The theoretical fundamentals
for the calculation
of the local cathodoluminescence (CL) signal and electron beam induced
current (EBIC) in the scanning electron microscope (SEM) are outlined.
Especially, the simulation of the signal contrast profile behavior of
individual
dislocation configurations is reviewed. Existing analytical models and
new numerical approaches are summarized.

Besides the evaluation of material
parameters, the
conception of combined SEM-CL/EBIC is applied for the quantitative
experimental
characterization of single defects in grown-in, misfit as well as glide
dislocation structures with respect to their recombination activity in
various III-V semiconductors. Recent CL data from dislocations in GaP,
GaAs, and CdTe in the low-temperature range are analyzed in the
framework
of temperature-dependent defect-related recombination kinetics.

During the last decades,
scanning electron microscopy
(SEM) has been developed towards a standard experimental method to
obtain
images from a large variety of materials. In semiconductor
characterization
and research, the investigation of local electronic and optical
properties
is of vital importance for problems ranging from micro- and
optoelectronic
materials, devices, and quantum structures to solar cells. Here, both
cathodoluminescence
(CL) and electron beam induced current (EBIC) mode have been
successfully
applied [1,3,4,25,50,59,74]
since they allow access to a defined specimen bulk region due to the
beam-induced
creation of electron-hole pairs. Besides the very important aspect of *imaging*
and identification of particular features (electrically and optically
active
dislocations, precipitates, stacking faults, microdefects etc.) with
high
lateral resolution, *combined* SEM-CL/EBIC offers the
possibility
to determine reliable *quantitative* information on
relevant local
electronic and optical material parameters [39]
and, especially, the recombination behavior at individual defects such
as dislocations [62].
This
purpose, however, requires an accurate simulation of the signals as a
function
of these parameters. The corresponding equations must also be related
to
the carrier recombination processes at the defect. Although this is a
complex
task in general, it may be largely simplified in many practical cases
or
even performed analytically. The appropriate model functions are then
fitted
to the experimental data, and the material parameter values are
derived.

If we follow a strategic scheme for
performing quantitative
SEM-CL/EBIC investigations such as that given in
Table
1, it is possible to obtain important information about the
electronic
properties and defect recombination activity which are significant for
the treatment of many semiconductor defect physics problems. The sui
tability
of the given strategy will be demonstrated by several theoretical and
experimental
examples in this paper. Some aspects of this scheme should be
emphasized
at this point. Investigations of the semiconductor matrix properties
are
a necessary prerequisite for the quantitative study of defects and
their
electrical activity. Under these conditions, a complete set of matrix
and
defect parameters may be obtained from combined CL/EBIC measurements.
This
requires, however, comprehensive simulation models on one hand and
information
about the structure and configuration of the extended defects on the
other.
The knowledge about the carrier recombination processes is important
for
a correct interpretation of the experiments. While bulk recombination
paths
in semiconductors are generally known, the identification of the defect
recombination mechanisms is a primary aim of these studies. Especially,
the temperature dependence of dislocation recombination and the
recombination
kinetics when state occupation is changed by varying the injection
level
should be correlated with structural details such as the interaction
with
point defects and models about electronic states in the dislocation
core
and the surrounding region.

In this paper, we will restrict
ourselves to an
outline of the theoretical fundamentals for basic defect geometries
such
as a single dislocation in a thick epilayer or bulk sample with the aim
of a *quantitative* experimental evaluation of
corresponding model
defect systems by *combined* CL and EBIC. We will
follow the widely
accepted generalized theoretical conception by Donolato, Pasemann, and
Hergert [11,14,21,28,45,47,49].
The large variety of results from mainly qualitative investigations
using
CL or EBIC, detailed calculations for particular geometries as well as
special aspects concerning quantum structures, devices or
instrumentation
are largely beyond the scope of our review. The interested reader is
referred
to some of the reviews cited above.

