Hole Subband Dispersion in Space Charge Layers under Pb/Si(001) Surfaces Measured by Angle-Resolved Photoelectron Spectroscopy∗

The dispersion structure of the hole subband in a p-type space charge layer on Si(001) was investigated for the first time by angle-resolved photoelectron spectroscopy. The space charge layer was made via adsorption of Pb. The dispersion curves were in qualitative agreement with the parabolic dispersion curves with bulk effective masses obtained by the k ·p perturbation method. The observed energy levels had smaller binding energy than the levels calculated by the triangle potential approximation. This was interpreted to reflect a change of the dopant atom concentration in the subsurface region due to diffusion of dopant during flashing. [DOI: 10.1380/ejssnt.2009.641]


I. INTRODUCTION
In modern metal-oxide-semiconductor field effect transistors (MOSFETs), the depth of space charge layer (SCL) channels reach the nano-meter scale due to scalingdown strategies for better device performance.The carriers in the channel are quantized and form discrete energy levels.In the in-plane direction, they form a multiple dispersion structure of "subbands."Information on the dispersion structure of subbands such as energy levels and effective mass is essential to understand and improve device performance.Thus, a thorough investigation is required.Although there are several theoretical studies on the dispersion structure of subbands, experimental determination had been lacking for quite a long time.We have recently developed an experimental method to obtain the dispersion structure of hole subbands (HSBs) in SCLs [1].The key techniques in this method are the use of angle-resolved photoelectron spectroscopy (ARPES) and the use of Schottky barriers induced by the surface superstructures (SSs) of the metal-adsorbed semiconductor surfaces.The dispersion structures of the HSBs on Si(111) SCLs were reported previously [1,2].
Here, we report on the dispersion structure of HSBs in the SCL on Si(001), which is most commonly used for MOSFETs.To apply the method to Si(001), we searched for a metal-adsorbed SS which induces a strong bandbending on Si(001) and found that a Pb-adsorbed SS (Si(001)2×1-Pb (1 ML)) is suitable for this purpose.In this paper, after a brief description of the experimental details, the formation process of the Si(001)2×1-Pb (1 ML) SS is described.Then, the results of the ARPES on clean Si(001)2×1 and Si(001)2×1-Pb (1 ML) surfaces are shown.The dispersion structure of the Si(001) HSBs and rough estimations of their effective masses are shown.Furthermore, by comparing the binding energy of the bulk bands of the clean and Pb-adsorbed surfaces, the amount of band-bending could be estimated.At the end, some discussion is given regarding the measured energy levels as compared with the approximate values calculated using the obtained band-bending.

II. EXPERIMENTAL
All experiments were performed in an ultra high vacuum chamber with a base pressure lower than 4×10 −10 Torr.A hemispherical electron analyzer (SES2002, VG SCIENTA AB, Sweden) was used for the ARPES measurements.Incident photon energy (hν) was 21.2 eV.The total energy resolution was ∼10 meV and the angler resolution was approximately 0.2 • .For the analysis of SSs, reflection high-energy electron diffraction (RHEED) was used.
As sample substrates, we used two different Si(001) wafers with different dopant species and carrier concentrations (N i ).We refer to the sample with lower N i as wafer A (Sb-doped, N i = 6.5×10 17 cm −3 ) and the sample with higher N i as wafer B (As-doped, N i = 1.1×10 19 cm −3 ) hereafter.These values are summarized in Table I.As reported in ref. [1], steeper band-bending is expected in samples with higher N i (wafer B).Every sample was cleaned by flashing at 1,250 • C about 100 times.
In the case of HSB, the relations between the binding energy (E B ), the surface in-plane wave vector (k // ), and the surface in-plane effective mass of holes (m * // ) are expressed as Eq. ( 1) [1][2][3].
ISSN 1348-0391 c 2009 The Surface Science Society of Japan (http://www.sssj.org/ejssnt) Here, n is a quantum number, and H n indicates the n-th HSB energy level.In the case of holes, m * // < 0 .

