implanted Bl show unexpectedly sharp and intense resonances identified with Landau level transitions. The observed spectra can be explained in terms of the strongly coupled twoband model originally proposed to explain the electronic structure of bismuth. 3, 4 The magnetoreflection results from the ion implanted samples show three unexpected features. A reversal in lineshape from the case of Bi or Bil_xSb x alloys is observed and interpreted in terms of an increase in carrier concentration and band overlap. A breakdown in the selection rules that apply to Bi and Bil_xSb x alloys is found and attributed to an increased concentration of symmetry breaking defects. An increase in the L-polnt band gap and effective mass is observed and is identified with an increase in the sublattlce displacement potential in the electronic structure. All three features differ markedly from the effect of chemical doping with the same isoelectronlc Sb species. 5
Introduction Magnetoreflectlon measurements provide a powerful experimental technique for the quantitative determination of the electronic structure of semiconductors and semimetals. 1,2 This technique is now applied for the first time to study the effect of ion implantation on the modification of the electronic structure of the host material. The magnetoreflection technique is especially sensitive to modifications of the electronic structure by ion implantation because the implantation depth Rp is roughly of comparable magnitude to the optical skin depth. Bismuth was chosen as the host material and antimony as the implanted ion for a variety of reasons. Of all semimetals, bismuth exhibits Landau level transitions having the sharpest and most intense resonant structures in the magnetoreflection spectra. 3,4 Antimony is an isoelectronic dopant in bismuth which goes into substitutional sites, so that the large ~cz of bismuth is not significantly degraded upon doping with antimony, and the Landau level transitions in Bil_xSb x alloys are readily observed in the magnetoreflection spectra. 5 The chemical introduction of Sb into Bi decreases the band gap and at a Sb concentration of x = 0.04, the L-polnt valence and conduction bands cross. The addition of Sb into Bi also decreases the band overlap between the L-polnt conduction band and the T-polnt valence band, so that at an Sb concentration of x ~ 0.07, the band overlap vanishes and semlconductlng behavior is achieved for the Sb concentration range 0.07 < x < 0.22. 6 In the present ion implantation study of Sb into Bi, the ion fluences were chosen so that the local Sb concentration in the implanted region between Rp - ARp and Rp + ~Rp would be in the semiconductlng range, where ~Rp is the width of the Gausslan distribution about the mean implan-
tCenter for Materials Science and Engineering. *Department of Electrical Engineering and Computer Science. §Francis Bitter National Magnet Laboratory, supported by NSF. 233
MAGNETOREFLECTION
234 Experimental
STUDIES OF ION IMPLANTED BISMUTH
Details
Table I. Electronic structure parameters for ion implanted Bi and other reference samples.(a)
Magnet oref lection measurements have been made on a binary face of an unimplanted bismuth sample (the reference sample) and on two binary faces of bismuth implanted with antimony at 150 keV to fluences of 2.2 x i015/cm2 and 5.5 x lol5/cm 2. The ion implantation was done in vacuum and at room temperature with a commercial ion implanter, using both a metallic powder of Sb and SbF 5 as a source for Sb ions. To avoid channelling, the beam was incident on the sample at an angle of ~ 7 °. Using the theory of Lindhard, Scharff and Schiott (LSS theory), 7 values of Rp ~ 380 A and ARp ~ 8 5 A are calculated, showing that the ion penetration is significantly less than the optical skin depth (~2 ~). The magnetoreflectlon measurements were made in the Faraday geometry in fields up to 150 kOe, with the sample attached to the cold finger of a dewar containing liquid helium. Experimental details relevant to the magnetoreflection measurements are given elsewhere. 3, Results and Discussion A typical magnetoreflection trace obtained for the binary face of a bismuth sample implanted wlth antimony to a fluence of 5.5 x 10 15 ions/cm 2 is shown in Fig. 1 at a photon energy of h e - 140 meV. Shown in the inset is the spectrum for an unimplanted binary Bi sample at the same h~. Using the coupled two-band model for the magnetic energy levels of Bi, the energies of the j ~ 0 levels at the conduction and valence band extrema of the magnetic subband (kH - O) are written as: 9- 12 E-+j~0,s - -+[(EGI2)2+
