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CMOS Analog Integrated Circuits Part 1. Basic Analog Models for CMOS Technology Emil D. Manolov Advanced level study programme in Electronics Design and Integration Technologies 28213-IC-1-2005-1-BE-ERASMUS-PROGUC-3 2006-2322 / 001-001 SO2 Technical University of Sofia Faculty of Electronics ECAD Laboratory 2008 1. Basic Analog Models for CMOS Technology CMOS Analog Integrated Circuits (introductory course) Emil D. Manolov, [email protected] Department of Electronics, Technical University – Sofia Integrated circuits design flow The design of an analog integrated circuit is very complicated interactive procedure. The first step is the initial (first-cut) design. It includes analysis, proposing of an appropriate circuit topology and hand-calculation the values of the currents and the sizes of the transistors by using simple expressions. This is very responsible task because it puts the fundament of the seeking solution. The next step is an extensive simulation of the circuit in order to optimize the parameters. This design stage aims to take in considerations the second-order effects and to examine the influence of the process variations on the performance. It gives to designer precise information about the circuit operation and allows in interactive way to achieve the final specification. Briefly, the fist stage is devoted to design and hand-calculation and the second – to efficiently and accurately simulation of the developed circuits. The different goals, which are seeking at the different design stages, determine the need from different type models of the used transistors. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 3 Hand-calculation and simulation models In practice, there are two types of transistor models, which are used in the design process. The first type are the hand-calculation models allowing to predict the performance of the circuit through simple expressions. These models present the operation of each transistor by means of as few equations as possible. They must include only the most fundamental parameters of the transistors. Employing the simple hand-calculation models, the designer describes the performance of the circuit only in an approximate way, but in the initial stage of the design, the clear understanding of the basic relations and the tradeoffs in the circuits is more important then the accuracy of the calculations. The second type are the transistor models, which are used to simulate the circuits. They are very sophisticated models, with large number of parameters included in exclusively complex relation. These models allow effectively and accurately circuit simulation, but are not appropriate for the first step initial hand-calculations. In this module we will discuss the most popular hand-calculation models for MOST and BJT. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 4 MOS transistor structure The figure reminds the typical Nchannel and P-channel MOSFET structures. They have four terminals: gate - G, drain - D, source - S and body (back gate, bulk) - B. The body B, is biased so that negligible current flows through it. The basic operating principle is that a voltage is applied between the gate and the source in order to control the conducting channel between the source and drain regions. If the device is fabricated so that there is no channel in the absence of a gate-to-source bias, this device is called normally off or enhancement mode MOST. In order to turn an enhancement mode MOST “on”, a channel must be created by applying bias to the gate. It is also possible to fabricate devices in which a channel exists even in the absence of any bias on the gate. Such a device is called a normally on or depletion mode MOST. To turn a depletion mode MOST “off,” a bias must be applied that cause the channel to disappear. The contemporary analog integrated circuits uses as a rule enhancement mode MOST. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 5 Symbols for MOSFET The picture shows the symbols used for n-channel and p-channel enhancement mode MOSTs. The MOST are four-terminal devices, but in some cases, when the bulk B of nMOST is connected to the minimum power supply voltage VSS or the bulk of p-MOST – to the maximum power supply VDD, it is possible to use the simplified symbols without the pin B. Important! We must remember that the source and the drain of the integrated MOST are interchangeable. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 6 Regions of operation The figure presents the square root of the drain current plotted as a function of the gatesource voltage for n-MOST. The left region, below the VTN0+∆, is characterized with an exponential-law behavior. It is called weak inversion or subthreshold region. The right region, above the VTN0+∆, is characterized with an square-law behavior. It is called strong inversion region. VTN0 is known as threshold voltage of the transistor. The quantity Δ=njT, where jT is the thermal voltage (about 25.8mV at 300K) and n is a constant. For practical estimations the value of the is about 100mV. