Optical Characterization of Semiconductors || Case Studies: Infrared Characterization

7 Case Studies: Infrared Characterization

7.1 Introduction

The infrared measurement of semiconductor parameters goes back some 30 years. Moss (1959) reviewed the infrared properties of germanium, silicon, group I I I - V compounds, and other semiconductors, in the region near the transverse optical ( T O ) mode. Spitzer and Whelan (1959) measured infrared absorption and reflection in nGaAs. Such early work was generally carried out in the near to middle infrared to determine fundamental parameters like effective mass. Characterization-oriented work appeared in the 1960s, primarily above 200 c m - 1 . N o w it is recognized that infrared spectroscopy over 1 0 - 1 0 4 c m _ 1 can determine band gap, impurity type and concentration, layer thickness, composition of ternary and quaternary alloy semiconductors, carrier density and mobility, and sample resistivity. These can be measured in bulk samples and complex microstructures. Some of these methods are valuable for the semiconductor industry. In silicon, for instance, it is essential to know the concentration of interstitial oxygen. The correct value leads to material with low leakage currents, an essential for good devices. Infrared spectroscopy during growth and processing can determine these important values.

Here I present characterization applications chosen to include many semiconductors of present interest, and to display the different possibilities. I begin primarily with bulk samples where geometric factors such as thickness are not of major importance. Then, because the infrared is especially useful to determine layer thickness, I examine thin films on substrates before considering the more complex quantum wells and superlattices.

There are several good reviews of infrared properties and characterization of semiconductors. Palik and Holm (1979) discuss free-carrier infrared analysis. Other reviews which cover a variety of topics include those by Pidgeon (1980), Perkowitz (1983), and Carr et al (1985). Krishnan et al (1990) treat impurities in silicon, especially carbon and oxygen, and review methods to find film thickness. Newman (1990) considers vibrational modes. Stradling (1990) surveys impurity and transport characterization in the infrared.

7.2 Band gap absorption

The most obvious fundamental application of infrared radiation is to examine the band gap itself. Interband transitions can be excited by an infrared photon for gaps from 0.001 to 1.24 e V . Important group I V and group I I I - V semiconductors have gaps in the near infrared, as illustrated in Table 3.1. I have already shown (Figs 3.7 and 3.9) examples of infrared gap absorption in GaAs . Other materials have smaller interband energies which can be spanned by mid- to far-infrared photons. In negative-

160 Case studies: infrared characterization

gap H g T e , for instance, valence electrons undergo interband transitions to the top of the Fermi level in the conduction band, which requires energies in the far infrared. A s CdTe with its conventional gap at 1.44eV is added to H g T e , the alloy H g ^ C d ^ T e changes its gap from negative to positive, becoming zero near χ = 0.15. This makes H g ! _ x C d x T e useful for infrared detectors, which is why considerable infrared work has probed H g T e and its alloys. Grynberg et al. (1974) examined the infrared reflectivity of H g T e between 80 and 700 c m - 1 by Fourier spectroscopy. They successfully analyzed the complex combination of free carrier, phonon, and interband effects. Later Polian et al. (1976) extended the infrared study to H g ^ ^ C d ^ T e . Their analysis also included an electron interband term.

McKnight et al. (1978a,b) made a similar infrared study for H g ^ M n / T e , another system which changes from a negative to a positive gap. They obtained reflectance data with a Fourier spectrometer. Low-temperature spectra like those in Fig. 7.1 clearly show the onset of the interband absorption, from the joint valence-conduction band to the Fermi level. Fits to such data yield phonon and free-carrier parameters, including the first effective-mass values reported for this ternary, as well as values for the inverted gap and the Fermi energy. Infrared gap measurements, of course, are useful for any semiconducting systems designed for service as infrared detectors. This includes Hgx-^Cd/Te , but also artificial structures. Jones et al. (1985), for instance, have made infrared measurements of the gap of the H g T e - C d T e superlattice, proposed as a new detector material. Similar work is reported in the new A l ^ G a ^ A s -based structures designed to absorb in the infrared.

A s I pointed out in Chapter 3, the infrared response of the free carriers in a semiconductor is influenced by the effective mass because the plasma frequency

Fig. 7.1 Imaginary part of the dielectric function α/ω versus wavenumber for Hgo.91Mno.09Te at 5.5 K. ( · ) Kramers-Kronig inversion of reflectance data. Theoretical fits with ( ) and without ( ) an interband term. The interband transition (inset) fixes the Fermi energy at 6.4 meV. The T O absorption is seen at 118 c m - 1 . (After McKnight et al. (1978b).)

http://Hgo.91Mno.09Te

Phonons and lattice properties 161

contains the ratio n/m*. Effective mass is a basic band parameter whose value can be important for device use. Since it is determined from infrared free-carrier measurements, I show case studies of these determinations in my discussion of carrier characterization.

7.3 Phonons and lattice properties

The discussion in Chapter 3 noted that two clear features occur in infrared lattice reflectance spectra from binary semiconductors; the peak at the transverse optical ( T O ) frequency, and the minimum at the longitudinal optical ( L O ) frequency. Neither mode appears in spectra from elemental silicon and germanium, but there is a variety of other phonon processes. These seem not to have been directly exploited for characterization, but must be taken into account if they interfere with other optical measurements. Krishnan et al. (1990) note this in their discussion of infrared characterization of oxygen in silicon, which I present later.

The strong T O modes in binary compounds have been examined extensively. Hass and Henvis (1962) made early measurements in a variety of group I I I - V semiconductors, with the results shown in Fig. 7.2. Other workers have continued such analysis. Jamshidi and Parker (1984), for instance, used Fourier transform infrared ( F T - I R ) spectroscopy to find the T O and L O frequencies for GaAs at 6 and 300 K . They report values of 269.1 and 295.1 c m - 1 respectively, and list other values as well, measured by Raman, infrared, and neutron scattering methods.

180 200 220 240 260 280 300

F R E Q U E N C Y ( c m " 1 )

Fig. 7.2 Infrared reflectance spectra for group I I I - V binary compounds. ( ) Experimental data. ( ) Theoretical fits from equation (3.24). The T O peaks and LO minima are clear. (After Hass and Henvis (1962).)


These observations have given essential fundamental knowledge and useful characterization information. For instance, Kachare et al. (1974) showed that ion implantation in GaAs changes the infrared phonon spectra. But infrared analysis of phonon modes becomes most useful for ternary and quaternary semiconductors. One important application is to use the phonon frequencies, which usually vary smoothly with x, to determine the degree of alloying. Figure 3.13 shows how the modes from the two sublattices clearly appear in A ^ G a ^ A s . Phonons from each sublattice are also observed in Raman spectra, as I have discussed. The differences in penetration depth and spatial resolution between the two techniques makes them somewhat complementary, as noted in Chapter 6.

T o relate the phonon frequencies of a ternary material like A l ^ G a ^ ^ A s to the alloying parameter*, it is helpful to understand the end-point compounds. This is not always straightforward, even for a widely used alloy. Although the T O and L O parameters for GaAs have been known for some time, the values for A l A s were more difficult to determine because this material tends to form an oxidized top layer. Perkowitz et al. (1987b) used F T - I R reflectance spectroscopy to examine a layer of A l A s protected by a 25 nm cap layer of G a A s , too thin to affect the spectra. These measurements gave the T O and L O parameters for A l A s . Based on such end-point data, and measurements like those shown in Fig. 3.12, complete phonon data exist for A l ^ G a ^ A s within the Lorentzian model (equation (3.28)) . The phonon mode frequencies are known versus x, as shown in Fig. 6.1, as are the mode strengths and damping constants.

Similar curves can be derived for other ternary materials, again usually starting from the endpoint lattices. Macler et al. (1992) give simple linear equations relating phonon frequency to χ value for the group I I I - V material I n ^ G a ^ S b . For the group I I - V I alloy H g ^ C d / T e , CdTe and H g T e have been thoroughly studied. Vodop'ya-nov et al. (1974) measured T O and L O frequencies of 140 and 167 c m - 1 in CdTe. Later Batalla et al. (1977) used F T - I R methods to obtain high-precision phonon data over 20-440 c m - 1 . They correlated these with neutron scattering data, and assigned each peak to a phonon mode. Such detailed knowledge of CdTe was essential to analyze H g ! _ x C d x T e , with its combination of CdTe-like and HgTe-like characteristics. A l l available phonon data for H g x _ x C d x T e have been unified by Rajavel and Perkowitz (1988) to yield accurate calibration curves for the T O frequencies, oscillator strengths, and damping constants in equation (3.28). Both T O frequencies vary nearly linearly with x, at temperatures from 6 to 300 K , as shown in Fig. 7.3. This gives a simple way of determining χ from infrared spectra. The alloy parameter can also be found from the relative peak heights.

Even an intricate quaternary semiconducting system can yield characterization information from infrared phonon spectra. Amirtharaj et al. (1980) measured the reflectance over 20-410 c m - 1 from thin film I n ^ G a ^ A S y P ^ grown on InP. With two separate concentration parameters χ and y, it is possible to set the film lattice spacing to that of the InP, and to independently set the film band gap to a desired value. Lattice match occurs when ylx — 2.2. A F T - I R spectrometer with a room-temperature detector gave reflectance for samples with y = 0.22 to 0.66. This yielded the T O and L O frequencies, whose complicated behavior could be related to the end-point compounds.

Impurities 163

110 t . 1 . 1 . ι . ι . I 0.0 0.2 0.4 0.6 0.8 1.0

Wavenumber (cm - 1 )

Fig. 7.3 Transverse optical frequency for the CdTe-like and HgTe-like mode in H g ^ C d / T e versus mole fraction χ of CdTe, at 6, 77 and 300 K. The lines are fits to all known data in the literature. (After Rajavel and Perkowitz (1988).)

7.4 Impurities

A s I discussed in Chapter 3, impurities can be seen in infrared spectra via their electronic absorption, or when they create local vibrational modes. I show examples of each.

7.4.1 Electronic excitation

The discussion in Chapter 3 has shown that shallow impurities can be excited or ionized by mid- to far-infrared photons, leading to absorption. This provides a mechanism to detect the impurities, which can be a challenging task for applications requiring extremely pure material. The most straightforward means of detection is conventional absorption spectroscopy, but photoconductive methods are more sensitive. Stradling (1990) notes that impurity concentrations as low as 1 0 l l c m ~ 3 can be found by absorption measurements in thin films, whereas photoconductive measurements have extended the sensitivity to 1 0 7 c m - 3 minority impurities in ultrapure germanium, and to 10 4 cm~ 3 neutral phosphorous donors in a silicon metal oxide semiconductor field-effect transistor ( M O S F E T ) structure. However , there is a price for the increased sensitivity, Photoconductive measurements require noninjecting and ohmic electrical contacts on the samples. Given the typical high resistivity of pure samples, such contacts can be difficult to fabricate and maintain over a range of measurement temperatures.

