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8.2.3 Semiconductor Resistor Model (R)

The resistor model consists of process-related device data that allow the resistance to be calculated from geometric information and to be corrected for temperature. The parameters available are:

name parameter units default example
TC1 first order temperature coeff. ohm/^oC 0.0
TC2 second order temperature coeff. ohm/^oC^2 0.0
RSH sheet resistance ohm/[] - 50
DEFW default width meters 1e-6 2e-6
NARROW narrowing due to side etching meters 0.0 1e-7
SHORT shortening due to side etching meters 0.0 1e-7
TNOM parameter measurement temperature ^oC 27 50
KF flicker noise coefficient - 0.0 1e-25
AF flicker noise exponent - 0.0 1.0

The sheet resistance is used with the narrowing parameter and l and w from the resistor device to determine the nominal resistance by the formula:

                                l -  SHORT
                     Rnom = rsh ----------
                                w - NARROW

DEFW is used to supply a default value for w if one is not specified for the device. If either rsh or l is not specified, then the standard default resistance value of 1k Ohm is used. TNOM is used to override the circuit-wide value given on the .options control line where the parameters of this model have been measured at a different temperature.

After the nominal resistance is calculated, it is adjusted for temperature by the formula:

                                                          2
       R(T) = R(TNOM) [1 + TC  (T - TNOM) + TC  (T - TNOM) ]
                             1                2
       where R(TNOM) = Rnom or Racnom

In the above formula, `T' represents the instance temperature, which can be explicitly using the temp keyword or os calculated using the circuit temperature and dtemp, if present.

If both temp and dtemp are specified, the latter is ignored.

Ngspice improves spice's resistors noise model, adding flicker noise (1/f) to it and the noisy keyword to simulate noiseless resistors. The thermal noise in resistors is modelled according to the equation:

     
                              ___
     			  2  4 k T
     			 i = ----- df
     			  r    R

where "k" is the Boltzmann's constant, and "T" the instance temperature.

Flicker noise model is:

     
                               ____        AF
     			   2     KF Ir
     			  i   = ------- df
     			   Rfn     f

A small list of sheet resistances (in Ohm/[]) for conductors is shown below. The table represents typical values for MOS processes in the 0.5 - 1 um range. The table is taken from: N. Weste, K. Eshraghian - Principles of CMOS VLSI Design 2nd Edition, Addison Wesley.

Material Min. Typical Max.
Intermetal (metal1 - metal2) 0.005 0.007 0.1
Top-metal (metal 3) 0.003 0.004 0.05
Polysilicon 15 20 30
Silicide 2 3 6
Diffusion(n+,p+) 10 25 100
Silicided diffusion 2 4 10
n-well 1000 2000 5000