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Microsoft Word - final assignment ECSE 433 – Physical Basis of Semiconductor Devices 1/5 Final Assignment Issued: 7 March 2022 Due: 11 April 2022 (at 23h59, eastern standard time) Complete your work individually. Please read each question carefully, be careful with units, and answer *all* parts. Submit your assignment electronically via MyCourses (in the Final Assignment Folder) by the deadline. Please assemble your submission into one PDF, and include your name and ID number in your submitted material. All figures must be clearly labeled with a title, axis labels, and units indicated as necessary. Illegible graphs will not be accepted. Include all scripts, livescripts, and code that you have used for your numerical calculations and figure production in your submission. You may attach it to the PDF submission, or submit as additional documents. ECSE 433 – Physical Basis of Semiconductor Devices 2/5 1. Consider an n-channel silicon MOSFET with the following device parameters: VT = -0.8 V, μn = 425 cm2 V-1 s-1, tox = 11 nm, W = 20 μm, and L = 1.2 μm at T = 300 K. Assume that an ideal MOSFET model applies. a) Plot the drain current ID [mA] versus drain-source voltage VDS over the range 0 < vds="">< 3v="" with="" vgs="-0.8" v,="" vgs="0" v="" and="" vgs="+0.8" v.="" [1pt]="" b)="" plot="" the="" root="" saturation="" current="" id1/2(sat)="" [ma1/2]="" versus="" gate-source="" voltage="" vgs="" over="" the="" range="" -0.8="" v="">< vgs="">< +0.8="" v.="" [1pt]="" c)="" plot="" the="" transconductance="" gm="" [ma/v]="" versus="" drain-source="" voltage="" vds="" over="" the="" range="" 0="">< vds="">< 3v="" with="" vgs="-0.8" v,="" vgs="0" v="" and="" vgs="+0.8" v.="" [1pt]="" d)="" plot="" the="" output="" resistance="" r0="" [v/ma]="" versus="" drain-source="" voltage="" vds="" over="" the="" range="" 0="">< vds="">< 3v="" with="" vgs="-0.8" v,="" vgs="0" v="" and="" vgs="+0.8" v.="" [1pt]="" for="" questions="" 2="" through="" 4,="" use="" the="" “fettoy”="" in="" nanohub,="" which="" you="" can="" find="" by="" the="" “search”="" tab="" or="" by="" browsing="" the="" “tools”="" section.="" note="" that="" you="" can="" download="" your="" simulation="" data="" from="" nanohub="" to="" analyze="" and="" plot="" simulation="" results.="" 2.="" the="" gate="" control="" parameter="" αg="CG/CΣ" and="" drain="" control="" parameter="" αd="CD/CΣ" determine="" the="" efficiency="" with="" which="" fet="" channel="" potential="" is="" modulated="" by="" gate="" and="" drain="" voltages="" respectively.="" cg="" is="" the="" gate="" capacitance="" to="" the="" channel,="" cd="" is="" the="" drain="" capacitance="" to="" the="" channel,="" and="" cσ="" is="" the="" total="" capacitance="" of="" the="" channel="" to="" the="" environment.="" good="" electrostatic="" design="" is="" essential="" for="" transistor="" performance.="" using="" the="" “fettoy”="" application="" on="" nanohub,="" simulate="" the="" double-gate="" mosfet="" with="" gate="" insulator="" thickness="" 2.0="" nm,="" gate="" insulator="" dielectric="" constant="" 3.9,="" effective="" mass="" ratio="" 0.19,="" valley="" degeneracy="" 2,="" body="" thickness="" 10="" nm,="" source="" doping="" density="" 1020/cc,="" threshold="" voltage="" 0.4="" v,="" series="" resistance="" of="" 0="" ωμm,="" drain="" voltage="" 0="" v="">< vd="">< 1="" v,="" gate="" voltage="" 0="" v="">< vg="">< 1="" v,="" and="" operating="" temperature="" 300="" k.