Low Power Magnetic Quantum Cellular Automata Realization Using Magnetic Multi-Layer Structures (Invited Paper in IEEE JETCAS) 2011

J. Das, S.M. Alam and S. Bhanja, "Low Power Magnetic Quantum Cellular Automata Realization Using Magnetic Multi-Layer Structures", in IEEE Journal of Emerging Technologies CAS, June 2011 (Invited Paper).

Abstract: In this paper, we report Magnetic Quantum Cellular Automata (MQCA) realization using multi-layer cells with tilted polarizer reference layer with a particular focus on the critical
need to shift towards the multi-layer cells as elemental entities from the conventional single-domain nanomagnets. We have reported a novel spin-transfer torque current induced clocking
scheme, theoretically derived the clocking current, and shown the reduction in power consumption achieved against the traditional mechanism of clocking using magnetic fields typically generated from overhead or underneath wires. We have modeled the multilayer
cell behavior in Verilog-A along with the underlying algorithm used in implementing the neighbor interaction between the cells. The paper reports the switching and clocking current magnitudes, their direction and the power consumption associated with switching and clocking operation. Finally, we present the simulation results from Verilog-A model of switching, clocking
and neighbor interaction. Low power consumption due to spin transfer torque current induced switching and clocking along with the reasonable Magneto-Resistance (MR) distinguishing the
two energy minimum states of the device, make these devices a promising candidate in MQCA realization.

Verilog-A Model File for Magnetic Tunnel Junction (MTJ) Cells in a Vertical Array

//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

Verilog-A Model File for Magnetic Tunnel Junction (MTJ) Cells in a Horizontal Array

//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.

//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_horz_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_horz_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_portc[0] && value_portb[0];

out1[1] = value_portc[1] && value_portb[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_horz_cell = 0.5;

else begin

if(out[0] == 0)

mtj_fsm_horz_cell = 0.0;

else

mtj_fsm_horz_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] = high;

out[1] = high;

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_horz_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

Downloadable Models for NanoMagnetic Logic

Please visit this link for the Non-Volatile Magnetic Logic Model Files

http://sanju-a-j.blogspot.com/search/label/Downloadable%20Model%20files%20and%20Tools%20for%20Unconventional%20Computing

FAST QCA Simulator

The following link contains a QCA Simulator that can capture the thermal and other physical effect of QCA layouts on parization. The simulator is fast and accurate. Download the simulator

Maximum Error Modeling for Fault-Tolerant Computation using Maximum a posteriori (MAP) Hypothesis ( Microelectronic Reliability 2010)

Karthikeyan Lingasubramanian, Syed M. Alam, Sanjukta Bhanja, "Maximum error modeling for fault-tolerant computation using maximum a posteriori (MAP) hypothesis," Microelectronics Reliability, In Press, Corrected Proof, Available online 15 September 2010, ISSN 0026-2714, DOI: 10.1016/j.microrel.2010.07.156.

Abstract: The application of current generation computing machines in safety-centric applications like implantable biomedical chips and automobile safety has immensely increased the need for reviewing the worst-case error behavior of computing devices for fault-tolerant computation. In this work, we propose an exact probabilistic error model that can compute the maximum error over all possible input space in a circuit-specific manner and can handle various types of structural dependencies in the circuit. We also provide the worst-case input vector, which has the highest probability to generate an erroneous output, for any given logic circuit. We also present a study of circuit-specific error bounds for fault-tolerant computation in heterogeneous circuits using the maximum error computed for each circuit. We model the error estimation problem as a maximum a posteriori (MAP) estimate [28] and [29], over the joint error probability function of the entire circuit, calculated efficiently through an intelligent search of the entire input space using probabilistic traversal of a binary Join tree using Shenoy–Shafer algorithm [20] and [21]. We demonstrate this model using MCNC and ISCAS benchmark circuits and validate it using an equivalent HSpice model. Both results yield the same worst-case input vectors and the highest percentage difference of our error model over HSpice is just 1.23%. We observe that the maximum error probabilities are significantly larger than the average error probabilities, and provides a much tighter error bounds for fault-tolerant computation. We also find that the error estimates depend on the specific circuit structure and the maximum error probabilities are sensitive to the individual gate failure probabilities.

Study of Magnetization State Transistion...JAP 2011

A. Kumari, S. Sarkar, J. Pulecio, D. Karunaratne and S. Bhanja,"Study of Magnetization State Transistion in Closely-Spaced Nanomagnet 2D Array for Comuptaion", Accepted in Journal of Applied Physics, 2011.

Abstract:

The work investigated the dipole-dipole interaction for nite 2D arrays of ferromag-
netic circular nanomagnet. Starting with two basic arrangements of coupled nanomagnets namely, longitudinal and transverse, different diameter and thickness are studied. The phase plot results exhibit that for longitudinal arrangements the single domain state is pervasive over a large range of thickness values as compared to the transverse arrangement or isolated nanomagnet cases. The study is further extended to finite arrays (3 x 3 and 5 x 5) of circular nanomagnets. The magnetic force microscopy (MFM) results show that arrays of nanomagnets favors anti-ferromagnetic ordering at remanence. We have correlated our experimental results with micro-magnetic simulations. Based on our study, we can conclude that nanomagnets with 100 nm diameter, 15 nm thickness and 20 nm spacing has single domain state in an array configuration with one-step switching, which results in fast operation, a property ideal for computing.