An electro-thermal model for metal-oxide-metal antifuses

1548 IEEE TRANSACTIONS ON ELECTRON DEVICES. VOL. 42, NO. 8. AUGUST 1995

An Electro-Thermal Model for Metal-Oxide-Metal Antifuses

Guobiao Zhang, Student Member, IEEE, Chenming Hu, Fellow, IEEE, Peter Y. Yu, Steve Chiang, Member, IEEE, Shafy Eltoukhy, Member, IEEE,

andEsmat Z. Hamdy,

Abstract-In this paper, a complete electro-thermal analysis is presented for the metal-oxide-metal antifuses. The application of the Wiedemann-Franz Law and the thin film effect on thermal and electrical conductivities of metal films were also discussed. Several key parameters for tungsten-oxide-tungsten antifuse were extracted. The reaction temperature between tungsten and oxide was estimated to be around 1300°C. The core resistivity was found to be around 250pR.cm. This model can be readily extended to the other metal-dielectric-metal systems.

V I R on P C

S

T C

Tc T C O

NOMENCLATURE General read voltage. General read current. General read resistance. Subscript for on-state during antifuse operation. Subscript for programming state. Subscript for values inside the core. Subscript for values outside the core. Value of the core radius. Temperature at the core boundary during read. Reaction temperature between electrode material and antifuse material.

I. INTRODUCTION NTIFUSES have been intensively used in Field Pro- A grammable Gate Arrays (FPGA’s) [ 11-[9]. Its on-state

resistance is an important parameter that determines the circuit speed and it is inversely proportional to the programming current. The existing technology provides a silicon-to-silicon antifuse with an on-state resistance of around 500 0, when the programming current is 5 mA [l], [2]. An electro-thermal model has successfully explained this behavior [l], [2].

Metal-to-metal antifuses have gained an increasing interest in industry [3]-[9]. It has advantages such as lower on-state resistance, shorter delay and higher packing density. Metal- to-metal antifuses (Fig. 1) made of dielectrics such as oxide, nitride of silicon, or amorphous silicon are attractive. In this work, using tungsten-oxide-tungsten antifuse as an example,

Manuscript received April 18, 1994; revised October 31, 1994. The review

G. Zhang and P. Yu are with the Department of Physics, University of

C. Hu is with the Department of Electrical Engineering and Computer

S. Chiang is with the Prolinx Corp., San Jose, CA 95119 USA. S. Eltoukhy and E. Hamdy are with the Actel Corp., Sunnyvale, CA 94086

IEEE Log Number 9412375.

of this paper was arranged by Associate Editor G. W. Neudeck.

California, Berkeley, Berkeley, CA 94720 USA.

Sciences, University of California, Berkeley, Berkeley, CA 94720 USA.

USA.

Senior Member, IEEE

Top Electrode

Fig. 1. A cross-sectional view of a metal-to-metal antifuse. The existing technology uses TiW, MO, AI, etc., as electrode material and amorphous silicon, silicon nitride, etc., as antifuse material.

we extended the electro-thermal analysis of the silicon-to- silicon antifuses to the metal-to-metal antifuses and found that there is a similar dependence of the on-state resistance Ron and the programming fuse resistance Rp, which is the antifuse resistance during programming, on the programming current,

Here, Vf is the characteristic fuse voltage and V f , p the programming fuse voltage. The on-state resistance is of primary interest in industry since it characterizes the antifuse during operation. Special attention was also paid to the programming fuse resistance because it contains much information of filament formation, which would in return affect the on-state resistance.

The plan for this paper is as following. In Section I1 we will describe the physical picture of the antifuse during programming and read. In Section 111 we will make a detailed electro-thermal analyses. In Section IV we will discuss the application of the Wiedemann-Franz Law and the thin film effect on the thermal and electrical conductivities. Section V will be focused on the parameter extraction. In Section VI we conclude this paper.

11. PHENOMENON AND PHYSICAL PICTURE

Fig. 2 gives a typical read resistance versus the read current (RI) curve for a W-ox (30 A)-W antifuse. The device

0018-9383/95$04.00 0 1995 IEEE

ZHANG et al.: ELECTRO-THERMAL MODEL FOR METAL-OXIDE-METAL ANTIFUSES 1549

I O k . . * 5 ' . * * . 10 ' . . - . I . . 15 . . ' 20

I ") Fig. 2. The RI curves for a prototype W-electrode antifuse experiencing four scans. The read current at the end point of each scan works as the programming current for the subsequent scan. A 5 R offset is added to the first scan curve in order to distinguish it from the second scan curve.

was initially programmed at 5 mA. Then four scans were performed. During the first scan, the read current went up to 5 mA and during the subsequent scans, 10 mA, 15 mA, 20 mA, respectively. During the first two scans, RI curves are identical when the read current is less than 5 mA. This implies that there is no structural change if the read current is smaller than the programming current. During the second scan, at the read current of 5 mA, the read resistance peaks. Then the read resistance decreases as the read current increases. For the third and fourth scans, RI curves show a similar behavior and they peak exactly at the end point of the previous scan. This supports a physical picture of the programmed metal-to-metal antifuses during read similar to that of the silicon-to-silicon antifuses [ l ] , [2].