III. RESULTS AND DISCUSSION
A. Making Si(001)2ˆ1-Pb (1 ML) SSs Si(001)2×1-Pb (1 ML) SSs were made by Pb deposition onto clean Si(001)2×1 SSs at room temperature.All SSs appearing in this study were double-domain (DD).During the deposition, successive structure transformation from initial Si(001)2×1 to streaky Si(001)2×3-Pb at 0.35 ML, Si(001)c(8×4)-Pb at 0.75 ML and Si(001)2×1-Pb at 1 ML was observed by RHEED (see Fig. 1(a)-(d)) as reported by several groups [4][5][6][7].Si(001)c(8×4)-Pb at 0.75 ML did not always appear during the deposition.RHEED pattern of Si(001)2×3-Pb at 0.35 ML was characterized by the development of the spots from 2-fold periodicity in Si(001)2×1 RHEED pattern to broad streaks.The spots from 3-fold periodicity were not clear.Thus the RHEED pattern of Si(001)2×3-Pb at 0.35 ML was similar to that of Si(001)2×1 and Si(001)2×1-Pb.Due to this similarity, it was difficult to distinguish Si(001)2×3-Pb and Si(001)2×1-Pb RHEED patterns without the appearance of Si(001)c(8×4)-Pb.This made the determination of the SS and thus the determination of the Pb coverage difficult.To make the surface reproducibly irrespective of the appearance of c(8×4) in the RHEED patterns, we monitored the intensity changes of RHEED spots during  of a clean Si(001)2×1 surface of wafer A. For clarity, the second derivative was performed on the raw spectra in the energy direction.The bands denoted as SA, SC, SE, SF, SG, and SH in Fig. 3 are found for the clean Si(001)2×1 surface.The band SA is well-known surface states which originate from the dangling bonds [8].Due to contaminants from the UV light source in operation, the intensity of the surface states SA started to decay immediately after the UV light source was turned on.Data in Fig. 3(a) was collected for 30 minutes just after turning on the UV light source.Fig. 3(c) shows data similar to Fig. 3(a) but was taken over a 30-minute period after the operation of the UV light source for 130 minutes.Due to the effect of the contaminants, the SA band is hardly seen in Fig. 3(c).This disappearance of the SA band is also clearly seen in the corresponding energy distribution curves shown in Figs.3(b) and (d), which are raw spectra at the Γ point

C. ARPES Measurement of Wafer B
Low and high resolution second-order derivative ARPES intensity maps of a clean Si(001)2×1 surface of wafer B along the [110] direction are shown in Figs.6(a) and (b), respectively.The high resolution original ARPES spectrum at the Γ point from this sample is shown in Fig. 6(c).Nine bands labeled as SA, SB, SC, SE, SF, SG, SH, SI, and SJ in Fig. 6 are found for the clean Si(001)2×1 surface.Except SB, the bands SA to SH are identical with those appearing in wafer A (Fig. 3(a)).SB is observed in Fig. 6(a) due to a wider wave vector range.The band SA disappeared in Fig. 6(b) due to the same reason described for wafer A (Fig. 3(b)).In Fig. 6(b), there is again a faint trace of the bands which have their top at 0.6 eV at the Γ point and disperse to the higher E B with k // .As mentioned in the previous section, their shapes are similar to the HH and LH of HSBs and to the projected bulk valence band edges.The photoelectron intensities from those bands are quite small so it was not possible to recognize them in the energy distribution curve shown in Fig. 6(c).
In a similar way, low and high resolution second-order derivative ARPES intensity maps of a Si(001)2×1-Pb ( PD, PE, PF', PG, PH, PI, and PJ in Fig. 7 are found for the Si(001)2×1-Pb (1 ML) surface.The bands PD, PE, PG, and PH are regarded as the same as those in Fig. 4(a).The intensity of the band PF is weaker in Fig. 7(a) in comparison with the data from wafer A (Fig. 4(a)).The multiple parabolic bands PB' and PC' appearing in Fig. 7(b) are similar to the HSBs observed on Si(111) in their shapes and energy positions.Furthermore, the appearance of these multiple bands only on the sample with higher N i suggests that they are from HSBs analogous to the discussion in ref. [1].To confirm this idea, however, a comparison of the quantized energy levels obtained by the observation and the calculation in the SCL of this sample is required, which will be done in the following section.
The black lines in Fig. 7 1).To see a relationship between the effective masses of the subband and the bulk band, we calculated the effective masses of bulk Si HHs (m * HH ) and LHs (m * LH ) along the [110] direction using the k •p perturbation method [3,9,10] as shown in Eq. ( 2): Here, A, B, and C are the Luttinger's parameters and their values were taken from Kittel [3,10].The values of the calculated effective masses are shown in Table III   (3) and ( 4) [1,2,14]:  In our study, it is suspected that the dopant atoms at the surface are reduced by diffusion after heat treatments such as flashing of the samples as pointed out in the previous study [2].We speculate that the actual carrier concentration N i of wafer B at the ARPES measurement may be reduced to an intermediate value between original carrier concentrations of wafer A and B.

IV. CONCLUSIONS
The correlation between the (1/2 0) spot intensity, Pb coverage, and Si(001)-Pb SSs below 1 ML during Pb deposition onto clean Si(001) surfaces was revealed.A steep SCL was found under the Si(001)2×1-Pb (1 ML) surface.By the ARPES from the steep SCL, HSBs with a multiple dispersion structure similar to the HSB on Si(111) was found.This is the first observation of the HSB dispersion on Si(001).The observed HSB shows strong N i dependence as with HSB on Si(111) .
Because the observed quantized levels of the HSB were at lower binding energies than the levels calculated by TPA, it is considered that the dopant atoms at the surfaces were reduced after flashing the samples.