J EG 8*H] tlz- 2GS*sH
Vol. 43, No. 4
(I)
where E G is the band gap, H is the magnetic field and the quantum number J is related to ~:he Landau level index n by J = n + I/2 - s, where s = -+ I/2 is the spin, 6" ~ eh/mc*C, and me* is the cyclotron effective mass at the band extrema, and G is the effective g-factor. The quantum number J is written as Jv and Jc for the valence and conduction bands, respectively. The factor G results from the k'p perturbation contribution from bands not included explicitly in the two band model, and G is assumed to be the same for all J # 0 levels. The energy of the J - 0 conduction and valence band levels (s = 1/2) at k H = 0 are nearly degenerate and are given by the modified two-band model. Ii, 12 As a first step in analyzing the magnetoreflection spectra (see Fig. I), the AJ = +- 1 transitions, which are allowed in unlmplanted Bi and Bil_xSb x alloys, are identified, yielding the solid lines of the fan chart for the magnetoreflection resonances given in Fig. 2. The results for the L-point energy gap EG and cyclotron effective mass mc* , obtained from the fit of the experimental points to the functional form in Eq. (I), are given in Table I. Also included in Table 1 are corresponding results for unimplanted Bi and for the binary Bi sample ion implanted with Sb to 2.2 x 10 15 ions/cm 2 as well as chemically doped Bil_xSb x and Bi under 1 kbar hydrostatic pressure. The results in Table I show that ion implantation significantly
Samples (b) EG(meV) mc*/m o
E G {mo/mc*} ~p(meV)
Bi (reference)
13.8
0.00185
7460
40 + I0
@ffi2.2xlOl5/cm 2
37.5
0.00582
6440
70 -+ 50
~'5.Sx1015/cm 2
46.0
0.00776
5930
140 + 50
Bi0.98Sb0.02 (c)
8.0
0.00116
6900
< 40
Bi0.97Sbo.03 (c)
4.9
0.00073
6700
< 40
Bi0.95Sb0.05 (c)
3.9
0.00059
6610
< 40
Bi0.88Sb0.12 (c) 17.5
0.00274
6390
0
Bi0.85Sbo. 15 (c) 20.0
0.00321
6230
0
Bi(l kbar) (c)
0.00215
8090
16.1
< 40
a) The table gives cyclotron masses at the band extremum for the magnetic field along a binary direction. b) The samples labeled ~ ffi 2.2 x lol5/cm 2 and = 5.5 x lOl5/cm 2 are ion implanted to the stated f luences. c) Results for five unimplanted but chemically alloyed Bil_xSb x samples are presented (data from Ref. 17) for comparison, as are also results for Bi under hydrostatic pressure (data from Ref. 18). increases the L-point band gap and effective mass, with a significant decrease in EG/mc* , or equivalently the square of the momentum matrix element coupling the valence and conduction bands, In contrast, chemical doping by comparable concentrations of Sb results in a small decrease in E G and mc* , though for both implanted and chemically doped Sb, the ratio EG/mc* decreases (see Table I). The second important effect of ion implantation is the reversal in lineshape of the magnetoref lection resonance in the implanted sample (Fig. I) relative to the unimplanted one (inset to Fig. I). In particular, the sharp resonances correspond to reflectivity max[me for the unimplanted sample and to reflectlvity minima for the implanted sample (see Fig. I). This identification of the resonance point within the llne width for the AJ ffi + 1 transitions provides a fit of the observed resonances to Eq. (i) and was used in the analysis of the magnetoreflection traces for the Sb implanted samples (see Fig. 2 and Table I). The calculated magnetic fields for the AJ = -+ I transitions in Fig. 1 are labeled on this basis. The reversal of the lineshape for the magnetoreflection resonances is indicative of a shift in the plasma frequencies ~p to significantly higher frequencies, insofar as the condition ~ >> ~p corresponds to resonances at the reflectivity maxima while ~ < ~p yields resonances at the reflectivity minima. 13 Thus the change in lineshape indicates that ion implantation results in a significant free carrier generation within the optical skin depth. This has been confirmed by direct measurement of the frequency dependence of the reflectivity using a
MAGNETOREFLECTION
Vol. 43, No. 4
STUDIES OF ION IMPLANTED BISMUTH
235
,-,.
c~ c o ,.c:
0
3~-4 V
4--
._~
50 I00 Mognetic field (kG)
t
"0
2-~-3
r-
t
o_
t
I-'I
Ix.
