CN101777389B - System and method for obtaining phase-change memory unit phase-change zone radius - Google Patents

System and method for obtaining phase-change memory unit phase-change zone radius Download PDF

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CN101777389B
CN101777389B CN 201010101396 CN201010101396A CN101777389B CN 101777389 B CN101777389 B CN 101777389B CN 201010101396 CN201010101396 CN 201010101396 CN 201010101396 A CN201010101396 A CN 201010101396A CN 101777389 B CN101777389 B CN 101777389B
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CN101777389A (en
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蔡道林
宋志棠
陈后鹏
陈小刚
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Shanghai Institute of Microsystem and Information Technology of CAS
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Abstract

The invention discloses a system and a method for obtaining phase-change memory unit phase-change zone radius. The method comprises the following steps that: step 1: according to the structure of a phase-change memory unit, a relationship model of voltage, current, temperature, time and the phase-change memory unit phase-change zone radius is built; step 2: the phase-change memory unit is set, and a voltage-current curve of the Set operation is obtained; and step 3: the intermediate parameters of the relationship model are obtained through the voltage-current curve of the Set operation, and the phase-change memory unit phase-change zone radius is obtained. The invention determines the phase change scope by obtaining the phase-change zone radius, provides support for the fatigue characteristic research on the phase-change memory unit, and simultaneously, provides means for the maintaining characteristic research on the phase-change memory unit.

Description

A kind of system and method that obtains phase-change memory unit phase-change zone radius
Technical field
The invention belongs to microelectronic, relate to a kind of system and method that obtains phase-change memory unit phase-change zone radius.
Background technology
Phase-changing memory unit is based on that conception that the phase-change thin film that proposes beginning of the seventies late 1960s can be applied to the phase change memory medium sets up, and is the memory device of a kind of low price, stable performance.Phase-changing memory unit can be made on the silicon wafer substrate, and its critical material is recordable phase-change thin film, heating electrode material, thermal insulation material and extraction electrode material, and its study hotspot also just launches around device technology.The physical mechanism research of device comprises how reducing device material etc.The ultimate principle of phase-changing memory unit is to act on the device cell with electric impulse signal, make phase-change material between amorphous state and polycrystalline attitude reversible transition occur, the low-resistance the when high resistant during by the resolution amorphous state and polycrystalline attitude realizes writing, wipe and read operation of information.
The advantages such as phase-changing memory unit owing to have reads at a high speed, high erasable number of times, non-volatile, component size is little, strong motion low in energy consumption, anti-and radioresistance are thought flash memories that most possible replacement is present by international semiconductor TIA and are become the device of following storer main product and become at first the device of commercial product.
The reading and writing of phase-changing memory unit, wiping operation are exactly voltage or the current pulse signal that applies different in width and height at device cell; Wipe operation (RESET): apply a phase-change material temperature in the short and strong pulse enable signal device cell be elevated to temperature of fusion above after, through thereby cooling realization phase-change material polycrystalline attitude is to amorphous conversion fast, namely one state is to the conversion of " 0 " attitude again; Write operation (SET): apply that a pulse enable signal phase-change material temperature long and medium tenacity is raised under the temperature of fusion, on the Tc after, and keep a period of time to impel nucleus growth, thereby realize amorphous state to the conversion of polycrystalline attitude, namely " 0 " attitude is to the conversion of one state; Read operation: apply a very weak pulse signal that can not exert an influence to the state of phase-change material, read its state by the resistance value of measuring element unit.
Because phase-changing memory unit is when carrying out read-write operation, the curtage that loads can cause the variation of phase-change material temperature, thereby causes phase-change material to undergo phase transition.Different voltage or electric current can cause the active component of phase change resistor phase change zone in the Reset process or the Reset phase transformation all occurs.The size of the radius of this part resistance that the phase change zone undergoes phase transition has determined the resistance of the Reset attitude of whole phase change cells, thereby has determined the logical zero or 1 of phase-changing memory unit.Therefore how to know the big or small most important of phase-changing memory unit phase change resistor radius.The method that tradition obtains the phase change resistor radius mainly is phase change cells to be carried out the simulation of heat distribution by matheematical equation, determines the phase change resistor radius according to the phase transition temperature zone of heat distribution again.This method is the relation of qualitative examination phase change resistor radius and voltage or electric current well, but can accurately not obtain the size of actual transformation cell radius.
Summary of the invention
Technical matters to be solved by this invention is: a kind of system and method that obtains phase-change memory unit phase-change zone radius is provided.
