Adaptive threshold voltage control with positive body bias for N and P-channel transistors

Information

  • Patent Grant
  • 6731157
  • Patent Number
    6,731,157
  • Date Filed
    Tuesday, January 15, 2002
    22 years ago
  • Date Issued
    Tuesday, May 4, 2004
    20 years ago
Abstract
A threshold control circuit for CMOS transistors wherein the voltage on the body of an n-channel reference transistor is controlled with a feedback circuit to produce a positive voltage on the body and decrease the threshold of the reference transistor to a desired value and the voltage on the body of a p-channel reference transistor is controlled with a feedback circuit to produce a negative voltage on the body and decrease the threshold of the reference transistor to a desired value.
Description




BACKGROUND OF THE INVENTION




1. Field of the Invention




This invention relates to the field of threshold voltage control and, more particularly, to the control of the threshold voltage of a transistor with a feedback control system, to bias the transistor body voltage in such a way as to reduce the threshold voltage to a desired value.




2. Description of the Prior Art




In the last few years, the desire to lower the power supply voltages applied to integrated circuits, ICs, and thus reduce the power consumption while maintaining high reliability, has resulted in a significant decrease in the speed of the ICs. There have been attempts, in the prior art, to alleviate this problem by controlling the threshold value of the transistors. In the 1976 International Solid State Circuit Conference of IEEE, an article entitled “A Threshold Voltage Controlling Circuit for Short Channel MOS Integrated Circuits” by Masaharu Kubo, Ryoachi Hori, Osamu Minato and Kikuji Sato was presented wherein a threshold controlling circuit which can automatically set a circuit threshold voltage free from the fluctuations in device fabrication processes, by adjusting the substrate voltage of a MOSIC chip with a negative feedback. Also, in the 1994 Custom Integrated Circuit Conference of IEEE, an article entitled “Self-Adjusting Threshold-Voltage Scheme (SATS) for Low-Voltage High-Speed Operation” by Tsuguo Kobayashi and Takayasu Sakurai was presented wherein the threshold voltage fluctuations were reduced by self-substrate-biasing technique. A major difficulty with the techniques set fourth in these papers is that the transistor body is biased in the wrong direction or sense, e.g. negatively, with respect to ground, for n-channel transistors and thus requires an extra power supply and a more complex controller.




SUMMARY OF THE INVENTION




The present invention increases the speed of integrated circuits, particularly with small power supply voltages and thus maintains low power consumption while maintaining high reliability. The present invention biases the transistor body only positively, with respect to ground, for n-channel transistors and only negatively, with respect to the supply voltage, for p-channel transistors thus simplifying the prior art and eliminating the cost of an extra power supply.











BRIEF DESCRIPTION OF THE DRAWINGS





FIG. 1

shows a graph of the gate voltage vs. drain current characteristics of an n-channel FET at various body voltages;





FIG. 2

shows a graph of the gate voltage vs. drain current characteristics of a p-channel FET at various body voltages;





FIG. 3

shows a graph of relative gate delay vs. supply voltage, with and without the adaptive threshold voltage control of the present invention; and,





FIG. 4

shows a schematic diagram of the present invention.











DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS




The present invention performs equally well for both p-channel and n-channel transistors and, as will be explained, the circuits employed for p-channel transistors are substantially the same as those employed for n-channel transistors except that p-channel and n-channel transistors operate in opposite senses.





FIG. 1

shows the actual effect of the body voltage on the gate voltage/drain current characteristics of an n-channel FET. The characteristic curve at a +0.5 body voltage, is shown by a curve


10


N, at a 0.0 body voltage by a curve


11


N, at a −0.5 body voltage by a curve


12


N, at a −1.0 body voltage by a curve


13


N, at a −1.5 body voltage by a curve


14


N, at a −2.0 body voltage by a curve


15


N and at a −2.5 body voltage by curve


16


N. (All body voltages are with respect to the source). Note that at a nominal 0.0 body voltage, the threshold voltage (i.e. the gate voltage at which the transistor turns on) is about 0.7 volts, as seen by arrow


20


.




For p-channel FETs, the effect of the body voltage on the gate voltage/drain current characteristics is approximately the same as for n-channel FETs, except for the sign convention appropriate to p-channel FETs as is seen in FIG.


