Inter-subband spectroscopy in hole space charge layers on (110) and (111) Si surfaces

Solid State Communications, Vol. 21, pp. 823—826, 1977.

Pergamon Press.

Printed in Great Britain

INTER-SUBBAND SPECTROSCOPY IN HOLE SPACE CHARGE LAYERS ON (110) AND (111) Si SURFACES Avid Kamgar* Physik-Department, Technische Universität MUnchen, 8046 Garching, Germany (Received 29 September 1976 by M. Cardona) Inter-subband spectroscopy in inversion and accumulation layers of holes on (110) and (111) Si surfaces have been performed. Sample characterization is made using capacitance vs voltage measurements at room and liquid helium temperatures. It is shown that the measured energy spacings are larger than the predictions of a calculation based on Hartree approximation. This is contrary to the conculsion reached from Shubnikov—de Haas measurements on (110) inversion layer of holes. INTER-SUBBAND spectroscopy measurements in MOS (metal oxide semiconductor) systems have contributed greatly to the understanding of the binding mechanism of charge carriers in space charge layers.1 Much work has been done, both experimentally and theoretically, on the electron space charge layers of MOS systems. Energy levels have also been studied in the space charge layer of holes on (100) surfaces.25 These studies show that exchange and correlation interactions play an important role in determining the subband energies. In (110) planes Shubnikov—de Haas measurements on hole inversion layers indicate filling of a second subband at considerably low surface charge densities.6’7 These measurements also yield information on the subband structure, and surprisingly the results seem to be in good agreement with predictions of a Hartree calculation of the potential well and subband energies.4 It is, therefore, of interest to extend the spectroscopy measurements to (110) and (111) Si surfaces to further examine the binding energies of holes. In the following after a brief description of the experimental apparatus we discuss the characteristics of samples in some detail, and then present the results of inter-subband spectroscopy. The influence of the interface states on the spectroscopy signals is also discussed. Experiments are done using a far-infrared laser spectrometer, and a transmission-line geometry.3 In the presence of laser radiation, with fixed frequency and r.f.-electric field perpendicular to the interface, the derivative of power transmitted through the sample as a function of the gate voltage is measured. Samples are nand p-type (110) and (111) Si planes. The n- and p-type wafers are doped with phosphorus and boron respectively. The oxide layers are grown to a thickness of about 2000 A onto the samples. An Al layer of 1—2 pm *

Present Address: Bell Laboratories, Murray Hill, NJ 07974, U.S.A. 823

thickness forms the gate. Ohmic contacts on the back side are made by sparked-contact method.8 For p-type samples B—Au and for n-type sample Sn—Au material with 99% gold are used. A simple mechanical contact is proved to be insufficient at low temperatures. In total about 20 samples form 6 different wafers have been measured. Some of the characteristics of a few samples are summarized in Table 1. The sample number indicates the type of the substrate, the plane, the wafer number and the number of individual samples. The amount of doping NA ND I is determined from capacitance vs voltage (C— V) measurements at room temperature.9 These are accurate to about 10%. The oxide thickness is measured by ellipsometry technique. The (110) and (111) samples have considerably more interface states than (100) samples studied in reference 3. For a rough estimate of the number of interface states C—V measurements have been employed. This is done by measuring the shift in the flat-band voltage between room and liquid helium temperatures.’°These numbers are also given in Table 1. Such an estimate can also be made by comparing the measured VFB VT with a calculated value for an ideal sample. The numbers obtained from these two methods are in good agreement. In the spectroscopy the influence of these trap centers is clearly seen in the lineshape of the signals that occur at low gate voltages. Examples are shown in Fig. 1. In this figure the signal at hw = 10.45 meV in two samples with considerably different number of interface states is shown. The number of interface states is given in Table 1. The traces show the derivative of power absorption (dP/dt’~)as a function of the applied gate voltage (Vg) at different temperatures (T). In all traces the amplitude of the low gate voltage side (a) is much smaller than the high gate voltage side (b). The a/b ratio is smaller in D2 sample as compared with Dl at T = 4.4 K. Increasing the temperature decreases this ratio in both samples. The effect is more pronounced in —

