Figures 5 and 6 show percentage of dopant density ionized as a function of total density for phosphorus-doped and boron-doped silicon, respectively, at 300 K for several models. The curve for a constant ionization energy of 0.045 eV (appropriate to both impurities) shows a rapid decrease in percent ionization for dopant densities greater than 1017 cm-3. Because of both effective mass and degeneracy factor differences, the fraction of ionized atoms is less for boron-doped silicon than for phosphorus-doped with the same dopant density.

imental results for phosphorus-doped silicon. For boron-doped silicon the same equation with identical parameters was used as ε do and a* are essentially the same as in phosphorus-doped material. As seen in the figures, the use of this equation results in a higher fraction of ionized atoms at large dopant densities. At 3 × 1018 cm-3 the ionization energy has decreased to zero. This is also the dopant density for which the theoretical calculations of Kleppinger and Lindholm [15] predict a disappearance of the ionization energy due to significant overlapping of the impurity and conduction bands. The assumption is made that all impurity atoms are ionized at higher dopant densities. This transition is indicated by a dashed vertical line. Complete ionization at high dopant densities is in agreement with Hall coefficient measurements in heavily doped n- and p-type silicon from 4 to 300 K which show no evidence of an ionization energy at impurity densities greater than 3 x 1018 cm 3 [16]. Furthermore Fistul' [17] argues that heavily doped semiconductors do not have shallow impurity levels and consequently the dopant is completely ionized as in the case of metallic conduction.

where the constant a was assigned the value 3.1 × 10-8 cm eV for both phosphorus- and boron-doped silicon to give zero ionization energy at a dopant density of 3 × 1018 cm-3 for comparison with eq (5). With eq (6) the ionization energy begins to decrease at lower doping densities than for eq (5) and because of the more gradual decrease in ɛ the ionized density decreases monotonically in contrast to the scallop in the curve between -3 1 and 3 × 1018 cm associated with Penin's

model.

d

The above calculations were made assuming a single energy level for the impurity states and a conduction or valence band density of states appropriate for lightly doped material. It is known [14] that as the doping density increases the impurity level broadens into a band and there is tailing in the density of states of the nearby intrinsic band edge. To some extent the use of an ionization energy which depends on doping density

incorporates these changes. However for densities greater than 101 cm-3 the above equations begin to lose their validity. Consequently calculations were also made using a model developed for gallium arsenide by Berg [18]. This model takes into account the broadening of the impurity level and the tailing of the conduction band. The density of states in the broadened impurity level was assumed to be Gaussian in nature as formulated by Dyakonov et al. [19]. Berg found that the model gave good computer fits to his data provided that the tailing of the conduction band edge was increased by the factor 1.6 over the theoretical value. This same factor was also used in the present calculations for n-type silicon. As seen in figure 5 the percent ionization is similar to that obtained from the Pearson and Bardeen model. Ionization is considered to be complete when the tail of the conduction band crosses the middle of the impurity band, which remains centered at 0.045 eV. This transition to complete ionization is indicated by the vertical line at a density of about 5 x 1018 cm-3. The model was not estended to calculations on p-type silicon but the results are expected to show similar trends.

Experimental data on percentage ionization are also shown in figures 5 and 6. For phosphorus-doped silicon, Gardner et al. [20] compared carrier density derived from plasma resonance with total density obtained from neutron activation analysis. On a phosphorus-implanted specimen Crowder and Fairfield [21] measured essentially the same impurity profile by neutron activation analysis as they obtained by differential Hall effect measurements. Nakanuma [22] studied the incorporation of phosphorus in epitaxial silicon by radiotracer studies and compared the phosphorus content with that obtained by Hall effect and conductivity measurements. He found no existence of electrically inactive phosphorus in the layers up to densities of 3 x 1019 cm 3. Using colorimetric analysis and Hall effect measurements, Esaki and Miyahara [23] determined that the percentage of ionized phosphorus in silicon at room temperature decreases gradually from nearly 100 to 60 percent with increasing phosphorus density in the range from 0.68 to 2.6 × 1020 cm-3. Mousty et al. [24] compared neutron activation analysis and Hall effect measurements on silicon doped with phosphorus in the

range 1017 to 1019 cm-3. With the assumption of complete ionization, they calculated the Hall scattering factor and found that it in

creased from 1.0 at 1017 cm-3 to 1.3 at 1018

-3

cm and then decreased to 1.0 at 1019 cm-3. There is the possibility that the peak in the scattering factor is due in part to incomplete ionization. Irvin [25] gives results on two specimens of arsenic-doped silcon on which both neutron activation analysis and Hall effect measurements were made and on one boron-doped specimen for which the total boron content was determined by a photometric technique for comparison with the Hall effect result. Based on the amount of boron impurity added to the melt and subsequent Hall effect measurements on the grown crystals, Pearson and Bardeen [13] concluded that each boron atom gave one charge carrier (within ±20 percent) except for one very heavily doped crystal in which only part of the boron went into solid solution. Hofker et al. [26] profiled a boron-implanted wafer by secondary ion mass spectrometry and compared it with Hall effect measurements on the same wafer.