1%
0
50
I00 Mognetic field (kG)
150
Fig. 12_. Experimental trace of the reflectivlty v_[s magnetic field for the binary face of Bi implanted with a fluence of 5.5 x 1015/cm2 Sb ions at 150 keV. The photon energy of 140 meV was used for both the implanted sample where the resonances appear as reflectlvlty minima, and the unlmplanted bismuth sample (inset) where the resonances correspond to reflectlvlty maxima. The arrows indicate the resonant ,~,n~etlc fields for Landau level transitions calculated from levels Jv in the valence band to Jc in the conduction band, using the model discussed in the text and the parameters from Table I. Fourier transform spectrometer. Estimates for ~p obtained from these reflectivlty measurements are given in Table i. The increase in free carrier density induced by ion implantation is attributed to a n increase in band overlap, as discussed below. This behavior is in contrast to the results for bismuth chemically alloyed with Sb, in which the plasma frequency decreases with the addition of smell concentrations of Sb (x ~ 7 at.%; see Table l). For an isoelectronlc impurity, the change in plasma frequency is associated with a change in the band overlap, which is directly related to the rhombohedral lattice distortion with respect to the simple cubic structure. The third effect induced by ion implantation is the appearance of Landau level transitions not present in unlmplanted bismuth. The additional resonances in the magnetoreflectlon spectrum in Fig. 1 can be explained in terms of AJ = + 2 and Aj = 0 transitions which can be
calculated from Eq. (i), and using the band parameters determined from analysis of the AJ = -+ I transitions (see Table I). Weak transitions identified with AJ ffi -+ 3 have also been identified. The AJ ffi 0, -+ 2, +- 3 resonances calculated in this way are indicated in Fig. 1 by arrows and labeled by the Jv ++ Jc quantum numbers. A good fit to the experimental resonances is obtained at 140 meV (Fig. |) and at other photon energies (Fig. 2), by the model of Eq. (1) and the band parameters of Table I. Since ~ - ~p, a detailed llneshape calculation should be carried out to obtain a quantitative identification of the resonance point within the magnetoreflectlon llneshape. The AJ - 0, + 2, + 3 transitions, which are symmetry forbidden in unlmplanted bismuth, have also been reported in tin-doped bismuth, 14 where the substitutional charged tin impurities on random sites lower the crystal symmetry and relax the usual selection rules, In the case of the ion-lmplanted sam-
MAGNETOREFLECTION
236 ~(o~o ~0 ~.
STUDIES OF ION IMPLANTED BISMUTH
•
20C 160 •
- ,2o
;~"
-
•
~
~
O.PI s,I/~
40 0
i O
20
I
J
I
40 60 BO Mogneticfieid (kG)
I
I
I00
120
2__~.Energy of the resonant peak positions vs magnetic field for the sample of Fig. I. The curves are calculated from the mirror band model discussed in the text using the parameters of Table I . Solid curves and open d r c l e s denote ~ = ± I transitions (allowed in bismuth), dotted curves and open triangles for the ~ = ± 2 transitions, dashed curves and solid circles for AJ ffi 0 transitions, and dashed-dot curves and plus signs for the weak ~ = ± 3 transitions (forbidden in bismuth).
ples, rule cant cies
the breakdown of the AJ - ± I selection is attributed to the presence of a signifidensity of structural defects (e.g., vacanor interstitlals). Because of the very small bandgap and the very strong interband coupling in bismuth, small perturbations to the local potential can result in significant changes in the L-point band parameters. The o b s e r v a t i o n of sharp magnetoreflection resonances indicates that significant annealing of the Implantatlon-lnduced lattice damage o c c u r s a t room t e m p e r a t u r e , and t h a t t h e mean f r e e p a t h of t h e e l e c t r o n s i s l o n g c o m p a r e d to the optical skin depth. The s h a r p n e s s of t h e resonance lines also indicates that the crystal potential has been modified over the entire optical s k i n depth. The results presented in the previous section can be interpreted in terms o f the theoretical m o d e l s f o r t h e Bi band s t r u c t u r e . 15 The Bi structure is baslcally a distorted simple cubic lattice, with a - 57 ° 14.2', u - 0.237, while a = 60 °, u = 0.25 represents a simple cubic structure. 16 To obtain the bismuth structure from the simple cubic structure, a displacement of t h e two interpenetrating fcc lattlces is made, which opens up band gaps at the zone faces (e.g., at b-points of the fcc Brillonin zone). If this were the only distortion in Bi, the material would be a semiconductor with gaps at the L-point in the fcc Brillonin zone. The semimetalllc properties of bismuth are produced
Vol. 43, No. 4
by an additional rhombohedral distortion along the (111) direction, making two of the 8 fcc Lpoints inequivalent. The two points along the three-fold axis, labeled T-polnts, are occupied by holes whereas the other 6 fcc L-polnts become centers of L-point electron pockets in Bi. _ Thus~s in the Bi electronic structure can be correlated with changes in the two perturbing potentials, Vsu b causing the sublattics displacement and Vrh m causing the rhombohedral distortion. An increase in the band gap is associated with an increase in Vsu b. An Increase in the band overlap (or in the carrier density for isoelectronic doping) is associated with an increase in Vrh m. The effect of Sb implantation is thus seen to increase both Vsu b and Vrh m. The sharpness of the Landau level transitions indicates that the perturbations to Vsu b and Vrh m extend over the optical skin depth. At the present time the driving mechanism for these changes in potential is not fully understood. Though strain could be responsible for the changes in the electronic structure, the values of the parameters are found to he functions of fluence $ and do not change with annealing (though ~cT increases with annealing). At the ion fluences and implantation energy of this experiment, the Sb atoms are expected to be confined to a region of ~ 170 A wide buried about 400 A into the sample, corresponding to a concentration of ~ 1021/cm S in this region. It seems unlikely that substitutional Sb could produce the large changes in band parameters that are observed, since chemical doping with Sb by ~ 1021/cm3 (e.g., Bi0.98Sbo.02 in Table I) 17 decreases both Vsu b and Vrhm, but by smaller amounts than the Increase found in the present experiment. $ The application of pressure increases the magnitude of Vsu b and decreases Vrh m (see Table I). 18 These observations suggest that ion implantation introduces interstitial Sb ions in the BI lattice. It would therefore be of great interest to carry out precise x-ray measurements to determine the change in a and u resulting from ion implantation. This work opens up a new field of investigation in the use of the msgnetoreflectlon technique to study, modifications to the electronlc structure due to ion implantation. The technique permits quantitative study of these modifications as a function of ion fluence, energy, species and annealing. It wlll be of particular interest to extend this work to ions that act as donors (e.g., Te) or as acceptors (e.g. Sn) to semlmetals (e.g., bismuth) and to ion implantatlon in semiconductors. Acknowledgement-We wish to thank Dr. E.W. Maby and M. Rothman for assistance with the ion implantations, P.D. Dresselhaus for help with the data analysls, and ON'R Grant # NO001477-C-0053 for support of this research. The experlmental work was carried out at the Francis Bitter National Magnet Laboratory. We wish to thank L. Rubin and B. Brandt of the FBNML for technical assistance.
