Hochschule Kempten      
Fakultät Elektrotechnik      
Microelectronics       Fachgebiet Elektronik, Prof. Vollrath      



Prof. Dr. Jörg Vollrath

02 History

Video of lecture 03 MOSFET, SPICE models, propagation delay 31.03.2021

Länge: 01:26:05
0:0:0 0

0:3:9 Goals today

0:6:36 Output and transfer curve

0:9:48 50 nm technology voltage limit

0:14:58 Subthreshold characteristic

0:16:49 Bulk source voltage and threshold voltage

0:19:25 Design by selecting W or number of unit transistors

0:24:29 MOSFET typical layout and rules

0:30:37 SPICE models 1 um, 50 nm

0:35:39 Infineon 130 nm MOSFET transistor parameters

0:40:29 SPICE models details

0:48:31 MOSFET as switch

0:50:39 Transistor RC model

0:52:39 Transistor Capacitances

0:59:19 Propagation delay

1:1:39 Rising and falling output

1:8:49 equivalent capacitance, Miller capacitance

1:16:49 Timing closure


Microelectronic products


mobile phone




Hierarchical Description

Top Down System

Subsystemi, Subsystemj

Subsystemk, Subsysteml
Bottom up

Find one solution and then optimize



“The First Rule of Program Optimization: Don't do it.
The Second Rule of Program Optimization (for experts only!): Don't do it yet.”
- Michael A. Jackson

Find a solution first

Diagnose problems

“We should forget about small efficiencies, say about 97% of the time:
premature optimization is the root of all evil.
Yet we should not pass up our opportunities in that critical 3%.
A good programmer will not be lulled into complacency by such reasoning,
he will be wise to look carefully at the critical code;
but only after that code has been identified”
- Donald Knuth

Identify the problem through test first

Design Flow


Comparison VLSI VL82C486 Single Chip 486 System Controller HV






Target market High volume Prototype to medium volume Single to high volume
Design speed Slow Fast Faster
Design Tools Expensive No cost No cost
Efficiency Optimum slow clock, parallel operation slow clock, seriell operation, analog function
ASIC: Application specific integrated circuit.
FPGA: File programmable gate array.


Raspberry Pi: µC, periphery

Operating system: Linux
Communication: Wifi, Webserver C(++), JavaScript
Application: C(++), JavaScript
Raspberry Pi 2 Model B v1.1 top new (bg cut out) ArduinoUnoSMD

Arduino: Microcontroller (µC)

No operating system
Application and Communication C

Zedboard: FPGA, µC

Field programmable gate array (FPGA)
FPGA programming: VHDL, Verilog, IP Wizard
Optional operating system: Linux
Communication: Wifi, Webserver C(++), JavaScript
Application: C(++), JavaScript

Switch matrix, logic and registers, programmable


Proprietory software for design
Electronic design automation (EDA) software tools:
linux, perl, phyton, JavaScript
Full custom ASIC
Standard cell ASIC
Gate Array Based Asic



Matlab, Labview can support some platforms.


Bottom up

MOSFET transistors, performance, layout and standard cells

NAND, AOI logic, scan flip flop

Place and route with VHDL

Make a chip with IOs, circuit and test structures

Electronic system

System Description

  • State diagram, truth table
  • Schematic (Graphic with symbols)
  • Logic diagram
  • Signal behaviour
  • Hardware description language (HDL): Verilog, VHDL
  • SystemC, Matlab, Simulink, Labview
  • Programming Language: JavaScript


Structural Description
Behavioral Description

Analog and digital signals

MOSFET Transistor

Transistor Evolution

How much area uses one transistor?
Theoretical minimum:
Active area: W*L*4
Contacts: W*L*4*3
Minimum Feature size F
F = 45 nm; 731M Transistors; 262 mm2
A = 262 mm2/(731*106)= 358413 nm2 = 177*F2

Courtesy of Intel
2008 Intel Core i7
731 Million MOS Transistors
45 nm process
263 mm2
2.6..3.2 GHz

Summary Transistor Evolution

MOSFET- transistor
Moore‘s law
Implications of reduced feature size:
30% Productivity gain per year
Power consumption, complexity/features, price
Hierarchical Design

Microelectronics deals with small electronic components
Transistor, diode, resistor, capacitor, inductance
Microelectronic systems are getting cheaper
Complex systems can be realized
Functions are getting cheaper

Typical microelectronic components of interest are:
Microcontroller (Microprocessor, memory, digital and analog functions)
FPGA (Field programmable gate arrays)
ASIC (Application specific integrated circuits)
This class shows how to design digital and analog CMOS microelectronic components and systems

Inverter schematic and layout

Schematic and layout are representing an inverter.
An inverter uses a NMOSFET and a PMOSFET.
The schematic shows the components and connections.
The layout has added different colors for different layers of the manufacturing process and each component.
These colors are transferred into the schematic showing the relationship between layout and schematic.
Wiring and transistor gates and diffusion have a minimum physical size of width and length of F.
There are also minimum distances required to prevent shorts.

It is difficult to automatically transform one view into the other.
A schematic is drawn to be able to easily understand the circuit. On the left is GND, on the right VDD, on the top inputs, on the bottom outputs.
In a schematic connection between 2 pins can be accomplished by labeling the pins with the same names. Lines can cross without resulting in short circuits.
A layout is drawn for symmetric and regular patterns, avoiding signal cross coupling and shape distortion, and having minimum size.