Un

The sharp decrease in electrical activity of dopant atoms at densities greater than about 1020 cm-3 appears to occur because many of the dopant atoms do not occupy substitutional sites at these high densities rather than because of incomplete ionization. fortunately, the available experimental data are insufficient to resolve the question of whether there is an intermediate range of dopant densities, near 1018 cm-3, for which ionization may not be complete. Therefore it is not possible at this time to establish the validity of any of the models used in the calculations. (W. R. Thurber)

*

As part of the comparative study of surface analysis techniques (NBS Spec. Publ. 400-12, pp. 17-18) a Rutherford backscattering experiment [27, 28] was performed." Only one of the four specimens included in the study was suitable for analysis by this technique. The atomic number of the impurity in each of the other three specimens was below the atomic number of the host matrix, and there was an insufficient amount of the impurity present for it to be observed over the background signal due to the host. The specimen which was measured, a silicon wafer implanted with 30 keV zinc ions to a dose of 5 × 1016 cm-2 was exposed to a 40 nA current of 2.0 MeV "He+ ions over a 1 mm2 area, to a total dose of 10 μС.

The experiment is conducted by recording the number of particles backscattered from the specimen at a fixed angle as a function of the energy of the backscattered particles using a silicon surface barrier detector and multi-channel pulse--height analyzer [27]. Two measurements were made, one with normal incidence and one with the beam incident at

The measurements were made by Prof. M. A. Nicolet at the van de Graaf accelerator facility of the California Institute of Technology, Pasadena, California.

4000

METHODS

45 deg.

7.

The results are presented in figure The energy scale was established by measuring the "Het backscattered energies from aluminum (1.102 MeV) and gold (1.845 MeV) surfaces; the channel width was determined to be 3.46 keV.

The projected range of the implanted particles may be estimated from the energy difference between the energy of the peak response obtained with normal incidence and the energy of a backscattered helium atom just after collision with a zinc atom. This energy loss corresponds to a range of about 37.5 nm which is somewhat larger than the value, 22.4 nm, predicted by LSS theory [29].

If the detector had sufficient resolution, the distribution profile of the implanted ions could be inferred from the shape of the response. However, the resolution of the detector used was only 15 keV. Since the expected range straggling, defined as the half width of the distribution profile at 1/√e of the maximum density, corresponds to an energy difference of only about 4 keV, it is clear that the width of the response peak is due primarily to the detector resolution, and no information regarding the shape of the implanted distribution can be inferred. Although detecting systems with significantly better resolution are available, they are much less sensitive than silicon detectors and their use requires much greater time to complete the measurement.

4000

20

It is also possible to determine the total zinc implantation dose, Dzn' from the ratio of the area of the response peak to the area under a portion of the silicon plateau [28]. If this is done for the two measurements in

=

figure 7, one obtains Dzn 4.99 x 1016 cm-2 and 5.52 × 1016 cm-2. These values are in reasonable agreement with the value of

(5 x 1016 cm-2) determined at the time

of implantation.

Although this technique is a rapid, nondestructive method for establishing identity, location, and density of impurity atoms, it has several important limitations. First, it is most sensitive to impurities of high atomic number; the bulk detection limit is proportional to the square of the atomic number. Furthermore, for elements of lower atomic number than the host matrix, the peak appears superimposed on the host plateau, which further degrades the detection limit. Second, the method lacks lateral resolution. If the beam diameter were reduced to increase lateral resolution, the duration of the measurement would have to be substantially increased or else the detection limits would suffer significantly. Third, the position of the peak depends on both the location and identity of the impurity atoms and also on the orientation of the crystal. This can complicate the analysis and may require that one have considerable knowledge of the specimen to sort out the various parameters of interest. Finally, the technique requires rather large amounts of the impurity to be present if it is to be seen; hence it is more frequently used for analysis of thin surface layers than for profiling trace impurity distributions. (A. G. Lieberman)

