2.3.2  Photoconductivity  17

2.3.3  Photocurrent generation in p-n junction solar cells.  19

2.3.3  Quantum efficiency  

2.4  Saturation and recombination current  28

2.5  Equivalent circuit of a solar cell  31

2.6  Fundamental parameter for solar cell characterization.  33

3  Experimental issues - Hardware.  36

3.1  Global system description.  36

3.2  Laser characterization system  38

3.2.1  He-Ne laser  39

3.2.2  Beam intensity monitoring.  40

3.2.3  Electrical measurements.  43

3.3  Laser-scribing system.  44

3.3.1  Nd-YAG laser.  44

3.3.2  Optical system.  45

3.4  Position control.  47

4  Experimental issues - Software  49

4.1  Main program  49

4.2  Low level programming of microcontrollers.  53

4.3  RS-232 programming of the Nd-YAG laser cutter  55

4.4  GPIB programming of digital multimeters  56

5  Cell characterization - results and discussion  58

5.1  Basic principles of photoresponse mapping  58

5.2  Calculations of expected photocurrents  59

5.3  I/V characteristics.  63

5.4  Spectral response.  69

5.5  Photoresponse mapping.  74

6  Prospective  80

6.1  Optical system for improved resolution  81

6.2  Transmittance maps  82

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6.3  UV laser beam for selective scribing.  83

6.4  Selective wavelengths for photoresponse mapping  83

6.5  Lock-in-technique  84

7  Conclusions  85

  References.  88

  Acknowledgements.  90

Appendix A  (Documentation of the designed programs)  90

Appendix C  (Security precautions)  108

Tables of  illustrations  112

Tables of  equations.  114

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Deutsche Zusammenfassung

Die Diplomarbeit wurde von mir in englischer Sprache verfaßt, da die Arbeit im Zuge eines LEONARDO DA VINCI Traineeship Programmes am CIEMAT (Centro de Investigaciones Energéticas, Medioambientales y Technológicas, Madrid, Spain) durchgeführt wurde und auch von der politechnischen Universität (Institut für Solarenergie) betreut wurde.

Diese Diplomarbeit beschreibt das Design und die Montage eines experimentellen Systems zur Charakterisierung und Strukturierung von Solarzellen und anderen Photovoltaikbauteilen. Das designte Lasersystem kombiniert ein Werkzeug zur Strukturierung von Dünnschichtsolarzellen mit einer Charakterisierungseinheit („Photoresponse Mapping“-Technik)

Das Charakterisierungsteilsystem arbeitet nach dem LBIC-Prinzip (laser beam induced currents). Das System zur Strukturierung von dünnen Schichten arbeitet mit einem NdYAG Lasercutter, der gewöhnlicherweise auch zu IC-Reparaturen verwendet wird.

Ziel dieser Diplomarbeit ist der „Set up“ des Lasersystems, welches die Anstrengungen in der Forschungsarbeit der Entwicklung neuer Materialen für Solarzellen und deren Charakterisierung unterstützen soll. Benutzt man Standardmethoden (I-V Kurven, Spektrale Empfindlichkeit), um optisch-elektrische Eigenschaften einer Solarzelle zu messen, erhält man ein quantitatives Ergebnis, das einem keine Rückschlüsse auf lokale Defekte innerhalb der Probe erlaubt. Kleine Defekte innerhalb eines photovoltaischen Bauelementes können die Leistung dieses Bauteils negativ beeinflussen. Der Vorteil der „Photoresponse-Mapping“ -Technik liegt in der Möglichkeit, lokale Messungen am Bauteil vorzunehmen.

„Laser-Scribing“ ist eine Schlüsseltechnologie im Herstellungsprozess von amorphen Silizium-Solarzellen. Diese Technologie deckt bereits 50% des

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Fabrikationsprozesses ab und hat die konventionelle Methode mittels Photolithografie bereits komplett ersetzt [18].

Der erste Teil dieser Arbeit soll in das Thema einführen und erläutert die vorgegebene Aufgabenstellung. Der Theorie folgend ([19], [3]) werden die fundamentalen Prinzipien des Energiewandlungsprozesses einer Solarzelle in Kapitel 2 erläutert, um den physikalischen Hintergrund der

Solarzellencharakterisierung zu verstehen.

Das Kapitel 3 gibt einen Überblick über die zum Design des Systems verwendete Laborausstattung und erläutert, wie die Einzelteile, funktionell zusammengesetzt zum System, eine nach dem ersten Set up zuverlässig funktionierende Laboreinheit bilden.