FIG. 2 :
FIG. 2: Changes of (1/2 0) spot intensity in the RHEED patterns during Pb deposition.(a) is for the series in which we observed the c(8×4) pattern and (b) is for the series in which did not observe the c(8×4) pattern.

Figs. 1
Figs. 1(a)-(d) and (e)-(h).In addition, we also found close similarity in changes of (1/2 0) spot intensity during the Pb deposition irrespective of the appearance of c(8×4) as shown in Figs.2(a) and (b).Therefore, the correlation between the (1/2 0) spot intensity and the Pb coverage was revealed as shown in Fig.2.Based on this finding, we could reproduce the Si(001)2×1-Pb (1 ML) SS monitoring the (1/2 0) spot intensity.For reproducible Si(001)c(8×4)-Pb structure formation, further investigation on the deposition conditions is needed, which is beyond our aim here.

FIG. 4 :
FIG. 4: (a) and (c) are second-order derivative ARPES intensity maps along the [110] direction of the Si(001)2×1-Pb (1 ML) surface of wafer A. (b) and (d), respectively, are their original ARPES spectra at the Γ point.(a), (b) were collected for 20 minutes just after the UV light source was turned on, and (c), (d) were measured over 20-minute period after the operation of the UV light source for 120 minutes.

Figure 5
shows a high resolution ARPES intensity map along the [110] direction of the Si(001)2×1-Pb (1 ML) surface of wafer A. Four bands PB, PC, PD, and PE are found in Fig.5.The bands PB and PC have their top at 0.6 eV at the Γ point and disperse to the higher binding energies.Their shapes are similar to the heavy hole (HH) and light hole (LH) of HSBs and also to the projected bulk valence band edges.A faint trace of the bands similar to PB and PC also exist in the clean Si(001)2×1 surface (Fig.3(c)).Detailed discussion of the origins of these bands would require further investigation.
FIG. 7: Second-order derivative ARPES intensity maps of the Si(001)2×1-Pb (1 ML) surface of wafer B along the [110] direction in (a) the large region and (b) the small region around the Γ point with high energy resolution.(c) The original ARPES spectrum of the high resolution data (b) at the Γ point.
(b) are parabolic curvatures intended to guide to the eyes to see the multiple bands PB' and PC'.Solid lines indicate HH subband-like dispersions, and dashed lines indicate LH subband-like dispersions.If we employ these black lines, tentative effective masses of HH along the [110] direction (m * [110]HH ) and of LH along the [110] direction (m * [110]LH ) and values of H n in the SCL under the Si(001)2×1-Pb (1 ML) surface are obtained as shown in Table II using Eq. ( TABLE II: Tentative effective masses m *[110]HH and m * [110]LH , and the energy levels at the Γ point (Hn) calculated from the black guide lines in Fig.7(b) using Eq.(1).m0 is the freeelectron mass.Tentative Experimental Values by ARPES MeasurementHn m
) Here, V (z) indicates the linear potential as the function of depth z from the surface, and V s indicates the VBM position at the surface.F and m * z stands for the electric field at the surface and the mass of careers along the depth direction, respectively.Here, m * z = m * [001] .m * HH and m * LH along the [001] direction calculated by the k •p perturbation method (Eq.(2)) are shown in Table III.The brown and red dashed-double-dotted lines in Figs.9(a) and (b) show the linear potentials V (z) used in the TPA calculation.The solid brown lines and solid red lines in Figs.9(a) and (b) respectively show HH levels of Si(001)2×1-Pb (1 ML) of wafer A and B calculated with TPA.In a similar way, the brown and red dashed lines in Figs.9(a) and (b) respectively show LH levels of Si(001)2×1-Pb (1 ML) of wafer A and B calculated with TPA.The green triangle marks in Figs.9(a) and (b) indicate tentative values of H n of the Si(001)2×1-Pb (1 ML) surface of wafer B observed by ARPES measurement.

From
Fig. 9(b), one finds a difference between the values of H n obtained by ARPES measurements and by TPA calculation for wafer B. From Fig. 9(a), the values of H n by ARPES of wafer B are found to be rather closer to the values of H n by TPA of wafer A .

TABLE I :
Dopant species and Ni of the samples.
. One finds that the bulk effective masses m * HH and m * LH in Table III are roughly equal to the tentative experimental effective masses m * [110]HH and m * [110]LH shown in Table II, respectively.Next, we estimate the amount of band bending by comparing the energy of the Si bulk bands of the clean http://www.sssj.org/ejssnt(J-Stage: http://www.jstage.jst.go.jp/browse/ejssnt/)