Sending report ...Schred Manual
A 1D, Self-Consistent Schrödinger-Poisson Solver Including Many Body and Exchange Effects for bulk and SOI structures
Dragica Vasileska and Zhibin Ren
Arizona State University, Purdue University
February, 2000
This brief document explains how to run the program, SCHRED_2.0, to simulate one-dimensional MOS/SOI structures. (SCHRED is a short name for Schrödinger, but with a Macedonian spelling.) Three example input files are also shown. For a description of typical applications of such simulations, see Refs. [1-5].
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Running schred_2.0:
To run schred_2.0, the user supplies an input file, a simulation is performed, and the results are written to an output file (containing dependence of 2D charge density and average carrier distance from top Si/SiO2 interface at each gate bias. If the quantum mode is chosen, it also contains all information regarding the subbands, such as subband energies and carrier occupancy in each subband etc.). Auxiliary output can also be produced as specified by the user in the input file. Each line of the input file specifies a set of parameters. Comment lines begin with a $, and a line may be continued by placing a + in the first column.
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Specification of the input file:
DEVICE:
The device command line is used to tell the program either to simulate a bulk structure or a SOI structure. The variable 'bulk' needs to be specified, 'bulk = yes' means a bulk device calculation, 'bulk = no' implies an SOI simulation.
Note: if an SOI simulation is to be done, all bulk structure related variables in the entire input file do not have to be removed, vice versa.
PARAMS:
The params command line is used to specify the temperature, gate dielectric thickness, and the corresponding dielectric constant by setting variables 'temp[K]', 'tox[nm]' and 'kox' respectively. Schred_2.0 will run for any temperature above 50 K. If a SOI simulation is to be conducted, both top and bottom gate variables need to be specified, these include 'tox1[nm]', 'tox2[nm]' 'kox1' and 'kox2'
BODY:
For bulk device simulations, the BODY command line is used to specify whether or not a uniform doping profile is to be used for the substrate. If the variable 'uniform = true', a uniform doping profile is chosen. A positive doping density means p type dopants, a negative value means n type dopants (variable 'Nb[cm-3]'). If the variable 'uniform = false', an option to read the doping profile from a data file is chosen. The name of the file that contains the doping profile data is specified by specifying the variable 'dop_profile'. The file name may not exceed eight characters. The user also needs to specify the background doping, i.e. the doping density deep within the substrate (which is set by the variable 'Ns[cm-3]'). The doping data file consists of two columns; the first is position in micrometers and the second is the net acceptor doping density per cubic meter.
For SOI device simulations, the body command line is used to specify the silicon film thickness (variable 't_b[nm]') and doping concentration (variable 'Nb[cm-3]'). The silicon body is always assumed uniformly doped.
Note: 1) for a bulk device, the average substrate doping concentration has to be greater than 1E14[cm-3] in order to conduct a quantum mode calculation properly.
2) A positive doping density implies that the dopant type is an acceptor, a negative doping density implies that the dopant type is a donor.
3) A very thick body (thicker than 0.1 micron) in a SOI quantum simulation may involve a long computation time.
GATE:
The gate command is used to specify the type of gate material. For a bulk device simulation, if variable 'metal = true', a metal gate is selected, and one needs to specify the value of the variable 'phi[eV]' (phi[eV]=metal workfunction). If 'metal=false', a polysilicon gate is selected, and one needs to specify the doping of the polysilicon gate by setting the value of the variable 'Ng[cm-3]'. For an SOI simulation, one needs to specify both top and bottom gate related variables. If a metal contact is chosen, one needs to specify the corresponding work function value, otherwise, one needs to specify the polysilicon gate doping concentration.
Note: the note regarding signs of doping density is also true for gate polysilicon.
IONIZE:
The ionize command line is used to specify whether or not the dopants are fully ionized. If the variable 'ionize = no', partial ionization of the dopants will not be taken into account (this is typically appropriate at 300K). If variable 'ionize=yes', one also needs to specify the acceptor and donor ionization energies through variables, 'Ea[meV]' and 'Ed[meV]'.
VOLTAGE:
The voltage command is used to specify the minimum (variable 'Vmin[V]') and maximum (variable 'Vmax[V]') gate voltages well as the gate voltage step (variable 'Vstep[V]'). For an SOI device simulation, if the variable 'dual' is set to 'yes', the top gate and bottom gate electrodes will be swept together, if it is set to 'no', the bottom gate electrode will be biased at 'V2min[V]', only the top gate will be swept.
