Subthreshold MOSFET Transistor Amplifier Operation Sherif M. Sharroush1, Yasser S. Abdalla2, Ahmed A. Dessouki3, and El-Sayed A. El-Badawy4 1 2
Dept of Elect Eng, Fac. of Eng., Port Said, Suez Canal Univ., Egypt. EM:
[email protected]
Dept of Electricity, Fac. of Industrial Edu., Suez, Suez Canal Univ., Egypt. EM:
[email protected] 3
Dept of Elect Eng, Fac. of Eng., Port Said, Suez Canal Univ., Egypt. EM:
[email protected]
4
Alex Higher Inst. Of Eng. and Tech & Fac. of Eng., Alex. Univ., Alexandria, Egypt. EM:
[email protected]
Abstract— Due to their ultra low-power consumption and the high demand of portable applications, subthreshold MOSFET transistor operation (where the power-supply voltage is lower than the threshold voltage, VDDVth).
Key Words: MOSFET transistor, ultra low power, subthreshold region, amplifier. I. INTRODUCTION In recent years, the demand for the battery-operated portable applications such as notebook and laptop computers, personal digital assistants, cellular phones, and other portable communication devices has been increased. So, the need increases also to reduce the power consumption. There are several methods to reduce the power consumption such as constant voltage scaling [1, 2], constant electric-field scaling [3], switching activity reduction [4, 5], architectural techniques such as pipelining and parallelism [6], and computer-aided design (CAD) issues of device sizing, interconnect [7, 8], and logic optimization [9, 10]. However, there are some applications such as portable computing gadgets, medical electronic equipments, and hand watches where ultra low-power consumption with low or medium frequencies (tens or hundreds of megahertz) is the primary requirement. As a solution to this problem, energy recovery or quasi-adiabatic techniques [6] can be used. However, this involves the use of high-quality inductors which is difficult to integrate [11]. So, in these applications, the use of the MOSFET transistor in the subthreshold region, where the power-supply voltage, VDD is lower than the threshold voltage, Vth, seems to be suitable as it reduces the power consumption considerably. The subthreshold leakage current of the MOSFET transistor in this case will be used as the operating current to perform the computations in logic circuits. However, the use of the MOSFET transistor in the subthreshold region to perform high-speed operations
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is not possible since the operating current in the subthreshold region is much lower than that in the triode or saturation regions, thus requiring longer intervals of time to charge or discharge the parasitic capacitances and thus performing the computations in digital circuits. We will, throughout this paper, refer to the MOSFET transistor operating in the subthreshold region (with VDDVth) as the superthreshold transistor. Thus, the two transistors can be made in the same fabrication process and with the same dimensions, but the two terms subthreshold and superthreshold simply refer to their regions of operation. As another benefit of operating the MOSFET transistor in the subthreshold region, the transistor input capacitance in the subthreshold region is much less than that in the superthreshold region [12]. On the other hand, the input capacitance in the superthreshold operation is dominated by the gate-oxide capacitance. Due to the smaller input capacitance and the lower-supply voltage in the subthreshold region, the power consumption will be much less than that in the superthreshold region. The subthreshold region operation was investigated and utilized especially in digital-circuit applications. The interested reader can refer to [12-15] for these applications. Impact of Scaling on the Subthreshold Operation There is no doubt that the MOSFET transistor dimensions are scaled down in order to squeeze more devices in the same area, thus performing more functions at the same time interval and increasing the speed. At earlier versions of the CMOS technologies, the power-supply voltage is maintained constant at 5 V [3], thus causing the electric field to increase and decreasing the reliability of the devices due to the increased probability of breakdown. So, the need arises to reduce the power-supply voltage, VDD in order to increase the device's reliability. Also, due to the increasing demand for the portable devices which are power-sensitive, VDD scales down in order to decrease the dynamic power consumption. This scaling scenario, where the power supply and the dimensions are scaled down with the same ratio, is known as the constant electric-field scaling.
However, scaling down VDD causes the device's speed to decrease [16]. To solve the problem of performance degradation, the threshold voltage must be reduced also to maintain the performance at an acceptable level. The price paid, however, is the increased subthreshold leakage current [17] and the associated increase in static power consumption. So, Vth decreases at a rate that is slower than that of VDD reduction. As a result, the VDD/Vth ratio decreases with CMOS technology scaling [16]. This illustrates the fact that Vth occupies a larger ratio of the VDD space as the CMOS technology scales down, thus further encouraging the operation of the MOSFET transistor in the subthreshold region. This can be illustrated with the aid of Fig. 1 which illustrates the ratio of Vth relative to VDD for the 0.35 and 0.13 μm CMOS technologies. For the first one, Vth is approximately one fifth VDD while for the second one, Vth is one third VDD. So, it can be concluded from Fig. 1 that the subthreshold region (shown shaded) has a greater relative extension in the space extending from 0 V to VDD as the technology scales.
In this Section, we will discuss the physical operation of the MOSFET transistor in the subthreshold region. Specifically, the ideal current-voltage relationship employed in simple design predicts zero current when the gate-to-source voltage, VGS is less than or equal to the threshold voltage. However, ID is not practically zero when VGS d Vth . Fig. 2 shows a comparison between the ideal characteristics and the experimental results. The drain current, in this region, is known as the subthreshold current.
