מודלים של חיבורי ביניים מודלים חשמליים של חיבורי ביניים עבור מעגלי VLSI פרופ ’ יוסי שחם המחלקה לאלקטרוניקה פיזיקלית, אוניברסיטת ת ” א.

Device scaling laws

Interconnect scaling laws

Example: Al and oxide technology Typical scaling factor over 4 years are: S=0.6, f=2, D=1.3, Since the metal and the dielectric materials are the same: r loc =2/3, r=1, k=1. The intrinsic gate delay drops by a factor of 0.6The intrinsic gate delay drops by a factor of 0.6 The local interconnect delay drops by 2/3The local interconnect delay drops by 2/3 The global interconnect delay increases by krD 2 /S 2 =4.69The global interconnect delay increases by krD 2 /S 2 =4.69

Example: Switching to Cu and low-k technology Typical scaling factor over 4 years are: S=0.6, f=2, D=1.3, The metal and the dielectric materials have been changed, The local interconnect technology has not changed: r loc =2/3, r~1/2, k~1/2. The intrinsic gate delay drops by a factor of 0.6The intrinsic gate delay drops by a factor of 0.6 The local interconnect delay drops by 1/3The local interconnect delay drops by 1/3 The global interconnect delay increases by krD 2 /S 2 =1.17The global interconnect delay increases by krD 2 /S 2 =1.17

The signal propagation effect The signal can not propagate faster than the speed of the electromagnetic wave: V c The speed of the electromagnetic wave: V c is proportional to 1/(LC)  The inductance L is constant while the capacitance is proportional to k. Therefore:

Clock frequency increases The global interconnect delay becomes dominant Coupling capacitance becomes important Inductance becomes an issue Clock skew variations limits the clock frequency Effect of scaling on Timing

Gate and Interconnect delays

1. Cross talk - signal propagation to neighboring wires 2. Simultaneous switching noise on the power line 3. Charge sharing effects - affects mostly dynamic logic 4. Leakage current - affects DRAM and switch capacitor filters. Effect of scaling on noise

1. Higher frequency - higher power dissipation (P) 2. Lowering VDD is a solution - limited by noise margins. 3. Higher capacitance increases P 4. Lowering threshold improves margins but increases the leakage current 5. Higher CMOS transition current and dissipation Effect of scaling on the power

1. Higher power per unit area  higher working temperature 2. Higher current density  higher electromigration 3. Higher interconnect stress levels  stress voiding Effect of scaling on the reliability

Interconnect models Resistors: R=  L/A At higher frequency the skin effect reduces the interconnect cross section. The skin depth, , is defined by the penetration distance at which the current density drops by 1/e: Where f is the frequency,  is the resistivity and  is the magnetic permeability

Interconnect models Capacitors: C=     A/d Inductors: Inductors are more difficult to calculate. Some models will be described I the next lecture.