MOSFET Scaling 1970s Apply Dennard Constant Field Scaling

# MOSFET Scaling (1970s): Step 2 — Applying Dennard Constant-Field Scaling

The 1974 rule set that turned ad hoc shrinks into a repeatable discipline. Robert Dennard, Fritz Gaensslen, Hwa-Nien Yu, Leo Rideout, Ernest Bassous, and Andre LeBlanc published 'Design of Ion-Implanted MOSFET's with Very Small Physical Dimensions' in the IEEE Journal of Solid-State Circuits in 1974. The paper's central idea — now called constant-field scaling or Dennard scaling — is deceptively simple: scale every linear dimension of the device by a factor k less than 1, and scale voltage by the same factor k, so the electric field inside the device stays constant. Step 2 works through the rule set and what it predicts.

## 1. The Scaling Rule Table

Dennard scaling specifies: channel length L, channel width W, and oxide thickness t_ox all scale by k; supply voltage V_DD scales by k; and substrate doping concentration N_a scales by 1/k (doping must rise to keep depletion widths scaling down proportionally with everything else). Under this rule set the electric field E = V/t_ox stays exactly constant, since both V and t_ox scale by the same factor k and the ratio is unchanged.

## 2. What Scales for Free and What Does Not

The predicted payoffs were large: device area scales by k^2 (more devices per unit area), gate delay scales by k (faster switching, roughly proportional to L/v for constant velocity), and power per device scales by k^2 (lower voltage and smaller capacitance both help). Multiply delay improvement and density improvement and power-delay product improves dramatically — this is the mathematical content behind the folklore claim that each process generation gave 'faster, smaller, and lower power, all at once,' which was unusually good news for a physical scaling law and is why the industry organized itself around chasing it for the next three decades.

## 3. Real Diagram: The Dennard Scaling Rule Set

## 4. Where the Rules Were Already Fragile in 1974

Even in the original paper, two assumptions were flagged as eventually breaking: constant mobility (carrier velocity assumed proportional to field at all scales, which fails once velocity saturation sets in at high fields — a concern this series returns to in step 13) and the ability to keep raising substrate doping indefinitely (heavier doping degrades mobility through impurity scattering and raises junction capacitance, partially offsetting the scaling benefit). Dennard's team treated these as second-order corrections applicable a few generations out; by the later 1970s, as this series will show, they were no longer second order.

## 5. Companion Diagram: Stage Sequence and Trend Summary

## Applying Dennard Constant-Field Scaling's Place in the Process Lineage

This is step 2 of 20 in the MOSFET Scaling (1970s) series, tracing planar NMOS scaling from early 1970s field pressure through the fixed-voltage-scaling break that opens the adjacent HMOS (1978) series.