6.5 Summary

Key results of the constrained optimization of devices with $\ensuremath {L}\xspace = \rm0.1\mu m$ are summarized in Table 6.4. The first column lists the parameters, the second column lists the values obtained with various speed criteria, and the third column lists the values obtained with various energy efficiency criteria. Despite the coarse sampling by the experiments some interesting conclusions can be drawn from these data:

1.

What strikes first is the fact that the optimum , i.e., the optimum worst-case leakage in all cases is $1\rm\mu A/\mu m$ (despite the constraints). In this respect high leakage currents are not specific to Ultra-Low-Power technologies, but a relaxed -constraint can also help the scalability of high-performance CMOS. What is ULP specific, however, is the idea and the techniques to make circuits work at higher leakage currents.

2.

The next interesting result is that the maximum for energy efficient devices is 0.32V and is quite small. Note that this includes devices with $\ensuremath{t_{\mathit{d}}}\xspace \le 2{\ensuremath{t_{\mathit{d}}}\xspace }_{\mathit{,min}}$.

3.

The energy efficiency can be improved by a factor of at least 7.2 at only a doubling of the optimum delay time.

4.

The optimum threshold voltage is at least 80mV, which is about three thermal voltage s (mind the definition of , see Section E.1).

5.

The achieved optimal values of and for high-performance technologies can vary by more than 20% depending on the criterion used. Thus, it is important to use the right criterion, and when a simpler one such as is used one must be aware that the actual optimum might be significantly different (especially, the unloaded-inverter delay).

Table 6.5 shows the same data for a channel-length range of $\ensuremath{L}\xspace = \rm0.18\ldots0.1\mu m$. The interesting information there are the values of the design and technology parameters. Note, that the optimum (electrical) of 3nm is caused by the criterion (otherwise lower values would be preferred).

=0.1em

Table 6.4: Optimization results for $\ensuremath {L}\xspace = \rm0.1\mu m$

parameter	$    $		$    $	opt. performance			$    $	opt. energy eff.
$    $		$    $	, , , ,			$    $	$\ensuremath{E_{\mathit{s}}}\xspace \ensuremath{t_{\mathit{d}}}\xspace$, $\ensuremath{E_{\mathit{s}}}\xspace (\ensuremath{t_{\mathit{d}}}\xspace =2{\ensuremath{t_{\mathit{d}}}\xspace }_{\mathit{,min}})$,
	$    $		$    $	$\ensuremath{V_{\mathit{DD}}}\xspace -\ensuremath{V_{\mathit{T}}}\xspace$			$    $	$\ensuremath{t_{\mathit{d}}}\xspace (\ensuremath{E_{\mathit{s}}}\xspace =2{\ensuremath{E_{\mathit{s}}}\xspace }_{\mathit{,min}})$
	$    $	$[\rm nA/\mu m]$	$    $	C00+			$    $	C00+
	$    $	$[\rm mA/\mu m]$	$    $	1.2	...	1.5	$    $	0.10	...	0.24
	$    $	$[\rm V]$	$    $	0.89	...	1.2+	$    $	0.2-	...	0.32
	$    $	$[\rm V]$	$    $	0.11	...	0.15	$    $	0.092	...	0.094
	$    $	$[\rm nm]$	$    $	0.9	...	1.8	$    $	0.6-
	$    $	$[\rm ps]$	$    $	5.5	...	6.7	$    $	14.3	...	21.4
	$    $	$[\rm ps]$	$    $	15.7	...	1A.5	$    $	30.6	...	47.9
	$    $	$[\rm ps]$	$    $	1.8	...	2.3	$    $	7.2	...	D.8
	$    $	$[\rm fJ]$	$    $	5.7	...	A.9	$    $	0.4	...	0.8

Table: Optimization results for $\ensuremath{L}\xspace = \rm0.18\ldots0.1\mu m$

parameter	$    $		$    $	opt. performance			$    $	opt. energy eff.
$    $		$    $	, , , ,			$    $	$\ensuremath{E_{\mathit{s}}}\xspace \ensuremath{t_{\mathit{d}}}\xspace$, $\ensuremath{E_{\mathit{s}}}\xspace (\ensuremath{t_{\mathit{d}}}\xspace =2{\ensuremath{t_{\mathit{d}}}\xspace }_{\mathit{,min}})$,
	$    $		$    $	$\ensuremath{V_{\mathit{DD}}}\xspace -\ensuremath{V_{\mathit{T}}}\xspace$			$    $	$\ensuremath{t_{\mathit{d}}}\xspace (\ensuremath{E_{\mathit{s}}}\xspace =2{\ensuremath{E_{\mathit{s}}}\xspace }_{\mathit{,min}})$
	$    $	$[\rm nA/\mu m]$	$    $	C00+			$    $	600	...	C00+
	$    $	$[\rm mA/\mu m]$	$    $	0.7	...	1.6	$    $	0.05	...	0.28
	$    $	$[\rm V]$	$    $	0.85	...	1.2+	$    $	0.2-	...	0.4
	$    $	$[\rm V]$	$    $	0.08	...	0.16	$    $	0.080	...	0.095
	$    $	$[\rm nm]$	$    $	0.9	...	3.0+	$    $	0.6-	...	1.3
	$    $	$[\rm ps]$	$    $	5.5	...	D.1	$    $	14.3	...	40.1
	$    $	$[\rm ps]$	$    $	15.7	...	34.3	$    $	30.6	...	B3.4
	$    $	$[\rm ps]$	$    $	1.8	...	4.0	$    $	7.2	...	1B.4
	$    $	$[\rm fJ]$	$    $	5.7	...	1B.0	$    $	0.3	...	2.2