2


. In

FIG. 2

, the body voltages are all with respect to the source and at a −0.5 body voltage the characteristic curve is shown for curve


10


P, at a 0.0 body voltage by a curve


11


P, at a +0.5 body voltage by a curve


12


P, at a +1.0 body voltage by a curve


13


P, at a +1.5 body voltage by a curve


14


P at a +2.0 body voltage by a curve


15


P and at a +2.5 body voltage by curve


16


P. Again, note that at a nominal 0.0 body voltage, the threshold voltage (i.e. the gate voltage at which the transistor turns on) is about 0.7 volts, as seen by arrow


20


. (As used herein, the threshold value of an enhancement mode p-channel transistor is considered to be positive).




In the present invention, I apply only positive voltages to the body of the n-channel transistors, as, for example, between 0.0 volts and +0.5 volts (i.e. between curves


11


N and


10


N in FIG.


1


), and thus the threshold voltage is controlled to below about 0.7 volts (arrow


20


). Similarly, I apply only negative voltages to the body of the p-channel transistors as, for example, between 0.0 volts and −0.5 volts (i.e. between curves


11


P and


10


P in FIG.


2


), and thus the threshold voltage is also controlled to below about 0.7 volts (arrow


20


).





FIG. 3

, which is applicable to both n-channel transistors and p-channel transistors, shows the worst-case normalized gate Relative Delay vs. supply voltage, V


DD


for a CMOS logic gate with and without the present invention. The worst-case variations in threshold voltages for Honeywell Silicon on Insulator (SOI) transistors were used to obtain the values shown. A temperature range of −55 degrees to +125 degrees Celsius was used. A curve


22


shows the test without the present invention and it will be noted that the delay varies from about 1.0 unit to about 30 or 40 units (off the scale) as the applied voltage, V


DD


approaches 1.0. Curve


24


shows the test when using the present invention and it will be noted that the delay now varies from about 0.7 units to about 8.0 units. With the present invention, it was found that the maximum threshold voltage was about 0.68 volts at +125 degrees C. and the minimum threshold voltage was about 0.75 volts at −55 degrees C. Note also that with a V


DD


at 1.8 volts, the delay is reduced by about 30%, with a V


DD


at 1.5 volts, the delay is reduced by about 40% and with a V


DD


at 1.2 volts, the delay is reduced by about a factor of 7, with the present invention. Thus, the present invention allows the use of a supply voltage of as low as 1.0 volt, shown by dashed line


26


, whereas, with a supply voltage at 1.0 volt, the speed is impractically slow without the present invention.





FIG. 4

shows a schematic diagram of a preferred embodiment of the present invention using CMOS transistors of both the p-channel and n-channel types. In

FIG. 4

, the upper portion of the controller is the n-channel controller,


30


N producing an output BN and the lower portion of the controller is the p-channel controller,


30


P, producing an output BP. Both the upper and lower portions utilize four basic sub-circuits: 1) constant current sources, shown by dashed line boxes


36


N and


36


P respectively, 2) reference voltage circuits shown by dashed line boxes


40


N and


40


P respectively, 3) clamping circuits shown by dashed line boxes


44


N and


44


P respectively, and 4) output circuits shown by dashed line boxes


48


N and


48


P respectively.




The constant current sources


36


N and


36


P are common circuits well known in the prior art and will not be described in detail. The constant current produced by the source


36


N is labeled Icn and the constant current produced by


36


P is labeled Icp. It is noted that because of the sign convention for p-channel transistors and n-channel transistors, Icn is shown flowing out of the constant current source


36


N while Icp is shown flowing into the constant current source


36


P. Except for the use of n-channel transistors in the n-channel controller,


30


N and p-channel transistors in p-channel controller,


30


P the remaining portions of controller


30


are the same, i.e. reference circuit


40


P is like reference circuit


40


N, the clamping circuit


44


P is like clamping circuit


44


N and output circuit


48


P is like output circuit


48


N. Accordingly, p-channel controller,


30


P, and n-channel controller,


30


N, operate in the same fashion except in the opposite sense.




As mentioned, the n-channel controller uses biases that are controlled with positive, rather than negative voltages applied to the body terminals of the transistors, (i.e. between curves


11


N and


10


N of FIG.


1


). In the prior art, the n-channel transistors start with threshold values that are too low so that a negative voltage must be applied to the body in order for it to increase the threshold to the desired value. This requires an additional power supply. In the present invention, the n-channel transistors start with threshold values that range from just right to too high and the voltage to the body is increased, rather than decreased, to get the desired threshold without requiring an additional power source.




In

FIG. 4

, the constant current source


36


N of the n-channel controller


30


N is shown receiving the supply voltage V


DD


and producing the constant current Icn to a junction point


50


N. Junction point


50


N, in turn, is connected to a) the drain terminal of a transistor T


1


in the reference circuit


40


N, b) the gate terminal of a transistor T


3


in the output circuit


48


N and c) both the gate and drain terminals of a transistor T


6


in the clamp circuit


44


N. Clamp circuit


44


N also contains a transistor T


7


having a body terminal connected to the body and source terminals of transistor T


6


and a source terminal, gate terminal and drain terminal all connected to ground. A reference voltage V


RN


is applied via a line,


51


N, to the gate terminal of transistor T


1


in the reference circuit


40


N, and to the gate terminal of a transistor T


2


in the output circuit


48


N. The voltage on the body of T


1


is connected by a line


52


N to a) the drain terminal of transistor T


2


, b) the source terminal of transistor T


3


, c) the body terminals of both transistors T


2


and T


3


at a junction point


54


N in the output circuit


48


N and d) to the output BN. The voltage at junction point


54


N is the feedback voltage from the output circuit


48


N and supplies the body terminal of transistor T


1


and the output, BN, of the controller


30


N. It is presumed that the n-channel transistors of the rest of the integrated circuit will operate in substantially the same way as the n-channel transistor T


1


which, as will be shown, supplies a body voltage of magnitude necessary to obtain the desired threshold for transistor T


1


and thus for the other n-channel transistors in the integrated circuit. Accordingly, the output BN is used to connect the n-channel transistors in the printed circuit, represented by transistor T


20


, to supply the threshold controlling voltage as is shown by dashed line


56


N.




As mentioned, in the p-channel controller the bias voltages are controlled with negative voltages applied to the body terminals of the transistors, (i.e. between curves


11


P and


10


P of FIG.


2


). In the present invention, the p-channel transistors start with threshold values that range from just right to too low with respect to the power supply, V


DD


, and the voltage to the body is decreased, rather than increased, to get the desired threshold without requiring an additional power source.




The constant current source


36


P of the p-channel controller


30


P is slightly different than the constant current source


36


N in that transistors T


13


and T


14


are located where the resistor R was placed in the constant current source


36


N. This circuit is also well known in the art and will not be described in detail. Constant current source


36


P is shown receiving the supply voltage V


DD


and producing the constant current Icp connected to a junction point


50


P. Junction point


50


P, in turn, is connected to a) the drain terminal of a transistor T


8


in the reference circuit


40


P, b) the gate terminal of a transistor T


10


in the output circuit


48


P and c) both the gate and drain terminals of a transistor T


11


in the clamp circuit


44


P. Clamp circuit


44


P also contains a transistor T


12


having a body terminal connected to the body and source terminals of transistor T


11


and a source terminal, gate terminal and drain terminal all connected to the power supply V


DD


. A reference voltage V


RP


is applied via a line,


51


P, to the gate terminal of transistor T


8


in the reference circuit


40


P, and to the gate terminal of a transistor T


9


in the output circuit


48


P. The voltage on the body terminal of transistor T


8


is connected by a line


52


P to a) the drain terminal of transistor T


9


, b) the source terminal of transistor T


10


, c) the body terminals of both transistors T


9


and T


10


at a junction point


54


P in the output circuit


48


P and d) to the output BP. The voltage at junction point


54


P is the feedback voltage from the output circuit


48


P and supplies the body terminal of transistor T


8


and the output, BP, of the controller


30


N. It is presumed that the p-channel transistors of the rest of the integrated circuit will operate in substantially the same way as the p-channel transistor T


8


which, as will be shown, supplies a body voltage of magnitude necessary to obtain the desired threshold for transistor T


8


and thus for the other p-channel transistors in the integrated circuit. Accordingly, the output BP is used to connect the p-channel transistors in the printed circuit, represented by transistor T


22


to supply the threshold controlling voltage as is shown by dashed line


56


P.




