Spectroscopy of the electron subbands on (1 1 1)-Si

Solid State Communications, Vol. 49, No. 5, pp. 505-507, 1984. Printed in Great Britain.

0038-1098/84 $3.00 + .00 Pergamon Press Ltd.

SPECTROSCOPY OF THE ELECTRON SUBBANDS ON (1 1 1)-Si F. Martelli, C. Mazurd and F. Koch Physik-Department, Technische Universit~it Miinchen, D8046 Garching, Federal Republic of Germany (Received 10 October 1983 by B. Miihlschlegel)

We present measurements of infrared inter-subband absorption for electron subbands on (11 1)-Si for densitiesNs up to ~ 10tacm -2 at 4.2K for both parallel- and perpendicular-excitation geometries. Contrary to previously published work the depolarization shift is identified as a sizeable splitting of the resonance energies Eoil and E~I. The comparison with a recent calculation is given.

THE RESONANT EXCITATION of the electron subbands on (11 1)-Si has been reported in a number of publications [ 1-4]. It has been recognized that because of the tilt of the electron ellipsoids the resonance can be excited in both polarization modes, i.e. with the r.f. electric field directed either along the surface (parallel excitation) or normal to it (perpendicular excitation). A recent theoretical paper [5] has treated the (1 11)resonance in considerable numerical detail. It has tried to sort out the various contributions to the resonance energy for the case of the two different valley-degeneracies gv = 2 and 6 that have been proposed from the interpretation of the Shubnikov-de Haas data [6]. Published experimental data for (11 1)-Si covers only the range o f N s to 1.5 x 10 ~2em-:. Moreover, the question of a possible dependence of the resonance energy on the excitation mode (± vs II) is not resolved convincingly. In [2, 3 ] the scatter of the data points from different samples ( ~ 2 meV) is found to exceed the energy splitting. Whether or not there is a splitting could not be decided. [4] demonstrates a splitting which is quite small but has, contrary to what is expected, the II-excited mode at the higher energy. A recent summary of all the data [7] concludes that, because of unknown and incompletely established depletion charge, the distinction of the two modes in [4] is not certain. The aim and motivation of our work has been to probe the question of a polarization-dependent splitting in (1 1 1)-Si and to provide an as complete as possible set of data over a large range of Ns. In addition we hope in this way to shed some light on the nature of the gv = 2 or 6 controversy, as it has been injected into subband spectroscopy experiments. The experimental procedure is straightforward and makes use of the apparatus and measurement procedures described elsewhere [8]. The sample is a (1 1 1)-Si wafer oxidized according to standard procedures to a thickness

of ~ 1000 A. The annealing and other treatments are such as are known to yield the nominal gv = 2 in Shubnikov-de Haas experiments. We use mostly n-type material in order to have the doping independent naccumulation layer. Some additional results with p-Si ( N A - - N D ~ 10 Is cm -3) are intended to show the sensitive dependence on depletion charge Nde p in order to point to a possible explanation for the differences with the previous data and to make the comparison with the calculation possible. For an unambiguous demonstration of the existence of a depolarization shift as in Fig. 1 we take the following experimental precautions: (a) We measure in n-accumulation where the Neep is of no importance. (b) The ± spectrum is obtained from the same sample after deposition of thick (~ 2000 A.) Al-gate on top of the semitransparent gate used for I)-excitation experiments. (c) The C - V curves are matched up for both sets of experiments in order to take the identical flat-band position. (d) We use sufficiently high h~o to assure a minimal fractional error in the Ns determination. With both lines in Fig. 1 superposed on different broad background structures whose form is not exactly known, there is some arbitrariness in marking the resonance position. The procedure we have followed throughout is to mark a point symmetric between the resonance maximum and minimum. The splitting is typically comparable to the full line width but is more than a reasonable uncertainty in the marking procedure. The relative accuracy is more than the possible absolute error in the resonance determination. The lineshape in Fig. 1 is typical of accumulation conditions. From a large number of experimental h6o the

505

506

SPECTROSCOPY OF THE ELECTRON SUBBANDS ON (1 1 1)-Si
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Fig. 2. Subband excitation energies Eoli and E~l vs Ns. For all but the highest Armrange, the estimated absolute uncertainty is of the order of the s~ze of the symbols. The difference between E~I and E~I is known with greater precision. accumulation resonance Eol(Nm)for both perpendicular and parallel-excRetion is recorded in Fig. 2. Values in the parallel mode above 4 x 10 ll cm -2 are obtained with a grating spectrometer. The splitting is clearly evident for the discrete frequency points of the laser data. In the range to 1.5 x l012 the splitting is only of the order of ~ 2 meV and could have been missed in [2-4]. In Fig. 3 we show the l-excited resonance in a p-type sample for ha.) = 21.8 meV. The lower trace corresponds to the inverted surface for an Ndep = (0.9 + 0.1) x 10" cm =2. This value is obtained according to the dark-sweep procedure established in earlier work [9]. Both the 0 --) 1 and 0 =~ 2 transition are resolved. The lineshape is typical for an inversion-layer resonance. It is interesting to notice the strong sensitivity of