Even if absorption spectroscopy is not the most sensitive method, it is extremely


fruitful. The hydrogenic model, although it has deficiencies, serves well to analyze data. The early result by Summers et al. (1970) in GaAs (shown in Fig. 3.15) is a good example. They measured absorption spectra for doped samples at 4.2 K , using a commercial F T - I R spectrometer operating at a resolution of l c m - 1 . The known dopants were germanium, silicon, selenium, or sulfur in concentrations near 10 1 5 cm~ 3 . The main features in the absorption spectrum come from the Is —> 2p hydrogenic transition and correlate with photoconductivity data. Using the values ra*/ m0 = 0.0665 and ε = 12.5 in equation (3.36), the authors calculated ionization energies not far from their measured results, confirming that the hydrogenic model is reasonable. Their analysis included small ( 1 - 4 % ) central-cell corrections, which take into account the fact that the potential near the impurity is not quite Coulombic. The authors note also that the hydrogen model assumes that each atom is perfectly isolated, whereas in reality the impurity wave functions overlap slightly, leading to another small discrepancy.

More recently, Fischer and Mitchel (1985) used F T - I R spectroscopy to determine absorption in neutron-irradiated silicon doped with gallium. Such irradiation, in the process called 'neutron transmutation doping' ( N T D ) , has been used to create phosphorus donors to compensate boron impurities. However, the neutrons can induce interstitials, vacancies, and complex defects, some persisting even after annealing to 1000°C. Fischer and Mitchel examined samples made by the float-zone method, with gallium concentrations of 4 x 10 1 6 to 5 x 1 0 1 6 c m - 3 . A commercial Fourier spectrometer obtained spectra at a resolution of 1 c m - 1 from samples 1 cm x 1 cm x 0.2 cm that were held at 5.5 K . The spectra were measured versus annealing temperature. Figure 7.4 illustrates structure from a G a X complex, which had been reported earlier; and a new acceptor level, designated A 4 in the plot. Its peaks at 341, 373, and 416 c m - 1 are characteristic of the spectrum from a group I I I related acceptor. This new spectrum is like that from the G a X system, but shifted down in energy. The complete analysis led to the identification of four shallow acceptors, A 2 , A 3 , A 4 , and GaX, including their binding energies, which can identify them in other samples.

Sopori (1985) also used infrared absorption to measure the amount of boron in silicon, at high doping levels. In earlier work by Pajot (1964) and Kolbesen (1975), a characteristic absorption line at 320 c m - 1 worked well to determine the presence and amount of boron at concentrations as low as 1 0 1 3 c m - 3 . However , this line did not serve well for all samples. A t high densities of boron, the absorbance at 320 c m - 1 was so large that the transmittance could not be accurately measured for samples of reasonable thickness. Therefore Sopori considered the use of a line of lower absorbance. The line at 668 c m - 1 , which corresponds to a P 3 / 2 — » P1/2 transition, was found to be a good choice for quantitative analysis.

Sopori examined a variety of float zone and Czochralski samples. Their resistivities, measured by a four-point probe, were converted into boron concentrations from published results. Absorbance spectra were obtained from samples held at 12 K . A commercial Fourier spectrometer was used, and a resolution of 2 c m - 1 was adequate to resolve the absorbance peaks. Figure 7.5 shows peaks due to boron at 668 and 693 c m - 1 . After analyzing a number of samples, Sopori determined that the boron concentration in units of cubic centimeters is given by NB = 2.575 x 1 0 1 5 a 6 6 8 (where a 6 6 8 is the sample absorption at 6 6 8 c m - 1 at 12 K , in units of wave numbers). This calibration holds for NB = 10 1 5 to 1 0 1 7 c m - 3 . Sopori points out that this method of determining boron concentration should also serve for polycrystalline silicon where

Impurities 165

Φ 'υ S ο

ο (Λ η ce "D Φ Ν ~â Ε ο Ζ

Α 4 (4)

υ GaX (4)

Α 4 (1 ) GaX(1) '

400°C

500°C

320 340 360 380 400 ,420 440


Fig. 7.4 Infrared absorption spectra of neutron-irradiated Si:Ga at 5.5 Κ, for various annealing temperatures. Bands A 4 and GaX come from photo-excitation of electronic states in shallow acceptors. (After Fischer and Mitchel (1985).)

the 668 c m - 1 line is not appreciably wider, and is unaffected by high concentrations of carbon and oxygen.

Krishnan et al. (1990) discuss the use of infrared absorption to detect shallow group I I I and group V impurities in silicon. Boron, phosphorus, arsenic, and antimony are among the most common, appearing in concentrations of 1 0 9 - 1 0 1 4 c m - 3 even in the purest silicon made. A t helium temperatures, these follow the hydrogenic model. Their absorption lines appear in transmission spectra of silicon samples 2-10 mm thick. Table 7.1 lists characteristic bands for several impurities.

Very recently, H o et al. (1992) examined infrared absorption in silicon doped with neutral magnesium donors. Magnesium, although a group I I element, is a donor rather than an acceptor, suggesting that it occupies an interstitial site, not a substitu-


65

151 ' 1 '

700 650 600 550 Wavenumber ( cm - 1 )

Fig. 7.5 Infrared absorption spectrum of 1.1 Ω-cm silicon doped with boron, showing boron bands at 668 and 693 cm" 1 due to excited-state transitions. The sample temperature is 12 K. Spectral resolution, 2cm - 1 . (After Sopori (1985).)

T a b l e 7.1 Position of important infrared electronic absorption bands for shallow impurities in silicon at 15 K.

Impurity species Peak position ( c m - f )

Ρ 316 Β 320 Sb 294 As 382 Al 472 Ga 548 In 1177

tional one. The infrared spectrum of magnesium donors had been measured in 1972 with a grating instrument. H o et al. used a modern F T - I R instrument, in the expectation that the improved resolution would be valuable. Their silicon samples were doped by a magnesium diffusion technique, which converted high-resistivity p-type samples into low-resistivity η-type material, with carrier concentrations of 2 x 10 1 5 to 5 x 10 1 5 cm~ 3 . The samples were held at helium temperatures and were mounted in a strain-free arrangement which eliminated line broadening due to stress. Figure 7.6 shows one of the absorbance spectra, with multiple narrow lines evident. Several lines not completely resolved in the earlier data are now resolved, and new peaks appear.

Impurities 167

-Q δ TO _Q <

196 100 102

Photon energy (meV)

Fig. 7.6 Infrared absorption features due to neutral magnesium donors in silicon with a carrier concentration (at room temperature) of 5 x 1015cm . The sample is held at liquid helium temperature. Peaks are marked according to the excited state hydrogen-like transition they represent. (After Ho et al. (1992).)

Among the most recent infrared work on impurities in silicon is that carried out by Haller and coworkers. Merk et al. (1990) examined the infrared absorption of zinc-doped silicon. They note that it has been difficult to examine group I I impurities in silicon, because they appear in relatively low concentrations (near 1 0 1 6 c m - 3 ) , and produce deep, highly localized states. However , these workers were able to obtain high resolution mid-infrared absorption spectra. They examined silicon samples made by the float-zone method, including high-purity material (p — 5000 Ω-cm) and moderately doped samples (p = 60 Ω - c m ) . Zinc was diffused into the silicon at approximately 1200°C. Auxiliary measurements put the zinc concentration at approximately 10 1 5 cm~ 3 and showed that most of the zinc was electrically active. Spectra were obtained from samples 1 cm x 1 cm x 0.3 cm, with a rapid-scan Fourier spectrometer. A cooled silicon detector sensed the signal transmitted through the sample, which was mounted on a cold finger connected to a liquid helium Dewar. This allowed controlled low temperatures.

Figure 7.7 shows a measured absorption spectrum. The sequence of lines is explained as arising from the helium-like neutral double acceptor zinc. They represent transitions from the ( I s ) 2 ground state to {\s){np) excited states. It is significant that despite the deep nature of this acceptor (the optical ionization energy is 319 m e V ) the sequence of lines is like that seen from relatively shallow group I I I acceptors in silicon, namely boron and indium; and from the beryllium double acceptor. This and other results cited in the paper establish that the deep zinc double acceptor can be described by effective mass theory, which gives a simple means to analyze its infrared spectra for purposes of characterization.


0.06 H

WAVENUMBER (cm 1 )

Fig. 7.7 Infrared absorption spectrum from double acceptor zinc in silicon at 4.5 K. Spectral resolution, 0.5 c m - 1 . The peaks represent transitions in a Lyman series of the helium-like acceptor, and are marked with the final state of the transition from the ( I s ) 2 ground state. (After Merk et al. (1990).)

Later Heyman et al. (1991) examined the infrared absorption spectra of beryllium in silicon. It was already known that the introduction of beryllium into silicon yields several defects, including four acceptor centers with infrared ionization energies of 103.5, 145.8, 191.9, and 198meV. There is evidence that two of these levels are associated with double acceptors or complexes. The authors examined the 145.8cm" 1

center and concluded that it is a double level. The samples were prepared by diffusing 99.9% pure beryllium metal into p- or n-

type floating-zone silicon. The samples for the infrared measurements measured 1 cm x 1 cm x 0.1 cm. Their transmission was measured over 450-4000 c m - 1 using a F T - I R spectrometer with 0 .5cm" 1 resolution. Figure 7.8 shows a sharp line absorption spectrum, consisting of two related series of lines, denoted α and β. The strengths and spacing of the strong α lines are consistent with transitions to acceptor Rydberg states from a ground state 145.8 m e V above the valence band. The β lines are shifted 2 meV above the a lines, and represent a second acceptor effective mass series. The ratio of intensities of the α and β lines is about 5:1, and did not vary in all the measured samples, which the authors took as evidence that both lines come from the same center.

T o extend their analysis, the authors obtained infrared spectra with the samples subjected to uniaxial stress from 0 to 150 MPa along the (100) and (111) directions. They found that the parameters defining the piezospectroscopic behavior were the same for the α and the β lines, again suggesting a common origin for the two series. The directional character of such stress makes it possible to deduce the geometry of the absorbing center. The authors conclude that the 145.8meV absorption comes from a center with trigonal symmetry. They suggest that it is formed from two beryllium atoms which occupy nearest-neighbor silicon sites.

