Modeling of the device SEYED AHMAD SHAHAHMADI Principal supervisor: Prof. Dr. Nowshad Amin

Modeling of the device

SEYED AHMAD SHAHAHMADI

Principal supervisor: Prof. Dr. Nowshad Amin

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What is a device model?

A device model is a representation of the characteristics of or conditions in a device, in the form of

• An equation• An equivalent circuit• A diagram/graph/table

Together with

The reasoning and assumptions / approximations leading to the representation.

Constituents of a device model

Qualitative Model

Quantitative Model

Intuitive visualization of phenomena by logical reasoning without involving intricacies of equations

Helps estimate device terminal characteristics (Equations or Equivalent circuit or Diagram)

Approximatio

ns

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Example 1: Ideal Diode Model

𝐼=𝐼 𝑠 [exp( 𝑉𝑉 𝑡)−1]

𝐼 𝑠=𝑞𝑛𝑖2[ √𝐷𝑛/𝜏𝑛

𝑁 𝑎

+√𝐷𝑝 /𝜏𝑝

𝑁 𝑑]𝐴

Approximations:

Structure:1. 1-D current flow2. Abrupt junction3. Uniform and long P/N regions4. Not grossly asymmetric (Na/Nd < 10)

Space-charge region:5. Fully depleted of mobile carries6. No excess gen./rec.7. |drift| = |diffusion|

Quasi-neutral region:8. Voltage drop << applied voltage9. Minority carrier flow by diffusion10.Injection level is low11.Length >> minority carr. Diff. length

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𝐼=𝐼 𝑠 [exp( 𝑉 𝑖

𝑉 𝑡)−1]

Approximations:




𝑉 𝑖=𝑉 − 𝐼 𝑅𝑠

+ I𝐺𝑅− 𝐼 𝐵

𝐼𝐺𝑅= 𝐼𝑆𝑅(1−𝑉 𝑖

𝑉 𝐽

)1 /2

[exp ( 𝑉 𝑖

𝑁𝑅𝑉 𝑖)−1]

𝐼𝐵=𝐼𝐵𝑉 exp(−𝑉 𝑖+𝐵𝑉𝑁𝑉 𝑖

)

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𝐼=𝐾𝑚 𝐼 𝑠[exp ( 𝑉 𝑖

𝑁𝑉 𝑡)−1]

Approximations:







𝑉 𝐽

)1 /2

[exp ( 𝑉 𝑖



)𝐾𝑚=√𝐼 𝐾𝐹 /(𝐼𝐾𝐹+𝐼𝐷)

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𝐼=𝐾𝑚 𝐼 𝑠[exp ( 𝑉 𝑖

𝑁𝑉 𝑡)−1]

Approximations:







𝑉 𝐽

)𝑚

[exp( 𝑉 𝑖



)𝐾𝑚=√𝐼 𝐾𝐹 /(𝐼𝐾𝐹+𝐼𝐷)

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Modeling is like cartooning

A model is a cartoon of a phenomenon

Mathematical Or equivalent circuit

Or diagram / graph / table

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Analysis, Modeling, Simulation, Design

Analysis: Separation of the whole into parts, understanding the parts in isolation, combining the understanding of the parts so obtained to understand the whole.

Modeling: Derivation of an approximate mathematical or equivalent circuit representation of phenomena.

Simulation: Replication of the behavior of one system by another system.

Design (includes optimization): Plan of construction of a system to a given specification.

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Analysis, Modeling, Simulation, Design of solar cell

Analysis: Separation of the solar cell into parts, understanding the parts in isolation, combining the understanding of the parts so obtained to understand the solar cell.

Modeling: Derivation of an approximate mathematical or equivalent circuit representation of the solar cell terminal characteristics.

Simulation: Replication of the behavior of a fabricated device by a computer or any kind of solar cell model.

Design (includes optimization): Plan of construction of a solar cell to a given specification.

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Analysis, Modeling, Simulation, Design of pn junction

p

p

n

n

Obtaining n, p, Jn, Jp, Ψ, E for each part

Combination of parts with respect to interfaces

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Levels of solar cell simulation at UKM

1. Process

InputProcess conditions (e.g. time and temperature)Process models

OutputGeometryDoping profile

Commercial packagesATHENA

2. Device

InputGeometry and dopingNumerical device modelBias conditions

OutputI-V curvesDistributions of carriers, field potential and current densityEQE curves

Commercial packagesATLAS, PC1D, AMPS, SCAPS and AFORS

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Challenge of modeling

• Models are not able to manipulate many phenomena

• Results are based on the consideration of the ideal case

• Most of the models have come from the experimental study of Silicon-based materials

Therefore:

In order to have a valid simulation a proper image has to be seen

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Literature review

0 10 20 30 40 50 60 70 80 90 1000

2

4

6

8

10

12

Germanium content [%]