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Fig. 4. Comparison of present results with the experimental data of [4] and the calculation in [5]. lineshape and position to changes in the depletion charge. When the sample is illuminated with a sufficiently strong bandgap light, the upper trace in Fig. 3 is recorded. The Ns-scale has been adjusted for the small (~ 1011cm -2) shift in the C - V curve that indicates quasi-accumulation conditions. The lineshape is now very nearly that in Fig. 1 for Eoil. The position is identical with those plotted in Fig. 2 for accumulation. A good check on whether or not accumulation conditions are really achieved in the course of the experiments is always the light-test. The accumulation signal is totally insensitive to light. Another relevant feature of the accumulation spectrum is the presence in the lowNm range of a broad signal weakly dependent on energy. It was suggested I1 ]

Vol. 49, No. 5

SPECTROSCOPY OF THE ELECTRON SUBBANDS ON (1 11)-Si

that it could be related to transitions into the quasicontinuum (0 -~ 2, 3, 4 . . . . ). This seems unlikely, because in the inversion case (lower trace, Fig. 3) the 0 ~ 2 transition is observed with much lower intensity compared to the 0 ~ 1 transition. Furthermore, according to the polarization rotation experiments for (110)Si in [8] such a precursor-absorption is shown not to be a subband signal. Its origin is under further investigation. In the final Fig. 4 we come to summarize our differences with the published Si (1 1 1) data. We first note the exact superposition of our EIoll(Ns) for accumulation with the set of points labeledgv = 6. The text of [4] describing the data talks of accumulation-like lineshape and a measured Ndep ~ 1 X 1011cm -2. These statements in view of the observations in the previous Fig. 3 are difficult to understand. The comparison suggests that the gv = 6 data points really represent accumulation. Other recent experimental results also support this idea [10]. The ± vs II splitting that we find for accumulation is evident from the comparison of the solid and broken lines. Although the difference is only of order 2 meV in the relevant range of Ns, it has been resolved in our experiments. The 1-resonances E011lie, as expected, above the [I-excited transitions E~t. As stated earlier, our samples are prepared in such a way as to be in Shubnlkov-de Haas terms "gv = 2" samples. In this sense the two lines should be compared with the middle set of points from [4] which are intended to describe an accumulation case. The perpendicularexcitation points lie significantly above ours. Moreover the parallel-excited energies EIolt come out to lie above the perpendicular-excitation energies[ For this there is no simple explanation. It appears to us that both polarization experiments in [4] for this sample involved a small depletion charge and were not true accumulation. A bandgap light test as in Fig. 3 of our data could have resolved this question. One must assume the parallel-excitation results to have been obtained for the

higher value OfNdep. Finally in Fig. 4 we have entered as the dashed line the energies E0il for a sample whose Ndep we have determined as 0.9 + 0.1 x l0 n cm -2. This line falls below the

507

set of data points given in [4] for agv = 2 sample with Ndep ~ 1 x 1011cm -2. The difference here is easily accounted for by the depletion charge and uncertainties in its determination. Why the parallel excitation falls at higher energies is not understood. The extrapolation of the sets of experimental points to N s = O both give energy values in good accord with the subband splitting Eel calculated according to the triangular well approximation. F o r N d e p = 1 X 1011 c m -2 this value is 11.6 meV. The theory line according to [5 ] is much too high in Fig. 4. In conclusion, we have shown that the depolarization shift resulting from the resonant screening effect can be observed on (111)-Si as a sizeable splitting of the resonance energies Eel1 and EIoll.We have come to learn that it is important to carefully monitor the depletion field in order to obtain consistent results. The fact that the n-accumulation results for our "'gv = 2" come to fall so close to data obtained for the "gv = 6" case may be fortuitous. It may also indicate that the distinction between subband resonances from one or the other type of sample is not as large as has been claimed in previous work.

Acknowledgements - We thank B,D. McCombe and J.P. Kotthaus for discussions. This work was supported by the Deutsche Forschungsgemeinschaft via SFB 128. REFERENCES

I. 2. 3. 4. 5. 6. 7. 8. 9. 10.

A. Kamgar, Solid State Commun. 29,719 (1979). B.D. McCombe & T. Cole, Surf. Sci. 98,496 (1980). T. Cole & B.D. McCombe, J. Phys. Soc. Jpn. 49(A), 959 (1980). T. Cole, Surf. ScL 113, 41 (1982). K.S. Yi & J.J. Quinn, Phys. Rev. B27, 2396 (1983). D.C. Tsui & G. Kaminsky, Solid State Commun. 20, 93 (1976);Phys. Rev. Lett. 42, 595 (1979). B.D. Combe, (private communication and to be published). S.M. Nee, U. Claessen & F. Koch, Phyz Rev. B, (in press). P. Kneschaurek, Avid Kamgar & F. Koch, Phys. Rev. BI4, 1610 (1976). A. Wieck & J.P. Kotthaus, (private communication).

NOTE ADDED IN PROOF The Si(111) subband energy splitting Eot has recently been calculated by S. Das Sarma & B. Vinter [Phys. Rev. B28, 3639 (1983)]. Their energy values compare favorably with the data points in Fig. 4 (Ndov ~ 1 X 1011 cm-2).