Chapter 2 Transmission and Reflection Spectroscopy on Ion Implanted Semiconductors

SEMICONDUCTORS AND SEMIMETALS,VOL. 46

CHAPTER 2

Transmission and Reflection Spectroscopy on Ion Implanted Semiconductors Antonios Seas Constantinos ChristoJdes DEPARTMENT OF NATURAL ScENCES UNIVERSITY OF CYPRUS

NICOSIA, CYPRUS

I. INTRODUCTION

. . . . . . . . . . . . . . . . . . . . . . . . . . . .

11. GENERAL OVERVIEW . . . . . . . . . . . . . . . . . . . . . 111. RECENTOPTICAL EXPERIMENTAL STUDIESON IMPLANTED SILICON.

. . . . . . . . . . .

1. Phosphorous-Implanted Silicon . . . . . . . . . . . . . . . . . . . . 2. Fourier Transform Infrared Optical Measurements . . . . . . . . . . . . IV. THEORETIC BACKGROUND. . . . . . . . . . . . . . . . . . . . . . . . V. DISCUSSION AND ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . 1. Influence of Annealing Temperature on the Plasma Wavelength . . . . . . . 2. Effective Mass versus Annealing Temperature . . . . . . . . . . . . . . VI. S U M M A R Y . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

39 40 47 47 49 60 62 62 67 68 69

I. Introduction During the last decades various types of measurements have been used for the characterization of implanted wafers (Christofides, 1992). Generally, the aim of experimental characterization of such materials is the study of effects concerning the induced damage (short and long-range disorder) due to the ion implantation and the annihilation processes that take place during annealing (Gibbons, 1968, 1972). Optical spectroscopic methods have been adopted by several groups for the characterization of implanted semiconducting materials because of the advantage of their giving quantitative and qualitative information concerning the defects state and annihilation process in implanted (unannealed and annealed) semiconducting wafers. In addition, these methods represent nondestructive and contactless techniques. In 1970, Crowder et al. used 39 Copyright 0 1997 by Academic Press All rights of reproduction in any form reserved. 0080-8784/97 $25

40

A. SEASAND C. CHRISTOFIDES

interference phenomena observed in the optical absorption spectra to estimate the depth of the damaged layer in silicon (Si) due to heavy implanted ions. Similar experiments also were performed by Kurtin, Shifrin, and McGill (1969) and Hart and Marsh (1969). During the mid 1970s, Kachare et al. (1976a, 1976b) performed normal incidence reflection and transmission measurements on gallium arsenide (GaAs) and gallium phosphide (Gap)-implanted wafers at high doses = 1 x 1017cm-2) and high energies (E = 3 MeV). By using the same technique, Wang et al. (1985) studied the effect of annealing on the optical properties of implanted germanium (Ge). Infrared (IR) studies on heavily implanted phosphorus (P) ( E = 0.2 to 2.7 MeV and @ = 10l6 to l O I 7 P+/cm2) also were performed to study the thickness and the refractive indices of such implanted layers (Hubler et al., 1979a; Hubler, Malmberg, and Smith, 1979b). Infrared spectroscopy on beryllium (Be)-implanted GaAs was carried out by Kwun et al. (1979). Refractive index profiles and range distribution of Si implanted with high-energy nitrogen has been studied by Hubler et al. (1979a, 1979b). Other researchers such as Fredrickson et al. (1982), Waddell et al. (1982), and Spitzer et al. (1977) have used similar techniques for the characterization of implanted semiconducting wafer. Brown et al. (1981) performed electroreflectance measurements on ion-implanted GaAs, and Brierley, Lehn, and Grabinski (1988) performed IR transmission measurements on Si+-implanted GaAs for mapping the implanted dose distribution. An excellent review paper on the optical effects of high-energy implantations in semiconductors is that by Tatarkiewicz (1989). This chapter covers several aspects concerning optical characterization of ion-implanted wafers and the influence of annealing on their optical properties. When possible, quantitative characterization of the implanted wafers and estimations concerning the activation of implanted impurities versus annealing temperature is presented. After a brief review of results obtained between the 1970s and the 1980s, we concentrate on recently obtained results. In Part I1 we review some key results that played a significant role in the development of optical studies on implanted semiconductors. Part I11 summarizes recent experimental results, and Part IV presents a useful theoretic background. The theoretic model is used in Part V to estimate the degree of activation of implanted impurities. A general summary and future perspectives are presented in Part VI. We apologize to those scientists in the field whose work we might have somehow omitted. 11. General Overview

Reflection is a powerful nondestructive technique for the determination of many physical parameters in implanted semiconductor wafers. In a series of

2 REFLECTIONSPECTROSCOPY ON ION IMPLANTEDSEMICONDUCTORS 41

papers, Kachare et al. (1974, 1976a; 1976b), Kwun et al. (1979), Hubler et al. (1979), Fredrickson et al. (1982), and Waddell et al. (1982) studied the reflection from various highly implanted semiconducting wafers. Using a simple model they tried to fit the interference fringes observed in the measured IR reflection spectrum to derive information such as refractive indices of the implanted and nonimplanted layers and layer thickness. In the model, they assumed that the implanted semiconductor consisted of three layers (layer 1: surface and near-surface region; layer 2 heavily implanted region; Layer 3: substrate) and by considering the dielectric properties of the various layers using the classic dispersion theory for a damped harmonic resonance, they tried to reproduce the measured spectral behavior. The real part of the complex dielectric constant is given by the expression &’(V)

N

n2 = A

+ R -Bv + V , ” -SV ’ ~

where the first two terms on the right-hand side of Eq. (1) represent the refractive index on the low-frequency side of the fundamental absorption edge, and the remaining term estimates the contribution to the refractive index from the IR resonance at v, (Kachare et al., 1976a). In Eq. (l), v is the frequency, v, is the resonance frequency, S is the resonance strength, A, B, and R are constants, and n is the refractive index. The reflectivity was computed using the expression given by Heavens (1964), which considers two absorbing layers on a nonabsorbing layer. Kwun et al. (1979) performed optical studies on high-fluence Be-implanted GaAs by using IR reflection and transmission measurements. The GaAs (100) wafers were implanted in the range of 1 x 1015 to 1 x 10l6Bef/cm2 and annealed between 500 and 800°C. Infrared reflection measurements were obtained in the range of 320 to 7600cm-’ by using a single beam spectrometer. Figure 1 shows reflection spectra of Be-implanted GaAs ((D = 1 x 10” Be+/cmz) as a function of photon frequency for various annealing temperatures. We note that all spectra show interference effects except the nonimplanted samples. Figure 2 shows typical IR transmission data obtained for the GaAs wafer implanted at 1 x 10l6Be+/cm2. The interpretation of the previous results comes from a simple reflection model also presented previously, which is able to take into account interference effects. In the case of the nonannealed samples it has been found that the implantation produces a layer of significantly larger refractive index than do the nonimplanted materials, while the refractive index increases with increasing implantation dose. After annealing at 500”C, a free-hole plasma layer contribution to the electric susceptibility was observed by analyzing reflection interference effects. It is important to note that similar

