Effect of temperature dependence on performance of Digital CMO S circuit technologies Shruti Kalra (Member IEEE) Department ofElectronics and Communication Jaypee Institute of Information Technology A-IO, Sector-62 Noida
[email protected]
Abstract- Aggressive technology scaling and an increasing demand of high performance VLSI circuits has resulted in higher current densities and increased power dissipation. A significant fraction of this power is converted to heat and an exponential rise in heat density is experienced. As a consequence, temperature measurement and control are critical tasks in many applications. Temperature variations often alter threshold voltage, carrier mobility and saturation velocity of MOSFET and thereby altering the performance of the CMOS circuits. This paper identifies the device parameters that characterize the variation of MOSFET current due to temperature fluctuations on 180nm CMOS technology. Further, the effect of temperature variation on performance of CMOS digital circuits and optimization of device parameters for temperature variation insensitive performance of the circuit is also presented.
Figure I shows the simulated transconductance characteristics of n-channel MOSFET, at the temperatures of 25 and 125 degrees, simulated on HSPICE version A-200S . 03 in I SOnm CMOS technology. It can be seen that the characteristics have a common intercept point known as zero-temperature coefficient (ZTC) point [6] . If transistor is biased to this point by a current source, then the gate-source voltage will not depend on temperature. It occurs when the transistor has mutual compensation of mobility and threshold voltage temperature effects.
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Keywords- Zero temperature coefficient point (ZTC ) , crossover point, threshold voltage, optimal supply voltage.
I.
INTRODUCTION
The increase in circuit density and clock speed has produced an increase in power consumption that has brought thermal issues in the limelight of VLSI design. Eenergy and thermal management
Gate to Sourc. Vol·ge Vgs M
Figure 1 Drain current vs gate to Source Voltage of n-channel MOSFET with L=O.18u and W=5u
for the CMOS devices are becoming progressively more important due to the demand for the energy savings. It is Section IT identifies the various temperature dependent important to note that the energy and thermal management parameters of MOSFET. Section TIT details the effect of have to be considered differently due to their governing change in temperature on performance of digital CMOS physics [ I ] . System level energy and thermal management circuits. Section IV concludes the entire paper. together with high performance cooling technology play a crucial role to control the system level temperature profile to IT. TEMPERATURE DEPENDENT PARAMETERS OF MOSFET govern the equipment design. Submicron scale device level A. Mobility energy and thermal management, on the other hand, determine two important features in operating devices: the heat Phonon, Surface and coulomb are the three major scattering dissipation and the intensity of the local hotspot (device-level mechanisms that govern the characteristics of carrier mobility temperature rise due to the self-heating.) The intensity is in the inversion layer of MOSFET with phonon scattering mainly governed by the heat generation and by the local heat being the dominant at higher temperature. To describe the conduction [ I ] . It gives additional temperature rise of the effect of mobility on temperature, a second order polynomial devices that cannot be controlled by the system level energy is used with Ua,Ub,Uc being linearly dependant on temperature [2] [3 ] . and thermal management. Temperature fluctuations often alter system speed, power, and T . V , + 2Vt (T) 2 . Ub (T) U (T) reliability by altering the threshold voltage and mobility in 1 + gS effT + ( c · Vbseff ) lletl T)= uo To ax each device. The resulting changes in current can lead to self V st + 2Vt(T) -1 heating and increased leakage current which in turn has a + Ua (T) . g effT (I) detrimental effect on performance and reliability of the system. ax Detailed analysis of dynamic and gate leakage and its temperature effects thereof is out of the scope of this paper. Here,
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length is increased, the zero temperature coefficient point voltage decreases.
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The values of Uo , Ua, Ua\ , Ub, Ub I , Uc , Uc \ , Ute can be extracted from measured I-V data. T is the device temperature in Kelvin, and Tnorm is the temperature at which the parameters such as Ua, Ub, Uc are extracted. Figure 2 plots the effect of change in electron mobility as the function of electric field .. It can be seen from the plot as the temperature is increased, the mobility decreases.