1 0

ε

§ 5

Ο

<

Impurities 169

α 1 2 3 4 4Α οο I I I

2 3 4 4Α οο β I I

Λ J

I I I

I I I I I I I I ι I ' ι ι 1 2 5 1 3 0 1 3 5 1 4 0

Energy (meV) 1 4 5

Fig. 7.8 Infrared absorption due to Be 2 in silicon. The sharp a and β lines are marked with the Rydberg series transition energies. The β lines are consistently 2meV higher than the a lines. (After Heyman et al. (1991).)

Impurity ionization can also affect the conductivity of a sample, when the electron (hole) ionized from a donor (acceptor) reaches the conduction (valence) band. If the sample is connected to contacts which monitor the current through it, an increase is seen when the impurities are ionized. This process is the basis of a whole class of impurity photoconductive infrared detectors. It always involves a phonon, which means that it is favored as temperature increases. However , low temperatures are necessary to supply deionized impurities. The result of these conflicting requirements is that the best temperatures for photoconductive measurements are intermediate values, typically about 10 K .

Very early photoconductive work was carried out in a group I I I - V material. Chamberlain et al. (1971) observed the Is — » 2p transition in InP, in data obtained with a Fourier spectrometer. They found the ionization energy Ed and derived the electron effective mass from the hydrogenic model, obtaining m*/m0 - 0.085 ± 0.005 in agreement with other results.

Haller and Hansen (1974) and Skolnick et ai. (1974) have used sensitive photothermal excitation in very pure germanium and silicon. Haller and Hansen examined over 50 samples of p-type germanium doped with a variety of acceptors at concentrations of 10 9 to 10 2 2 cm~ 3 . They were careful to ensure that the electrical contacts for the photoconductivity measurements added no new impurities to the samples, and were ohmic to 1.2 K . Photothermal spectra like that shown in Fig. 7.9 were measured with a F T - I R instrument, at the high resolution of 0.25 c m - 1 , which is necessary because the peaks are so sharp. The data were compared to energy level schemes for known impurities to determine the impurity types. Gallium, indium, and aluminum impurities were identified, as well as an unknown contaminant. Skolnick et ai. extended these methods to identify simultaneously phosphorus donors and boron acceptors in

Ι Ι Ι Ι Ι I I I I .1 Ι ι Ι Ι ι Ι Ι Ι Ι ι I I Μ


ENERGY (meV)

0) 4-* c

CO

LU (0 Ζ ο a. c/> LU CE - I

< rr LU x ΙΟ ΙΟ χ CL

Wavenumber (cm" 1 )

Fig. 7.9 Photothermal spectrum of electronic states in ultrapure germanium at 8K, with net impurity concentration of 1 0 n c m - 3 . Each peak is labeled with its originating impurity, aluminum, gallium, indium, or the unknown X. A given impurity produces several lines, such as the four from indium, labeled A - D . (After Haller and Hansen (1974).)

silicon. In germanium they saw unidentified peaks which probably came from lattice defects, not chemical impurities.

Cooke et al. (1978) used infrared-induced photoconductivity as well, to examine donor impurities in GaAs . First they measured the central-cell corrections to the hydrogenic theory for known dopants. These corrections were then used as signatures for unknown impurities. Some measurements were made in a magnetic field which sharpened the structure, to allow accurate determination of the corrections, also known as chemical shifts. Combined with earlier work by Stillman et al. (1972), these experiments generated the assignment of chemical shifts for eight dopants. Cooke et al. applied the results to unintentionally doped high-purity samples made by three growth methods at several laboratories. They found that all samples made by the same technique, regardless of where they were grown, displayed nearly identical central-cell data; for example, all vapor-phase grown material contained silicon, carbon, and a third contaminant, either lead or a gallium vacancy.

The hydrogenic states are affected by a magnetic field, in analogy to Zeeman splittings and other well-known atomic phenomena. Hence spectroscopy in a mag-

Impurities 171

netic field yields additional characterization information. Afsar et al. (1980), for instance, have used infrared magnetospectroscopy to identify donors in high-purity epitaxial GaAs . With a F T - I R unit operating at a resolution of 0.14 c m - 1 , they measured photoconductive response versus field up to 16 T. This produced characteristic signature curves for different dopants including sulfur, silicon, selenium, and germanium.

More recent photothermal work has been carried out in silicon-doped molecular beam epitaxy ( M B E ) grown epitaxial G a A s by Skromme et al. (1985). In a massive study of over a dozen GaAs layers, doped to concentrations of 2 x 10 1 4 to 8 x 1 0 1 4 c m - 3 , they coordinated photothermal ionization spectroscopy with Hall, capacitance-voltage, photoluminescence, and deep level transient measurements. I have discussed in Chapter 5 their photoluminescence ( P L ) results, which they used primarily to identify acceptor levels. These authors considered photothermal ionization spectroscopy the best available technique to identify residual donors in GaAs , superior to P L measurements in this case, which could be obscured by defect-related lines.

The photothermal data were obtained at the high resolution of 0.05 c m - 1 , at sample temperatures from 4.2 to 7 K . The measurements were made in a 6.5 Τ magnetic field, to give additional information. Figure 7.10 shows photothermal results for three of the MBE-grown samples, compared to a high-purity reference sample (G-110) grown by vapor-phase epitaxy ( V P E ) . The M B E samples were grown with different ratios of arsenic to gallium. A l l the observed peaks come from Is — » 2p transitions in the magnetic field, from three different hydrogenic donors. The peaks in the V P E sample correspond to silicon, sulfur, and germanium. A l l three M B E samples show the same silicon and sulfur peaks, with their positions shifted downward in sample 11 060 because of saturation in the absorption. The line widths of the best M B E samples (those grown with As/Ga = 15 to 25) are somewhat larger than those in the V P E samples. This indicates that the MBE-grown material is not quite as pure as the V P E material, but still shows a high level of purity.

Also among recent photothermal work is the extremely high-resolution, high-sensitivity spectroscopy reported by Haller (1986). H e measured lines as narrow as 17 \LQV in spectra over 5 0 - 1 0 0 c m - 1 from ultra-pure p-germanium held at 7.5 K . The sample contained the acceptors boron, aluminum, and arsenic, at a net concentration of 6 x 1 0 1 0 c m - 3 .

Deep impurities, with their large ionization energies, are usually less tractable than shallow ones, because they are more tightly bound into the crystal lattice. Hence they have strongly localized wave functions which are generally not accurately described by the combination of hydrogenic and effective-mass models. Kazanskii et al. (1979) studied such localization in germanium, using as spectroscopic source for the extreme far-infrared a backward wave oscillator working between 3.6 and 1 7 c m - 1 . Sample temperatures ranged from 4.2 to 20 K . Kazanskii et al. measured the far infrared absorbance α in germanium samples containing either the deep impurity beryllium or the shallow impurity gallium. For each type of impurity, α increased smoothly with wavenumber, indicating that the impurity density was great enough for individual atoms to interact. However , at the same concentration, the absorption due to beryllium was less than one-tenth the absorption due to gallium. The authors consider this difference to represent the increased localization of the deep donors, which reduces the rate of electron transitions among them.


34 35 36 37 38


Fig. 7 .10 Photothermal ionization spectra from three MBE silicon-doped GaAs samples in a magnetic field of 6.3 T. The samples were grown at 630 °C. A spectrum from a vapor-phase grown sample (VPE) is shown for reference. Peaks due to silicon, sulfur, and germanium are marked. (After Skromme et al. (1985).)

7.4.2 Local vibrational modes

I have already cited the review by Newman (1990) of local vibrational modes ( L V M ) arising from semiconductor impurities. In addition to a general discussion, this shows several examples, for instance to examine impurity oxygen in η-type silicon. Krishnan et al. (1990) extensively review the infrared characterization of impurities in silicon. They note that L V M analysis is extremely useful in determining the presence and concentration of oxygen and carbon. Oxygen has proven especially important. It is

Impurities 173

0 t 1 1 1 ! 1 1 3 1 1 1— 1400 1200 1000 800 600


Fig. 7 .11 Infrared absorbance from float zone (FZ) and Czochralski ( C Z ) silicon. The peaks from the very pure FZ sample come from phonons. In the less pure CZ sample, the new peaks at 1107 and 515 c m - 1 are related to interstitial oxygen. (After Krishnan et al. (1990).)

easily introduced into silicon during growth, from the crucibles and from the surrounding air. Oxygen atoms enter interstitially between two silicon atoms in concentrations as high as 2 x 10 1 8 cm~ 3 , forming a strong S i - O bond with each neighboring silicon atom. This gives a molecule-like nonlinear S i - O - S i entity, with a bond angle of 164°. A s processing of the silicon continues, part of the incorporated oxygen turns into S i 0 2 precipitates. Surprisingly, small concentrations of these precipitates are helpful. They provide a gettering action which gathers other impurities, giving a better quality of silicon. But if their concentration is too high, the precipitates cause mechanical changes which weaken the material. Hence knowledge of the oxygen concentration is a key step in making high-quality material. L V M analysis can help.

Krishnan et al. note that before examining the impurity L V M s in silicon, it is necessary to understand the innate phonon spectrum. Figure 7.11 shows spectra from high-purity silicon grown by the floating zone ( F Z ) method, expected to give the highest quality, and the Czochralski ( C Z ) method. A l l the bands in the F Z spectrum come from phonons. Although not all have been assigned, the strong band at 610 c m - 1 is known to represent the combination of a T O and a transverse acoustic ( T A ) phonon. The presence of impurities adds unmistakable vibrational modes to this spectrum. The strong band at 1107 c m - 1 in the C Z spectrum is definitely connected to the presence of interstitial oxygen. The weak band at 515 c m - 1 is also so connected, according to Krishnan et al. The impurity modes are clearer in Fig. 7.12, which displays the difference in absorption between C Z and F Z silicon. A l l the bands which remain in this difference spectrum are related to interstitial oxygen, except the peak at 607 c m - 1 , which comes from carbon. This carbon band is ordinarily not visible in


Λ Oxygen • Carbon I CO

1500 1000 Wavenumber (cm - 1)

500

Fig. 7 .12 Difference between measured absorbances for float zone silicon and Czochralski silicon as shown in Fig. 7.11. The phonon peaks are eliminated, showing peaks due to interstitial oxygen, carbon, and oxygen-carbon. (After Krishnan et al. (1990).)

direct (nondifference) spectra like that in Fig. 7.11, because it is overwhelmed by the two-phonon band at 610 c m - 1 .