42

4u i$ d-

A. SEASAND C. CHRISTOFIDES

m -a -

z 0

W

a Be -GOAS 280 KeV Ix 10'5/cmf

FIG. 1. Reflection of beryllium (Be)-implanted gallium arsenide (GaAs) as a function of photon frequency for various annealing temperatures for a fluence of Q, = 1 x 10l5Be+/cm2 The scale is indicated by a data point at the top of the scale. Kwuan, S., Spitzer, W. G., Anderson, C. L., Dunlap, H. L., and Vaidyanathan, K. V. (1979). Optical Studies of BeImplanted GaAs. J . Appl. Phys. 50, 6873-6880.

qualitative results have been obtained by Hubler et al. (1979) for Si wafers. However, in the case of annealed samples it was found that after annealing the refractive index is almost identical to that of the crystalline substrate. The absorption coefficient of the implanted layers are calculated from the transmission expression T=

(1 - R)' exp[-(add 1 - R2 exp[ -2(add

+ ~,t,)] + a,t,)]

where R is reflection of the GaAs at a given wavelength, ad and a, are the mean absorption coefficient of the implanted layer and substrate, respectively, and d and t, represent the thickness of the implanted layer and substrate, respectively. From transmission measurements and by knowing the various thicknesses of the samples and the optical characteristics of the substrate, we can obtain the optical absorption spectra of the implanted films. Figure 3 presents absorption spectra obtained by using optical transmission data. We note that add increases with increasing annealing temperature.

2 REFLECTIONSPECTROSCOPY ON ION IMPLANTED SEMICONDUCTORS 43

WAVE NUMBER (cm-3 FIG. 2. Transmission of beryllium (Be)-implanted gallium arsenide (GaAs) as a function of photon frequency and annealing temperature for a fluence equal to 1 x 10l6 ions/cm*. Kwuan, S., Spitzer, W. G., Anderson, C. L., Dunfap, H. L., and Vaidyanathan, K. V. (1979). Optical Studies of Be-Implanted GaAs. J . Appl. Phys. 50, 6873-6880.

The optical properties of As-implanted and annealed Si were studied by Wagner and Schaefer (1979) using IR spectroscopy. These authors presented several experimental results with both qualitative and quantitative analysis. They showed how nondestructive IR optical measurements can be used to monitor several properties, such as sheet resistance, electrical activation, and concentration, using (100) p-type Si samples implanted with As between 1 x 1015 and 2 x 10l6 As/cmZ. Figures 4(a) and 4(b) show the variation of the optical reflection and transmission versus wavelength for various implantation doses. The strong dependence of the reflectance and transmittance on the implanted dose is clearly shown. The influence of annealing on the optical reflectance and transmittance is presented in Figs. 5(a) and 5(b). We note that while annealing strongly influences the reflectance, it does not significantly affect the transmittance. Wagner and Schaefer (1979) used the theoretic model of Schumann and Phillips (1967) (see Part IV) for the interpretation of these results.

44

A. SEASAND C. CHRISTOFIDES

FIG.3. Absorption spectra versus photon frequency for beryllium (Be)-implanted gallium arsenide (GaAs) for a fluence of 1 x 10l6ions/cm* at various annealing temperatures. Kwuan, S., Spitzer, W. G., Anderson, C. L., Dunlap, H. L., and Vaidyanathan, K. V. (1979). Optical Studies of Be-Implanted GaAs. J . Appl. Phys. 50, 6873-6880.

Several IR measurements were performed by Engstrom (1980) on Si wafer implanted with boron (B) at 35 keV (doses: 1 x 1014 and 1 x 10l6B/cm2). After implantation the samples were laser annealed. Reflection and transmission measurements in the range of 2.5 to 20 pm were obtained by using Fourier transform infrared (FTIR) spectroscopy. Figures 6(a) and 6(b) present reflectance and transmittance spectra, respectively. Note the strong influence of implantation dose both on reflection and transmission. From these results, Engstrom (1980) put forth the following conclusions: (1) the relaxation time is independent of the implantation dose and (2) the optical properties are linearly affected by implantation dose. Infrared reflectance studies of amorphous silicon (a-Si) produced by Si ion implantation have indicated that after annealing at 5WC, the asimplanted a-Si forms an anneal stabilized state whose IR reflectance behavior is distinct from both the unannealed as-implanted a-Si obtained after epitaxial regrowth (Fredrickson et al., 1982). Differential reflectometry was used by Hummel et al. (1988) to identify whether an implanted layer is crystalline, damaged crystalline, or amorphous. These authors performed optical differential reflectometric measurements on Si-implanted Si wafers (dose: 1 x 1015ions/cm2; energy 60 to 180 keV). Figure 7 presents a series of differential reflectograms for various implantation energies. We note that for all presented implantation energies,

2 REFLECTIONSPECTROSCOPY ON

ION IMPLANTED SEMICONDUCTORS

45

FIG. 4. Influence of the implanted dose on the infrared (a) reflectance and (b) transmittance spectra (curve A: 1 x lot5;curve B 6 x lOI5; curve C: 8 x curve D 1 x lot6 and curve E: 2 x 10l6As/cm2.As, arsenic. Wagner, H. H., and Schaefer, R. R. (1979). Contactless Probing of Semiconductor Dopant Profile Parameters by IR Spectroscopy. J. Appl. Phys. SO, 26972704.

we can distinguish three characteristic Si interband transition peaks near 3.4, 4.2, and 5.6 eV. According to the authors, some implanted-induced damage occurred for all implantation energies. Hummel et al. (1988) introduced the idea that the type of implantation damage depends on the implantation energy. These authors also showed that by exploiting the

A. FIG.5. Influence of 20-min (curve A) and 180-min (curve B) annealing time on their (a) reflectance and (b) transmittance spectra (implantation dose: 8 x lot5 As+/cmZ).As, arsenic. Wagner, H. H., and Schaefer, R. R. (1979). Contactless Probing of Semiconductor Dopant Profile Parameters by I R Spectoscopy. J. Appl. Phys. 50, 2697-2704.

46

A. SEASAND C. CHRISTOFIDES 4 .O

0.8 W

u

+ f u) a a l-

0.6 0.4

o.2 0

0.2 II

1

-

Re. 6. Transmittance and reflectance spectra of boron-implanted, laser-annealed silicon. Implant doses in ions/cm2 are shown at the right of the graphs. At these wavelengths, the spectra of an unimplanted sample is virtually indistinguishable from the sample implanted with 1 x loL4ions/cm2. Engstrom, H. (1980). Infrared Reflective and Transmissivity of BoronImplanted, Laser-Annealed Silicon. J . Appl. Phys. 51, 5245-5249.

intensity of interband transitions, we can determine the thickness of the implanted-induced damaged layer over a submerged amorphous layer. In addition, they showed a direct relation between interference effects and the thickness of the implanted amorphized layer.

2 REFLECTION SPECTROSCOPY ON IONIMPLANTED SEMICONDUCTORS 47

60 KoV

I

I

800 1

1.5

1

I

SO0 I

I

1

2

400

I

3

l

I 1

4

a

1

1

5 6 E(oV)

FIG. 7. Differential reflectograms of silicon ion-implanted wafers. The implantation energies are shown for each curve. The fluence is 1 x 10" ion/cmz.The ordinate is constant for all spectra. The individual curves have been shifted for clarity. The zero point for each curve is shown by the dashed lines. Hummel, R. E., Xi, W., Holloway, P. H., and Jones, K. A. (1988). Optical Investigations of Ion Implant Damage in Silicon. J . Appl. Phys. 63,2591.

