Continue to Site
`resetall
`include "constants.vams"
`include "disciplines.vams"
`define explimit 85.0
`define exp(x) exp(min(max((x),-`explimit),`explimit))
`define sqrt(x) pow( (x), 0.5)
//Shape definition
`define rec 1
`define ellipse 2
`define circle 3
/*-------------------------------------------
Electrical Constants
---------------------------------------------*/
/*----------Elementary Charge---------------*/
`define e 1.6e-19
/*----------Bohr Magnetron Costant----------*/
`define ub 9.27e-28
/*----------Boltzmann Constant------------- */
`define Kb 1.38e-23
/*----------Electron Mass------------- */
`define m 9.10e-31
/*----------Euler's constant---------------*/
`define C 0.577
module Model(T1,T2,x,Ttrans,PI,Temp);
inout T1, T2;
electrical T1, T2;
electrical n1,n2;
//virtual terminals of RC circuit for time modelisation for temperature
/*----------X=store the state of the MTJ, non-volatile way------------- */
/*----------Ttrans=store the state of the MTJ with time influence, non-volatile way------------- */
/*----------PI=switching probability------------- */
/*----------Temp=store the temperature------------- */
inout x,Ttrans,PI,Temp;
electrical x,Ttrans,PI,Temp;
/*------------------------------------------
MTJ Technology Parameters
(Corresponds to the HITACHI MTJ Process)
-------------------------------------------*/
/*----------Gilbert Damping Coefficient---------------*/
parameter real alpha=0.027;
/*----------GyroMagnetic Constant in Hz/Oe---------------*/
parameter real gamma=1.76e7;
/*----------Electron Polarization Percentage % ---------------*/
parameter real P=0.52;
/*----------Out of plane Magnetic Anisotropy in Oersteds---------------*/
parameter real Hk=1433;
/*----------Saturation Field in the Free Layer in Oersteds---------------*/
parameter real Ms=15800;
/*----------The Energy Barrier Height for MgO in electron-volt---------------*/
parameter real PhiBas=0.4;
/*----------Voltage bias when the TMR(real) is 1/2TMR(0) in Volt---------------*/
parameter real Vh=0.5; //experiental value with MgO barrier
/*------------------------------------------
Device Parameters
(Corresponds to the HITACHI 240 x 80 MTJ)
-------------------------------------------*/
/*----------Height of the Free Layer in nm---------------*/
parameter real tsl=1.3e-9 from[0.7e-9:3.0e-9];
/*----------Length in nm---------------*/
parameter real a=40e-9;
/*----------Width in nm---------------*/
parameter real b=40e-9;
/*----------Radius in nm---------------*/
parameter real r=20e-9;
/*----------Height of the Oxide Barrier in nm---------------*/
parameter real tox=8.5e-10 from[8e-10:15e-10];
/*----------TMR(0) with Zero Volt Bias Voltage ---------------*/
parameter real TMR=0.7;
/*----------Shape of MTJ---------------*/
parameter real SHAPE=2 from[1:3]; //SQUARE
/*----------Neel-Brown model parameter ---------------*/
parameter real tau0=8.7e-10; //experiental value, prototype Hitachi 2007m with CoFe layer
/*----------Error probability Ps=1-Pr(t) ----------------*/
parameter real Ps=0.999999;
/*----------Threshold for Neel-Brown model----------------*/
parameter real brown_threshold=0.0;
/*----------MTJ State Parameters----------------*/
/*----------Initial state of the MTJ, 0 = parallele, 1 = anti-parallele----*/
parameter integer PAP=1 from[0:1];
/*----------Room temperature in Kelvin----------------*/
parameter real T= 300;//$random % 50 +323;