Table 7.2 lists the oxygen-related absorption lines in silicon at room temperature. Krishnan et ai. note that the origin of the 515 c m - 1 line has been the subject of much discussion, including the possibility that it is not related to S i 2 0 at all. However , they present data to show that its strength correlates with that of the 1107 c m - 1 band, as evidence that their assignment to the symmetric S i - O - S i stretching mode is correct. Other discussion of the spectra, including details of fine structure related to silicon isotopes, can be found in their review.

The conversion of these observed peaks into a reliable quantitative tool is an involved task. Several studies have been made to establish a conversion factor, which

T a b l e 7.2 Positions, full width at half maximum (FWHM) and intensity relative to the line at 1107 cm" 1, for modes due to interstitial oxygen in silicon.*

Position FWHM Relative intensity ( c m - 1 ) ( c m - 1 )

1720 31 0.016 1226 22 0.011 1107 33 1.000 1059 — — 1013 8 0.006 560 — — 515 8 0.260

* After Krishnan et al. (1990).

Impurities 175

translates the absorption coefficient at 1107 c m - 1 into oxygen concentration. The measured absorption was correlated with the oxygen concentration as determined by other methods, such as inert gas fusion analysis and photon activation analysis. Considerable variety has been found from different investigations. The factor to convert absorption coefficient into atoms of oxygen per cubic centimeter has been measured from 2.45 x 10 1 7 to 6.00 x 10 1 7cm - 2 . Much of the scatter comes from the wide variation of results from different nonspectroscopic methods of determining oxygen content. The latest internationally agreed-on conversion factor, the result of a round-robin effort, is 3.1 x 1 0 1 7 c m - 2 . Fig. 7.13 shows data from this effort, expressed in parts per million atomic of oxygen versus absorption coefficient.

Care is required to ensure that the infrared measurement of the absorption is carried out accurately. A reproducibility of 1% has been achieved from laboratory to laboratory, using F T - I R spectroscopy. Guidelines for the measurements include the use of polished silicon samples 2-4 mm thick, and an FZ-grown comparison sample of matched thickness. It is also important, Krishnan et al. note, that the data be corrected for the multiple internal reflections that occur in the sample. Otherwise an incorrect absorption coefficient is obtained.

In addition to the valuable ability to sense and measure the presence of the S i 2 0 complexes, infrared spectra also reflect the presence of the oxygen precipitates which occur when oxygen concentrations exceed 10-20 ppm. These produce additional infrared bands, the strongest of them at 1100 and 1250 c m - 1 . The 1250 c m - 1 band can be used to estimate the concentration of precipitates, and other possibilities for analysis are now under study.

The carbon band at 607 c m - 1 in Fig. 7.12 comes from carbon substituting for silicon, to form C-Si bonds. Its proximity to the 6 1 0 c m - 1 band means that its

Absorption coefficient (cm - 1)

Fig. 7.13 Calibration curve to determine interstitial oxygen content in silicon (in parts per million atomic) from the infrared absorption coefficient at 1107 cm" 1. The data points come from an international round-robin measurement. The line represents the agreed-upon conversion factor. The conversion factor for the oxygen content per cubic centimeter is 3.1 x 10 1 7cm" 2. (After Krishnan et al. (1990).)


3 L ο CZ

3 4 0 2 Absorption coefficient (cm - 1)

Fig. 7 .14 Calibration curve to determine substitutional carbon content in silicon from the infrared absorption coefficient at 607 cm" 1. The data points come from an international round-robin measurement. The line represents the agreed-on conversion factor, 0.81 X 101 7cm~2. (After Krishnan et al. (1990).)

measurement in difference spectra requires extra care, including the use of exactly matched test and reference samples polished on both sides. Nevertheless, standards have been established to convert the absorption at 607 c m " 1 to carbon concentration. The results of the most recent round robin are shown in Fig. 7.14, and yield a factor of 0.81 x 10 1 7 cm~ 2 to convert absorption coefficient to carbon atoms per cubic centimeter.

Krishnan et al. note that infrared methods may also be useful to detect nitrogen and hydrogen in silicon. Nitrogen has been reported to reduce slip in silicon and to keep dislocations from spreading. It produces absorption peaks at 766 and 963 c m " 1 , but quantitative calibration is difficult, because some fraction of the nitrogen is infrared inactive. Hydrogen can enter crystalline silicon during growth and processing by such processes as plasma etching, and produces characteristic modes. In amorphous silicon used for solar cells, incorporated hydrogen produces bands near 600 and 2000 c m " 1 . These have been analyzed and give quantitative information, some of which I discuss later in this section.

T o emphasize that calibration can be a thorny issue, the work of Geist (1989) illustrates how difficult it is to determine a highly accurate infrared absorption cross-section, the absorption coefficient per density of absorbing atom. Geist examined arsenic-doped silicon which is used in solid state photon detectors. For best device performance, it is important to know the absorption cross-section of the arsenic versus wavelength and arsenic concentration NAs. Geist examined three epitaxial silicon samples doped with arsenic to different levels, a bulk wafer uniformly doped with arsenic, and a nominally pure silicon wafer. Careful analysis yielded ± 8 % uncertainties in the arsenic concentration in the epitaxial layers, and a ± 2 % uncertainty in the uniformly doped sample. The transmittance measurements were also made with care, and yielded uncertainties of < 2 % between 530 and 330 c m " 1 , with greater errors outside this range. The cross-section versus wavelength for a sample with NAs = 1.6 x

Impurities 177

250 500 750


Fig. 7 .15 Infrared absorption cross-section for arsenic in silicon as measured by Geist (1989) ( ) compared with another determination ( ) . The solid part of the bottom curve is the estimated uncertainty, which becomes larger than indicated where the curve is dashed. (After Geist (1989).)

1 0 1 8 c m - 3 , is shown in Fig. 7.15 along with the estimated error, which averages 7% over the region of maximum accuracy.

Krishnan et al. (1990) also point out the importance of defects for the silicon semiconductor industry. Many of the processing steps, including ion implantation and reaction ion etching, can cause radiation damage, and this is also a concern for devices for space-based application. In Chapter 4, I have discussed photoluminescence analyses of defects. Infrared absorption is also an excellent probe, as has been reviewed by Newman (1969, 1974, 1982) and Krishnan et al. (1990). Figure 7.16 shows a typical spectrum of neutron-irradiated silicon. Among the many features related to the effects of the irradiation is the strong band at 830 c m - 1 , which comes from a so-called Ά center', an oxygen atom trapped in a single vacancy. The concentration of such centers per cubic centimeter is approximately 6.1 x 10 1 6 a 8 3 0 , with a 8 3 0 in units of wavenumbers.

Wolk et al. (1991a,b) give a recent example of the use of vibrational analysis to understand impurities in G a A s . They analyze an L V M due to D X centers in GaAs doped with silicon. The D X center is a deep defect found in A l ^ G a ^ A s for JC>0.22, in GaAs under hydrostatic pressure, and in other group I I I - V systems. It appears to be related to a shallow substitutional donor which becomes deep under certain conditions of alloying or pressure. The mechanism causing this is not understood, and the details of the D X center remain controversial.


0.06-J

0.04

03 - Q

< 0.02.

0.00 -I

A center

" t II ι III hAJ

1200 1000, 800


600

Fig. 7 .16 Infrared absorbance spectrum from neutron-irradiated silicon. The sharp band at 830 c m - 1 comes from an oxygen trapped at a single vacancy and can be used to determine the concentration of this so-called Ά center'. (After Krishnan et al. (1990).)

The authors carried out a difficult experiment, the observation of an infrared spectrum designed to illustrate the local mode behavior of the D X center under pressure. They designed an assembly which allowed high sensitivity infrared transmission to be performed with the sample mounted in a diamond anvil pressure cell. The signal-to-noise ratio in such a cell is poor, because it can accommodate a sample no larger than a few hundred micrometers across. The authors used a sensitive detector and a light-focusing cone to enhance the system's performance, and obtained spectra of good quality.

Figure 7.17 shows absorbance spectra from two samples of silicon-doped GaAs under pressure. Sample I I (80 μπι thick) had been irradiated with l M e V electrons. These form electronic levels in mid-gap which absorb all free carriers; as a result, the transformation of shallow donors to deep D X centers is suppressed. Sample I I at 35 kbar shows a single peak at 405 c m - 1 , characteristic of the shallow donor S i G a , silicon substituting for gallium. Sample 1U, not irradiated, shows the S i G a peak, and a second peak at 395 c m - 1 . By examining the latter under white light and under pressure, the authors identify it as the L V M of the D X center. A set of such measurements yields the plot displayed in Fig. 7.18, showing the local mode frequency versus pressure for the shallow donor and for the D X center. Both show the same slope, 0.61 c m - 1 kba r - 1 . The similarity of the dependence suggests a model where a substitutional donor becomes a D X center by breaking its bond with a nearest-neighbor arsenic atom and moving to an interstitial site. In this case, one of the possible

Impurities 179

0.00 » • • · ι I ι I 390 395 400 405 410


Fig. 7 .17 Absorbance from irradiated ( I I ) and unirradiated (1U) silicon-doped GaAs under pressure. The single peak at 405 c m - 1 for II is identified with a local vibrational mode ( L V M ) from the shallow donor Si G a . The new peak at 395 c m - 1 for 1U is identified with an L V M from the deep DX center. (After Wolk et al (1991a).)

resulting geometries would give a mode frequency near that of the original substitutional donor.

One of the most recent applications of infrared L V M modes is in the study of hydrogenated amorphous silicon (a-Si :H) , where they characterize hydrogen content, and eludicate the bonding configurations of the hydrogen. Hydrogen introduced into silicon at temperatures below 250 °C introduces extended planar defects along {111} crystallographic planes. Heyman et al (1992) examined hydrogenated silicon by FT-I R methods. They found that the hydrogen-induced platelets create four broad absorbance bands over 2000-2200 c m - 1 , which they connect to hydrogen-related stretching vibrations. They correlated hydrogen concentration with absorbance, and related the spectra to proposed structural models for the incorporated hydrogen. Langford et al (1992) focused on the relation between infrared absorption and hydrogen content. They claim to have improved previous calibrations by including interference effects important for thin films. They found several modes which give a convenient calibration for the concentration of hydrogen: for instance, the hydrogen concentration NH per cubic centimeter is given by (9.0 ± 0.1) χ 10 1 9 a 2 1 0 o , where α 2ιοο is the integrated absorbance in wavenumbers of the stretching mode at 2100 c m " 1 .