111. Recent Optical Experimental Studies on Implanted Silicon

1. PHOSPHOROUS-IMPLANTED SILICON

Two-inch-diameter Si wafers (100) lightly doped with boron (20 to 25 51 cm) were implanted with phosphorus at various doses (@ = 1 x 10' to 1 x 10l6P+/cm2and E = 150 keV) and energies ( E = 20 to 180 keV and @ = 5 x l O I 4 P+/cmz) through a thin oxide layer at room temperature.

48

A. SEASAND C. CHRISTOFIDES TABLE I

JUNCTION’S DEPTHS OF SAMPLES IMPLANTED WITH 150 keV AT VARIOUS DOSES (@ (P+/cmz)), UNANNEALED AND ANNEALED AT VARIOUS ANNEALING TEMPERATURES ( Ta(“C)) @(p+/cm2)

T,(“C) NA 800 850 900 950 loo0 1100

1 x loi3 (W1)

1 x loi4

0.45 0.45 0.48 0.46 0.50 0.48 0.60 0.53 0.60 0.63 0.68 1.32 0.80

0.48 0.50 0.64 0.49 0.65 0.50

(W2)

0.80

0.57 0.85 0.72 0.90 1.55 1.15

5 x loi4 (W3)

1 x loi5 (W4)

5 x loi5 W5)

1 x loi6 04‘6)

0.50 0.52 0.65 0.53 0.65 0.54 0.70 0.60

0.51 0.53 0.63 0.52 0.67 0.55 0.70 0.60 0.75 0.78 0.80 1.74 1.52

0.52 0.63 0.75 0.75 0.80 0.90 0.90 0.97 1.10 0.97

0.53 0.63 0.69 0.80

0.80

0.75 0.90

1.70 151

1.30

2.03 1.81

0.80

1.02 1.01 1.45 1.50 1.90 1.50 2.40 2.60

The values of the first lines for each annealing temperature were obtained from ID-SUPREM 111 simulation (I&); the second lines (bold face) were obtained from spreading resistance measurements (dR).

TABLE I1 JUNCTION’S DEPTHS (IN pm) OF SAMPLES IMPLANTED AT VARIOUS IMPLANTATIONENERGIES WITH DOSE 5 x loi4 (P’ (P’/cm2), UNANNEALED AND ANNEALED AT VARIOUS TEMPERATURES T, (“C) 140 (W11)

NA 800 850 900 950 1000 1100

0.12 0.25 0.24 0.23 0.32 0.55 1.56

0.16 0.16 0.22 0.22 0.33 0.55 1.56

0.26 0.26 0.27 0.29 0.37 0.38 1.59

0.37 0.38 0.38 0.40 0.47 0.65 1.63

0.48 0.48 0.48 0.50 0.56 0.73 1.68

0.50 0.50 0.51 0.53 0.56 0.73 1.70

0.57 0.57 0.58 0.59 0.65 0.81 1.75

These values were obtained from spreading resistance measurements.

After implantation, the wafers were cut along the crystallographic axes into several 1 x 1 cmz samples, which were then thermally annealed isochronally at various temperatures, T, between 300 and 1100°C for 1 h in an inert nitrogen atmosphere. After annealing, the oxide overlayer was etched away and the samples were used for FTIR spectroscopic characterization. Tables

2 REFLECTIONSPECTROSCOPY ON ION IMPLANTEDSEMICONDUCTORS 49

I and I1 give several characteristics of the implanted and annealed samples such as implantation dose, energy, and implanted layer thickness, as obtained by simulation and spreading resistance measurements Stanford University PRocess Engineering Model (SUPREM) (Christofides et al., 1994; Seas et al., 1995). 2. FOURIER TRANSFORM INFRARED OPTICAL MEASUREMENTS a.

Measurement between 0.75 and 4.0 pin

Figures 8(a) to 8(e) present several FTIR reflective spectra obtained at room temperature in the range of 0.75 to 4 pm ( NN 14,000 to 2500 cm- l). As expected, for lightly implanted samples (1 x 1013P+/cm2) the difference between the reflection spectra of low and high annealing temperatures is not significant (Christofides et al., 1994). Figure 8(a) presents spectra obtained from Si implanted at higher doses (1 x 1014P+/cm2) and annealed at various temperatures. The low-annealed sample (R300) already shows a certain trend of differentiation vis-a-vis the rest of the spectra (see the inset in Fig. 8(a)). For samples implanted at a slightly higher dose, 5 x 1014P + / cm2 (Fig. 8(b)), unannealed and low annealed, the increase of the fringe amplitude can be seen. The fringes of these samples and those presented in Figs. 8(b) to 8(e) indicate that the materials implanted at high doses present a bilayer form, whereas the implanted and highly annealed materials seem more homogeneous. For implantation doses equal to and higher than the critical dose Qc (ac= 5 x l O I 4 P+/cm2; Prussin, Margolese, and Tauber, 1985), we note that all the samples, except from those that have been annealed at very high temperatures (900 and 1lOOOC), present interference fringe patterns due to the amorphous-crystalline (a-c) interface (Fig. 8(c) to 8(e)). It is also important to note that the fringe separation changes slightly with increasing implantation dose, which is due to the fact that there is an increase in the difference between the reflective index of the two layers. In addition to the fringe patterns that arise from interferences between light reflected by the front-implanted surface and the light reflected by the amorphized disorder-to-crystalline interface, Figs. 8(d) and 8(e) show some other very interesting features. There appears to be a significant decrease in the reflection spectrum, and sometimes reflection minima, for the highly annealed samples at long wavelengths (between 3 and 4 pm). This phenomenon does not appear in the samples implanted at a lower dose. It is also important to note that in this IR region, the variation of the reflectivity of the implanted and very highly annealed samples undergoes an anomalous dispersion. The same phenomenon was also noted by Wang et al. (1985) in implanted wafers and was explained by the theory of plasma effect. In Figs. 8(d) and 8(e) we note that a characteristic minimum appears only for the

A. SEASAND C. CHRISTOFIDES FTlR REFLECTION MESUREMENTSOF SAMPLE 2

Implanted 1 ~ 1 0 ' ~

0.5

1.0

1.5

2.0

2,s

3.0

3.5

WAVELENGTH (mlcmns)

m R REFLECTION MESUREMENTS OFSAMPLE 3 Implantad 5x10"

I

0.5

\\

1.0

1.5

2.0

2.5

3.0

3.5

4.0

WAVELENGTH (mlcmns)

FIG.8. Fourier transform infrared (FTIR) reflection measurements of phosphorus-implanted silicon (Si) wafers at various doses, CJ(P'/cm2): (a) 1 x (b) 5 x loL4;(c) 1 x (d) 5 x loL5;and (e) 1 x (f) FTIR transmission measurements of phosphorus-implanted Si wafers at doses cD(P'/cm2): 1 x The implantation energy is 150keV. The samples were annealed isochronally (1 h) at various temperatures. The dashed line indicates a nonimplanted sample.