Equations of a n-channel MOSFET

\( I_{DS}= \cases{ \begin{matrix} 0 & \text{for} & V_{GS} \leq V_{th} & \text{Off} \\ I_{on} exp^{\frac{ V_{GS}-V_{th} - \frac{kT}{e}}{\frac{kT}{e}}} \left( 1+\lambda V_{DS} \right) & \text{for} & 0 \leq V_{GS} - V_{th} \lt \frac{kT}{e} & \text{Weak inversion} \\ \beta \left( V_{GS}-V_{th} \right)^2 \left( 1+\lambda V_{DS} \right) & \text{für} & \frac{kT}{e} \leq V_{GS} - V_{th} \lt V_{DS} & \text{Saturation} \\ \beta \left( 2 \left( V_{GS}-V_{th} \right) V_{DS} - V_{DS}^2 \right) & \text{for} & \frac{kT}{e} \leq V_{GS} - V_{th} \geq V_{DS} & \text{Linear} \end{matrix} } \)
\( \beta = \frac{\mu_n \epsilon_{ox}}{2d_{ox}} \frac{W}{L} = \frac{1}{2} \mu_n C_{ox}^{'} \frac{W}{L} = \frac{1}{2} K_{n}^{'} \frac{W}{L} = \frac{1}{2} K_{n} \)
Quelle Vollrath
Quelle Vollrath
Vth threshold voltage
λ Output conductance
W width, L length
µ mobility
Cox = e /dox Gate oxide capacitance
Vt = kT/q (300K) = 0.0259 V

Simulation verifies first correct Vth and maximum current IDS at maximum voltage Vdd.
Then the input capacitance Cox is confirmed with AC simulation of a RC circuit having the MOSFET gate as capacitance C.

Microelectronic has only transistors as elements.
Design is done using transistors with choosing W and L.
MOS transistors are also used as capacitances, resistors, diodes and lateral bipolar transistors.
In sub 50nm processes FINFETs are used having a fixed L and W. These transistors are called unit transistors. Circuits are designed combining transistors in series or parallel to get the desired W/L ratio. This makes automated design easier.

Elektronik 3, 08 MOSFET

NFET Transistor subthreshold characteristic

MOSFET transistors can also be operated in the subthreshold region for low voltage power supply.
The graph shows an increase in current by a factor of 10 for 100 mV change in VGS.

Threshold voltage Vth

\( V_{th}= V_{th0} + \left( \gamma \sqrt{V_{SB}+2\phi_F}-\sqrt{2\phi_F}\right) \)
  • Vth: Threshold voltage
  • VSB: Source-bulk voltage
  • \( \phi_F \): Fermipotential of semiconductor
  • \( \gamma \): Body factor

  • Graph:
    • \( V_{th0}=1V \)
    • \( \phi_{F}=0.3V \)
    • \( \gamma=0.75 \sqrt{V} \)

MOSFET Transistor design

  • Process sensitivity analysis: Process window lot (PWL)
    Check in simulation different Vth and W L variations
  • MOSFET layout

    • Simple: crossing of polysilicon and contact diffusion
    • Finger structure
    • Serpentine
    • Common centroid layout

    MOSFET SPICE models

    Long channel MOSFET F = 1 µm, VDD = 5 V
    VTh 0.8 V 0.9 V Typical
    KP 120 µA/V240 µA/V2dox = 20 nm
    C'ox 1.75 fF/µm2 1.75 fF/µm2 Cox = C'ox W L
    λ 0.01 V-1 0.0125 V-1 L = 2
    R 15 kΩ L/W 45 kΩ L/W
    Short channel MOSFET F = 50 nm, VDD = 1 V
    VTh 0.28 V 0.28 V Typical
    KP 60 µA/V230 µA/V2 dox = 1.4 nm
    C'ox 25 fF/µm2 25 fF/µm2 Cox = C'ox WL
    λ 0.6 V-1 0.3 V-1 L = 2
    R 34 kΩ/W 68 kΩ/W
    Table according to Baker. Width W and L length are applied in multiples of feature size F for KP.

    Propagation delay can be calculated with tPD = 0.7 · R · C
    R is the resistance of NFET or PFET. C is the sum of the output capacitance (Coxn) and input capacitance (3/2 Cox).
    C = (3/2 + 1 ) (Coxn + Coxp)

    A 1 µm unit transistor has a Cox of 1.75 fF and R of 15 kΩ (45 kΩ).
    tPD = 0.7 · 2 · 1.75 fF · 0.5 · ( 15 kΩ + 45 kΩ) = 73.5 ps

    A 50 nm unit transistor has a Cox of 25 fF/µm2 · 50nm · 50 nm = 62.5 aF and R of 34 kΩ (68 kΩ).
    tPD = 0.7 · 2 · 25 fF · 50 nm · 50 nm · 0.5 · ( 34 kΩ + 68 kΩ) = 2.23 ps

    Simulated inverter 24..32 ps

    More models:

    Baker: 1 µm MOSFET model, 50 nm MOSFET model, cmosedu_models.txt
    Sedra Smith Level=1 5 µm, 0.5 µm: sedra_lib.lib
    Allen, Holberg Level=3 0.8 µm: Holberg.txt
    TSMC 0.25um CMOS MOSFETs (level 3) t14y_tsmc_025_level3.lib from MOSIS .


    .model CD4007N NMOS(LEVEL=1 KP=500u VT0=1 LAMBDA=0.002 CGSO=45n CGBO=2n CGDO=45n)
    .model CD4007P PMOS(LEVEL=1 KP=500u VT0=-1 LAMBDA=0.002 CGSO=45n CGBO=2n CGDO=45n)

    ALD1106, ALD1107

    .model ALD1106N NMOS(LEVEL=1 KP=0.48m VT0=0.7 LAMBDA=0.018 CGDO=100n CGSO=100n)
    .model ALD1107P PMOS(LEVEL=1 KP=0.2m VT0=-0.7 LAMBDA=0.018 CGDO=100n CGSO=100n)

    130 nm Infineon MOSFET transistors

    Infineon 130 nm platform


    04 Inverter