/*----------Resistance area product in ohmum2----------------*/
parameter real RA=5 from[5:15];
parameter real Pwidth=2e-8;
/*----------Parameters of RC circuit for time modelisation for temperature---------------*/
/*----------Heat capacity per unit volume in J/m3*K----------------*/
parameter real Cv= 2.74e6 from[2.735e6:2.7805e6];
/*----------Thermal conductivity of the thermal barrier(MgO) in W/m*K----------------*/
parameter real lam= 84.897 from [84.8912:84.9449];//
/*----------Total thickness of MTJ nanopillar in nm----------------*/
parameter real thick_s= 3.355e-8;//
/*----------RC circuit for time modelisation for temperature---------------*/
parameter real resistor=100e6; //R=100M
parameter real coeff_tau=12; //Coefficient to increase tau_th
real capacitor; //virtual capacitor
real tau_th; //characteristic heating/cooling time
real temp; //real temperature of MTJ
real temp_init; //temperature initialised
real R; //resistance of MTJ
real delay;
parameter real p=1.0;
parameter integer STO=0 from[0:2]; //choice of stochastic dynamic, 0 no stochastic, 1 random exponential distribution,2 random gauss distribution
parameter integer RV=0 from[0:2]; //choice of stochastic static intrinsically, 0 no stochastic, 1 random uniform distribution,2 random gauss distribution
parameter integer Temp_var=0 from[0:1]; //choice of time modelisation for temperature
parameter real DEV_tox=0.03; //choice of standard deviation of stochastic static gauss distribution for tox when RV=2
parameter real DEV_tsl=0.03; //choice of standard deviation of stochastic static gauss distribution for tsl when RV=2
parameter real DEV_TMR=0.03; //choice of standard deviation of stochastic static gauss distribution for TMRwhen RV=2
parameter real STO_dev=0.03; //choice of standard deviation of stochastic dynamic gauss distribution when STO=2
//variables
//Polaristion constant for the two states of STT-MTJ
real PolaP; //Polarization state parallel of STT-MTJ
real PolaAP; //Polarization state anti-parallel of STT-MTJ
real surface; //Surface of MTJ
//Critical current density for the two states of STT-MTJ
real gp; //Critical current density for P state
real gap; //Critical current density for AP state
real Em,EE; //Variable of the Slonczewski model
//TMR real value for the two states of STT-MTJ
real TMRR; //TMR real value for P state
real TMRRT; //TMR real value for AP state
//Resistance of MTJ
real Ro; //Resistance of MTJ when bias voltage = 0V
real Rap; //Resistance value for AP state
real Rp; //Resistance value for P state
//Voltage of MTJ
real Vb; //V(T1,T2)
real Vc; //V(T2,T1)
real Id; //Current of MTJ
//critial current for the two states of STT-MTJ
real IcAP; //Critial current for AP state
real IcP; //Critial current for P state
real ix; //Current used to store the state of the MTJ
real tau; //Probability parameter
real FA; //Factor for calculating the resistance based on RA
integer seed; //Used to initialize the random number generator
//Stochastic effects
real durationstatic,duration; //time needed to be sure that the switching is effected
real toxreal; //real thickness of oxide layer
real tslreal; //real thickness of free layer
real TMRreal; //real TMR
real pp;
(*cds_inherited_parameter*)parameter real seedin = 0; //generation of a real random value of seed for random distribution function modified 20140223
real VPI;
real P_APt;
real AP_Pt;
real NP_APt,NAP_Pt;