—

824

SPECTROSCOPY IN HOLE SPACE CHARGE LAYERS

Vol.21, No.8

Table 1. The doping concentration, oxide thickness, size and the approximate number of interface states of a few samples NA —ND I

Sample

cm

n(1 10)-Di

2 x 2 x 2x lx 3x 1 x

n(110)-D2

n(1l1)-K3 p(ll0)-D4 p(lll)-Kl p(lll)-D2

A

Size 3 mm

2430 2430 2330 2430 2475 2440

6 6 8 6 7 6

0~

1014 l0’~ 1014 10’s 1014 iO’~

n Si (110)—DI T=44K

d

3

fl Si (110)— D2

-

-

i7~

x x x x x x

Interface States -2 cm

6x 6x 8x 6x 7x 6x

0.205 0.205 0.455 0.205 0.255 0.265

HOLE— INVERSION n SI (110)— Dl T=44K

3.0 x 5.5 x 1.5 x 4.5 x 11.0 x 12.5 x

1011 1011 1011 1011 1011 1011

HOLE-ACCUMULATION p Si (110) -D4 T=55K

T~4.4K

~~-lO45mev

~1045meV

T=12.5K

>0~

-

~2K

-

~

Th8K~ Vq (VI

fl\7~ L=15.8lmeV

-12

A~1581rneV VFB

Fig. 1. Absorption spectra for hole inversion layer at hw = 10.45 meV in two samples at different temperatures.

Fig. 2. Resonance signals for hole inversion and accumulation layers in (110) plane. Threshold and flat band voltages are indicated in the figure.

D2, and by about 8 K the signal appears as a cutoff of absorption, rather than with a resonance lineshape. This is not the case in signals which occur at high gate voltages. The reason, we believe, is that at low Vg most of the absorption is done by the interface states. By increasing Vg bands bend more and more down, and the trap centers which exist mainly in the gap move below the Fermi level (EF). When all of these states are occupied they can no longer absorb the laser radiation. The gate voltage at which this absorption ceases depends on the sample and to a degree on temperature. This is simply because at high temperatures due to the broadening of EFhigher the edge the localized states to is less sharp and slightly gate of voltages are required lower all the states below EF. We should mention that at higher laser

The absorption spectra for hole inversion in (110) and (111) planes, and hole accumulation in (110) plane have been observed. The accumulation and inversion spectra for (110) plane are shown in Fig. 2 at two frequencies. In each case one single absorption line is observed. This absorption signal, in the inversion layers, is attributed to the transition from the lowest subband E0, which corresponds to heavy holes, to the E2-level. In the hole potential well the sequence of subbands is the following: E0, lowest heavy hole; E1, lowest light hole; E2, next heavy hole;E3, next light hole, and so on. Heavy hole to light hole transition, i.e. E0 shown E1, isinalso 5 has case an (100) allowed transition, but as Ohkawa of plane, the amplitude of this signal is much smaller than the E 0 E2 transition. The lineshape of hole inversion signals in both planes are very similar. Only the lines in (111) plane are slightly broader than in (110). Hole accumulation signals, on the other hand, have different lineshapes, as seen in Fig. 2. The a/b ratio in these signals are greater than one in contrast to the signals in hole 3inversion. though inThis thistrend plane was also seen in the (100) plane, -+

—~

energies and consequently high gate voltages the absorption signal in both samples are identical. When the number of interface states is very large, for example in both p (111) wafers that we have studied, the spectroscopy signals are completely obscured by the absorption due to interface states. Therefore at present we have no data on (ill) hole accumulation layer.