Figure
1 contains schematically the various carrier and photonic
processes
occurring in CL and EBIC experiments in the SEM. The carrier behavior
is
primarily represented by the electron-hole pair generation distribution
*g*(** r**), the
minority carrier diffusion length ,
and the radiative and non-radiative bulk lifetimes

For the generation rate, various models have been used in the literature. For the given partial differential equation of Helmholtz type, a delta-function point source leads to the determination of Green's function

Finally, by choosing the appropriate light generation function, the considerations of this paper may be readily applied to light beam induced current (LBIC) and photoluminescence (PL) which might be very useful in view of the recent progress in scanning PL investigations of dislocations [68].

In order to perform an EBIC experiment, the sample must contain a potential barrier to separate the generated electron-hole pairs such as the surface Schottky barrier of Figure 1 or a p-n junction so that the major part of the EBIC signal is given by the diffusion current towards the edge of the depletion region

The spectral CL signal (photon flux leaving the sample surface) collected by an ideal spectrometer [22]

An important advantage for the calculation of the matrix signals from a defect-free region was the introduction of a unified formalism [21] being valid for all sample geometries with rotational symmetry. Induced current and luminescence signals are expressed in terms of a universal function describing the specific exponential losses by diffusion or absorption and the effect of an

In connection with the calculation of the matrix signals using the unified formalism, the concept of information depth

For comprehensive studies on the formation of the defect contrast from dislocations it is necessary to take into account the intrinsic nature of dislocation recombination, effects due to interaction with surrounding point defects as well as geometric contrast factors. Generally, defects are supposed to change the local recombination properties of the sample. Hence, their electric activity resulting in a recombination contrast has to be considered with respect to bulk recombination rates. The knowledge of matrix signals and corresponding parameters is therefore a general requirement for a quantitative analysis of the defect contrast. In our fundamental considerations we will mainly refer to the model case of a surface-parallel dislocation applicable for many both misfit and glide dislocation geometries (Figure 2). Beyond the basic configurations of single surface-parallel or -perpendicular dislocation lines, the large variety of possible situations such as inclined, curved, or composed defect features should be the subject of numerical modelling (cf. below).

In the

It is noted that in the alternative "surface" recombination model [34] the dislocation is represented by a recombination velocity at the cylinder boundary instead. This model may yield partly analogous results as the VRM, however, it will deviate if defect and generation region overlap each other - a common experimental situation - since this would result in an unrealistic 100 % contrast contribution from this region. These difficulties could be overcome by the introduction of an "effective" radius [34].

A defect

The CL defect contrast has been derived [49,59] as

Obviously, the central task of the contrast calculation is the determination of the carrier density

In

Finally, we can see from (12 a) and (12 b) that for

For a surface-perpendicular dislocation, the theorem of reciprocity allows a rigorous calculation of

Results of simulations of the
matrix signals *I*_{0}* ^{EBIC}*
and

CL and EBIC dislocation contrasts show a characteristic behavior as a function of the beam voltage. The typical behavior for a surface-parallel dislocation is illustrated in Figure 3. Since the contrast value is strongly influenced by geometric factors such as generation range

An example for the influence of the matrix parameters on the contrast profiles is shown in Figure 4. It is seen that a variation of the bulk diffusion length results in rapid changes in maximum contrast and profile half-width predominantly in the range

We expect from (12 a) that may be obtained from a comparison of the experimental contrast and the theoretical profile function which can be calculated if the other parameters are given. However, the defect strength determined in this way cannot grow arbitrarily high. Even if a defect is considered as a "black sphere" (' = 0), the contrast will not range above a saturation value [14] due to the defect-induced local reduction of

It is thus concluded that has to be generally interpreted as a

During the last years, increased efforts have been made to develop

In the framework of the above given model, arbitrary defect and sample geometries may be treated by a finite difference scheme. A first result for the numerical simulation of

Despite of the fast advances in available computing capacity, a full numerical treatment of the spatial carrier behavior still needs high memory and time requirements. The general problem of the solution of the coupled basic electronic and transport equations is rather extensive and closely related to complex tasks in device simulation [36,64]. We conclude here that these methods exhibit a big potential, however, it should be considered which cases really require a numerical treatment. The symmetry of the problem as well as the fact that the calculation of the contrast (10) requires

