2.2 Characteristic Voltages

So far, there are no well-established quantitative criteria for classifying a certain technology as ``Ultra-Low-Power''. Yet, there are some relations between characteristic voltages ( , , and ) and material parameters ( ), which could be used for classification. Considering the fundamental component of digital circuits, the switch, we can identify two characteristic voltages - regardless of the actual realization of the switch:

The supply voltage is the operating voltage of the circuit, i.e., the maximum value for the control and clamp voltages.

In an Ultra-Low-Power technology the supply voltage is several hundred millivolts, which is less than the band gap voltage of silicon, and the threshold voltage is between zero (high-performance) and the supply voltage (low-power), and is typically much less than the band gap. The reduction of the power consumption is achieved mainly by the reduced supply voltage, which results in reduced dynamic power.

The threshold voltage is the control voltage required to turn the switch on.

In a typical CMOS technology the threshold voltage is around 0.8V which is close to the band gap, and the supply voltage is 2.5V-5V which is well above the band gap. This is also the case for low-power CMOS, where reduction of the power consumption is achieved mainly by down-scaling which results in reduced capacitances. The difference $\ensuremath{V_{\mathit{DD}}}\xspace -\ensuremath{V_{\mathit{T}}}\xspace$ which is some times referred to as voltage drive, determines the speed through the on-state current which is for a MOSFET in strong inversion

$$\ensuremath{I_{\mathit{on}}}\xspace \propto (\ensuremath{V_... ...remath{V_{\mathit{T}}}\xspace )^\zeta, \qquad \zeta = 1\ldots2$$ (2.8)

The thermal voltage determines the maximum rate of change, i.e., the transition between on and off state of the switch.

In the case of semiconductor transistors (bipolar and MOS) the thermal voltage $\ensuremath{U_{\mathit{T}}}\xspace = \ensuremath{k}\xspace \ensuremath{T}\xspace / \ensuremath{q}\xspace$ is the lower limiting quantity to the threshold and supply voltage. The reason for this is the fact that the current flowing across the switch can change by at most ${e^{(\Delta V / \ensuremath{U_{\mathit{T}}}\xspace )}}$ which limits the ratio of the on and off-state current to

$${\displaystyle\frac{\ensuremath{I_{\mathit{on}}}\xspace }{\... ...{\mathit{DD}}}\xspace }{\ensuremath{U_{\mathit{T}}}\xspace }} ,$$ (2.9)

and

$$\ensuremath{I_{\mathit{off}}}\xspace \propto e^{\frac{\ensu... ... }{n\ensuremath{U_{\mathit{T}}}\xspace }}, \qquad n = 1\ldots2$$ (2.10)