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Figure 3 Threshold Voltage Vs Temperature plot of n-channel MOSFET with L=O.18u and W=5u
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Figure 4 ZTC point Voltage Vs Channel Length variation of n-channel MOSFET with L=O.18u and W=5u
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Figure 2 Electron Mobility Vs Electric field plot of n-channel MOSFET with L=O.18u and w=5u
B. Threshold Voltage
C. Saturation Velocity Saturation Velocity V sat is the weak function of temperature. BSIM3 v3 uses following temperature model for temperature dependence of saturation velocity[2] [3 ] :
Threshold Voltage is another important parameter that increases as temperature decreases due to the shift in Fermi level and bandgap energy. For long channel devices, threshold voltage depends linearly on temperature. BSIM3v3 uses following temperature model[2] [3 ] : nmos: pmos :
[
l
KTI T Vt(T)=Vt(To)+ KTI + --L + vbseff KT2 [To - I 1 Lef!
[
l
KTI T Vt(T)=Vt(To)- KTI + --L + Vbseff KT2 [To - I 1 Lef!
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(2) (3)
Where Vt (T0) is the threshold voltage at room temperature. The parameters KT 1 , KTIL and KT2 are extracted from experiments. KnJL is the minor term introduced to improve the fitting accuracy further. Figure 3 shows the plot of variation of threshold voltage with respect to temperature for n-channel MOSFET with I=O . 1 8u and w=5u. It can be seen from the plot that the threshold voltage decreases almost linearly with increase in temperature. As per equation (2) and (3), threshold voltage of MOSFET also depends on channel length, varying the channel length shifts the ZTC point of the MOSFET. Figure 4 shows the plot of variation of ZTC point voltage with respect to change in channel length. It can be seen from the plot that as the channel
(4 )
Where AT is the parameter extracted from data.
D. Parasitic Drain/Source Resistance As the supply voltage reduces and MOSFET current becomes larger, drain/source series resistance becomes one of the most important parameter to describe the I-V characteristics accurately. The component of RIs includes contact resistance, drain and source diffusion sheet resistance and the spreading resistance at the edge of the inversion layer due to current crowding. Rds increases almost linearly with increasing temperature. The effect of temperature on Rds is expressed as[2] [3 ] :
Rds(T) {Rdsw (T) [ 1 + Prwg Vgsteff + Prw b (.) 0s - Vbs )0;:)]} [( 1 06Weff tT" =
(5)
-
and
(6)
Where RIsw(Tnonn) is the resistance per unit width, P,wgV gsteff is the dependence of gate bias on resistance Prw b (.J0s - Vbs - )0;:)
393
is the term that describes the effect of body bias on resistance. Wr is the fitting parameter to improve the accuracy.
P rt
[
T __ - 1 Tnorm
resistance.
]
describes
the temperature
dependence
of
consider the equation (7) and (8) for propagation delays derived using curr ent-voltage relationships originally developed for long channel transistors. In general, the saturation current of NMOS transistor is described as [4] [5] : 4.S · 1 0'
Ill. EFFECT OF TEMPERATURE DEPENDENCE ON CMOS CIRCUIT PERFORMANCE
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The high-to-low and low-to-high propagation time for CMOS INVERTER gate can be expressed as[4] [5] :
(7)
(8)
where
are the transconductance parameters for NMOS and PMOS respectively and CL is the effective load capacitance of the CMOS inverter circuit. The propagation delay of the NOT gate is therefore defined as: tplh Tp = -'--
tphl -+--'-
2
(9)
Equation (7), (8) and (9) contains the temperature dependent MOSFET parameters threshold voltage Vt and mobility 11. As temperature increases, both mobility and the threshold voltage will decrease. Tn the case of supply voltage Vdd much larger than threshold voltage VI . the thermal effect on the propagation delay will be dominated by the mobility [7] [8] . Ring oscillator provides an efficient and highly accurate temperature measurement by exhibiting a linear dependence of oscillation frequency on junction temperature. As mentioned above, the delay of any CMOS circuit depends on the temperature and hence it is expected that the delay of a ring oscillator and hence its frequency will change as we vary the temperature. Therefore, at any specific temperature, the oscillator will exhibit a fixed frequency of oscillation [9] . Figure 5 shows the plot of variation of frequency with the supply voltage Vdd of 5 1 stage CMOS inverter based Ring Oscillator with Ln=Lp=O. 1 8u, Wn=5u, Wp= l 1 .2u on 1 80nm technology node at two different temperatures of 25 and 125 degrees . The plot shows that as the temperature is increased, the frequency decreases. A very important point to be noted here is that there is a supply voltage Vdd at which the frequency of the ring oscillator becomes independent of temperature. This point is known as crossover point. Before this crossover point, the frequency exhibits reverse temperature dependence on supply voltage i.e. the as the temperature is increased, frequency increases. Tn order to analytically derive the supply voltage on which the delay of the inverter becomes independent of temperature,
