Intrinsic and doped amorphous silicon carbide films for the surface passivation of silicon solar cells

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INTRINSIC AND DOPED

AMORPHOUS SILICON CARBIDE FILMS FOR THE SURFACE

PASSIVATION OF SILICON SOLAR CELLS

Dissertation

zur Erlangung des akademischen Grades des Doktors der Naturwissenschaften (Dr. rer. nat)

an der Universität Konstanz Fakultät für Physik

vorgelegt von

Dominik Suwito

Fraunhofer Institut für Solare Energiesysteme (ISE)

Freiburg im Breisgau

2011

Konstanzer Online-Publikations-System (KOPS) URL: http://nbn-resolving.de/urn:nbn:de:bsz:352-193464

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ii

Referenten:

Prof. Dr. Giso Hahn Prof. Dr. Paul Leiderer

Tag der mündlichen Prüfung:

11. Februar 2011

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iii

I have seen everything that is done under the sun, and behold, all is vanity and a striving after wind.

(Ecclesiastes 1:14)

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1 Introduction

Amorphous silicon carbide (a-SiC_x) is in the focus of researchers associated to di- verse scientific fields. In combination with fabrication techniques such as sputtering or plasma enhanced chemical vapor deposition (PECVD), this considerable interest is due to the low-temperature manufacture of a material offering a wide range of desir- able properties.

In medicine, a-SiC_x coatings are researched owing to its biocompatible character.

In clinical studies, for example, stents covered by a-SiCx films have been proved to effectively reduce the thrombogenicity of the patients [1]. Its high mechanical stability (hardness) and its low friction coefficient make a-SiCx furthermore an interesting material for tribological applications and wear-resistant coatings [2]. The chemical inertness of a-SiCx and hence its stability in many aqueous etching solutions such as HF, KOH, HNO₃ and CH₃COOH (acetic acid) allow for its application as an etch-stop layer, as for example in photovoltaic applications [3]. Dense a-SiCx films are promis- ing candidates for diffusion barriers against metal impurities such as iron and copper and are moreover discussed as diffusion barriers against dopant impurities such as phosphorous and boron [3].

Optoelectronics states a major field of application for a-SiC_x due to the tunability of its optical and electrical properties. The latter are controlled by altering the band gap of the alloy via composition (Si/C ratio) and by doping of the material with atoms such as phosphorous and nitrogen (n-type) or boron (p-type). Owing to its increased energy gap, a-SiC_x is used as a window layer in a-Si:H solar cells and is investigated in con- junction with photoluminescence devices (LEDs) [4] and photodetectors [5]. The sinusoidal tuning of the refractive index of successive a-SiC_x layers allows furthermore for the fabrication of complex optical (rugate) filters [6]. a-SiCx is also investigated in the context of third generation photovoltaics [7] which comprises the concept of quantum dot lattices for engineering of the band gap and hence for increasing the spectral collection efficiency of the solar cell device. The physical background relies on the quantum confinement in silicon dots which precipitate from matrices such as a-SiCx

[8].

A relatively new application for PECVD deposited a-SiC_x is the electrical passivation of silicon surfaces [9]. The latter is of primary concern for the fabrication of to- day´s and future crystalline silicon solar cells since the conversion efficiency and ultimately the manufacturing costs of this technology crucially depend on the electrical losses at the device surface. In this respect, a particular interest in a-SiC_x arises from

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2 Introduction

the reported elevated thermal stability of the passivation scheme [3, 10] and from the prospect of multi-functionality taking advantage of beneficial material characteristics as outlined above.

The central topic of this work is the electrical performance of passivating (Si-rich) amorphous silicon carbide layers (a-Si1-xCx) on silicon surfaces. Besides the quantita- tive level of surface passivation, the mechanism by which this effect is achieved is of paramount importance for device implementation. In this respect, the combination of electrical and chemical studies concerning the a-Si1-xCx film properties before and after thermal treatment provides valuable information. Equivalent investigations are ex- panded to a variety of film compositions, differing in carbon content, dopant density, dopant polarity and deposition temperature. On the substrate side, the physical per- spective is widened by comparing and discussing respective results on silicon as well as on germanium wafers. Several solar cell concepts on the basis of a-Si1-xCx surface passivation on the rear and on the solar cell front side are presented. The performance of the amorphous silicon carbide approach on the device level is completed by C-rich films which fulfill optical requirements on the rear as well as on the front side of the solar cell.

Chapter 2 positions the electrical passivation of silicon surfaces in the context of basic solar cell operation. The latter is approached by balancing the light generated current and the voltage dependent recombination losses in the device, eventually resulting in the simplified two diode model. Different types of realization for the surface passivation are reviewed ranging from high-low and pn-junctions to dielectric layers such as SiO2, SiNx and Al2O3. As a starting point for this work, basic properties of passivating a-Si1-xCx as reported in literature are summarized.

Chapter 3 gives an introduction to the characterization techniques utilized for ac- cessing the chemical and electrical properties of the amorphous films and their performance on device level. Fourier transform infrared spectroscopy (FT-IR) is presented as an adequate means of tracking the chemical composition of the films. The working principles of the quasi steady state photoconductance (QSS-PC) and lumines- cence (QSS-PL) technique as well as the microwave photoconductance decay method (MW-PCD) for the measurement of the effective lifetimes of the silicon and germanium samples are outlined. Furthermore, spectral response (SR) measurements, the Suns-Voc method as well as the surface photovoltage (SPV) technique are briefly introduced.