Fig. 2 Comparison of the ideal and experimental plots of
Fig. 1 The ratio of the threshold voltage, Vth to VDD for the 0.35 μm (on the left) and for the 0.13 μm (on the right) CMOS technologies.
We will, in this paper, investigate the utilization of the subthreshold transistor as an amplifier. As with any other semiconductor device, the physical operation is first studied, thus disclosing the physical reason behind the current flow in this device along with the charge carriers' movement. Second, the current-voltage relationship will be derived and the various regions of operation of the device will be studied along with the applications of this device in these regions. Finally, the small-signal analysis of the device will be studied and the ac small-signal equivalent circuit of this device will be developed. The preceding philosophy will be adopted in this paper with the subthreshold transistor. The remainder of this paper is organized as follows. Section II gives an explanation of the physical operation of the MOSFET transistor in the subthreshold region along with the statement of the current-voltage relationship in this region. Section III describes the small-signal analysis and the linear application concept of the subthreshold transistor along with the development of the ac small-signal equivalent circuit of the subthreshold transistor. Section IV discusses the utilization of the subthreshold transistor as an amplifier in a common-source configuration with a diodeconnected subthreshold transistor as a load. The quantitative analysis will be merged with Sections III and IV. Section V concludes the paper. Finally, Section VI presents two points for future work concerning the subthreshold transistor. II.
PHYSICAL OPERATION OF THE SUBTHRESHOLD TRANSISTOR
ID
versus VGS.
Fig. 3 shows the energy-band diagram of a MOS structure with a p-type substrate biased so that Is 2I fp . At the same time, the Fermi level is closer to the conduction band than to the valence band at the surface, so the semiconductor surface develops the characteristics of a lightly doped n-type material. We would expect, then, to observe some conduction between the n+ source and drain contacts through this weakly inverted channel. This conduction is due to the diffusion of minority carriers in the channel. The condition of I fp I s 2I fp is known as weak inversion. A detailed study of the conduction in this region reveals that the drain current depends exponentially on VGS.
Fig. 3 Energy-band diagram when I I 2I for the case of weak fp s fp inversion.
The following Equation is the current-voltage relationship for the subthreshold transistor [17] vGS Vth0 JvSB KvDS v DS nVT VT sub 0 (1)
i
with
Ie
§ ¨1 e ¨ ©
· ¸ ¸ ¹
I0
§ W · 2 1.8 ¸VT e ©L¹
P 0 C ox ¨
(2)
where W and L are the transistor channel width and length, respectively, μ0 is the electron mobility at low electric fields, Cox is the gate-oxide capacitance per unit area, VT is the thermal voltage and is given by kT (3) VT q where k is Boltzmann's constant, T is the environmental temperature, and q is the electronic charge, n is the subthreshold swing factor, J is the linearized body-effect coefficient, K is the drain-induced barrier lowering (DIBL) coefficient, and Vth0 is the threshold voltage at zero source-tosubstrate voltage. If the body-effect coefficient and the drain-induced barrier lowering (DIBL) coefficient are neglected, then Eq. 1 can be written simply as
isub
I 0e
vGS Vth nVT
v DS § ¨1 e VT ¨ ©
· ¸ ¸ ¹
isub
§W P 0Cox ¨ ©L
· 2 1. 8 ¸VT e e ¹
v DS VT
vGS Vth nVT
to be much less than
.
(5)
III.
SMALL-SIGNAL ANALYSIS OF THE SUBTHRESHOLD TRANSISTOR In this Section, we will develop the ac small-signal equivalent circuit of the subthreshold transistor. Toward that end, assume that the applied gate-to-source voltage is vGS VGS v gs (6) where we have adopted the convention that the voltages or currents with small symbols and large subscripts refer to total voltages or currents and those with capital symbols and subscripts refer to pure dc values and those with small symbols and subscripts refer to pure ac values [18]. In this case, the total value of the subthreshold leakage current will be equal to i subt
§W © L
P 0 C ox ¨
· 2 1 .8 ¸V T e e ¹
§ W · 2 1 .8 ¸V T e e © L ¹
V GS v gs V th
V GS V th
P 0 C ox ¨
nV T
nV T
.
(7)
v gs
e nV T
where isubt is the total (dc+ac) subthreshold current. Expressing the exponential term evgs in a Taylor-series expansion, we obtain i subt
§ W · 2 1 .8 ¸V T e e © L ¹
P 0 C ox ¨
§ ¨ 1 v gs §¨ v gs ¨ nV ¨ nV T T © ©
· ¸¸ ¹
2
V GS V th nV T
§ v gs ¨¨ © nV T
P 0C I sub
? isubt
· ¸¸ ¹
3
. · ...... ¸ ¸ ¹
(8)
§W ¨ © L I sub nV T ox
· 2 1 .8 ¸V T e e ¹
V GS V th nV T
v gs § ¨¨ 1 nV T ©
· ¸¸ ¹
v gs
I sub g m vgs
(9)
where gm represents the transconductance of the subthreshold transistor and is given by
I sub . nVT
gm
(4)
If the drain-to-source voltage, vDS is larger than 3VT, then we can consider the factor e 1, and thus Eq. 4 can be written as
For small ac values of the gate-to-source voltage; that is when vgs
