A versatile computer-controlled high-resolution LBIC system

PROGRESS IN PHOTOVOLTAICS: RESEARCH AND APPLICATIONS

Prog. Photovolt: Res. Appl. 2004; 12:283–295 (DOI: 10.1002/pip.528)

A Versatile Computer-controlledHigh-resolution LBIC SystemJ. Martın*,y, C. Fernandez-Lorenzo, J. A. Poce-Fatou and R. AlcantaraDepartamento de Quımica Fısica, Facultad de Ciencias, Apartado de Correos 40, 11510 Puerto Real (Cadiz), Spain

This paper presents the design of versatile equipment for obtaining laser-beam-

induced current (LBIC) images which allows the study of large surfaces as well as

conversion areas of a few micrometers. The modular optomechanical design enables

the user to modify the size of the irradiation spot by simply changing the microscope

objective used as focal lens, albeit within the limits set by the wavelength. The use of

an appropriate calculation algorithm makes it possible to rely on a computerized sys-

tem to adjust the distance at which the focusing lens must be placed with respect to

the sample plane. The possibility of working at micrometer resolution allows one to

obtain very significant information for the study of irregularities, manufacturing

defects, impurities, grain boundaries, dislocations, recombination centers, etc. in

photovoltaic wafers. Copyright # 2004 John Wiley & Sons, Ltd.

key words: LBIC; high resolution; computerized system; OBIC; solar cell

INTRODUCTION

The overall conversion efficiency of a photovoltaic device depends on the efficiency of every point of the

photoactive surface. These depend on the underlying microstructure generated during the manufactur-

ing process (semiconductor material growth, doping diffusion, texture structure, contaminants, etc.). A

point-by-point characterization of the surface quantum yield is therefore a powerful tool for an accurate and

effective description of the device.

One approach to obtaining conversion efficiency maps is through a point-by-point irradiation of the surface

by means of a highly focused photon beam. This ensures that the smaller the irradiation zone, the better will be

the definition of the photoconversion properties and the better the resolution shown by the photoresponse maps.

This is not, however, the only necessary condition in order to obtain high spatial resolution photoresponse maps.

It is equally necessary that, in overall terms, the optomechanical device used for scanning the surface be free of

fluctuations, in both its mechanical and optical aspects, being therefore capable of controlling with precision the

exact position of the zone to be irradiated and the photonic stability of the beam used for the irradiation.

The present paper describes the essential characteristics of the instrumentation developed to obtain submicro-

meter resolution quantum efficiency images. The essential elements of the system are: (a) an irradiation beam opti-

cal path as simple as possible; (b) the use of computer-controlled motorized stages for micropositioning of the most

critical elements; (c) positioning of the mobile elements so that gravitational torsion forces are minimized; (d) the

use of irradiation power stability control sensors; (e) the use of an optimized protocol to focus, to position and to

scan the surface to be studied; and (f) the use of an adequate computerized control of the whole system.

Published online 16 March 2004 Received 24 June 2003

Copyright # 2004 John Wiley & Sons, Ltd. Revised 23 October 2003

* Correspondence to: J. Martın, Departamento de Quımica Fısica, Facultad de Ciencias, Apartado de Correos 40, 11510 Puerto Real (Cadiz),Spain.yE-mail: [email protected]

Contract/grant sponsor: CICYT; contract/grant number: 1FD97-0685-C02-02.

Research

A number of publications detailing the use of the laser beam induced current (LBIC) technique as ground-

work or as a means to provide further information can be found in the bibliography. We have been able to find

several commercially available units,1,2 and patents related to equipment that might well be used for this pur-

pose or to equipment that might involve in an LBIC application. Most of these systems have a characteristically

low spatial resolution as a result of the conditions set for the obtaining a quick response or of a large group of

signals to be measured. Most of the time, these systems use a laser beam surface irradiation system. However, it

is also possible to find a system in which the light emitted by a halogen lamp is used as an irradiation source.3 In

this case, it is necessary to take into account the complex geometry of the emitting focus, and the several pro-

blems posed to the reimaging function. Other types of problems have their origin in the polychromaticity of the

emission, and are partially dealt with by the use of a monochromator to select a narrow spectral range, at all

times greater than the one which would correspond to a laser emission.