380 I . . . . ι • • • • » • • • • ' • • • ' » 0 10 20 30 40

Pressure (kbar)

Fig. 7 .18 L V M frequencies from the S i G a shallow donor and DX deep center seen in Fig. 7.17, versus pressure. The similarity in behavior suggests a model for the conversion of a donor to a DX center. See text. (After Wolk et al. (1991a).)

7.5 Free carriers: electronic properties

The conventional method of determining sample resistivity, carrier density, and mobility is by d.c. electrical measurements. The resistivity is measured directly, through a four-point method such as the van der Pauw technique. A measurement in a magnetic field yields the Hall constant, from which the carrier density can be extracted. This extraction of η is exact if all the scattering processes can be taken into account; otherwise it is approximate, with an error as large as 10-20%, depending on the material. Once η has been found, it is combined with the value of ρ to give the mobility μ.

There are some limitations to the electrical technique which are not shared by infrared analysis. My examination of the Drude model in Chapter 3 showed that if m* is known, η and μ can be found from infrared spectra. The resistivity ρ can be calculated even without knowledge of ra*. Either reflectance or transmittance may be measured. Reflectance spectra can be immediately analyzed, whereas transmittance data are not useful until converted into absorbance a, which depends on η and τ (equation (3.34)). But this conversion requires additional information (sample reflectance and thickness). Al so , back-surface polishing is sometimes needed. Transmittance measurements fail at high carrier densities, where the intensity becomes too low to measure. For these reasons, more reflectance work has been reported than transmittance work. Reflectance methods, however, are insensitive below approximately

Free carriers: electronic properties 181

1 0 1 6 c m - 3 for most semiconductors, whereas transmittance can measure concentrations as low as 1 0 1 4 c m - 3 . The infrared determination of η can be inverted: when η is known from another source such as a Hall measurement, ra* can be found from infrared data. I give case studies of all these applications.

Infrared transport behavior is simplest in silicon and germanium, for the reason I noted in Chapter 3: the free carriers appear without the complications of the lattice T O and L O modes. Work in bulk silicon and germanium appeared very early, when Spitzer and Fan (1957) measured their infrared reflectance. Later Subashiev et al. (1964) invoked the Drude model to analyze spectra of silicon over 3-15 μπι. They developed a calibration curve relating carrier densities of 10 1 8 to 1 0 2 0 c m - 3 to the infrared parameters. Kukharskii and Subashiev (1966) were perhaps the first to note that both η and μ can be found if ra * is known. They analyzed reflectance spectra from silicon between 400 and 5000 c m - 1 . Gaur (1970) examined plasma edge reflectance in silicon group I I I - V materials. From this he derived ra*, with results that confirmed the Drude model. One of the earlier infrared determinations of spatially varying carrier parameters was made in silicon when Gardner et al. (1966) showed how to find semiconductor surface concentrations from the infrared reflectivity. Bilenko et al. (1972) also examined spatial variation in silicon.

Barta (1977a,b) analyzed reflectance from n- and p-type silicon with different concentrations, between 30 and 1600cm - 1 . Her spectra showed plasmon effects, which gave valid results for ra*, confirming the Drude model for η-type samples. For p-silicon an additional term was needed. Vindevoghel et al. (1978) measured transmission through p-silicon over 2.5-400 c m - 1 . Below 60 c m " 1 Drude theory fit the data, but at higher frequencies they invoked interband transitions; Gopal (1979) used a frequency-dependent scattering time to explain the same high frequency results.

Other characterization of silicon followed. Engstrom (1980) examined p-silicon implanted with boron at levels of 1 0 1 4 - 1 0 1 6 c m " 2 , and laser annealed. H e measured reflectance and transmittance over 500-4000 c m - 1 , which he analyzed by Drude theory. His analysis included the variation of boron concentration with depth into the sample. Drude theory worked well, as shown by the quality of his fits to the data. He found that carrier scattering time was independent of the implant dose, and that the boron concentration varied linearly with dose.

More recently, Borghesi et al. (1985a) have thoroughly examined the infrared behavior of bulk silicon heavily doped with phosphorus and boron. The samples were (111) single crystal slices (1 in. diameter) grown by either floating zone or Czochralski methods. The dislocation density was low ( < 1 0 3 c m - 3 ) . The sample resistivities were determined by four-point probe, and converted into dopant densities using published calibrations. The reflectance spectra of the samples were measured by a commercial F T - I R system. The authors fit the spectra with the Drude model, modified to include averages over the energy-dependent scattering, although this is expected to make little difference (Perkowitz and Breecher, 1974; Perkowitz and Thorland, 1974).

I have shown in Fig. 3.14 the results of Borghesi et al. for phosphorus-doped n-silicon with η = 1.1 Χ 10 1 7 to 1.0 X 1 0 2 0 c m - 3 . Figure 7.19 shows spectra at room temperature for p-type boron-doped material, with ρ = 2.5 X 10 1 9 to 2.7 X 1 0 2 0 c m - 3 . Both the n- and the p-type spectra display the plasma edge. Drude theory gives good fits to the data. The authors treated η or ρ as given, and from their fits extracted values of the high-frequency dielectric constant ε ( ο ° ) , the scattering time τ , and the effective mass ra*. The dependence of ra* on impurity concentration followed theoretical


Wavenumber (cm 1 )

Wavelength (μπι)

Fig. 7 .19 Infrared reflectance at room temperature for boron-doped p-silicon with different carrier concentrations (indicated). The plasma edge appears and moves with concentration. Corresponding plots for phosphorus-doped η-silicon are shown in Fig. 3.14. (After Borghesi et al. (1985a).)

predictions to within 10%. This work demonstrates how infrared spectra with a simple model serve to thoroughly characterize silicon.

These authors noted that the same nondestructive method can work for ion-implanted samples. Borghesi et al. (1985b) used infrared methods to analyze silicon implanted with arsenic at high dose rates, which give complex damage behavior. The samples were (100) p-silicon wafers implanted with arsenic at 100 keV and fluences of 10 1 4 to 10 1 6 cm~ 2 . Rutherford backscattering gave evidence of amorphous layers, and damaged surface layers, depending on the dose rate. Ultraviolet-visible reflectance spectra over 230-500 nm also showed structure related to the damage. Infrared spectra were obtained near the plasma minimum, as can be seen in Fig. 7.20 for an as-implanted sample, and an implanted sample after laser annealing. Each curve shows plasma effects, but with different carrier parameters. The authors analyzed the data with the Drude model, taking into account the spatial distribution of arsenic shown in the figure. This yielded a valid result for the effective mass, and gave values for the scattering time in a surface amorphous layer and in the underlying crystalline region.

Geddo et al. (1985) have used a variant of the direct measurement of infrared reflectance to determine carrier density in η-type silicon epitaxial layers, grown on n +

or n~ silicon substrates. They point out the difficulties of conventional electrical measurements for the film-on-a-substrate configuration. A s an alternate approach, they note that the polarization properties of light reflected from the silicon film are related to the carrier density. For incoming unpolarized light, there is a particular angle of incidence, the Brewster angle θ#, such that the light reflected from a surface is fully polarized parallel to the surface. Geddo et al. derived the relation between Θ Β

and carrier density for carriers described by a Drude model.


0.8

8 0-6 c Β ο ω Φ ^ 0.4

0.2

0.0 1 10 100

Wavelength (μππ)

Fig. 7 .20 Infrared reflectance from silicon implanted with arsenic. ( ) Before annealing; ( ) after laser annealing. Analysis of change in the plasma edge, including the spatial distribution in the implanted arsenic (inset), gives parameters for a surface amorphous layer and the underlying crystalline region. (After Borghesi et al. (1985b).)

They applied this analysis to epitaxial layers 5-10 μηι thick on (100) Czochralski-grown silicon crystals, which were doped in the range 10 1 4 to 10 1 8 cm~ 3 . The films were grown by chemical vapor deposition. The measurement was made at a fixed wavelength of 10.53 μπι from a C 0 2 laser operating at 0.4 W . A t this wavelength, the penetration depth is less than the film thickness, so the influence of the substrate is unimportant. The polarized reflected power was measured versus angle of incidence, to give Θ Β . Figure 7.21 shows the results, comparing Θ Β with carrier density as deter-

101

10°

% io- 1

ΙΟ"2

10~3

1 0 1 6 1 0 1 7 1 0 1 8 10 1 9

Free carrier concentration ( cm - 3 ) Fig. 7.21 Change in the Brewster angle Δ 0 Β (relative to 0 B for a pure single crystal) versus carrier concentration for silicon. The line is the theoretical relation for η-type material. Individual points are data from epitaxial η-type films ( · ) , bulk η-type single crystal ( + ) , and bulk p-type single crystal ( Δ ) . Only the p-type result deviates significantly from theory. (After Geddo etal. (1985).)

Si : As


mined from a detailed analysis of electrical properties. The data follow the theoretical prediction for η-type silicon, deviating only for a p-type sample. The method is valid over 2 x 10 1 6 to about 1 0 1 9 c m - 3 . A b o v e 1 0 1 9 c m - 3 , the Brewster angle cannot be found so exactly and other techniques are better to determine n, but the authors comment that the technique can be extended to lower carrier densities at longer wavelengths.

Jevtic et al. (1985) have explicitly considered the infrared plasma minimum in silicon as a means to determine carrier concentration. Their self-consistent treatment relates the wavelength of the plasma minimum to the carrier density over the range 10 1 8 to 10 2 0 cm~ 3 , giving calibration curves for n- and p-silicon which agree with experiment.

GaAs and other group I I I - V compounds also have a long history of infrared measurement of free carrier properties. For instance, Edwards and Maker (1962) used the plasma edge to measure spatially inhomogeneous carrier concentration in In A s , observing variations as small as 0.5%. Moss et al. (1968) showed how reflectance data near the plasma edge could give η , τ and p, and displayed data between 220 and 2000 c m - 1 for GaAs . These are among the earliest spectra approaching the longer wavelengths where the Drude model is expected to hold. Black et al. (1970) found η and μ in 11 samples of GaAs by reflectance and transmittance measurements over 285-2000 c m - 1 . Their results agreed with Hall data to within 30% for η between 5 x 10 1 6 and 1 x 1 0 1 9 c m - 3 . They also produced a detailed two-dimensional map of η over a 1cm 2 wafer, showing the power of infrared methods to determine spatial information.

