PHOSPHORUS

Set the coefficients of phosphorus kinetics.

SYNOPSIS

phosphorus
( silicon | oxide | oxynit | nitride | gas | poly | gaas )
[ Dix.0 = n ] [ Dix.E = n ] [ Dim.0 = n ] [ Dim.E = n ]
[ Dimm.0 = n ] [ Dimm.E = n ]
[ Dvx.0 = n ] [ Dvx.E = n ] [ Dvm.0 = n ] [ Dvm.E = n ]
[ Dvmm.0 = n ] [ Dvmm.E = n ]
[ implanted ] [ grown.in ]
[ ss.clear ] [ ss.temp = n ] [ ss.conc = n ]
[ ( /silicon | /oxide | /oxynitr | /nitride | /gas | /poly | /gaas ) ]
[ Seg.0 = n ] [ Seg.E = n ] [ Trn.0 = n ] [ Trn.E = n ]
[ ( donor | acceptor ) ]

DESCRIPTION

This statement allows the user to specify values for coefficients of phosphorus diffusion and segregation. The diffusion equation for phosphorus is [1,2]:

where CT is the total chemical concentration of phosphorus, CV and CI are the vacancy and interstitial concentrations, the superscript * refers to the equilibrium concentration, DV and DI are the diffusivities with vacancies and interstitials, and n and ni refer to the electron concentration and the intrinsic concentration respectively. The diffusivities are given by:

DIX, DIM, DIMM, DVX, DVM, and DVMM are described in greater detail below.

The segregation at material interfaces is computed using the following expression:

where C1 and C2 are the concentrations in material 1 and 2 respectively, and the M12 and Tr terms are computed using expressions shown below with the parameters of the models.

silicon, oxide, oxynitr, nitride, gas, poly, gaas
These allow the specification of parameters for that material. Only one of these can be specified per statement. The parameters specified in that statement will apply in the material listed. These parameters specify which material is material 1 for the segregation terms.

Dix.0, Dix.E
These floating point parameters allow the specification of the phosphorus diffusing with interstitial neutral defects. Dix.0 is the pre-exponential constant and Dix.E is the activation energy. Dix.0 defaults to 3.85 cm2/sec in silicon, and Dix.E defaults to 3.66 eV in silicon [3]. DX is calculated using a standard Arrhenius relationship.

Dim.0, Dim.E
These floating point parameters allow the specification of the phosphorus diffusing with singly negative interstitial defects. Dim.0 is the pre-exponential constant and Dim.E is the activation energy. Dim.0 defaults to 4.44 cm2/sec in silicon, and Dim.E defaults to 4.00 eV in silicon [3]. DM is calculated using a standard Arrhenius relationship.

Dimm.0, Dimm.E
These floating point parameters allow the specification of the phosphorus diffusing with doubly negative interstitial defects. Dimm.0 is the pre-exponential constant and Dimm.E is the activation energy. Dimm.0 defaults to 44.2 cm2/sec in silicon, and Dim.E defaults to 4.37 eV in silicon [3]. DMM is calculated using a standard Arrhenius relationship.

Dvx.0, Dvx.E
These floating point parameters allow the specification of the phosphorus diffusing with neutral vacancy defects. Dvx.0 is the pre-exponential constant and Dvx.E is the activation energy. Both of these are 0.0, since phosphorus is an interstitial diffuser [4].

Dvm.0, Dvm.E
These floating point parameters allow the specification of the phosphorus diffusing with singly negative vacancy defects. Dvm.0 is the pre-exponential constant and Dvm.E is the activation energy. Both of these are 0.0, since phosphorus is an interstitial diffuser [4].

Dvmm.0, Dvmm.E
These floating point parameters allow the specification of the phosphorus diffusing with doubly negative vacancy defects. Dvmm.0 is the pre-exponential constant and Dvmm.E is the activation energy. Both of these are 0.0, since phosphorus is an interstitial diffuser [4].

implanted, grown.in
Specifies whether the Dix, Dim, Dimm, Dvx, Dvm, Dvmm, or Fi coefficients apply to implanted or grown-in phosphorus. If neither is specified then a specified parameter applies to both.

ss.clear
This parameter clears the currently stored solid solubility data.

ss.temp, ss.conc
These parameters add a single temperature solid solubility concentration point to those already stored. The default values are [5]:

/silicon, /oxide, /oxynit, /nitride, /gas, /poly, /gaas
These parameters specify material 2. Only one of the these parameters can be specified at one time.

Seg.0, Seg.E
These parameters allow the computation of the equilibrium segregation concentrations. M12 is calculated using a standard Arrhenius relationship.

Trn.0, Trn.E
These parameters allow the specification of the transport velocity across the interface given. The units are in cm/sec. Tr is calculated using a standard Arrhenius relationship.

donor, acceptor
These parameters determine whether the impurity is to be treated as a donor or as an acceptor in a semiconductor material. These parameters are not presently material specific. By default phosphorus is a donor.

EXAMPLES

phosphorus silicon Dix.0=3.85 Dix.E=3.65
This command changes the neutral defect diffusivity in silicon.

phosphorus silicon /oxide Seg.0=30.0 Trn.0=1.66e-7 Seg.E=0.0
This command will change the segregation parameters at the silicon - silicon dioxide interface. The silicon concentration will be 30.0 times the oxide concentration in equilibrium.

BUGS

As far as the implemented models are physically correct, there are no known bugs.

REFERENCES

  1. M. E. Law and J. R. Pfiester, "Low Temperature Annealing of Arsenic/Phosphorus Junctions," IEEE Trans. on Elec. Dev., 38(2), p. 278, 1991.
  2. D. Mathiot and J.C. Pfister, "Dopant Diffusion in Silicon: A consistent view involving nonequilibrium defects," J. Appl. Phys., 55(10), p. 3518, 1984.
  3. R. B. Fair, "Concentration Profiles of Diffused Dopants in Silicon," Impurity Doping Processes in Silicon, Yang ed., 1981, North-Holland, New York.
  4. P. Fahey, G. Barbuscia, M. Moslehi and R. W. Dutton, "Kinetics of Thermal Nitridation Processes in the Study of Dopant Diffusion Mechanisms in Silicon," Appl. Phys. Lett., 46(8), p. 784, 1985.
  5. F. A. Trumbore, "Solid Solubilities of Impurity Elements in Germanium and Silicon," Bell System Tech Journal, 1960.

SEE ALSO

The antimony, arsenic, boron, interstitial, and vacancy statements