During programming, the high voltage impact on the antifuse material breaks it down at a certain weak point. As the programming current flows through the breakdown spot, it generates large enough Joule heat to raise the temperature around the breakdown spot above the reaction temperature between metal electrode and antifuse layer. Then a conductive channel (filament) is formed through the reaction between metal and antifuse material (Fig. 3) [5]. The possible reaction product could be a mixture of metal silicide and metal oxide. As an example, Table I gives a list of the reaction products between tungsten and silicon dioxide and their heat of formation [lo]. Here, we would use another term for the conductive channel, core. Core is a key word in this physical picture: outside the core, it remains metal; inside the core, it is the reaction product of metal with antifuse material, i.e., metal oxide and metal silicide. During programming, the size of the core is determined by the contour of a threshold temperature-the reaction temperature between metal and antifuse material. If the temperature is below this threshold temperature, no reaction would occur (Fig. 3). After the programming current is terminated, the conductive channel cools down and the core is left behind.

One thing to clarify here is the definition of the programming current. The programming current is the largest current

Programming Current _.- A --._ ----

Fig. 3. The current flow and temperature profile of an antifuse during programming. Inside the core, it is the reaction product between tungsten and silicon dioxide. Outside the core, it remains tungsten.

TABLE I THE REACTION PRODUCTS BJTWEEN TUNGSTEN

AND OXIDE AND HEAT OF FORMATION [lo]

W+SiO2

Reaction Proabets

Si+ WO3

Si+ W205

Si+ WO2

WSi2+ WO3

W S i p W2O5

WSi2+ WO2

W$ip WO3

W5Si3+ W2O5

WSSi.+- WO2

Heat of Formation &a& atom)

19.5

18.5

17.3

14.5

13.7

12.9

10.9

10.4

9.9

that flows through an antifuse which lasts at least 10 ns. The necessity to include the time period in the above definition is from the consideration of dynamic thermal transport. The time period to reach the thermal equilibrium is on the order of

where 1 is the dimension of the volume being heated during programming (from Fig. 16, the temperature rise during programming is negligible when T > 1 pm) and D is the thermal diffusivity of metal ("1 cm2/s [ l l ] ) . If the duration of the programming current is shorter than 10 ns, a stable state will not be reached and no stable conductive link can be formed. Of course, reaction also takes time, which makes the required programming time much longer than that required for thermal equilibrium.

During read, as the read current increases, the whole antifuse is heated up (Fig. 4(a)). This causes the increase of the read resistance. As the read current is equal to the programming current, the temperature at the core boundary reaches again

1550 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 42, NO. 8, AUGUST 1995

2) find out the core radius; - 3) evaluate the on-state resistance.

T c o K ( T ) dT Tc = I p - s,

A. T h e m 1 Transfer Equation /- Considering the temperature field outside the core during

point T , the current density is ' - \

\

\ T > T,.

I J=- -I / 2TT2 ' - /

Inside the core, a uniform current density is assumed, (a) (b) (C)

-1

. (7)

Fig. 4. The temperature field inside a programmed antifuse during read: (a) at a low read current, the high temperature region is small; (b) when the read current reaches the programming current, the whole core goes hot again; (c) when the read current is larger than the programming current, the core begins to grow. The shadowed areas are within the temperature contour of the reaction temperature.

the reaction temperature (Fig. 4(b)). Any further increase in the read current will cause more reaction between metal electrode and antifuse layer, and therefore, enlargement of the core (Fig. 4(c)). This enlargement of the core will reduce the read resistance. Thus, the read resistance peaks when the read current equals the programming current. At a typical ramping rate of HP4145B (~0.1-1 mA/s), any read current larger than the previous programming current will be considered as a new programming current, according to the previous definition of the programming current.

111. ELECTRO-THERMAL MODEL

The above system can be modeled as a conductive system, in the middle of which, there is an infinitely large thin insulating layer with a circular hole of radius TO (Fig. 3). If it can be assumed that there is only a single conductive medium in the system, the resistance of this system is simply R = ( p / 2 ~ 0 ) [12], where p is the electrical resistivity of the conductive medium. But, as pointed in the previous section, the material inside the core is quite different from that outside the core (Fig.

(4)

(5)

In comparison, the simulated current flow lines and equapotentials are plotted in Fig. 5(b). Apparently, our model is a fairly good approximation when T > 2r, (Fig. 5(c)) and we are going to base our model on this approximation throughout this paper.