Focusing our study on the laser-based systems, it is possible to describe three different methodologies: (a)

movable beam and fixed surface; (b) fixed beam and movable surface; and (c) mixed systems. The systems

based on option (a) are generally faster than the others. They work by deflecting the laser beam according to

a pattern similar to that followed by an electron beam in a TV set. This deflection is achieved by means of a

coordinated rotation of mirrors set in orthogonal directions,4,5 by removing lenses from the main optical axis,6

or by means of telecentric lenses.7–9 These systems present some problems related to the maintenance of a cor-

rect focusing when a large surface is scanned, since the distance between the deflecting device and the incident

point is not constant. In order to solve this problem, photon beams, either non-focused or focused by long focal

distance lenses are used.10 It is never possible, however, to obtain a high spatial resolution owing to the spot

size, having in addition a different illumination surface morphology on the optical axis and off it. Some devices

have been designed to quantify a very specific property, such as the etch pitch density, by using very complex

deflection systems,11 though these are hardly useful for a superficial response micrometer characterization.

The systems based on option (b) do not pose deflection problems, although they are generally slower than the

former, since the time they need to scan a surface is limited by the speed of the movement of the sample holder

system.12 The information provided by these systems can have a good spatial resolution as long as the beam is

kept accurately focused on any surface point and the images it shows do not present geometric distortions since

they correspond to linear movement patterns of the cell. However, almost every single system of this type

referred to in the bibliography has been designed to work with many sensors placed between the focusing lens

and the surface of the sample. This design makes it necessary the use of long focal distance lenses at the expense

of spatial resolution.13–17

A better solution is obtained when standard microscope heads18–20 are used. These systems work with very

short focal distance lenses, thus obtaining a good spatial resolution. The main disadvantage is the rigidity pro-

vided by the optical assembly when it comes to measuring the specular reflectance of the surface or the stability

of the irradiation source.

Finally, the use of a deflecting device in the systems based on option (c)21,22 makes it necessary that the beam

performs an arch-shaped scan as the cell moves linearly. The matrix of analyzed points does not present an

orthogonal pattern and it is necessary to apply a correcting program.

MATERIAL AND METHODOLOGY

The equipment developed for this study (Figure 1) is based upon a maximally simplified optical path (x-axis),

defined by a He–Ne laser emission (Uniphase, model 1125, nonpolarized, 5 mW power in 632�8 nm emission).

A TEM00 mode laser beam presents a Gaussian irradiance distribution. This distribution is not modified by

the focusing or reflecting of the beam by means of spherical optical elements and the irradiance is calculated by

means of the expression:

IðrÞ ¼ I0 exp � 2r2

w2

� �ð1Þ

284 J. MARTIN ET AL.

Copyright # 2004 John Wiley & Sons, Ltd. Prog. Photovolt: Res. Appl. 2004; 12:283–295

where r is the distance from the center of the optical axis and w is the so-called Gaussian radius, defined as the

distance from the optical axis to the position at which the intensity decreases to 1/e2 of the value on the optical

axis.

When a monochromatic Gaussian beam is focused, the Gaussian radius in the area near the focus fits the

equation

w2ðxÞ ¼ w20 1 þ �x

�nw20

� �2" #

ð2Þ

where x is the coordinate along the propagation axis with the origin of coordinates being defined at the focal

point, � is the wavelength value, n is the refraction index of the medium and w0 is the Gaussian radius value at

the focus. The latter can be obtained from the expression

w0 ¼ 2�

�

� �F

D

� �ð3Þ

where F is the focal distance of the lens and D is the Gaussian diameter of the prefocused beam.

Another relevant magnitude is the depth of focus (DOF), defined (somewhat arbitrarily) as the distance

between the values of x where the beam isffiffiffi2

ptimes larger than it is at the beam waist. This magnitude can

be calculated from the expression

DOF ¼ 8�

�

� �F

D

� �2

ð4Þ

Figure 1. General diagram of the system

HIGH-RESOLUTION LBIC SYSTEM 285


where the different magnitudes represent the same concepts we have previously defined. As can be observed,

the beam size at the focus and the depth of focus depend on the same factors, so that the smaller the former is,

the smaller the latter will be, which in fact is going to determine some of the most relevant features of the sys-

tem. That is why, if we intend to have the maximum possible spatial resolution, it is necessary to be provided

with an optimum focusing system given that the DOF value will also be very small; at the same time any non-

essential optical elements that may contribute to the generation of distortions in the geometry of the beam must

be avoided.

The different components which make up the subsystems of the equipment, such as the elements used for

focusing the beam on the active surface, controlling the radiant power, controlling the reflected radiant power,

etc., are placed along the optical axis. We now describe each of these subsystems.

Optical board

This consists of a beehive-shaped optical board supplied by TMCTM, onto which the different optomechanical

elements are fixed. This board is mounted on external vibration damping devices. In addition, the structure has

been optically isolated so as to avoid the entry of diffuse light, and thermically isolated in order to keep a steady

temperature, within a maximum variability range of �0�5�C.