In operation of the n-channel controller


30


N, if it is assumed, for example, that the threshold voltage of T


1


is, say 0.6 volts and the reference voltage V


RN


, is 0.5 volts, then T


1


will be “off” and the voltage at the gate of transistor T


3


will begin increasing due to the current Icn into junction point


50


N. The feedback, i.e. body voltage of transistor T


1


, at junction point


54


N, will begin to increase positively and, as seen in

FIG. 1

, as the body voltage increases, the threshold voltage goes down.




When the feedback voltage reaches the reference voltage, V


RN


, i.e. 0.5 volts, transistor T


1


will be turned “on” and the constant current, Icn, will now begin to flow through transistor T


1


. This reduces the voltage to the gate of transistor T


3


and the output at junction point


54


N will start decreasing. An equilibrium will be reached when the body voltage on transistor T


1


is just high enough to maintain the voltage to the gate of transistor T


3


at a value which maintains the current flow through transistor T


1


and to the gate of transistor T


3


at a constant level. At this point, the threshold of transistor T


1


(and all of the n-channel transistors such as T


20


of the integrated circuit) will be at the desired threshold. It should be noted that by changing the value of V


RN


, the desired threshold voltage can be changed. Because of this, one can obtain multiple different values for the threshold voltage on the same chip and may change the threshold voltage of a given part type without process changes.




The clamp


44


N may not be necessary, but in some cases, the increase of the body voltage to transistor T


1


may never get high enough to reach an equilibrium. In this event, clamp


44


N will put a stop to the increase. It is seen that transistors T


6


and T


7


receive the same voltage as the gate of transistor T


3


and act rather like two diodes connected in series. Thus, when the voltage at junction point


50


N reaches a predetermined value, current will flow through clamp


44


N to ground and prevent the body voltage to transistor T


1


from further increasing. While the threshold voltage reached at that point may not be ideal for the n-channel transistors, it will still be a considerably lower threshold than would be the case without the present invention.




In operation of the p-channel controller


30


P, if it is assumed, for example, that the threshold voltage of T


8


is, say 0.6 volts and the reference voltage V


RP


, is 0.5 volts below V


DD


, then T


8


will be “off” and the voltage at the gate of transistor T


10


will begin decreasing due to the current Icn out of junction point SOP. The feedback, i.e. the body voltage of transistor T


8


, at junction point


54


P, will begin to decrease negatively, and, as seen in

FIG. 2

, as the body voltage decreases, the threshold voltage goes down.




When the feedback voltage reaches the reference voltage V


RP


, i.e. 0.5 volts, transistor T


8


will be turned “on” and the constant current, Icp, will now begin to flow through transistor T


8


. This increases the voltage to the gate of transistor T


10


and the output at junction point


54


P will start increasing. An equilibrium will be reached when the body voltage on transistor T


8


is just high enough to maintain the voltage to the gate of transistor T


10


at a value which maintains the current flow through transistor T


8


and from the gate of transistor T


10


at a constant level. At this point, the threshold of transistor T


8


(and all of the p-channel transistors such as T


22


of the integrated circuit) will be at the desired threshold. It should be noted that by changing the value of V


RP


, the desired threshold voltage can be changed. Because of this, one can obtain multiple different values for the threshold voltage on the same chip and may change the threshold voltage of a given part type without process changes.




As with claim


44


N, the clamp


44


P may not be necessary, but in some cases, the decrease of the body voltage to transistor T


8


may never get low enough to reach an equilibrium. In this event, clamp


44


P will put a stop to the decrease. It is seen that transistors T


11


and T


12


receive the same voltage as the gate of transistor T


10


and act rather like two diodes connected in series. Thus, when the voltage at junction point


50


P reaches a predetermined value, current will flow through clamp


44


P to V


DD


and prevent the body voltage to transistor T


8


from further decreasing. While the threshold voltage reached at that point may not be ideal for the p-channel transistors, it will still be a considerably lower threshold than would be the case without the present invention




It is seen that the p-channel controller operates the same as the n-channel controller except that the voltage produced by the output circuit


40


P is negative with respect to the supply voltage and the reference circuit


40


P responds to the negative feedback voltage to produce a negative bias to the bodies of the p-channel transistors and produce a decreased absolute value for the threshold voltage, which in the case of a p-channel transistor, will also operate to increase the speed of operation.