2 REFLECTIONSPECTROSCOPY ON IONIMPLANTEDSEMICONDUCTORS 51 FTlR REFLECTION MESUREMENTS OF SAMPLE 4

Implanted 1 ~ 1 0 ' ~

20

~

I

WAVELENGTH (microns) FTlR REFLECTION MESUREMENTS OF SAMPLE 5

Implanted 5 ~ 1 0 ' ~

45

E. W

i

W

a

30

25

20

WAVELENGTH (microns)

FIG. 8. (Continued)

A. SEASAND C. CHRISTOFIDES FTlR REFLECTION MESUREMENTSOF SAMPLE 6 Implanted IX~O'' 5(1

45

I

1.o

1.5

2.0

2.5

3.0

3.5

4.0

WAVELENGTH (mlcrons)

FTlR TRANSMISSION MESUREMENTS OF SAMPLE 6 Implanted 1x10'' 35

25

15

10

5

0

0.5

1.0

1.5

2.0

2.5

WAVELENGTH (mlcrons)

FIG. 8. (Continued)

3.0

3.5

4.0

2 REFLECTIONSPECTROSCOPY ON ION

IMPLANTED SEMICONDUCTORS

53

samples annealed at 900°C (R900). One would also expect to see such a minimum on the highly annealed samples (1l00OC) because it is well known that these possess more free carriers. Although this is true, Table I shows that these carriers are diffused in a very large thickness in the material, and thus the number of free carriers per unit volume is lower than in the R900 sample. Finally, for the two samples annealed at 900"C, note that the reflectivity minimum appears at lower wavelength, Ap (x3.1 pm), for the sample implanted at higher dose (@ = 1 x 10l6P+/cm2) than for the sample implanted at lower dose (@ = 5 x 10'' P+/cm2), Ap x 3.5 pm. In any case, confusion should be avoided between reflectivity minima and interference fringes because for samples annealed at high temperatures (> 600 to 700°C) the a-c interface disappears. Therefore, no possibility exists of observing any interference fringes from the samples annealed at 900 and 1100°C from our samples in Fig. 8(e). Finally, Fig. 8(f) presents the transmission spectra of samples implanted at 1 x 10'6P+/cm2. We note that in the spectral range of 1 to 4 p m for samples annealed at 900 and llOO°C, both transmission ( T ;Fig. 8(f)) and reflection ( R ;Fig. 8(e)) decrease drastically. In fact, as T R A = 1 at 3.1 pm, we can have A = 1 - T - R x 0.69, which is due to a very high absorption. This low absorbance can be explained only by the free-carrier absorption phenomenon.

+ +

b. Fourier Transform Infrared Measurement between 3 and 25 pm

On all the implanted layered Si wafers, we measured the reflection and transmission as a function of wavelength in the spectral range of 2.5 to 25pm. To do this we used a Fourier transform infrared (FTIR) spectrophotometer, with a wavelength resolution of 8 cm- '. Spreading resistance measurements are used to obtain the profile of the implanted impurities for all the P-implanted, nonannealed and annealed Si wafers (Othonos et al., 1994). Van der Pauw (Hall effect) measurements were performed for the high-dose implantation wafer series (W6) to better understand the underlying annealing kinetics and to complement data concerning the conductive effective mobilities. These measurements are reported in Tables I to IV. Figures 9(a) to 9(f) present several FTIR transmisson spectra, obtained at room temperature, in the range of 2.5 to 25pm. As expected, for lightly implanted samples (W1 and W2) the difference between the transmission spectra of low and high annealing temperatures is not significant. O n those spectra we note that the influence of annealing temperature for each dose of implantation plays a role only at long wavelengths. The solid line with no marks refers to a nonimplanted sample (NI). In fact, for low-dose implantation (W1 and W2)-that is,

54

A. SEASAND C.CHRISTOFIDES

FIG. 9. Fourier transform infrared (FTIR) transmission spectra of phosphorus-implanted (b) 1 x lOI4; (c) 5 x lOI4; (d) silicon wafers at various doses, cP(Pt/cm2): (a) 1 x 1x (e) 5 x and (f) 1 x

below the critical amorphization dose- the various spectra do not show any significant variation in the wavelength range that the measurement was performed. However, for higher implantation doses (W3-W6) -that, is around and over @,-the samples annealed at high temperatures present significant differences at wavelengths even shorter than 5 pm. In the case of

2 REFLECTIONSPECTROSCOPY ON

ION IMPLANTED SEMICONDUCTORS

55

TABLE 111 CONCENTRATION OF FREECARRIERS FOR SAMPLES IMPLANTED WITH 150 keV AT VARIOUSDOSES (W1 to W6), NONANNEALED AND ANNEALED AT VARIOUS TEMPERATURES (T, ("C) N (P'/cm3)

I x 1019 (W4i ____

~~

800 850 900 950

1000 1100

2.08 2.00 1.66 1.66 1.47 1.25

1 x lozo (W6i

1.56 1.54 1.25 1.18 1.11 1.15

0.77 0.77 0.7 1 0.62 0.55 0.33

1.59 1.49 1.43 1.33 1.25 0.66

6.61 6.25 5.55 4.54 3.85 2.76

1.45 1.25 0.99

0.66 0.67 0.38

N was obtained for each annealing temperature from spreading resistance measurements by assuming that all implanted impurities are electrically active.

the wafer series W5 and W6, note that the annealing temperature T, monotonically influences the variation of transmission versus 1. For the heavily implanted samples the transmission spectra change monotonically with annealing temperatures. For example, in Figs. 9(c) to 9(f9 we can observe that the transmission for highly annealed samples (over 600°C) decreases with increasing T, because of free-carrier absorption. For the sample W6 series (see Fig. 9(f)) annealing at 1100°C and for A > 7 pm, the transmission spectrum is practically zero mainly due to high reflection (0.8) and free-carrier absorption. Figures 10(a) to 10(f) present FTIR reflection spectra obtained at room temperature. Figures lO(a) and 10(b) show the behavior of a series of low-implanted and annealed samples (W1 and W2). The influence of annealing temperature on the reflectivity can be realized from Figs. 10(a) and 10(b). We note that the low-dose samples do not present any minima, whereas the samples implanted around and over the critical implantation dose (W3 to W6) present minima. These wavelength minima depend on the implantation dose and, of course, on the annealing temperature. The plasma wavelength minimum Ap is a function of the concentration of free activated carriers N , which depends on the annealing temperature. This dependence can be expressed as (Kireev, 1975)

Ap(Ta)cc

J 16n2e2cZN(T,) m*(T,)

(3)

56

A. SEASAND C . CHRISTOFIDES

FIG.10. Fourier transform infrared (FTIR) reflection spectra of phosphorus-implanted silicon wafers at various doses, @(Pf/cm2): (a) 1 x (c) 5 x 1014; (d) (b) 1 x 1 x 10”; (e) 5 x 10”; and (f) 1 x

where m* is the conductive effective mass, and the constants e and c are the electron charge and light velocity in vacuum, respectively. Figure 1O(f) presents FTIR reflection measurements of heavily implanted, nonannealed and annealed Si layers (W6: 1 x 1OI6P’/cm’). Again, note the shift of the reflection minimum due to the variation of the free-carriers