Initi

al e

fficie

ncy

[%]

SiGe single junctions efficiencies

1. The electronic properties of the SiGe thin-film solar cell deteriorate with increasing Ge ratio owing to the increase of the density of midgap states

2. The crystal quality has a direct proportion to the solar cell efficiency.

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Simulation: PC1D

Parameters c-Si c-Si c-Ge c-Si

Layer p-layer i-layer i-layer n-layer

Thickness (nm) 25100-1000

100-1000

30

Doping concentration (/cm3)

1018 1012 1012 1018

Bandgap (eV) 1.12 1.12 0.664 1.12

Electron affinity (eV) 4.05 4.05 4 4.05Nc/Nv 1.777 1.777 2 1.777Electron mobility (cm2/Vs)

160 160 641 160

Hole mobility (cm2/Vs)

155 155 175 155

bulk recombination τn (µs) 12.6 12.6 43 12.6

bulk recombination τp (µs) 4.6 4.6 20 4.6

Simulation assumption:

• results are based on the consideration of the ideal case

(Crystalline phase)

• Used models:

• Auger recombinatin

• SRH surface and bulk recombination

• Field-Enhanced recombination

• Bandgap narrowing model

• Exterior front reflectance is 10 %.• Emitter contact is 10-6 Ω.• Base contact is 0.015 Ω.

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Simulation: PC1D

1.12 eV

0.66 eV1.12 eV

pi

n

1.12 eV

p-c-Si 25 nm

i-c-Ge 100-1000 nm

n-c-Si 30 nm

p-c-Si 25 nm

i-c-Si 100-1000 nm

n-c-Si 30 nm

100 200 300 400 500 600 700 800 900 10000

1

2

3

4

5

6

7

8

9

Ge

Si

Absorber layer thickness [nm]

Effi

ciency

[%

]

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Simulation: PC1Dp-c-Si 25 nm

i-c-SiGe200 nm

n-c-Si 30 nm0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0

0.5

1

1.5

2

2.5

3

3.5

4

x=0

x=0.1

x=0.2

x=0.3

x=0.4

x=0.5

x=0.6

x=0.7

x=0.8

x=0.9

x=1

Voltage [Voc]

Curr

ent

densi

ty [

mA

/cm

2]

0 10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6

7

8

Germanium content [%]

Effi

ciency

[%

]

Increasing Ge ratio

Hypothetical line

Simulated line

300 500 700 900 1100 1300 1500 17000

10

20

30

40

50

60

70

80

90

100

x=0

x=0.1

x=0.2

x=0.3

x=0.4

x=0.5

x=0.6

x=0.7

x=0.8

x=0.9

x=1

Wavelength [nm]

EQ

E [

%]

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Simulation: Atlas

Parameters a-Si:Hµc-Si0.25

Ge0.75:Ha-Si:H

Layer p-layer i-layer n-layerThickness (nm) 25 200 30

Doping concentration (/cm3)

1018 1012 1018

Bandgap (eV) 1.8 1.1 1.8Electron affinity (eV) 4 4.17 4.15Dielectric Function 7.2 14.95 11.9Electron mobility

(cm2/Vs)20 40 20

Hole mobility (cm2/Vs) 1.5 3 1.5Electron density of

state (percc)2 × 1020 1.48 × 1019 2 × 1020

Hole density of state (percc)

1020 0.71 × 1019 1020

Electron lifetime 10-6 3 × 10-5 10-6

Hole lifetime 10-6 10-5 10-6

Donor activation energy

0.3576 - 0.2397

Acceptor activation energy

0.3576 - 0.2397

Absorption coefficient - Resige22.nk -

Simulation assumption:

• Although some electrical properties have been derived from realistic studies, however, some electrical data were adopted from ideal case.

• Specifies interface parameters at boundaries are used based on Si study.

• Used models:• Auger recombinatin• SRH surface and bulk recombination• Doping concentration dependent model• The effects of Fermi statistic• Bandgap narrowing model• Defect models

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Simulation: Atlas

0 0.05 0.1 0.15 0.2 0.25 0.3 0.350

5

10

15

20

25

30

µc-Si0.25 Ge0.75:H

Voc (V)

Jsc

(mA

/cm

2)

Jsc=27.76Voc=0.3FF=0.55Eff=4.58 %

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Conclusion

Equations get lengthy and parameters increase in number while developing a model. The basic approximations of the models are the important point and as long as the model can be used in experiments, process is valid, therefore a proper model has to be taken into consideration. Finally a realistic simulations have been carried out by PC1D and Atlas.

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Modeling of the device SEYED AHMAD SHAHAHMADI Principal supervisor: Prof. Dr. Nowshad Amin