For solving the problems of the technologies described above, the present invention adopts following technical scheme.
A kind of method that obtains phase-change memory unit phase-change zone radius may further comprise the steps:
Step 1 is set up the relational model of voltage, electric current, temperature, time and phase-change memory unit phase-change zone radius according to the structure of phase-changing memory unit;
Step 2 is carried out the Set operation to phase-changing memory unit, obtains the voltage-to-current curve of Set operation;
Step 3, the intermediate parameters of the described relational model of voltage-to-current curve acquisition by described Set operation draws phase-change memory unit phase-change zone radius.
As a preferred embodiment of the present invention, described phase-changing memory unit is from bottom to up successively by bottom electrode, heating electrode, and phase change cells and top electrode form; Described phase change cells is divided phase change zone and radiating area; Described phase change zone is mushroom, and joins with described heating electrode; The zone of described phase change cells except the phase change zone is radiating area.
As another kind of preferred version of the present invention, the Temperature Setting of described phase change zone is homogeneous; The temperature of described radiating area outer boundary is room temperature T 2, the temperature constant of radiating area inside surface is T1=T, the thermograde of radiating area is constant; The total heat Q of resistance through described phase-changing memory unit is:
Q = - Σk ▿ T = 2 πk ( T - T 2 ) r 1 r 2 r 2 - r 1 + π k 1 r 2 ( T - T 2 ) d
Wherein, k and k 1Be respectively the thermal conductance of described phase change cells and the thermal conductance of described heating electrode; Be the thermograde of described radiating area, r, r 1And r 2Be respectively the radius of described heating electrode, phase change zone and radiating area; D is the height of described heating electrode;
The Joule heat W that the temperature T of phase change cells is produced by voltage or electric current jThermal diffusion W with phase change cells dDetermine:
T = ∫ t 0 t 1 W j - W d C × V dt
Wherein, C and V are respectively the thermal capacitance of phase change cells and the volume of phase change zone, W j=I R* V R, I RAnd V RBe respectively electric current and the voltage of the phase change zone of flowing through; T represents the time, t 0The initial time of expression voltage or current load, t 1The concluding time of expression voltage or current load; 25% to 35% heat diffuses away from heating electrode, and the total heat Q of described resistance is reduced to:
W d = Q = 2 πk ( T - T 2 ) r 1 r 2 r 2 - r 1 + 0.3 W j
To equation
Figure GSA00000006854700033
Differentiate can obtain:
∂ T ∂ t = W j - W d C × V
Described relational model is:
T = 0.7 W j ( r 2 - r 1 ) 2 πk r 1 r 2 ( 1 - exp ( - 3 k r 1 ( r 2 - r 1 ) r 1 2 C t ) ) + T 2 .
As another preferred version of the present invention, when the temperature T of described phase change cells was higher than Tc Tx and is lower than temperature of fusion Tm, phase change cells began crystallization; When the temperature T of described phase change cells was higher than temperature of fusion Tm, phase change cells began to change to amorphous state from crystalline state.
As another preferred version of the present invention, described room temperature T 2Be 300K.
As another preferred version of the present invention, described radiating area isothermal radiation, and the material of radiating area is the crystalline phase-change resistance material.
As another preferred version of the present invention, the material of described phase change cells is GeSbTe, SiSbTe, SiGe, SbTe or SiSb material.
As another preferred version of the present invention, in described Set operating process, the ohmically voltage of Reset attitude that is carried in described phase change zone equals the voltage after the voltage before the phase transformation on the voltage-to-current curve of Set operation deducts phase transformation.
A kind of system that obtains phase-change memory unit phase-change zone radius comprises modeling unit, Set operating unit, radius acquiring unit; Described modeling unit is in order to set up the relational model of voltage, electric current, temperature, time and phase-change memory unit phase-change zone radius according to the structure of phase-changing memory unit; Described Set operating unit obtains the voltage-to-current curve of Set operation in order to phase-changing memory unit is carried out the Set operation; Described radius acquiring unit draws phase-change memory unit phase-change zone radius in order to the intermediate parameters according to the described relational model of voltage-to-current curve acquisition of described Set operation.
Beneficial effect of the present invention is: it is by determining the scope of phase transformation to the acquisition of phase change zone radius, for the fatigue properties research of phase-changing memory unit provides support, also provides a kind of means for the retention performance research of phase-changing memory unit simultaneously.