Chapter 4 reveals details on the deposition conditions and on the composition of the studied a-Si1-xCx films. The difference between the two types of available excita-

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Introduction 3 tion sources (microwave and high-frequency) are discussed and the process transfer of passivating a-Si1-xCx films from a laboratory type to an industrial inline PECVD reac- tor is described.

Chapter 5 addresses the evolution of chemical composition and electrical per- formance of the a-Si1-xCx films under thermal stress. The experiments are conducted on c-Si as well as on c-Ge substrates and the results are compared. Special attention is paid to the role of hydrogen for the passivation level of the film on the respective substrates. The band bending at the respective interfaces (passivating film/substrate) is investigated and finally conclusions are drawn as to the passivation mechanism of the two different systems.

Chapter 6 presents solar cells with a-Si_1-xC_x rear passivation schemes. The impact of intrinsic as well as doped passivating films on the solar cell performance is discussed. A highly efficient rear passivation and contacting scheme on the basis of a-Si1-xCx is introduced (PassDop). The benefit of this industrial feasible approach is shown to be threefold: a very effective suppression of the rear surface recombination and a high optical confinement are assured and, at the same time, local laser doping is facilitated by a dopant source inherently forming part of the passivation scheme.

Chapter 7 analyzes the performance and applicability of a-Si1-xCx passivation schemes for the solar cell front side. The passivation level of the respective layers is determined on diffused n⁺- as well as p⁺-emitters and the impact of the surface condition is investigated. C-rich a-SiyC1-y for the application as anti-reflection coatings (ARC) are introduced and optimized regarding their optical properties. Finally, solar cells featuring merely amorphous silicon carbide based films on the rear and on the front side are presented.

Chapter 8 gives a summary of the main results of this work.

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2 Basic solar cell operation and surface passiva- tion

Comprehensive text books provide a detailed description of the physical principles of solar cells in general and of cells on the basis of semiconductor material in particular (e.g.[11-14]). Most approaches to silicon solar cells are based on the solution of the current density equations (drift plus diffu- sion) in combination with the continuity equation therefore accentuating the current transport. However, the operation of a well-designed solar cell is primarily determined by generation and recombination. This chapter is based on an integral formulation of the continuity equation as proposed by Swanson et al. [15] aiming at a more intuitive understanding of basic cell operation. The output of current is revealed to originate from the balance be- tween generation and recombination and the output of voltage is shown to depend on the splitting of the quasi-Fermi potentials. The sources of recom- bination are addressed and the principles of surface passivation are out- lined. As an introduction to the practical realization of solar cell surface passivation, a review on the most common passivation schemes is given.

2.1 Basic equations of semiconductor device physics

The basic equations for modeling the carrier transport in semiconductor devices (neglecting heavy doping effects) are:

1. Current transport equations

n n n

i n

n q n qD n q n

Jr =− μ ∇rψ + ∇r =− μ ∇rφ

(2-1)

p p p

i p

p q p qD p q p

Jr =− μ ∇rψ + ∇r =− μ ∇rφ

(2-2) 2. Continuity equations

3. Poisson´s equation

(

ph

)

n qr g

J = −

⋅

∇r r

(2-3)

(

ph

)

p qr g

J =− −

⋅

∇r r

(2-4)

(

⁺ ⁺⁻ ⁻ ⁻

)

−

=

∇ _i q p N_D n N_A ψ ε

2 (2-5)

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6 Basic solar cell operation and surface passivation

4. Carrier density equations

( )

_⎟

⎠

⎜ ⎞

⎝

⎛ −

= kT

n q

n _i ψⁱ φⁿ

exp (2-6)

( )

⎟⎟⎠

⎞

⎜⎜⎝

⎛ −

= kT

n q

p _i φ^p ψⁱ

exp (2-7)

The symbols have the following meanings:

th

th g

r

r= − net recombination rate per unit volume

gph photogeneration rate per unit volume Jrn

electron current density Jrp

hole current density n electron concentration

p hole concentration

ni intrinsic carrier concentration

p

n μ

μ , electron and hole mobilities

p

n D

D , electron and hole diffusivities

p nφ

φ, electron and hole quasi-Fermi potentials ψi potential referenced to the intrinsic level ε dielectric permitivity

q magnitude of electron charge

− +

A

D N

N , ionized doping density

k Boltzmann´s constant

T temperature

Eliminating the current densities, eq. (2-1) to (2-5) finally define three coupled non- linear differential equations in three unknowns, n, p and ψi. Eq. (2-6) and (2-7) are used for relating the terminal voltage to carrier densities.

2.2 Terminal current

The terminal current I of a general two terminal device (Fig. 2-1) is given by

( )

^ˆ

( )

^ˆ ^,

2 1

dS n J J dS n J J

I=

∫

S ^rn+^rp ⋅ =−

∫

S ^rn+^rp ⋅ ^(2-8) where n is an outward unit vector normal to the surface (responsible for the minus sign when integrating over S2) and the electron and hole current densities Jn and Jpare

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Basic solar cell operation and surface passivation 7 given by eq. (2-1) and (2-2). The surface used for the integration may be the surface of contact 1 (S1) as well as of contact 2 (S2) or an arbitrary surface surrounding (not necessarily including) one of the contacts (indicated by the dashed lines in Fig. 2-1). Both electrons and holes contribute to the total output current and therefore have to be treated equally. J_n and J_pcan be calculated by integrating the continuity equations (2-3) and (2-4) over the device volume V

( )

∫

V^∇r^⋅Jrndv⁼qV r⁻gphdv

(2-9)

( )

∫

V^∇r^⋅Jrpdv⁼⁻qV r⁻gphdv .