2 REFLECTIONSPECTROSCOPY ON

57

ION IMPLANTED SEMICONDUCTORS

TABLE IV MOBILITYAND ESTIMATED FREE-CARRIER CONCENTRATION OF VARIOUS SILICON SERIESW6 FOR DIFFERENT ANNEALING TEMPERATURES

T,("C) Ir (cm2/Vs)

N (P+/cm3)

700

BOO

72 69 1.1 x lozo 1.02 x lozo

850

I1

1 x lozo

900

950

87 87 1.4 x loL9 1.4 x l O I 9

WAFERS OF

1050

80 1.7 x 10''

concentration as a function of the annealing temperature. This shift easily can be explained using Eq. (3) and Table IV. Table IV presents the concentration of free carriers for all samples calculated using the experimentally determined layer thickness and implantation dose and the electrical experimental results. For the nonannealed and low annealed samples, no minima are present at least in the spectral range under investigation. Howarth and Gilbert (1962) showed that in P-doped Si, reflection minima can be observed in the range of 2 to 20 pm for doses over 7 x lo1' Pf/cm3. Figures 11 and 12 present transmission and reflection FTIR spectra for samples implanted with various energies at a dose equal to 5 x 1014P+/cm2 (see Table 11, wafers W7-Wl2) (Seas et al., 1995). As expected, the implantation energy does not play a significant role either in the transmission or on the reflection spectra. In addition, samples implanted around QC,at the low implantation energy of 20 keV (W7), and annealed at various temperatures show the same behavior as those implanted at energies almost one order of magnitude higher. Figures 13(a) and 13(b) show the reflection and transmission coefficients at 25 pm as a function of the annealing temperature. It is evident from Fig. 13 that for low-dose implantation (wafer series W1 and W2), the optical transmission and reflection are independent of the annealing process because there is no significant change in the concentration of free carriers with annealing. However, the wafer series (W3) implanted at 5 x 10'4P+/cm2 shows a slight increase in reflectivity for annealing temperatures over 700°C. For wafers implanted at a high dose (W4 to W6), where the implantation is over mC,the reflection coefficient changes drastically. The reflection coefficient varies from 0.35 for the nonannealed (or low-annealed) layers, to almost 0.90 in the case of samples annealed at over 800°C. In Fig. 13(a) it is important to note that samples implanted with a dose of 5 x 1015P+/cm2 (W5) reach a high reflectivity after annealing at 80O0C, whereas samples implanted at the highest dose (W6: 1 x 10'6P+/cm2) reach the maximum reflectivity at lower temperatures. Similar behavior was observed by Engstrom (1980) for B-implanted and laser-annealed Si layers.

58

A. SEASAND C. CHRISTOFIDES

FIG. 11. Fourier transform infrared (FTIR) transmission spectra of phosphorus-implanted silicon wafers at various implantation energies, E (keV): (a) 20, (b) 30, (c) 60, (d) 100, (e) 150, and (f) 180.

All previous comments concerning the reflection coefficient are also valid for the transmission coefficient. In Fig. 13(b) we show the transmission coefficients versus the annealing temperature plotted on a logarithmic scale for presentation reasons. The transmission measurements clearly show the distinction between the two samples (W5 and W6) implanted at high doses.

2

REFLECTIONSPECTROSCOPY ON

0.55 L

0.5

g 0.45

% s

59

ION IMPLANTED SEMICONDUCTORS

i

t w8

i

0.4

* 0.35

03 0

15 20 Wavelength (microns) 5

10

0.55 1 051

25

-

0.25 t . - - .' . - .- ' . - - 0 5 10 15 20 Wavelength (microns)

1

25

1 1

w9

Wavelength (microns) 0.51

g

z 8

5

0.45

wll

1

055 r 051

1

w12

0.4

0.35 0.3

0

5

1 0 1 5 2 0 2 Wavelength (microns)

5

FIG.12. Fourier transform infrared (FTIR) reflection spectra of phosphorus-implanted silicon wafers at various implantation energies, E (keV): (a) 20, (b) 30, (c) 60,(d) 100, (e) 150, and (f) 180.

For example, after annealing at 1100°C we note that the transmission at 25 pm for the W6 series is only 0.08, whereas under the same conditions the corresponding wafer of W5 series presents a transmission almost one order of magnitude higher. Wafers implanted with a smaller dose (W1 series), present a transmission that is more than two orders of magnitude higher than the heavily implanted samples.

60

A. SEASAND C. CHRISTOFIDES

FIG. 13. (a) Reflection coefficient and (b) transmission coefficient,each as a function of the annealing temperature for various implantation doses.

IV. Theoretic Background The reflectivity minimum of FTIR spectra associated with plasma resonance has been an important tool for the determination of free-carrier concentration in semiconductors for many years. A great deal of experimental and theoretic work has been carried out to improve and increase the accuracy of the calculation. One can cite, for example, the classic theoretic

2 REFLECTIONSPECTROSCOPY ON ION IMPLANTEDSEMICONDUCTORS

61

approach of Smith (1959) and the interesting development to this approach made by Schumann and Phillips (1967). The principal equations of Smith (in MKS) for the expression of the optical coefficient n and k were written as

2 n k = L op,E,m*

(1 + ) z

w2z2

where E~ is the permittivity due to the lattice, cr, is the dc conductivity, pa is the dc mobility, m* is the conductivity effective mass, and z is the relaxation time. Schumann and Phillips (1967) have shown, under the assumption of nondegenerate statistics, that the previous two equations can be written as

where J(D) and 40)are nondimensional and depend on the product d z 2 , N is the carrier concentration, 1 is the wavelength, pa is the dc resistivity, which is also a function of N (like po), c is the velocity of light in vacuum, D is a function of N and A, and r(4) is the gamma function. According to Seeger (1988), the approximation of small damping, where oz >> 1, is valid for most semiconductors even in the far-IR spectrum. As pointed out by Schumann and Philips (1967) this is the used most approximation and leads to J ( D ) = 40)= I. Taking into account this approximation from the system of Eqs. (5.1) and (5.2), we can evaluate the index of refraction and the extinction coefficient k, each as a function of wavelength 1. The reflectivity was calculated from the well-known expression R=

(n - 1)2 (n + 1)’

+ k2 + k2

The minima in the reflectivity obtained from the derivative of the previous equation are plotted in Fig. 14 (solid line):

62

A. SEASAND C. CHRISTOFIDES

100

W3 - W6

10

1' . . lo'*

. . ' . . . I

1019

'

.

.

. ' " ' I

1020

'

'

..'-

Id'

FIG. 14. Mobility as a function of the logarithm of the carrier concentration. min. refl., minimum reflectivity.

For the numeric calculation, the effective mass is assumed to be 0.26. The value of resistivity as a function of carrier concentration is obtained from various sources (Chapman et al., 1963; Irvin, 1962). It is important to note that this model is valid for concentrations ranging between 1 x l O I 9 and 1 x 102'cm-3. When this model is used with our implanted unannealed and annealed results the following three points must be taken into account: 1. The dc conductivity a, and the mobility, p, are dependent of the annealing temperatures (Christofides, Guibaudo, Jaouen, 1987, 1989a, 1989b). 2. The conductivity effective mass m* depends on the degree of inhomogeneity of the material. 3. E is not constant for implanted Si annealed at various temperatures.