Vol. 21, No.8

SPECTROSCOPY IN HOLE SPACE CHARGE LAYERS

the hole accumulation signals were extremely broad and asymmetric. The absorption in the accumulation layer starts at voltages slightly higher than VFB. This is the case even at h~ 15.81 meV in contrast to the inversion layer spectra. This type of spectrum, as discussed in reference 11, seems to indicate that there exists only one bound level in the hole accumulation layer. A detailed lineshape analysis in case of holes is very complicated. Calculations of lineshape should take image effects, many-body interactions, non-parabolic band structure, as well as the plasma and exciton-like shifts of the position of resonance into account. For the lack of a lineshape calculation the determination of the subband splittings cannot be done with a great accuracy. In case of electrons Ando’2 has shown that the maximum of absorption gives very nearly the subband splittings. In case of holes because of the complex structure ofvalence band this may not be true. At present we cannot predict

20

=

how the non.parabolicity of the hole band structure influences the position of the absorption peak. For an estimate of the value of E20 we have therefore plotted the maximum of absorption as a function ofN8. N8, the surface charge density, and N~epi,the effective depletion charge, are determined from C—V measurements as described in detail in reference 3. Lines are drawn through the data points for visual aid. The inaccuracy in N8 determination, which is mainly due to the uncertainties in VT or VFB, are also indicated. is seenarethat the smaller subbandthan splittings in accumulationIt layer much in inversion layers. This is expected because a strong depletion field does not exist in the accumulation layer. Comparison of the inversion layer signals between the two planes is not easy due to the difference in the number Of N~epij1i two samples. There are twoand Hartree calculations of subband splittings by Ohkawa Uemura,4 and by Garcia.’3 At 2 or less, low surface charge densities, 1012subband cm Garcia’s calculation seems toi.e. giveabout the same splitting, £20, for all planes. This is certainly not the case. The subband splitting in (100) is considerably larger than in thebyother two and planes. This isThey bornealso out in the calculations Ohkawa Uemura. show that in (110) plane E 20 is larger than in (111). In the first sight this is in contradiction with our data, but the problem could lie with the difference in Ndepi in the two planes. For a meaningful comparison one needs the calculation for the experimental Ndepi. On whether a calculation of the potential based on a Hartree approximation is adequate or not we can reach a conclusion based on the following observation. In Fig. 3 we have indicated2the of planes. the Hartree in result the two This calcuis the lation for lowest N N8 1012 cm 8 for used whichinthe subband splittings arexcalcu4 Ndepi these calculations is 8.5 1010 cm2, lated.

THEORY

-

-

~

.~_

~_

-~.__

_~_~.o___~_

15 - -‘.

10

825

- ~°‘

— —

—

— — — — ~

~

• ~~o-

0CC *

S -

2

0(110)—mv.

N~pI =2.4 x 1010 cm~

~

Nd~I.= 3.6 x 1010 cm—2

f1)

~‘

0

Ns [1011cm2]

Fig. 3. Resonance positions at different frequencies as a function of surface charge density. The two points indicated as theroy are the results of Hartree calculations. Ndepi used in these calculations is 8.6 x 1010 cm2. The experimental N~~ given 1 in the figure are accurate to about 10%. which is a factor of 3—4 higher than the experimantal In reference 3 we have reported that the subband splittings depend strongly on Ndepi. In fact a doubling of Ndepi in electron inversion layer increases E10 by more than 30%. This would mean that the result of the calculation for ourNdepi would lie considerably below the experimental points. This is not surprising because simi~ lar situations have been 4’11 observed in allhas thetocases and one take which account have so far beeninteractions studied, in the calculations. of many-body So far we have discussed the transitions from the lowest heavy hole subband which is the only filled level at low gate voltages. At higher densities the lowest light hole subband, E 1, could be populated as well. In fact, in 6 have (110) plane Landwehr and Dorda reported thatvon theKlitzing, E 1-level at N 2, in a crosses samplethe withFermi Ndepilevel = 8 x 3.2 x 1012 cm different results have been obtained 1.2 1011. Slightly by Lakhani, Cole and Stiles.7 When E 1 is filled one should observe the 1 3 transition as well, providing 4 showsthe laserthe energy is suitable. Hartree that energy splittingThe between thecalculation lowest two light Ndepi.