(2-10) Using Gauss´ divergence theorem, the volume integrals on the left side can be con- verted into surface integrals over the complete surface of the device Stot:

( )

∫

S Jn^⋅ndS⁼qV r⁻gphdv

tot

r ˆ

(2-11)

( )

.

ˆ

∫

S Jp^⋅ndS⁼⁻qV r⁻gphdv

tot

r (2-12)

The surface integral can be split in integrations over the three distinct surfaces indicated in Fig. 2-1, which are the contact areas S1 and S2 and the remainder of the device surface S₀:

∫

^⋅ ⁼ 1 ^⋅ ⁺ 2 ^⋅ ⁺ 0 ^⋅

ˆ ˆ

ˆ

ˆ S n S n S n

S Jn ndS J ndS J ndS J ndS

tot

r r

r

r (2-13)

∫

^⋅ ⁼ 1 ^⋅ ⁺ 2 ^⋅ ⁺ 0 ^⋅

ˆ . ˆ

ˆ

ˆ S p S p S p

S Jp ndS J ndS J ndS J ndS

tot

r r

r

r (2-14)

Choosing contact 1 for a further analysis, e.g. eq. (2-14) can be solved for the integral over S1 and inserted into eq. (2-8):

ˆ . ˆ

ˆ ˆ

0 2

1

∫ ∫ ∫

∫

^⋅ ⁻ ^⋅ ⁻ ^⋅ ⁺ ^⋅

=

Stot p

S p

SJn ndS J ndS J ndS J ndS

I r r r r

(2-15)

Fig. 2-1: Model of a general two terminal device. S1 and S2 refer to the areas of contact 1 and 2 and S0 is the remainder of the device surface.

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Using eq. (2-12) yields

∫ ∫

∫

^⋅ ⁻ ^⋅ ⁻ ^⋅ ⁻ ⁺

= SJn ndS SJp ndS SJp ndS qVrdv qVgphdv

I ˆ ˆ ˆ .

0 2

1

r r

r (2-16)

Contact 1 is now defined to be p-type and contact 2 to be n-type, allowing in eq. (2-16) for a surface integration over S1 and S2 considering minority carriers. This choice is in accordance with Fig. 2-1, since a positive current I out of the p-type contact corre- sponds to a positive output power of an illuminated solar cell. Finally, eq. (2-16) can be written in the form

rec ph rec cont rec s rec b

ph I I I I I

I

I= − _, − _, − _, = − (2-17)

rec cont rec s rec b

rec I I I

I = _, + _, + _, _(2-18)

with

dv g q

Iph⁼

∫

V ph photogenerated current

dv r q

Ib^,rec ⁼

∫

V bulk recombination

dS n J Isrec⁼

∫

S0 p^⋅

, ˆ

r surface recombination

dS n J dS n J

Icontrec⁼

∫

S2 p^⋅ ⁻

∫

S1 n^⋅

ˆ

, ˆ

r

r contact recombination

(2-19)

The terminal current is therefore simply the photogeneration current less the recombination current. It is important to stress that eq. (2-17) is derived without any approximation and hence states an exact result of the continuity equation [15].

At this point it is suggestive to introduce the concept of effective surfaces. The related physical magnitudes are the effective surface recombination velocity (Seff) as well as the commonly used recombination currents such as the emitter and bulk saturation currents (J0e,J0b). The basic idea is that any surface surrounding (and not necessarily including) the contact can be used for the calculation of the terminal current. The surface can therefore be moved away from the actual metal-semiconductor surface (dashed lines in Fig. 2-1). The recombination current flowing through this surface is then due to recombination at the contact as well as in/at the device volume/surface present in the region between contact and integration surface. This concept is often used in combination with diffused, highly doped regions such as emitters or back surface fields since the recombination dynamics in non-homogenously doped material are harder to determine.

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Basic solar cell operation and surface passivation 9

2.3 Terminal voltage

The terminal voltage is determined by the splitting of the quasi-Fermi levels under illumination (generation) and the voltage drops due to resistive losses in the base, the metal and at the metal-semiconductor contact [16]. To a very good approximation, Φn

and Φp can be considered to be constant throughout the highly doped n⁺ and p⁺ regions underneath the contacts, respectively, and throughout the adjacent space charge regions (SCR). Referring to the band diagram of a typical high efficiency solar cell depicted in Fig. 2-2 (highly doped regions underneath both types of contact for ohmic contact formation and reduction of contact recombination), the terminal voltage is given by

met cont B jp

jn V V V V

V

V= + − − − (2-20)

with

( )

_⎟⎟

⎠

⎜⎜ ⎞

⎝

= ⎛

−

=

i n

i

jn n

n q kT

V q1ψ φ ln voltage evaluated at edge of quasi-neutral base near n⁺ contact

( )

_⎟⎟

⎠

⎜⎜ ⎞

⎝

= ⎛

−

=

i i

p

jp n

p q kT

V q1 φ ψ ln voltage evaluated at edge of quasi-neutral base near p⁺ contact

( )

⁻

( )

⁼

∫

^∇ ^⋅

= ^a

b i

i i

B a b dl

V ψ ψ rψ r voltage drop due to bulk resistance

Vcont voltage drop due to contact resistance Vmet voltage drop due to metal resistance

(2-21)

Fig. 2-2: Band diagram of a solar cell (highly doped regions underneath both types of contact). Ec and Ev refer to the conduction and valence band potential, Φn and Φp

are the electron and hole quasi-Fermi potential and ψi is the potential of the in- trinsic level, respectively.