Focusing system

This system is most important since an optimum focusing of the laser on the photoactive surface is one of the

main limiting factors of the spatial resolution. Indeed, according to Equation (3) and (4), the greater the spatial

resolution is (smaller spot size), the smaller will be the depth of focus, and any focusing errors will lead to

unacceptable results. The focusing system designed consists basically of three subsystems: a focusing lens

mounted on a motorized stage with micrometric movement, a beam expander built with two opposing micro-

scope objectives, and a calculation algorithm which allows a computer to optimize the focusing process, and

which we will analyze in detail later.

According to Equation (3), the spot size at the focus is directly related to the focal distance and inversely

related to the size of the prefocused beam. In this case, the focusing lenses we have used were, either a

16� microscope objective (F:11 mm) or a 10� one (F:16 mm), both supplied by Owis GMBH.

The beam emitted by the laser we previously mentioned has a size of 0�81 mm in the TEM00 mode, and it has

been enlarged up to 7�6 mm by means of a beam expander made up of two microscope objectives, coaxially and

confocally arranged, with a 63�:4� rate. Table I shows the geometric parameters of the beam at the focus

obtained with this system.

In order to eliminate as many parasitic emissions as possible, a spatial filter is placed at the confocal point of

expander system and the resulting emission of the system is diaphragmed to the indicated nominal diameter

(7�6 mm). Focusing with objectives of different magnification values will produce different beam parameters

at the focus, affecting the resolution capacity to which photoactive surfaces can be studied.

Sample holder system

As we have previously mentioned, we have decided to use a system configuration consisting of a fixed beam and

a mobile sample moving along orthogonal directions (y–z plane) with respect to the irradiation optical axis. The

Table I. Calculated geometric parameters of the beam at the focus with and without beam expander

Without expander With expander

Objective F(mm) D(mm) w0(mm) DOF(mm) D(mm) w0(mm) DOF(mm)

16� 11 0�81 5�47 297�2 7�6 0�58 3�410� 15�7 0�81 7�81 605�4 7�6 0�83 6�9



biaxial movement of the photoactive surface is achieved by using a system of motorized stages with numerical

control and a displacement resolution of 0�5 mm. Special care has been taken to ensure the minimization of the

asymmetrically suspended masses so as to avoid the generation of gravitational torsional forces. All optome-

chanical elements utilized in this work have been provided by Owis GMBH.

Specular reflectance and incident power measuring system

A highly transparent nonpolarizing beamsplitter, made from BK7 glass with antireflecting coating, has been

placed on the optical path. This beamsplitter plays a double role, depending on whether it is working in trans-

mission or in reflection. In transmission, the transmitted beam is used for irradiating the sample, whereas the

reflected beam allows one to monitor the stability of the laser power emission by using a silicon photodiode. By

means of the ratio between the induced current and this signal it is possible to obtain a normalized value for the

external quantum efficiency.

The optical system between the beamsplitter and the sample works similarly to a confocal system, so that the

beam specularly reflected by the sample surface follows an optical path which coincides with the irradiation

path, but in the opposite sense. The intensity of this beam that is reflected by the beamsplitter is measured by a

second silicon photodiode which allows one to obtain information on the reflecting properties of the photoactive

surface. This information is particularly interesting for the evaluation of the photoconversion internal quantum

efficiency.

Focusing algorithm and computer monitoring for its implementation

Although a lens focal distance can be known, e.g., 11 mm for our 16� objective or 15�7 mm for the 10� , its

exact manual positioning at such distance is a very difficult goal, even when fine adjusters are used, owing to the

low value of DOF. In order to limit errors, focusing is computer controlled, following an accurate calculation

algorithm. It is thus possible to position the focal lens at the optimum distance from the photoactive surface.

The focusing algorithm is based on finding the lens position which maximizes the derivative of the signal

generated when we perform consecutive linear scans on the Y–Z plane between two points of the cell surface

for different focal lens distances. Essentially, this algorithm is based on the alterations of the signal produced

when a photon beam, with a Gaussian energy distribution, moves across photoactive areas with a net difference

in its quantum efficiency. In this case, the photocurrent generated ISC presents a variation similar to that shown

in Figure 2, defining the beam size or resolution to the scan distance at which the signal is within the 10–90%

limits with respect to the maximum value.23 Figure 3(a) shows the derivative of the numerical values shown in

Figure 2. It follows that the better the resolution, the deeper will be the minimum associated with the derivative

of the signal, and the greater the difference � between the maximum and the minimum.24