Description of drawings
Fig. 1 is the phase-changing memory unit cross-sectional view;
Fig. 2 is phase-changing memory unit vertical structure schematic diagram;
Fig. 3 is phase-changing memory unit side structure schematic diagram;
Fig. 4 is the current-voltage curve figure of phase-changing memory unit Set operation;
Fig. 5 is the process flow diagram of the method for the invention;
Fig. 6 is system chart of the present invention.
The primary clustering symbol description:
1, bottom electrode; 2, heating electrode;
3, phase change cells; 4, top electrode;
31, phase change zone; 32, radiating area;
5, modeling unit; 6, Set operating unit;
7, radius acquiring unit.
Embodiment
The method of acquisition phase-change memory unit phase-change zone radius of the present invention is that phase-change material is divided into phase change zone and radiating area, sets up phase change zone radius relationship model.The radius that the difference of voltage or electric current can cause phase change resistor to undergo phase transition in the Reset phase transition process is different, so the size of phase change zone radius has determined the resistance of the Reset attitude of phase change cells.The relational model of model of the present invention phase change zone radius, the voltage-to-current curve acquisition current/voltage parameter of the operation of the Set by phase-change memory cell finally draws the phase change zone radius again.Foundation for the phase change cells circuit model among the present invention has better portability.Below in conjunction with accompanying drawing the specific embodiment of the present invention is described in further detail.
Embodiment one
The present embodiment provides a kind of method that obtains phase-change memory unit phase-change zone radius, and the method may further comprise the steps:
Step 1 is set up the relational model of voltage, electric current, temperature, time and phase-change memory unit phase-change zone radius according to the structure of phase-changing memory unit;
Step 2 is carried out the Set operation to phase-changing memory unit, obtains the voltage-to-current curve of Set operation;
Step 3, the intermediate parameters of the described relational model of voltage-to-current curve acquisition by described Set operation draws phase-change memory unit phase-change zone radius.
Described phase-changing memory unit is from bottom to up successively by bottom electrode, heating electrode, and phase change cells and top electrode form; Described phase change cells is divided phase change zone and radiating area; Described phase change zone is mushroom, and joins with described heating electrode; The zone of described phase change cells except the phase change zone is radiating area.The temperature of described phase change zone is assumed to be homogeneous; The temperature of described radiating area outer boundary is room temperature T 2=300K, the temperature constant of radiating area inside surface is T1=T, the thermograde of radiating area is constant; The total heat Q of resistance through described phase-changing memory unit is:
Q = - Σk ▿ T = 2 πk ( T - 300 ) r 1 r 2 r 2 - r 1 + π k 1 r 2 ( T - 300 ) d - - - ( 1 )
Wherein, k and k 1Be respectively the thermal conductance of described phase change cells and the thermal conductance of described heating electrode;
Figure GSA00000006854700052
Be the thermograde of described radiating area, r, r 1And r 2Be respectively the radius of described heating electrode, phase change zone and radiating area; D is the height of described heating electrode;
The Joule heat W that the temperature T of phase change cells is produced by voltage or electric current jThermal diffusion W with phase change cells dDetermine:
T = ∫ t 0 t 1 W j - W d C × V dt - - - ( 2 )
Wherein, C and V are respectively the thermal capacitance of phase change cells and the volume of phase change zone, W j=I r* V R, I RAnd V RBe respectively electric current and the voltage of the phase change zone of flowing through; T represents the time, t 0The initial time of expression voltage or current load, t 1The concluding time of expression voltage or current load; About heat of 25% to 35% diffuses away (therefore getting intermediate value 30%) from heating electrode, and the total heat Q of described resistance is reduced to:
W d = Q = 2 πk ( T - 300 ) r 1 r 2 r 2 - r 1 + 0.3 W j - - - ( 3 )
To equation Differentiate can obtain:
∂ T ∂ t = W j - W d C × V - - - ( 4 )
Described relational model is:
T = 0.7 W j ( r 2 - r 1 ) 2 πk r 1 r 2 ( 1 - exp ( - 3 k r 2 ( r 2 - r 1 ) r 1 2 C t ) ) + 300 - - - ( 5 )
When the temperature T of described phase change cells was higher than Tc Tx and is lower than temperature of fusion Tm, phase change cells began crystallization; When the temperature T of described phase change cells was higher than temperature of fusion Tm, phase change cells began to change to amorphous state from crystalline state.Described radiating area isothermal radiation, and the material of radiating area is the crystalline phase-change resistance material.The material of described phase change cells is GeSbTe, SiSbTe, SiGe, SbTe or SiSb material.In described Set operating process, the ohmically voltage of Reset attitude that is carried in described phase change zone equals the voltage after the voltage before the phase transformation on the voltage-to-current curve of Set operation deducts phase transformation.
