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

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) Approximations 2

Example 1: Ideal Diode Model 3 Approximations: Structure: 1.1-D current flow 2.Abrupt junction 3.Uniform and long P/N regions 4.Not grossly asymmetric (Na/Nd < 10) Space-charge region: 1.Fully depleted of mobile carries 2.No excess gen./rec. 3.|drift| = |diffusion| Quasi-neutral region: 1.Voltage drop << applied voltage 2.Minority carrier flow by diffusion 3.Injection level is low 4.Length >> minority carr. Diff. length

Example 1: Ideal Diode Model 4 Approximations: Structure: 1.1-D current flow 2.Abrupt junction 3.Uniform and long P/N regions 4.Not grossly asymmetric (Na/Nd < 10) Space-charge region: 1.Fully depleted of mobile carries 2.No excess gen./rec. 3.|drift| = |diffusion| Quasi-neutral region: 1.Voltage drop << applied voltage 2.Minority carrier flow by diffusion 3.Injection level is low 4.Length >> minority carr. Diff. length

Example 1: Ideal Diode Model 5 Approximations: Structure: 1.1-D current flow 2.Abrupt junction 3.Uniform and long P/N regions 4.Not grossly asymmetric (Na/Nd < 10) Space-charge region: 1.Fully depleted of mobile carries 2.No excess gen./rec. 3.|drift| = |diffusion| Quasi-neutral region: 1.Voltage drop << applied voltage 2.Minority carrier flow by diffusion 3.Injection level is low 4.Length >> minority carr. Diff. length

Example 1: Ideal Diode Model 6 Approximations: Structure: 1.1-D current flow 2.Abrupt junction 3.Uniform and long P/N regions 4.Not grossly asymmetric (Na/Nd < 10) Space-charge region: 1.Fully depleted of mobile carries 2.No excess gen./rec. 3.|drift| = |diffusion| Quasi-neutral region: 1.Voltage drop << applied voltage 2.Minority carrier flow by diffusion 3.Injection level is low 4.Length >> minority carr. Diff. length

Modeling is like cartooning 7 A model is a cartoon of a phenomenon Mathematical Or equivalent circuit Or diagram / graph / table

Analysis, Modeling, Simulation, Design 8 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.

Analysis, Modeling, Simulation, Design of solar cell 9 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.

Analysis, Modeling, Simulation, Design of pn junction 10 p p n n Obtaining n, p, Jn, Jp, Ψ, E for each part Combination of parts with respect to interfaces

Levels of solar cell simulation at UKM Process Input Process conditions (e.g. time and temperature) Process models Output Geometry Doping profile Commercial packages ATHENA 2. Device Input Geometry and doping Numerical device model Bias conditions Output I-V curves Distributions of carriers, field potential and current density EQE curves Commercial packages ATLAS, PC1D, AMPS, SCAPS and AFORS

Challenge of modeling 12 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

Literature review SiGe single junctions efficiencies 13 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.

Simulation: PC1D Parametersc-Si c-Gec-Si Layerp-layeri-layer n-layer Thickness (nm) Doping concentration (/cm 3 ) Bandgap (eV) Electron affinity (eV) N c /N v Electron mobility (cm 2 /Vs) Hole mobility (cm 2 /Vs) bulk recombination τ n (µs) bulk recombination τ p (µs) 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 Ω. Base contact is Ω. 14

Simulation: PC1D 1.12 eV p i n p-c-Si25 nm i-c-Ge nm n-c-Si30 nm p-c-Si25 nm i-c-Si nm n-c-Si30 nm 15

Simulation: PC1D p-c-Si25 nm i-c-SiGe200 nm n-c-Si30 nm Increasing Ge ratio Hypothetical line Simulated line 16

Simulation: Atlas Parametersa-Si:Hµc-Si 0.25 Ge 0.75 :Ha-Si:H Layerp-layeri-layern-layer Thickness (nm) Doping concentration (/cm 3 ) Bandgap (eV) Electron affinity (eV) Dielectric Function Electron mobility (cm 2 /Vs) Hole mobility (cm 2 /Vs)1.53 Electron density of state (percc) 2 × × × Hole density of state (percc) × Electron lifetime × Hole lifetime Donor activation energy Acceptor activation energy 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 17

Simulation: Atlas 18

Conclusion 19 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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