Sub Threshold Current

The sub threshold current always flows from source to drain even if the gate to source voltage is lesser than the threshold voltage of the device. This happens due to the carrier diffusion between the source and drain regions of the CMOS transistor in weak inversion. When gate to source voltage is smaller than but very close to threshold voltage of the device then sub threshold current becomes significant.

As observed by [4] currently, sub threshold leakage is still playing the main part in the three mechanisms. However, researchers believe that gate leakage and reverse-biased junction Band To Band Tunneling (BTBT) will be as important as sub threshold from 45 nm process downwards. In addition, with technology scaling, the gate oxide thickness will be reduced and the substrate doping densities will be increased. As a result other factors such as gate-induced drain leakage (GIDL) and drain-induced barrier lowering (DIBL) will also become more and more evident. Therefore, future effective low leakage design will need to target at several components since all of them play an important role in the total leakage consumption. Various techniques at process and circuit level exist to reduce leakage consumption, including modifying doping profile, oxide thickness and channel length. Forward or inverse body biasing is also one of them, which is a technique resulting in variable threshold CMOS.

Sub threshold current Isub, which occurs when gate voltage is below threshold voltage Vth, is a main part of leakage current [2]. Isub depends on different effects and voltages, which are formulated in following equations [1]:

Where

q is the electrical charge.

T is the temperature,

n is the sub threshold swing coefficient,

kB is the Boltzmann constant,

η is the drain induced barrier lowering (DIBL) coefficient,

γ is the body effect coefficient,

μ is the mobility,

Vth0 is the zero-bias threshold voltage,

Vgs is the gate-source voltage,

Vbs is the bulk-source voltage,

Vds is the drain-source voltage,

εox and εSi are the gate dielectric constants of gate oxide and silicium,

NSUB is the uniform substrate doping concentration and

NDEP the channel doping concentration,

Tox is the thickness of the oxide layer,

ФS is the surface potential,

DSUB and ETA0 are technology dependent DIBL coefficients, and

ETAB is a body-bias coefficient of the BSIM4-Modell.

The delay Td of a CMOS device can be approximated by equation (5).

Where

k’ is a technology constant,

CL is the load, and

α models the short channel effects [3].

Variation of Vth is a common technique to reduce leakage because Isub exponentially scales with Vth (see Equation 1). Thus, higher Vth results in lower leakage. However, from equation (5) follows higher Vth additionally results in longer delay [2]. Hence, optimize the design with the balance application of low Vth (LVT) and high Vth devices (HVT).

Transfer characteristics of MOSFET for VGS near Vth are shown in below figure.

Transfer characteristics of MOSFET V_GS near Vth [2]

From the above figure it can be observed that I_D increases exponentially with reduction in Vth.

As noted by [4] key dependencies of the sub threshold slope can be summarized as follows:

- Tox ↓ =>Cox ↑=> n ↓ =>sharper sub threshold

- NA ↑ =>Csth ↑ =>n ↑ =>softer sub threshold

- VSB ↑ =>Csth ↓ =>n ↓ =>sharper sub threshold

- T ↑ =>softer sub threshold

How to minimize sub threshold leakage?

A increase in the threshold voltage of the device keeps the Vgs of the NMOS transistor safely below the Vt,n. This is the case for logic zero input. For the logic one input increase in the threshold voltage of the device keeps the |Vgs| of the PMOS transistor safely below the |Vt,p|.

References

[1] Anantha P. Chandrakasan, Samuel Sheng and Robert W.Broadersen, “Low Power CMOS Digital Design”, IEEE Journal of Solid State Circuits, vol. 27, no. 4, pp. 472-484, April 1992

[2] Massoud Pedram, “Leakage Power Modeling and Minimization”, University of Southern California, Dept. of EE-Systems, Los Angeles, CA 90089, ICCAD 2004 Tutorial, www.ceng.usc.edu, 10/10/2007

[3] Frank Sill, Frank Grassert and Dirk Timmermann, “Reducing Leakage with Mixed-Vth (MVT)”, 18th International Conference on VLSI Design, IEEE, pp.874-877, January 2005

[4] Wei Liu ,Techniques for Leakage Power Reduction in Nanoscale Circuits: A Survey1, Department of Informatics and Mathematical Modeling ,Technical University of Denmark , IMM Technical Report 2007