CHARGE:
The charge command line is used to specify how the mobile charges in the substrate are treated. If the variable 'quantum=no', a classical charge description is used. In this case, the user also has to select either Fermi-Dirac statistics (variable 'Fermi=yes') or Maxwell-Boltzmann statistics (variable 'Fermi=no')
If variable 'quantum=yes', a quantum-mechanical charge description is selected for the electrons in the inversion layer. Fermi-Dirac statistics is automatically used. The number of subbands taken into account also needs to be specified. For electrons, variable 'e_nsub1' indicates the number of subbands from the unprimed or the first set, and variable 'e_nsub2' indicates the number of subbands from the primed or the second set. For holes, variable 'h_nsub1' indicates the number of subbands from the heavy hole band, and variable 'h_nsub2' indicates the number of subbands from the light hole band. The maximum number allowable in the simulation is 100, but according to our experience, six subbands (4 from the first set, 2 from the second set) are accurate enough for most simulations.
If variable 'exchange=no', no exchange-correlation corrections to the ground state energy are taken into account, and if 'exchange=yes', these corrections are accounted for in the calculation of the subband structure.
CALC:
The calc command line is used to specify whether or not the low-frequency CV-curve is computed by setting variable 'CV_curve=yes' or 'CV_curve=no'. It also requires that the file name (upto 8 characters) for storing the calculated capacitance data needs to be specified if 'CV_curve=yes'. For bulk device simulations (`bulk=yes'), if the quantum calculation is needed in accumulation range, one needs to set variable 'accumula' to 'yes'. In this case, the program will automatically account for 100 subbands from each subband set to accomplish the quantum calculation (the reason for considering large number of subbands can be found in 'Schred_2.0 description'). Since the size of the output data is huge, only C-V data is saved, subband information is discarded.
Note: Quantum mode calculation in accumulation range may involve long computation times. In doing the simulation, one has to specify a uniformly doped body (`uniform=true'). The program will be modified to accommodate a nonuniformly doped body.
SAVE:
The save command line is used to specify whether or not to save the conduction band edge and charge density data in a file by setting the variable 'charges=yes' or 'charges=no'. If 'charges=yes', the user has the option to specify the name of the file by setting file_ch to a name of up to 8 characters. In the example, the file name that saves this information for all bias points is chosen to be 'chrg.dat'. The wavefunctions are saved if variable 'wavefunc=yes'. The file name is set by the variable, 'file_wf'. In the examples shown below, the name of the file is chosen to be 'wfun.dat'. Note that these file names must not exceed eight characters.
CONVERGE:
The converge command line is used to specify the solution tolerance by assigning a value to the variable tolerance, which specifies the convergence criterion for the solution of the Poisson equation. The tolerance should be always less than 10-3. The variable 'max_iter', limits the maximum number of iterations to a given value (2000 in the examples). If the solution has not converged by this time, schred will signal a convergence problem. When using polysilicon gates, 'max_iter' should be set to a large value because, due to the high doping, the convergence is very poor at the beginning.
If one runs the program in command line manner (not on HUB), the program running progress information is output to the screen. This includes the ongoing bias voltage, iteration number, and maximum error after each iteration. If running on HUB, the information is printed in the `output' file.
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Example Input Files:
Ten example input files are given to illustrate how to use Schred_2.0 for device simulations. We summarize the examples as follows, and present the first three here, the other files can be found in HUB example folder.
For the first nine examples, the oxide thickness is 4 nm, and the temperature is 300 K. The ionization of the impurity atoms and inversion layer carrier correlation energy are not taken into account. The gate voltage is stepped with an increment of 0.1 V, the calculation of the low-frequency CV-curves is enabled. The last example simulates the device at liquid nitrogen temperature (77K), and also enables the options of accounting for inversion layer carrier correlation energy and partial ionization of dopants.
Example 1: uniformly doped p body MOS capacitor with a metal gate (Qunatum mode)
Example 2: uniformly doped p body MOS capacitor with a n+ polysilicon gate (Classical mode)
Example 3: nonuniformly doped n body MOS capacitor with a metal gate
Example 4: nonuniformly doped n body MOS capacitor with a p type polysilicon gate
Example 5: nonuniformly doped p body MOS capacitor with an n type polysilicon gate. QUANTUM MECHANICAL TREATMENT IN ACCUMULATION RANGE IS ASSUMED
Example 6: a symmetrically-gated double gate SOI structure, metal gate contact is assumed.
Example 7: an asymmetrically-gated double gate SOI structure, n+ and p+ ploysilicon electrodes are assumed for top and bottom gates.
Example 8: an example of single-gated SOI structure
Example 9: an example of ground plane SOI structure
Example 10: a liquid nitrogen simulation of MOS
In Example 1, an Aluminum gate is used, a uniform substrate doping of Nb=1E17 cm-3, and a quantum-mechanical charge description without exchange-correlation corrections. Four subbands are taken from the unprimed and 2 from the primed ladder of subbands. Information about the subband energies, subband population, average carrier distance is stored in the output file. The low-frequency CV curve is stored in a file called `cv.dat'. The conduction band edge for all the gate voltages is stored in a file called `chrg.dat'. The wavefunctions are saved in a file called `wfun.dat'.