integer counter;
analog begin
if (SHAPE==1)
begin
surface=a*b; //SQUARE
end
else if (SHAPE==2)
begin
surface=`M_PI*a*b/4; //ELLIPSE
end
else
begin
surface=r*r; //ROUND
end
Vc=V(T2,T1); //potential between T2 and T1
Vb=V(T1,T2); //potential between T2 and T1
//initial conditions
@(initial_step)
begin
counter=0;
seed=1000000000*seedin; //initialization of seed modified 20140516
FA=3322.53/RA; //initialization of resistance factor according to RA product
if (RV==1)
begin
//real thinkness of oxide layer, free layer and real TMR considering the random distribution(uniform distribution)
toxreal=$rdist_uniform(seed,(tox-tox*DEV_tox),(tox+tox*DEV_tox));
tslreal=$rdist_uniform(seed,(tsl-tsl*DEV_tsl),(tsl+tsl*DEV_tsl));
TMRreal=$rdist_uniform(seed,(TMR-TMR*DEV_TMR),(TMR+TMR*DEV_TMR));
end
else if (RV==2)
begin
//real thinkness of oxide layer, free layer and real TMR considering the random distribution(gauss distribution)
toxreal=abs($rdist_normal(seed,tox,tox*DEV_tox/3));
tslreal=abs($rdist_normal(seed,tsl,tsl*DEV_tsl/3));
TMRreal=abs($rdist_normal(seed,TMR,TMR*DEV_TMR/3));
end
else
begin
toxreal=tox;
tslreal=tsl;
TMRreal=TMR;
end
temp=T;
temp_init=T;
tau_th= Cv*thick_s / (lam/thick_s);
capacitor=coeff_tau*tau_th/resistor; //tau_th=resistor*capacitor
Ro=(toxreal*1.0e10/(FA*`sqrt(PhiBas)*surface*1.0e12))*exp(1.025*toxreal*1.0e10*`sqrt(PhiBas)); //resistance
Em=Ms*tslreal*surface*Hk/2;
duration=0.0;
if(analysis("dc"))
begin
//States inititialisation
ix=PAP;
end
else
begin
ix=-PAP;
I(x)<+ PAP;
VPI=p;
I(PI)<+p;
end
I(Ttrans)<+ -PAP;
// I(T1,T2)<+ Id; //Actualisation of the current of MTJ with the value calculated
end
if(Temp_var==0)
begin
temp=temp_init; //temperature constant
end
else
begin
temp=V(Temp); //time modelisation for temperature
end
EE=Em/(`Kb*temp*40*`M_PI); //result of E/kbT
if(analysis("dc"))
begin
if(ix==0) //Case which the magnetizations of the two layers are parallel
begin
TMRR=TMRreal/(1+Vb*Vb/(Vh*Vh));
//Parallel resistance
Rp=Ro;
R=Rp;
Id=Vb/Rp;
//Calcul of critical current
PolaP=`sqrt(TMRreal*(TMRreal+2))/(2*(TMRreal+1)); //Polarization state parallel
gp=alpha*gamma*`e*Ms*tslreal*Hk/(40*`M_PI*(`ub*PolaP)); //Critical current density
IcP=gp*surface;
//$display("gp=%g",gp);
if(Vb<(IcP*Rp))
begin
ix=0.0;
end
else
begin
ix=1.0;
end
end
else
begin
//TMR real
TMRRT=TMRreal/(1+Vb*Vb/(Vh*Vh));
// Antiparallel resistance
Rap=Ro*(1+TMRRT);
Rp=Ro;
R=Rap;
Id=Vb/(Rap);
PolaAP=`sqrt(TMRreal*(TMRreal+2))/(2*(TMRreal+1)); //Polarization state anti parallel
gap=alpha*gamma*`e*Ms*tslreal*Hk/(40*`M_PI*(`ub*PolaAP)); //Critical current density
IcAP=gap*surface; // Critical current
if(Vc>=(IcAP*Rap))
begin
ix=0.0;
end
end
V(Ttrans)<+ix;
I(T1,T2)<+Id; //Actualisation of the current of MTJ with the value calculated
end
else
begin
if(STO==1||STO==2) //considering the stochastic behaviors
begin
if(I(Ttrans)>-0.5) //Case which the magnetizations of the two layers are parallel
begin
if (pp==1)
begin
VPI=1;
pp=0;
end
//TMR real
TMRR=TMRreal/(1+Vb*Vb/(Vh*Vh));
//Parallel resistance
Rp=Ro;
R=Rp;
Id=Vb/Rp;
if(ix==0) //Dynamic=parallel state,static=parallel state
begin
//Calcul of critical current
PolaP=`sqrt(TMRreal*(TMRreal+2))/(2*(TMRreal+1)); //Polarization state parallel
gp=alpha*gamma*`e*Ms*tslreal*Hk/(40*`M_PI*(`ub*PolaP)); //Critical current density
IcP=gp*surface; // Critical current
if(Vb>=IcP*Rp)
begin //Current higher than critical current
