# hw06sol - ECE 315 Homework 6 Solution Spring 2009 1(MOSFET...

• Notes
• 10

This preview shows pages 1–4. Sign up to view the full content.

ECE 315 Homework 6 Solution Spring 2009 1. (MOSFET subthreshold and saturation behavior) Consider a NMOSFET with a threshold voltage of V th =0.7V, threshold current I th =10 μ A and the substrate factor κ =0.8, (a) If the gate oxide thickness is 10nm, what is the depletion region width in silicon to obtain this substrate factor (hint: the dielectric constant of SiO 2 ε ox at 3.9 and Si ε si at 11.7)? (4 pts) C ox = ε ox ε 0 /t ox = 3.45 × 10 -7 F/cm 2 . κ =0.8= si ox ox C C C + , and we can find C si = C ox /4 = 8.63 × 10 -8 F/cm 2 = ε si ε 0 /W d . Hence, W d = 0.12 μ m. (b) Estimate I D at V GS =0.3V and V DS =0.0V. (4 pts) At V DS =0, I D is required to be 0. Notice this is the beginning of the linear region. (c) Estimate I D at V GS =0.3V and V DS =1.0V. What is the operating region under this bias? Notice that a rough estimate using the subthreshold slope is sufficient here. (4 pts) V GS < V th , and V DS > 3kT/q, and therefore this is the subthreshold saturation region. We will use the subthreshold slope of 60mV/0.8 = 75mV to estimate the current. Given I th =10 μ A at V th =0.7V, with V GS at 0.3V, the current will be: 10 μ A × 10 (0.3 – 0.7)/0.075 = 46.4pA. For perfectionist, you can see the subthreshold line should have a prefactor of 2I th instead of I th . However, in the subthreshold current calculation, we often only need to be correct on the order of magnitude. (d) To obtain I D =10pA with V DS =0.13V, what will be the required V GS ? (4 pts) V DS =0.13V > 3kT/q, so we can assume it is in saturation (independent of V DS ). V GS = V th 75mV × log 10 (10 μ A/10pA) = 0.25V. 2. (CMOS inverter voltage transfer curve) For a CMOS inverter with a PMOS in the pull-up network and a NMOS in the pull-down network, the output is an open circuit. Assume k p ’W p /L p = k n ’W n / L n =1mA/V 2 , V thn = |V thp | =1V and V An =|V Ap |= 10V. V DD = 5V. (a) Plot the load line curves as the output characteristics ( V OUT vs. I D for NMOS and PMOS respectively with V IN as a parameter). Mark the intersections of NMOS and PMOS IV curves for the steady-state solution for V IN = 0, 1, 2, 3, 4, 5V. At those intersections, mark the operation regions (subthreshold, linear or saturation) for NMOS and PMOS. (6 pts) 1

This preview has intentionally blurred sections. Sign up to view the full version.

(b) From (a), derive the plot of the voltage transfer curve VTC ( V IN vs. V OUT ). (3 pts) V IN V OUT NMOS PMOS V DD - V O for PMOS I V DD V O for NMOS V I =5V V I =4V V I =3V V I =2V V I =1V V I =0V V I =0V V I =1V V I =2V V I =3V V I =4V V I =5V k p W p /L p = k n W n /L n here V IN =0V: NMOS sub- V th , PMOS linear V IN =1V: NMOS sat., PMOS linear V IN =2V: NMOS sat., PMOS linear V IN =5V: NMOS linear, PMOS sub- V th , V IN =4V: NMOS linear, PMOS sat. V IN =3V: NMOS linear, PMOS sat. 2
(c) From (a), derive the plot of the transconductance curve ( V IN vs. I DD ). (3 pts) (d) What is the input voltage when V IN =V OUT (this is called the switching threshold V M of the inverter)? What are the operating regions for NMOSFET and PMOSFET there? (4 pts) Since k p ’W p /L p = k n ’W n /L n (that is, the PMOSFET and NMOSFET have matched current drive capability), the VTC is symmetrical, and hence V M = V DD /2 = 2.5V by symmetry requirement. For NMOSFET, V GS =2.5V, V DS =2.5V, and it is in saturation. For PMOSFET, V GS = - 2.5V and V DS = - 2.5V, which is in saturation too.

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern