//This VerilogA program models the behavior of a multi-layer cell (MTJ) in a horizontal array.
`include "constants.vams"
nature Current
units = "A";
access = I;
abstol = 1e-12;
blowup = 1e32;
endnature
nature Voltage
units = "V";
access = V;
abstol = 1e-12;
blowup = 1e32;
endnature
discipline electrical
potential Voltage;
flow Current;
enddiscipline
discipline voltage
potential Voltage;
enddiscipline
discipline current
flow Current;
enddiscipline
nature Magnetic_induction
abstol = 1e-12;
access = H;
units = "A/m";
endnature
discipline magnetic_ports
potential Magnetic_induction;
enddiscipline
//rf and rp are the terminals of the free and the fixed layers.
//mag_a, mag_b, mag_c and mag_d are the 2-bit magnetic ports that are used to communicate with neighboring cells.
//The magnetic ports are used to model the neighbor interaction among the free layers of the multi-layer cells.
module mtj_vert_cell(rf,rp,mag_porta,mag_portb,mag_portc,mag_portd);
inout rf,rp;
inout [0:1]mag_porta,mag_portb,mag_portc,mag_portd;
electrical rf,rp;
magnetic_ports [0:1] mag_porta,mag_portb,mag_portc,mag_portd;
//The gyromagnetic ratio
`define gamma -1.76e11
// Paramter constants:
//Length, Width, thickness --- dimensions of the free layer of the MTJ.
//alpha --- Gilbert damping factor.
//R0 and R1 --- resistances of the logic 0 and logic 1 states.
//P --- polarization factor.
//gamma_p, alpha_p --- direction cosines of the magnetization of the reference layer along the x and z directioni.
//Hd --- Coupling field from the reference layer onto the free layer.
//Hk --- Anisotropy field.
//Gp,Gap --- conductances of MTJ when the magnetization of the free layer is parallel and anti-parallel to the magnetization of the reference layer.
//theta0 --- angle subtended by the magnetization of the reference layer with the z-axis.
//I_delta --- deviation in the clocking current magnitude about the calculated value.
//low, high --- low and high signal level for the magnetic ports.
//V_delta --- differential voltage to determine the voltage across the device crossing the zero level.
//tdelay, trise, tfall --- transition delay, rise time and fall time of the signal at the magnetic ports.
//t_delta --- model the delay in the device to respond to the switching and clocking voltage pulse.
parameter real Length = 100e-9,
Width = 50e-9,
thickness = 2e-9,
alpha = 0.01,
Ms = 8e5, //in A/m
R0 = 412.72, //in ohms
R1 = 423.13, //in ohms
P=0.35,
gamma_p = 0.707,
alpha_p = 0.707,
Hd = 5000, //in A/m
Hk = 795.77, //in A/m
I_upper=200e-6, //in A
Gp = 2.82e-3, //in mho
Gap = 1.967e-3, //in mho
theta0 = `M_PI/4,
I_delta = 1e-6; //in A
parameter real low=0,
high=1,
V_delta=10e-3;
parameter real tdelay=2p from [0:inf),
trise=1p from [0:inf),
tfall = 1p from [0:inf),
t_delta = 1p from [0:inf);
electrical int_nodea,int_nodeb;
real Resistance,I_max,I_prev,tpulse,t_prev_pulse;
real theta,Volume,t_precession,I_switch,fsm_out;
real trise_pos,tfall_neg,tfall_pos,trise_neg,tswitch;
real g,geff,aj_piby2,Iclk;
integer out[0:1],out_prev[0:1];
integer value_porta[0:1],value_portb[0:1],value_portc[0:1];
integer switch_out,switch_prev_out,clocked;
// This function computes the critical switching current for a multi-layer stack with the given device specifications.
analog function real critical_switching_current;
input Volume,I_rfrp;
real Volume,I_rfrp,eta;
begin
if(I_rfrp < 0) begin
eta = P/(1+pow(P,2));
critical_switching_current = (2*`P_Q/(`P_H/(2*`M_PI)))*(alpha*Ms*Volume/eta)*`P_U0*(Ms/(2*sqrt(2)));
end
else begin
eta = P/(1-pow(P,2));
critical_switching_current = (2*`P_Q/(`P_H/(2*`M_PI)))*(alpha*Ms*Volume/eta)*`P_U0*(Ms/(2*sqrt(2)));
end
end
endfunction
// This function computes the angle of magnetization of the free layer of the multi-layer device as function of the current through it.
