# mos2ex23.in : Device Degradation due to Hole Trapping in a Silicon pMOSFET

Requires: S-Pisces

Minimum Versions: Atlas 5.32.0.R

This example shows the effects of device degradation caused by stressing a transistor at a negative gate bias and an elevated temperature. The used model is based on hole trapping into the gate oxide but also accounts for the permanent component by an interface reaction. The example shows how to:

- Create a PMOS structure using the Atlas syntax and refine the simulation grid in the gate oxide.

- Set up a deck with the four-state NMP model enabled.

- Simulate the temporal response of oxide and interface traps during a stress and a relaxation phase.

- Visualize the local degradation using the hole occupancy of the oxide traps.

The input file consists of three separate runs, where each of them starts with ** go atlas.** In the first section, the geometry, the mesh, the electrodes, and the doping of the simulated device are specified using the statements ** mesh,** ** region,** ** electrodes, ** and ** doping,** respectively. Since the four-state NMP model requires a fine mesh in the gate oxide region between the substrate and the gate, the mesh is refined based on the potential using the statement ** regrid.** The resulting structure is saved in an output file called mos2ex23_0.str.

In the next section, ATLAS is restarted and the refined structure is read in again. Then the four-state NMP model is enabled by the parameter ** nmp4.sto** after the ** trap ** statement. The oxide traps are placed into the material ** sio2** and confined to the region defined by coordinates ** x.min, ** ** x.max, ** ** y.min,** and ** y.max.** Their oxide and interface state density are set to 1e20/cm3 and 1e11/cm2, respectively. The parameter ** nmp4.sample ** specifies the number of simulated traps at each gate oxide point. In this example, a small number of traps have been chosen in order to reduce the computation time. However, this number should be increased for more realistic simulations, especially if one is interested in the degradation of large-area devices. The traps have distributed parameters, given by their mean values and their variance. The meaning of each of those parameters is described in the ATLAS user manual. Furthermore, the traps are enabled to capture/emit charge carriers from/to the silicon substrate by setting the parameter ** subcontact ** to the material ** silicon.**

Next, the device is simulated for steady-state conditions using the statements ** solve init** and ** solve prev.** The obtained oxide and interface trap charges correspond to their respective pre-stress levels and are saved in the structure file mos2ex23_1.str that will be used for the extraction of the threshold voltages in the last section. Note that the ** output** statement requires the flag ** devdeg ** for saving the trap charges in the output file mos2ex23_1.str. The stored charges are visualized using TONYPLOT. The figure clearly shows that the trapped charges are inhomogeneously distributed in the gate oxide due to the assumed defect-to-defect variations in the amorphous SiO2 gate oxide.

In the next step, the device is stressed by applying a gate bias of -1.55 V for 1 s, including an initial ramptime of 1e-6 s. The temperature of this stress phase is set 100 C by ** model temp=373.** The bias temperature stress leads to a device degradation, saved in the output file mos2ex23_2.str. The gate oxide is found to have an increased concentration of trapped holes compared to the pre-stress level. The stress period is followed by a relaxation phase of 1e3 s at 0 V, where the degradation at the end of this phase is saved in the structure file mos2ex23_3.str. The TONYPLOT figure demonstrates that a substantial fraction of the trapped charges has been removed during device recovery.

For studying critical spots in the gate oxide, the local degradation may be of interest. Therefore, the corresponding ** output ** statements are followed by the flags ** u.trantrap ** and ** traps ** in order to write out the trap occupation probabilities at a specified position within the gate oxide. This position together with the requested states ** msc.state ** must be set after the ** probe ** statement. In this input deck, the stress and relaxation data are written out into the log file mos2ex23_1.log and mos2ex23_2.log, respectively. In both phases, the plotted degradation curves show a behavior that is almost logarithmic and therefore reminiscent of negative bias temperature instability.

In the following section, ATLAS is restarted. In a loop, the trapped oxide and interface charges of the unstressed, the stressed, and the relaxed device are loaded and a gate bias sweep is performed. The calculated output characteristics are recorded in the log files mos2ex23_3.log, mos2ex23_4.log, and mos2ex23_5.log, respectively. The comparison of the Id(Vg) curves demonstrates a pronounced shift of the threshold voltage due to hole trapping at the end of the stress phase. The following relaxation period of 1e3 s leads to an incomplete recovery of the device degradation.

To load and run this example, select the ** Load** button in DeckBuild > Examples. This will copy the input file and any support files to your current working directory. Select the ** Run** button in DeckBuild to execute the example.

