Routing Resistance Influence in Loading Effect on
Leakage Analysis
Paulo F. Butzen, André I. Reis, Renato P. Ribas
PGMICRO – UFRGS
{pbutzen,andreis,rpribas}@inf.ufrgs.br
Abstract. Leakage currents represent emergent design parameters in nanometer
CMOS technologies. Leakage mechanisms interact with each other at device
level (through device geometry and doping profile), at gate level (through intracell node voltage) and at circuit level (through inter-cell node voltages). In this
paper, the impact of loading effect in the standby power consumption is evaluated in relation to the gate oxide leakage magnitude and the routing resistivity.
Simulation results, considering a 32nm technology node, have demonstrated an
increase of up to 15% in the total circuit leakage dissipation due to the loading
effect influenced by wire resistance.
Keywords: Loading effect, subthreshold leakage, gate tunneling leakage, routing resistance.
1 Introduction
Leakage currents are one of the major design concerns in deep submicron technologies due to the aggressive scaling of MOS device [1-2]. Supply voltage has been reduced to keep the power consumption under control. As a consequence, the transistor
threshold voltage is also scaled down to maintain the drive current capacity and
achieve performance improvement. However, it increases the subthreshold current
exponentially. Moreover, short channel effects, such as drain-induced barrier lowering (DIBL), are being reinforced when the technology shrinking is experienced.
Hence, oxide thickness (tox) has to follow this reduction but at expense of significant
gate oxide tunneling. Furthermore, the higher doping profile results in increasing
reverse-biased junction band-to-band tunneling (BTBT) leakage mechanism, though it
is expected to be relevant for technologies bellow 25nm [3].
Subthreshold leakage current occurs in off-devices, presenting relevant values in
transistor with channel length shorter than 180nm [4]. In terms of subthreshold leakage saving techniques and estimation models, the ‘stack effect’ represents the principal factor to be taken into account [5]. Gate oxide leakage, in turn, is verified in both
on- and off-transistor when different potentials are applied between drain/source and
gate terminals [6]. Sub-100nm processes, whose tox is smaller than 16Å, tends to present subthreshold and gate leakages at the same order of magnitude [7]. In this sense,
high-К dielectrics are been considered as an efficient way to mitigate gate leakage at
process level [8].
Since a certain leakage mechanism cannot be considered as dominant, the interaction among them should not be neglected. In [9], the interaction between leakage
currents in logic cells has been accurately modeled. However, in nanometer technologies, the total standby power consumption of a circuit cannot be estimated just by
summing individual leakages from logic cells, since leakage currents of distinct cells
interact with each other through internal circuit nodes (inter-cell connectivity). Such
interaction is known as ‘loading effect’. In [10] and [11], the impact of loading effect
in total leakage estimation is analyzed. Those works claims the loading effect modifies the leakage of logic gates by approximately 5% to 8%.
In this work, two important aspects are carefully taken into account in such a kind
of evaluation. At first, the gate oxide leakage magnitudes to attain the relevant impact
suggested in [10]. Secondly, the influence of routing resistance in loading effect, not
mentioned in previous works [10-11].
2 Loading Effect
In logic circuits, different leakage currents, in particular gate oxide leakages, from
distinct logic cells interact with each other through the internal circuit node voltages.
Such interaction modifies the inter-cell node potentials, changing thus the total leakage of individual logic gates connected at this node. The loading effect can either
increase or decrease the static currents of cells. For an easier comprehension of loading effect analysis, fig. 1 illustrates the leakage currents of two cascaded CMOS inverters. Considering input logic value equal to ‘0’ (0V), all leakage currents (subthreshold, gate oxide, BTBT) on the first inverter, and the gate leakage currents of
second inverter contribute to decrease the voltage at intermediate voltage Vi (ideally
in Vdd – power supply voltage). Such potential reduction, on the other hand, tends to
reduce those leakage components directly associated to this node. However, the voltage reduction in Vi changes the gate-source potential (Vgs) at PMOS on the second
inverter, increasing significantly its subthreshold current (exponentially dependent of
Vgs). BTBT leakage on the second inverter is not affected. Similar analysis is easily
done considering the input logic value of the inverter chain equal to ‘1’ (Vdd).