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 7 Threshold voltage Figure shows the transconductance characteristics of n-MOS and p-MOS transistors. With VTN0 and VTP0 are denoted the threshold voltages of n-MOST and p-MOST, when theirs body B and source S are short connected. If between these two terminals some voltage is applied, the threshold voltage change its value and is denoted as VTN (or VTP). The values of VTN0 and VTP0 depends on the technology. The typical values for VTN0 are between 0.3V and 0.8V and between -0.4V and -1V for VTP0. The threshold voltages depend also on the temperature and on the transistor dimensions. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 8 Body effect Figure shows the linearization of transconductance characteristic of n-MOS transistor. The threshold voltage increases as the body potential becomes more negative. The phenomena is known as the body effect. The value of threshold voltage for n-MOST can be hand-calculated by using the following formula VTN VTN 0 n V SB 2 F 2 F where VTN0 denotes the threshold voltage when VSB=0, n is process dependent, often called the body effect constant, |2ϕF| is the strong inversion surface potential. Usually n ≈0.5…0.8 V1/2 and |2ϕF|≈0.6 V. The corresponding equation for p-MOST is similar VTP VTP 0 p CMOS Analog IC Emil D. Manolov, TU-Sofia V BS 2F 2F Basic analog models for CMOS Technology 9 About equations for p-MOS transistors In this module we will present and discuss the basic DC relations and formulas mainly on the base of n-MOS transistors. To obtain the corresponding equations for p-MOS transistors it is necessary to put negative signs in front of all voltages in DC relations for n-MOST. Example From previous slide the equation for the threshold voltage of the n-MOST is VTN VTN 0 n V 2 F SB 2 F To obtain the equation for p-MOST we put negative signs in front of all voltages VTP VTP 0 p After simple transformations we obtain VTP VTP 0 p V SB V BS 2 F 2F 2 F 2F which coincides with presented in previous slide formula. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 10 Weak, moderate and strong inversion Figure depicts the log ID against VGS characteristic, where an another transition region of operation called moderate inversion appears. This region (in red) is situated between weak (in light brown) and strong (in green) inversion regions (i.e. from VTN0- up to VTN0+∆). The operation in strong inversion is a typical solution in the practice of contemporary analog integrated circuits design. Therefore our introductory course will concentrate thoroughly on the models and circuits operating in strong inversion. Recently the weak and moderate inversion operations (i.e. subthreshold region) become very actual when low-power circuits are desired. This is the reason to make a short description of the basic relations in this region of operation. The detailed study of the weak and moderate inversions is a purpose of the others advanced courses. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 11 Operation in strong inversion The n-MOS transistor operates in strong inversion when VGS VTN In most practical cases the typical value of is about 0.1V, i.e. VGS VTN 0.1V The difference VGS-VTH is called the effective gate-source voltage Veff . Finally the n-MOST is in strong inversion when Ve ff VGS VTN 0.1V The figure shows the family of output characteristics of the n-MOST (ID vs. VDS for different values of VGS). The area of characteristics is separated in two regions by curve, which fulfill the condition VDS = VGS-VTN . The first region is on the left side and it is characterized with nearly linear dependence between ID vs. VDS. It is called linear (ohmic or triode) region. In the another region the current ID is practically independent on the VDS. It is called saturation (active, pinch-off) region. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 12 DC modeling in linear region The condition for operation in strong inversion is Ve ff VGS VTN 0.1V The condition for operation in linear region is VDS Veff VGS VTN The equation for the drain current where mn is the mobility of electrons, Cox is the gate capacitance per unit area, W is the gate width and L is the effective gate length. The above figure presents the DC equivalent circuit of the n-MOST in linear region. The transistor is modeled with resistance RLIN, which is practically independent of VDS. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 13 Small signal model in linear region The high-frequency equivalent circuit of the MOST in linear region include a resistor and four parasitic capacitors. In case of low-frequency operation only the resistor is important. rds is the small signal drain-source resistance, which is equal to the RLIN from DC model. Cgs and Cgd are gate-to-source and gate-to-drain capacitances. Csb and Cdb consist of depletion capacitances of source and drain junction. Each of them includes also the corresponding junction-to-substrate and junction-sidewall capacitance. The respective equations are where Cox is the gate capacitance per unit area; LD is the gate-source (or gate-drain) overlap; Cj0 is the depletion capacitance per unit area; As (Ad) is the area of the source (drain); VSB (VDB) is source (drain)-to-substrate voltage; F0 is the built-in voltage of the junction. