Device

1. EE5900 Advanced Algorithms for Robust VLSI CAD Dr. Shiyan Hu Office: EERC 731 shiyan@mtu.edu Device Adapted and modified from Digital Integrated Circuits: A Design Perspective by Jan M. Rabaey, Anantha Chandrakasan, and Borivoje Nikolic.

2. Goal of this chapter • Present intuitive understanding of device operation • Introduction of basic device equations

3. MOS Transistor Types and Symbols D G S NMOS D G S PMOS

4. Circuit Under Design

5. Circuit on the Chip A transistor

6. The MOS (Metal-Oxide-Semiconductor) Transistor Polysilicon Aluminum

7. |V | GS A Switch! An MOS Transistor Simple View of A Transistor

8. Silicon Basics • Transistors are built on a silicon substrate • Silicon forms crystal lattice with bonds to four neighbors

9. Doped Silicon • Silicon is a semiconductor • Pure silicon has no free carriers and conducts poorly • Adding dopants increases the conductivity • extra electrons (doped Borons) – n-type • missing electrons (doped Arsenic/Phosphorus) more holes) – p-type n-type p-type

10. NMOS Transistor Diffusion

11. NMOS - II • Refer to gate, source, drain and bulk voltages as Vg,Vs,Vd,Vb, respectively. • Vab=Va-Vb • Device is symmetric. Drain and source are distinguished electrically, i.e., Vd>Vs. • P regions have acceptor (Boron) impurities, i.e., many holes. • N regions have donor (Arsenic/Phosphorus) impurities, i.e., many electrons. • N+ and P+ are heavily doped N and P regions, respectively.

12. NMOS - III • Gate oxide are insulators, usually, silicon dioxide. • Gate voltage modulates current between drain and source, how?

13. Enhancement NMOS

14. Enhancement NMOS - II • Does not conduct when Vgs=0, except that there is leakage current. • When Vgs is sufficiently large, electrons are induced in the channel, i.e., the device conducts. This Vgs is called threshold voltage.

15. Enhancement NMOS III Positively Changed Negatively Changed

16. Enhancement NMOS - IV • When Vgs is large enough, the upper part of the channel changes to N-type due to enhancement of electrons in it. This is refereed to as inversion, and the channel is called n-channel. • The voltage at which inversion occurs is called the Threshold Voltage (Vt). • A p-depletion layer have more holes than p-substrate since its electrons have been pushed into the inversion layer. • Does not conduct when Vgs<Vt (Cut-off).

17. Enhancement NMOS V

18. Enhancement NMOS - VI • When Vgs>Vt, the inversion layer (n channel) becomes thicker. • The horizontal electrical field due to Vds moves electrons from the source to the drain through the channel. • If Vds=0, the channel is formed but does not conduct.

19. Case when Vds=0

20. Linear Region

21. Linear Region - II • When Vgs>Vt and Vgd>Vt, the inversion layer increases in thickness and conduction increases. • The reason is that there are non-zero inversion layer at both source and drain (our previous analysis works for both Vgs and Vgd).This is called linear region. • Vgd>Vt means that Vgd=Vgs-Vds>=Vt, i.e., Vds<=Vgs-Vt • Ids depends on Vg, Vgs and Vds.

22. Saturation Region

23. Saturation Region - II • When Vgs>Vt and Vgd<Vt, we have non-zero inversion layer at source but zero inversion layer at drain. • Inversion layer is said to be pinched off. This is called the saturation region. • Vgd<Vt means that Vgs-Vds<Vt, i.e., Vds>Vgs-Vt. • Electrons leaves the channel and moves to drain terminal through depletion region.

24. Saturation Region - III • In saturation region, the voltage difference over the channel remains at Vgs-Vt. This is because if Vds=Vgs-Vt, the inversion layer is barely pinched off at the drain. If Vds>Vgs-Vt, the channel is pinched off somewhere between the drain and source ends. Thus, the voltage applied across the channel is Vgs-Vt. • As a result, Ids depends on Vgs alone in this region, so we cannot keep raising Vds to get better conduction.