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Again the knowledge of the physical details in the diffused regions is not mandatory for the determination of the terminal voltage of the device. The set of equations (2-21) is merely based on n, p and ψi in the base region.

Neglecting the voltage drops due to resistive losses (open circuit conditions), eq. (2-20) reduces to

( )

_⎟⎟

⎠

⎞

⎜⎜⎝

= ⎛

−

=1 ln ₂

i n

p n

pn q kT

V qφ φ (2-22)

that is, the maximum terminal achievable is equal to the separation of the quasi-Fermi potentials (implied Voc).

2.4 Recombination paths

Eq. (2-17) suggests that the current output of a solar cell is basically determined by the recombination currents prevailing in the device. It is therefore necessary to have a closer look at the phenomenological description of the respective recombination processes. The dependence of theses processes on the carrier densities n and p and hence on the terminal voltage of the device directly results in its current voltage characteristics. In the following, only the case of low injection conditions will be considered.

Reference [15] presents a more detailed view on the sources of recombination including the case of high-level injection particularly relevant for concentrator applications.

2.4.1 Recombination in diffused regions

As pointed out above, it is convenient to introduce an effective surface at the edge of the respective space charge region (SCR) just inside the neutral base. Assuming no recombination in the SCR (which is a good approximation for high efficiency solar cells), the recombination current due to the diffused region and the contact is equal to the recombination current flowing through this surface. Due to minority carrier injection (e.g. injection of holes from the p-type base into a highly doped n-type region), the minority carrier concentration at the edge of the depletion region increases exponen- tially with voltage [12]. The net flow of holes into this n-region Jp (which is the part of the injected minority carriers that recombine) can be determined to be

,

2 1

0 ⎟⎟⎠

⎜⎜ ⎞

⎝

⎛ −

=

i n

p n

J pn

J (2-23)

where J0n is a temperature dependent quantity denominated the diffusion saturation current density. The pn product refers to the internal edge of the highly n-doped region, but to a good approximation, the product can be evaluated at the edge of the SCR

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Basic solar cell operation and surface passivation 11 region in the neutral base. The same relation holds for electrons injected into a p-type diffused region (pn-junction or high-low junction)

.

2 1

0 ⎟⎟⎠

⎞

⎜⎜⎝

⎛ −

=

i p

n n

J pn

J (2-24)

In combination with eq. (2-22) this yields

⎟⎟⎠

⎜⎜ ⎞

⎝

⎛ ⎟−

⎠

⎜ ⎞

⎝

= ₀ exp⎛ 1

kT J qV

J_p _n (2-25)

⎟⎟⎠

⎜⎜ ⎞

⎝

⎛ ⎟−

⎠

⎜ ⎞

⎝

= ₀ exp⎛ 1

kT J qV

J_n _p (2-26)

for the voltage dependence of the recombination current density in the diffused regions. In praxis the diffusion saturation currents J0nand J0p are often determined experimentally. Since this is commonly done by using injection dependent lifetime measurements, the theory and practical issues concerning the determination of the emitter saturation current are outlined in chapter 3.2. Note that eq. (2-22) is based on the assumption of constant quasi-Fermi levels throughout the base (no voltage drops), which is equivalent to a constant pn product. This approach is often referred to as narrow base approximation.

2.4.2 Recombination in the base

There are three types of recombination processes present in the base, namely radiative recombination, Auger recombination and the recombination catalyzed by intrinsic (related to the crystal structure) and extrinsic (impurity related) material defects. Note that in the following section the phenomena are addressed in terms of recombination rates r. The respective recombination lifetimes τ can, however, be directly inferred by the definition

r , Δn

τ≡ (2-27)

where Δn=Δp is the excess carrier density in the absence of trapping. The experimental measurement of the overall effective recombination lifetime (corresponding to different simultaneously occurring recombination mechanisms in the material) and the means of distinguishing between the different contributions are outlined in chapter 3.2.

Radiative recombination – This recombination is the reverse of the absorption process and is proportional to the pn product. The radiative recombination rate rrad can be written as

(

i²

)

^.

rad Bpn n

r = − (2-28)

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B is the coefficient for radiative recombination and was determined experimentally to B=9.5×10^-15cm³/s at 300°C [17]. Since this value is very small for indirect semicon- ductors such as silicon (phonon-mediated radiative process) this recombination path can be neglected for silicon solar cells for one-sun applications. However, it should be mentioned that the proportionality to the pn product results in the same voltage dependence as observed for the recombination current in diffused regions (eq. (2-25) and (2-26)) and therefore exhibits a diode ideality factor of one.