Plasma effects are more complicated in these binary materials than in silicon, because of the plasmon-phonon interaction discussed in Chapter 3. Perkowitz and Breecher (1973) were the first to exploit the plasmon-phonon coupling to determine η and μ from the coupled-mode minima at ω ± . This requires only a limited measurement rather than a full spectral analysis. T o determine the validity of the method, Perkowitz and Breecher examined a set of samples they had already analyzed by fitting the full spectrum. They presented a simple graphical method to relate the position and height of the plasmon-phonon minima to η and μ, shown in Fig. 7.22. This gave results within 4% of those from the fit, for η = 5 x 10 1 5 to 4 x 1 0 1 7 c m - 3 . Later Holm et al. (1977) published another version of the graphical method to extract η and μ. Sobotta (1970) also examined the plasma reflection of GaAs at 300 Κ between 70 and 260 c m - 1 . Tata and Arora (1984) have discussed an alternative way to use plasmon-phonon minima to determine n.

Others have also analyzed different aspects of infrared characterization of GaAs . Holm et al. (1977) measured reflectance over 80-600 c m - 1 . They found good agreement between infrared and Hall values of η and μ for bulk samples chemically polished with a bromine-methanol solution. With mechanical surface polishing, however (Holm and Palik, 1976), the reflectance changed, especially near the minima. This was interpreted in terms of a damaged layer with thickness comparable to the grit size, where η and μ changed. Holm et al. (1977) also determined carrier homogeneity in GaAs . They scanned the surface of a wafer to determine reflectance at 320 c m - 1 , chosen at the plasma edge. This gave a two-dimensional map of carrier concentration with a spatial resolution of 1-2 mm, showing variations from 6.4 x 10 1 7 to 7.3 x 1 0 1 7 c m - 3 .

Chandrasekhar and Ramdas (1980) determined effective mass in GaAs from the


0 I I I I I I I I I I Sj I I I I I I I I I I I I I I I 1 • 1 0 40 80 120 1160 200 240 280

(u_(crrf1)

Fig. 7 .22 Graphical method to determine carrier concentration and mobility in n-GaAs, from the lower coupled-mode frequency ω_ and the reflectance Rmin at that frequency. Curves A , B, C, etc., are lines of constant mobility, from 500 to 7500cm 2 (Vs) _ 1 . Curves 1, 2, 3, etc., are lines of constant carrier concentration, from 1 x 1015 to 101 9cm . The dashed lines show that a sample with Rmin = 0.2 and ω_ = 98cm" 1 has η = 7.5 x 10 1 6cm~ 3 and μ = 3500cm 2(Vs)" 1. (Perkowitz, unpublished data.)

infrared reflectance of samples with carrier densities of 1.8 x 10 1 6 to 7 x 10 1 8 cm~ 3 , as found by Hall measurements. A n F T - I R instrument gave reflectance data over 10-450 c m - 1 . Spectra were obtained at different locations on each sample and averaged, to reduce the influence of inhomogeneities. When the plasma frequencies from the spectra were combined with the carrier densities, the results were extremely accurate values of ra*/ra0 (average error ±0.001). The data showed that ra* is nonparabolic in GaAs at high carrier densities—that is, the quadratic energy dependence in equation (3.1) is not obeyed—and also displayed the temperature dependence of ra*. In a more recent example, Macler et al. (1992) used a similar method to report the first measurements of ra* in In^^Ga^Sb films for certain values of x.

Most of the infrared work I have described in G a A s was carried out in n-type material. Rheinlander et al. (1975) considered p-GaAs, with its much lower mobility. Despite the greater electronic damping, the authors could fit reflectance data with the Drude model, except for line shape deviations near the peak which they ascribed to surface effects. In the alternate method of transmittance spectroscopy, the absorbance is derived from measured values of Γ using equation (2.28) or (2.30). Then, according to equation (3.34), a plot of α versus ω - 2 should give a straight line, whose slope and y intercept define ω ρ and τ . A s an example, consider transmittance data obtained by Perkowitz (1971) from G a A s samples with η = 2.6 x 10 1 5 to 2.5 x 10 1 6 cm~ 3 ,


measured between 20 and 210 c m - 1 with an F T - I R instrument and a room-temperature detector. The reflectance needed to extract α from the transmittance was not measured, but calculated assuming only a lattice contribution, which was reasonable at these carrier densities. The free-carrier absorption is shown in Fig. 7.23. The values for η and μ obtained from these data agreed with values from electrical measurements to within 25%, comparable with the total experimental uncertainty.

Transmission spectroscopy has been used in other materials as well. Boone et al. (1985) showed that measurements of transmission through samples of CdS, over 850-1050 c m - 1 , could give free-carrier density with a sensitivity limit below 5 x 10 1 4cm - 3 . The absorption coefficient was found to be proportional to n, as expected. Infrared and Hall values for η differed by only 5% on average. Perkowitz (1985) examined high-purity CdTe and Cdn.96Zno.04Te substrate material in transmission between 10 and 60 c m - 1 at 300 K . Ten samples showed distinct differences in absorption. In the sample with the lowest absorption, the measured value came primarily from the T O phonon mode with weak added multiphonon effects, showing high sample purity. Excess absorption in the other samples could be correlated with their carrier densities, with a minimum detectable level of about 2 x 10 1 4cm " 3 .

5I 1 1 1 1—1—L—j—I 40 60 80 100 120 160 200

Wavenumber (cm - 1) Fig. 7 .23 Measured free carrier absorption a' in three GaAs samples with different carrier densities, at 77 and 300K. The lines are drawn with a slope corresponding to a' oc ω~2^ as predicted by equation (3.34). The data follow this prediction to yield valid free carrier parameters. See text. (After Perkowitz (1971).)

http://Cdn.96Zno.04Te


Reflectance work has also been carried out in group I I I - V ternary alloys. Kim and Spitzer (1979) examined the plasmon-coupling minimum for A ^ G a ^ ^ A s in order to observe the effect in an alloy material and to determine m*. Here the two main phonon modes of the alloy complicate the spectra, but free-carrier effects are apparent, as I have shown in Fig. 3.13. Kim and Spitzer found that the d.c. sample resistivities from the infrared data were about 30% greater than the electrically measured values. They thought this might reflect the partial failure of the Drude model over part of their wavenumber range (240-780 c m - 1 ) . Nevertheless, the agreement is sufficiently good to serve for rapid characterization. Maty as and Karoza (1982) analyzed the plasma edge in I n ^ A ^ A s , showing that the Drude model held at frequencies below 100 c m " 1 , although they made no comparison with d.c. results.

These methods have been extended to group I I - V I and I V - V I materials. I have already shown reflectance spectra from bulk CdTe (Perkowitz and Thorland, 1974) in Fig. 3.12, where the theoretical fit is good and yields values of carrier density in agreement with Hall data for ft = 1.4 x 10 1 7 to 1.3 x 1 0 1 8 c m - 3 . The analysis included a consideration of energy-averaged scattering times; this refinement did not substantially improve the fits or the validity of the fitting parameters. In the group I V - V I compound PbTe , Perkowitz (1975) showed that good infrared-Hall agreement occurred for η = 1.7 x 10 1 7 to 1.5 χ 1 0 1 8 c m - 3 . Group I V - V I alloys have also been treated. Pickering (1977) showed that p-type Pbo.79Sno.21Te obeyed the Drude result even at short wavelengths (10-16 μηι) , giving an absorption proportional to ηω~2 for η = 1.6 x 10 1 7 to 6.3 x 1 0 1 7 c m " 3 at 300 K . Kucherenko et al. (1977) made similar but extended observations in Pbx-^Sn^Se. Gopal (1978) has used the plasmon-phonon minima to analyze Pbi_j.Srij.Te. T o show the overall validity of the infrared analysis, Fig. 7.24 compares electrical and optical values of η for bulk samples of G a A s , PbTe , and CdTe with carrier densities of 10 1 6 to 1 0 1 9 c m - 3 .

Fig. 7 .24 Comparison of carrier density from infrared reflectance or transmittance, to values from standard electrical measurements, for bulk GaAs, CdTe, and PbTe. The line represents perfect agreement. Similar agreement is seen in comparisons of resistivity as determined from infrared and from standard electrical measurements. (Perkowitz, unpublished data.)

http://Pbo.79Sno.21Te

http://Pbi_j.Srij.Te


7.6 Layered systems

In this section, I discuss the use of infrared methods to examine layered systems, from an epitaxial film on a substrate, to complex multiple quantum wells and superlattices. The discussion is divided into two parts; the determination of layer thickness for epitaxial systems; and a full infrared analysis of multiple carrier, phonon, and thickness parameters, often on a layer-by-layer basis, for quantum wells and superlattices. It is important to recall that mid- to far-infrared radiation typically penetrates several micrometers, sufficient to probe one of these systems from front surface to back.

The same basic methods that worked to determine η and μ in bulk samples also apply in a layered system. In Chapter 3, I pointed out that analysis could be carried out by making a computer fit that considers each layer and interface in turn; or for a superlattice, by using the effective dielectric function 8 S L ( w ) defined by equation (3.39). I show examples of both approaches.

7.6.1 Layer thickness

In a semi-infinite or highly absorbing sample, light is reflected from the front surface only. In a thin or nonabsorbing film, light is also reflected from the back surface, if it adjoins a material with sufficiently different optical characteristics. This light re-emerges from the front surface, blending with the light directly reflected there to give interference effects. The basic equations for reflectance and transmittance as modulated by interference are given in Chapter 2. For a nonabsorbing film, the result given there for the spacing in wavenumbers between interference fringes is Δ / = 112nd, where d is layer thickness and η is the real part of the refractive index. For semiconductor films micrometers thick, this means that several fringes can be seen in the mid-to far-infrared range, and used to determine d.

Early work by Sato et al. (1966) displayed such fringes from a heterogeneous silicon structure. These workers examined the reflectance spectrum over 400-900cm - 1 from η-type epitaxial silicon layers up to 8 μπι thick, deposited on n +-silicon substrates heavily doped with arsenic to resistivities of 0.004-0.03 Ω-cm. The difference between doping levels was enough to make the substrate optically distinct from the layer. Hence light was reflected at their interface, yielding fringes. Sato et al. could fit the interference spectra, by assuming a diffused region rather than an abrupt change at the interface. This is a very early example of the use of infrared spectroscopy to determine interface conditions, as well as layer thickness.

Krishnan et al. (1990) review the use of infrared radiation to measure layer thickness in silicon systems, and motivate the value of such measurements. They point out that many silicon devices include an epitaxial layer grown at the same crystalline orientation as the substrate, but doped differently, as in the system examined by Sato et al. (1966). Device performance is contingent on leakage, breakdown voltage, and other quantities which depend critically on the epitaxial layer thickness. Hence nondestructive methods to determine this are important. Typically, although not always, the epitaxial layer is of high resistivity, grown on a low-resistivity substrate. Figure 7.25 shows such an arrangement. The lightly doped top layer transmits infrared radiation, to be reflected by the highly doped, highly reflecting substrate. That the resulting interference fringes have a spacing which depends inversely on the layer thickness is shown clearly in Fig. 7.26.