B. Core Radius program-

ming, heat is generated inside the core as well as outside the core. The temperature in the vicinity of the core might be well above 1OOO"C (Section V). Notice that metal electrical resistivity typically has a large temperature coefficient. For example, from room temperature to 13Oo0C, the electrical resistivity of tungsten increases by a factor of 6 [13]. It's necessary to take into account the temperature dependence in our derivation.

In the spherical coordinate, we can solve (3) outside the core (Appendix),

I ) Complete Electro-Them1 Analysis: During

3), it is necessary for us to consider two regions separately. The approach of this electro-thermal model is as following: where Ta is the ambient temperature. Eq. (6) yields an

analytical solution for the core radius T,, 1) solve the heat transfer equation outside the core;

be preferable to further simply them. It is plausible to assume

density is the highest around it (Fig. 5(c)), namely, the heat generated inside the core dominates. Thus, the heat transfer (3) can be easily solved,

where J(r) is the current at position r; K . ( T ) and p ( T ) , that heat is solely generated inside the core since the current the thermal and electrical conductivities of the conductive medium, are the unique function of temperature. To determine the temperature field T ( r ) from this equation, we need to know the functional form of the current density J ( r ) . This can be

(8)

K e f f , the effective thermal conductivity, is introduced to match (8) to (6). From Fig. 6, one can observe that, with an appropriate K e f f , the temperature profile predicted by (8) is quite close to that by (5). Hence, the core radius can be

achieved by taking advantage of symmetry of the system. As I' . R 4 T K e f f T

T ( T ) = ~ + Ta a first order approximation, we are going to use a spherical symmetry in our model, i.e., we would simplify this 3D system into a 1D system. Fig. 5(a) gives the current flow lines and equapotentials that will be used in our model. We assume a spherical core and all equapotentials are concentric. Outside the core, the current is approximated as a radial flow and at


-2 -1 0 1 2 r/rc

(a)

--2 -1 0 1 2 @)

I .2 I . , . , . , .

rlrc (c)

Fig. 5 . (a) The current flow and equapotentials in the upper half space used in our model; (b) is a simulated current flow and equapotentials; (c) makes a comparison between the current density along the bisector of the first quadrant in (a) and (b).

approximated as

It is important to note that, in (7) and (9), the core radius is proportional to the programming current. The proportionality

1 o3 cr" + II

e o I O 2

cd Complete analysis

Fig. 6. A comparison of the temperature profile predicted by different thermal models. The dashed curve uses a of 1.7 W/cm K. The dotted curve uses a IE of 1.2 W/cm . K (IE of tungsten at 85OoC, half of the melting temperature of silicon dioxide).

constants are determined by the properties of electrode and antifuse materials.

C. On-State Resistance

Since the conductive medium is different inside and outside the core, these two regions should be treated separately. The on-state resistance is the sum of the core resistance and the spreading resistance (including upper and lower electrode spreading resistance) (Fig. 7(a)). During operation, i.e., when the read current is small, there is little temperature rise (<5OC) in the system (Fig. 16). It could be assumed that there is a uniform electrical resistivity outside the core. The same assumption can be held inside the core. However, during programming, the temperature rise outside the core is well above 1000°C (Fig. 16). It is necessary to consider the temperature dependence of the electrical resistivity of electrode material. Inside the core, the temperature rise is relatively small (Fig. 16), it can be assumed that there is no resistivity variation inside the core.

Inside the core, a uniform current density implies a constant electric field strength. Thus, from (5), the core resistance is

Notice that the electrical resistivity of the material inside the core is different during operation and during programming, because, during operation, the core is cold; during programming, it is hot. Hence,

Pc , o n

TI-, &,or2 = -

The on-state spreading resistance is


(a) (b)

Fig. 7. (a) The on-state resistance of a programmed antifuse is composed of three parts: the upper spreading resistance, the core resistance, the lower spreading resistance; (b) When a finite antifuse layer thickness is considered, we have to add the contribution from the conductive channel in the antifuse layer.

where p s , on is the electrical resistivity of the electrode material at room temperature. On the other hand, the programming spreading resistance is

The programming fuse resistance is 1

R p = R c 3 p + R s ) p 0; -. I P

(15)

It is clear that the on-state resistance and the programming fuse resistance are inversely proportional to the programming current, as indicated by (1) and (2). This can be qualitatively explained by following. As the programming current increases, more heat is generated and therefore, the core expands. There is a larger contact area between the top and bottom electrodes, namely, a smaller contact resistance.