If we perform several scans at different positions of the focusing lens, we will obtain a set of � values, the

graphical representation of which, as a function of the lens position, will lead us to a curve such as the one

shown in Figure 3(b), where the position of the maximum corresponds with the focusing distance of the objec-

tive xf. Theoretical studies based on computational simulation show that this curve could be fit to a peak func-

tion as a special form of pseudo-Voigt function24 named type 2, which, mathematically, is a linear combination

of both a Lorentzian and a Gaussian function with the same maximum position

�ðxÞ ¼ �0 þ A2

�

dL

4 x� xfð Þ2þd2L

þ B

ffiffiffiffiffiffiffiffiffiffiffi4 ln 2

p ffiffiffi�

pdG

exp�4 ln 2

d2G

x� xfð Þ2

� �ð5Þ

where �(x) is the value of the derivative at every position of the focal lens, �0 is the vertical displacement

constant, A and B are the intensity factors of the Lorentzian and Gaussian functions respectively, dL and dG

are the widths at half height (FWHM) for each function and xf is the maximum common position. It is precisely

the value of xf which defines the focusing lens optimum positioning coordinate.



This methodology provides optimum results when we want to focus the lens on a specific point of the photo-

active surface. However, using one unique point is not sufficient when the photoactive surface plane is not nor-

mal to the laser beam axis. The problem comes down to finding the angle between the vector normal to the plane

and the irradiation optical axis. In this way we can spatially define the surface plane and automatically adjust the

distance between the focal lens and the plane at every point of the analysis. This methodology involves deter-

mining the focal distance for three points as far from each other as possible, although inscribed within the area

to be studied.

Figure 2. Diagram of the ISC variation between two areas with different photoconversion efficiency. The scan distance

between the 10–90% limits with respect to the ISC maximum value is usually defined as the beam size

Figure 3. (a) Derivative of the numerical values represented in Figure 2. The difference � between the maximum and

minimum value is related to the laser spot; (b) plot of � against position of the focusing lens. The peak position of the

function corresponds to the optimal focal distance xf of the lens and can be calculated by adjusting to a pseudo-Voigt (type 2)

peak function



EXPERIMENTAL FOCUSING: CHARACTERISTICSOF THE DESIGNED INSTRUMENT

Experimental focusing

The focusing method can be applied to all heterogeneities commonly found in solar cells such as the cell edge, a

finger, or a grain boundary. Thus, Figure 4 shows an LBIC image corresponding to a circular area approximately

20 mm in diameter in a polycrystalline cell. In this area one observes a substantial reduction of the signal in

relation to the solar cell’s active surface surrounding it.

For focusing, a 100 mm linear scan, with a step of 1 mm, along the cell surface has been performed (Figure 4), for

each position of the focusing lens stepped at 10 mm. Figures 5(a) and (b) show the three-dimensional surfaces

obtained from the LBIC signal and its numerical derivative, respectively. The difference between the maximum

and the minimum was plotted against the position of the focusing lens, generating the curve shown in Figure 6.

The resulting data were fit to the pseudo Voigt type 2 function, with a regression coefficient R2, of 0�997, and a

maximum at 27�964 mm, the optimum focusing distance with respect to the motorized stage displacement origin.

The focusing method can also be applied with lower resolution. Thus, Figure 7 shows an LBIC image of a

grain boundary in a polycrystalline solar cell to which the focusing technique was applied through consecutive

300-mm-long linear scans, with a step of 5 mm, for different positions (step of 50 mm) of the focusing lens, per-

formed in the direction indicated by the arrow.

A three-dimensional surface plot of the LBIC signal data obtained when performing consecutive linear scans at

different positions of the focusing objective, and their derivatives, can be observed in Figures 8(a) and (b), respec-

tively. It can clearly be seen in Figure 8(a) that the LBIC surface has two plateaus at different photoconversion

levels, both determined by the different quantum efficiency of the crystal grains it separates. The curve shown in

Figure 9 is generated by the plotting of the differences between the maximum and minimum for every scan �against the position of the focusing lens. The fitting of this curve presents a regression coefficient R2 of 0�989.

The results carried out confirm the utility of both the focusing method and the designed instrument.

Figure 4. LBIC image of an area in which a point defect is observed. The arrow indicates the direction in which the focusing

technique was applied



Versatility

This LBIC system was initially conceived to study commercial photovoltaic solar cells. Based on this, the sys-

tem was designed with a sufficient degree of versatility so as to obtain LBIC images of a surface with variable

resolution.