For the performance of CL and
EBIC experiments, the
SEM should permit a beam voltage variation from below 1 kV up to high
values
of at least 40 kV. The range between 40 and 50 kV which is accessible
using
our SEM Tesla BS 300 is, however, hardly offered by commercial
suppliers
today. The electron gun (preferably LaB_{6}
cathode) and optics
must be able to supply small stable beam currents to ensure low
injection
conditions with beam powers of *U _{b} I_{b}*
<
20 µW over the whole

Samples are epitaxial and bulk material of (001) or (111) orientation. For glide dislocation generation, plastic microdeformation is achieved by Vickers indentation at room temperature with typically 0.05 to 0.4 N load to activate the principal {111}<110> glide systems. For GaAs, it is followed by a thermal treatment of 15 min at 400 °C. The qualititative characterization of the defect configuration is performed by means of crystallographic considerations of the dislocation rosette geometry or by TEM investigations. Semitransparent Au Schottky contacts on n-type III-V sample surfaces are produced by vacuum evaporation using standard preparation methods. For ohmic contacts, an Au-Ge eutectic on the sample backside is annealed at 350 °C for 10 min.

It has been demonstrated in a
number of papers how
material parameters such as *L*, ,
and *Q* in compound semiconductors can be determined
from fits to
EBIC and CL data of homogeneous sample regions based on the results of
the theoretical simulation. In order to investigate the recombination
mechanisms
in optoelectronic materials, the parameter variation with doping level
in bulk n-GaAs (*n*_{0} = 7 · 10^{16}
to 3
· 10^{18} cm^{-3}) [39,55]
and GaAsP was studied using EBIC and *panchromatic*
CL. The diffusion
length *L*(*n*_{0})
does not always show a systematic
doping dependence. However, because of * _{r
}*~

More detailed information about material properties may be derived from

For the quantitative investigation of single defects, the conception of combined beam-voltage dependent CL and EBIC contrast profile measurements has been successfully applied to dislocations in GaAs, GaP, and GaAsP by the authors [59,60,61,62]. Other workers [32,33] have also investigated either

A comparison of CL defect contrasts from an edge-type misfit dislocation in GaAs

Representative defect strength results are compiled in Table 2. A wide range of values is obtained from experiments on various dislocation configurations. It should be noted that data intervals given in the table do not represent the experimental or analysis error but indicate the variation along a dislocation line or on several dislocations in a sample. This reveals the influence of the interaction or decoration with point defects as well as others factors such as inhomogeneous bulk doping. Especially, a large local variation is found for dislocations introduced by Zn diffusion/thermal stress in p-GaAs. Furthermore, the data clearly confirm the typical occurrence of smaller defect strengths < 0.95 of fresh glide screw dislocations compared to grown-in, weakly decorated misfit dislocations ( > 1.26) in the direct gap III-V materials GaAs and GaAsP. values for glide dislocations in GaAs:Si calculated from [69,72] agree well with our results although these results were obtained on a different geometric configuration. They also show the trend of somewhat higher recombination activity for an glide dislocation. Several authors [19,65,72] found a slightly stronger CL contrast on - than on ß-dislocations in n-GaAs and vice versa in p-type material. Conclusions were drawn concerning the defect-related electronic gap states for these dislocation types. Only relative recombination activity data were given. Recently, essential differences in the recombination activity of polar glide dislocations have been observed in CdTe [40,63]. There, dislocations show a localized, defect-related sub-band-gap CL radiation at low temperatures whereas ß dislocations are characterized by the usual non-radiative recombination contrast. Since absolute values are available from a small number of papers only, further systematic and comparable defect strength measurements remain a current task of combined CL/EBIC experiments.

New and more detailed insight into the defect recombination mechanisms are expected from temperature-dependent contrast experiments [19,65], especially in the low-temperature region below

Figure 10 (a) shows typical results of CL contrast measurements as a function of temperature from a surface-parallel misfit dislocation in n-GaP. Contrasts of dislocations perpendicular to the surface behave essentially in the same way. It is seen that as the dark contrast varies rather little with temperature above 70 K, it diminishes quickly below 50 K. In this material the bulk diffusion length

On the other hand, on GaAs the observed defect contrast behavior hints at a more complicated correlation between the temperature dependence of dislocation recombination activity and the effect of altered material parameters. Measurements of an individual threading dislocation contrast in the branch of a microindentation glide rosette show a CL contrast increasing only slightly by 3 % between 300 and 5 K (Figure 11) (see also [17,19]). Since the diffusion length in GaAs is a strong function of temperature, this effect alone would cause a rapid change in contrast (cf. the theoretical example of Figure 4). Indeed, we also observed a clear increase in the contrast profile half-width from 2.7 µm at

The results emphasize the relevance of a comprehensive contrast model with inclusion of all material and geometry parameters. This will allow us to combine the straightforward recombination-kinetic analysis with the spatial modelling of the carrier behavior as performed earlier for the room temperature experiments.

