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SERIS is a research institute at the National University of Singapore (NUS). SERIS is supported by

NUS, the National Research Foundation Singapore (NRF), the Energy Market Authority of Singapore

(EMA) and the Singapore Economic Development Board (EDB).

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Modelling of contact resistivity of fire-through Ag-Al contacts to B-doped

polysilicon layers

Pradeep PADHAMNATH, Nitin NAMPALLI, Jeremie WERNER, Armin G. ABERLE, Shubham DUTTAGUPTA

10th Metallization & Interconnection Workshop, Genk, Belgium

15 Nov, 2021

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SERISSolar Energy Research Institute of Singapore

National Lab founded at NUS in 2008;

supported by NUS, NRF, EMA & EDB

Focuses on applied solar energy research

(solar cells, PV modules, PV systems)

> 120 staff & PhD students; state-of-the-art labs, ISO

certified (9001, 17025)

Close collaborations with industry & government agencies

Strategic priorities: To develop & commercialize solar

technologies suited for urban and tropical applications,

and support industry development and the energy

transformation towards higher solar adoption

SERIS

Solar cells

电池

PV modules

组件

Solar PV systems

PV系统

3

SERIS’ monoPolyTM celliOx + Poly-Si deposited using PECVD tool (no wrap-around)

PECVD poly-Si

Best group Voc (mV) Jsc (mA/cm2) FF (%) η (%)

Batch median 701 41.04 82.5 23.7

Best cell 703 41.17 82.5 23.9

SDE + Texture

In-situ oxide + n+:a-Si (PECVD)

Annealing

Chemical edge isolation

Screen-printing + Firing

B-diffusion

Rear side etch

8 S

TE

PS

ARC + passivation

4

p+ c-Si

n+ Poly-Si

SiNx

AlOx

SiNx

n-type c-Si

Front metal contact

iOx

Rear metal contact

n+ c-Si

p+ Poly-Si

SiNx

SiOx

SiNx

n-type c-Si

Front metal contact

iOx

Rear metal contact

monoPolyTM cellPossible configurations

Front Emitter n-type monPolyTM cell Rear Emitter n-type monPolyTM cell

5

Metallization of n+ poly-Si has rapidly progressed.

Possible to contact 25nm poly-Si layers with

decent contact properties

Passivation properties largely independent of the

thickness of poly-Si layer

All experimental data shown here achieved on

planar surface with large area (156x156 mm2)

wafers

Contacts to n+ poly-SiWith screen-printed fire-through Ag metallization

Padhamnath et al., SolMat, 2019

25 50 100 150 200 2500.0

0.5

1.0

1.5

2.0

2.5

3.0

Thickness of poly Si [nm]

rc [mW

cm

2]

0 50 100 150 200 250251

10

100

1000 J0,metal

J0,surf

J0 [fA

/cm

2]

Thickness [nm]

J0,metal for Ag contacts on n+ c-Si

6

Contacts to p+ poly-SiWith screen-printed fire-through Ag-Al metallization

Padhamnath et al., Solar Energy, 2021

P1 P2 P34

6

8

10

12

14

16

18

20

22

24

rc [mW

-cm

2]

FT Metal pastes50 100 150 200 250

0

10

20

30

40

50

60

rc [mW

-cm

2]

Poly-Si thickness [nm]

50 100 150 200 2500

5

10

15

J0,p

ass [fA/c

m2]

Thickness of poly-Si layer [nm]

50 100 150 200 250

100

1000

J0

,me

tal [

fA/c

m2]

poly-Si thickness [nm]

J0,metal on p+ c-Si Contacts to p+ poly-Si with FT Ag-Al pastes

not mature enough.

All experimental data shown here achieved on

planar surface with large area (156x156 mm2)

wafers

150nm poly-Si

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Contacts to p+ poly-SiWith screen-printed fire-through Ag-Al metallization

Padhamnath et al., Solar Energy, 2021

P1 P2 P34

6

8

10

12

14

16

18

20

22

24

rc [mW

-cm

2]

FT Metal pastes

Contact resistivity shows

dependency on glass layer

distribution.

Contact resistivity also

dependent on:

metal crystallites size

distribution of metal

crystallites

Surface texture

P1 P2 P32

4

6

8

10

12

14

16

18

20

% a

rea

co

ve

rag

e [

%]

FT Metal pastes

8

Contacts to p+ poly-SiWith screen-printed fire-through Ag-Al metallization

Padhamnath et al., Solar Energy, 2021

Contact resistivity shows

dependency on glass layer

distribution.

Contact resistivity also

dependent on:

metal crystallites size

distribution of metal

crystallites

Surface texture

Plan Tex0

2

4

6

8

10

rc [

mW

-cm

2]

Data shown for 150nm poly-Si

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Contacts to p+ poly-SiWith screen-printed fire-through Ag-Al metallization

Padhamnath et al., Solar Energy, 2021

Ag-Al crystallites formed during high temp firing vary

greatly in size

For contacts to c-Si deeper junctions result in lower ρc

and J0,metal.

