HW#3 Solution. Dr. Parker. Spring 2014
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1 HW#3 olution r. Parker pring 2014 Assume for the problems below that V dd = 1.8 V, V tp0 is -.7 V. and V tn0 is.7 V. V tpbodyeffect is -.9 V. and V tnbodyeffect is.9 V. Assume ß n (k n )= W/L µ A(microamps)/V 2 and ß p (k p )= 51 W/L µ A/V 2 1. (10%) A PMO transistor has Vs = 1.8 V, V d =.9 V. Vg =.6 V. What region of operation is it in? Vgs=.6 1.8= -1.2 V Vtp= -.7 V (there is no body effect since the source is tied to the highest potential) Vds=.9-1.8= -.9 V Vds > Vgs-Vtp? -.9 > -1.2 (-.7)? -.9 > -.5? False, transistor is in ATURATION region 2. (10 %) An NMO transistor has Vg = 1.8 V. V d =.9 V. Is the transistor in the linear region of operation when Vgs =1.3 V? Vg-Vs=Vgs 1.8 Vs=1.3 V Vs= =.5 V There is body effect since the transistor source is not connected to the lowest potential. Vds=.9-.5=.4 V Vds< Vgs Vtnbodyeffect?.4 < ?.4 <.4? The transistor is in the border between linear a saturation region since Vds=Vgs-Vtnbodyeffect. The channel is said to be pinched-off. 3. a) (5 %) A PMO transistor is used as a pass transistor (switch). The input voltage is Vin = 1.1 V. The gate voltage Vg=.4 V. The voltage Vout = 1.7 V at time t = 0. What is the final output voltage at t = infinity? The source is at the output. At t=infinity, the minimum voltage that it can be transferred to the output is Vg+ Vtpbodyeffect, so Vout=.4 V+.9 V= 1.3 V. Note that Vgs Vtpbodyeffect (condition for the transistor to be ON)! Vg-Vs Vtpbodyeffect! Vs Vg-Vtpboyeffect! Vs.4 (-.9)!Vs 1.3 V
2 b) (3%) oes the PMO transistor have body effect when t approaches infinity? Yes, it does have body effect because the source terminal is different from the maximum potential. c) (10%) Assume the transistor width is 8 lambda and the length is twice minimum size. Compute the drain current flow I at t=0 and at t = infinity. First we need to determine the region of operation of the transistor at t=0 and at t=infinity. at t=0 Vds= = -.6 V Vgs=.4-1.7= -1.3 V Vtpbodyeffect= -.9 V (the source is lower than the highest potential) Vgs Vtpbodyeffect? If this condition is true, the transistor is ON ? The condition is true, so the transistor is ON. Vds > Vgs-Vtpbodyeffect? -.6 > -1.3 (-.9)? -.6 > -.4? False, so the transistor is in ATURATION Idsp = µp*cox*w/l*(vgs-vtpbodyeffect)^2 =(51x10^-6)(8/4)(-1.3-(-.9))^2 = ua (negative sign indicates the current flow direction) At t=infinity Vds= = -.2 V Vgs=.4 1.3= -.9 V Vtpbodyeffect= -.9 V Vgs Vtpbodyeffect? If this condition is true, the transistor is ON ? The condition is true, so the transistor is ON. Vds > Vgs-Vtpbodyeffect? If the condition is true the transistor is in linear region -.2 > -.9 (-.9)? -.2 > 0? False, so the transistor is in ATURATION Idsp = µp*cox*w/l*(-.9-(-.9))^2 Idsp= 0 A
3 4. a) (7 %) Identify the sources and drains in a transmission gate at t=0+ when Vin = 1.1 V and Vout =.3 V. Vgn = 1.4 V, and Vgp =.4 V. b) (8 %) What regions are the two transistors in when t approaches infinity? Be sure to justify your answers. PMO: Vgs = = -.7 V Vgs Vtpbodyeffect? -.7 V -.9 V? False, thus the transistor is in cutoff NMO: A t= infinity the output voltage is Vg-Vtnbodyeffect = =.5 V Vgs= =.9 V Vds= =.6 V Note that if the output voltage we to rise any further, the NMO transistor would have Vgs <.9v so the transistor is cutoff. 5. (10%) Assume we have N NMO transistors connected in series. If at t=0 the input voltage is Vdd and all internal nodes are 0 V (V1, V2,..., V N ), what is the maximum voltage at the output V N at t=infinity? A t= infinity, the maximum voltage that can be transfered at V N is V dd V tnbodyeffect, so V N = =.9 V
4 6. (10%) Find the voltages V 1, V 2, and V 3 at t=infinity. Assume that at t=0, V 1,V 2, and V 3 are equal to 0 V. V1MAX= 2*Vdd- Vtnbodyeffect = 2*1.8-.9= 2.7 V V2MAX= (2*Vdd- Vtnbodyeffect) Vtnbodyeffect = = 1.8 V V3MAX = (2*Vdd- Vtnbodyeffect) Vtnbodyeffect Vtnbodyeffect = =.9 V V1 = 1.5 V V2 = 1.5 V - Vtnbodyeffect =.6V V3 = 0.0V 7. (5%) You might need to solve this problem after Thurs. lecture. What is the effective channel resistance of a 3 times width of a unit size PMO transistor? Assume Vg=0.2V, Vs= 1.5V, Vd=1.4V. Vgs = =-1.3 V Vds = = -.1 V Vds> Vgs Vtpbodyeffect? -.1 > -1.3 (-.9)? -.1 > -.4? This is true, so the transistor is in linear region. Rchp = 1/( ß p *W/L*(Vgs-Vtpbodyeffect)) Rchp = 1/(51X10^-6*((3*4)/2)*(-1.3-(-.9)) = 8.17 KΩ 8. (5%) What is the parasitic effect that is created when we have current flowing between Vdd and ground away from the transistor channels in a CMO process? Latchup How can we avoid it? 1) build guard rings around transistors. 2) For NMO! p+ guard rigns, for PMO! n+ guard rings. 3) Trench in isolation with io 2. 4) Turn off Vdd. 5) Change the technology (OI, O, FinFET).
5 9. (5%) oes the threshold increase or decrease if we use thick oxide instead of thin oxide under the poly in the gate region? Why? It increases because an increase in the thickness decreases the oxide capacitance which is inversely proportional to the body-effect coefficient (equation 3.23 and 3.24) 10. (7%) Why is the substrate in NMO connected to ground and in PMO to Vdd? In an NMO transistor, substrate is connected to ground to reverse bias the pn junctions that are formed between p- substrate and n+ diffusions, so that no current flow occurs between the substrate and the n+ diffusions. In a PMO transistor, substrate is connected to Vdd to reverse bias the pn junctions that are formed between p+ diffusions and n-well. 11. (5%) ketch the crossection of a PMO transistor when Vds < Vgs-V tp0. how clearly the shape of the channel. Note that the PMO transistor is in saturation when Vds < Vgs-V tp0. If Vds is lower than Vgs-Vtp0, the channel pinch-off point slightly moves away from the drain. 12. (10%) In an inverter, if Vin rises slowly, so there is a subthreshold current through the NMO transistor when Vin<Vthn, will the NMO transistor still move from cutoff to saturation when Vin=Vthn? The transistor is in saturation. By definition if Vgs is greater than or equal to Vthn, then the NMO transistor is ON. The condition for saturation is true, since Vdsn> Vgs-Vthn.
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