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These are arranged with the transistor tied to be always on. A MOSFET is classified into 3 areas of operation:

• NMOS
• Cutoff (VGS < Vth): little conduction
• Triode (VGS > Vth and VDS < (VGS - Vth)): resistive
• Saturation (VGS > Vth and VDS > (VGS - Vth)): conductive
• PMOS
• Cutoff (VGS > Vth): little conduction
• Triode (VGS < Vth and VDS > (VGS - Vth)): resistive
• Saturation (VGS < Vth and VDS < (VGS - Vth)): conductive

In essence a MOSFET is off if you don't apply any voltage between gate and source. Its fully on if you apply lots of voltage between drain and source and a little between the gate and source (ie switching a high voltage load). And then there are the cases in between which is what we want.

Pulldown PMOS resistor on Intel 4004 (IC images courtesy of Flylogic, mask from http://www.4004.com):

Which translates to the following schematic:

( : compare with analysis at [NMOS logic design] The metal is VDD (-10V). For PMOS, cutoff occurs when VGS > Vth and assume Vth = -3V or something like that. If VGS is 0 the resistor does nothing as there is no potential difference. Now note that since VG = VD and so VGS = VDS. We are in the triode region if VDS > VGS - Vth and so if 0 > 0 - -3V or 0 > 3V)

# Active area

One common way to form resistors is to lay out one type of active area (ex: p) inside of another (ex: n) in a thin strip. Then reverse bias the junction to increase the resistance by shrinking the conductive area within the inner region. Example: (ST 24C02):

Which translates into:

I've grayed out the irrelevant parts and added labels for power and the two resistor terminals (T1/T2). The heavily doped green P+ areas form a connection to the P-well around the resistor while the resistor is N doped. VSS keeps a negative bias on the P doped region pulling charge away and thus making the region less conductive. VDD is applied to this essentially huge gate N channel transistor to keep it always on. (TODO; what are those reddish marks between squiggles?)

Unfortunately, because the size of the depletion region is a function of the voltage applied to it the actual resistance is non-trivial to calculate. For example, if you know the total resistance is 10k and it was tapped in the center you would not get two 5k resistors. The higher the voltage the larger the gap so in the above example if T1 was connected to ground, T2 to center tap would have a larger resistance than center tap to T1. Fortunately, in many applications we only need a single pullup or pulldown resistor and such things aren't an issue. However, above is a clock generator where one might actually want to know the clock frequency. The best solution is probably to simply measure it.

# Thin film

Thin film resistors “are fabricated by vacuum evaporation or sputtering of thin films of resistive materials directly on top of the oxide layer of the substrate” [Resistor Fabrication on Semiconductor Wafers]. Additionally, these can be laser trimmed by blasting away the metal. Example laser trimmed resistor (AD534):

# Polysilicon

Polysilicon is a so-so conductor and so simply making a long strip of it will create a significant resistance.

1. Resistor Fabrication on Semiconductor Wafers: http://www.siliconfareast.com/resistor-fab.htm 