V. Discussion and Analysis 1. INFLUENCE OF ANNEALING TEMPERATURE ON THE PLASMA WAVELENGTH Figures 8(b) to 8(e) clearly show that the increase of annealing temperature provokes a decrease of the fringe amplitude, which indicates that the

2 REFLECTION SPECTROSCOPY ON ION IMPLANTED SEMICONDUCTORS 63

index of refraction was decreased during the isochronal annealing. In fact, the difference between the refractive index of implanted layers and substrate disappears as the annealing temperature increases. Samples implanted with 5 x l O I 4 P+/cm2 (Fig. 8(b)) need only an annealing of up to 550°C for 1 h to make the fringes disappear, whereas annealing over 800°C is necessary in the case of samples implanted at high doses. Using the data presented in Table I and the relation

the concentration of free carriers, N , is calculated. This concentration N assumes that all the implanted carriers are electrically active. The constant d is the average value [d zz 1/2(d, + d,)] where d , and d, are the thicknesses of implanted layers obtained from spreading resistance and SUPREM I11 simulation of the junction depth, respectively (Othonos et al., 1994). In Table 111, we can find the concentration of free carriers for several implanted and highly annealed samples. Using Eq. (3) and Table I, it is easy to understand why 1, (of sample R900, 1 x 10l6 P+/cmZ)is smaller than 1, (of sample R900, 5 x 1015Pf/cm2). The plasma wavelength 1, of the samples annealed at 1100°C are presented in longer wavelengths because their carriers per volume are smaller due to their high diffusion in the wafer. Table V reports some experimental and theoretic data concerning 8 samples annealed at temperatures over 800°C. In Table V, we also report the values of the “spreading” and “SUPREM” concentrations, the freeTABLE V VARIOUS VALUES FOR EIGHTSAMPLES IMPLANTEDAND ANNEALED AT DIFFERENT CONDITIONS @ (P +/cm2)

5

x 1014

1 5 1 1 1

x x x x x x

1 5x

T,(“C)

1015 1015 1OI6

1016

10l6 loL6 1 0 1 ~

1100 1100 1100 1100 lo00 900 800 900

N , (cm-3)

N , (cm-’)

3.31 x 6.58 x 2.76 x 4.16 x 6.67 x 0.99 x 1.43 x 5.56 x

2.94 x 5.74 x 2.46 x 3.86 x 5.26 x 0.97 x 1.59 x 5.56 x

10” 10” 1019

10” 10” lo2’ 10” 10”

x,annealing temperature; N , ,

10” 1ol8

10” 10”

N ( ~ m - ~ ) A,(m) 3.11 x 6.13 x 2.60 x 4.00 x

lo’* 10”

1019 1019

1019

5.88 x 1019

10’’

0.98 x lo2’ 1.51 x lo’’ 5.56 x 1019

10”

10”

12.8 10.5 6.3 5.0 5.2 3.3 3.1 3.6

spreading free-carrier concentration ( %@,hin);N , , A,, plasma wavelength taking into account the average free-carrier concentration.

@, implantation dose;

SUPREM free-carrier concentration ( %@/d>; N , average free-carrier concentration (%@id);

64

A. SEASAND C. CHRISTOFIDES

carrier impurities concentration N (obtained from Eq. (8)), and the experimental plasma wavelength A, (Christofides et al., 1994). Figure 14 presents the plasma wavelength of the minimum reflectivity as a function of carrier concentration for n-type Si (Seas et al., 1995). The solid line is obtained from the theoretic model presented in Part IV. In Fig. 14, we can see the good fitting of our experimental data. The good agreement of the theory with the data shows that w2z2>> 1 is a good approximation for implanted and highly annealed Si wafers. However, from these data one can conclude that only after annealing at 800°C is there almost complete activation of implanted impurities. The theoretic curve (Schumann and Phillips, 1967) of Fig. 14, which was the main test of these experimental results, was calculated with well-determined p,,,'E and m* at each concentration. Here, we consider p,, cL, and m* as constant with annealing temperature over than 800°C. The assumption of constant mobility is justified since the mobility varies slightly in the range of 800 to 1100°C (Christofides et al., 1987; 1989a, 1989b), as indicated in Table IV. The variation of the mobility of the various wafers also was observed from the Hall effect. A small deviation of our experimental points from the theoretic curve in Fig. 14 is expected for three main reasons: 1. Annealing at 800°C is probably not sufficient for a complete recrystallization. 2. There is a slight variation of mobility due to the fact that the plasma wavelength in implanted materials and materials annealed at low temperatures, which are not completely recrystallized, shifts to a longer wavelength. 3. The Schumann and Phillips (1967) model assumed that the numeric value of m* was 0.26, whereas in $2 of Part I1 it is shown that the effective mass for the sample series W3 to W6 varies. It is also important to note that in Fig. 10(f) even annealing at 700°C is not sufficient to activate the implanted impurities. In fact, according to Eq. (8), where a complete activation is assumed, this sample possesses 1.88 x 10'' cm-3 carriers. In the case in which 1% of these impurities are activated, there would appear a reflectivity minimum for A, = 20 pm, according to the Schumann and Phillips model. This has not happened in our case. However, this conclusion is not completely realistic. As shown in Eq. (3), A, does not only depend on the concentration N but also on the dc reflectivity and mobility and on the effective mass. In fact, according to the theoretic curve presented in Fig. (14), in the case in which 1% of the carriers are activated (1.88 x 10'' cmP3),there corresponds a plasma wavelength of 20pm. How-

2 REFLECTIONSPECTROSCOPY ON ION IMPLANTEDSEMICONDUCTORS65

ever, it should not be ignored that this theoretic curve corresponds to completely crystalline Si. Christofides et al. (1987, 1989a) and Othonos et al. (1994) have shown, by performing electrical measurements, that dc conductivity and mobility vary even for annealing temperatures up to 700°C. In our case, annealing at 700°C is probably not sufficient for a complete recrystallization. However, the value of the effective mobility taken for this model (n-type c-Si) may be different from that of an inhomogeneous material. Thus the plasma wavelength in implanted materials and at low temperature materials annealed, which are not completely recrystallized, shifts to a longer wavelength. Electrical activation lower than 1%, no doubt, is an underestimation. Another point, which we believe is an additional important test of the theoretic model adopted in this study, is to check whether the obtained carrier density corresponds to each experimental point I , of Fig. 14 by using the following well-known relation: 1

Po =epo N

(9)

The dc mobility can be calculated by using the carrier density given in Table V and the spreading resistance data for the resistivity. Figure 15 shows the mobility as a function of the carrier density. The space included between the two solid lines corresponds to experimental data found by several researchers (Masetti, Severi, Solmi, 1983). There is close agreement between the experimental points obtained in this work and previously published data. Minor disagreement exists in the literature between experimental data obtained for samples annealed at temperatures lower than 1100°C. Figure 16 presents the reflection minimum as a function of the annealing temperature for the implanted series W3 to W6 (Seas et al., 1995; Christofides, Seas, and Othonos, 1995). We note that 1, remains almost constant versus the annealing temperature for samples implanted with a lower dose (series W3), whereas 1, increases versus implantation dose, in qualitative agreement with Eq. (3). Samples implanted at higher doses present reflectivity minima at shorter wavelengths. For example, the highly implanted samples (series W6) present a reflectivity minimum around 3 pm after an annealing at 800°C. It is also important to note that the minimum reflectivity for the four wafers implanted at around (Dc (W3) and over (Dc (W4 to W6) increases as a function of the annealing temperature. From Eq. (3) and Tables I11 and IV, it is easy to understand why I , increases with T,, with a decrease in the volume of free-carrier concentrations due to their diffusion under the surface of the wafer.

