Calculating Propagation delay

[r_usso]

Hello Everyone,

I have used HSpice to simulate propagation delay for Inverter. Now I have to calculate the delay mathematically. I have the following variables:

1. Wn, Wp
2. Ln, Lp
3. Capacitive load
4. Vth
5. Temperature

How do I calculate the delay using all the variables at a time?

Till now I have found the equation with Wn, Wp, Ln, Lp, Cox, Vdd, Vtn, µn, µp but not with relation to temperature.

And where will I found the value of µn and µp and Cox? The data from the library I have found is:

* Customized PTM 45 NMOS

.model  NMOS_VTL  nmos  level = 54

+version = 4.0    binunit = 1    paramchk= 1    mobmod  = 0
+capmod  = 2      igcmod  = 1    igbmod  = 1    geomod  = 1
+diomod  = 1      rdsmod  = 0    rbodymod= 1    rgatemod= 1
+permod  = 1      acnqsmod= 0    trnqsmod= 0

* parameters related to the technology node
+tnom = 27    epsrox = 3.9
+eta0 = 0.0049    nfactor = 2.1    wint = 5e-09
+cgso = 1.1e-10    cgdo = 1.1e-10    xl = -2e-08

* parameters customized by the user
+toxe = 1.75e-09    toxp = 1.1e-09    toxm = 1.75e-09    toxref = 1.75e-09
+dtox = 6.5e-10    lint = 3.75e-09
+vth0 = 0.471    k1 = 0.53    u0 = 0.04359    vsat = 147390
+rdsw = 155    ndep = 3.3e+18    xj = 1.4e-08

* secondary parameters
+ll      = 0            wl      = 0            lln     = 1            wln     = 1          
+lw      = 0            ww      = 0            lwn     = 1            wwn     = 1          
+lwl     = 0            wwl     = 0            xpart   = 0               
+k2      = 0.01         k3      = 0          
+k3b     = 0            w0      = 2.5e-006     dvt0    = 1            dvt1    = 2       
+dvt2    = -0.032       dvt0w   = 0            dvt1w   = 0            dvt2w   = 0          
+dsub    = 0.1          minv    = 0.05         voffl   = 0            dvtp0   = 1.0e-009     
+dvtp1   = 0.1          lpe0    = 0            lpeb    = 0               
+ngate   = 2e+020       nsd     = 2e+020       phin    = 0          
+cdsc    = 0.000        cdscb   = 0            cdscd   = 0            cit     = 0          
+voff    = -0.13        etab    = 0          
+vfb     = -0.55        ua      = 6e-010       ub      = 1.2e-018     
+uc      = 0            a0      = 1.0          ags     = 1e-020     
+a1      = 0            a2      = 1.0          b0      = 0            b1      = 0          
+keta    = 0.04         dwg     = 0            dwb     = 0            pclm    = 0.04       
+pdiblc1 = 0.001        pdiblc2 = 0.001        pdiblcb = -0.005       drout   = 0.5        
+pvag    = 1e-020       delta   = 0.01         pscbe1  = 8.14e+008    pscbe2  = 1e-007     
+fprout  = 0.2          pdits   = 0.08         pditsd  = 0.23         pditsl  = 2.3e+006   
+rsh     = 5            rsw     = 85           rdw     = 85        
+rdswmin = 0            rdwmin  = 0            rswmin  = 0            prwg    = 0          
+prwb    = 6.8e-011     wr      = 1            alpha0  = 0.074        alpha1  = 0.005      
+beta0   = 30           agidl   = 0.0002       bgidl   = 2.1e+009     cgidl   = 0.0002     
+egidl   = 0.8          

+aigbacc = 0.012        bigbacc = 0.0028       cigbacc = 0.002     
+nigbacc = 1            aigbinv = 0.014        bigbinv = 0.004        cigbinv = 0.004      
+eigbinv = 1.1          nigbinv = 3            aigc    = 0.012        bigc    = 0.0028     
+cigc    = 0.002        aigsd   = 0.012        bigsd   = 0.0028       cigsd   = 0.002     
+nigc    = 1            poxedge = 1            pigcd   = 1            ntox    = 1          