The importance of combined
SEM-CL/EBIC investigations
for the identification and quantitative characterization of
recombination-active
individual defects in compound semiconductors has been demonstrated.
New
developments such as advanced realistic analytical and numerical
modelling
of the defect contrast and investigations in the low-temperature range
have been illustrated. The detailed interpretation of derived defect
and
recombination strength values and the temperature dependence of the
material
and defect recombination rates remains a challenge in future
investigations.
For experimental defect studies, the defined preparation of clean or
decorated
dislocation configurations is a major issue. SEM injection conditions,
especially in the low-injection regime, should be carefully considered
since it is known that both bulk and defect parameters may be
influenced
by the carrier injection level and density [2,68,71].

Renewed interest is directed to effects
of defect-related
*radiative* recombination as it has been observed in
recent experiments
on polar glide dislocations in CdTe at temperatures below 100 K where
it
gives rise to bright CL contrasts originating from the Te(g) segments [40,63].
An activation energy of 11 meV for the defect emission determined from
the temperature dependence of the local CL spectra is well described by
defect-bound excitonic recombination [30].
A further structural and quantitative analysis is in progress.

Finally, other EBIC contrast mechanisms
not discussed
here such as charge separation at the potential barrier of a charged
dislocation
connected with one-dimensional conduction along the dislocation line [2,17,26]
may also be taken into account, especially at low temperatures.

This work was partially supported by the research grant no. 1557A0024 from the Ministerium für Wissenschaft und Forschung des Landes Sachsen-Anhalt and a PROCOPE project support no. 312/pro-gg from the Deutscher Akademischer Austauschdienst.

**T. Sekiguchi**: As for the experimental point
of view, the excitation
energy (*E*) dependence is somewhat ambiguous. It
comes from the different
behavior of total number of generated carriers and their density on the
excitation energy (*E*). If we accept the uniform
generation sphere
model and the generation radius is proportional to *E*^{1.75},
the excess carrier density is proportional to *E*^{-4.25},
while total number of excess carriers to *E*. Which
parameter is required
to be constant, the density or the total number of generated carriers?

Please suggest us how experimental
procedure should
be done.

**Authors**: From a physical perspective, the
experiments should
be performed at a small constant excess carrier density in the low
injection
range at the defect or in the sample region to be investigated.
However,
the exact evaluation of the excitation level inside the sample is not
straightforward.
Values for the carrier density *q *calculated on the
basis of simplified
generation models can only be a rough estimate. *q*(** r**)
may vary by several orders of magnitude over

Experimentally, the validity of the low injection regime should be proved

**T. Sekiguchi:** Do you have some idea about
the value of
and the physical parameter of dislocation? (
Table
2)

**Authors:** As the defect strength
is given in first order approximation by (13),
it depends on the ratio of /* _{D}*
of lifetimes for defect and matrix recombination paths as well as on
the
dislocation radius

**J C H Phang:** It has been shown in [75]
that various semiconductor parameters may be extracted entirely from CL
experimental data by varying the incident beam energy. Is it necessary
to use both CL and EBIC data to determine the parameters as suggested
in
Table
1?

**Authors:** The correlation of *L*
and
in the *U _{b}* dependence of the
CL matrix signal means that
the global minimum of the sum of least squares in parameter space is a
very shallow one. You have demonstrated that it may still be possible
to
find this minimum by using sophisticated and extensive minimization
techniques.
However, it is doubtful if this can be achieved for any limited set of
realistic data couples with both statistical and systematic errors. For
example, it is possible to fit the data in Fig. 8 of [75]
using