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Detection of defects

We've seen a lot of defect data on the previous pages, but how do you actually measure them? Various methods have been applied over the years, including photo-conductivity, photoluminescence, field effects in junctions, deep level transient spectroscopy (DLTS), and various others. Most of them are indirect which means that they require some interpretation, or they need special device configurations. Below are two rather direct methods that have been used successfully and consistently throughout the literature.

Electron spin resonance

Unpaired electrons in broken silicon bonds should exhibit an eletron spin resonance (ESR). Haneman showed this effect for crystalline silicon surfaces that were cleaved in vacuum [Haneman-1968pr]. Because the density of dangling bonds is known for various surface orientations, their densities allow the calibraton of the signal strength. Later, Brodsky found a similar ESR signal in various amorphous materials like silicon, germanium and silicon carbide which had been sputtered or evaporated [Brodsky-1969prl]. The density of spins was in the range of 10¹⁹ to 10²⁰ cm^-3 which is obviously too high for dangling bonds sitting at the surface, they were thus attributed to dangling bonds within the material.

Note that the ESR method cannot be applied to doped samples. As we have seen in the previous section, doping creates charged defects, they are thus either empty (positive defect) or doubly charged (negative defect). In both cases, there is no unpaired spin associated with the defect. ESR can be used to detect charged defects when they are excited by an additonal light pulse that promotes a charge carrier into a band (light induced ESR, LESR). In case of negative defects one electron is excited into the valence band where it eventually gets trapped. Both, the trapped electron and and the neutral defect with its single occupation contribute to the signal. Total defect densities are difficult to evaluate with this method because the trapped charge will eventually recombine.

Sub gap absorption

Defects are responsible for the absorption of light with energy below the band gap. The graph below shows the absorption coefficient of a-Si:H in a wide spectral range. The dashed line illustrates the theoretical absorption of an indirect band gap of 1.7 eV which should naturally drop to zero. Instead, there is a remaining absorption in real a-Si:H with two distinct regions; directly below the gap there is an exponential part which is due to the band edge signature of the Urbach tails. Its slope relates quite directly to the valence band tail, only its magnitude depends on both, the valence- and the conduction band shape [Redfield-1982ssc]. At yet lower energy, we find again a deviation; the absorption remains considerably above the exponential tail, and this difference is generally attributed to defect absorption.

Absorption coefficient of amorphous silicon. The dashed line illustrates an indirect band gap of 1.7 eV, the full blue line represents idealized material, the black lines are actually measured data with a remaining contribution of interference fringes due to sample thickness.

Looking at the numerical values of the absorption coefficient, we note that they are quite low in the defect region. Let's illustrate a value of about 1 cm^-1 by plugging it into the absorption law of Lambert and Beer; a typical sample thickness of hundred nanometers will absorb only an amount of 1-e^-0.00001 or 10^-5 of its intial intensity. Measuring absorption at this level required the development of sensitive methods like PDS or CPM. The former is short for photothermal deflection spectroscopy and uses an effect you may have noticed by the flickering of distant objects when seen above a hot surface, say the hood of a car on a sunny day. For a measurement a sample is immersed into a liquid whose refractive index changes with temperature, normally CF₄, and a laser is aligned parallel to the surface as close as possible above the film. Then, the sample is illuminated with monochromated light of the desired wavelength. Absorbed light heats the film and eventually the liquid next to the film, resulting in a measurable deflection of the grazing laser light [Boccara-1980apl]. Obvously such a measurement uses chopped light and lock-in detection for high sensitivity. The second method is called constant photocurrent measurement; it requires the deposition of electric contacts on the film; then, photocarriers that are excited again by monochromated light are extracted by a bias voltage. In order to establish the same occupancy of states during the measurement, the light intensity must be adjusted for a constant photocurrent [Vanecek-1981ssc]. The method was later modified by using the sample as detector in the external port of an IR spectrometer and is called FTPS (Fourier transform photocurrent spectroscopy) [Vanecek-2002apl]. Compated to CPM, FTPS is a much faster measurement, in fact the wavelength sweep may be too rapid for long-lived trap states in a-Si:H and thus cause difficulties with transient effects.

Jackson presented a calibration of the absorption signal with defect densities measured by ESR and proposed to assess the defect contribution by an integral over the area between the measured absorption coefficient and the exponential background of the underlying Urbach tail [Jackson-1982prb]. Wyrsch argued that the calibration can also be carried out with the value at 1.2 eV [Wyrsch-1991jncs]. The calibration curve is illustrated by the line in the graph below.

Defect density vs. absorption coefficient for a variety of samples, including doped material. Triangles: [Jackson-1982prb], Squares [Wyrsch-1991jncs].

Note that PDS measures the heat generated by the recombination of all transitions taking place from occupied to unoccupied states, including those from a defect into immobile tail states. CPM measures only transitions that promote carriers into mobile band states, but in undoped material the photocurrent is dominated by electrons because of the poor hole mobility [Vanecek-1995jap]. A big advantage of CPM and PDS over electron spin resonance is the applicability to doped films.

Recently it has been suggested that there are actually different types of defects with varying absorption strength. They can be deconvoluted into contributions below 1.1 eV and another signature that is typically found between 1.24 and 1.3 eV [Stradins-2002jncs]. See the separate section on defect types.

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Last updated August 20th, 2010