=

-~

hole subbands E31 is on the average much smaller than that of the heavy holes E20. Indeed, the 1 3 transition should take place at a density about 10 times higher than the 0 2 transition. We have increased the voltage to achieve densities somewhat higher than 10 times the N8 for the 0 2 transition at hw 10.45 meV, but no other transition has been observed. Because of the breakthrough in the oxide layer we were not able to applyOne much higher voltages to the samples. interesting observation was made when the -+

—~

-÷

=

=

sample temperature waslowest increased K. K) As a shown in Fig. 1, in the traceabout (at T20 22 =

826

SPECTROSCOPY IN HOLE SPACE CHARGE LAYERS

broad structure appears at about 30 V. At this temperature the 0 2 transition is also broad and there is no clear separation between the two structures. Nevertheless, a second transition seems to be taking place at highgate voltages, which could be attributed to the 1 3 transition. The low temperature data and the absence of 1 3 transition in the predicted position could be another indication of the insufficiency of the Hartree calculation. As is seen in the case of electrons~the light charge carriers are less affected by the many-body interactions which would mean that the 1 3 transition should take place at higher densities than 10 times the 0 2 transition. Next is the effect of temperature. This is also studied in case of electrons.1’ There the net effect of increase in temperature was to increase the subband splittings, and to shift the resonance position to lower gate voltages. This seems to be happening here also, although the effect on the heavy hole is hardly noticeable. —~

-÷

—~

—~

-÷

Vol. 21, No. 8

In summary we have measured the subband splittings in (110) and (111) hole space charge layers. The subband splittings, £20, are shown to be larger than the result of a Hartree calculation. A calculation of the potential which takes the exchange and correlation interactions into account seems to be necessary. This is in contrast with the conclusion reached from Shubnikov de Haas experiments. In these experiments the density at which the lowest light hole subband crosses the Fermi level is measured. This result surprisingly agrees with the prediction of a Hartree calculation. The difficulty could lie in the uncertainty in the determination of Ndepi in samples on which the Shubnikov— de Haas experiments have been performed.

Acknowledgements For providing me with the samples i am indebted to G. Dorda. I thank Tsuneya Ando and P.J. Stiles for many interesting discussions. —

REFERENCES

3.

See, for example, KOCH J.F., Surf Sci. 58, 104 (1976), and references contained therein. KAMGAR A., KNESCHAUREK P., BEINVOGL W. & KOCH J.F.,Proc. 12th mt. Conf Phys. Semicond., p. 709. Teubner, Stuttgart (1974). KNESCHAUREK P., KAMGAR A. & KOCH J.F., Phys. Rev. BlS, 1610 (1976).

4.

OHKAWA F.J. & UEMURA Y.,F~og.Theor. Phys. 57, 164 (1975).

5.

OHKAWA F.J.,J. Phys. Soc. Japan 41, 122 (1976).

6.

von KLITZING K., LANDWEHR G. & DORDA G., Solid State Commun. 14, 387 (1974).

7.

LAKHANI A.A., COLE T.L. & STILES P.J. (to be published).

8. 9.

FLORES J.M.,Rev. Sci. Instrum. 35, 112(1964). GOETZBERGER A., Bell Syst. Tech. J. 45, 1097 (1966).

10. 11.

BROWN D.M. & GRAY P.V., I Electrochem. Soc. 115, 760 (1968). KAMGAR A. (submitted to Phys. Rev. Lett.).

12.

ANDO T. (submitted toPhys. Rev. Lett.).

13.

GARCIA N., Solid State Commun. 18, 1021(1976).

1.

2.