analog function real angle;
input aj_piby2;
real aj_piby2,cos_angle;
begin
cos_angle = (Hd*gamma_p*(4*`M_PI/1e7) - aj_piby2/alpha)/((4*`M_PI*Ms + 0.5*Hk)*(4*`M_PI/1e7));
angle = acos(cos_angle);
end
endfunction
// This function computes the resistance of the multi-layer stack as a function of the angle of magnetization of the free layer.
analog function real resistance;
input theta;
real theta,G_theta;
begin
G_theta = 0.5*((1+cos(theta))*Gp + (1-cos(theta))*Gap);
resistance = 1/G_theta;
end
endfunction
// This function computes the magnitude of the clocking current that is required to align the magnetization of the free layer along the y-axis into a
// stationary magnetization state.
analog function real clocking_current;
input Volume;
real Volume;
real Hdz,G,Jp;
begin
Hdz = Hd*cos(theta0);
G = 1/(-4 + (pow((1+P),3))*3/(4*pow(P,1.5)));
Jp = `P_U0*(pow(Ms,2))*(`P_Q)*Volume/((`P_H)/(2*`M_PI));
clocking_current = Hdz*Jp/(G*(sin(theta0))*Ms);
end
endfunction
// This function is used to compute the post-clocking neighbor interaction among the free layers of the neighboring multi-layer cells.
// The neighbor interaction is implemented as a Finite State Machine.
analog function real mtj_fsm_vert_cell;
input [0:1] value_porta,value_portb,value_portc;
integer value_porta[0:1],value_portb[0:1],value_portc[0:1];
integer portb_and,porta_and,portb_xor_porta;
integer bitwise_xor[0:2];
integer out1[0:1],out2[0:1],out3[0:1],out[0:1];
begin
bitwise_xor[0] = (value_porta[0] ^ value_porta[1]);
bitwise_xor[1] = (value_portb[0] ^ value_portb[1]);
bitwise_xor[2] = (value_portc[0] ^ value_portc[1]);
portb_and = (value_portb[0] && value_portb[1]);
porta_and = (value_porta[0] && value_porta[1]);
portb_xor_porta = portb_and ^ porta_and;
out1[0] = value_portb[0] && !value_portc[0];
out1[1] = value_portb[1] && !value_portc[1];
out2[0] = (value_portb[0] || !value_portc[0]);
out2[1] = (value_portb[1] || !value_portc[1]);
out3[0] = !value_porta[0];
out3[1] = !value_porta[1];
out2[0] = out2[0] && out3[0];
out2[1] = out2[1] && out3[1];
out1[0] = out1[0] || out2[0];
out1[1] = out1[1] || out2[1];
if(bitwise_xor[0]) begin
if(bitwise_xor[1] && bitwise_xor[2]) begin
out[0] = low;
out[1] = high;
end
else if(bitwise_xor[1]) begin
out[0] = value_portc[0];
out[1] = value_portc[1];
end
else if(bitwise_xor[2]) begin
out[0] = !value_portb[0];
out[1] = !value_portb[1];
end
else begin
out[0] = value_portc[0];
out[1] = value_portc[1];
end
end
else begin
if(bitwise_xor[1] && bitwise_xor[2]) begin
out[0] = !(value_porta[0]);
out[1] = !(value_porta[1]);
end
else if(bitwise_xor[1])
begin
out[0] = value_portc[0];
out[1] = value_portc[1];
end
else if(bitwise_xor[2]) begin
if(portb_xor_porta) begin
out[0] = low;
out[1] = high;
end
else begin
out[0] = !(value_porta[0]);
out[1] = !(value_porta[1]);
end
end
else begin
out[0] = out1[0];
out[1] = out1[1];
end
end
if(out[0] ^ out[1])
mtj_fsm_vert_cell = 0.5;
else begin
if(out[0] == 0)
mtj_fsm_vert_cell = 0.0;
else
mtj_fsm_vert_cell = 1.0;
end
end
endfunction
// This function is used to decide the specific writing or clocking or no operation that needs to be performed on the cell.