t.•
Figure 5 Frequency Vs Supply Voltage Vdd plot of 51 stage Ring Oscillator Is a t = K Wn
( Vgs - Vt )
2
(10)
where K is the function of carrier saturation velocity, the channel length and the degree of velocity saturation in the channel. Assuming the discharge current of NMOS transistor varying Vout from Vdd to VSO% is approximated by the saturation current (first order approximation), high-to-Iow propagation delay can be estimated by average current method as: (1 1 ) Vdd tphl ""
Cload VS O O/O Is a t
Cload
( 2)
(1 2 )
Let K I be the technology dependent parameter defined as: (13)
and the dependence of mobility on temperature is defined as [5] : (14)
Let the mobility constant KJi is defined as: ( 1 5)
The threshold voltage dependence on temperature IS gIven as[5] : (1 6)
Putting equation ( 1 4) and ( 1 6) in ( 1 2), the expression of high to low propagation delay becomes:
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(1 7) •
Further, for simplification, let
(1 8 )
Therefore, equation ( 1 7) becomes
•
(19)
•
Differentiating equation ( 1 9) with respect to temperature and putting d tphl dT
--
at T
=
To
=
0
gIves (20)
•
Equation (20) represents the optimal supply voltage Vdd applied in order to get delay of the inverter independent of change in temperature. According to equation (2) and (3), the threshold voltage also varies with the change in channel length. Figure 6 shows the plot of variation of the crossover voltage of frequency at different temperatures with respect to the change in channel length. It can be seen the crossover point voltages decreases as the channel length is increased.
•
REFERENCES [I]
[2] � i Uti i
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!
UI!I
[3] [4]
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. 1 0'"
-+---;-----C'�---}-->'
[5]
Figure 6 Crossover point Voltage Vs Channel length plot of 51 stage Ring Oscillator
[6]
TV. CONCLUSION
[7]
The variation of propagation delay with respect to temperature has been investigated in this paper. MOSFET device parameters that cause variation in drain current are also identified. Following points are concluded: • As the temperature is increased, the drain current of n-channel MOSFET decreases at a fixed gate to source bias applied. There is a zero temperature coefficient point where the drain current becomes independent of gate to source voltage. Before the ZTC point, the drain current exhibits opposite
behaviour i.e. it increases as the temperature is increased at a fixed gate to source bias applied. As the length of the channel is increased, the value of the ZTC point voltage decreases i.e. the value of the gate to source voltage for which the drain current becomes independent of temperature decreases as the length of the channel is increased. The mobility of the electrons and the threshold voltage of n-channel MOSFET decrease as the temperature increases. The frequency of the CMOS digital circuit decreases as the temperature is increased at a fixed supply voltage Vdd . There is a crossover point where the frequency becomes independent of temperature i.e. there is a supply voltage at which the frequency of the circuit or the speed becomes temperature independent. Before the crossover point, the frequency exhibits opposite behaviour I.e. it increases as the temperature is increased. The optimum value of the supply voltage at which the frequency becomes independent of temperature or the crossover point can be found analytically using equation (20). As the length of the channel is increased, the value of the crossover point voltage decreases i.e. the value of the supply voltage Vdd for which the frequency becomes independent of temperature decreases as the length of the channel is increased.
[8] [9]
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[ 1 0]
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