Im Kapitel 4 wird die Wahl der Software und der unterschiedlichen verwendeten Schnittstellen (GPIB, low-level-programming, RS232) begründet. Ebenfalls wird ein kurzer Überblick über die Leistungsfähigkeit der Programmierwerkzeuge gegeben.

Nach dem Aufbau eines solchen Systems ist es natürlich von großem Interesse, erste erhaltene Meßergebnisse zu verifizieren. Dies wird im Kapitel 5 getan. Hier wird auch der Zusammenhang zu anderen opto-elektrischen

Charakterisierungsmöglichkeiten aufgezeigt und die erhaltenen Messergebnisse werden unter Einbeziehung dieser komplementären Charakteristiken der verwendeten Solarzellen interpretiert.

Kapitel 6 sollte einige Ideen zur weiteren Entwicklung und Verbesserung des Systems aufzeigen und einen Anreiz geben, dieses entwickelte System für weitere Diplom- oder Promotionen zu verwenden.

Eine Zusammenfassung der Arbeit ist als siebtes Kapitel angefügt und drei angehängte Kapitel (Appendix 1-3) ermöglichen einen tieferen Einblick in das Systemdesign.

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Abstract

This thesis, submitted for a diploma, describes the set up of an experimental system which basically includes two lasers and one precision positioning system. The facility designed should be used for the characterization of solar cells by photoresponse mapping and for scribing thin films.

The photoresponse-mapping equipment uses a He-Ne laser, an intensity-measuring photodiode, a sample holder with electrical tips mounted on the x-y positioning tables and a set of electrical-measurement facilities, such as digital voltmeters and operational amplifiers. Photoresponse maps are obtained by laser beam induced currents (LBIC). The scribing system consists of a Nd-YAG laser cutter, a special microscope, and a sample holder mounted on the x-y positioning table. It was the objective of this work to put all parts properly together and to reach in a first set up a reliable working facility as well as to do a number of initial measurements with the characterization part of the system. Individual tasks included:

Designing a global platform for the system, mountings and sample holders, fixing the two lasers, the positioning system and the sample holders on this platform. Installing a photodiode for monitoring the He-Ne laser intensity. Making the electrical connections for measuring the short-circuit currents generated by the device under test for photoresponse mapping, which includes connecting the operational amplifiers and the digital multimeters. Developing individual control subroutines for the positioning table, the Nd-YAG laser and the voltmeters.

Measuring a number of photoresponse maps in order to establish the validity of the experimental set up.

The system set up represents an automated system controlled by a personal computer (type 80286) via different interfaces. The double laser facility already works reliable and performs the characterization of solar cells by photoresponse

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mapping and the scribing and cutting of thin films. With the experimental results carried out by initial photoresponse mappings, it was possible to determine the active area, to identify local defects, to generate maps of surface heterogeneity, and to calculate local spectral response values of solar cells or other photovoltaic

devices.

After the set up, the laser scribing system is ready to be tested and should initially be used to optimize scribing and cutting conditions. Moreover it should be used for research and development of photovoltaic materials and devices.

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1 Introduction

Worldwide 80% of all energy used comes from fossil fuels like coil, oil, and natural gas. Since these energy resources are exhaustible, low energy consumption and the search for renewable energy resources should be the basis of the world energy structure of the 21st century. Obviously, solar energy can not solve all energy problems but could deliver a part of the energy consumed worldwide. Nevertheless, it is not part of this thesis to discuss social and political questions. They should be discussed elsewhere.

The topic of this thesis is the set up of a double laser facility which should support the efforts of CIEMAT’s laboratory staff to investigate in the field of photovoltaic device development. CIEMAT is the main Spanish RTD (Research and Technological Development) center working on energy resources. One of its groups focuses on the preparation and characterization of thin film materials (a-Si:H, CIS and CdS) for photovoltaic-device applications.

Part of the motivation for thin-film work is its ability to use layers only a few microns thick rather than the freestanding silicon wafers, which are hundreds of microns thick [18].