//STT-MTJ dynamic behavior : Sun model
//Time needed to be sure that the switching is effected
durationstatic=(`C+ln(`M_PI*`M_PI*(Em/(`Kb*temp*40*`M_PI))/4))*`e*1000*Ms*surface*tslreal*(1+P*P)/(4*`M_PI*2*`ub*P*10000*abs(Id-IcP));
$display("durationstatic=",durationstatic);
if(STO==1)
begin
duration=abs($rdist_exponential(seed, durationstatic)); //stochastic effect(exponential distribution)
end
else if(STO==2)
begin
duration=abs($rdist_normal(seed,0.995*durationstatic,durationstatic*STO_dev/3)); //stochastic effect(gauss distribution)
end
else
begin
duration=durationstatic;
end
if(duration<=Pwidth)
begin //Switching of the free layer always occurs
if(duration>VPI)
begin
ix=-1.0; //change the current state of MTJ
pp=1;
end
else
begin
VPI=duration;
duration= 100000000;
end
end
end
else
begin //Current smaller than critical current
ix=0.0; //save the current state of MTJ
//STT-MTJ dynamic behavior : Neel-Brown model
tau=tau0*exp(Em*(1-abs(Id/IcP))/(`Kb*temp*40*`M_PI));
if(Vb>brown_threshold)
begin
if (Vb<0.8*IcP*Rp)
begin
if(STO==1||STO==2)
begin
duration=abs($rdist_exponential(seed, tau)); //stochastic effect
end
else
begin
duration=tau;
end
if (Pwidth >= duration)
begin
if(VPI<=duration)
begin
ix=-1.0; //change the current state of MTJ
end
else
begin
VPI=duration;
duration= 100000000;
end
end
end
end
end
end
end
else if(I(Ttrans)<-0.5) //Case which the magnetizations of the two layers are antiparallel
begin
if (pp==1)
begin
VPI=1;
pp=0;
end
//TMR real
TMRRT=TMRreal/(1+Vb*Vb/(Vh*Vh));
// Antiparallel resistance
Rap=Ro*(1+TMRRT);
Rp=Ro;
R=Rap;
Id=Vb/(Rap);
if(ix==0)
begin
PolaAP=`sqrt(TMRreal*(TMRreal+2))/(2*(TMRreal+1)); //Polarization state anti parallel
gap=alpha*gamma*`e*Ms*tslreal*Hk/(40*`M_PI*(`ub*PolaAP)); //Critical current density
IcAP=gap*surface; // Critical current
if(Vc>=(IcAP*Rap))
begin //Current higher than critical current
//STT-MTJ dynamic behavior : Sun model
durationstatic=(`C+ln(`M_PI*`M_PI*(Em/(`Kb*temp*40*`M_PI))/4))*`e*1000*Ms*surface*tslreal*(1+P*P)/(4*`M_PI*2*`ub*P*10000*abs(-Id-IcAP));
//time needed to be sure that the switching is effected
if(STO==1)
begin
duration=abs($rdist_exponential(seed, durationstatic)); //stochastic effect
end
else if(STO==2)
begin
duration=abs($rdist_normal(seed,0.995*durationstatic,durationstatic*STO_dev/3)); //stochastic effect(gauss distribution)
end
else
begin
duration=durationstatic;
end
if(duration<=Pwidth)
begin //Switching of the free layer always occurs
if(VPI<=duration)
begin
ix=0.0; //change the current state of MTJ
pp=1;
end
else
begin
VPI=duration;
duration= Pwidth;
end
end
end
else
begin //Current smaller than critical current
ix=-1.0; //save the current state of MTJ
//STT-MTJ dynamic behavior : Neel-Brown model
tau=tau0*exp(Em*(1-abs(Id/IcAP))/(`Kb*temp*40*`M_PI));
if(Vc>brown_threshold)
begin
if (Vc<0.8*IcAP*Rap)
begin
if(STO==1||STO==2)
begin
duration=abs($rdist_exponential(seed, tau)); //stochastic effect
end
else
begin
duration=tau;
end
if (duration<=Pwidth)
begin
if(VPI<=duration)
begin
ix=0.0; //change the current state of MTJ
end
else
begin
VPI=duration;
duration= 100000000;
end
end
end
end
end
end
end
end
else //without consideration of stochastic behaviors
begin
if(I(Ttrans)>-0.5) //Case which the magnetizations of the two layers are parallel
begin
if (pp==1)
begin
VPI=1;
pp=0;
end
//TMR real
TMRR=TMRreal/(1+Vb*Vb/(Vh*Vh));
//Parallel resistance
Rp=Ro;
