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The Metal-Oxide-Semiconductor Field-Effect-Transistor (MOSFET) (or just MOS) is widely used and presents many advantages over the bipolar transistors (BJT) in many applications.
It requires less silicon area and its fabrication process is relatively simpler. It is possible to implement most analog and digital circuits using almost exclusively MOS transistors. All these properties allow packing a large number of devices in a single integrated circuit.
Additionally, and most important, its operation requires less power, making it extremely suitable to RFID circuits.
This chapter aims to provide background on MOS transistors, from its physical operation to modeling, including RF modeling. The basic knowledge is essential to analyze and to design RFID circuits implemented using CMOS transistors. The chapter also presents noise analysis which is essential to low voltage signal, as it is the case of RFID circuits.
Fig. 1 shows the physical structure of the n-channel MOS transistor, or just nMOS transistor. The transistor is fabricated in a p-type silicon substrate. Two heavily doped n-type regions, indicated as n+, are created in the substrate and will act as the source and drain (in terms of structure, source and drain can be interchanged). A thin layer of silicon oxide (SiO2), of thickness tox(typically between 2 and 50 nm), is formed on the surface of the substrate, between the drain and the source regions. The silicon oxide is an excellent electrical isolator. Metal (or polysilicon, which is conductor) is deposited on top of the oxide layer to form the gate electrode. Metal contacts are also made in the source and drain regions, in addition to contact to the bulk, also known as the substrate or body. Therefore, the four contacts were formed: D-drain, S-source, G-gate and B-bulk.
The gate region has a length Land a width W, which are two important design parameters of the MOS transistor. Usually Lis in the range of 0.1μm to 3μm while Wis in the range of 0.2μm to 100μm.
There is also the p-channel MOS transistor, or just pMOS transistor, in which the dopings are reversed to the nMOS transistor.
2.1. Forming the channel
As can be observed from the Fig. 1, the substrate forms pnjunctions with the drain and the source. In normal operation both junctions must be kept reverse-biased, or at least out of the
forward condition all the time. Since the drain is biased at a positive voltage, it is only necessary to connect the bulk to the ground in order to keep both junctions cut off.
With no bias applied to the gate, there are two back-to-back diodes between drain and source, and consequently, there is no current. This is true since each pnjunction forms a diode. In fact, the resistance between drain and source under this circumstance is in the range of 1012Ω.
When a positive voltage is applied between gate and source - vGS, holes (which are positively charged) are repelled from the surface of the substrate. As the voltage increases, the surface becomes completely depleted of charge. The voltage at which this occurs is known as threshold voltage – Vt.
If vGSis further increased, electrons (which are negative charges) accumulate near the surface, under the gate, and an nregion is created, thus forming a channel between drain and source, as indicated in Fig. 2. The channel was formed by inverting the substrate surface from ptype to ntype. Fig. 2 also shows the depletion region that forms around the channel and the two junctions.
The symbols for the nMOS transistor are given in Fig. 3, although other symbols may be found in the literature. The symbol in Fig. 3.a corresponds to the four terminal connection, and the symbol in Fig. 3.b corresponds to the three terminal connection, where source and substrate are shorted.
2.2. Triode condition
Now, if a very small voltage vDSis applied between drain and source, as indicated in Fig. 4, there will be a current flow through the channel. The current through the channel, named drain current - iDis directly dependent on the voltage vGSand the voltage vGS. If vGSincreases, the channel becomes deeper and more current can flow. If vDSis increased, based on Ohm`s Law, there will be more current, since the channel behaves as a resistance. If follows that the transistor is operating as a linear resistance whose value is controlled by vGS. The resistance is very high for vGS≤ Vtand it decreases as vGSincreases.
This condition of operation is known as ohmic, linear or triode.
2.3. Saturation condition
As vDSincreases, the difference vDS– vDSbecomes smaller at the edge between the gate and the drain diffusion, and therefore the channel becomes shallow. Therefore, the channel assumes a tapered shape, as indicated in Fig. 5. Since the channel becomes smaller at the drain end, its resistance increases, and therefore, the transistor does not operate ideally as a linearly controlled resistor.
At the condition vDS= vGS- Vt, the channel ceases to exist at the drain side, as shown in Fig. 6. This situation is known as pinch off. At this point, further increases in vDSmoves the end of the channel further away from the drain, as presented in Fig. 7. This condition of operation is referred as saturation, therefore vDSis referred as vDSSAT= vGS- Vt.
Once the transistor enters the saturation region of operation, the drain current iDbecomes independent of the vDS.
Fig. 8 summarizes the conditions of operation of an nMOS transistor. Close to vDS= 0, current iDis directly proportional to vDS,with slope proportional to vGS- Vt. As vDSapproaches vDS= vGS- Vt, the curve of bends because the channel resistance increases. After the vDS= vGS- Vt, the current becomes independent of vDS.
2.4. Deriving the iD- vDSrelationship
Consider the biasing depicted in Fig. 9. Since the channel potential varies from zero at the source to vDSat the drain, the local voltage difference between gate and the channel varies from vGSto vGS– vDS. Therefore, the channel density, or charge per unit length, is given as:
where v(x)is the potential at xand Coxis the capacitance, per unity area, formed by the gate and the channel.
Since, by definition, current is proportional to charge times velocity, and considering the current is the same along the channel, then:
The minus signal is due to the negative charge of electrons. The velocity of carriers at low fields is the product of mobility (μ) and the electric field (E). Noting that and representing the electrons mobility by μn, then expression (2) can be rewritten as:
Now integrating along the channel, one obtains:
Thus, the expression for the drain current in the triode region is:
The value of the current for the saturation operation can be obtained by replacing vDS= vGS- Vtinto expression (5), as:
As described earlier, the current does not depend on vDS. It can be observed from expressions (5) and (6) that the current is proportional to the ratio, which is know as the aspect ratio. The designer can alter the aspect ratio to obtain the desired i-vcharacteristic.
Observe that expression (6) was obtained using the value of L, as given in Fig. 9. Nevertheless, when the transistor is saturated, the channel becomes shorter, as shown in Fig. 7. A reduction in the length of the channel, known as channel length modulation, means a variation in the resistance, and therefore a variation in the current iD.
Expression (6) can be modified in order to include the variation in the channel length, represented as L-ΔL, as:
which can be approximated to:
Since ΔL/Lis proportional to vDS(the larger vDSthe larger will be ΔL), then:
where λis the parameter of proportionality.
The effect of channel length modulation can be seen in the iD- vDScharacteristic of a MOS transistor shown in Fig. 10. The dependence of vDSon iDin the saturation region can be seen is represent by in expression (9) and can be observed in Fig. 10.
An extrapolation of iD- vDSintercepts the vDSaxis at vDS= − VA, known as Early voltage. For a given process, VAis proportional to L, selected by the designer. Typically, VAis in the range of 5 V/μm to 50 V/μm.
2.5. Output resistance
Fig. 10 and expression (9) show that an increase in vDScauses an increase in iD, meaning a resistive behavior. The value of the resistance is given as:
which can be simplified to:
Therefore, a MOS transistor in the saturation region is not totally independent of vDSand presents an output impedance given by (11)
Considering the transistor operating in the triode region, as given by expression (5), if the value of vDSis sufficiently small, can be neglected, and therefore:
This relationship represents the behavior of the MOS transistor as a linear resistance whose value is controlled by vGS, as given by:
The large signal behavior of a MOS transistor in the saturation region is given by expression (6). Nevertheless, for a given biasing, the designer may be interested in the small signal behavior of the transistor. For a given small variation in the vGS, around the biasing, there will be a variation in the iDcurrent, given by the transconductance, as:
which results in:
Observe the transconductance depends on the ratio W/Land on the value of vGS, and they can be controlled by the designer. By using expression (6), then expression can be written as:
In this case, the transconductance depends on the ratio W/Land the iDcurrent. That expression can be written also as:
It clearly does not depend on ratio W/Lbut it depends on both vGSand iD.
2.7. Body effect
In many circuits, the substrate and the source are not at the same potential, as it is possible to stack transistors. In that case, the substrate it is at lower potential than the source, and therefore the source-substrate junction becomes reversed biased. This reverse biasing widens the depletion layer, which in turn reduces the channel depth.
The effect of the bulk-source voltage VSBcan be easily represented by a change in the threshold voltage - Vt, as given by:
where Vt0is the threshold voltage for VSB= 0, is a physical parameter (usually = 0.6V) and γis a fabrication-process parameter given by:
where qis the electron charge (1.6 x 1019C), NAis the doping concentration of the substrate and εsis the permissivity of silicon (1.17ε0= 1.17 x 8.854 x 10-14= 1.04 x 10-12F/cm).
Any signal between substrate and source promotes a drain current component. The substrate acts as a second gate, and in turn will present a corresponding trasnconductance, named body transconductance, given as:
From expressions (6), (17) and (18), then it is possible to state that:
where is given by:
And it is in the range of 0.1to 0.
2.8. Small signal model
Considering the output impedance, the transconductance and the body effect, the small signal model of a nMOS transistor is given by Fig. 11, known as hybrid-π model.
If the source and the substrate are at the same potential, then the model can be simplified, as the term gmbvbsgoes to zero. The simplified hybrid-π model is shown in Fig. 12.
In a pMOS transistor, a pchannel is formed on an nsubstrate. Therefore, its operation is virtually the same as the nMOS transistor, except that all voltages and currents are opposite as in the nMOS transistor. Fig. 13 shows the symbols for the nMOS transistor, although other symbols may be found in the literature. The symbol in Fig. 13.a corresponds to the four terminal connection, and the symbol in Fig. 13.b corresponds to the three terminal connection, where source and substrate are shorted.
Unfortunately, the structure and the operation of a MOS transistor present parasitic capacitances that limit its frequency of operation. The parasitic capacitances may result from the capacitor formed between the gate and the channel, between gate and source/drain, and between drain/source and substrate.