## Input Deck

# (c) Silvaco Inc., 2021 go atlas # generation of the device structure mesh width=0.150 x.m l=0.00 s=0.05 x.m l=0.15 s=0.02 x.m l=0.30 s=0.01 x.m l=0.40 s=0.01 x.m l=0.55 s=0.02 x.m l=0.70 s=0.05 y.m l=-0.003 s=0.001 y.m l=-0.0022 s=0.001 y.m l=0.0 s=0.001 y.m l=0.1 s=0.025 y.m l=0.4 s=0.1 region num=1 y.min=+0.000 y.max=1 material=Silicon region num=2 y.min=-0.003 y.max=0.0 x.min=0.0 x.max=0.7 material=SiO2 electrode num=1 name=gate x.min=0.30 x.max=0.40 y.max=-0.0022 y.min=-0.003 electrode num=2 name=source x.min=0.00 x.max=0.15 y.max=0.0 y.min=-0.003 electrode num=3 name=drain x.min=0.55 x.max=0.70 y.max=0.0 y.min=-0.003 electrode num=4 substrate doping uniform conc=1.5e17 n.type doping erfc p.type conc=2e18 char=0.07 lat.char=0.0004 reg=1 x.r=0.30 doping erfc p.type conc=2e18 char=0.07 lat.char=0.0004 reg=1 x.l=0.40 material material=Si taun0=1e-7 taup0=1e-7 model temp=373 mos contact name=gate workf=4.75 # refinement of the simulation grid solve init solve prev solve vgate=-2 solve vgate=-5 solve vgate=-10 regrid potential ratio=0.5 max.level=2 smooth.k=4 save outf=mos2ex23_0.str go atlas mesh infile=mos2ex23_0.str master.in trap material=SiO2 subcontact=Silicon \ x.min=0.3 x.max=0.4 y.min=-0.002 y.max=-0.000 \ nmp4.sto nmp4.samples=10 \ density=1.0e+20 sign=1e-14 sigp=1.0e-14 \ nmp4.et1=4.2 nmp4.et1.sd=-0.4 nmp4.s12s=2.0 nmp4.s12s.sd=1.0 nmp4.r12s=1.0 nmp4.r12s.sd=0.3 \ nmp4.et2=6.0 nmp4.s1s2=3.0 nmp4.s1s2.sd=0.5 nmp4.r1s2=1.0 \ nmp4.nu=1e13 nmp4.epsT2s=0.6 nmp4.epsT2s.sd=0.2 nmp4.eps2s2=0.2 nmp4.eps2s2.sd=0.2 nmp4.eps1s1=3.0 \ nmp4.nit=1e11 nmp4.Ea=1.65 nmp4.Ea.sd=0.40 nmp4.Ed=0.15 nmp4.Ed.sd=0.0 nmp4.gamma=8e-8 nmp4.nup=1e12 material material=Si taun0=1e-7 taup0=1e-7 material material=SiO2 me.tunnel=0.3 mh.tunnel=0.3 model temp=373 mos contact name=gate workfunction=4.75 # simulation of the pre-stress conditions solve init solve prev solve vdrain=0.1 probe ft.msc msc.state=1 x=0.351 y=-0.00051 probe ft.msc msc.state=2 x=0.351 y=-0.00051 probe ft.msc msc.state=3 x=0.351 y=-0.00051 probe ft.msc msc.state=4 x=0.351 y=-0.00051 probe ft.msc msc.state=5 x=0.351 y=-0.00051 # save the trapped oxide charges output devdeg save outf=mos2ex23_1.str tonyplot mos2ex23_1.str -set mos2ex23_1.set # transient simulation of the stress phase output u.trantrap traps method tol.time=1.0e+2 quasi log outf=mos2ex23_1.log solve vgate=-2.0 vdrain=0.1 ramptime=1.0e-6 tstep=1.0e-8 tfinal=1.0e+0 log off tonyplot mos2ex23_1.log -set mos2ex23_2.set # save the trapped oxide charges output devdeg save outf=mos2ex23_2.str tonyplot mos2ex23_2.str -set mos2ex23_3.set # transient simulation of the relaxation phase output u.trantrap traps method tol.time=1.0e-2 quasi log outf=mos2ex23_2.log solve vgate=0.0 vdrain=0.1 ramptime=1.0e-6 tstep=1.0e-8 tfinal=1.0e+3 log off tonyplot mos2ex23_2.log -set mos2ex23_4.set # save the trapped oxide charges output devdeg save outf=mos2ex23_3.str tonyplot mos2ex23_3.str -set mos2ex23_5.set go atlas mesh infile=mos2ex23_0.str master.in material material=Si taun0=1e-7 taup0=1e-7 model temp=373 mos contact name=gate workfunction=4.75 loop steps=3 assign name="i_str" print n.value=1 delta=1 assign name="i_log" print n.value=3 delta=1 solve init solve prev # loading the trapped oxide charges load infile=mos2ex23_${i_str}.str master solve vdrain=+0.005 solve vdrain=+0.005 vgate=+0.25 solve vdrain=+0.005 vgate=+0.5 solve vdrain=+0.005 vgate=+1.0 solve vdrain=+0.005 vgate=+1.5 solve vdrain=+0.005 vgate=+2.0 solve vdrain=+0.005 vgate=+2.5 # calculation of the Id(Vg) curves log outf=mos2ex23_${i_log}.log solve vgate=+3.0 vstep=-0.1 vfinal=-3.0 name=gate # extraction of the Vth extract name="Vth${i_str}" -(xintercept(maxslope(curve(abs(v."gate"),abs(i."drain"))))\ -abs(ave(v."drain"))/2.0) log off l.end tonyplot -overlay mos2ex23_3.log mos2ex23_4.log mos2ex23_5.log -set mos2ex23_6.set quit