Example 1: uniformly doped p body MOS capacitor with a metal gate (Qunatum mode)
It runs about 3 minutes on a SPARC 5 worksation.
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device bulk=yes
params temp[K]=300, tox[nm]=4, kox=3.9
body uniform=true, Nb[cm-3]=1.e17
gate metal=true, phi[eV]=4.00
ionize ionize=no, Ea[meV]=45, Ed[meV]=45
voltage Vmin[V]=0.0, Vmax[V]=3.0, Vstep[V]=0.1
charge quantum=yes, Fermi=yes, exchange=no, e_nsub1=4, e_nsub2=2
calc CV_curve=yes, file_cv=cv.dat
save charges=yes, file_ch=chrg.dat,
+ wavefunc=yes, file_wf=wfun.dat
converge toleranc=5.e-6, max_iter=2000
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In the Example 2, a poly-silicon gate with Ng=-1E20 cm-3, a uniform substrate doping of Nd=1E17 cm-3, and a classical charge description (with Fermi-Dirac statistics) are specified. Again, the information about the average carrier distance is stored in the output, the low-frequency CV curve is stored in a file called `cv.dat', the conduction band edge for all the gate voltages is stored in a file called `chrg.dat'.
Example 2: uniformly doped p body MOS capacitor with a polysilicon gate (Classical mode)
It runs about 40 seconds on a SPARC 5 worksation.
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device bulk=yes
params temp[K]=300, tox[nm]=4, kox=3.9
body uniform=true, Nb[cm-3]=1.e17
gate metal=false, Ng[cm-3]=-1.0e20
ionize ionize=no, Ea[meV]=45, Ed[meV]=45
voltage Vmin[V]=0.0, Vmax[V]=3.0, Vstep[V]=0.1
charge quantum=no, Fermi=yes
calc CV_curve=yes, file_cv=cv.dat
save charges=yes, file_ch=chrg.dat,
+ wavefunc=yes, file_wf=wfun.dat
converge toleranc=5.e-6, max_iter=2000
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
In the Example 3, a metal gate with middle gap workfunction of `phi[eV]=4.6', a nonuniform substrate doping prescribed by an external file called `dopingn', and a quantum mechanical charge description are specified. Again, the information about the average carrier distance is stored in the output, the low-frequency CV curve is stored in a file called `cv.dat', the conduction band edge for all the gate voltages is stored in a file called `chrg.dat'.
Example 3: nonuniformly doped n body MOS capacitor with a metal gate
It runs about 2 minutes on a SPARC 5 worksation.
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device bulk=yes
params temp[K]=300, tox[nm]=4, kox=3.9
body uniform=false, dop_prof=dopingn, Ns[cm-3]=-2.e16
gate metal=false, phi[eV]=4.60
ionize ionize=no, Ea[meV]=45, Ed[meV]=45
voltage Vmin[V]=-3.0, Vmax[V]=-1.0, Vstep[V]=0.1
charge quantum=yes, Fermi=yes, exchange=no,
+ h_nsub1=4, h_nsub2=2
calc CV_curve=yes, file_cv=cv.dat
save charges=yes, file_ch=chrg.dat,
+ wavefunc=yes, file_wf=wfun.dat
converge toleranc=5.e-6, max_iter=2000
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
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References:
[1] D. Vasilska, D.K. Schroder, and D.K. Ferry, "Scaled Silicon MOSFET's: Degradation of the Total Gate Capacitance," IEEE Trans. Electron Dev., 44, pp. 584-587, 1997.
[2] D. Vasileska and D.K. Ferry, "The Influence of Space Charge Quantization Effects on the Threshold Voltage, Inversion layer and Total Gate Capacitance in scaled Si-MOSFETs," in the Technical Proceedings of the First International Conference on Modeling and Simulation of Microsystems, Semiconductors, Sensors and Actuators, Santa Clara, California, April 6-8, 1998, pp. 408-413.
[3] H.-S. Wong, D.J. Frank, and P.M. Solomon, "Device design considerations for double-gate, ground-plane, and single-gated ultra-thin SOI MOSFET's at the 25nm channel length generation," IEDM Tech. Dig., p. 407, 1998.
[4] T. Tanaka, H. Horie, S. Ando, and S. Hijiya, "Analysis of p+ poly Si double-gate thin-film SOI MOSFETs" IEDM Tech. Dig., pp. 683-686, 1991.
[5] J.G. Fossum, Z. Ren, K. Kim, and M.S. Lundstrom, "Extraordinarily High Drive Currents in Asymmetrical Double-Gate MOSFETs," submitted for publication, 2000.