25. Summary • Three regions of conduction • Cut-off: 0<Vgs<Vt • Linear: 0<Vds<Vgs-Vt • Saturation: 0<Vgs-Vt<Vds • Vt depends on gate and insulator materials, thickness of insulators and so forth – process dependant factors, and Vsb and temperature – operational factors.

26. Analysis (for linear region)

27. Analysis - II • Denote by V(x) the voltage at a point x along the channel. The gate-to-channel voltage is Vgs-V(x). Since it needs to be > Vt for every point along the channel, the charge per unit area at x is • Cox is the capacitance per unit, which is • where is a constant called the permittivity of the gate oxide and tox is the thickness of gate oxide.

28. Analysis - III • Gate width W, so the total charge is QW. • I=QW/t=QWv, v being velocity of carrier. • Given surface mobility u of electrons, which depends on process, an empirical formula for v is • We have • Integrate x from 0 to L, we have • For saturation region, replace Vds by Vgs-Vt, we have . It does not depend on Vds. I 1 Q W 1

29. Summary - II • Three regions of conduction • Cut-off: 0<Vgs<Vt, I=0 • Linear: 0<Vds<Vgs-Vt, • Saturation: 0<Vgs-Vt<Vds

30. PMOS

31. PMOS - II • Dual of NMOS • Three regions of conduction • Cut-off: 0>Vgs>Vt • Linear: 0>Vds>Vgs-Vt • Saturation: 0>Vgs-Vt>Vds • Current computation is the same as NMOS except that the polarities of all voltages and currents are reversed. • Mobility of holes u in PMOS is usually half of the mobility of electronics in NMOS due to process technology.

32. Sub-threshold conduction (Leakage) • Vgs<Vt, cut-off and I=0. Not true. • In practice, for Vgs<Vt, • I is exponentially dependent on Vgs. Id0 and n are experimentally determined, k is Boltzmann’s constant and T is temperature. • Source of standby power consumption in portable devices. • Some extremely low-power circuits use sub-threshold conduction, e.g., digital watch.

33. Transistor Equivalent Resistance • In linear region, R=V/I, so • In saturation region, the voltage applied across the channel is Vgs-Vt. Thus, • Roughly speaking, channel resistance inversely depends on W since

34. Transistor Resistance - II • Larger gate width (larger gate area) -> smaller resistance -> device runs faster • This means that power/area increases with delay decreases. A lot of power-delay tradeoff like this.

35. Polysilicongate Source Drain W x x + + n n d d L d Top view Gate oxide t ox + + n n L Cross section Overlap Capacitance Overlap capacitance=2Cox Xd W

36. Channel Capacitance Cut-off Resistive Saturation Larger gate width -> Larger capacitance

37. In Standard Cell Library • A gate type has multiple gate sizes (widths) • Larger gate width means larger gate capacitance and smaller driving resistance. • Thus, for a gate type, we have a variety of transistors with different capacitance and resistance tradeoff. • Larger width means larger capacitance and thus larger power due to charging and uncharging the capacitance. • Usually, larger width transistor has smaller delay.

38. Technology Scaling • Devices scale to smaller dimensions with advancing technology. • A scaling factor S describes the ratio of dimension between the old technology and the new technology. In practice, S=1.2-1.5.

39. Technology Scaling - II • In practice, it is not feasible to scale voltage since different ICs in the system may have different Vdd. This may require extremely complex additional circuits. We can only allow very few different levels of Vdd. • In technology scaling, we often have fixed voltage scaling model. • W,L,tox scales down by 1/S • Vdd, Vt unchanged • Area scales down by 1/S2 • Cox scales up by S due to tox • Gate capacitance = CoxWL scales down by 1/S • scales up by S • Linear and saturation region current scales up by S • Current density scales up by S3 • P=Vdd*I, power density scales up by S3 • Power consumption is a major design issue

40. Summary • NMOS • Cut-Off, Linear and Saturation Regions • How to compute I • PMOS is the dual device of NMOS • I-V characteristics of MOS transistors • Resistance • Capacitance