D. Finite Antifuse Layer Thickness

In the above discussions it was assumed that the antifuse layer is infinitely thin. This is true if the antifuse layer thickness is small compared with the core radius (Fig. 7(a)). However, when the programming current is small or the antifuse layer is thick, the core radius is comparable to or even smaller than the antifuse layer thickness. In this case, it is necessary to consider the resistance contribution from the conductive channel. If this conductive channel is modeled as

a cylinder of height d and radius rc (Fig. 7(b)), the on-state resistance would take the form of

Ps,on I Pc,on I ~ c , o n d Ron = - rrc rrc rr,”

where the superscript [n] denotes the order term of d . Making use of (9), (14) and keeping the terms up to the first order of d , we got

2,- d

IP I,”

. 2 r ~ , f f ( T c o - Ta) . (16)

From the above expression, the correctional term for the finite oxide thickness is proportional to the antifuse layer thickness. This agrees with our intuition that, the thicker the antifuse layer, the higher the on-state resistance. Notice that the second term is inversely proportional to the square of the programming current. This means that the on-state resistance is no longer inversely proportional to the programming current when we take into account the finite antifuse layer thickness. But when the programming current is large enough, we would still believe that (1) and (2) are fairly good approximations.

I Pc, on

x { ~ c , o n + p s , on

Iv. APPLICATION OF THE WEIDEMANN-mANZ LAW

The Wiedemann-Franz Law states that, for metals, the ratio of the thermal conductivity and the electrical conductivity is directly proportional to temperature, with proportionality constant being independent of the particular metal [ 141. It can be expressed as

where L is Lorentz number, taking the value of 2.45 x lo-’ W.R/K2. This law simply states that, if a metal is electrically conductive, it is also thermally conductive. Fig. 8(a) compares the thermal and electrical conductivities for different metals at room temperature. Fig. 8(b) and (c) give the thermal and electrical conductivities and their ratio for bulk tungsten at different temperatures, respectively.

The data in Fig. 8 are bulk values. In practice, due to surface scattering, grain boundary reflection, frozen-in structural defects and impurities, the thin film values are smaller than the bulk values [15]-[18]. Even so, both theory [18] and experiment [ 161 revealed that the Wiedemann-Franz Law is still valid. This is because, for metals, both the thermal and the electrical transport are carried by electrons and are under the same influence of these effects [16]. By introducing a new variable, effective radius, Teff , the thin film effect can be accounted for and the original form of (8) can be kept


-2 I....,. 0 1

100

80

F 60

k 40

20

n

Y si

Bulk Tungsten

2 :I 3

I . . . .

Fitted Slope = 0.0277

Bulk Tungsten

-0 1 2 3 T ( ~ 1 0 ~ ~ )

(C)

Fig. 8. (a) Some examples of the thermal conductivity versus the electrical conductivity for different metals ranging from the poorest to the best conduc- tors at room temperature; (b) shows the temperature dependence of the thermal and electrical conductivities of bulk tungsten; (c) compares the experimental and theoretical value of the ratio between the thermal conductivity and electrical conductivity of bulk tungsten at different temperatures.

where

(19) &Film @Film

&Bulk @Bulk r= - r = K . r . Teff = -

Here, K is the scaling factor accounting for the thin film effect. Without further notice, all the thermal and electrical conductivities used in the equations in this paper refer to their bulk values. The only modification to the equations in Section I11 is to (16)

.27%f f ( T c o - T a ) . (20) 1 Pc, on

p c , on + P s , on

A useful conclusion that the Wiedemann-Franz Law can draw is that, up to the first order, the characteristic fuse voltage is substantially independent of electrode material and equal to 0.53 V [19]. This is surprising since people would generally believe that the antifuse with a better conductor as electrode material would have a lower on-state resistance. But according to the Wiedemann-Franz Law, when the electrode material is more electrically conductive, it is also more thermally conductive. For a more thermally conductive electrode, the heat generated inside the core would be much easier to transfer to the ambient. This implies a larger temperature drop around the core and therefore a narrower conductive link, namely, less contact area between the top and bottom electrodes. This cancels out the high electrical conductivity of the electrode material. Thus, the on-state resistance of metal-oxide-metal antifuses has little variation.

v. PARAMETER EXTRACTION AND DISCUSSIONS

A. Characteristic Fuse Voltage and Programming Fuse Voltage

Tungsten-oxide-tungsten antifuses were fabricated. The antifuse material-silicon oxide of thickness ranging from 30-160 8, was made using plasma enhanced chemical vapor deposition (PECVD) [20]. Measurement similar to Fig. 2 was performed on the programmed antifuses. In order to have a precise control on the programming current, the antifuses were programmed with a Hewlett-Packard 4145B Semiconductor Parameter Analyzer with the current compliance set to the value of the desired programming current. During programming, there was a 20 k R resistor on the probe tip to limit capacitor discharge current. Even so, precaution has to be taken to avoid setting too small a programming current while the capacitor discharging current is in fact larger than this nominal programming current. The simplest way to estimate the magnitude of the effective programming current is by measuring the device’s RI curve after it is programmed [21]. The kink on the RI curve roughly corresponds to the effective programming current since any RI curve would just peak at its effective programming current (Figs. 2 and 9). In order to minimize the effect of the antifuse layer thickness, we used the programming current in the range of 10 mA to 25 mA. The on-state resistance was taken at the read current of 1 mA. Below 1 mA, the resistance measurement is not very accurate.

