Resistor example (1D)

This example shows how to create and simulate a simple 1D n-type resistor. After creating a 1D structure, we plot the output current as an external bias is applied. Once you run and understand this example, you should study the PN diode example (1D).

New Concepts

• Creating a structure (i.e. grid) with 1 material
• Declaring the 3 basic device solution variables
• Declaring and using tcl variables (set, expr, $), and tcl procedures
• Using a constant dopant profile
• Storing "Equation" strings in the parameter database (pdb)
• Initial conditions, guesses, and solves
• "Ramping," i.e. consecutive DC solves

1D Resistor Deck

Create 1D struture - explanation

#Grid
line x loc=0.0 spac=0.1 tag=Top
line x loc=1.0 spac=0.1 tag=Bottom
mater add name=Silicon
region Silicon xlo=Top xhi=Bottom
init

#Contacts
contact name=VSS Silicon xlo=-0.1 xhi=0.1 add
contact name=GND Silicon xlo=0.9  xhi=1.1 add

Declare solution variables - explanation

DevicePackage
solution add name=DevPsi pde solve negative damp
solution add name=Elec   pde solve !negative
solution add name=Hole   pde solve !negative

Define constants - explanation

set T 300.0
set k 1.38066e-23
set q 1.619e-19
set Vt [expr {$k*$T/$q}]
set ni 1.1e10
set esi [expr 11.8 * 8.85418e-14]
set eps [expr $esi / $q]
set Emob 350.0
set Hmob 150.0
set small 1.0e-10

Ionized dopant profile - explanation

set Nd 1.0e19
set Na 1.0e15
set Doping [expr {$Nd-$Na}]

Bulk Equations - explanation

set eqnP "$eps * grad(DevPsi) + $Doping - Elec + Hole"
set eqnE "ddt(Elec) - ($Emob) * $Vt * sgrad(Elec, DevPsi/$Vt)"
set eqnH "ddt(Hole) - ($Hmob) * $Vt * sgrad(Hole, -DevPsi/$Vt)"
pdbSetDouble Silicon DevPsi DampValue $Vt
pdbSetString Silicon DevPsi Equation $eqnP
pdbSetString Silicon Elec   Equation $eqnE
pdbSetString Silicon Hole   Equation $eqnH 

Contact Equations - explanation

proc OhmicContact {Contact} {
    global Vt ni Nd Na
    pdbSetBoolean $Contact Elec Flux 1
    pdbSetBoolean $Contact Hole Flux 1
    pdbSetBoolean $Contact DevPsi Flux 1
    pdbSetBoolean $Contact Elec Fixed 1
    pdbSetBoolean $Contact Hole Fixed 1
    pdbSetBoolean $Contact DevPsi Fixed 1
    pdbSetDouble $Contact Elec Flux.Scale 1.619e-19
    pdbSetDouble $Contact Hole Flux.Scale 1.619e-19
    pdbSetString $Contact DevPsi Equation "$Nd - $Na - Elec + Hole"
    pdbSetString $Contact Elec Equation "DevPsi - $Vt*log((Elec)/$ni) -$Contact"
    pdbSetString $Contact Hole Equation "DevPsi + $Vt*log((Hole)/$ni) -$Contact"
}
OhmicContact VSS
OhmicContact GND

Initial Conditions - explanation

#Bias Voltage on the Contacts
contact name=VSS voltage supply=0.0
contact name=GND voltage supply=0.0

#Initial Guess at Zero Bias
sel z=($Vt*log(($Doping+$small)/$ni)) name=DevPsi
sel z=$ni*exp(DevPsi/0.025) name=Elec
sel z=$ni*exp(-DevPsi/0.025) name=Hole

#DC Solve at Zero Bias
device

DC solve / plot I-V as output - explanation

window
set bias 0.0
for {set bias 0.0} {$bias < 1.01} {set bias [expr $bias+0.1]} {
	contact name=VSS supply = $bias
	device
	set cur [expr abs([contact name=VSS sol=Elec flux] - [contact name=VSS sol=Hole flux])]
	chart graph=IV curve=IV xval=$bias yval=$cur
}

Full Deck Without Explanations

Copy-paste this entire deck into a file (for example, 1dres.tcl) to make running it easy. Use the startup script to alias your paths to the floods executable. Then, on the BASH and then flooxs command line type:

$ floods
flooxs> source 1dres.tcl

Exercises

• This was an n-type resistor. Now make a p-type resistor.
• Read the plotting examples section. Use the plot.1d method to plot the electron and hole profiles on the same plot (Elec vs x and Hole vs x). Then use the [CreateGraphWindow] method to do the same thing.
• The 1D PN diode is next

Notes

This deck was successfully run by Nicole on 10/26/10 using TEC ~flooxs/linux64