Contact resistivity also dependent on metal crystallites

size and distribution

Ideal contact – crystallites stay within the poly-Si layer

Modeling of Ag-Al contacts to p+ poly-Si less explored

0.0 0.2 0.4 0.6 0.8 1.01015

1016

1017

1018

1019

1020

B (

cm

-3)

depth [mm]

c-Si

poly-Si

Al crystallites

10

Modeling of Contacts to p+ poly-SiModeling approach

Padhamnath et al., Solar Energy, 2021

Huge difference exist between theoretical and

experimentally achievable ρc .

Glass layer could impede the crystallites formation

and charge flow, especially on planar surfaces.

Glass layer could lead to artificially increased effective

Schottky barrier height (Φb) 1.00 1.05 1.10 1.15-20

-15

-10

-5

0

Ln(r

c)

1/ÖNpoly (x10-10)

Current FT paste

Ideal FT paste

Ideal contact

11

Modeling of Contacts to p+ poly-SiModeling approach

Crystallites divided into strips of δx (one order of

magnitude smaller than estimated depth)

ρc calculated for each individual crystal by parallel

summation of individual strips.

Dopant change considered as per the dopant profile

Fermi-Dirac statistics used for charge carrier

distribution including BGN effect for [B]>1x1019 cm-3

Crystallites within the poly-Si layer – larger influence

on ρc

δx

Assumption

Constant dopant

concentration over the

width of single strip

For detailed modeling approach and theory : E. Lohmüller, et al. "Impact of boron doping profiles on the specific contact resistance of screen printed Ag–Al contacts on

silicon," Solar Energy Materials and Solar Cells, vol. 142, pp. 2-11, 2015

12

Modeling of Contacts to p+ poly-SiModeling approach

Current transport mechanism Specific contact resistance Eq

Thermionic Emission (TE)

(N < 1018 cm-3) [1]𝜌𝑐(𝑇𝐸) =

𝑘𝐵𝑞𝐴∗𝑇

𝑒𝑥𝑝𝑞∅𝑏

′

𝑘𝐵𝑇(1)

Thermionic Field Emission (TFE)

(1018 cm-3 < N < 1020 cm-3 ) [2,3]

𝜌𝑐(𝑇𝐹𝐸) = 𝐶𝑇𝐹𝐸𝑘𝐵𝑞𝐴∗𝑇

𝑒𝑥𝑝𝑞∅𝑏

′

𝐸0(2)

𝐶𝑇𝐹𝐸 =𝑘𝐵𝑇 𝑐𝑜𝑠ℎ 𝐺 𝑐𝑜𝑡ℎ 𝐺

𝜋 𝑞∅𝑏′ +𝐸𝐹 𝐸00

𝑒𝑥𝑝𝐸𝐹

𝐸0−

𝐸𝐹

𝑘𝐵𝑇, 𝐺 =

𝐸00

𝑘𝐵𝑇

(3)

Field Emission (FE) (N > 1020 cm-3) [2,3]

𝜌𝑐(𝐹𝐸) = 𝐶𝐹𝐸𝑘𝐵𝑞𝐴∗𝑇

𝑒𝑥𝑝𝑞∅𝑏

′

𝐸00(4)

𝐶𝐹𝐸 = ቈ

𝜋

𝑠𝑖𝑛𝜋𝑘𝐵𝑇

2𝐸00𝑙𝑛 𝑀

−

2𝐸00𝑘𝐵𝑇 𝑙𝑛 𝑀

𝑒𝑥𝑝 −𝐸𝐹 𝑙𝑛 𝑀

2𝐸00𝑀 = 𝑙𝑛

4𝑞∅𝑏′

𝐸𝐹

(5)

𝜌𝑐 Τ𝑇𝐹𝐸 𝐹𝐸 [2] 1/1

𝜌𝑐 𝑇𝐹𝐸+

1

𝜌𝑐 𝐹𝐸(6)

𝜌𝑐 Τ𝑇𝐸 𝑇𝐹𝐸 [4] 1/1

𝜌𝑐 𝑇𝐸+

1

𝜌𝑐 𝑇𝐹𝐸(7)

Characteristic Energy, E0 [5] 𝐸0 = 𝐸00 𝑐𝑜𝑡ℎ 𝐺 (8)

Characteristic Energy, E00 [5]𝐸00 =

𝑞ℎ

4𝜋

𝑁

𝑚𝑡∗𝜀𝑟𝜀0

(9)

[1] S. Sze and K. Ng, Physics Of Semiconductor Devices. John Wiley& Sons. Inc.,

2007.

[2] K. Varahramyan and E. Verret, "A model for specific contact resistance applicable

for titanium silicide-silicon contacts," Solid-State Electronics, vol. 39, no. 11, pp.