Fig. 10 depicts the dependence of on-state resistance on the programming current for an antifuse sample with 30 8, oxide. The characteristic fuse voltage was extracted from the


0 5 10 15 20 1“)

Fig. 9. From this typical RI curve for an antifuse sample programmed at 10 mA, the programming fuse voltage was extracted from the part where the read current is larger than the programming current. The series resistance contributed from the substrate was added on ( 2 ) as a constant. Not all data points were plotted.

1 8ot R,, = :

0.04 0.08 0.12 I/$, (mA)”

Fig. 10. The dependence of the on-state resistance of antifuses programmed at different programming current in the range of 10 mA to 25 mA for a W-ox (30 A)-W antifuse. The characteristic fuse voltage was extracted from the slope of this curve.

slope of Fig. 10. The programming fuse voltage was extracted directly from the RI plot (Fig. 9). The dependence of the characteristic fuse voltage and the programming fuse voltage on the oxide thickness is plotted in Fig. 11. In general, the programming fuse voltage is around 30% larger than the fuse voltage, because the programming fuse voltage was taken during programming, when the antifuse is hot. Fig. 11 also shows that there is not much dependence of the characteristic fuse voltage on the oxide thickness up to 160 A, while there is a little increase in the programming fuse voltage.

B. Estimation of the Reaction Temperature

Consider two antifuses A , B programmed under the identical condition, i.e., both at room temperature with 10 mA programming current. By reading these two devices at different

1.0, I I I 1

0 50 100 150 200 T, (4

0.0

Fig. 1 I . do not depend on the insulating oxide thickness very much.

The characteristic fuse voltage and the programming fuse voltage

temperatures, we are able to estimate the reaction temperature. The RI curves are depicted in Figs. 9 and 12. It was observed that the peak of RI curve measured at 295°C (antifuse B) shifts from 10 mA to 8.9 mA and the programming fuse voltage changes from 0.592 V to 0.547 V. This can be explained as following: Since both devices were programmed at the same ambient temperature and the same programming current, they have the same core radius (Fig. 13(a)). But when read at 295”C, the temperature field in antifuse B is different from antifuse A which is read at room temperature. Under the same read current, antifuse B has a higher internal temperature than antifuse A (Fig. 13(b)). It would be easier for the temperature at its core boundary to reach the reaction temperature if it is read at a higher ambient temperature. In other words, the temperature at its core boundary will reach the reaction temperature at a lower read current (Fig. 13(c)). That’s why the peak of its RI curve shifts. Fig. 14 depicts the temperature profiles for both antifuses at the peak of their RI curves, or, when the temperature at the core boundary reaches the reaction temperature. The intersection of the temperature profiles corresponds to the reaction temperature. Thus, the reaction temperature between tungsten and silicon oxide is estimated to be 130°C. This is a reasonable temperature as tungsten is chemically reactive. It reacts with silicon at 600°C and forms oxide in air at 400°C [22] . The above mentioned methodology provides a simple way to estimate the reaction temperature. But there is a large statistical variation of the estimated reaction temperature, ranging from 9 W 1500°C. Further studies have to be done in this area.

C. Scaling Factor and Core Resistivity

So far, we have been avoiding to talk about the core radius because all of our discussions ignore the thin film effects and are based on the effective radius. In order to get the “real” core radius, we must find out the scaling factor K in (19). This can be done by studying the dependence of the on-state resistance on the insulating oxide thickness.

The on-state resistance of antifuse samples with varying oxide thicknesses was measured at various programming currents


Fig. 12. The RI plot for a W-ox (30 A)-W antifuse programmed at room temperature and measured at 295OC shows a shift in the read current corresponding to the peak resistance. Not all data points were plotted.

l i

I=8.9mA 4

I=.lOmA

(a) Both antifuses have the same core radius when beina programmed under the same condition. Antifuse A is read at room temperature, antifuse B is read at 295OC; (b) As the read current is increased, the core is heated up. But antifuse B has a hotter core since the ambient temperature is higher; (c) At 8.9 mA read current, the temperature at the core boundary of antifuse B has reached the reaction temperature. On the contrary, the temperature at the core boundary of antifuse A is still below the reaction temperature; (d) At 10 mA read current, the temperature at the core boundary of antifuse A reaches the reaction temperature too. The dark area is the high temperature area.