The double laser facility designed combines one tool for the treatment with one tool for the characterization of photovoltaic devices. Using standard methods like current-voltage - and spectral response characterization to measure optical device performance, the measured quantity is usually an average value over the entire wafer. Small defects within a wafer, that can negatively influence the performance of the device, may not be discovered. By scanning the whole sample with laser light one can induce short circuit currents in the device under test, measure these currents, and present them by a photoresponse map. The advantage of photoresponse mapping is the possibility to obtain a lateral resolution. Using a scanning technique, the measurement is performed locally in limited areas of the probe, whereby the relative influence of

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the defect on the signal is more pronounced and hence detectable. The simplicity in equipment using photons instead of electrons for scanning a sample might be the most attractive feature. There is no need for vacuum and the scanning of light is easy to accomplish. (Kai Wilhelm and Birger Drugge give in their doctoral dissertations a detailed comparison of advantages and disadvantages of using photons or electrons as excitation sources to scan photovoltaic devices ([5], [30]). For thin film fabrication it is very important to be able to cut metal contacts and ablate selective thin film material deposited on glass or other materials. The above mentioned processes of thin film fabrication are usually named “laser scribing”. Laser scribing is a key technology in the manufacturing process of amorphous silicon integrated modules. It covers about 50% of the fabrication process steps and has completely replaced the conventional metal masking or photolithography methods [7].

2 Physical principles of silicon solar cell characterization

2.1 Conventional structure of a silicon solar cell [19]

Solar cells require a particular p-n junction design, which is depicted in figure 2.1 as a schematic representation of a conventional silicon solar cell. It consists of a shallow junction built near the front surface, a front ohmic contact, usually in the form of stripes and fingers, and a back ohmic contact that covers the entire back surface. Usually, an antireflective coating is applied to the illuminated side to increase the fraction of incident light not reflected.

An electrical field is created between two regions of a crystalline semiconductor having opposed types of conductivity. One of these regions (n-type) is doped with phosphorus, which has five valence electrons. This region has a much higher concentration of electrons than holes. The other region (p-type) is doped with boron, having three valence electrons. Here the concentration of holes is greater.

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The large difference in concentrations from one region to another causes a permanent electric field from the

n-type region towards the p-type region. This is the field responsible for separating the additional electrons and holes produced when light shines on the cell.

figure 2.1: structure of a conventional silicon solar cell, W p is the width of the p-type base region, W is

the width of the depletion region, W n is the width of the n-type emitter region, x n is the depth of then n-side depletion edge and x p is the depth of the p-side depletion edge, whereas x is the depth in general

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In silicon cells the junction is obtained by diffusing a phosphorus layer into a wafer of silicon previously doped with boron. The junction is typically very near to the surface (about 0.2 to 0.5 µm). This shallow, diffused layer is commonly called the emitter. The electrical contact with the illuminated side of the cell has to leave most of the surface uncovered. Otherwise light cannot enter the cell. However, the electrical resistance of the contact should not be too high. The compromise usually adopted is to use contacts with the form of a comb. In contrast, the electrical contact on the dark side of the cell covers the whole surface of the cell except in the particular case of bifacial cells.

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2.2 Operating principles of silicon solar cells [19]

If a solar cell is connected to a load and is illuminated, as shown in figure 2.2, a potential difference will be produced across the load and current will flow. The current leaves the cell from the positive terminal and returns to the negative terminal. Under such operating conditions the cell operates as an energy generator.

figure 2.2: internal currents in a solar cell; the unshaded circles represent holes and the black circles

represent electrons; the left arrow represents the photogenerated current I L caused by electron/hole-generation; the right arrow represents the diode current caused by the diffusion of electrons and holes

The processes going on inside the cell can be described as follows: Photons that reach the interior of the cell and have an energy equal or greater than the bandgap are absorbed in the bulk of the semiconductor, generating electronhole pairs.

The internal electric field, or potential difference, produced by a p-n junction is responsible for separating as many carriers (electrons and holes) as possible and producing the photocurrent I L in reverse-bias direction as shown. The total current I produces a voltage drop across the load which forward biases the p-n junction and this forward-bias voltage produces a forward-bias current, the diode, or dark current I D .

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In summary, when a load is connected to an illuminated solar cell, the current flow is the net result of the two counteracting components of internal currents I L and I D :

Assuming that the two currents can be superimposed linearly, the current in the external circuit can be calculated as the difference between the two components. Taking the photocurrent as the positive, we can write:

L − = ) (U I

D

equation 2.1: fundamental characteristic equation of a solar cell

This is the fundamental characteristic equation of a solar cell. It is valid over all operating conditions, even when the device consumes rather than generates electricity, in which case the recombination outweighs the photogeneration.