Vol. 43, No. 4
MAGNETOREFLECTION STUDIES OF ION IMPLANTED BISMUTH
237
REFERENCES
1. M.H. Weiler, Semiconductors and Semimetals, edited by R.K. Willardson and A.C. Beer, Academic Press, New York, 1981, p. 119. 2. H.S. Dresselhaus, The Physics of Semimetals and Narrow Gap Semiconductors, edited by D.L. Carter and R.T. Bate, Pergamon Press, New York, 1971, p. 3. 3. R.N. Brown, J.G. Mavroldes and B. Lax, Phys. Rev. 129, 2055 (1963). 4. M.S. Maltz and M.S. Dresselhaus, Phys. Rev.
B2, 2877 (1970). 5. E. J. Tlchovolsky and J.O. Mavroldes, Solid State Commun. 7, 927 (1969). 6. A.L. Jaln, Phys. Rev. 114, 1518 (1959); F.A. Buot, The Physics of Semimetals and Narrow Gap Semiconductors, edited by D.L. Carter and R.T. Bate, Pergamon Press, New York, 1971, p. 99. 7. J. Llndhard, M. Scharff and H. E. Schlott, Kgl. Danske Vldenskab. Selskab, Hat. Fys. Medd. 33, 14 (1963). 8. B.S. Elman, M.S. Dresselhaus, G. Dresselhaus, E.W. Maby, and H. Mazurek, Phys. Rev. B24, 1027
(1981).
9. M.H. Cohen and E.I. Blount, Phil. Hag. 5, 115 (1960). I0. P.A. Wolff, J. Phys. Chem. Solids 25, 1067 (1964). II. G.A. Baraff, Phys. Rev. 137, A842 (1965). 12. M.P. Vecchl, J.R. Perelra and M.S. Dresselhaus, Phys. Rev. B14, 298 (1976). 13. P.R. Schroeder, Ph.D. Thesis, HIT, 1968, (unpublished). 14. A. Misu, J. Heremans and M.S. Dresselhaus, Phys. Rev. BI5 (in press). 15. M.H. Cohen, L.H. Fallcov, and S. Golln, IBM J. Res. Develop 8, 215 (1964). 16. R.W.G. Wyckoff, Crystal Structures, Vol. I (New York: Interselence, 1964). 17. M.P. Vecchl, Ph.D. Thesis, MIT, 1975, (unpubllshed). 18. E.E. Mendez, A. Misu and M.S. Dresselhaus, B24, 639 (1981).
Solid State Communications, Vol.43,No.4, pp.233-237, Printed in Great Britain.
]982.
0038-I098/82/280233-05503.00/0 Pergamon Press Ltd.