When we want to obtain information on a large surface, it is possible to obtain quantum efficiency LBIC

maps with resolutions similar to those used by standard LBIC systems mentioned in the bibliography. By

Figure 5. (a) LBIC signals, three-dimensional surface, obtained by applying the focusing technique of micro-defect of

Figure 4; (b) three-dimensional surface, numerical derivative of Figure 5(a) constituent vectors

Figure 6. Evolution of the difference between the maximum and the minimum of the LBIC signal derivatives plotted against

position of the focusing lens for micro-defect shown in Figure 4. The continuous trace shows the fitting function



way of example, Figure 10 shows the external quantum efficiency LBIC image (a) and the specular reflection

image (b) of the surface of a polycrystalline silicon solar cell, obtained at a resolution of 25 mm. Since the reflec-

tivity is mainly diffusive, the information available from the specular reflection image is just partial. However it

could be of use in the interpretation of external quantum efficiency images.

When we want to study the system response at a microscopic level, the information must be obtained with the

highest possible level of discernment between the points which make up every pixel of the LBIC image.

Figure 7. LBIC image of an area of a polycrystalline silicon photovoltaic cell showing a grain boundary. The horizontal

arrow indicates the direction in which the focusing technique was applied

Figure 8. (a) LBIC signals; three-dimensional surface, obtained by applying the focusing technique of sample shown in

Figure 7; (b) three-dimensional surface, numerical derivative of Figure 8(a) constituent vectors



Figure 11 shows the LBIC image (a) and the specular reflection image (b) obtained at a 0�5 mm resolution, cor-

responding to the transition between Si crystals related to the example shown in Figures 7–9. It can clearly be

observed how different crystal growth orientation presents different external photoconversion values, and that

there is a sharp fall of the photoconversion value at the grain boundary, which is shown as a dark line. At the

same time, it is also possible to see in the left-hand side of the image that the texture of the wafer has pyramidal

Figure 9. Evolution of the difference between the maximum and the minimum of the LBIC signal derivatives plotted against

position of the focusing lens for the grain boundary shown in Figure 7. The continuous trace shows the fitting function

Figure 10. (a) External quantum efficiency LBIC image; (b) specular reflection image of a 20� 20 mm2 surface of a

polycrystalline silicon photovoltaic solar cell scanned at a resolution of 25 mm



morphologies with a face orientation close to the image plane that we can see as triangular pattern. Also, we can

see that the photoconversion efficiency at the edges of these triangular faces is slightly higher than at the center.

Figure 12 shows a monocrystalline silicon solar cell LBIC and the specular reflection images obtained at 1 mm

resolution. In this case, the wafer texture has a micropyramidal structure with its symmetric axis perpendicular

to the wafer plane then its visual appreciation is azimuthal in the vertix–base plane direction. There are areas of

Figure 11. (a) External quantum efficiency LBIC image; (b) specular reflection image of a 215� 215mm2 surface of a

polycrystalline silicon photovoltaic solar cell showing a grain boundary. The scan was performed at a resolution of 0�5mm.

Note the pyramidal microstructure

Figure 12. (a) External quantum efficiency LBIC image; (b) specular reflection image of a 500� 500mm2 surface of a

monocrystalline silicon solar cell, performed at out a resolution of 1 mm. Note the low photoconversion points associated

with the breakage of the peaks of the pyramidal surface obtained with the texturing process



low photoconversion corresponding to some of the peaks of these pyramids possibly deriving from the breakage

of such peaks. In this type of wafers, in which the diffusion distance of phosphorus in the silicon crystalline

structure is just a few tenths of a micrometer, the breakage of the peaks of pyramids due to mere friction elim-

inates the semiconducting structure pn, there being no photoconversion in these areas.

CONCLUSIONS

We have described the fundamentals of computer-controlled equipment for scanning the surface of photovoltaic

devices, which is capable of obtaining simultaneously LBIC and specular reflection based images. Even thought

reflectivity is mainly diffusive the information contained in the latter represents an important reference for the

interpretation of the LBIC image.

Resolution of these images depends on the laser beam size at the focus, however the mathematical relation-

ship between this value and the DOF implies that the better the resolution, the greater the difficulties for focus-

ing the laser beam on the studied surface. This complication is avoided by the use of a focusing methodology

based on the external quantum efficiency heterogeneities commonly found in photovoltaic devices such as

micro-defects, grain boundaries or surface boundaries.

The implementation of this focusing method on the LBIC system allows one to obtain images of variable

sizes and resolutions, which demonstrates its usefulness and versatility in the study of photovoltaic devices.

Acknowledgements

We would like to thank ISOFOTON, S. A. for supplying the solar cells used in this work and the CICYT under

grant 1FD97-0685-C02-02.

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A versatile computer-controlled high-resolution LBIC system