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2.3.1 Absorption of light [21]

The light generated current I L is partly determined by the absorption behavior of the semiconductor. The fraction of the incident light D = 1 - R that actually penetrates the absorbing material can be calculated from the complex refraction index n c = n - iκ, where κ is the extinction coefficient and R is the reflectivity, given by

= R

equation 2.2: reflectivity

where n and κ are functions of the wavelength of the incident light (perpendicular light penetration is assumed). Substituting the appropriate values shows that for many semiconductors a considerable fraction of light is reflected. It is therefore desirable from the perspective of making an efficient solar cell to decrease R. This can be achieved by means of an antireflection coating or a textured surface structure.

The important process for photovoltaic conversion is the excitation of electrons from the valence into empty states of the conduction band, which can occur if the energy of the incident photons is larger than the band gap energy. The light passing through the material is absorbed then, and the number of generated electron-hole pairs depends on the number of incident photons S 0 (ν) per unit area, unit time and unit energy, that can be calculated from the spectral distribution of the sunlight in figure 2.3.

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figure 2.3 : spectral distribution of sunlight, referring to different air mass factors (AM)

The frequency ν, or the photon energy νh, is related to the wavelength λ by the relation λ[µm] = c/ν = 1.24/hν[eV] where c is the velocity of light. Inside the crystal the photon flux S(x,ν) decreases exponentially according to

S

The absorption coefficient α(ν) is determined by the absorption process in the semiconductor and can be used to calculate the generation rate G(x,ν) of electronhole pairs (per unit time, volume and energy) at a distance x from the semiconductor surface. The fraction of photons that penetrate into the crystal is given by S 0 (ν)*(1-R); therefore, the number of electron-hole pairs generated per unit time in the volume between x and

x + ∆x can be calculated from the negative derivative of equation 2.3 with respect to x:

( ) ( ) ( ) ( )( ) ( ) ( ) − = exp ) ( 1 , ν α ν α ν η ν x R S x G ⁰ qi

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The internal quantum efficiency η qi (ν) takes into account that only a fraction of the absorbed photons generates electron-hole pairs. For many compound semiconductors it is observed that η qi (ν) << 1 near the absorption edge. This fact is due to the formation of excitons or bound electron-hole pairs, which carry no charge and do not contribute to the conductivity. However, for the elemental semiconductor germanium and particularly silicon, and some III-V compounds, values of η qi (ν) ≈ 1 are measured at room temperature even near the absorption edge.

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2.3.2 Photoconductivity [21]

First we assume a homogeneous semiconductor under illumination and after that we consider the photocurrent generation in a p-n junction cell (chapter 2.3.3). If p 0 and n 0 are the carrier concentrations in thermodynamic equilibrium, which are determined by the doping concentrations of donors and acceptors, the changes in the electron δn and hole concentrations δp can be expressed by δp = p - p 0 and δn = n - n 0. The basic equations describing the flux of electrons and holes in a semiconductor under illumination are the current-density equations and the continuity equations:

− = E J ) grad ( µ p D p q

p P

+ = E J ) grad ( µ n D n q

n

equation 2.5: flux of electrons and holes in a semiconductor

with τ p : minority carrier lifetime in the n-type region

with τ n : minority carrier lifetime in the p-type region

equation 2.6: continuity equations

The diffusion coefficients D n and D p are related to the mobility of the carriers µ n , µ p by the general Einstein relationship D n/p = (KT/q) µ n/p . For light-generated carriers, the generation rates for electrons and holes are equal to G n = G p = G. If the excess concentrations are low, one can assume additionally that δn = δp and combine equation 2.5 and equation 2.6. For instance, for holes, one obtains

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equation 2.7: time derivation of hole concentration

where the ambipolar diffusion coefficient D and the ambipolar mobility µ are given by

= D

equation 2.8: ambipolar diffusion coefficient and ambipolar mobility

A corresponding equation is obtained for electrons if p is replaced by n. The lifetimes for electrons and holes are assumed equal in this case, τ n = τ p = τ, and can be calculated, for instance, by the Shockley-Read-Hall statistics. Under steady-state conditions, a homogeneous generation of electrons and holes and for a homogeneous doped crystal, the time derivative and the gradient of p (or n) are zero, and equation 2.7 leads to the condition δp = Gτ. For negligible electric fields, the quasi-Fermi energies under illumination then can be calculated, and yield:

− = E Fp

= E + Fn

Under normal illumination conditions for solar cells (AM1.5), the product Gτ is usually smaller than the majority carrier concentration; therefore, only the quasi-Fermi energy of the minority carriers is essentially changed.