MAGNETOREFLECTION STUDIES OF ION IMPLANTED BISMUTH C. Nicollni t, T.C. Chieu t*, G. Dresselhaus § and M.S. Dresselhaus t* Massachusetts Institute of Technology Cambridge, MA 02139
(Received
5 March 1982 by R.H. Silsbee)
The effect of the implantation of Sb ions on the electronic structure of the semimetal bismuth is studied by the magnetoreflectlon technique. The results show long electronic mean free paths and large implantatlon-lnduced increases in the band overlap and L-polnt band gap. These effects are opposite to those observed for Bi chemically doped with Sb. tation depth Rp. 7 Finally, because of the low melting point of bismuth (Tm = 271°C), it was expected that the lattice damage produced by the ion implantation could be readily annealed. Several arguments suggest that the magnetoreflection spectra from ion-lmplanted samples would be unsuitable for quantitative study. On the basis of Raman scattering studies of ion implanted graphite, 8 it was expected that the lattice damage caused by ion implantation would seriously degrade the mean free path so that the condition ahz >> I could no longer be satisfied. Because of the strong spaclal dependence of the profile for the implanted ions, it is expected that the contribution to the magnetoreflectlon spectrum from the ion rich region between Rp-- ARp and Rp + ~Rp would differ signiflcantly from that for both the region through which the ions pass before coming to rest (d < R p - ARp), and the region not significantly penetrated by ions (d > Rp + ~Rp). This variation in ion concentration within the skin depth is expected to result in a smearing out of the resonant structures. Finally, the total ion concentration within the optical skin depth is low (~ 400 ppm), so that if a uniform ion concentration were achieved, little effect on the magnetoreflection spectrum would be expected. The mmgnet oref lection results presented here for Sb implanted Bl show unexpectedly sharp and intense resonances identified with Landau level transitions. The observed spectra can be explained in terms of the strongly coupled twoband model originally proposed to explain the electronic structure of bismuth. 3, 4 The magnetoreflection results from the ion implanted samples show three unexpected features. A reversal in lineshape from the case of Bi or Bil_xSb x alloys is observed and interpreted in terms of an increase in carrier concentration and band overlap. A breakdown in the selection rules that apply to Bi and Bil_xSb x alloys is found and attributed to an increased concentration of symmetry breaking defects. An increase in the L-polnt band gap and effective mass is observed and is identified with an increase in the sublattlce displacement potential in the electronic structure. All three features differ markedly from the effect of chemical doping with the same isoelectronlc Sb species. 5
Introduction Magnetoreflectlon measurements provide a powerful experimental technique for the quantitative determination of the electronic structure of semiconductors and semimetals. 1,2 This technique is now applied for the first time to study the effect of ion implantation on the modification of the electronic structure of the host material. The magnetoreflection technique is especially sensitive to modifications of the electronic structure by ion implantation because the implantation depth Rp is roughly of comparable magnitude to the optical skin depth. Bismuth was chosen as the host material and antimony as the implanted ion for a variety of reasons. Of all semimetals, bismuth exhibits Landau level transitions having the sharpest and most intense resonant structures in the magnetoreflection spectra. 3,4 Antimony is an isoelectronic dopant in bismuth which goes into substitutional sites, so that the large ~cz of bismuth is not significantly degraded upon doping with antimony, and the Landau level transitions in Bil_xSb x alloys are readily observed in the magnetoreflection spectra. 5 The chemical introduction of Sb into Bi decreases the band gap and at a Sb concentration of x = 0.04, the L-polnt valence and conduction bands cross. The addition of Sb into Bi also decreases the band overlap between the L-polnt conduction band and the T-polnt valence band, so that at an Sb concentration of x ~ 0.07, the band overlap vanishes and semlconductlng behavior is achieved for the Sb concentration range 0.07 < x < 0.22. 6 In the present ion implantation study of Sb into Bi, the ion fluences were chosen so that the local Sb concentration in the implanted region between Rp - ARp and Rp + ~Rp would be in the semiconductlng range, where ~Rp is the width of the Gausslan distribution about the mean implan-
tCenter for Materials Science and Engineering. *Department of Electrical Engineering and Computer Science. §Francis Bitter National Magnet Laboratory, supported by NSF. 233
MAGNETOREFLECTION
234 Experimental
STUDIES OF ION IMPLANTED BISMUTH
Details
Table I. Electronic structure parameters for ion implanted Bi and other reference samples.(a)
