1. Semiconductor Device Modeling
Sts. Cyril and Methodius University - Skopje FACULTY OF ELECTRICAL ENGINEERING AND INFORMATION TECHNOLOGIIES
Semiconductor Device Modeling
Lecture 1. INTRODUCTION
1. Technology Trends
2. Need for Modeling and Simulation
3. What is Computational Electronics?
4. The Hierarchy of Transport Models
prepared by Katerina Raleva and Dragica Vasileska
Knowledge Alliance EPP BG-EPPKA2-KA
Micro-Electronics Cloud Alliance (MECA)

2. I. Technology Trends … Transistor Scaling Transistor Scaling

3. Technology Trends: Scaling
Downsizing of the components has been the driving force for circuit evolution:
VT Transistor IC LSI ULSI
10 cm cm mm µm nm
In 100 years, the size reduced by one million times.
We have never experienced such a tremendous reduction of devices in human history.

4. Transistor Scaling - Drive For…
“Every years complexity doubles”
Dense Memory
Speed
Scaling Down
Low Power
Complexity
High Frequency
Space

5. Technical Drivers of Semiconductor Industry: DRAM and MCUs
Microprocessor
Different performance criteria for these two major product families
More memory density
More speed

6. The key parameter in MCUs: Gate Length
MOSFET Gate Length (nm)
Transistors per processor chip
Year

7. Technology Trends: Traditional Scaling
Gate Oxide Thickness Scaling
-key enabler for Lg scaling
Junction Scaling
-another enabler for Lg scaling
-improve abruptness (Rext reduction)
Vcc Scaling
-reduce xdepl (improve SCE)
-did not follow constant E field

8. Technology Trends: Post “Traditional Scaling” Innovations
90 nm
2003
65 nm
2005
45 nm
2007
32 nm
2009
22 nm
2011
FinFET
Mobility booster: uniaxial strain
Gate leakage reduction: HiK
Poly depletion elimination: metal gate

9. II. Need for Modeling and Simulation

10. Modeling Nano-Devices and Parallel Computing…
As semiconductor feature sizes shrink into the nanometer scale regime, even conventional device behavior becomes increasingly complicated….
Typical modeling and simulation efforts directed towards the understanding of electron transport at the nanometer scale utilize single workstations as computational engines…. Very long computational time!!!
Parallelization of scientific and engineering oriented simulation codes can provide significant computational speed-up.

11. Need for Modeling and Simulation
Increased costs for R&D and production facilities, which are becoming too large for any one company or country to accept.
Shorter process technology life cycles.
Emphasis on faster characterization of manufacturing processes, assisted by modeling and simulation.

12. Modeling and Simulation
Modeling and simulations are two closely related computer applications which play a major role in science and engineering today.
They help scientists and engineers to reduce the cost and time consumption for research.
They are also useful for ordinary people to understand and be trained for something easily.

13. What is Modeling ?
Modeling is creating a ‘model’ which represents an object or system with its all or subset of properties. A model may be exactly the same as the original system or sometimes approximations make it deviates from the real system.
A mathematical model describes a system with equations.
Modeling can reduce the cost of a process and make the progress faster.

14. What is Simulation?
Simulation is a technique of studying and analyzing the behavior of a real world or an imaginary system by mimicking it on a computer application.
A simulation works on a mathematical model that describes the system.
In a simulation, one or more variable of the mathematical model is changed and resulted changes in other variables are observed.

15. Diferences between Modeling and Simulation
1. Both computer modeling and simulations are computer applications which represent a real world or imaginary system.
2. Both computer modeling and simulations help designers to save time and money.
3. A simulation is changing one or more variables of a model and observing the resulted changes.
4. Although a model always tries to represent the actual system, a simulation may try to observe the results by doing impossible (in real world) changes.
5. A model can be considered as a static and a simulation can be considered as dynamic as the variables of a simulation get always changed.

16. III. What is Computational Electronics?
UNIVAC
ENIAC

17. What is Computational Electronics ?
Customer Need
Process Simulation
-refers to the physical simulation of semiconductor devices in terms of charge transport and the corresponding electrical behavior.
Device Simulation
Parameter Extraction
Circuit Level Simulation no
yes

18. The Goal of Computational Electronics
-to provide simulation tools with the necessary level of sophistication to capture the essential physics while at the same time minimizing the computational burden…
Building a Simulator from Scratch…
Physics
Output
Examples
Documentation
Downloads
Input

19. Basic Elements of Device Simulations
There are two main kernels in device simulations that need to be solved self-consistently with one another:
Electronic Structure, Lattice Dynamics
Transport Equations
Electromagnetic Fields
Device Simulation
J, r
E, B
KERNEL 2 (driving charge flow)
KERNEL 1 (governing charge flow)

20. IV. The Hierarhy of Transport Models
Electronic Structure, Lattice Dynamics
Transport Equations
Electromagnetic Fields
Device Simulation
J, r
E, B

21. Hierarhy of Transport Models
Approximate
1. Compact models
Easy,fast
2. Drift–Diffusion Equations
3. Hydrodynamics Equations
Semi-classical
4. Boltzmann Transport Equation (Monte Carlo methods)
5. Quantum Hydrodynamics
Covered in this course
6. Quantum Monte Carlo methods
7. Quantum-Kinetic Equation (Liouville, Wigner-Boltzmann)
Quantum
8. Green’s Functions method
9. Direct solution of the n-body Schrodinger Equation
Exact
Difficult,slow

22. Diffusive vs. Ballistic Transport
‘Classical’
Transport regime depends on length scale:
l - Phase coherence length
lin - Inelastic mean free path
le - Elastic mean free path
‘Quantum’

23. Nanoscale Transistors

24. Advantages and Disadvantages of Existing Semi-classical Simulators
DRIFT-DIFFUSION MODEL:
Good for devices with LG>0.5mm.
Can’t deal with hot-carrier effects.
HYDRODYNAMIC MODEL:
Hot-carrier effects,such as velocity overshoot, included.
Overestimates the velocity at high fields.
PARTICLE-BASED DEVICE SIMULATION:
Accurate up to classical limits. Allow proper treatment of the discrete impurity effects and e-e and e-i interactions.
Time consuming.

25. Range of Validity of Various Transport Regimes
Scattering
Rare
Nanowires, Superlattice
Ballistic Transistor
Current IC’s
Older IC’s
e-e (Many), e-ph (Few)
Many
Model
Drift Diffusion
Hydrodynamic
Monte Carlo
Schrodinger/ Green’s Functions
Quantum hydrodynamic
Wave
Applications
Transport regime
Quantum
Ballistic
Fluid
Diffusive
L<le-e
L<l
L>>le-e
L>>le-ph
L~le-ph
L<<le-ph

26. Summary
Different transport models exist with different accuracy and different computational needs for modeling the wide variety of devices that are used in practice every day.
The goal of Computational Electronics is to teach one what models are appropriate for modeling specific device structure and what are the limitations and the advantages of the model used.