The present embodiment also provides a kind of system that obtains phase-change memory unit phase-change zone radius, and as shown in Figure 6, this system comprises modeling unit 5, Set operating unit 6, radius acquiring unit 7; Described modeling unit is in order to set up the relational model of voltage, electric current, temperature, time and phase-change memory unit phase-change zone radius according to the structure of phase-changing memory unit; Described Set operating unit obtains the voltage-to-current curve of Set operation in order to phase-changing memory unit is carried out the Set operation; Described radius acquiring unit draws phase-change memory unit phase-change zone radius in order to the intermediate parameters according to the described relational model of voltage-to-current curve acquisition of described Set operation.
The present invention obtains the phase change zone radius when phase change resistor is undergone phase transition by the curtage heating, determine the scope of phase transformation by the phase change zone radius; The size of the radius of phase change zone compares after operating to the phase change zone radius of the initial state of phase-changing memory unit with through n time simultaneously, for the fatigue properties research of phase-changing memory unit provides support; Can compare in the variation through phase change zone radius after the uniform temperature phase-changing memory unit in addition, for the retention performance research of phase-changing memory unit provides a kind of means.
Embodiment two
The present embodiment provides the method for a kind of acquisition phase-change memory unit phase-change zone radius as shown in Figure 1.Phase-changing memory unit is from bottom to up successively by bottom electrode 1, heating electrode 2, and phase change cells 3 and top electrode 4 form.The material of phase change cells can be GeSbTe, SiSbTe, SiGe, SbTe or SiSb material.Because current density is maximum in the bottom of phase change cells, so the maximum temperature point of phase change cells is in the bottom of phase change cells layer.As shown in Figure 2, phase change cells 3 is comprised of phase change zone 31 and radiating area 32, and the heat radiation of radiating area 32 is isothermal radiation.Phase change zone 31 is mushroom, and the phase change zone is mutually conversion between crystalline state and amorphous state.Heat mainly is that the metal by top electrode 4 distributes.Fig. 3 is the side structure schematic diagram of Fig. 2.
The temperature of at first supposing phase change zone 31 is homogeneous, and the temperature of radiating area 32 outer boundaries is room temperature (300K), and the thermograde of radiating area 32 is constant, and the internal surface temperature of radiating area 32 maintains T1=T.Extrapolate through the total heat of phase change cells resistance according to above hypothesis and to be:
Q = - Σk ▿ T = 2 πk ( T - 300 ) r 1 r 2 r 2 - r 1 + π k 1 r 2 ( T - 300 ) d - - - ( 6 )
Wherein, k and k 1Be respectively the thermal conductance of phase change cells 3 and heating electrode 2;
Figure GSA00000006854700072
Be the thermograde of radiating area 32, r, r 1And r 2Be respectively the radius of heating electrode 2, phase change zone 31 and radiating area 32; D is the height of heating electrode 2.
The Joule heat W that the temperature T of phase change cells is produced by voltage or electric current jThermal diffusion W with phase change cells dDetermine:
T = ∫ t 0 t 1 W j - W d C × V dt - - - ( 7 )
Wherein, C and V are respectively the thermal capacitance of phase change cells 3 and the volume of phase change zone 31, W jDetermined by voltage and current:
W j＝I R×V R (8)
Wherein, I RAnd V RBe respectively electric current and the voltage of the phase change zone 31 of flowing through.About 30% heat diffuses away from heating electrode 2, and in order to simplify calculating, equation (6) can be reduced to following formula:
W d = Q = 2 πk ( T - 300 ) r 1 r 2 r 2 - r 1 + 0.3 W j - - - ( 9 )
Can obtain again from equation (7):
∂ T ∂ t = W j - W d C × V - - - ( 10 )
With the W in equation (8) and (9) jAnd W dBe updated to equation (10), can obtain:
T = 0.7 W j ( r 2 - r 1 ) 2 πk r 1 r 2 ( 1 - exp ( - 3 k r 2 ( r 2 - r 1 ) r 1 2 C t ) ) + 300 - - - ( 11 )
T represents the time.By the principle of work of phase-changing memory unit as can be known, when but temperature T was higher than Tc Tx is lower than temperature of fusion Tm, phase change cells began crystallization; When amorphous state all transferred crystalline state to, phase-changing memory unit converted the Set attitude to from the Reset attitude.When temperature T was higher than temperature of fusion Tm, phase change cells began to change to amorphous state from crystalline state.This crystalline state of phase change cells and amorphous mutually co-conversion have realized the conversion of phase change cells switch.