(Fig. 15). At a lower programming current, the dependence of the on-state resistance on the oxide thickness is much greater than when they were programmed at a higher current. This agrees with the physical picture (Fig. 7(b)). As the programming current increases, the ratio between the core radius and the oxide thickness increases, so the resistance contribution from the conductive link in the oxide layer drops. From Fig. 15, we found

0.435 2.9 x lop3 Ron=-+ ( Ip ) . d (21)

I P where, Ip is in ampere and d is in A. Making use of (14), (19), and (20), we conclude that the scaling factor K is around 0.1. Thus, the core radius is around 220 A when the programming current is 10 mA. Accordingly, the core resistivity is about 250

I I '1

o 0

i= 102:

....___... 27OC

295'C

Ip=l OmA

20 L 1 I 10' 1 o2 1 o3

reff (4 Fig. 14. The temperature profiles for the antifuse measured at room temperature and 295°C were plotted using-room temperature: the read fuse resistance of 59.2 R, the read current of 10 mA; at 295OC: the read fuse resistance of 61.5 R and the read current of 8.9 mA. The intersection of two curves corresponds to the reacting temperature.

"0 50 100 150 200 T,, (4

Fig. 15. The on-state resistance of antifuse samples shows a much stronger dependence on the insulating oxide thickness when the programming current is smaller. The solid lines are the prediction from (4.3).

pR cm. This is a relatively high resistivity compared with that of the tungsten silicide, whose value ranges between 10-40 pR -cm [23], [24]. One reason for this is the thin film effect. Another possible reason is the existence of tungsten oxide (Section 11) and silicon dioxide inside the core which blocks the conductive path and increases the overall resistivity of the core in a manner similar to the silicon-to-silicon antifuses [2].

D. Temperature ProJile in an Antijbse During Read

Temperature rise outside the core has been well established in Section III. Using (9, the temperature rise inside the core during read can be calculated in a similar manner,

T(r ) =T, + ~

TcO 6 Ta ( R , ,"R,iZ) (z) ( 1 - 5 ) (;)2. (22)

(22) and (8) give the temperature profile in the antifuse. When the read current is smaller than the programming current, the


core VI. CONCLUSION boundary

In this paper, we developed a thermal analysis suitable for the metal-to-metal antifuse with thin antifuse layers. The reaction temperature between tungsten and oxide is estimated around 130O0C, lower than the melting temperature of silicon dioxide and tungsten, The core radius is estimated around 220 A when the programming current is 10 mA. The core resistivity is relatively high probably due to the existence of

5

Fig. 16.

tungsten oxide. During programming, the temperature profile scales linearly with the programming current. These conclu- sions can be readily extended to other metal-to-metal antifuse systems.

101/ .c. ~ . . . , y --3O I I -2oc

I=0.5mA : 1 oo

1 o2 1 o3 APPENDIX

r (4 The detailed temuerature urofile in an ideal antifuse samole pro-

DERIVATION OF (6) FROM (3) By using (4), we rewrite (3) in the spherical coordinate with

grammed at 10 mA when it i s read aidifferent current. When the read curknt is small, there is not much temperature rise in the antifuse at all. When the read current reaches the programming current, the temperature at the core boundary goes up to the reaction temperature. As the read current goes even larger, the core boundary moves farther from the center of the core.

the assumption that the system is spherically symmetric (Figs. 3(b) and W ) ,

d [6(T)r2 $ T] = - p ( T ) . (&)’. r2 dr

Multiplying both sides by 6(T)r4 , we got, temperature at the core boundary as predicted by (8) is,

I 2 . R I2 T, + T, (Tco - T,) . =, + T,. (23) ~

4T)P(T) 12. 4 7 r ~ e f f r c I P

Thus, the temperature profile is, [s(T)r’ g] . $ [a(T)r2 g] = - 4x2

T ( r ) = (T, - T,) 2 + T, r > r, (24) Integrating it from cc to r , and making use of the fact,

dS . [ri(T)VT]

I . V 47r ’

- where we approximated the thermal conductivity of the core

larger than the programming be kept at the reaction temperature and the temperature profile is

as that of tungsten. On the other hand, when the read current is the ‘Ore boundary we found the expression for the temperature field inside the

spreading region,

T(T) = 1300 x 5 T > r, (26)

Equations (24)-(27) are plotted in Fig. 16 for the different read currents. From this picture, the temperature rise in the antifuse will be less than 1°C during normal operation, when the operating current is on the order of 100 PA. Thus the read disturb [6], [7] caused by temperature rise during operation is trivial. On the other hand, for an ideal antifuse with an infinitely thin antifuse layer, during programming, the temperature profile linearly scales with the programming current,

T ( ~ / ~ P ) l I p = z p l = T(r/~,) l lp=Ip2. (28)

The highest temperature inside an antifuse during programming will not change as we increase the programming current.

K ( T ) dT

which is (6).

REFERENCES

[ l ] E. Hamdy, J. McCollum, S. Chen, S. Chiang, S. Eltoukhy, J. Chang, T. Speers, and A. Mohsen, “Dielectric based antifuse for logic and memory IC’s,” IEEE IEDM Tech. Dig., pp. 786-787, 1988.

[2] S. Chiang, R. Wang, J. Speers, J. McCollum, E. Hamdy, and C. Hu, “Conductive channel in ONO formed by controlled dielectric breakdown,” in Symp. VLSI Technol. Dig. Techn. Papers, 1992, 1992, pp. 20-21.