Magnet oref lection measurements have been made on a binary face of an unimplanted bismuth sample (the reference sample) and on two binary faces of bismuth implanted with antimony at 150 keV to fluences of 2.2 x i015/cm2 and 5.5 x lol5/cm 2. The ion implantation was done in vacuum and at room temperature with a commercial ion implanter, using both a metallic powder of Sb and SbF 5 as a source for Sb ions. To avoid channelling, the beam was incident on the sample at an angle of ~ 7 °. Using the theory of Lindhard, Scharff and Schiott (LSS theory), 7 values of Rp ~ 380 A and ARp ~ 8 5 A are calculated, showing that the ion penetration is significantly less than the optical skin depth (~2 ~). The magnetoreflectlon measurements were made in the Faraday geometry in fields up to 150 kOe, with the sample attached to the cold finger of a dewar containing liquid helium. Experimental details relevant to the magnetoreflection measurements are given elsewhere. 3, Results and Discussion A typical magnetoreflection trace obtained for the binary face of a bismuth sample implanted wlth antimony to a fluence of 5.5 x 10 15 ions/cm 2 is shown in Fig. 1 at a photon energy of h e - 140 meV. Shown in the inset is the spectrum for an unimplanted binary Bi sample at the same h~. Using the coupled two-band model for the magnetic energy levels of Bi, the energies of the j ~ 0 levels at the conduction and valence band extrema of the magnetic subband (kH - O) are written as: 9- 12 E-+j~0,s - -+[(EGI2)2+
J EG 8*H] tlz- 2GS*sH
Vol. 43, No. 4
(I)
where E G is the band gap, H is the magnetic field and the quantum number J is related to ~:he Landau level index n by J = n + I/2 - s, where s = -+ I/2 is the spin, 6" ~ eh/mc*C, and me* is the cyclotron effective mass at the band extrema, and G is the effective g-factor. The quantum number J is written as Jv and Jc for the valence and conduction bands, respectively. The factor G results from the k'p perturbation contribution from bands not included explicitly in the two band model, and G is assumed to be the same for all J # 0 levels. The energy of the J - 0 conduction and valence band levels (s = 1/2) at k H = 0 are nearly degenerate and are given by the modified two-band model. Ii, 12 As a first step in analyzing the magnetoreflection spectra (see Fig. I), the AJ = +- 1 transitions, which are allowed in unlmplanted Bi and Bil_xSb x alloys, are identified, yielding the solid lines of the fan chart for the magnetoreflection resonances given in Fig. 2. The results for the L-point energy gap EG and cyclotron effective mass mc* , obtained from the fit of the experimental points to the functional form in Eq. (I), are given in Table I. Also included in Table 1 are corresponding results for unimplanted Bi and for the binary Bi sample ion implanted with Sb to 2.2 x 10 15 ions/cm 2 as well as chemically doped Bil_xSb x and Bi under 1 kbar hydrostatic pressure. The results in Table I show that ion implantation significantly
Samples (b) EG(meV) mc*/m o
E G {mo/mc*} ~p(meV)
Bi (reference)
13.8
0.00185
7460
40 + I0
@ffi2.2xlOl5/cm 2
37.5
0.00582
6440
70 -+ 50
~'5.Sx1015/cm 2
46.0
0.00776
5930
140 + 50
Bi0.98Sb0.02 (c)
8.0
0.00116
6900
< 40
Bi0.97Sbo.03 (c)
4.9
0.00073
6700
< 40
Bi0.95Sb0.05 (c)
3.9
0.00059
6610
< 40
Bi0.88Sb0.12 (c) 17.5
0.00274
6390
0
Bi0.85Sbo. 15 (c) 20.0
0.00321
6230
0
Bi(l kbar) (c)
0.00215
8090
16.1
< 40
a) The table gives cyclotron masses at the band extremum for the magnetic field along a binary direction. b) The samples labeled ~ ffi 2.2 x lol5/cm 2 and = 5.5 x lOl5/cm 2 are ion implanted to the stated f luences. c) Results for five unimplanted but chemically alloyed Bil_xSb x samples are presented (data from Ref. 17) for comparison, as are also results for Bi under hydrostatic pressure (data from Ref. 18). increases the L-point band gap and effective mass, with a significant decrease in EG/mc* , or equivalently the square of the momentum matrix element coupling the valence and conduction bands, In contrast, chemical doping by comparable concentrations of Sb results in a small decrease in E G and mc* , though for both implanted and chemically doped Sb, the ratio EG/mc* decreases (see Table I). The second important effect of ion implantation is the reversal in lineshape of the magnetoref lection resonance in the implanted sample (Fig. I) relative to the unimplanted one (inset to Fig. I). In particular, the sharp resonances correspond to reflectivity max[me for the unimplanted sample and to reflectlvity minima for the implanted sample (see Fig. I). This identification of the resonance point within the llne width for the AJ ffi + 1 transitions provides a fit of the observed resonances to Eq. (i) and was used in the analysis of the magnetoreflection traces for the Sb implanted samples (see Fig. 2 and Table I). The calculated magnetic fields for the AJ = -+ I transitions in Fig. 1 are labeled on this basis. The reversal of the lineshape for the magnetoreflection resonances is indicative of a shift in the plasma frequencies ~p to significantly higher frequencies, insofar as the condition ~ >> ~p corresponds to resonances at the reflectivity maxima while ~ < ~p yields resonances at the reflectivity minima. 13 Thus the change in lineshape indicates that ion implantation results in a significant free carrier generation within the optical skin depth. This has been confirmed by direct measurement of the frequency dependence of the reflectivity using a
MAGNETOREFLECTION
Vol. 43, No. 4
STUDIES OF ION IMPLANTED BISMUTH
235
,-,.
c~ c o ,.c:
0
3~-4 V
4--
._~
50 I00 Mognetic field (kG)
t
"0
2-~-3
r-
t
o_
t
I-'I
Ix.
