Fall 2005 6.012 Microelectronic Devices and Circuits Prof. J. A. del AlamoHomework #5 - October 14, 2005Due: October 21, 2005 at recitation 2 PM latest)(late homework will not be accepted)Please write your recitation session time on your problem set solution.1. [20 points] Consider the output I-V characteristics of an n-MOSFET for VSB= 0 below.The device has a gate length Lg=1µm and a gate oxide thickness xox=10nm. Theoutput characteristics have b een normalized for a unity width device.a) Estimate the threshold voltage of the device.b) Estimate the mobility of the electron inversion layer.c) Estimate the transconductance gmat a bias of VGS=3V , and VDS=3V for Wg=10 µm.d) At a bias of VGS=3V , and VDS=3V , estimate the gate-source capacitance Cgsof aWg=10µm device.2. [20 points] Consider an n-MOSFET with an n+-polySi gate characterized by the followingparameters: L =1µm, W =5µm, xox=20nm, Na=1017cm−3. The device is biased(with VGS=3V , VDS=4V and VBS=0V . Assume µn= 400 cm2/V · s for electrons inthe inversion layer.a) In what regime is the MOSFET biased? Justify your answer with suitable calculations.b) Calculate the electron concentration per unit area at the source-end of the channel.c) Calculate the extent of the depletion region underneath the inversion layer at the source-end of the channel.d) What is the value of VBSthat would drive this transistor to cut-off (VGSand VDSdon’tchange).3. [10 points] Analog designers often need to shift DC bias levels in circuits. This is bestaccomplished using p-n diodes. In standard CMOS, floating p-n diodes (that is, diodesnot in direct contact with the power rails) are not readily available. A common way to”synthesize” a diode is to tie up an enhancement-mode MOSFET (VT> 0) with the gateand drain shorted as sketched below.+-VIDerive suitable equations for the I-V characteristics of the ”diode”, Ivs.V for V<VT,and V>VT. Sketch the I-V characteristics in a linear scale.4. [50 points] MOSFET characterizationIn this project, you will characterize the current-voltage characteristics of an n-channelMOSFET. To do this, you will use the MIT Microelectronics WebLab. Refer to the UserManual for instructions on how to use the system.Several identical 3 µm long n-channel MOSFETs are available through WebLab. The termi-nal connection for these devices (labeled ”3 um NMOSFET”) is identical for all of them andis available on line. This exercise involves three separate phases: measurement, graphing,and analysis. The exercise will continue in the next homework. Take the measurementsspecified below. When you are happy with the results (as judged by the characteristicsdisplayed through the web), download the data to your local machine for more graphingand further analysis.Important note: For all measurements, hold VGSbetween 0 and 2 V , and VDSbetween 0and 4 V . Unless sp ecified, use VBS=0V . When relevant, examine VBSbetween 0 and−3 V . As inputs to this exercise, you need the dimensions of the MOSFET: L =3µm andW =20µm.Here is your assignment.1. Obtain the output characteristics of the MOSFET. This is a plot of IDvs. VDSwithVGSas parameter. Use ∆VGS=0.25 V and VBS=0V . Take a screen shot of thesecharacteristics. Turn in this graph. Download the data to your local machine forlater use in the next problem set.2. Obtain the transfer characteristics of the MOSFET. This is a plot of IDvs. VGSwithVDSas parameter. Use ∆VDS=1V and VBS=0V . Take a screen shot of thesecharacteristics. Turn in this graph. Download the data to your local machine.3. Obtain the backgate characteristics of the MOSFET in the saturation regime. Thisis a plot of IDvs. VGSwith VBSas parameter. Use ∆VBS= −0.5 V and VDS=4V .Take a screen shot of these characteristics for later use. Turn in this graph. Downloadthe data to your local machine.4. From the transfer characteristics and using the model described in class, extractµnCoxand the threshold voltage, VTo, for this MOSFET [Suggestions: use the transfercharacteristics in saturation, say for VDS=4V , to determine VTo. You can defineVToas the gate-source voltage that results in a drain current of 5 µA. Then scale theµnCoxproduct to get the best possible match to the transfer characteristics. Don’t bedisappointed if the match is not great. These MOSFETs do not perfectly follow thebehavior of the ideal MOSFET model].5. From the backgate characteristics, and using the model described in class, extract thevalues of γ and φpthat best describe this MOSFET [Suggestion: use the procedurementioned above to extract VTas a function of VBS; then try values of φpin the −0.3to −0.5 V range and extract the value of γ that is most consistent among the entiredata
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