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[71

[91

S. Wang, G. Misium, J. Camp, K. Chen, and H. Tigelaar, “High performance metaysilicide antifuse,” IEEE Electron Device Lett. vol. 13, pp. 471-473, Sept. 1992. S. Cohen, J. Raffel, and P. Wyatt, “A novel double-metal structure for voltage-programmable links,” IEEE Electron Device Lett. vol. 13, pp. 488-491, Sept. 1992. S. Cohen, A. Soares, E. Gleason, P. Wyatt, and J. Raffel, “A novel metal-insulator-metal structure for field-programmable devices,” IEEE Trans. Electron Devices, vol. 40, pp. 1277-1283, July 1993. C. Hu, “Interconnect devices for field programmable gate array,” IEEE IEDM Tech. Dig., pp. 591-594, 1992. S. Chiang, R. Forouhi, W. Chen, F. Hawley, J. McCullum, E. Hamdy, and C. Hu, “Antifuse structure comparison for field programmable gate arrays,” IEEE IEDM Tech. Dig., pp. 611-614, 1992. K. Gordon and R. Wong, “Conductive filament of the programmed metal electrode amorphous silicon antifuse,” IEEE IEDM Tech. Dig.,

M. Takagi, I. Yoshii, N. Ikeda, H. Yasuda, and K. Hama, “A highly reliable metal-to-metal antifuse for high-sped field programmable gate arrays,” IEEE ZEDM Tech. Dig., pp. 31-34, 1993. T. P. Chow and A. J. Stecki, “A critique of refractory gate applications for MOS VLSI,” in V U 1 Electronics. Orlando, FL: Academic Press, 1985, vol. 9, p. 44. Y. Touloukian, R. Powell, C. Ho, and M. Nicolaou, T h e m 1 Difisivity. New York-Washington: IFI/Plenum, 1973, p, 198. This is a typical problem in the classical electrodynamics, see, for example, J. D. Jackson’s Classical Electrodynamics. 2nd ed. New York John Wiley, 1975, p. 128, problem 3.3. The potential can be solved as a summation of Legendre polynomials. Landolt-Bomstein, Numerical Data and .Functional Relationship in Science and Technology, New Series, K. Hellwege, Ed. vol. 15a, p. 87. C. Kittel, Introduction to Solid State Physics, 6th ed. New York: John Wiley, 1986, p. 144. T. P. Chow and A. J. Stecki, “A critique of refractory gate applications for MOS VLSI,” in V U 1 Electronics. Orlando, FL: Academic Press, 1985, vol. 9, p. 39. P. Nath and K. Chopra, “Thermal conductivity of copper films,” Thin Solid Films, vol. 20, pp. 53-62, 1974. K. Dua and R. Aganvala, “Thermal conductivity of thin films of alkali metals,” Thin Solid Films, vol. 10, pp. 137-139, 1972. K. Klose, Z. Naturforsch., vol. 13a, p. 978, 1958. G. Zhang, C. Hu, P. Yu, S. Chiang, and E. Hamdy, “Characteristic voltage of the programmed metal-to-metal antifuses,” IEEE Electron Device Lett., vol. 13, pp. 166-168, May 1994. -, “Metal-to-metal antifuses with very thin silicon dioxide films,’’ IEEE Electron Device Lett., vol. 13, pp. 310-312, Aug. 1994. G. Zhang, C. Hu, P. Yu, S. Chiang, S. Eltoukhy, and E. Hamdy, “A

pp. 27-30, 1993.

Chenming Hu (S’7 I-M’76-SM’83-F‘90) received the B.S. degree from the National Taiwan Univer- sity, and the M.S. and Ph.D. degrees in electrical engineering from the University of California, Berkeley, in 1970 and 1973, respectively.

From 1973 to 1976, he was an assistant professor at the Massachusetts Institute of Technology, Cambridge. In 1976, he joined the University of California, Berkeley, as professor of Electrical En- gineering and Computer Sciences. He is also the Director of Industrial Liaison Program. While on

industrial leave from Berkeley in 1980 and 1981, he was manager of nonvolatile memory development at National Semiconductor. Since 1973, he has served as a consultant to the electronics industry. He has also been an advisor to many government and educational institutions. His present research areas include VLSI devices, silicon-on-insulator devices, hot electron effects, thin dielectrics, electromigration, circuit reliability simulation, and nonvolatile semiconductor memories. Dr. Hu has also conducted research on electro- optics, solar cells, and power electronics. He has been awarded several patents on semiconductor devices and technology. He has authored or co-authored three books and over 350 research papers. He has delivered more than a score of keynote addresses and invited papers at scientific conferences, and has received many best-paper awards. Dr. Hu is an Honorary Professor of Beijing University and of Tsinghua

University, China, and of the Chinese Academy of Science. He has been a guest editor of PROCEEDINGS OF THE IEEE and the IEEE TRANSACTIONS ON ELECTRON DEVICES. He serves on an editorial board of Semiconductor Science and Technology, Institute of Physics, England.