Layered systems 189

\ \ \ . IR source

7 / Phase 1

W W ρ >0.1 Ω-cm

DEP\ 1

Epilayer W W Phase 2 J #

Outdiffusion zone

"epi*3.42

Substrate ρ <0.01 Ω-cm

Fig. 7 .25 Typical epitaxial silicon structure, a lightly doped silicon layer on a heavily doped silicon substrate. At infrared wavelengths, the difference in refractive indices between the two is great enough to produce reflection at their interface. The multiply reflected rays produce interference fringes. (After Krishnan et al. (1990).)

0.3CM J j 1 1 1 1 1

1600 1400 1200 1000 800 600 Wavenumber ( c m 1 )

Fig. 7 .26 Interference fringes from three n/n+ silicon structures like that shown in Fig. 7.25, with layer thickness indicated. The fringe spacing varies inversely with thickness. These fringes are seen in absorbance derived from transmittance data. Reflectance fringes also occur. (After Krishnan et al. (1990).)


Analysis of such spectra according to the interference equations gives the layer thickness. The analysis has been put into routine form for silicon by Schumann and Schneider (1970) and Severin and Everstyn (1975), which requires only that the doping level of the substrate be known. Krishnan et al. offer an alternative method. A n epitaxial sample produces features in the interferogram recorded by an F T - I R spectrometer, which give layer thickness in a simple, direct way. In the interferogram, the usual central maximum at zero path difference is accompanied by paired side bursts. Each is separated from the central maximum by twice the distance the infrared beam travels through the epitaxial layer before encountering the substrate. The spacing of the side bursts is accurately known, because the movable mirror position is continually measured in an F T - I R system, often by counting fringes from a H e N e laser.

The effect is illustrated in Fig. 7.27. The top trace is the interferogram from an 8 μπι epitaxial silicon layer on an η + substrate. The central maximum and the symmetric side bursts are apparent. The middle trace comes from a 2 μπι epitaxial layer. The side bands have moved closer to the center, and are hard to distinguish from the central structure. The bottom trace is the difference between the top and the middle traces. Little evidence is left of the large peak at zero path difference, and the two sets of side bands—one from the 8 μπι layer, one from the 2 μπι layer—are now clear. Although some modifications of the analysis are needed for very thin and very thick epitaxial layers, this kind of measurement, it is claimed, yields accurate layer thickness in a short time.

Taroff et al. (1989) have analyzed fringes in group I I I - V systems. They note that any semiconductor is somewhat transparent at energies below its gap value. Commenting on the long history of infrared measurements in thin film silicon placed on

I.OH (1)

> 0.5H

Ε 0.0-

C

(3)

600 700 800 900 1000 1100 1200 1300 1400

Mirror travel (a.u.)

Fig. 7 .27 FT-IR reflectance interferograms from two n/n+ silicon structures like that shown in Fig. 7.25. Epitaxial layer thickness: (1) 8 μπι; (2) 2 μπι; (3) difference between (1) and (2). (After Krishnan et al. (1990).)

Layered systems 191

Edge" i3 .937 μιτι

t = 3.907 μιτι

4.083 μιτι

1.0 1.1 1.2 Wavenumber (μτη)

1.3 1.4

Fig. 7 .28 Infrared interference scans from an epitaxial GaAs film on silicon. Each dashed line joins the peaks from a given interference order. The shift of the peaks at a given order across the surface tracks variations in film thickness. The top, middle, and bottom scans correspond to the thicknesses indicated. The relative thickness from this scan is shown in Fig. 7.29. (After Taroff etal. (1989).)

silicon of different doping, they note that these are made primarily between 10 and 30 μπι. Only at these wavelengths is the optical difference between layer and substrate sufficient to cause reflection and hence interference. For true heterostructures, however, there can be large differences in optical properties between adjacent layers even at shorter wavelengths. For alloys based on G a A s and InP, sharp interference fringes can be seen in the range 0.6-2 μπι.

T o exploit this, the authors modified a near infrared P L spectrometer, adding capability to measure reflectance with a spot size of 35 μηι. A sample scanning facility was also added, to allow the mapping of thickness variations. Figure 7.28 shows a scan of a film of G a A s on a silicon substrate, made along tracks spaced 2 mm apart. The variation in thickness is apparent. Figure 7.29 shows that this nondestructive infrared measurement of thickness compares favorably with other techniques. The comparison is to a destructive mechanical method. Channels of G a A s , 100 μηι wide and spaced at 2 mm intervals, were removed by etching. The thickness of the G a A s was then determined by the D E K T A K ® method of stylus profilometry. T o illustrate that their thickness determination was also valid for a group I I I - V / I I I - V heterostructure, Taroff et al. compared their infrared measurement of epitaxial Alo.3Gao.7As on G a A s with results from a scanning electron microscope. The agreement was excellent. Macler et al. (1992) have seen similar good agreement between infrared and scanning electron microscope determinations of the thickness of In^^Ga^Sb layers on G a A s , as shown in Fig. 7.30.

Infrared methods can also determine the average thickness of the layers making up a superlattice. Each individual layer, generally nanometers thick, is too narrow to affect the infrared spectrum, but their aggregate effect in a superlattice with hundreds of layer pairs is like that from a micrometers-thick film, as I show in the next section.

http://Alo.3Gao.7As


ο Reflectance spectra

0 10 20 30 40 50 60 70 80

Position (mm)

Fig. 7 .29 Relative film thickness for the GaAs/silicon system shown in Fig. 7.28 versus position across the wafer. The infrared reflectance determination agrees with a surface profile obtained by a combination of etching and mechanical measurement, but is nondestructive. (After Taroff etal. (1989).)

0 . 0 0 . 5 1 . 0 1 . 5 2 . 0 2 . 5 3 . 0

THICKNESS FROM SEM PHOTOGRAPHS (jim) Fig. 7 .30 Comparison of thickness of In^Ga^Sb films on GaAs, as derived from infrared reflectance spectra and from scanning electron microscope (SEM) images. The line represents perfect agreement. (After Macler et al. (1992).)

Layered systems 193

7.6.2 Complete analysis

One of the early infrared analyses of a layered system which dealt with more than layer thickness comes from Tennant and Cape (1976), who studied free-carrier effects and interface behavior. They examined an 8 μιτι film of p-Pbo.88Sno.12Te with ρ — 1 0 1 6 c m - 3 , grown by L P E on p-Pbo.7sSno.22Te with ρ — 10 1 8 cm~ 3 . The data were taken at 300 and 77 Κ over 40-320 c m - 1 , using a Fourier spectrometer. A noteworthy feature was the small sample size, only 2 mm in diameter.

The film spectra were far more complex than what would be obtained from a bulk sample, because the film was transparent above 1 2 0 c m - 1 . The difference in optical properties was sufficient to give reflection at the interface. Hence interference fringes appeared, combined with free-carrier effects, as shown in Fig. 7.31. The spectra were first fitted with a two-layer model which assumed that each interface was abrupt, the dielectric function of each layer being taken from equation (3.31). This gave a good fit below 2 3 0 c m _ 1 (curve A in Fig. 7.31), and yielded a film thickness of 8μιτι, in agreement with the value from microscopic examination. But the fit above 230 c m - 1

was poor. Tennant and Cape improved the high frequency fit by including a continuous variation of the carrier concentration over the interface region, such as might occur from diffusion during or after growth. Three models for the grading were considered (curves Β and C in Fig. 7.31 show fits from two of them). A l l three improved the fit, indicated that the graded region was approximately 1 μηι thick, and gave the same film thickness of 8-9 μηι. The fits also gave a set of free-carrier

100,

Ol 1 1 1 0 100 200 300


Fig. 7 .31 Reflectance of a Pbo.ssSno.oTe film on a Pb 0 7 8Sn 0.22Te substrate. Plasma effects dominate below 120 c m - 1 , the upper coupled plasmon-phonon frequency, and interference fringes appear above 120 c m - 1 . The curves are fits using the following models: ( A ) two-layer, abrupt interface; (B) graded interface, linear variation; (C) graded interface, exponential variation. (After Tennant and Cape (1976).)

http://p-Pbo.88Sno.12Te

http://p-Pbo.7sSno.22Te


parameters for both layers, with small statistical errors. Although the large number of fitting parameters makes it difficult to reliably choose among the different spatial distributions, this analysis established the presence of grading and gave valid parameters.

Amirtharaj et al. (1977) made further extensive analysis of infrared spectra to obtain detailed information about layered systems. They examined three different film-substrate arrangements between 20 and 350 c m - 1 , using a commercial F T - I R system and an optically pumped laser for reflectance and transmittance spectra respectively. The systems were a 2 μπι film of PbSe on NaCl , a 25 μιη film of low concentration Pbo.79Sno.21Te on high concentration Pbo.79Sno.21Te, and a 17 μπι film of In A s on high-resistivity GaAs . These gave a gradation of complexity. For PbSe/ NaCl, the abrupt interface model should work very well, since diffusion is limited; and in fact the quality of the fits to the data were comparable with those for bulk material.

The other two systems were more complex. Neither could be entirely described by an abrupt model. The InAs/GaAs system was especially interesting. Analysis of the reflectance spectrum (Amirtharaj and Perkowitz, 1979) using a two-layer, abrupt-interface model returned far too high a carrier density of 10 1 6 cm~ 3 for the high-resistivity substrate. Moreover, the sample transmission was too high to originate from such a carrier density spread throughout the substrate. These results suggested that the carriers were narrowly localized near the film-substrate interface. The reflectance and transmittance spectra could be simultaneously fitted by assuming lattice and free carrier mixing at the interface, approximated as an additional transition layer. Analysis showed that this region consisted of I n ^ G a ^ ^ A s with thickness 0.7 μπι and η = 6 x 10 1 7 cm~ 3 . This analysis yielded parameter values consistent with Hall data, and results from Auger and energy-dispersive X-ray analysis by Wagner (1976).

Another study of group I I I - V epitaxial layers was made by Holm et al. (1977), who examined reflectivity from low concentration GaAs films on high concentration GaAs substrates. The films were grown by V P E and M B E in thicknesses of 0.3-3 μπι. The differenccce in carrier concentration was sufficient to optically differentiate film from substrate. The spectra yielded valid film concentrationns and thicknesses, and reasonable values of mobility for films thicker than approximately 105m. One film was scanned at a fixed frequency of 686 c m - 1 , giving a reflectance which could be connected with spatial variations of film thickness and plasma frequency.