A. SEASAND C . CHRISTOFIDES

66

01 I8

'

19

.

Log(N)

. . 'ao'

. ".' 21

'

. * . '

22

[N: cm"]

FIG. 15. The wavelength minimum reflectivity I , versus the logarithm of the carrier concentration N (solid line). Schumann, Jr., P. A., and Phillips, R. P. (1967). Comparison of Classical Approximations to Free Carrier Absorption in Semiconductors.Solid State Electron. 10, 943.

5

.g e,

*oh

800

-

900

1000

Iloc

Aanealing Temperature ( "C) FIG. 16. The wavelength minimum reflectivity. I , as a function of annealing temperature for four different implantation doses.

2 REFLECTIONSPECTROSCOPY ON ION IMPLANTED SEMICONDUCTORS67

2. EFFECTIVE MASSVERSUS ANNEALING TEMPERATURE This section describes the variation of the effective mass m* as a function of the free-carrier concentration. An attempt to study the influence of the annealing temperature on the effective mass of free carriers in implanted and annealed Si wafers is presented. As is well known, the effective mass theory for doped semiconductors cannot be applied directly to disordered or amorphous semiconductors (the cases of unannealed and partially annealed semiconductors) because it is formulated in terms of the momentum-space wave functions of the crystal. High doses produce the incorporation of species other than the introduced impurities, such as vacancies, bivacancies, vacancy complexes, and structural disorder. In the case of amorphous materials, there have been numerous discussions as to whether the effective mass concept has any realistic meaning. Street (1991) and Kivelsen and Gelatt (1979) strongly support the idea that m* remains a significant physical parameter even in the case of amorphous materials. Our optical measurements indicate the influence of all the previous effects, and such measurements can result in useful information. In the following, we use the results presented in Fig. 16 concerning reflection minima to get an idea of how the conductive effective mass changes for the various samples of series W3 to W6. From Eq. (3) we define the ratio

in order to study the effect on the effective conductive mass as a function of the annealing temperature. Therefore, the ratio of the conductive effective masses can be written as follows:

It is obvious that due to the distribution of carrier density in the implanted layer it is impossible to determine an exact value for concentration of carriers and there is always an error associated with such measurements. The two different methods used to estimate the carrier concentration in the implanted layer indicate that there is an error of approximately 30%, which is shown in Fig. 17 as error bars. Figure 17 presents the variation of the normalized effective conductive mass of free carriers as a function of the

A. SEASAND C. CHRISTOFIDES

68

2.5

w4

10

1

0.0

800

900

lo00

0.0

1100

Annealing temperature 2.5 2.0

1 F

0.5

0.0

900

lo00

1100

Annealing Temperature ( "C) 1

2.5

c W6

w5

T

& u t

800

T

800

900

law,

1100

0.0

Annealing Temperature ( "C)

800

sa,

loo0

1100

Annealing Temperature ( "C)

FIG. 17. Normalized ratio of conductive effective masses as a function of the annealing temperature (TJ

annealing temperature. We note that the effective mass of the heavily implanted samples changes with annealing temperature. It is accepted that annealing of ion-implanted wafers leads to annihilation of defects, which, in turn, leads to a decrease in carrier scattering and therefore to a change of the effective mass. The variation of m* as a function of the annealing temperature shows the sensitivity that this physical parameter has to annealing.

VI. Summary

In conclusion, optical reflection and transmission measurements can be used to obtain information concerning the influence of implantation dose and annealing temperature on the kinetics of reconstructions. From the

2 REFLECTIONSPECTROSCOPY ON ION IMPLANTEDSEMICONDUCTORS 69

interference fringes, we can obtain information concerning the amorphouscrystalline transition as a function of the annealing temperature. From the presence of the absorption of free carriers in such samples, we can obtain information concerning the electrical activation of these carriers. The main results of our study can be summarized as follows. 1. FTIR spectroscopy is a promising technique toward nondestructive evaluation of implanted materials. 2. This technique is sensitive to the implantation dose and to the annealing temperature. 3. The free-carrier absorption phenomenon is sensitive in the case of heavily implanted and highly annealed samples. 4. The minimum reflectivity is a practical reference for the evaluation of the percentage of the activation of free carriers. 5. For implantation doses lower than the critical dose Oc,the energy of implantation does not influence the optical properties. 6. The classic model by Schumann and Phillips is in good agreement with our experimental results. The fit of the plasma wavelength as a function of the concentration of free carriers shows that an annealing of 800°C or more for 1h is sufficient for a complete activation of carriers. 7. As expected from the theory, all the highly annealed samples present a wavelength at which we have a minimum in the reflectivity. In the case of samples implanted at temperatures lower than Oc, A, remains constant with the annealing temperature, whereas for samples implanted with high doses, the plasma wavelength increases with the annealing temperature. 8. The effective mass has been studied as a function of the annealing temperature. Our analysis suggests that m* is influenced by the annealing temperature due to the annealing kinetics of defects. More research on this subject is needed to verify and further develop understanding in this area of semiconductors. REFERENCES Brierley, S. K., Lehn, D. S., and Grabinski, A. K. (1988). Implant-Dose Mapping Using Infrared Transmission.J . A p p l . Phys. 63, 5085-5087. Brown, R. L., Schoonveld, L., Abels, L. L., Sundararn, S., and Raccah, P. M. (1981). Electroreflectance of Ion-Implanted GaAs. J . A p p l . Phys. 52, 2950-2957. Chapman, P. W., Tufte, 0. N., Zook, J. D., and Long, D. (1963). Electrical Properties of Heavily Doped Silicon. J . A p p l . Phys. 34, 3291. Christofides, C. (1992). Annealing Kinetics of Defects of Ion-Implanted and Furnace-Annealed Silicon Layers: Thermodynamic Approach. Sernicond. Sci. Technol. 7, 1283- 1294.

