1 Abstract
CMOS transistors. Don’t conflate general analog design versus CMOS design in particular. MOS Transistor models, the inverter, combinational circuits, sequential circuits, arithmetic circuits and architectures, interconnect parasitics, and timing issues in digital circuits.
2 The goal and a bird’s eye view
The two most important characteristics of circuits are
- the time taken, or delay. This is measured in seconds.
- the energy used to do the task. This is measured in joules.
3 Estimating the time taken
iThe propagation delay Logical effort Sutherland.
4 My mental model
History; Moore and Dennard scaling: power used by chip remains constant even as transistor counts double every 18-24 months. Free HW performance. Further, as they shrink, they become faster (switching frequency) consume less power and are cheaper to manufacture.
The transistor is a non-linear device giving it great flexibility and range in application. It may be made to operate in linear and non-linear modes.
Its physical underlying mechanism is a
Therefore as an engineer, you are constantly thinking in terms of measurements which correspond to its performance as a switch, and measurements in terms of its performance as an amplifier of electrical signals.
5 A CMOS model
Base:
- The feature size (device size) is the minimum dimension of a transistor which may be built reliably.
5.1 Doping
Silicon is a 3D lattice of atoms. All of its valence electrons are involved in chemical bonds, making silicon a poor conductor. A dopant from Group V of the periodic table, like arsenic, replaces a silicon atom in the lattice but still bonds to four neighbours, leaving one free valence electron. Heat at room temperature (thermal vibration) causes the electron free to move, leaving a positively charged As+ ion and a free electron. This is an n-type semiconductor because the free carriers are negatively charged.
Take the same with a group III dopant, like boron. In this case, the boron may borrow an leectron from a neighbouring silicon atom. If that atom borrows electrons from its neighbours, the “hole” (missing electron) propagates. Since the hole, through the absence of an electron, is “positively charged”, this is a p-type or positively charged semiconductor.
5.2 Diodes
A junction between p-type and n-type silicon is called a diode. Let the p-type material be named the anode and the n-type material the cathode. Take the cathode as the origin of measurement. If the voltage of the anode is greater than 0, the diode is forward biased and current flows. If the voltage of the anode is less than 0, the diode is reverse biased and very little current flows.
5.3 cMOS structure
A metal-oxide-semiconductor (MOS) structure is formed from stacking layers of conducting versus insulating materials. The base device has a structure with five parts: the source material, drain material, polysilicon barrier, silicon dioxide, and bulk silicon. The only difference between the pMOS and nMOS transistor is the source and drain material of nMOS transistors is n-type semiconductor, while for pMOS it is p-type. This otherwise symmtery makes the relationship between matched nMOS and pMOS (nMOS and pMOS of otherwise the same dimension) behave like exact opposites around thresholds. Matched transistors are an important topic and we will come back to them later.
6 Sizing using transconductance
https://github.com/dreoilin/pygmid
7 References
https://pages.hmc.edu/harris/cmosvlsi/4e/index.html
https://users.cs.utah.edu/~elb/cadbook/