Auger recombination – Instead of emitting light, the excess energy released during the so-called Auger recombination process is given to a third particle, either an electron or a hole. The suggestive description of the Auger recombination rate rAug is therefore given by

( ) (

0

)

^.

2 0 2 0 2 0

2p n p C p n p n

n C

r_Aug= _n − + _p − (2-29)

n0 and p0 are the electron and hole densities in thermal equilibrium and Cn and Cp are the n- and p-type Auger coefficients, respectively. Again, in silicon, these coefficients are small and the recombination current due to the Auger process may to a good approximation be neglected for low injection application. However, this recombination path becomes dominant for higher injection levels as it quickly increases with rAug ~ (Δn)³. The empirical parameterization for the Auger recombination rate rAug used throughout this work was established by Kerr et al. [18]

(

¹^.⁸¹⁰ ⁶¹⁰ ⁰0^.⁶⁵ ³¹⁰²⁷ ⁰^.⁸

)

^.

25 65 . 0 0

24n p n

np

r_Aug= ⋅ ⁻ + ⋅ ⁻ + ⋅ ⁻ Δ (2-30)

Defect mediated recombination – Carrier recombination through defects (often re- lated to as traps) in the band-gap is usually described following the phenomenological approach introduced by Shockley, Read [19] and Hall [20]. The recombination rate for a single defect level rSRH is given by

(

1

) (

1

)

^,

2

p p n n

n r np

no po

i

SRH + + +

= −

τ

τ ^(2-31)

where τ_po and τ_no are the fundamental hole and electron lifetimes which are related to the thermal velocity of charge carriers νth, the density of recombination defects Nt, and the capture cross-sections σp and σn for the specific defect by

t th p

po σν N

τ ≡ ¹ and ¹ ^.

t th p

no σν N

τ ≡ _(2-32)

p1 and n1 are statistical factors defined as:

⎟⎠

⎜ ⎞

⎝

⎛ −

≡ kT

n E

p _i ψⁱ ^t

1 exp and ⁿ¹^≡ⁿⁱ^exp^⎜_⎝^⎛^E^t_kT⁻ψⁱ^⎟_⎠^⎞ ^,

(2-33)

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Basic solar cell operation and surface passivation 13 where ψiagain refers to the potential referenced to the intrinsic level and Et is the energy level of the defect. Of course the total recombination rate due to defects in the bulk is the sum of the single defect rates.

Assuming a p-type base, the defect mediated recombination rate in the bulk (eq. (2-31)) for low level injection rSRH,li and deep defects (n1, p1 << p) can be written as

, .

no li SRH

r n τ

≈Δ _(2-34)

In the narrow base approximation, the integration over the base yields a recombination current density JSRH,li of

no li SRH

qW n

J τ

= Δ

, (2-35)

with W the thickness of the base. Using again eq. (2-22), the voltage dependence of the low injection defect mediated current density results in

⎟⎟⎠

⎜⎜ ⎞

⎝

⎛ ⎟−

⎠

⎜ ⎞

⎝

= exp⎛ 1

2

, kT

qV N

J qWn

no A

i li

SRH τ ^(2-36)

with NA the acceptor density of the p-type bulk.

2.4.3 Surface recombination

The charge carrier recombination at the surface or interface of the silicon device is dominated by a large number of intrinsic defects since the discontinuity of the crystal results in partially bonded silicon atoms (referred to as silicon dangling bonds). The phenomenological description of the recombination dynamics at the surface follows the model by Shockley, Read and Hall of the bulk defect recombination with the mere difference of introducing surface instead of volume related quantities. For a single defect at the surface, the rate of surface recombination rS is given by

,

0 1 0

1 2

n S p S

i S S S

S p p S

n n

n p

r +n + +

= −

(2-37)

where nS and pS are the concentrations of electrons and holes at the surface, and Sno and Spo are the fundamental surface recombination velocities of electrons and holes related to the density of surface states per unit area Nts and to the capture cross-sections σp and σn for the specific defect by

ts th n

no N

S ≡σν _and S_po≡σ_pν_thN_ts . (2-38)

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To account for the continuous character of the defect distribution throughout the band- gap, it is appropriate to refer to defect energy dependent capture cross-sections σp(E) and σn(E) as well as an energy dependent density of interface states Dit(E). The surface recombination rate is obtained by integration over the band-gap energies

( )

( ) ( )

∫

₊

( )

+ +

= ^C −

V E

E it

n S p S

i S S th

S D EdE

E p p E

n n

n p n

r v .

1 1

2

σ σ

(2-39)

The quantity related to surface or interface related recombination is the (effective) surface or interface recombination velocity S. Its relation to the surface recombination rate is given by

S .

S S n

r ≡ Δ (2-40)

In general, S is an injection dependent quantity (or equivalently: rS does not increase linearly with ΔnS) which depends strongly on the surface condition. It is therefore particularly dependent on the surface passivation applied and, conversely, allows for the deduction of passivation specific quantities which in turn allow for conclusions on e.g. the passivation mechanism. This type of analysis is presented in chapter 5.4 for surface passivation by silicon rich a-Si1-xCx.