From equation (11) as can be known, I R, V R, r 1And r 2Jointly determined the value of temperature T.I R, V RProvided by voltage-to-current (V-I) curve of Set operation with t.r 2Equal the thickness of phase change cells, this is determined by preparation technology, r 1Radius for the phase change zone.For given phase change cells, the Set temperature is as can be known, can determine I according to voltage-to-current (V-I) the curve transformation temperature of Set operation R, V RAnd t, those these known parameter substitution equation (11) just can obtain r 1Value, also namely obtained the radius r of phase change zone 1
Fig. 4 is the V-I curve of the phase-changing memory unit Set operation of the present embodiment.What the phase change cells of the present embodiment adopted is Ge2Sb2Te5 (GST) material.In the Set operating process, be carried in the phase change zone ohmically voltage of Reset attitude and approximate voltage after the voltage before the phase transformation on the Set operation V-I curve deducts phase transformation.Adopt the parameter of the phase change cells of GST material to be: r 2=120nm, Tc T=473K, k=4.63 * 10 -3W/Kcm, C=1.25J/Kcm 3
The time t=50ms of step-length when adopting direct current scanning, Fig. 4 have shown the Set operating voltage-current curve of a, b, three kinds of phase-changing memory units of c.The voltage of phase-changing memory unit a when transformation temperature is 0.99002V, and electric current is 3 * 10 -5A, the voltage after the phase transformation is 0.31989V; The voltage of phase-changing memory unit b when transformation temperature is 1.07177V, and electric current is 2.2 * 10 -5A, the voltage after the phase transformation is 0.10874V; The voltage of phase-changing memory unit c when transformation temperature is 2.22363V, and electric current is 1 * 10 -5A, the voltage after the phase transformation is 0.02329V.Above data substitution equation (6), the phase change zone radius that can obtain phase-changing memory unit a is r 1=22.6nm, the phase change zone radius of phase-changing memory unit b is r 1=23.6nm, the phase change zone radius of phase-changing memory unit c is r 1=24.4nm.
Here description of the invention and application is illustrative, is not to want with scope restriction of the present invention in the above-described embodiments.Here the distortion of disclosed embodiment and change is possible, and the various parts of the replacement of embodiment and equivalence are known for those those of ordinary skill in the art.Those skilled in the art are noted that in the situation that do not break away from spirit of the present invention or essential characteristic, and the present invention can be with other forms, structure, layout, ratio, and realize with other elements, material and parts.

Claims (7)

1. a method that obtains phase-change memory unit phase-change zone radius is characterized in that, may further comprise the steps:
Step 1 is set up the relational model of voltage, electric current, temperature, time and phase-change memory unit phase-change zone radius according to the structure of phase-changing memory unit; Described phase-changing memory unit is from bottom to up successively by bottom electrode, heating electrode, and phase change cells and top electrode form; Described phase change cells is divided phase change zone and radiating area; Described phase change zone is mushroom, and joins with described heating electrode; The zone of described phase change cells except the phase change zone is radiating area; The Temperature Setting of described phase change zone is homogeneous; The temperature of described radiating area outer boundary is room temperature T 2, the temperature constant of radiating area inside surface is T1=T, the thermograde of radiating area is constant; The total heat Q of resistance through described phase-changing memory unit is:
Q = - Σk ▿ T = 2 πk ( T - T 2 ) r 1 r 2 r 2 - r 1 + π k 1 r 2 ( T - T 2 ) d
Wherein, k and k 1Be respectively the thermal conductance of described phase change cells and the thermal conductance of described heating electrode;
Figure FSB00000888799400012
Be the thermograde of described radiating area, r, r 1And r 2Be respectively the radius of described heating electrode, phase change zone and radiating area; D is the height of described heating electrode;
The Joule heat W that the temperature T of phase change cells is produced by voltage or electric current jThermal diffusion W with phase change cells dDetermine:
T = ∫ t 0 t 1 W j - W d C × V dt
Wherein, C and V are respectively the thermal capacitance of phase change cells and the volume of phase change zone, W j=I R* V R, I RAnd V RBe respectively electric current and the voltage of the phase change zone of flowing through; T represents the time, t 0The initial time of expression voltage or current load, t 1The concluding time of expression voltage or current load; 25% to 35% heat diffuses away from heating electrode, and the total heat Q of described resistance is reduced to:
W d = Q = 2 πk ( T - T 2 ) r 1 r 2 r 2 - r 1 + 0.3 W j
To equation Differentiate can obtain:
∂ T ∂ t = W j - W d C × V
Described relational model is:
T = 0.7 W j ( r 2 - r 1 ) 2 π kr 1 r 2 ( 1 - exp ( - 3 kr 2 ( r 2 - r 1 ) r 1 2 C t ) ) + T 2 ;
Step 2 is carried out the Set operation to phase-changing memory unit, obtains the voltage-to-current curve of Set operation;
Step 3, the intermediate parameters of the described relational model of voltage-to-current curve acquisition by described Set operation draws phase-change memory unit phase-change zone radius.
