Basic Principles of Optical Beam Induced Current Method

An account is given here of the phenomenological theories that concern the quantitative evaluation of image properties in electron beam induced current (EBIC) [36, 37] mode of scanning electron microscopy (SEM) and optical beam induced current (OBIC) [38, 39] mode (also called light beam induced current, LBIC) of scanning optical microscopy (SOM) (a wide literature can be found in Holt and Yacobi [40]).

Since Everhart and Hoff’s pioneering investigations in 1958 [41], the early use of an electron beam to locally probe the electrical properties of semiconductors in the current induced (EBIC) configuration has been extended to other kinds of sources, such as photon and ion beams, giving rise to the development of optical beam induced current (OBIC) [36, 37] and ion beam induced current (IBIC) [42] methods, respectively, which arose immediate interest.

By these techniques the beam scans the sample surface (see Figure 5.12), with resolu­tions depending on the beam source used (see below). Wherever a space-charge region exists, due for example to a localized defect, its associated electric field E separates and sweeps away the photogenerated carriers that are collected by the electrodes, giving rise to a current profile I (x), where x is the beam position along the scanning direction, describing the local distribution of the electric field.

image194

Figure 5.12 Experimental setup of the OBIC method.

Подпись: (a) (b) (c) Figure 5.13 Con figurations used for charge-collection investigations. Reprinted with perm is- sion from Microelectronics Reliability, Charge carrier recombination and generation analysis in materials and devices by electron and optical beam microscopy by Cavallini, A.; Polenta, L. and Castaldini, A, 50, 9-11, 1398-1406. Copyright (2010) Elsevier Ltd.

The model reported here below [43] applies to measurements performed with either an electron or a light beam scanning the sample surface, where charge collection occurs through a Schottky barrier or a shallow p-n junction, either in planar (Figures 5.13(a) and 5.13(b)) or normal (Figure 5.13(c)) collector geometry.

In the following we shall refer to the case of Figure 5.13(a). It is assumed that the motion of the beam generated carriers inside the sample is purely diffusive and that the barrier imposes an infinite surface recombination velocity, vs = to.

The minority carrier recombination can be related to the diffusion by the lifetime т in the bulk and т’ at the defects, which are known to be sites of enhanced recombination.

The collected current is, thus, calculated as

I = qD j j j-dx dy (5.13)

z =0

Подпись: Y(r) Подпись: 1 то Подпись: 1 > 0 т(г) Подпись: (5.14)

where q is the electron charge, D the minority carrier diffusion coefficient, p = p (~Ґ) = p(x, y, z) the minority carrier concentration, with z the coordinate along the beam axis. The current I(~Ґ) depends on the position of the beam relative to the defect F and, thus, I is the beam induced current image of the defect itself. The defect, characterized by a region where the lifetime т’ is smaller than the bulk value т, has a ‘defect recombination strength’ у (r) defined as

It was demonstrated [44] that the beam induced current I can be expressed by:

I = Io(E) +1 * (f, E)

where f is the lateral beam position relative to the defect By defining the contrast profile of the defect, i. e., the linescan over the defect, by

Подпись: (5.15)i*(f, E) = I*(f, E)/Io(E)

it is possible to express the two basic properties of the beam induced current images:

1. contrast c(E) = max of (|i*| = |i*(0, E)|)

2. resolution w(E) = half width of |i*(f, E)|

The mathematical procedure so far reported describes the overall beam induced current images whatever the minority carrier generation source is. However, the actual evaluation of minority carrier density p(r) and the other quantities differ when considering the generation function g (r) relative to either electron or photon beam.

In what follows we will deal with the photon beam induced current and relevant generation volume.

Подпись: g (r) image202 Подпись: exp(-az) Подпись: (5.16)
image205

From the three-dimensional distribution of the light intensity the generation function g (r) may be determined [45] as:

where g0 is a constant that takes into account the surface reflectivity and quantum efficiency [10] and c is the width of the probe beam. The expression for the spatial distribution of minority carriers p(r, z) is then deduced. Figure 5.14 shows the calculated minority carrier concentration p(r, z) in units Gа/2пD for L ^<x>, with G the total generation rate (s-1) and а the absorption coefficient.

The convenience to use the EBIC or OBIC method depends on their peculiar charac­teristics and capabilities [46], mainly related to their charge carrier generation volume, indepth profiling and resolution (Figure 5.15, left side), even if in some cases from the beam-sample interaction the information inferred may be highly sensibly comparable (Figure 5.15 right side). Figure 5.15, right side, shows grain-boundary profiles in poly­crystalline silicon, and the similarity is well evident between EBIC and OBIC maps in spite of their different generation volumes.