However, assuming S to be constant in a first approximation, it becomes evident that the description of defect mediated recombination in the silicon volume and at the surface is similar (eq. (2-34) and (2-40)) and the voltage dependence of the surface recombination current density in low injection considering a p-type surface can analo- gously be written as

. 1 exp

2

, ⎟⎟⎠

⎜⎜ ⎞

⎝

⎛ ⎟−

⎠

⎜ ⎞

⎝

= ⎛

kT qV N

Sn J qA

A i surf li

S (2-41)

Asurf refers to the fraction of surface where recombination takes place which, however, is not yet accounted for by the recombination currents in the diffused regions (Jn or Jp).

2.4.4 Recombination in the space charge region

The defect mediated bulk recombination rSRH (eq. (2-31)) is most effective for regions of equal hole and electron carrier densities n ≈ p when assuming deep defects (n1 ≈ p1) and similar cross sections for both types of carriers (σn ≈ σp). Hence, if SRH recombination in the space charge region (SCR) cannot be neglected, then the dominant contribution to SCR recombination stems from narrow regions of equal electron and hole density. Here eq. (2-22) results in

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Basic solar cell operation and surface passivation 15

2 , exp ⎟⎟⎠

⎜⎜ ⎞

⎝

⎛ ⎟

⎠

⎜ ⎞

⎝

= ⎛

= kT

n qV p

n _i (2-42)

and the voltage dependence of the SRH recombination current density in the SCR can be approximated to

. 2 1

02 exp ⎟⎟⎠

⎜⎜ ⎞

⎝

⎛ ⎟−

⎠

⎜ ⎞

⎝

= ⎛

kT J qV

JSCR (2-43)

J02 is the temperature dependent dark saturation current of the SCR [21]. Given the outlined simplifications, note that the diode ideality factor referring to SCR recombination is two.

2.4.5 Current voltage characteristics

Following the superposition principle, the overall current voltage characteristics of the device are given by eq. (2-17) when introducing the above derived voltage dependent recombination current densities for the various recombination paths. In low injection, the voltage dependence of the output current density J =I/A is therefore

, ,

,li Sli SCR

SRH n p

ph J J J J J

J

J= − − − − − (2-44)

. 2 1

exp 1

exp ₀₂

2 2 0

0 ⎟⎟⎠

⎜⎜ ⎞

⎝

⎛ ⎟−

⎠

⎜ ⎞

⎝

− ⎛

⎟⎟⎠

⎜⎜ ⎞

⎝

⎛ ⎟−

⎠

⎜ ⎞

⎝

⎟ ⎛

⎟

⎠

⎞

⎜⎜

⎝

⎛ + + +

−

= kT

J qV kT

qV N

Sn qA N J qWn J J J

A i surf n A

i p n

ph τ ^(2-45)

Note that the diode ideality factor of the space charge recombination generally deviates from 2 for real solar cells since the assumptions made in the preceding section over- simplify the conditions in the SCR. Series losses of the device may be accounted for by approximating

, ' V JR_S

V≈ − ^(2-46)

where RS is the overall series resistance of the cell. Leakage currents in a real device may be considered as an additional recombination current density Jleak characterized by a parallel resistance Rp

. / ' _p

leak V R

J ≈ (2-47)

The current voltage characteristics can then be written as

( ) ( )

2 , exp 1

exp ₀₂

01

p S S

S

ph R

JR V kT

JR V J q

kT JR V J q

J

J −

⎟⎟−

⎠

⎜⎜ ⎞

⎝

⎛ ⎟

⎠

⎜ ⎞

⎝

⎛ −

⎟⎟−

⎠

⎜⎜ ⎞

⎝

⎛ ⎟−

⎠

⎜ ⎞

⎝

⎛ −

−

= ^(2-48)

with J01 referring to all saturation currents in the device except for the SCR and leakage currents. For high-injection conditions (Δn >> n0, p0), Auger and radiative recombination in the base can no longer be neglected and the behavior of the recombination

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currents may change, which is particularly reflected by a change in the corresponding diode ideality factor (Table 2-1).

Table 2-1: Diode ideality factors for different recombination paths in low and high injection conditions [15].

diode ideality factor recombination path low injection high injection

diffused region 1 1

radiative 1 1

Auger 1 2/3

SRH (bulk, surface) 1 2

SCR 2 2

2.5 Electrical surface passivation of silicon solar cells

The focus of this work is the surface passivation of silicon solar cells. The SRH model for the surface recombination given in eq. (2-39) suggests that there are basically two different practical approaches for the suppression of recombination, that is (i) the reduction of the interface state density D_it (chemical passivation) and (ii) the reduction of one carrier type (electrons or holes) at the surface (field-effect passivation). On the device level, the chemical passivation is generally done by depositing or growing of a passivating film on/into the silicon surface. The surface silicon dangling bonds, responsible for the dominant effective recombination levels (deep defects) in the silicon band-gap, are thereby “saturated”, that is, the states are driven out of the band-gap by the formation of covalent bonds to atoms of the passivating film. The field-effect passivation can be implemented by changing the Fermi level position with respect to the band edges near the silicon surface. The latter is commonly realized by additional doping or by electrical charges in an overlying dielectric film [22].