It is thus seen that I have provided an improved threshold voltage supply with negative feedback to supply a positive bias to the bodies of an n-channel transistors and a negative bias to the bodies of p-channel transistors thus increasing the speed without requiring an additional power supply. Many changes will occur to those having skill in the art. For example, constant current sources other than


36


P and


36


N may be used, clamps other than


44


P and


44


N may be substituted and output circuits other than the circuit


48


P and


48


N may be employed so long as the feedback voltage to the body of the reference transistor T


1


is controlled in a manner such as described herein. I therefore do not wish to be limited to the specific descriptions used in connection with the preferred embodiment. The scope of the present invention is determined by the appended claims.



Claims
  • 1. A CMOS transistor threshold value controller comprising:a reference transistor having a body, the voltage on which can be varied in a first direction to decrease the threshold voltage of the reference transistor; a feedback circuit operable to produce a feedback voltage which increases in the first direction; and means connecting the body of the reference transistor to receive the feedback voltage to decrease the threshold of the reference transistor to a desired value.
  • 2. Apparatus according to claim 1 wherein the increase of feedback voltage to the reference transistor operates to reduce the magnitude of the feedback voltage until an equilibrium is reached where the threshold is maintained at the desired value by the feedback voltage.
  • 3. Apparatus according to claim 1 wherein the controller is an n-channel transistor threshold value controller, the reference transistor is an n-channel transistor having a body, the direction is positive, and the feedback circuit is operable to produce a positive voltage.
  • 4. The controller of claim 3 further including a source of reference voltage and the reference transistor has a gate electrode that is connected to the source of reference voltage.
  • 5. The controller of claim 4 further including a source of constant current and the reference transistor has a drain electrode connected to the source of constant current.
  • 6. The controller of claim 5 wherein the feedback circuit includes a first output transistor having a gate electrode connected to the source of constant current.
  • 7. The controller of claim 6 wherein the feedback circuit includes a second output transistor having a gate electrode connected to the source of reference voltage.
  • 8. The controller of claim 7 wherein the second output transistor has a source electrode connected to ground.
  • 9. The controller of claim 8 further including a source of supply voltage and the first output transistor includes a drain electrode connected to the source of supply voltage.
  • 10. The controller of claim 9 wherein the first output transistor includes a source electrode, the second output transistors includes a drain electrode connected to the source electrode of the first output transistor and both the first and second output transistors include a body connected to the body of the reference transistor to supply the positive voltage thereto.
  • 11. The controller of claim 10 further including an output terminal connected to the body of the reference transistor to supply the positive voltage to downstream n-channel transistors.
  • 12. The controller of claim 11 further including a clamp connected to the gate electrode of the first output transistor to prevent the positive voltage to the body of the reference transistor from exceeding a predetermined value.
  • 13. The controller of claim 3 further including a clamp connected to the feedback circuit to prevent the positive voltage from exceeding a predetermined value.
  • 14. Apparatus according to claim 1 wherein the controller is a p-channel transistor threshold value controller, the reference transistor is a p-channel transistor having a body, the direction is negative, and the feedback circuit is operable to produce a negative voltage.
  • 15. The controller of claim 14 further including a source of reference voltage and the reference transistor has a gate electrode that is connected to the source of reference voltage.
  • 16. The controller of claim 15 further including a source of constant current and the reference transistor has a drain electrode connected to the source of constant current.
  • 17. The controller of claim 16 wherein the feedback circuit includes a first output transistor having a gate electrode connected to the source of constant current.
  • 18. The controller of claim 17 wherein the feedback circuit includes a second output transistor having a gate electrode connected to the source of reference voltage.
  • 19. The controller of claim 18 wherein the first output transistor has a drain electrode connected to ground.
  • 20. The controller of claim 19 further including a source of supply voltage and the second output transistor includes a source electrode connected to the source of supply voltage.
  • 21. The controller of claim 20 wherein the first output transistor includes a source electrode, the second output transistors includes a drain electrode connected to the source electrode of the first output transistor and both the first and second output transistors include a body connected to the body of the reference transistor to supply the negative voltage thereto.