Peter Y. Yu received the Ph.D. degree in 1972. He was a staff member for six years at the IBM Thomas J. Watson Research Center, Yorktown Heights, NY. He became a professor in physics at the University of Califomia, Berkeley, in 1982.

He is a fellow of the American Physical Society.

reliable metal-to-metal oxide antifuse,” in Proc. I994 IEEE Znt. Electron Device Meeting, 1994, pp. 281-284.

[22] S. Wolf and R. Tauber, Silicon Process for VLSI Era. Sunset Beach, CA: Lattice Press, 1986, vol. 1, p. 400.

[23] T. P. Chow and A. J. Stecki, “A critique of refractory gate applications for MOS VLSI,” in V U 1 Electronics. Orlando, FL: Academic Press, 1985, vol. 9, p. 59.

New York Academic Press, 1983, p. 31.

[24] S . P. Murarka, Silicides for VLSI Applications.

Steve Chiang (M’88) received the B.S. degree in physics from National Taiwan University, and the M.S. and Ph.D. degrees in materials science and engineenng from University of California, Berkeley, in 1976, 1978, and 1981, respectively.

From 1982 to 1987, he was with the Intel Cor- poration, Aloha, OR, and worked in vanous technology development areas in package assembly and wafer process integration. He has demonstrated the process feasibility of the first Flash EPROM product at Intel. From 1987 to 1993, he was with Ac-

development manager. He did extensive work in antifuse area, both in technology development and in production engineering environments. In 1994, he cofounded Prolinx Corp., San Jose, CA, serving as the vice president of technology. He is currently engaged in developing high speed, low cost programmable elements using printed circuit board technologies and applications of the technologies to a new series of products as well as to improvements of general printed circuit board manufacturing capabilities. Dr. Chiang has authored or co-authored more than 20 technical papers and has received 9 patents with others pending.

Guobiao Zhang (S’94) is pursuing the Ph.D. degree

of IC device fabrication, testing, and modeling.

Society.

at the University of California, Berkeley, in the area yvale, CA, and last served as a senior technology

H~ is a student member of the ~ ~ ~ r i ~ ~ ~ Physical


Shafy Eltoukhy (S’8&M’82) received the B.Sc. and M.Sc. from Cairo University, Cairo, Egypt, in 1976 and 1979, respectively and the Ph.D. from the University of Waterloo, Waterloo, Ontario, Canada in 1982, all in electrical engineering.

From 1976 to 1979, he served as an instructor in the Department of Electrical Engineering, Cairo University, Egypt. From 1980 to 1982, he was a research and teaching assistant in the Department of Electrical Engineering, University of Waterloo, where he was involved in modeling Biuolar transis-

tors with Polysilicon emitter. In 1982, he joined Fairchild kesiarch Center, Palo Alto, CA, to work on high speed Bipolar process. From 1983 to 1986, he was a senior device engineer with the Technology Development group at Intel Corporation, Aloha, OR, involved in device physics of the one micron technology for 1M DRAM and Microprocessors. In 1986, he joined Actel Corporation, Sunnyvale, CA, where he is now Director of the Technology Development group. He authored over 20 papers on device physics of both Bipolar and MOS devices, and holds several patents.

&mat 2. Hamdy (S’76-M’8&SM’89) was bom in Cairo, Egypt on Feb. 2, 1950. He received the B.Sc. and M.Sc. degrees from Cairo University, Cairo, Egypt in 1971 and 1975, respectively, and the M.A.Sc. and Ph.D. degrees from the University of Waterloo, Waterloo, Ontario, Canada in 1977 and 1980, respectively, all in electrical engineering.

From 1971 to 1975, he served as an instructor in the Department of Electrical Engineering, Helwan University, Helwan, Egypt. From 1975 to 1980, he was a research and teaching assistant in the

Department of Electrical Engineenng, University of Waterloo, where he was engaged in the analysis, modeling, and design of high density Bipolar and MOS integrated structures for LSWLSI technologies. He joined the Intel Corporation, Aloha, OR, in 1981, where he was a senior staff engineerlproject manager in the technology department involved in device physics and circuit design of the world first 256K CMOS DRAM and Submicrometer CMOS for Microprocessors. In 1985, he cofounded Actel Corporation, Sunnyvale, CA, where he is now Vice President of Technology. At Actel, he managed and co-invented the PLICE antifuse technology used in the world first antifuse FPGA. He has authored or co-authored over 25 papers on LSWLSI circuits including contributions to IIL, single-device-well (SDW) MOSFET’s, CMOS latch-up and PLICE antifuse. He is winner of the best student paper at the 1979 IEDM meeting. He also has more than 10 granted or pending patents.

An electro-thermal model for metal-oxide-metal antifuses

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