R=Rp;
Id=Vb/Rp;
//Calcul of critical current
PolaP=`sqrt(TMRreal*(TMRreal+2))/(2*(TMRreal+1)); //Polarization state parallel
gp=alpha*gamma*`e*Ms*tslreal*Hk/(40*`M_PI*(`ub*PolaP)); //Critical current density
IcP=gp*surface; // Critical current
if(Vb>=IcP*Rp)
begin //Current higher than critical current
//STT-MTJ dynamic behavior : Sun model
//Time needed to be sure that the switching is effected
durationstatic=(`C+ln(`M_PI*`M_PI*(Em/(`Kb*temp*40*`M_PI))/4))*`e*1000*Ms*surface*tslreal*(1+P*P)/(4*`M_PI*2*`ub*P*10000*abs(Id-IcP));
duration=durationstatic;
if(duration<=Pwidth)
begin //Switching of the free layer always occurs
ix=-1.0; //change the current state of MTJ
end
else
begin
ix=0.0;
end
end
else
begin //Current smaller than critical current
ix=0.0; //save the current state of MTJ
//STT-MTJ dynamic behavior : Neel-Brown model
tau=tau0*exp(Em*(1-abs(Id/IcP))/(`Kb*temp*40*`M_PI));
if(Vb>brown_threshold)
begin
if (Vb<0.8*IcP*Rp)
begin
duration=tau;
if (Pwidth >= duration)
begin
ix=-1.0; //change the current state of MTJ
end
else
begin
ix=0.0;
end
end
end
end
end
else if(I(Ttrans)<-0.5) //Case which the magnetizations of the two layers are antiparallel
begin
if (pp==1)
begin
VPI=1;
pp=0;
end
//TMR real
TMRRT=TMRreal/(1+Vb*Vb/(Vh*Vh));
// Antiparallel resistance
Rap=Ro*(1+TMRRT);
Rp=Ro;
R=Rap;
Id=Vb/(Rap);
PolaAP=`sqrt(TMRreal*(TMRreal+2))/(2*(TMRreal+1)); //Polarization state anti parallel
gap=alpha*gamma*`e*Ms*tslreal*Hk/(40*`M_PI*(`ub*PolaAP)); //Critical current density
IcAP=gap*surface; // Critical current
if(Vc>=(IcAP*Rap))
begin //Current higher than critical current
//STT-MTJ dynamic behavior : Sun model
durationstatic=(`C+ln(`M_PI*`M_PI*(Em/(`Kb*temp*40*`M_PI))/4))*`e*1000*Ms*surface*tslreal*(1+P*P)/(4*`M_PI*2*`ub*P*10000*abs(-Id-IcAP));
duration=durationstatic; //time needed to be sure that the switching is effected
if(duration<=Pwidth)
begin //Switching of the free layer always occurs
ix=0.0; //change the current state of MTJ
end
else
begin
ix=-1.0;
end
end
else
begin //Current smaller than critical current
ix=-1.0; //save the current state of MTJ
//STT-MTJ dynamic behavior : Neel-Brown model
tau=tau0*exp(Em*(1-abs(Id/IcAP))/(`Kb*temp*40*`M_PI));
if(Vc>brown_threshold)
begin
if (Vc<0.8*IcAP*Rap)
begin
duration=tau;
if (duration<=Pwidth)
begin
ix=0.0; //change the current state of MTJ
end
else
begin
ix=-1.0;
end
end
end
end
end
end
I(x)<+ix; //Actualisation of the state of x with the value calculated
if(counter==0)
begin
if(I(Ttrans)!=0)
begin
ix=0;
end
end
I(Ttrans)<+ transition(ix,duration,1e-11,1e-11); //Ttrans has the same function than x but it includes the time effects
if(counter==0)
begin
if(I(Ttrans)!=0)
begin
ix=-1;
end
end
I(T1,T2)<+Id; //Actualisation of the current of MTJ with the value calculated
I(PI)<+VPI;
counter=counter+1;
end //la fin de transient analysis
if(Temp_var==1)
begin
V(n1) <+ ( V(T1,T2)*V(T1,T2) )/ ( R*surface*lam/(thick_s )); //Definition of the maximum incrase of temperature
I(n1,n2) <+ V(n1,n2) / resistor; // RC circuit definition,RC circuit parallel
I(n2) <+ capacitor * (ddt(V(n2)));
V(Temp) <+ V(n2) + temp_init;
end
else
begin
V(Temp) <+ temp_init;
end
// $display("The resistance R=",R);
// $display("The current Id=",Id);
// $display("Parallel to antiparallel critical current IcP=",IcP);
// $display("Antiparallel to parallel critical current IcAP=",IcAP);
end //la fin d'analog begin
endmodule