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9 Boundary Conditions
9.1
Outer boundary of the device structure
9.1.1
Natural boundary
9.1.2
Ohmic contacts
9.1.3
Gate contacts
9.2
Semiconductor-Insulator Interface
9.3
Exercise: 1D Shockley equations (PN junction diode)
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10 Automatic Differentation
10.1 Computation Graph
10.2 Forward- and Backward-Accumulation
10.3 Operator Overloading
10.4 Further Readings
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11 Circuit Simulation
11.1 KCL and Nodal Analysis
11.1.1
Independent Voltage Source and Auxiliary Variable
11.2 Circuit Elements
11.2.1
Resistor
11.2.2
Capacitor
11.2.3
Inductor
11.2.4
Diode
11.2.5
MOSFET
11.2.6
Others
11.3 Summary
11.4 Exercise
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12 Floating-Point Rounding Error
12.1 IEEE 754 Standard for Floating-Point Arithmetics
12.2 Examples of Rounding Error
12.3 Function Evaluation to Machine Precision
12.4 High Precision and Adaptive Precision Arithmetics
12.5 Variable Scaling
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13 Linear Solvers and Conditioning
13.1 Direct Solvers based on LU Decomposition
13.2 Iterative Solvers
13.2.1
Condition Number
13.3 Direct Solvers Based on Multi-Frontal Method
13.4 Condition Number of Shockley Equations
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Reading Mathematical Expressions