Method and apparatus for modeling memristor devices
View Patent ↗A method and apparatus for modeling the characteristics of memristor devices. The invention provides methods and an apparatus for accurately characterizing the linear and non-linear Lissajous current-voltage behavior of actual memristor devices and incorporating such behavior into the resultant model. The invention produces a model that is adaptable to large scale memristor device simulations.
1. A method for producing a model of a memristor device for facilitating integrated circuit modeling and simulation, comprising the steps of:
inputting a periodic signal into a memristor, said periodic signal having a minimum voltage amplitude, a maximum voltage amplitude, and a frequency;
measuring and recording said memristor's output current at a plurality of
discrete time intervals over at least one period of said periodic signal;
plotting said output current versus input voltage over said at least one time period of said periodic signal;
plotting said output current versus time over said at least one time period of said periodic signal;
determining a high resistance state R on of said memristor from the slope of a high resistance portion of said plotted output current versus said input voltage;
determining a low resistance state R off of said memristor from the slope of a low resistance portion of said plotted output current versus said input voltage;
determining, from said plotted output current versus said input voltage
a low threshold voltage T 1 at which said memristor transitions from a high resistance state to a low resistance state, and
a high threshold voltage T h at which said memristor transitions from a low resistance state to a high resistance state;
determining from said plot of output current versus time a value of a magnitude fitting parameter K h1 when said input voltage is positive;
determining from said plot of output current versus time a value of a curvature fitting parameter K h2 when said input voltage is positive;
determining from said plot of output current versus time a value of a magnitude fitting parameter K l1 when said input voltage is negative;
determining from said plot of output current versus time a value of a curvature fitting parameter K l2 when said input voltage is negative; and
WHEN input voltage V in is greater than said high threshold voltage T h ,
THEN generating a model of said memristor device according to the expression
R
mem
(
t
)
=
R
mem
(
t
-
Δ
t
)
-
Δ
tK
h
1
ⅇ
K
h
2
(
V
in
(
t
)
-
T
h
)
{
if
R
mem
(
t
)
<
R
on
else
R
mem
(
t
)
=
R
on
WHEN input voltage V in is less than said low threshold voltage T 1 ,
THEN generating a model of said memristor device according to the expression
R
mem
(
t
)
=
R
mem
(
t
-
Δ
t
)
-
Δ
tK
l
1
ⅇ
K
l
2
(
V
in
(
t
)
-
T
l
)
{
if
R
mem
(
t
)
>
R
off
else
R
mem
(
t
)
=
R
off
where
R mem (t) is the resistance of said memristor at time t;
R mem (t−Δt) is the resistance of said memristor at time t−Δt:
R on is the resistance of said memristor in its high resistance state;
R off is the resistance of the memristor in its low resistance state;
V in is the voltage input to the memristor;
T 1 is the low threshold voltage of said memristor;
T h is the high threshold voltage of said memristor:
K h1 is the magnitude fitting parameter when said input voltage is positive;
K h2 is the curvature fitting parameter when said input voltage is positive;
K l1 is the magnitude fitting parameter when said input voltage is negative;
K l2 is the curvature fitting parameter when said input voltage is negative; and
Δt is the minimum integral time step parameter between successive memristor resistance measurements.
2. The method of claim 1 , wherein said plurality of discrete time intervals comprises at least 1000 discrete time intervals.
3. The method of claim 1 wherein Δt is 0.001 times said frequency or said input signal.
4. An apparatus for producing a model of a memristor device for facilitating integrated circuit modeling and simulation, comprising;
a fixture for applying a voltage across a memristor;
voltage measuring and recording means;
a current measuring and recording means;
a time measuring and recording means;
a computer having an external data bus,
wherein said computer receives said voltage, current, and time recorded measurements over said external data bus;
a software program;
wherein said software program further comprises computer executable instructions which, when said instructions are executed by said computer, said instructions perform the steps of:
inputting a periodic signal into a memristor, said periodic signal having a minimum voltage amplitude, a maximum voltage amplitude, and a frequency;
measuring and recording said memristor's output current at a plurality of
discrete time intervals over at least one period of said periodic signal;
plotting said output current versus input voltage over said at least one time period of said periodic signal;
plotting said output current versus time over said at least one time period of said periodic signal;
determining a high resistance state R on of said memristor from the slope of a high resistance portion of said plotted output current versus said input voltage;
determining a low resistance state R off of said memristor from the slope of a low resistance portion of said plotted output current versus said input voltage;
determining, from said plotted output current versus said input voltage
a low threshold voltage T 1 at which said memristor transitions from a high resistance state to a low resistance state, and
a high threshold voltage T h at which said memristor transitions from a low resistance state to a high resistance state;
determining from said plot of output current versus time a value of a magnitude fitting parameter K h1 when said input voltage is positive;
determining from said plot of output current versus time a value of a curvature fitting parameter K h2 when said input voltage is positive;
determining from said plot of output current versus time a value of a magnitude fitting parameter K l1 when said input voltage is negative;
determining from said plot of output current versus time a value of a curvature fitting parameter K l2 when said input voltage is negative; and
WHEN input voltage V in is greater than said high threshold voltage T h ,
THEN generating a model of said memristor device according to the expression
R
mem
(
t
)
=
R
mem
(
t
-
Δ
t
)
-
Δ
tK
h
1
ⅇ
K
h
2
(
V
in
(
t
)
-
T
h
)
{
if
R
mem
(
t
)
<
R
on
else
R
mem
(
t
)
=
R
on
WHEN input voltage V in is less than said low threshold voltage T 1 ,
THEN generating a model of said memristor device according to the expression
R
mem
(
t
)
=
R
mem
(
t
-
Δ
t
)
-
Δ
tK
l
1
ⅇ
K
l
2
(
V
in
(
t
)
-
T
l
)
{
if
R
mem
(
t
)
>
R
off
else
R
mem
(
t
)
=
R
off
where
R mem (t) is the resistance of said memristor at time t;
R mem (t−Δt) is the resistance of said memristor at time t−Δt:
R on is the resistance of said memristor in its high resistance state;
R off is the resistance of the memristor in its low resistance state;
V in is the voltage input to the memristor;
T 1 is the low threshold voltage of said memristor;
T h is the high threshold voltage of said memristor:
K h1 is the magnitude fitting parameter when said input voltage is positive;
K h2 is the curvature fitting parameter when said input voltage is positive;
K l1 is the magnitude fitting parameter when said input voltage is negative;
K l2 is the curvature fitting parameter when said input voltage is negative; and
Δt is the minimum integral time step parameter between successive memristor resistance measurements.
5. The apparatus of claim 4 , wherein said plurality of discrete time intervals comprises at least 1000 discrete time intervals.
6. Apparatus of claim 4 , wherein said voltage, current, and time measuring and recording means comprise a semiconductor parameter analyzer.
7. Apparatus of claim 4 , wherein said fixture for applying a voltage across a memristor comprises a microprobe station.
8. Apparatus of claim 4 wherein Δt is 0.001 times said frequency of said input signal.