Fig. 1. Leakage currents illustration associated to the intermediate node potential Vi (loading
effect) in two cascaded CMOS inverters
Based on the analysis above, it is possible to conclude:
• Gate leakage is the main leakage mechanism responsible for loading effect. In
the given example, four from six leakage components that affect the node potential Vi are gate oxide leakage currents.
• Loading effect reduces all currents directly linked to the evaluation node.
• Loading effect increases significantly the subthreshold leakage on the next
stage. It is due to the increasing in gate-to-source potential, creating a conducting channel in an original turned off transistor.
2.1 Routing Resistance Influence
In previous section, the connection wire resistance between two logic cells is neglected in the analysis.
In [12] is presented the evaluation of routing wire characteristics in nanometer
technologies, and the authors concluded that the wire resistance (per unit length)
grows under scaling. From data presented on that work, the resistance of equivalent
wire segments increases around 10% to 15% for each technology node. Simulation
results have showed a routing resistance varies from units of ohms until kilohms for
an 8 bit processor designed using FreePDK technology [13]. In the same manner, gate
oxide leakage, which represents the major contributor of loading effect, is predicted to
increase at a rate of more than 3X per technology generation [11].
Fig. 2 shows the circuit used to investigate the influence of routing resistance in
loading effect analysis. In Fig. 2, a resistor representing the routing resistance has
been included in the circuit discussed in previous section (see Fig. 1). By doing so,
the logic cells do not have a common node anymore. There are two distinct potentials,
the output voltage of first stage (V1) and the input voltage of second one (V2). From
Kirchhoff’s Current Law (KCL), it can be verified that, for the steady state condition
defined in Fig. 2:
• V1 is larger than Vi.
• V2 is smaller than Vi.
Fig. 2. Evaluation of routing resistance in the loading effect
Similar analysis can be done by considering the opposite logic static condition.
Thus, the influence of routing resistance in loading effect analysis can be summarized
as:
• Leakage currents on the first cell do not reduce as much as when routing resistance is ignore, because V1 is larger than Vi.
• Gate oxide leakage current on the second cell reduces even more by taking into
account the routing resistance, once V2 is smaller than Vi.
• Subthreshold current on the second cell increases significantly due to the routing resistance influence, again because V2 is smaller than Vi.
3 Simulation Results
Electrical simulations were carried out in order to validate the assumptions outlined in
previous sections. Experiments were divided in three different goals. First of all, four
technology processes have been characterized in terms of NMOS and PMOS transistor current values, to be used as reference in the proposed investigation. At second,
the relevance of gate oxide leakage current magnitude on the loading effect has been
verified, without considering the routing wire parasitic influence. Such routing resistance has been taken into account in the last set of simulations.
3.1 Technology Characterization
Table 1 presents device characteristics of four Berkeley Predictive BSIM4 models
[14], obtained through HSPICE simulations. Those processes represent CMOS technologies from 90 nm down to 32 nm, with specific gate oxide thickness (tox) values.
The current components characterized for each transistor type in each technology
node were: subthreshold leakage current (Isub); and gate oxide leakage currents (Igate)
for turned on and turned off devices, i.e. Igate_ON and Igate_OFF, respectively.
Table 1. Devices current characterization for different PTM CMOS processes
Transistor
Type
NMOS
PMOS
Technology Node
tox (Å)
Isub (A/m)
Igate_ON (A/m)
Igate_OFF (A/m)
Isub (A/m)
Igate_ON (A/m)
Igate_OFF (A/m)
90nm
17
0.16
0.05
0.01
0.11
< 0.01
< 0.01
65nm
15
0.24
0.19
0.05
0.16
< 0.01
< 0.01
45nm
13
0.44
0.71
0.19
0.26
0.03
0.01
32nm
11
0.89
2.90
0.86
0.77
0.16
0.08
3.2 Loading Effect in Different Technology Process
Table 2 presents DC simulation results performed by considering the circuit depicted
in Fig. 3. CMOS inverters present the same sizing, that is, NMOS transistor width
equal to 1.0 μm and PMOS transistor width equal to 2.0 μm, keeping transistor length
at minimum dimension allowed at process node. This table provides the comparison
between the four different devices models, described in Table 1. The voltage at node
N and the total leakage currents in cells G0 and G1 are given. Cells G2 and G3 have
the same total leakage of cell G1.
