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Basic Interconnects VLSI Design EE213

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1 Basic Interconnects VLSI Design EE213
These slides contain some notes on interconnections in VLSI circuits. Full details are in Pucknell and Eshraghian pages

2 Introduction Wiring-Up of chip devices takes place through various conductors produced during processing Today, interconnects constitute the main source of delay in MOS circuits We will examine: Sheet Resistance – Resistance / Unit Area Area Capacitance Delay Units CMOS Inverter Delay Rise and Fall Time Estimation

3 Sheet Resistance A Resistance of a square slab of material RAB = ρL/A
=> R = ρL/t*W Let L = W (square slab) => RAB = ρ/t = Rs ohm / square t w L B RAB = ZRsh Z = L/W

4 Layer Rs (Ohm / Sq Aluminium 0.03 N Diffusion 10 – 50 Silicide 2 – 4
Typical sheet resistance values for materials are very well characterised Layer Rs (Ohm / Sq Aluminium 0.03 N Diffusion 10 – 50 Silicide 2 – 4 Polysilicon N-transistor Channel 104 P-transistor Channel 2.5 x 104 Typical Sheet Resistances for 5µm Technology

5 N-type Minimum Feature Device
Polysilicon L N - diffusion 2λ W 2λ R = 1sq x Rs = Rs = 104 Ώ

6 Polysilicon W = 8λ L = 2λ N - diffusion R = Z Rs R = (L/W) * Rs R = Ώ

7 Exercise Calculate the ON resistance for a depletion pull – up Nmos inverter with Zpu : Zpd ratio 4:1 Use sheet resistance values given in earlier slide

8 Area Capacitance of Layers
Conducting layers are separated from each other by insulators (typically SiO2) This may constitute a parallel plate capacitor, C = є0єox A / D (farads) D = thickness of oxide, A = area, єox = 4 F/µm2 Area capacitance given in pF/µm2

9 Capacitance Standard unit for a technology node is the gate - channel capacitance of the minimum sized transistor (2λ x 2λ), given as Cg This is a ‘technology specific’ value

10 References Pucknell and Eshraghian pages

11 Delay Unit For a feature size square gate, τ = Rs x Cg
i.e for 5µm technology, τ = 104 ohm/sq x 0.01pF = 0.1ns Because of effects of parasitics which we have not considered in our model, delay is typically of the order of ns Note that τ is very similar to channel transit time τsd

12 CMOS Inverter Delay Pull-down delay = Rpd x 2 Cg
Pull-up delay = Rpu x 2Cg Asymmetry in rise and fall due to resistance difference between pull-up and pull-down (factor of 2.5) (due to mobilities of carriers) Delay through a pair of inverters is 2 τ (fall time) + 5 τ (rise time) Delay through a pair of CMOS inverters is therefore 7 τ

13 CMOS Inverter Delay Asymmetry can be improved by reducing resistance of pull - up Reduce resistance of pull - up by increasing channel width ( typically by a factor of 2.5) Note that increasing channel width also increases the capacitance The overall delay (after increasing channel width by 2.5) will be the same 7 τ

14 CMOS Inverter Rise and Fall Time Estimation
Tf ~ 3CL / βVDD Τr ~ 3CL / βVDD (Derivations for the above are in Pucknell and Eshraghian Pages ) So, τ r/ τf = βn/βp Given that (due to mobilities) βn = 2.5 βp, rise time is slower by a factor of 2.5 when using minimum dimensions of n and p transistors

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