2. the method for acquisition phase-change memory unit phase-change zone radius according to claim 1 is characterized in that:
When the temperature T of described phase change cells was higher than Tc Tx and is lower than temperature of fusion Tm, phase change cells began crystallization; When the temperature T of described phase change cells was higher than temperature of fusion Tm, phase change cells began to change to amorphous state from crystalline state.
3. the method for acquisition phase-change memory unit phase-change zone radius according to claim 1 is characterized in that: described room temperature T 2Be 300K.
4. the method for acquisition phase-change memory unit phase-change zone radius according to claim 1 is characterized in that: described radiating area isothermal radiation, and the material of radiating area is the crystalline phase-change resistance material.
5. the method for acquisition phase-change memory unit phase-change zone radius according to claim 1, it is characterized in that: the material of described phase change cells is GeSbTe, SiSbTe, SiGe, SbTe or SiSb material.
6. the method for acquisition phase-change memory unit phase-change zone radius according to claim 1, it is characterized in that: in described Set operating process, the ohmically voltage of Reset attitude that is carried in described phase change zone equals the voltage after the voltage before the phase transformation on the voltage-to-current curve of Set operation deducts phase transformation.
7. a system that obtains phase-change memory unit phase-change zone radius is characterized in that, described system comprises:
Modeling unit is in order to set up the relational model of voltage, electric current, temperature, time and phase-change memory unit phase-change zone radius according to the structure of phase-changing memory unit; Described phase-changing memory unit is from bottom to up successively by bottom electrode, heating electrode, and phase change cells and top electrode form; Described phase change cells is divided phase change zone and radiating area; Described phase change zone is mushroom, and joins with described heating electrode; The zone of described phase change cells except the phase change zone is radiating area; The Temperature Setting of described phase change zone is homogeneous; The temperature of described radiating area outer boundary is room temperature T 2, the temperature constant of radiating area inside surface is T1=T, the thermograde of radiating area is constant; The total heat Q of resistance through described phase-changing memory unit is:
Q = - Σk ▿ T = 2 πk ( T - T 2 ) r 1 r 2 r 2 - r 1 + π k 1 r 2 ( T - T 2 ) d
Wherein, k and k 1Be respectively the thermal conductance of described phase change cells and the thermal conductance of described heating electrode;
Figure FSB00000888799400032
Be the thermograde of described radiating area, r, r 1And r 2Be respectively the radius of described heating electrode, phase change zone and radiating area; D is the height of described heating electrode;
The Joule heat W that the temperature T of phase change cells is produced by voltage or electric current jThermal diffusion W with phase change cells dDetermine:
T = ∫ t 0 t 1 W j - W d C × V dt
Wherein, C and V are respectively the thermal capacitance of phase change cells and the volume of phase change zone, W j=I R* V R, I RAnd V RBe respectively electric current and the voltage of the phase change zone of flowing through; T represents the time, t 0The initial time of expression voltage or current load, t 1The concluding time of expression voltage or current load; 25% to 35% heat diffuses away from heating electrode, and the total heat Q of described resistance is reduced to:
W d = Q = 2 πk ( T - T 2 ) r 1 r 2 r 2 - r 1 + 0.3 W j
To equation Differentiate can obtain:
∂ T ∂ t = W j - W d C × V
Described relational model is:
T = 0.7 W j ( r 2 - r 1 ) 2 π kr 1 r 2 ( 1 - exp ( - 3 kr 2 ( r 2 - r 1 ) r 1 2 C t ) ) + T 2 ;
The Set operating unit in order to phase-changing memory unit is carried out the Set operation, obtains the voltage-to-current curve of Set operation;
The radius acquiring unit, the intermediate parameters in order to according to the described relational model of voltage-to-current curve acquisition of described Set operation draws phase-change memory unit phase-change zone radius.
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