="" consider="" three="" mosfet="" designs:="" ="" the="" ideal="" mosfet="" with="" αg="1.0" and="" αd="0.0," ="" a="" typical="" short-channel="" mosfet="" with="" αg="0.85" and="" αd="0.04," ="" a="" poorly="" designed="" short-channel="" mosfet="" with="" αg="0.4" and="" αd="0.2." observing="" your="" simulation="" results="" and="" answer="" the="" following="" questions.="" you="" may="" find="" it="" useful="" to="" download="" the="" numerical="" simulation="" data="" for="" plotting="" and="" analysis.="" ecse="" 433="" –="" physical="" basis="" of="" semiconductor="" devices="" 3/5="" a)="" plot="" log="" id="" versus="" vg="" with="" vd="1" v="" for="" all="" three="" mosfets.="" [1pt]="" b)="" consider="" the="" sub-threshold="" behaviour="" of="" the="" mosfets.="" what="" is="" the="" sub-threshold="" swing="" (mv="" decade)="" of="" the="" drain="" current="" for="" the="" three="" mosfets?="" you="" may="" want="" to="" fit="" a="" linear="" function="" to="" log="" id="" versus="" vgs="" in="" the="" sub-threshold="" regime.="" [2pts]="" c)="" what="" is="" the="" on/off="" ratio="" ion/ioff,="" comparing="" the="" drain="" current="" in="" deep-sub-threshold="" with="" the="" drain="" current="" in="" deep-saturation,="" for="" the="" three="" mosfets?="" [2pts]="" d)="" plot="" id="" versus="" vd="" with="" vg="1" v="" for="" all="" three="" mosfets.="" [1pt]="" e)="" is="" there="" a="" difference="" in="" the="" saturation="" behaviour="" of="" the="" three="" mosfets?="" your="" answer="" need="" not="" be="" longer="" than="" several="" sentences.="" [1pt]="" 3.="" the="" high-κ="" dielectric="" hfo2="" has="" replaced="" sio2="" in="" many="" transistor="" technologies.="" consider="" the="" effect="" of="" increasing="" gate="" dielectric="" constant="" on="" transistor="" performance.="" the="" on="" current="" is="" proportional="" to="" gate="" capacitance,="" ion="" ="" cg.="" using="" the="" “fettoy”="" application="" on="" nanohub,="" simulate="" the="" double-gate="" mosfet,="" varying="" the="" gate="" insulator="" dielectric="" constant.="" as="" in="" question="" 2,="" simulate="" the="" double="" gate="" mosfet="" with="" gate="" insulator="" thickness="" 2.0="" nm,="" effective="" mass="" ratio="" 0.19,="" valley="" degeneracy="" 2,="" body="" thickness="" 10="" nm,="" source="" doping="" density="" 1020/cc,="" threshold="" voltage="" 0.4="" v,="" gate="" control="" parameter="" αg="0.85," drain="" control="" parameter="" αd="0.04," series="" resistance="" of="" 0="" ω-μm,="" drain="" voltage="" 0="" v="">< vd="">< 1="" v,="" gate="" voltage="" 0="" v="">< vg="">< 1="" v,="" and="" temperature="" 300="" k.="" determine="" the="" on="" current="" ion="" for="" transistors="" with="" the="" following="" gate="" dielectrics:="" vacuum="" (εr="1.0)," sio2="" (εr="3.9)," si3n4="" (εr="7.5)," al2o3="" (εr="9.8)," hfsio4="" (εr="11)," y2o3="" (εr="15)," ta2o5="" (εr="22)," zro2="" (εr="25)," hfo2="" (εr="30)" and="" tio2="" (εr="50)." note="" that="" the="" dielectric="" constant="" of="" a="" thin="" film="" often="" depends="" upon="" the="" deposition="" process,="" so="" there="" is="" variation="" in="" dielectric="" constant="" in="" practice.="" a)="" plot="" the="" on="" current="" ion="" versus="" gate="" insulator="" dielectric="" constant="" εr.