4.2. X-Ray Photoelectron Spectroscopy Previous studies of the angular dependence of x-ray photoelectron spectra from dirty surfaces, which revealed depth profile information about carbon and oxygen overlayers on silicon (NBS Spec. Publ. 400-12, pp. 1517), were extended to clean silicon surfaces. The angular dependence of the Si(2p) photoline at about 1160 eV, its associated first surface (Sp) and bulk (Bp) plasmon peaks at about 1150 and 1145 eV, respectively, the Si(2s) photoline at about 1110 eV, the background signal at about 1000 eV, and the KLL Auger complex near 1600 eV were measured. The results are shown in figure 8.

The background region shows only a smooth

variation with angle. At small and negative angles, the intensity falls off due to shadowing of the x-ray beam by the specimen surface. At angles near 90 deg, the specimen subtends a small solid angle at the analyzer. slits. Also, microscopic surface irregularities tend to reduce the electron intensity.

The behavior of the other spectral regions is much more interesting, showing a number of sharp peaks with angular widths as small as 2 or 3 deg. Similar effects have been reported previously on single crystals of sodium chloride and gold, although not with such sharp angular resolution. The explanation for these regions of enhanced emission has been attributed to internal electron diffraction or channeling effects. While a channeling description is apparently valid for heavy particles and high (~ 100 keV) energy electrons, there is some doubt that this description is valid for electrons in the 1 keV energy range. However, data reported for emission of B- particles (with energy up to 450 eV) from radioactive 175yb implanted in a silicon single crystal [30] appear to substantiate the validity of the channeling concept at low energies.

Ratios of certain pairs of intensities are also shown in figure 8. The Si(2s) to Si(2p) ratio (not plotted) is essentially constant. The bulk plasmon (Bp) to Si(2p) ratio, however, shows a number of peaks and valleys. In particular, at angles where the Si(2p) intensity goes through a maximum, the Bp intensity does not increase proportionately as much. This has some profoundly interesting implications. One of the most important, but also most difficult, questions faced by the ESCA Task Force of the Surface Analysis Subcommittee of ASTM Committee E-2 on Emission Spectroscopy is the question of how should one measure XPS peak intensities to derive quantitative elemental ratios. The difficulty arises in part because one has not known to what extent plasmon and other energy loss peaks should be included with the main photopeak intensity. Previously, there has been no good way of distinguishing whether the plasmon peaks seen are an intrinsic process associated with the primary photo-ionization event or an extrinsic process produce during the path of the electron out of the solid. The existing data are contradictory and inconclusive. For magnesium, aluminum, and sodium, one group maintains that plasmon creation is entirely an extrinsic process [31], while for graphite, another group maintains that the process is entirely intrinsic [32].

If, in silicon, the bulk plasmon creation were entirely an intrinsic process, one might assume that the effective origin of the emitted electron would be associated with its original silicon lattice site, in which case the Bp intensity should scale with the Si(2p) line intensity. If the plasmon were created during the passage of this electron from the solid, its effective origin would be expected to correspond to a non-substitutional location and the Bp/Si (2p) intensity ratio should then decrease along channeling directions. This is precisely what is observed to happen in the vicinity of the <111> channeling direction at = 0 deg. This may be the first solid experimental evidence and method for deciding between the intrinsic versus extrinsic character of a plasmon excitation.

The surface plasmon (Sp) to Si (2p) ratio is quite scattered due to poor statistics on the Sp count rate, but it also appears to show

a dip near the <111> direction at ≈ 0 deg.

The more interesting behavior is the increase in the ratio at large angles where the electrons are leaving nearly parallel to the specimen surface. It is under these angular conditions that the surface tends to be emphasized in the spectra so the Sp count rate tends to become proportionally larger.

The KLL/Si(2p) ratio shows still another interesting behavior. At small angles, the x-ray beam strikes the specimen at near grazing incidence and eventually approaches the critical angle for total reflection. Under these conditions, the x-ray penetration depth is limited to approximately the wavelength of the radiation which is in the order of 1 nm. Since the escape depth of the Auger electrons at about 1600 eV is greater than that of the Si (2p) photoelectrons at about 1160 eV, the limited penetration depth of the x-rays selectively decreases the effective depth from which the Auger electrons originate and hence causes the KLL/Si (2p) ratio to decrease near grazing incidence.

Figure 8.

SPECIMEN

X-RAY SOURCE

C.

Geometric arrangement