  • 22. The method of controlling the threshold of an CMOS transistor to increase speed while maintaining power consumption including a reference transistor having a source electrode, a gate electrode, a drain electrode and a body, with a voltage on the body that produces a decreased threshold when the voltage increases in a first direction, and a feedback circuit comprising the steps of:A. connecting a feedback circuit to produce a feedback voltage that increases in the first direction; and B. connecting the body of the reference transistor to receive the feedback voltage from the feedback circuit to decrease the threshold of the reference transistor to a desired value.
  • 23. The method of claim 22 further including the step of:C. providing a source of reference voltage to the gate electrode of the reference transistor.
  • 24. The method of claim 23 further including the step of:D. providing a source of constant current to the drain electrode of the reference transistor.
  • 25. The method of claim 24 wherein the feedback circuit includes a first output transistor having a source electrode, a gate electrode, a drain electrode and a body and further including the step of:E. connecting the gate electrode of the first output transistor to the source of constant current.
  • 26. The method of claim 25 wherein the feedback circuit includes a second output transistor having a source electrode, a gate electrode, a drain electrode and a body and further including the step of:F. connecting to the gate electrode of the second output transistor to the source of reference voltage.
  • 27. The method of claim 26 including a source of supply voltage and further including the step of:G. connecting the source electrode of the second output transistor to ground for n-channel transistors and to the source of supply voltage for p-channel transistors.
  • 28. The method of claim 27 further including the step of:H. connecting the drain electrode of the second output transistor and the bodies of the first and second output transistors to the body of the reference transistor to supply the feedback voltage thereto.
  • 29. The method of claim 28 further including the step of:I. connecting the body of the reference transistor to an output terminal to supply the feedback voltage to downstream CMOS transistors.
  • 30. The method of claim 29 further including a clamp and further including the step of connecting the gate electrode of the first output transistor to the clamp to prevent the voltage to the body of the reference transistor from exceeding a predetermined value.
  • 31. The method of claim 22 including a clamp and further including the step of:J. connecting the feedback circuit to the clamp to prevent the voltage from exceeding a predetermined value.
  • 32. A threshold controller comprising:a supply voltage source; a first source of reference voltage; a first constant current source; a first reference circuit, the first reference circuit including an n-channel transistor having a grid electrode connected to the first source of reference voltage, and having a source electrode, a drain electrode and a body; a first output circuit including first and second n-channel output transistors each having a source electrode, a grid electrode, a drain electrode and a body; means connecting the bodies of the first and second transistors in the first output circuit to the source electrode of the first transistor of the first output circuit and to the drain electrode of the second transistor of the first output circuit; means connecting the body of the transistor in the first reference circuit to the bodies of the first and second transistors of the first output circuit; a second reference circuit including a p-channel transistor having a source electrode, a grid electrode, a drain electrode and a body; a second source of reference voltage; a second constant current source; a second reference circuit, the second reference circuit including an p-channel transistor having a gate electrode connected to the second source of reference voltage, and having a source electrode, a drain electrode and a body; a second output circuit including first and second p-channel output transistors each having a source electrode, a grid electrode, a drain electrode and a body; means connecting the bodies of the first and second transistors in the second output circuit to the source electrode of the first transistor of the second output circuit and to the drain electrode of the second transistor of the second output circuit; means connecting the body of the transistor in the second reference circuit to the bodies of the first and second transistors of the second output circuit; means connecting the drain electrode of the p-channel transistor in the reference circuit and the gate electrode of the first transistor in the output circuit to the constant current source; means connecting the gate electrode of the transistor of the reference circuit and the grid electrode of the second transistor of the output circuit to the source of reference voltage; and, output means connected to the bodies of the transistors in the reference circuits respectively, to provide signals to n-channel and p-channel transistors downstream.
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Number Date Country
1081573 Mar 2001 EP
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Entry
Author: Masaharu Kubo, Ryoichi Hori, Osamu Minto and Kikuji Sato Title: “A Threshold Voltage Controlling Circuit For Short Channel MOS Integrated Circuits”, 1976 International Solid State Circuit Conference of IEEE (all pages), no month.
Author: Tsuguo Kobayashi and Takayasu Sakurai Title: “Self-Adjusting Threshold-Voltage Scheme (SATS for Low-Voltage High-Speed Operation”, 1994 Customer Integrated Circuits Conference (all pages), no month.
Author: Ricardo Gonzalez, Benjamin M. Gordon and Mark A. Horowitz Title: “Supply and Threshold Voltage Scaling For Low Power CMOS”, IEEE Journal of Solid State Circuits, vol. 12, No. 2, Aug. 1997 (all pages).