="" what="" is="" the="" physical="" reason="" that="" your="" curve="" deviates="" from="" a="" straight="" line?="" [2pts]="" b)="" is="" there="" any="" benefit="" to="" introducing="" ultra-high="" dielectric="" constant="" materials="" such="" as="" srtio3="" (εr="2000)" into="" mosfet="" gate="" stacks?="" [1pt]="" note="" that="" materials="" with="" ultra-high="" dielectric="" constants="" may="" exhibit="" ferroelectricity,="" which="" may="" introduce="" undesired="" device="" hysteresis.="" ecse="" 433="" –="" physical="" basis="" of="" semiconductor="" devices="" 4/5="" 4.="" consider="" the="" role="" of="" effective="" mass="" in="" the="" characteristics="" of="" a="" ballistic="" mosfet.="" using="" the="" “fettoy”="" application="" on="" nanohub,="" simulate="" the="" double-gate="" mosfet,="" varying="" the="" effective="" mass="" ratio.="" as="" in="" question="" 2,="" simulate="" the="" double="" gate="" mosfet="" with="" gate="" insulator="" thickness="" 2.0="" nm,="" gate="" insulator="" dielectric="" constant="" 3.9,="" valley="" degeneracy="" 2,="" body="" thickness="" 10="" nm,="" source="" doping="" density="" 1020/cc,="" threshold="" voltage="" 0.4="" v,="" gate="" control="" parameter="" αg="1.0," drain="" control="" parameter="" αd="0.0," series="" resistance="" of="" 0="" ω-μm,="" drain="" voltage="" 0="" v="">< vd="">< 1="" v,="" gate="" voltage="" 0="" v="">< vg="">< 1="" v,="" and="" operating="" temperature="" 300="" k.="" a)="" plot="" the="" drain="" current="" id="" versus="" gate="" voltage="" vg="" curves="" for="" effective="" mass="" ratios="" 0.1,="" 1.0,="" and="" 10.="" [1pt]="" b)="" what="" differences="" do="" you="" observe="" in="" the="" id="" -="" vg="" curves="" as="" effective="" mass="" changes?="" what="" is="" the="" physical="" reason="" for="" these="" differences?="" [2pts]="" 5.="" finally,="" consider="" the="" role="" of="" temperature="" in="" the="" characteristics="" of="" a="" ballistic="" mosfet.="" using="" the="" “fettoy”="" application="" on="" nanohub,="" simulate="" the="" double-gate="" mosfet,="" varying="" the="" operating="" temperature.="" as="" in="" question="" 2,="" simulate="" the="" double="" gate="" mosfet="" with="" gate="" insulator="" thickness="" 2.0="" nm,="" gate="" insulator="" dielectric="" constant="" 3.9,="" effective="" mass="" ratio="" 0.19,="" valley="" degeneracy="" 2,="" body="" thickness="" 1="" 0nm,="" source="" doping="" density="" 1020/cc,="" threshold="" voltage="" 0.4="" v,="" gate="" control="" parameter="" αg="0.85," drain="" control="" parameter="" αd="0.04," series="" resistance="" of="" 0="" ω-="" μm,="" drain="" voltage="" 0="" v="">< vd="">< 1="" v,="" and="" gate="" voltage="" 0="" v="">< vg="">< 1 v. a) calculate and plot the on current ion versus operating temperature t = 50k, 77k, 100k, 200k, 300k, 400k and 500k. [1pt] b) explain the observed trend, appealing to your knowledge of the temperature dependence of fermi velocity and thermal velocity. [2pts] ecse 433 – physical basis of semiconductor devices 5/5 6. in this question, you will consider the quantum of transconductance for a field effect transistor with a 2-dimensional electron gas (2deg). this is relevant to the design of hemts, for example. a) consider the definition of capacitance per unit area c’ = dq / dv [ f cm-2 ] of a 2deg to a metal gate electrode, and the definition of density of states g(e) = dn/de [ electrons cm-2 ev-1 ]. assuming ideal