Micrologic 1960 Resistor Contact End Effect Resistance
# Fabricate a Resistor From the Same Diffusion That Makes a Base: What the Ends of the Strip Add
## 1. Why a Resistor's Value Is Never Quite the Number the Layout Drew
This step completes the diffused resistor Step 1 sized by its length-to-width ratio and Step 2 diffused alongside every transistor base on the chip, by forming a metal contact at each end of the resistor strip — the same contact-window and metallization sequence this project established across the 1959 series — and those two contacts add a small but unavoidable resistance of their own, on top of the value the geometry alone was designed to produce. A contact is never a perfect, zero-resistance connection; current has to cross from the metal into the diffused silicon, and that crossing carries its own resistance, set by the contact's area and the properties of the metal-semiconductor interface rather than by anything the resistor's length-to-width ratio controls. The resistor this layout actually gets is therefore the sum of two physically distinct contributions:
where $R_{\text{contact}}$ is the resistance added at each end of the strip by the metal-to-silicon contact. For a long, high-value resistor this correction is negligible, but for the short, low-value resistors a dense logic gate often needs, $2R_{\text{contact}}$ can be a significant fraction of the intended value — meaning the layout decisions Step 1 made in terms of pure geometry have to be revisited once this step's actual contacts are added, because the number this circuit designed for and the number this circuit gets are not quite the same thing.
## 2. Real Diagram: Two Metal Contacts, One Diffused Strip Between Them
The finished resistor is a single diffused strip with a metal contact window at each end, identical in form to the single-transistor contact windows this project documented across 1959, except that here two of them sit at opposite ends of the same strip, each adding its own small resistance the circuit has to account for on top of the strip's own geometric value.
## 3. Why No Single-Transistor Series Ever Needed to Account for a Contact's Own Resistance
Every contact this project built in 1959 connected one metal lead to one transistor's base or emitter, and that contact's own resistance, while real, was simply absorbed into the overall device characteristic a circuit designer would measure and accept as the transistor's given behavior. A diffused resistor is different, because its entire purpose is to realize a specific, predicted numerical value from geometry alone, and a contact resistance large enough to shift that value measurably is a design error in a way it never was for a transistor's own terminal. This is the first component in this project's history whose contacts are not merely a way to connect it to the rest of a circuit, but an active source of error against the one number the component was drawn to produce.
Step 4 does not add a new fabrication technique; it forces this series to admit that even a component defined entirely by geometry still owes something to the two small, unavoidable contacts at its ends.