Modeling of the device SEYED AHMAD SHAHAHMADI Principal supervisor: Prof. Dr. Nowshad Amin.
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Transcript of 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
2
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
3
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
4
Example 1: Ideal Diode Model
𝐼=𝐼 𝑠 [exp( 𝑉 𝑖
𝑉 𝑡)−1]
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
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
)
5
Example 1: Ideal Diode Model
𝐼=𝐾𝑚 𝐼 𝑠[exp ( 𝑉 𝑖
𝑁𝑉 𝑡)−1]
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
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
)𝐾𝑚=√𝐼 𝐾𝐹 /(𝐼𝐾𝐹+𝐼𝐷)
6
Example 1: Ideal Diode Model
𝐼=𝐾𝑚 𝐼 𝑠[exp ( 𝑉 𝑖
𝑁𝑉 𝑡)−1]
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
𝑉 𝑖=𝑉 − 𝐼 𝑅𝑠
+ I𝐺𝑅− 𝐼 𝐵
𝐼𝐺𝑅= 𝐼𝑆𝑅(1−𝑉 𝑖
𝑉 𝐽
)𝑚
[exp( 𝑉 𝑖
𝑁𝑅𝑉 𝑖)−1]
𝐼𝐵=𝐼𝐵𝑉 exp(−𝑉 𝑖+𝐵𝑉𝑁𝑉 𝑖
)𝐾𝑚=√𝐼 𝐾𝐹 /(𝐼𝐾𝐹+𝐼𝐷)
7
Modeling is like cartooning
A model is a cartoon of a phenomenon
Mathematical Or equivalent circuit
Or diagram / graph / table
8
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.
9
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.
10
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
11
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
12
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
13
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.
14
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.
15
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
[%
]
16
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 [
%]
17
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
18
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 %
19
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.
questions and answers