3.1. Gate capacitances
The gate, the dielectric and the channel form a capacitor. When the transistor is working in the triode region with a small voltage vDS, the channel will be of uniform depth, as shown in Fig. 4. Therefore, the gate-channel capacitance can be considered equally divided between the source and the drain, and their values are:
When the transistor is working in the saturation region, the channel presents a tapered shape and it is pinched off at the drain end, as presented in Fig. 7. It can be seen that the gate to channel capacitance is almost entirely modeled at the source, since the drain does not present a channel. It can be shown that the capacitances are:
If the transistor is cut off, there is no capacitance between gate and channel, since there is no channel for cut off. The entire capacitance is then between the gate and the substrate, therefore:
As can be observed from Fig. 1, the gate extends over the drain and the source areas. Therefore, there is an overlapping capacitance between the gate and the drain/source. Denoting the overlapping length by Lov, then the overlap capacitance can be seen to be:
For modern processes, Lovis usually in the range of 5% to 10% of L.
3.2. Junction capacitances
As shown by Fig. 2 there are two reversed biased junctions formed between the substrate and source/drain. Each junction consists of two semiconductors (drain/source and the substrate) and the depletion layer, thus forming a capacitor. The source-substrate capacitance can be found to be:
where V0is the junction built-in voltage (0.6 V to 0.8 V), VSBis the magnitude of the reversed bias voltage and Csbois the capacitance at zero reverse bias voltage.
By the same way, the drain-substrate capacitance is given by:
3.3. The high frequency model
The small signal model of the MOS transistor given in Fig. 11 can be update to include the gate and the junction capacitances, as presented in Fig. 14. Although this model represents the transistor for high frequencies, it is very complex for manual analysis.
If the source and the substrate are shorted, the model can be greatly simplified, as shown in Fig. 15.
An important Fig. of merit for the MOS transistor is the unit gain frequency that is defined as the frequency in which the short circuit current gain becomes unit. This definition is based in the common source configuration, as shown in Fig. 16.
The current Ioin the short circuit is given by:
The approximation is due to the fact that Cgdis very small and can be neglected. Also, from the circuit, Vgscan be expressed as:
Since the magnitude of should be 1, as per definition, and considering physical frequencies (s=jω), then:
Therefore, the unit gain frequency is:
As can be observed, the unit gain frequency is directly proportional to gmand inversely proportional to the internal capacitances. Therefore, in terms of frequency response the transistor should have large gmand small capacitances.
The two most important types of noise in MOS devices are the 1/fnoise and the thermal noise.
4.1. Thermal noise
The main source of thermal noise in a MOS transistor is due to the resistive channel in the active region, and has a value of:
where kis the Boltzmann’s constant (about 1.38 x 10-23J/K), Tis the absolute temperature in kelvins and γis a constant that is approximately 2/3for long channel transistors and increase to the range 1-2for short channel devices.
The other source of thermal noise is the gate. Fluctuation in the channel potential couples capacitively into the gate terminal, which in turn translates into a noise gate current. Noise gate current can also be produced by the resistive material of the gate. This total noise gate can be ignored at low frequencies but becomes significant at high frequencies as it is the case of RF circuits. It has been shown the gate noise may be expressed as:
where δis approximately 4/3for long channel transistors and increase to the range 2-4for short channel devices, and ggis given by:
Mostly of the time, instead of using a current source at the gate, it is more convenient to consider an equivalent voltage source. The equivalent voltage source of expressions (31) and(32) is given by:
where rgis given by:
The 1/fnoise, also known as flicker noise or pink noise, arises mainly due to the surface imperfections that can trap and release charges. Since MOS devices are naturally surface devices, they produce much more 1/fthan bipolar devices (which are bulk devices). This noise is also generated by defects and impurities that randomly trap and release charges. The trapping times are statistically distributed in such a way that lead to a 1/fnoise spectrum.
The 1/fnoise can be modeled by a voltage source in series with the gate, of value:
For pMOS devices, βis typically about 10-28C2/m2, but it can be up to 50 times larger for nMOS devices.
As can be observed from expression (53), the 1/fnoise is smaller for larger devices. This occurs because the large capacitance smoothes the fluctuation in the channel charge. Therefore, in order to achieve good 1/fperformance, larger devices should be used.
The 1/fcan also be modeled as a current source at the drain whose value is:
where Ais the area of the gate.
4.3. Noise model
The noise model of an nMOS transistor is presented in Fig. 17, where the transistor is considered noiseless. The decision of placing the noise sources as a voltage source at the gate, or as a current source at the drain is just a matter of convenience according to the circuit under analysis. As an example, the values of Fig. 17 could be:
The proper understanding of physical operation to modeling of CMOS transistors is essential to the analysis and design of RFID circuits. Among its advantages, the CMOS transistors demands lower power consumption than other transistors.
Noise analysis of CMOS transistors is also fundamental to analysis and design of any circuit, including RFID.
1.AllenP. E.HolbergD. R.2002
2.JohnsD. A.MartinK.1997Analog Integrated Circuit Design, John Wiley & Sons,0-47114-448-7
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Tales Pimenta, Robson Moreno and Leonardo Zoccal
Submitted: November 9th, 2010Reviewed: March 8th, 2011Published: July 20th, 2011