Pickering (1986) examined the more complex epitaxial group I I I - V system Inx-^Ga^As^Sbi-y, grown by L P E on InAs and GaSb substrates. Hall measurements could not be used because the substrates were heavily doped. Instead, Drude analysis of reflectance spectra (see Fig. 7.32) between 100 and 500 c m " 1 established mobility versus mole fraction of antimony. The mobility increased sharply as y increased, which may be evidence that alloy scattering is less important in I n j ^ G a ^ A s ^ S b ^ than in I n ^ ^ G a ^ A s ^ P ^ .

Other thin-film systems have been analyzed as well. Perkowitz (1985, 1986) has examined epitaxial layers of Hg!_^Cd x Te . Figure 7.33 shows measured and fitted reflectance for two H g j ^ C d / T e films on CdTe substrates. Sample A A is η-type and D D is of unknown type. The 120 c m - 1 peak for sample A A comes from the HgTe-like T O lattice resonance; the small 1 5 0 c m - 1 peak represents CdTe or CdTe-like modes; and the peak at 170 c m - 1 is an interference fringe. The rising reflectance below 9 0 c m - 1 comes from free carriers. In sample D D , the shift to higher frequency and broadening of the main peak are clear evidence of a larger χ value than in A A .



Layered systems 195

100 200 300

Wavenumber ( cm - 1 )

Fig. 7 .32 Reflectance spectrum from an Ino.1Gao.9Aso.15Sbo.85 film with η = 1.5 x 10 1 7cm" 3 on an n + In As substrate. Free carrier, phonon, and interference features appear and are accommodated in the fits using Lorentzian and Drude theories from Chapter 3. (After Pickering (1986).)

101 1 1 ' 1 1

50 100 150 200 Wavenumber (cm - 1 )

Fig. 7.33 Measured ( · ) and fitted ( ) infrared reflectance at room temperature for films of Hg!_ xCd xTe on CdTe. The fits come from equation (3.31) applied to the film and to the substrate. (After Perkowitz (1985).)

http://Ino.1Gao.9Aso.15Sbo.85


1.0 71

Ε ο à

Œ Α.

0.001

0.01 U

0.1

. . . . I

0.01 ι ι ι ι ι η i l

0.1

PHall ( Q ~ c m )

» I I l l l l 0.001 1.0

Fig. 7 .34 Comparison of infrared ( P I R ) and electrical values (PHAII) for d.c. resistivity of n- and p-type Hg^CÔyTe/CdTe films several micrometers thick, with χ = 0.2 to 0.4. 'Full IR spectral fit' points come from fits to the entire spectrum over 20-230 c m - 1 . 'Fit using only first minimum' points come from analysis of the plasmon-phonon minimum. ( ) Perfect agreement. (After Jones etal. (1986).)

The figure shows that equation (3.31), applied to the film and to the substrate, gives a good fit to the data. The fits yield thickness, η, μ, ρ and χ value for the film. Similar measurements on 12 n- and p-type H g i ^ C d ^ T e films show good correlation between resistivity values from the infrared data, and those obtained by conventional electrical measurements, as displayed in Fig. 7.34. The agreement is sufficiently good to serve for rapid characterization with minimal sample preparation. Group I V - V I semiconductor films have been examined as well. Burkhard et al. (1976) obtained the reflectance of PbTe layers 1-27 μηι thick, on NaCl substrates. They determined that the Drude model described the data, with minor adjustments.

The most complex systems yet studied are semiconductor microstructures. One early infrared analysis was made by Holm and Calviello (1979). They examined systems designed for use in varactors and mixed diodes, consisting of an active n-type GaAs layer approximately 1 μηι thick on an n + - G a A s buffer which lay in turn on an η + - G a A s substrate. These structures were made by V P E . The authors obtained good fits to reflectance spectra over 100-800 c m - 1 , using Drude theory and a three layer model. In one case a fourth layer had to be added to account for interface effects. Layer thickness and layer-by-layer carrier concentration determined from the infrared analysis agreed well with other methods of evaluation, although the infrared fits alone were not definitive, because so many parameters were varied. Some prior estimates, from electrical measurements and auxiliary thickness measurements, were needed.

Another early example of infrared analysis of a complex microstructure comes from Durschlag and DeTemple (1981), who examined singles quantum wells of GaAs buried between A l ^ G a ^ ^ A s layers. They measured reflectance over 100-400 c m - 1

Layered systems 197

Substrate

I CC

200 300


400

Fig. 7 .35 Single GaAs quantum well 20 nm wide under 0.3 μπι of A l ^ G a ^ A s , and the reflectance spectrum of the structure. ( ) Theoretical fit using bulk phonon values. The improved fit ( ) comes from modified phonon values which may be related to effects at the layer interfaces. (After Durschlag and De Temple (1981).)

using an F T - I R spectrometer. The well structure and its reflectance spectrum are shown in Fig. 7.35. These fits give phonon and carrier parameters for wells as thin as 8nm, below A l ^ G a ^ ^ A s layers 0.3 μπι thick, showing how penetrating infrared radiation probes interior parts of microstructures.

Sudharsanan et al. (1988) analyzed A l A s - G a A s superlattices, using the effective superlattice dielectric function 8 S L ( a ) ) . Figure 7.36 shows an infrared reflectance spectrum from a superlattice with 100 layer pairs. These structures had low carrier densities and no free-carrier features appear. The main features are a T O phonon peak from each material, interference fringes, and longitudinal-mode minima. The minima are sensitive to layer thickness, because they appear where e S L ( o ) ) = 0. According to equation (3.39), the frequency at which this occurs depends on the ratio of layer thickness dGaAJdAXAs. The fit to the entire spectrum, and the positions of the interference fringes, depend on dGaAs and dA\As separately. Hence a fit to the data, using equation (3.31) for each layer with known parameters for A l A s and G a A s , fits the


1.0


Fig. 7 .36 Infrared reflectance from an AlAs-GaAs superlattice with 100 layer pairs. Individual points, data. TO maxima, LO minima, and interference fringes (denoted by F) are indicated. The best-fit curve uses known phonon parameters for GaAs and AlAs, and thickness dA]As = 7.5 nm and dGaAs = 8.2 nm. Fits with other thickness diverged at the fringes and the LO minima. See text. (After Sudharsanan etal. (1988).)

main spectral features and determines layer thickness, giving values that agree with X -ray analysis to within experimental error. This is an example of the determination of layer thickness when a sufficient number of thin layers is available.

This analysis by Sudharsanan et al. (1988) was one of the first confirmations that the effective medium model leading to e S L ( a ) ) as defined in equation (3.39) is valid in the far infrared. The reliability of this model was further established by the work of Lou et ai. (1988). This report did not give explicit characterization data for the A l A s - G a A s superlattice which it investigated, but did show that the model correctly described the uniaxial nature of the superlattice optical response to light at oblique incidence, and its behavior under polarized light. Dumelow et al. (1990) have also examined the infrared bulk and surface properties of long-period A l ^ G a x - ^ A s - G a A s superlattices and short-period G a A s - A l A s systems. They find that the former can be described by an effective medium model, as shown in Fig. 7.37, whereas the latter require a more detailed approach which includes the effects of confined optic phonons, as derived by Chu and Chang (1988). This added effort leads to good fits to the data, as shown in Fig. 7.38.

Far infrared work in other quantum well or superlattice structures is still limited. Perkowitz et al. (1986) and Perkowitz et al. (1987a) examined a group I I - V I system, the H g T e - C d T e superlattice. This artificial material offers gap tunability like the alloy Hg i -^Cd^Te , with potential advantages in reproducibility and stability. However , a crucial question is whether such MBE-grown structures contain well-defined layers of H g T e and CdTe , or whether interdiffusion at the interfaces or other mixing processes degrade them. Because H g T e , CdTe , and Hgi -^Cd^Te have infrared lattice modes, reflectance spectra can address this question. Figure 7.39 shows spectra for two

Layered systems 199

0.0-4 1 1 1 1 1 1 1 1

225 250 275 300 i 325 350 375 400 Wavenumber (cm - 1 )

Fig. 7 .37 Measured ( ) and calculated ( ) spectra at 77 Κ of a superlattice structure (inset). Regions 1 and 3: Alo.35Gao.65As. Region 2: superlattice, with 60 periods of 5.5 nm GaAs and 17 nm Alo.35Gao.65As. Region 4: GaAs substrate. Data obtained at an incident angle of 22°, in ρ polarization. Interference fringes in the substrate appear below 250 cm" 1 and above 376 c m - 1 . The fit uses the effective medium theory which leads to a superlattice dielectric function (equation (3.39)). (After Dumelow et al (1990).)

260 270 280 290 300 310 260 270 280 290 300 310

Wavenumber (cm 1 )

Fig. 7 .38 Measured ( ) and calculated ( ) spectra at 77 Κ for a GaAs/AlAs superlattice with six monolayers in each layer. The radiation was incident at a 45° angle, (a) s Polarization; (b) ρ polarization. Confined modes used in the calculations are marked. See text. (After Dumelow etal (1990).)

H g T e - C d T e superlattices, obtained with an F T - I R spectrometer. The data were taken at resolutions of 1-2 c m - 1 to display small structure. Virtually all the peaks come from phonons in H g T e , CdTe , and H g ^ C d / T e layers. The data were analyzed with an e S L ( a ) ) constructed to allow mercury to enter into what should have been pure CdTe regions. The resulting fits reproduce many of the observed features. This analysis made it possible to distinguish virtually ideal superlattices, with pure layers of

http://Alo.35Gao.65As

http://Alo.35Gao.65As


Wavenumber ( c m - 1 )

Fig. 7 .39 Measured ( · ) and fitted ( ) reflectance spectra from two nominal HgTe/CdTe superlattices. The main peaks at 118 and 155 cm" 1 are HgTe and CdTe TO modes. The fits, which reproduce most of the fine structure, come from a superlattice dielectric function e S L

incorporating H g ^ C d / T e regions. The split peak at 118 c m - 1 for sample BMCCT1 comes because it includes two superlattice structures with different stress. (After Perkowitz et al. (1986).)

H g T e and CdTe , from degraded structures like those shown, which are H g T e -H g ^ C d / T e superlattices with χ = 0.6 to 0.8. Other infrared work in the H g T e - C d T e superlattice, by Perkowitz et al. (1989), and Kim et al. (1990), have yielded carrier density, effective mass, and the controversial valence band offset in this complex system.

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