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 14 DC operation in saturation The condition for operation in strong inversion is Ve ff VGS VTN 0.1V The condition for operation in saturation region is VDS Ve ff VGS VTN The drain current in saturation is given with equation As it is shown on the figure, ID rises somewhat for increasing the VDS. This is the channellength modulation effect, which causes the nonzero slope in the output characteristic. To rend an account this effect, the parameter ln is included in the above equation. It is is denoted as a channel-length modulation parameter. ln is inverse proportional to the channel length. For hand-calculations, usually the simplified formula, shown bellow is used. In this formula the new parameter VE [V/mm] is a constant for a certain technology. l CMOS Analog IC Emil D. Manolov, TU-Sofia 1 VEL Basic analog models for CMOS Technology 15 DC model in saturation The figure presents the DC equivalent circuit of the n-MOS transistor in saturation. This model is based on the equation for the ID discussed in the previous slide The equivalent circuit consists of an voltage-controlled current source IDSAT and a resistor RDS. Their values are In most cases, for hand-calculations, a simplified DC model of the MOS transistor is used. This model neglects the slope in the output characteristics and contains only the voltage-controlled current source. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 16 Small signal low-frequency model in saturation The low-frequency equivalent circuit of the MOST in saturation consists of a resistor and two voltage-controlled current sources. The source gmvgs is the basic component of the model. It presents the dependency of the output current from the input control voltage vgs. The gm is known as transistor transconductance. The second source models the body effect in the transistor - when the vsb is applied between the source and the body, the output current decreases. The gmb is called body transconductance. The small signal source-drain resistor ro gives an account the finite output impedance of the transistor. In most applications the body and the source of the transistors are short connected, which remove the second source from the equivalent circuit. The gmb is much smaller then gm and the second source can be ignored even in the case when the source is connected to small-signal generator. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 17 Small signal parameters - definitions Based on the discussions in the previous slide now we will define the parameters of the low-frequency equivalent circuit of the MOS transistor. Using the equation for DC output current in saturation we can find the transistor transconductance gm as gm ID W W 2I m nCox Ve ff 2m nCox ID D VGS L L Ve ff After complex transformations the body transconductance gmb is determined as g mb ID I D VTN g m VSB VTN VSB 2 VSB 2j F Usually the body transconductance gmb is about (10…30)% from the transistor transconductance gm. The small-signal drain-source (output) resistance of the MOS transistor is equal of rds CMOS Analog IC Emil D. Manolov, TU-Sofia VDS lI DSAT lI D ID Basic analog models for CMOS Technology 18 Small-signal common gate equivalent circuit The figure shows the smallsignal common gate equivalent circuit for low-frequency operation of the MOS transistor in saturation. The circuit is obtained from the previous general model through appropriate transformations. The model consists of a small-signal source-gate (input) resistor and voltage-controlled current sources. The small-signal output (drain-gate) resistance is ignored, because of its very high value. The input resistance is inverse proportional of the sum of the transistor and body transconductances. Its value is small (usually between 2k and 20k). The output current is a product of the sum of the two transconductances and the input small-signal source-gate voltage. In most cases the value of the body transconductance gmb is smaller then the transistor transconductance gm and can be ignored for hand-calculations. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 19 High-frequency equivalent circuit The high-frequency equivalent circuit of the MOS transistor in saturation has the same structure as the low-frequency circuit. Additionally the parasitic capacitors are included. Cgd is a gate-drain overlap capacitor. It is caused to the unwanted diffusion under the gate and drain regions. Cgs includes gate-source overlap capacitor and a part of the gate-bulk capacitor. Cdb and Csb are the capacitances of the bulk-drain and bulk-source junctions. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 20 Equations for the parasitic capacitances 2 WLC ox WL DCox; 3 Csb ( A s WL )C js PsC jsw ; Cgs C js C j0 1 VSB / F 0 ; C jd Cgd WL DCox; Cdb A dCid PdC jsw ; C j0 1 VDB / F 0 ; C jsw C jsw0 1 VSB / F 0 . Above are presented the equations for computation of the parasitic capacitances, where -Cox is the gate capacitance per unit area; - LD is the gate-source (or gatedrain) overlap; - As (Ad) is the area of the source (drain); - Ps (Pd) is the length of the perimeter of the source (drain) junction; - Cjs (Cjd) is the depletion capacitance of the source (drain) junction; - Cj0 is the depletion capacitance per unit area of the source (drain); -Cj-sw is the sidewall capacitance per unit length of the drain (source); Cj-sw0 is the sidewall capacitance per unit length at 0V bias voltage; F0 is the builtin voltage of the junction. Very often the designers avoid to hand-calculate the above described capacitors, relying on the result from the simulations. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 21 MOS transistor frequency response The transition frequency fT specifies the frequency capability of the MOST. fT is defined as frequency where the magnitude of the short-circuit, common-source current gain falls to unity. The high-frequency behavior of the transistor is controlled by the capacitors in the small-signal model, which cause the input gate current to increase as frequency increases. To determine fT the above circuit is used. It is built on the base of the previous discussed high-frequency model. From this circuit we can find io gm 1 i i 2fT Cgs Cgd fT gm 3 m n ( VGS VTN ) 2 Cgs Cgd 4 L2 Hence, for high-speed circuit design minimum channel length should be used. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 22 Short-channel MOS transistor The figure presents the output characteristics of two n-MOST, implemented on 0.35mm CMOS technology. The first transistor (dashed lines) has the minimum allowed channel length L=0.35mm. It is known as short-channel transistor. The second transistor (solid lines) has L=3mm. This is long-channel transistor. The W/L ratio of both transistors is 1. The comparison of the output characteristics of the transistors gives the conclusions that the short-channel devices have a smaller output impedance than the long-channel transistors and that their output current is smaller than the discussed above formulas predict. To avoid the above problems, some authors propose to modify the classical square-law equations in order to make the characteristics more linear. This approach is more complex and it is not appropriate for the hand-calculations. The general solution is to design deliberately the many of the transistors in the analog circuits to have channel lengths from 5 to 20 times larger than the minimum allowed by the technology. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 23 Temperature dependence in MOST The transconductance characteristic of n-MOS transistor for different temperatures is shown on the figure. The threshold voltage VTN and the transconductance parameter mnCox change with temperature. The threshold voltage VTN has a negative temperature coefficient TCVTN 1 dVTN ppm 3000 VTN dT C The temperature coefficient of the transconductance parameter mnCox is connected with the temperature coefficient of the mobility 1.5 T 1.5 m n (T) m n (T0 ) TCmn T T0 At low-drain currents the negative TCVTN dominates the changes in the drain current, while at higher currents the temperature coefficient of the mobility is dominating. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 24 Noise v i2 2 1 Kf 4kT f 3 gm WLC oxf The figure shows typical equivalent input noise voltage spectral density for MOST in saturation. The dominant noise sources are flicker and thermal noises. The flicker noise is modeled as a voltage source in series with the gate. The thermal noise can be modeled as current source between drain and source. To simplify analysis the voltage and current sources can be replaced by one equivalent input noise source, which is given with the above formula. The first component presents the thermal noise and the second – flicker noise. The thermal noise is inverse proportional to the transconductance of the transistor and the flicker noise is the inverse proportional to the transistor area, i.e. larger devices have less 1/f noise. The constant Kf in the equation depends on device characteristics and can vary widely for the different devices in the same process. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 25 Variation of the parameters The device parameters in integrated circuits vary from run to run and from wafer to wafer. As a result, the values of the threshold voltage VTN and the transconductance parameter mnCox can change up to ±50% from its nominal value. Most parameters follow a "normal" (Gaussian) distribution. It is characterized with a mean value, at which the number of occurrences is maximum. A deviation of ±s (sigma) from this point contains 68.3% of all measured values. If the deviation is three times larger (±3s) - the 99.73% of all measurements are enclosed. The goal of the design is to create a product, which can withstand a variation of each and every device parameter to at least 3s. So, we have to know how to check the output parameters of the designed circuit at 3s deviation. The most reliable approach is Monte Carlo analysis, which varies the device parameters in a random fashion, so that every combination of variations is covered. This is also what we get in production. There is in use what is called a "four-corner analysis". Device parameters are combined together in four groups, representing extremes, or worst cases. This is a simple method, which is intended to predict the fastest or slowest speed of digital ICs. Despite of this method does not guarantee the reliable results for analog circuits, for the present time it have a large application in practice. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 26 Subthreshold operation The MOST operates in subthreshold region when Veff<100mV. In this area the accuracy of the square-law equations is poor. The current is more accurately modeled by an exponential relationship so, the MOST transfer characteristics look like to the BJT. The figure shows the drain current against drain-source voltage for five values of Veff. The drain current is almost constant when VDS > (3…4)jT and the equation for ID is V VTN 0 W where I D I D0 exp GS njT L n 1 CBC Cox The constant ID0 depends on the technology and is around 20nA. CBC is the depletion bulkchannel capacitance. The value of n is around 1.5. Because of the small bias currents the presented region is characterized with small value of the transconductance and slow transistors. The matching of the transistors is difficult because it now strongly depends on transistor threshold voltage matching. MOST operates in subthreshold rarely, mainly in low frequency and low power applications. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 27 Vertical bipolar transistor Figure shows a vertical pnp bipolar transistor implemented in standard CMOS technology. The n-well forms the base of transistor, the source (drain) diffusion – the emitter, and collector is tied to the p-substrate. If the substrate is n-type – the corresponding transistor is npn. This type of transistors are particularly employed in band-gap references, and in output stages. The main disadvantage of this transistor is that its collector (the substrate of the IC) is definitely connected to a power supply. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 28 Lateral bipolar transistor Figure shows a lateral pnp BJT implemented in standard CMOS technology. The n-well forms the base, the source (drain) diffusion – the emitter and the lateral collector. The emitter and collector of this transistor correspond to the source and the drain of a p-MOS transistor. To disallow its operation, the gate is connected to the highest supply voltage. The base width corresponds to the channel length of the MOS transistor, which can be very small. Thus, the bF and fT of the lateral transistors can be very high. The limitation of this structure is that the vertical parasitic transistor appears. Its emitter and base are the same as for the lateral transistor, but the collector is the substrate. This causes the appearance of the undesired current ICV, which is comparable to the basic current ICL. To minimize the losses different layout techniques are applied. CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 29 DC modeling of BJT IE IC IB IC V V I C J S A exp BE 1 CE jT VAF IB V JS A exp BE bF jT bF aF 1 aF VBE jT ln CMOS Analog IC Emil D. Manolov, TU-Sofia aF IC JSA bF 1 bF In analog integrated circuits BJT operates mostly in the forward active region. Picture shows the DC equivalent circuit of npn BJT. The model for pnp is similar, only the polarities of the voltages and the directions of the current must be inverted. Below the picture are presented the basic DC equations. The condition to operate in active region is: VBE>0.5V and VCE>0.3V. JS, bF, aF and VAF are process dependent parameters: JS is the transport saturation current density; bF and aF are well known current gain coefficients; VAF is the Early voltage. A is the design parameter. It is equal to the area of the emitter. Typically in hand calculations, the emitter and collector currents are considered to be equal, as well as the VCE/VAF ratio usually is neglected. Basic analog models for CMOS Technology 30 Small-signal BJT model The typical small-signal equivalent circuit of BJT consist of: rb - the resistance of the semiconductor material between the base contact and the effective base region; Cbe the capacitance of the emitter junction; Ccb - the capacitance of the collector junction; Ccs - the capacitance of the collector-substrate junction; r - the small-signal emitter resistance; gm - the transconductance; ro - the small output resistance; Cj0 - the depletion capacitance per unit area of the source (drain). r VBE j T b F IB I B gm ro Cbe C j Cd 2A EC je0 g m b CMOS Analog IC Emil D. Manolov, TU-Sofia IC V AF VC E IC Ccs A TC js0 V 1 C S F s0 12 Basic analog models for CMOS Technology gm IC I b C F VBE j T g m Ccb A CC jc0 V 1 C B F c0 13 31 Instructions for self-study The past presentation gives only a first sight on the hand-calculation models for CMOS active devices. After reading and understanding the presented information you have to study the material from at least one of the following textbooks: - R. Baker, H. Li, D.Boyce. CMOS Circuit Design, Layout and Simulation, IEEE Press, New York, 2005, ISBN 0-7803-3416-7. Chapter 5, pp.84-105.Chapter 9, pp.165-184. - Ph. E. Allen, D. R. Holberg. CMOS Analog Circuit Design, Oxford University Press, Inc., 2002. ISBN 0-19-511644-5, Chapter 3, pp. 72-112, Appendix B, pp. 744-767. - F. Maloberti. Analog design for CMOS VLSI Systems. Kluwer Academic Publishers, 2003, eBook ISBN: 0-306-47952-4, Print ISBN: 0-7923-7550-5, Chapter 1, pp.1-54. The next step in the learning process is to study the examples and complete the experiments, which are presented in Guided exercise 1 After that you can go on to the next part : CMOS Biasing Circuits CMOS Analog IC Emil D. Manolov, TU-Sofia Basic analog models for CMOS Technology 32