By evaluating the data from Table 2, one is possible to conclude that the loading
effect influences the leakage analysis when the gate leakage current achieves similar
magnitude of subthreshold leakage. Different loading effect contribution in total cell
leakage is also verified, observing the reduction of total leakage in cell G0, while it
increases in cells G1, G2 and G3.
Fig. 3. Circuit for loading effect evaluation at node N
Table 2. Loading voltage at node N in circuit from Fig. 3, and the total leakage currents in cells
G0 and G1, for different processes presented in Table 1
CMOS
PROCESS
90 nm
65 nm
45 nm
32 nm
90 nm
65 nm
45 nm
32 nm
V(N) (V)
ILeak (G0) (μA)
A)
NLE *
LE **
NLE *
LE **
INPUT = ‘0’ (low logic value)
1.00
0.999
0.17
0.17
1.00
0.999
0.29
0.29
1.00
0.998
0.68
0.68
1.00
0.991
2.07
2.00
INPUT = ‘1’ (high logic value)
0.00
< 0.001
0.27
0.27
0.00
< 0.001
0.51
0.51
0.00
0.001
1.25
1.25
0.00
0.002
4.60
4.58
ILeak (G1) (μA)
A)
NLE *
LE **
0.27
0.51
1.25
4.60
0.28
0.52
1.27
4.78
0.17
0.29
0.68
2.07
0.17
0.29
0.69
2.09
* NLE = No Loading Effect ** LE = Considering Loading Effect.
3.3 Routing Resistance Influence
In Table 3, in turn, DC simulation results for circuit depicted in Fig. 4 are given. The
resistance value is equal to 2kΩ and CMOS inverters keep the same sizing from previous analysis. The voltages at node N0 and N1, in Fig. 4, area provided, as well as
the total leakage current in cells G0 and G1. The cells G2 and G3 present the same
leakage value of cell G1.
Fig. 4. Circuit for loading effect evaluation at node N0 and N1, according to the influence of
connection resistance
When compared to Table 2, it is clear the influence of routing resistance in the
leakage current through loading effect voltage shift. As mentioned before, the loading
effect increases some leakage currents and decreases other ones. However, the total
leakage in circuit cells becomes worst when routing resistance is taken into account.
The decrement of some leakage components is not as significant while the increment
in other leakages is more severe. The loading effect, when routing resistance is considered, modifies the total leakage of a logic cell up to 15%, while with no routing
resistance influence it is changed up to 4%. Fig. 5 compares the total leakage current
in cells G0 and G1 when routing resistance is considered (LE + R) in the loading
effect analysis.
The influence of routing resistance in loading effect analysis can also be observed in
Table 4. In this experiment, the resistor depicted in Fig. 4 varies from 10 Ω to 10 kΩ.
The voltage at nodes N0 and N1, as well as the total leakage current in cells G0 and G1
are obtained, while the cells G2 and G3 present the same leakage value of cell G1.
Table 3. Considering routing resistance in the loading voltage at nodes N0 and N1, and the total
leakage currents in cells G0 and G1 (as illustrated in Fig. 4), for different processes presented in
Table 1
CMOS
PROCESS
90 nm
65 nm
45 nm
32 nm
90 nm
65 nm
45 nm
32 nm
V(N0)
V(N1)
ILeak (G0)
(V)
(V)
(μA)
INPUT = ‘0’ (low logic value)
0.999
0.999
0.17
0.999
0.998
0.29
0.998
0.993
0.68
0.992
0.975
2.01
INPUT = ‘1’ (high logic value)
< 0.001
0.000
0.27
0.000
0.001
0.51
0.001
0.002
1.25
0.002
0.009
4.59
ILeak (G1)
(μA)
0.28
0.53
1.31
5.28
0.17
0.30
0.70
2.20
(a)
(b)
Fig. 5. Total leakage in cells G0 (a) and G1 (b), from circuit in Fig. 4, for different processes:
‘NLE’ – without loading effect influence; ‘LE’ – considering loading affect but no wire resistance; and ‘LE+R’ – including the routing resistance in analysis
Fig. 6 shows the total leakage current in cells G0 and G1 according the results presented used in Table 4. The graphics show more clearly the huge increment in total
leakage current due to routing resistance influence in loading effect. The voltage difference created by the resistance increases significantly the subthreshold current of
subsequent cells connected to evaluation node.