1601-1607, 1996

[3] A. Y. C. Yu, "Electron tunneling and contact resistance of metal-silicon contact

barriers," Solid-State Electronics, vol. 13, no. 2, pp. 239-247, 1970/02/01/ 1970

[4] E. Lohmüller, et al. "Impact of boron doping profiles on the specific contact

resistance of screen printed Ag–Al contacts on silicon," Solar Energy Materials and

Solar Cells, vol. 142, pp. 2-11, 2015

[5] F. Padovani and R. Stratton, "Field and thermionic-field emission in Schottky

barriers," Solid-State Electronics, vol. 9, no. 7, pp. 695-707, 1966.

13

Modeling of Contacts to p+ poly-SiModeling approach

Symbol Definition Value Units

kB

Boltzmann

constant1.38x10-23 m2 kg s-2 K-1

T Temperature 300 K

q Electronic charge 1.6x10-19 C

hPlanck’s

constant6.62 x10-34 m2 kg/s

me Mass of electron 9.31 x10-31 kg

m*t/me [1]

Ratio of

tunnelling mass

to electronic

mass

0.5 No unit

ε0

Permittivity of

free space8.85 x10-12 C2 (Nm2)-1

εSi

Relative

permittivity of Si11.7 No unit

A*

Effective

Richardson

constant [12]

32 (Acm-2K-2)

Assumptions

No illumination

No voltage bias

If dopant density is known

then, Φb can be calculated

𝑉𝑏𝑖 = ∅𝑏 −1

𝑞𝐸𝐹 − 𝐸𝑉 = 0

14

Modeling of Contacts to p+ poly-SiModeling approach

A) SEM micrograph of etch pits for a 250-nm p+ poly-Si layer

deposited on a planar sample metallized with a FT Ag-Al

paste. B) Image converted to 8-bit. C) Processed image

showing the area of the etch pits analyzed. To reveal the etch

pits, the bulk metal and the metal crystallites were etched

away

50 100 150 200 250 300 350 400 4500

50

100

150

200

250

Co

un

t

Area of the etch pits [nm2]

etch pits area fraction - 9.5%

3 6 9 12 15 18 21 24 270

20

40

60

80

100

120

140

160

180

200

220

27%

Count

Edge length of etch pits [nm]

59%

9% 4%

Ignored

(< 0.2%)

Histogram of the edge lengths of the pits. The bin width is

taken as 5 nm. 0.2% of the etch pits were ignored (shown

by the shaded region).

15

Modeling of Contacts to p+ poly-SiModeling results

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.23.95

3.96

3.97

3.98

3.99

4.00

rc [

mW

-cm

2]

fB [eV]

TETFE TE/TFE

TFE/FE

rc,exp

rc,theo

Model ϕB [eV] ρc,exp [mΩ-cm2] ρc,theo [mΩ-cm2]

TE 0.51568 ± 0.00111 3.98 ± 0.45335 3.98213 ± 0.00278

TFE 0.95697 ± 0.00228 3.98 ± 0.45335 3.98287 ± 0.00167

TE/TFE 0.94697 ± 0.00236 3.98 ± 0.45335 3.98231 ± 0.00 135

TFE/FE 1.16548 ± 0.00872 3.98 ± 0.45335 3.98133 ± 0.00025

Ideal ϕB for contact to p-type silicon - 0.53 - 0.55 eV for Ag contacts and 0.57 -

0.58 eV for Al contacts

Ideal model for the dopant range : TFE / or TE/TFE

ϕB obtained for TE model agrees with literature

For TFE model, ϕB almost 2x the expected value

16

Modeling of Contacts to p+ poly-SiDiscussion

Ideal ϕB range - 0.53 - 0.55 eV for Ag contacts and 0.57 - 0.58 eV for Al contacts

Ideal ϕB obtained for TE model applicable for dopant conc <1018

ϕB higher for TFE or TE/TFE models – charge transport hindered

Increased ρc due to the increased ϕB

Thick and uniform glass layer on planar samples → increased ϕB→ Increased ρc

17

Summary

Industrial metallization solutions needed for commercial success of p+ poly-Si.

FT Ag-Al or Al pastes ideal candidate for commercial screen-printed

metallization.

Hypothesis – thick glass layers impede the charge carriers – high ρc

0 50 100 150 200 250 3000

20

40

60

80

100

Mod. %

cry

sta

llite

s [%

]

Distance from the surface [nm]

Tex

Planideal FT paste

(front application)

Ideal FT paste

(rear application,

crytallites limited to

150 nm poly-Si)

Probable values

J0,metal <50fA/cm2

rc <0.5 mW-cm2

Probable values

J0,metal <200fA/cm2

rc <0.5 mW-cm2

Methods to improve ρc

Limiting the penetration depth of Al

crystallites by alloying with Si

Achieving thinner glass layer

Doping the glass layer

Developing FT Al pastes

18

Acknowledgment 致谢

SERIS is a research institute at the National University of Singapore (NUS). SERIS is

supported by NUS, the National Research Foundation Singapore (NRF), the Energy Market

Authority of Singapore (EMA) and the Singapore Economic Development Board (EDB).

19

Thank you for your attention!

Contact:

Pradeep Padhamanth (pradeep_p@nus.edu.sg)

Head, Solar Cell Metallization Group

Next-Generation Industrial Solar Cells & Modules

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