modulation of electron energy with gate electrode voltage, de = edv, show that the capacitance: c’ = e2g(e). this is known as the quantum capacitance. [1pt] b) the density of states for a simple 2deg is g(e) = m*/πħ2. calculate the quantum capacitance per unit area for a si 2deg (m* = 1.06 m0) and for an insb 2deg (m* = 0.013 m0). calculate the capacitance per unit area of a 3 nm thick silicon dioxide dielectric layer (ε = 3.9ε0) for comparison. [2pts] c) the transconductance of a ballistic hemt in saturation can be expressed gm = w c’ veff, where veff = 2ħkfs/πm* is the effective velocity, w is the transistor width, and c’ the gate capacitance. consider the limit where gate capacitance is equal to the quantum capacitance. derive an expression for the transconductance in terms of the conductance quantum e2/h, channel width w, and fermi wavevector kfs. [1pt] notice that wkfs/2π is the number of electron modes that fit within the width of the transistor channel. 1="" v.="" a)="" calculate="" and="" plot="" the="" on="" current="" ion="" versus="" operating="" temperature="" t="50K," 77k,="" 100k,="" 200k,="" 300k,="" 400k="" and="" 500k.="" [1pt]="" b)="" explain="" the="" observed="" trend,="" appealing="" to="" your="" knowledge="" of="" the="" temperature="" dependence="" of="" fermi="" velocity="" and="" thermal="" velocity.="" [2pts]="" ecse="" 433="" –="" physical="" basis="" of="" semiconductor="" devices="" 5/5="" 6.="" in="" this="" question,="" you="" will="" consider="" the="" quantum="" of="" transconductance="" for="" a="" field="" effect="" transistor="" with="" a="" 2-dimensional="" electron="" gas="" (2deg).="" this="" is="" relevant="" to="" the="" design="" of="" hemts,="" for="" example.="" a)="" consider="" the="" definition="" of="" capacitance="" per="" unit="" area="" c’="dQ" dv="" [="" f="" cm-2="" ]="" of="" a="" 2deg="" to="" a="" metal="" gate="" electrode,="" and="" the="" definition="" of="" density="" of="" states="" g(e)="dn/dE" [="" electrons="" cm-2="" ev-1="" ].="" assuming="" ideal="" modulation="" of="" electron="" energy="" with="" gate="" electrode="" voltage,="" de="edV," show="" that="" the="" capacitance:="" c’="e2g(E)." this="" is="" known="" as="" the="" quantum="" capacitance.="" [1pt]="" b)="" the="" density="" of="" states="" for="" a="" simple="" 2deg="" is="" g(e)="m*/πħ2." calculate="" the="" quantum="" capacitance="" per="" unit="" area="" for="" a="" si="" 2deg="" (m*="1.06" m0)="" and="" for="" an="" insb="" 2deg="" (m*="0.013" m0).="" calculate="" the="" capacitance="" per="" unit="" area="" of="" a="" 3="" nm="" thick="" silicon="" dioxide="" dielectric="" layer="" (ε="3.9ε0)" for="" comparison.="" [2pts]="" c)="" the="" transconductance="" of="" a="" ballistic="" hemt="" in="" saturation="" can="" be="" expressed="" gm="W" c’="" veff,="" where="" veff="2ħkFS/πm*" is="" the="" effective="" velocity,="" w="" is="" the="" transistor="" width,="" and="" c’="" the="" gate="" capacitance.="" consider="" the="" limit="" where="" gate="" capacitance="" is="" equal="" to="" the="" quantum="" capacitance.="" derive="" an="" expression="" for="" the="" transconductance="" in="" terms="" of="" the="" conductance="" quantum="" e2/h,="" channel="" width="" w,="" and="" fermi="" wavevector="" kfs.="" [1pt]="" notice="" that="" wkfs/2π="" is="" the="" number="" of="" electron="" modes="" that="" fit="" within="" the="" width="" of="" the="" transistor="">