Table 4. Routing resistance influence at nodes N0 and N1, and the total leakage currents in
cells G0 and G1 (illustrated in Fig. 4) for different resistance values, considering the 32 nm
technology model
RESISTANCE
(Ω)
10
100
1000
10000
10
100
1000
10000
V(N0)
V(N1)
ILeak (G0)
(V)
(V)
(μA)
A)
INPUT = ‘0’ (low logic value)
0.991
0.991
2.00
0.991
0.990
2.01
0.992
0.983
2.01
0.993
0.927
2.02
INPUT = ‘1’ (high logic value)
0.002
0.002
4.58
0.002
0.002
4.58
0.002
0.005
4.58
0.002
0.033
4.59
ILeak (G1)
(μA)
A)
4.78
4.81
5.01
8.59
2.09
2.09
2.14
2.76
(a)
(b)
Fig. 6. Total leakage in cells G0 and G1 (see Fig. 4) for a resistance variation range from 1 Ω to
10 kΩ, in 32 nm process node, when input = ‘0’ (a) and input = ‘1’ (b)
4 Conclusions
In this paper the loading effect has been reviewed. The direct relation to gate oxide
leakage current has been reinforced, and the influence of routing wire resistance, not
mentioned in previous works reported in the literature, have been analyzed. The first
evaluation shows that the loading effect starts to modify the leakage analysis only
when the gate leakage current achieves the same magnitude of subthreshold leakage.
In the second analysis, where the influence of the routing resistance in the loading
effect is investigated, experimental results show that the loading effect modifies
the total leakage of a logic cell up to 15%, instead of 4% when routing resistance is
ignored.
References
1. Semiconductor Industry Association, International Roadmap for Semiconductor (2006),
http://public.itrs.net
2. Roy, K., et al.: Leakage Current Mechanisms and Leakage Reduction Techniques in Deepsubmicron CMOS Circuits. Proc. IEEE 91(2), 305–327 (2003)
3. Agarwal, et al.: Leakage Power Analysis and Reduction: Models, Estimation and Tools.
IEE Proceedings – Computers and Digital Techniques 152(3), 353–368 (2005)
4. Narendra, S., et al.: Full-Chip Subthreshold Leakage Power Prediction and Reduction
Techniques for Sub-0.18um CMOS. IEEE Journal of Solid-State Circuits 39(3), 501–510
(2004)
5. Cheng, Z., et al.: Estimation of Standby Leakage Power in CMOS Circuits Considering
Accurate Modeling of Transistor Stacks. In: Proc. Int. Symposium Low Power Electronics
and Design, pp. 239–244 (1998)
6. Rao, R.M., et al.: Efficient Techniques for Gate Leakage Estimation. In: Proc. Int. Symposium Low Power Electronics and Design, pp. 100–103 (2003)
7. Ono, et al.: A 100nm Node CMOS Technology for Practical SOC Application Requirement. Tech. Digest of IEDM, pp. 511–514 (2001)
8. Gusev, E., et al.: Ultrathin High-k Gate Stacks for Advanced CMOS Devices. Tech. Digest
of IEDM, pp. 451–454 (2001)
9. Butzen, P.F., et al.: Simple and Accurate Method for Fast Static Current Estimation in
CMOS Complex Gates with Interaction of Leakage Mechanisms. In: Proceedings Great
Lakes Symposium on VLSI, pp. 407–410 (2008)
10. Mukhopadhyay, S., Bhunia, S., Roy, K.: Modeling and Analysis of Loading Effect on
Leakage of Nanoscaled Bulk-CMOS Logic Circuits. IEEE Trans. on CAD of Integrated
Circuits and Systems 25(8), 1486–1495 (2006)
11. Rastogi, W., Chen, S.: On Estimating Impact of Loading Effect on Leakage Current in
Sub-65nm Scaled CMOS Circuit Based on Newton-Raphson Method. In: Proc. of Design
Automation Conf., pp. 712–715 (2007)
12. Horowitz, M.A., Ho, R., Mai, K.: The Future of Wires. Proceedings of the IEEE 89(4),
490–504 (2001)
13. Nangate FreePDK45 Generic Open Cell Library (2009),
http://www.si2.org/openeda.si2.org/projects/nangatelib
14. Zhao, W., Cao, Y.: New generation of Predictive Technology Model for sub-45nm early
design exploration. IEEE Transactions on Electron Devices 53(11), 2816–2823 (2006)