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When an external electric field E is applied to the semiconductor, under the above mentioned assumptions, a current flows. The total current density J derived from equation 2.5 is given by

= + = E J σ

n p

equation 2.10: total current density under illumination

with the conductivity σ

( ) + = µ σ n p q n p

equation 2.11: conductivity

One can separate the conductivity into two terms σ = σ 0 + σ ph with the following expressions for the dark conductivity σ 0 and the photoconductivity σ ph :

( )

+ = µ σ n p q 0 n p 0

( ) τ + = µ σ G q n ph

equation 2.12: dark conductivity and photoconductivity

In doped crystals, the dark conductivity depends on the concentration and mobility of the majority carriers, whereas the photoconductivity is mainly determined by the lifetime of the minority carriers.

2.3.3 Photocurrent generation in p-n junction solar cells [21]

Photovoltaic energy conversion requires the separation of electrons and holes by an internal electric field. This means solar cells require a particular p-n junction design, which is depicted in the schematic representation of figure 2.2.

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The internal electric field E = - grad Φ leads to an inhomogeneous distribution of electrons and holes, and the calculation of the currents requires the solution of the complete current-density equation 2.5 and continuity equation 2.6. The potential Φ is determined from Poisson’s equation,

q

− = ∆Φ

equation 2.13: Poisson´s equation

where N D and N A are in general, functions of the position and are equal to the concentrations of the ionized acceptors and donors. ε is the dielectric constant of the material and ε 0 is the permittivity of the vacuum.

For an abrupt p-n junction with uniform doping concentrations on each side of the junction, the usual approximation is that within a certain width W, the semiconductor is completely free of charge carriers. The depletion width W, derived from the upper equation is then given by

W

where the built in voltage V bi is determined by the doping concentrations N D and N A on either side of the junction

= V

bi

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When light is incident on the front surface and penetrates the crystal, the number of electrons and holes generated at a distance x from the surface is given by the generation rate (equation 2.4), which was determined in the previous section. In thermodynamic equilibrium, when no current flows, minority carriers reaching the edges of the depletion region are immediately accelerated by the electric field to the opposite side of the junction. One can approximately assume in this case that the boundary conditions for the minority carrier concentrations at the depletion edges are

δp ≈ 0 at x = x n and δn ≈ 0 at x = x p. (see figure 2.4) A current flows under illumination when the two sides of the p-n junction are connected externally. The external load resistance determines the corresponding voltage drop U across the junction in forward bias direction. If the current is small, the solution of Poisson’s equation can easily be derived in the depletion approximation which is depicted schematically in figure 2.4.

figure 2.4: schematic representation of the p-n junction band diagram. Under low illumination, the quasi-

Fermi energies of majority carriers E Fn and E Fnp in the n- or p-doped region, respectively, remain almost

constant and equal to the Fermi energy in thermal equlibrium E F , and extend horizontally into the space

charge region.

The electric field outside the depletion region remains small compared to the field across the junction and can be ignored; thus E = 0.

Under low illumination the minority carrier concentrations increase noticeable with respect to the thermal equilibrium whereas the majority carrier

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concentrations remain almost constant. In figure 2.4 this fact is illustrated by means of the quasi-Fermi energies in the n- or p-doped region, respectively. The quasi-Fermi energies vary only slowly as long as the carrier concentrations are large. Therefore, if the recombination in the depletion region is small, the quasi-Fermi energies of the majority carriers can be extended approximately horizontally into the depletion region. Considering the situation depicted in figure 2.4, the quasi-Fermi energies of the minority carriers at the depletion edges are then given by

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E Fp

+ = at x = x p qU E Fn

equation 2.16: quasi-Fermi energies of the minority carriers at the depletion edges

The excess carrier concentrations δp and δn at the depletion edges under illumination are given by the following expressions:

= δ p

= δ n

equation 2.17: excess carrier concentrations at the depletion edges

The increased carrier concentrations at the edges of the depletion region lead to diffusion currents of the minority carriers (electrons and holes) into the p- and ndoped region, respectively. If recombination in the depletion region can be ignored, these currents flow unchanged through the depletion region. The total current can thus be determined by calculating the minority currents at the edges of the depletion region.

Calculation of the photocurrent densities collected from the base, emitter and depletion region [21]:

For n- or p-type semiconductors, the expressions in equation 2.5 for the minority currents can be simplified if the electrical field outside the depletion region is negligible. Under steady-state conditions, the time derivatives of p and n in the continuity equations are zero and equation 2.7 outside the depletion region on the n- and p- side, respectively, reduces to

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