2.5.1 High-low junctions

High-low junctions (HLJ) can be used for the passivation of the front and the rear side of solar cells and are accordingly referred to as front (FSF) and back surface fields (BSF), respectively. An increased doping level below the silicon surface (p⁺p or n⁺n) results in a so-called built-in field which is commonly said to “repel” the minority carriers from the surface and hence decreases surface recombination. Although this

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Basic solar cell operation and surface passivation 17 picture is instructive, it has to be kept in mind that there is no resulting force on the carriers under equilibrium conditions and that an (electrochemical) force can only result from a gradient in the quasi-Fermi levels. The strength of the built-in field or equivalently the doping ratio between the lowly and highly doped regions (referred to as HLJ barrier factor f) is one of the principal quantities determining the performance of a HLJ. The other quantities are the depth of the junction d and the minority carrier diffusion length L in the highly doped region (often dominated by Auger recombination) [23, 24]. For a shallow junction (d <<L), the effective SRV Seff can be approximated by

surf ,

eff f S

S = ⋅ (2-49)

with Ssurf the SRV at the very surface. To date, most industrial p-type silicon solar cells feature an aluminium BSF formed by screen-printing of an Al-based paste onto the rear of the cell and by alloying the Al into the silicon in a subsequent firing step (700- 900°C for a few seconds). Alloyed Al BSFs typically provide SRVs in the range 200- 2000 cm/sand the built-in voltages are in the range of a few hundred meV [22]. The passivation of solar cells via an in-situ diffused HLJ from doped a-Si1-xCx is the subject of chapter 6.3.

2.5.2 pn-junctions

A floating (i.e. non-contacted) pn-junction (FJ) states an effective means for de- creasing the surface recombination velocity. The voltage across the FJ is determined by the minority carrier concentration in the base near the depletion region of the FJ.

Hence for a homogenous carrier distribution throughout the base and the ideal case of no carrier recombination in the FJ, the FJ exhibits the same voltage as the emitter (contacted junction) of the solar cell [25]. The instructive picture of the passivation principle of a FJ is the re-injection of bulk minority carriers flowing into the junction towards the surface of the cell, thereby effectively suppressing recombination. The re- injection of minority carriers into the bulk is determined by the voltage across the FJ and like any junction the voltage depends on the prevailing recombination currents.

Accordingly recombination in the FJ such as surface or shunt recombination reduce the passivation quality of the junction [26]. On device level, one-sun open-circuit voltages of up to 720 mV were reported by Altermatt et al. [25] for so-called PERF (passivated emitter, rear floating p-n junction) cells, featuring a diffused FJ with thermal oxide passivation on the rear.

Conceptually the same approach for the description of a FJ applies to inversion layer passivation induced by high fixed charge densities in an overlying dielectric layer

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[27]. The practical implications for solar cell devices based on this passivation approach are further discussed in chapter 6.1.

2.5.3 Thermal silicon oxide

Due to microelectronic industry (metal-oxide-semiconductor (MOS) applications), the Si-SiO2 interface has become the most intensively studied semiconductor-insulator system. The thermal oxidation of silicon surfaces at temperatures 800-1200°C strongly reduces defect interface states. Therefore chemical passivation is the dominant mechanism suppressing recombination at Si-SiO2 interfaces. Upon oxidation the silicon oxide grows into the silicon (consuming a silicon layer of about 0.45 d_ox) and thereby dis- places the actual interface into clean regions. The non-stoichiometric sub-oxide between the crystalline silicon and the stoichiometric SiO2 (< 2 nm) gives rise to defect states (stretched Si-Si bonds and Si dangling bonds with different number of back- bonded Si/O atoms). The unoccupied ·Si≡O state (Si dangling bond with three back- bonded O-atoms) is supposed to be responsible for the fixed (immobile) positive charge density localized in this interface near region [28]. Energetically this defect is located above the silicon conduction band and its charge condition is therefore insensi- tive to the position of the surface Fermi level. Typical fixed charge densities are in the range 5-20×10¹⁰ cm^-3 [28]. An improvement of the surface passivation is yielded by annealing in a hydrogen-containing ambient at temperatures 350-500°C. Lowest interface densities are observed for a post-metallization anneal with an Al film evaporated onto the oxide (“alneal”). The oxidation of Al by residual water molecules within the oxide is believed to release atomic hydrogen which very effectively passivates Si dangling bonds. This technique may result in Dit values as low as 10⁹ cm^-2eV^-1 [29].

The capture cross sections for defects near mid-gap are higher for electrons as compared to holes. The ratio of the cross sections was determined to be in the range σn/σp=10-500 [28]. It is noteworthy that the growth of an oxide film on the surface of a silicon wafer may result in dopant depletion in the case of boron doping and in dopant accumulation in the case of phosphorous doping close to the interface due to segrega- tion effects.

Thermal silicon oxide is well suited for the reduction of the SRV at lowly doped n- and p-type (base) silicon surfaces as well as for the passivation of highly doped n⁺and p⁺ emitters [30-33]. However, the latter p⁺-Si/SiO2 system turned out to be unstable, deteriorating its passivation properties severely under storage in the dark [34].

On the device level, silicon solar cells relying on thermal silicon oxide surface passivation present the highest conversion efficiencies yielded so far (η=25.0 % at 1 sun

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Basic solar cell operation and surface passivation 19 [35]). Comprehensive studies on the Si-SiO2 interface are presented in references [14, 28, 36].