1%
0
50
I00 Mognetic field (kG)
150
Fig. 12_. Experimental trace of the reflectivlty v_[s magnetic field for the binary face of Bi implanted with a fluence of 5.5 x 1015/cm2 Sb ions at 150 keV. The photon energy of 140 meV was used for both the implanted sample where the resonances appear as reflectlvlty minima, and the unlmplanted bismuth sample (inset) where the resonances correspond to reflectlvlty maxima. The arrows indicate the resonant ,~,n~etlc fields for Landau level transitions calculated from levels Jv in the valence band to Jc in the conduction band, using the model discussed in the text and the parameters from Table I. Fourier transform spectrometer. Estimates for ~p obtained from these reflectivlty measurements are given in Table i. The increase in free carrier density induced by ion implantation is attributed to a n increase in band overlap, as discussed below. This behavior is in contrast to the results for bismuth chemically alloyed with Sb, in which the plasma frequency decreases with the addition of smell concentrations of Sb (x ~ 7 at.%; see Table l). For an isoelectronlc impurity, the change in plasma frequency is associated with a change in the band overlap, which is directly related to the rhombohedral lattice distortion with respect to the simple cubic structure. The third effect induced by ion implantation is the appearance of Landau level transitions not present in unlmplanted bismuth. The additional resonances in the magnetoreflectlon spectrum in Fig. 1 can be explained in terms of AJ = + 2 and Aj = 0 transitions which can be
calculated from Eq. (i), and using the band parameters determined from analysis of the AJ = -+ I transitions (see Table I). Weak transitions identified with AJ ffi -+ 3 have also been identified. The AJ ffi 0, -+ 2, +- 3 resonances calculated in this way are indicated in Fig. 1 by arrows and labeled by the Jv ++ Jc quantum numbers. A good fit to the experimental resonances is obtained at 140 meV (Fig. |) and at other photon energies (Fig. 2), by the model of Eq. (1) and the band parameters of Table I. Since ~ - ~p, a detailed llneshape calculation should be carried out to obtain a quantitative identification of the resonance point within the magnetoreflectlon llneshape. The AJ - 0, + 2, + 3 transitions, which are symmetry forbidden in unlmplanted bismuth, have also been reported in tin-doped bismuth, 14 where the substitutional charged tin impurities on random sites lower the crystal symmetry and relax the usual selection rules, In the case of the ion-lmplanted sam-
MAGNETOREFLECTION
236 ~(o~o ~0 ~.
STUDIES OF ION IMPLANTED BISMUTH
•
20C 160 •
- ,2o
;~"
-
•
~
~
O.PI s,I/~
40 0
i O
20
I
J
I
40 60 BO Mogneticfieid (kG)
I
I
I00
120
2__~.Energy of the resonant peak positions vs magnetic field for the sample of Fig. I. The curves are calculated from the mirror band model discussed in the text using the parameters of Table I . Solid curves and open d r c l e s denote ~ = ± I transitions (allowed in bismuth), dotted curves and open triangles for the ~ = ± 2 transitions, dashed curves and solid circles for AJ ffi 0 transitions, and dashed-dot curves and plus signs for the weak ~ = ± 3 transitions (forbidden in bismuth).
ples, rule cant cies
the breakdown of the AJ - ± I selection is attributed to the presence of a signifidensity of structural defects (e.g., vacanor interstitlals). Because of the very small bandgap and the very strong interband coupling in bismuth, small perturbations to the local potential can result in significant changes in the L-point band parameters. The o b s e r v a t i o n of sharp magnetoreflection resonances indicates that significant annealing of the Implantatlon-lnduced lattice damage o c c u r s a t room t e m p e r a t u r e , and t h a t t h e mean f r e e p a t h of t h e e l e c t r o n s i s l o n g c o m p a r e d to the optical skin depth. The s h a r p n e s s of t h e resonance lines also indicates that the crystal potential has been modified over the entire optical s k i n depth. The results presented in the previous section can be interpreted in terms o f the theoretical m o d e l s f o r t h e Bi band s t r u c t u r e . 15 The Bi structure is baslcally a distorted simple cubic lattice, with a - 57 ° 14.2', u - 0.237, while a = 60 °, u = 0.25 represents a simple cubic structure. 16 To obtain the bismuth structure from the simple cubic structure, a displacement of t h e two interpenetrating fcc lattlces is made, which opens up band gaps at the zone faces (e.g., at b-points of the fcc Brillonin zone). If this were the only distortion in Bi, the material would be a semiconductor with gaps at the L-point in the fcc Brillonin zone. The semimetalllc properties of bismuth are produced