// The specific operation that needs to be performed depends on the magnitude of the current through the cell and the duration of the current pulse.
analog function integer switch_output;
input [0:1]out_prev,switch_prev_out;
input I_switch, Iclk, t_precession, tpulse, I_max;
integer out_prev[0:1],switch_prev_out;
real I_switch,Iclk,t_precession,tpulse,I_max;
integer out[0:1];
real Imax_abs,Iswitch_abs;
begin
Imax_abs = abs(I_max);
Iswitch_abs = abs(I_switch);
if(abs(Imax_abs - Iclk) < I_delta) begin
if(I_max > 0) begin
out[0] = high;
out[1] = low;
switch_output = 01;
end
else begin
out[0] = out_prev[0];
out[1] = out_prev[1];
switch_output = 10;
end
end
else if((Imax_abs > Iswitch_abs) && (tpulse > t_precession/2)) begin
if(I_max < 0) begin
out[0] = high;
out[1] = high;
switch_output = 11;
end
else begin
out[0] = low;
out[1] = low;
switch_output = 00;
end
end
else begin
out[0] = out_prev[0];
out[1] = out_prev[1];
switch_output = switch_prev_out;
end
end
endfunction
// Main body of the program.
analog
begin
Volume = Length*Width*thickness;
t_precession = abs(`M_PI/`gamma);
geff = sqrt(P) + 1/sqrt(P);
g = 1/(-4 + (pow(geff,3))*0.75);
aj_piby2 = ((`P_H/(2*`M_PI))/(2*`P_Q))*g*I(rf,rp)/(Ms*Volume);
theta = angle(aj_piby2);
Resistance = resistance(theta) ;
I_switch = critical_switching_current(Volume,I(rf,rp));
Iclk = clocking_current(Volume);
@(initial_step) begin
trise_pos = 0;
tfall_pos = 0;
tfall_neg = 0;
trise_neg = 0;
tswitch = 0;
out[0] = low;
out[1] = low;
out_prev[0] = out[0];
out_prev[1] = out[1];
clocked = 0;
Resistance = R0;
I_prev = 0;
t_prev_pulse = 0;
switch_prev_out = 10;
end
@(cross(V(rf,rp) - V_delta,+1)) begin
trise_pos = $abstime;
end
@(cross(V(rf,rp) + V_delta,-1)) begin
tfall_neg = $abstime;
end
@(cross(V(rf,rp) - V_delta,-1)) begin
tfall_pos = $abstime;
t_prev_pulse = tpulse;
tpulse = tfall_pos - trise_pos;
tswitch = tfall_pos + t_delta;
end
@(cross(V(rf,rp) + V_delta,+1)) begin
trise_neg = $abstime;
t_prev_pulse = tpulse;
tpulse = trise_neg - tfall_neg;
tswitch = trise_neg + t_delta;
end
if (tpulse < 1.5e-12) begin
tpulse = t_prev_pulse;
end
@(timer(tswitch)) begin
switch_out = switch_output(out_prev,switch_prev_out,I_switch,Iclk,t_precession,tpulse,I_max);
switch_prev_out = switch_out;
case (switch_out)
00 : begin out[0] = low; out[1] = low; clocked=0; end
11 : begin out[0] = high; out[1] = high; clocked=0; end
01 : begin out[0] = high; out[1] = low; clocked=1; end
default : begin out[0] = out_prev[0]; out[1] = out_prev[1]; clocked=0; end
endcase
end
V(int_nodea,int_nodeb) <+ ddt(V(rf,rp));
if((abs(V(int_nodea,int_nodeb)) < 2e10) && ((abs(I(rf,rp))>I_upper) || (abs(I(rf,rp)-Iclk)
I_max = I(rf,rp);
I_prev = I_max;
end
else begin
I_max = I_prev;
end
value_porta[0] = (H(mag_porta[0]) > 0);
value_porta[1] = (H(mag_porta[1]) > 0);
value_portb[0] = (H(mag_portb[0]) > 0);
value_portb[1] = (H(mag_portb[1]) > 0);
value_portc[0] = (H(mag_portc[0]) > 0);
value_portc[1] = (H(mag_portc[1]) > 0);
H(mag_portd[0]) <+ transition(out[0],tdelay,trise,tfall);
H(mag_portd[1]) <+ transition(out[1],tdelay,trise,tfall);
if(clocked == 1) begin
fsm_out = mtj_fsm_vert_cell(value_porta,value_portb,value_portc);
if((fsm_out - 0.5) == 0) begin
out[0] = low;
out[1] = high;
end
else if(fsm_out == 1) begin
out[0] = high;
out[1] = high;
end
else begin
out[0] = low;
out[1] = low;
end
clocked = 0;
end
out_prev[0] = out[0];
out_prev[1] = out[1];
if(out[0] ^ out[1]) begin
Resistance = resistance(theta);
end
else begin
if(out[0] == 0) begin
Resistance = R0;
end
else begin
Resistance = R1;
end
end
I(rf,rp) <+ V(rf,rp)/Resistance;
end
endmodule