70

A. SEASAND C. CHRISTOFIDES

Christofides, C., Guibaudo, G., and Jaouen, H. (1987). Etude de silicium implante a I’arsenic par effet de transport. Influence du recuit thermique. Revue Phys. Appl. 22,407-412. Christofides, C., Jaouen, H., and Guibaudo, G. (1989a). Electronic Transport Investigation of Arsenic-Implanted Silicon. 1. Annealing Influence on the Transport Coefficients. J . Appl. Phys. 65,4832-4839. Christofides, C., Guibaudo, G., and Jaouen, H. (1989b). Electronic Transport Investigation of Arsenic-Implanted Silicon. 11. Annealing Kinetics of Defects. J . Appl. Phys. 65,4840-4844. Christofides, C., Othonos, A,, Bisson, M. Boussey-Said, J. B. (1994). Optical Spectroscopy on Implanted and Annealed Silicon Wafers: Plasma Resonance Wavelength. J. Appl. Phys. 75, 3377-3384. Christofides, C., Seas, A,, and Othonos, A. (1995). Reconstruction Mechanisms in Ion Implanted and Annealed Silicon Wafers. Defects Difusion Forum 117, 45-64. Crowder, B. L., Title, R. S., Brodskey, M. H., and Pettit, G. D. (1970). ESR and Optical Absorption Studies of Ion-Implanted Silicon. Appl. Phys. Lett. 16, 205-208. Engstrom, H. (1980). Infrared Reflective and Transmissivity of Boron-Implanted, LaserAnnealed Silicon. J . Appl. Phys. 51, 5245-5249. Fredrickson, J. E., Waddell, C. N., Spitzer, W. G., and Hubler, G. K. (1982). Effect of Thermal Annealing of the Refractive Index of Amorphous Silicon Produced by Ion Implantation. Appl. P h p . Lett. 40, 172- 174. Gibbons, J. F. (1968). Ion Implantation in Semiconductors. Part I: Range Distribution Theory and Experiments. Proc. IEEE 56, 295-320. Gibbons, J. F. (1972). Ion Implantation in Semiconductors. Part 11: Damage Production and Annealing. Proc. IEEE 60, 1062-1096. Hart, R. R., and Marsh, 0. J. (1969). Changes of Optical Reflectivity (1.8 to 2.2eV) Induced by 40-keV Antimony Ion Bombardment of Silicon. Appl. Phys. Lett. 14, 225-226. Heavens, 0.S. (1964). Optical Properties of Thin Films. Butterworths, London, 77-79. Howarth, L. E., and Gilbert, J. F. (1962). Solid State Commun. 10, 236-237. Hubler, G. K., Waddell, C. N., Spitzer, W. G., Fredrickson, J. E., Prussin, S., and Wilson, R. G. (1979a). High-Fluence Implantations of Silicon: Layer Thickness and Refractive Indices. J . Appl. Phys. 50, 3294-3303. Hubler, G. K., Malmberg, P. R., and Smith, T. P. (1979b). Refractive Index Profiles and Range Distributions of Silicon Implanted with High-Energy Nitrogen. J . Appl. Phys. 50, 71477155. Hubler, G. K., Malmberg, P. R., Waddell, C. N., Spitzer, W. G., Fredrickson, J. E. (1982). Electrical and Structural Characterization of Implantation Doped Silicon by Infrared Reflection. Radiation Efects 60, 35-47. Hummel, R. E., Xi, W., Holloway, P. H., and Jones, K. A. (1988). Optical Investigations of Ion Implant Damage in Silicon. J. Appl. Phys. 63, 2591-2594. Irvin, J. C. (1962). Resistivity of Bulk Silicon and of Diffused Layers in Silicon. Bell Systems Tech. J . 41, 387-410. Kachare, A. H., Spitzer, W. G., Euler, F. K., and Kahan, A. (1974). Infrared Reflection of Ion-Implanted GaAs. J. Appl. Phys. 45, 2938-2946. Kachare, A. H., Spitzer, W. G., Fredrickson, J. E., and Euler, F. K. (1976a). Measurements of layer thicknesses and refractive indices in high-energy ion-implantation GaAs and Gap. J. Appl. Phys. 47, 5374-5381. Kachare, A. H., Spitzer, W. G., and Fredrickson, J. E. (1976b). Refractive Index of IonImplanted GaAs. J. Appl. Phys. 47,4209-4212. Kireev, P. (1975). The Physics of Semiconductors, Mir, Moscow. Kivelsen, S., and Gelatt, Jr., C. D. (1979). Phys. Rev. B19, 5160-5177.

2 REFLECTIONSPECTROSCOPY ON ION IMPLANTED SEMICONDUCTORS71 Kurtin, S., Shifrin, G . A., and McGill, T. C. (1969). Ion Implantation Damage of Silicon as Observed by Optical Reflection Spectroscopy in the 1 to 6 e V Region. i p p l . Phys. Lett. 14,223-225. Kwun, S., Spitzer, W. G., Anderson, C. L., Dunlap, H. L., and Vaidyanathan, K. V. (1979). Optical Studies of Be-Implanted GaAs. J . Appl. Phys. 50, 6873-6880. Masetti, G., Severi, M., and Solmi, S. (1983). IEEE Trans. Electron Devices, ED-30, 764-769. Othonos, A., Christofides, C., Boussey-Said, J., and Bisson, M. (1994). Raman Spectroscopy and Spreading Resistance Analysis of Phosphorus Implanted and Annealed Silicon. J . Appl. Phys. 75, 8032-8038. Prussin, S., Margolese, D., and Tauber, R. N. (1985). Formation of Amorphous Layers by Ion Implantation. J . Appl. Phys. 57, 180-185. Seas, A., Eleftheriou, M.-E., Christofides, C., and Theocharis, C. R. (1995). Infrared Spectroscopy and Electrical Characterization of Phosphorus Implanted and Annealed Silicon Layers. Nucl. Instrum. Meth. Phys. Res. B103,46-55. Seeger, K. (1988). Semiconductor Physics, Springer Series in Solid State Sciences 40 (M. Cardona, P. Fudle, K. von Klitzing and H.-J. Queisser, eds.). 4th ed. Springer-Verlag, Berlin, New York, Pans, Tokyo, Chapt. 11. Smith, R. A. (1959). Semiconductors, Cambridge University Press, Cambridge. Spitzer, W. G., Waddell, C. N., Narayanan, G. H., Fredrickson, J. E., and Prussin, S. (1977). Free-Carrier Plasma Effects in Ion-implanted Amorphous Layers of Silicon. Appl. Phys. Lett. 30,623-626. Street, R. A. (1991). Hydrogenated Amorphous Silicon, Cambridge University Press, Cambridge, Chapt. 5. Tatarkiewicz, J. (1989). Optical Effects of High Energy Implantations in Semiconductors. Phys. Status Solidi (b) 153, 11-47. Schumann, Jr., P. A,, and Phillips, R. P. (1967). Comparison of Classical Approximations to Free Carrier Absorption in Semiconductors. Solid State Electron 10, 943-948. Ure, R. W. (1972). Semiconductors and Semimetals. Thermoelastic effect in 111-V compounds. R. K. Willarson and A. C. Beer, eds.), Vol. 8, Transport and optical phenomena. Academic Press, New York, 86. Waddell, C. N., Spitzer, W. G., Hubler, G . K., and Fredrickson, J. E. (1982). Infrared Studies of Isothermal Annealing of Ion-Implanted Silicon: Refractive Indices, Regrowth Rates, and Carrier Profiles. J . Appl. Phys. 53, 5851-5862. Wagner, H. H., and Schaefer, R. R. (1979). Contactless Probing of Semiconductor Dopant Profile Parameters by IR Spectroscopy. J . Appl. Phys. 50, 2697-2704. Wang, K.-W., Spitzer, W. G., Hubler, G . K., and Donovan, E. P. (1985). Effect of Annealing on the Optical Properties of Ion-implanted Ge. J . Appl. Phys. 57, 2739-2751.