+xrcrg1  = 12           xrcrg2  = 5          
+cgbo    = 2.56e-011    cgdl    = 2.653e-10     
+cgsl    = 2.653e-10    ckappas = 0.03         ckappad = 0.03         acde    = 1          
+moin    = 15           noff    = 0.9          voffcv  = 0.02       

+kt1     = -0.11        kt1l    = 0            kt2     = 0.022        ute     = -1.5       
+ua1     = 4.31e-009    ub1     = 7.61e-018    uc1     = -5.6e-011    prt     = 0          
+at      = 33000      

+fnoimod = 1            tnoimod = 0          

+jss     = 0.0001       jsws    = 1e-011       jswgs   = 1e-010       njs     = 1          
+ijthsfwd= 0.01         ijthsrev= 0.001        bvs     = 10           xjbvs   = 1          
+jsd     = 0.0001       jswd    = 1e-011       jswgd   = 1e-010       njd     = 1          
+ijthdfwd= 0.01         ijthdrev= 0.001        bvd     = 10           xjbvd   = 1          
+pbs     = 1            cjs     = 0.0005       mjs     = 0.5          pbsws   = 1          
+cjsws   = 5e-010       mjsws   = 0.33         pbswgs  = 1            cjswgs  = 3e-010     
+mjswgs  = 0.33         pbd     = 1            cjd     = 0.0005       mjd     = 0.5        
+pbswd   = 1            cjswd   = 5e-010       mjswd   = 0.33         pbswgd  = 1          
+cjswgd  = 5e-010       mjswgd  = 0.33         tpb     = 0.005        tcj     = 0.001      
+tpbsw   = 0.005        tcjsw   = 0.001        tpbswg  = 0.005        tcjswg  = 0.001      
+xtis    = 3            xtid    = 3          

+dmcg    = 0e-006       dmci    = 0e-006       dmdg    = 0e-006       dmcgt   = 0e-007     
+dwj     = 0.0e-008     xgw     = 0e-007       xgl     = 0e-008     

+rshg    = 0.4          gbmin   = 1e-010       rbpb    = 5            rbpd    = 15         
+rbps    = 15           rbdb    = 15           rbsb    = 15           ngcon   = 1

 

[erikl]

And where will I found the value of µn and µp and Cox? The data from the library I have found is:

* Customized PTM 45 NMOS

.model  NMOS_VTL  nmos  level = 54

+version = 4.0    binunit = 1    paramchk= 1    mobmod  = 0
+capmod  = 2      igcmod  = 1    igbmod  = 1    geomod  = 1
+diomod  = 1      rdsmod  = 0    rbodymod= 1    rgatemod= 1
+permod  = 1      acnqsmod= 0    trnqsmod= 0

* parameters related to the technology node
+tnom = 27    epsrox = 3.9
+eta0 = 0.0049    nfactor = 2.1    wint = 5e-09
+cgso = 1.1e-10    cgdo = 1.1e-10    xl = -2e-08

* parameters customized by the user
+[B]toxe = 1.75e-09[/B]    [B]toxp = 1.1e-09[/B]    toxm = 1.75e-09    toxref = 1.75e-09
+dtox = 6.5e-10    lint = 3.75e-09
+vth0 = 0.471    k1 = 0.53    [B]u0 = 0.04359[/B]    vsat = 147390
+rdsw = 155    ndep = 3.3e+18    xj = 1.4e-08
...

You have u0 , different for NMOS (µn) and PMOS (µp).

Cox should depend on which parameter calculation you need it for (electrical or physical parameters):
EPSROX=3.9 for SiO₂ gate dielectric layer.

 

[r_usso]

Thank you erikl. I also need a equation with temperature, as I will be varying the temperature to find the change in delay. Do you have any idea?

 

[erikl]

I also need a equation with temperature, as I will be varying the temperature to find the change in delay. Do you have any idea?

Sure: Try this one

 

[r_usso]

Thank you very much. I have never heard of google before.