2.5.4 Amorphous silicon nitride

Amorphous silicon nitride (SiNx) presents a low temperature approach for the passivation of silicon surfaces. Due to the reduced involved processing costs as compared to thermal SiO2 passivation and due to its multi-functionality in terms of surface/bulk passivation and anti-reflection coating on the front side of the solar cell, SiNx has become state-of-the-art in PV industry. Although SiNx film preparation by sputter techniques have proven to yield good results [37, 38], so far the most widely spread deposition technique for SiNx is the plasma enhance chemical vapor deposition (PECVD). The typical precursor gases used for the deposition of SiN_x are silane (SiH4), ammonia (NH3) and/or nitrogen (N2) and the deposition temperature is in the range 300-500°C. The resulting film contains a large amount of hydrogen (10-40 at.%) and its optical and electrical properties are essentially determined by its composition, i.e. by the N/Si ratio [39, 40]. The band-gap of SiN_x can be changed from approx.

5.3 eV in the case of quasi stoichiometric Si3N4 down to approx. 1.7 eV for amorphous silicon (a-Si) by reducing the nitrogen content in the film. In this respect, it is important to notice that the silicon dangling bond defects remain near mid-gap and therefore present the dominant recombination centers in SiNx independently of the film composition. The transition from a Si-N-H alloy to a doped semiconductor (donor like N in an a-Si:H matrix) is found to occur for a nitrogen content ≤ 2 at.% [28]. A review of the bonding and electronic structure of crystalline and amorphous silicon nitride is given in Ref. [41].

The Si-SiN_x interface is characterized by a large positive charge density Q_f in the range 1×10¹¹-5×10¹² cm^-2 and by an interface state density Dit at mid-gap in the range 1×10¹¹-5×10¹² cm^-2eV^-1 on n- as well as on p-type silicon. The excellent suppression of surface recombination by SiNx [33] despite the relatively large amount of defect states is due to a dominant field effect passivation owing to Qf. That is, on non-diffused surfaces the SiNx film induces an accumulation of majority carriers at the interface for n-type material and inversion conditions (the number of electrons exceeds the number of holes) for p-type material. The contribution to the fixed charge density is supposed to be two fold. A smaller part is due to an interfacial oxynitride film (≤ 2 nm) giving rise to dangling bond defects in the silicon band-gap as well as to a fixed positive charge due to unoccupied ·Si≡O states as encountered at the SiO2/c-Si interface. The by far larger contribution to the fixed charge density is ascribed to unoccupied ·Si≡N states (so-called K⁺ centers) which extend rather deep (20-30 nm) into the bulk of the SiNx film [42]. Whereas the neutralisation of the K⁺ centers (K⁺↔K⁰) by UV illumina-

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tion has been soon demonstrated by means of ESR (electron spin resonance) [43] and lifetimes measurements [44], the dependence of the charge density on excess carrier density (light density) was discussed controversially. In an experiment applying corona charges in combination with lifetime measurements, Dauwe et al. finally showed that the charges Qf at the SiNx/c-Si are independent of light intensity [45].

Amorphous SiNx demonstrates excellent passivation performance on lowly doped n and p silicon as well as on n⁺ diffused surfaces and is in this respect comparable to alnealed SiO2 [33]. Contrary, the passivation of p⁺ emitters by SiNx is poor. This find- ing is commonly attributed to the creation of depletion conditions at the SiNx/p⁺-Si interface due to the high fixed positive charge density in the SiNx film [33]. Altermatt et al., however, attribute the poor performance to a defect type at the SiNx/p⁺-Si interface exhibiting a high cross-section for electron capture rather than to a deteriorating field effect [34].

2.5.5 Aluminium oxide

Recently amorphous aluminium oxide (Al2O3) as a dielectric passivation for silicon surfaces has attracted a lot of attention in the PV community. Al2O3 films deposited by plasma or thermal ALD (atomic layer deposition) [46-48] as well as by large scale deposition techniques such as PECVD [49, 50] and RF sputtering [51] have proven an excellent level of surface passivation on crystalline silicon. In the as- deposited state, the Al2O3 films typically deposited at temperatures 170-300°C (de- pending on the deposition technique) do not show a significant level of surface passivation. In all cases a post-deposition anneal at moderate temperatures (≈ 425°C) is necessary to “activate” the passivation properties. The annealing step was demonstrated to drastically increase the fixed negative charge density in the Al₂O₃ film up to 10¹²-10¹³ cm^-2 as well as to decrease the interface defect state density (≈10¹¹ eV^-1cm^-2) [52]. The characteristic negative charge density is believed to be located directly at the interface to the substrate and a thin (≤ 1.5 nm) oxide layer present at the interface is assumed to play a major role for the charge formation [52, 53].

Owing to the large negative charge density, Al2O3 has proven to be especially well-suited for the passivation of highly doped p⁺ surfaces. Hoex et al. showed that in this case Al2O3 clearly outperforms SiNx and high quality SiO2 passivation schemes, demonstrating that p⁺emitters can be as effectively passivated as n⁺ emitters [54]. On the solar cell level, the excellent passivation properties are preserved and solar cell efficiencies of up to 21.5% for p-type cells with Al2O3 rear passivation [55] and of up to 23.2% for n-type cells with Al2O3 passivated boron emitter are reported [56].

Intrinsic and doped amorphous silicon carbide films for the surface passivation of silicon solar cells