Vol. 43, No. 4
by an additional rhombohedral distortion along the (111) direction, making two of the 8 fcc Lpoints inequivalent. The two points along the three-fold axis, labeled T-polnts, are occupied by holes whereas the other 6 fcc L-polnts become centers of L-point electron pockets in Bi. _ Thus~s in the Bi electronic structure can be correlated with changes in the two perturbing potentials, Vsu b causing the sublattics displacement and Vrh m causing the rhombohedral distortion. An increase in the band gap is associated with an increase in Vsu b. An Increase in the band overlap (or in the carrier density for isoelectronic doping) is associated with an increase in Vrh m. The effect of Sb implantation is thus seen to increase both Vsu b and Vrh m. The sharpness of the Landau level transitions indicates that the perturbations to Vsu b and Vrh m extend over the optical skin depth. At the present time the driving mechanism for these changes in potential is not fully understood. Though strain could be responsible for the changes in the electronic structure, the values of the parameters are found to he functions of fluence $ and do not change with annealing (though ~cT increases with annealing). At the ion fluences and implantation energy of this experiment, the Sb atoms are expected to be confined to a region of ~ 170 A wide buried about 400 A into the sample, corresponding to a concentration of ~ 1021/cm S in this region. It seems unlikely that substitutional Sb could produce the large changes in band parameters that are observed, since chemical doping with Sb by ~ 1021/cm3 (e.g., Bi0.98Sbo.02 in Table I) 17 decreases both Vsu b and Vrhm, but by smaller amounts than the Increase found in the present experiment. $ The application of pressure increases the magnitude of Vsu b and decreases Vrh m (see Table I). 18 These observations suggest that ion implantation introduces interstitial Sb ions in the BI lattice. It would therefore be of great interest to carry out precise x-ray measurements to determine the change in a and u resulting from ion implantation. This work opens up a new field of investigation in the use of the msgnetoreflectlon technique to study, modifications to the electronlc structure due to ion implantation. The technique permits quantitative study of these modifications as a function of ion fluence, energy, species and annealing. It wlll be of particular interest to extend this work to ions that act as donors (e.g., Te) or as acceptors (e.g. Sn) to semlmetals (e.g., bismuth) and to ion implantatlon in semiconductors. Acknowledgement-We wish to thank Dr. E.W. Maby and M. Rothman for assistance with the ion implantations, P.D. Dresselhaus for help with the data analysls, and ON'R Grant # NO001477-C-0053 for support of this research. The experlmental work was carried out at the Francis Bitter National Magnet Laboratory. We wish to thank L. Rubin and B. Brandt of the FBNML for technical assistance.
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MAGNETOREFLECTION STUDIES OF ION IMPLANTED BISMUTH
237
REFERENCES
1. M.H. Weiler, Semiconductors and Semimetals, edited by R.K. Willardson and A.C. Beer, Academic Press, New York, 1981, p. 119. 2. H.S. Dresselhaus, The Physics of Semimetals and Narrow Gap Semiconductors, edited by D.L. Carter and R.T. Bate, Pergamon Press, New York, 1971, p. 3. 3. R.N. Brown, J.G. Mavroldes and B. Lax, Phys. Rev. 129, 2055 (1963). 4. M.S. Maltz and M.S. Dresselhaus, Phys. Rev.
B2, 2877 (1970). 5. E. J. Tlchovolsky and J.O. Mavroldes, Solid State Commun. 7, 927 (1969). 6. A.L. Jaln, Phys. Rev. 114, 1518 (1959); F.A. Buot, The Physics of Semimetals and Narrow Gap Semiconductors, edited by D.L. Carter and R.T. Bate, Pergamon Press, New York, 1971, p. 99. 7. J. Llndhard, M. Scharff and H. E. Schlott, Kgl. Danske Vldenskab. Selskab, Hat. Fys. Medd. 33, 14 (1963). 8. B.S. Elman, M.S. Dresselhaus, G. Dresselhaus, E.W. Maby, and H. Mazurek, Phys. Rev. B24, 1027
(1981).
9. M.H. Cohen and E.I. Blount, Phil. Hag. 5, 115 (1960). I0. P.A. Wolff, J. Phys. Chem. Solids 25, 1067 (1964). II. G.A. Baraff, Phys. Rev. 137, A842 (1965). 12. M.P. Vecchl, J.R. Perelra and M.S. Dresselhaus, Phys. Rev. B14, 298 (1976). 13. P.R. Schroeder, Ph.D. Thesis, HIT, 1968, (unpublished). 14. A. Misu, J. Heremans and M.S. Dresselhaus, Phys. Rev. BI5 (in press). 15. M.H. Cohen, L.H. Fallcov, and S. Golln, IBM J. Res. Develop 8, 215 (1964). 16. R.W.G. Wyckoff, Crystal Structures, Vol. I (New York: Interselence, 1964). 17. M.P. Vecchl, Ph.D. Thesis, MIT, 1975, (unpubllshed). 18. E.E. Mendez, A. Misu and M.S. Dresselhaus, B24, 639 (1981).