Modulation Doping HEMT/HFET/MODFET
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1 ecture 7: High lectro Mobility raitor Modulatio opig HM/HF/MOF evice tructure hrehold voltage Calculate the curret uig drit ect o velocity aturatio ecture 7, High Speed evice 04
2 Fudametal MSF Problem g (egative) Source Gate rai N d b epletio Regio a y Semi-iulatig g 00 m N N d d qnd a a bi 00 g High dopig degrade mobility ad caue gate leakage! High dopig icreae 00! epletio thicke (a-b) mut be large (~ 50 m) to avoid tuelig! g 3 a to avoid hort chael eect g mmax, meet ~ 0.3 ms/µm g mmax,hm ~.7 ms/µm ecture 7, High Speed evice 04
3 Heterotructure F Gate t b N d d N d ~0 AlA AlGaA AlSb t b c N d ~0 ()GaA y lectro accumulate i the ()GaA + µ ca be very large o chael dopig + High electro cocetratio i chael + GaA chael higher mobility + AlA barrier ( g =.5 e) large B + t b thi (5-0 m!) large badgap barrier limit tuelig leakage ( g >3t b ) - More advaced deig require heterotructure growth N i ued to tue the threhold voltage/acce reitace ecture 7, High Speed evice 03 3
4 wo dimeioal electro ga N d d N d ~0 N d ~0 WG NG c y lectro are coied i the y-directio Part o waveuctio that peetrate ito WG hould alo be kept away rom ay impuritie d Form a quatum well! (riagular or quare) -dimeioal electro ytem ytem deity o tate! ecture 7, High Speed evice 03 4
5 Modulatio opig : eity o tate ecture, High Speed evice 03 0, d m m h m m 4 3 * * 3 * * 3 k k k k exp l exp l (, ) Fermi-irac * 4 m h For =0K Fermi irac i a tep uctio S = N F 0 (η F,i ) N = 4πk h m Γ
6 miute excercie Plot a i varied i the quatum well =0K F C C ecture, High Speed evice 03 6
7 Modulatio opig : ergy evel riagular Well: deped o charge i well. q i, ~ q i, x Square well: almot idepedet o t w AlGaA GaA AlGaA h 8 m * 3 q k l exp i, k k 4 /3 /3 h 8m* tw iite quare well k l exp k ecture, High Speed evice 03 7
8 (e) v or a QW 0.5 d ubbad 0 0. =0K =300K ( )- c = 0 +a t ubbad QW (m - ) x ecture, High Speed evice 0 8
9 lectro cocetratio: ( g ) t b GaA d AlGaA N d, d Charge y t b q B q G, C qn d, x -ield q i -q GB 0 (re. level) N d, c N d, 0 q q t b G, 0 y x dx q qn ( ) G c qb qgb, d, c q tb d GB B t b q ecture 7, High Speed evice 03 9
10 Chael Charge quatio q q qnd, tb d tb t t 0 qnd Quatum well, =0K, 0 GB b b c q c t b d B q GB B c0 eed to chage a chage t b h q 4m * Å (Si) 4Å (GaA) 74Å (A) q C ox GB riagular well eed umerical approximatio, t b ~68Å or GaA, 0 ~ e detical to that o a MOSF! A HM without dopig i the barrier i eetial equivivalet to a F-SO Si MOSF ecture 7, High Speed evice 04 0
11 t b? - Semicoductor (Quatum) Capacitace Ordiary parallell-plate capacitor C ox = ε t b MOS capacitor C ox = ε t b + Δt b riagular well eed umerical approximatio, t b ~68Å or GaA, 0 ~ e MM Capacitor: C ox Semicoductor quatum well C q q q q C ox C q here mut be a voltage drop over the oxide ad the emicoductor! ecture 7, High Speed evice 04
12 HM Structure Calculatio Source g rai S Wide badgap N d Wide badgap itriic Small badgap, triagular or quare well Wide badgap, S. or itriic Charge (cm - ) x=0 x= x otal potetial dierece over wide badgap regio: ( g - )- chael (x) q ch x, t C v ( t) v ( x, t) ox c x hi i the ame udametal equatio a or a ordiary MOSF! ecture 7, High Speed evice 04
13 HM o-curret drit oly q ch t x, t v ( t) v ( x, t) t b C ox b c B 00 qn d, c q 0 t d b 00 0, at WCox dx WCox WCox, at c c ( ) (0) 0 S S S, at S S c S Writte uig aturatio idex d c S S S, at S, at S, at S, at og chael curret aturate whe q ch ()=0 S, at ecture, High Speed evice 03 3 Curret (ma) g - = g - =.33 g - = oltage ()
14 Chael potetial - C u U ch ch ( x, t) v ( t) x u ( x, t) ch v c ( x, t) U U CH CH 0 U CH 0 WCox x U CH xu WC U 0U CH ox CH CH Aumig drit oly imple aalytical expreio or q ch ad ch i obtaied! U CH x x U 0 CH q ch ch x, t CoxU ch x U ch x x x We will ue thi exteively or the AC-aalyi o the HM ecture 7, High Speed evice 04 4
15 rit elocity (/cm) Short Chael ect elocity Saturatio g m WCox High g m : ecreae! ε x = U CH 0 α x α Chael lectric Field (x)> c! lectro velocity doe ot icreae. at ery importat correctio or moder device. peak ~ 4x0 3 /cm ecture 7, High Speed evice 04 5
16 elocity Saturatio Short chael traitor ( g < µm) Moder F g =6-50 m => c Aalytical modelig tart to become tricky v d = μ ε No velocity aturatio uphyical or g < µm! + ε ε c WC ox S S d = WC ox μ + S ε c S S riode Regio S, at S,at = + + ε c Saturatio oltage, at WCox 0 d WC ox ε c μ = WC ox v at ecture 7, High Speed evice 04 6
17 elocity Saturatio Curret (ma) 0 0 Curret at aturatio Gate egth (µm) WC ox v at v d = μ ε + ε ε c S = - = W = µm C ox = µf/cm c = 4k/cm µ =0000 cm / For gate legth below ~ µm velocity aturatio i very importat! For very hort gate-legth quai-ballitic traport! ecture 7, High Speed evice 03 7
18 Chael egth Modulatio elocity aturario occur approximately whe =du/dx> at d = d,at v drit v at ε x = U CH 0 α x α (x) < crit S 3 at -ield WCox S, at S, at S q ch (x) q ch (x) = at at x= q ch (x) ow-ield elocity aturatio x x = at at x= ecture 7, High Speed evice 04 8 x
19 Chael egth Modulatio S 3 g d = d S d S Chael egth modulatio caue output coductace! electrotatic eect alo give a imilar S ery mportat or hort chael F! WCox ( d ) S, at S, at Moder HM with g =30-50 m Sig o velocity aturatio: S almot idepedet o g S ~ - g m /g d ~ 5-50 However thee device are quai ballitic ecture 7, High Speed evice 04 9
20 rai Source MSF / HM Breakdow mpact oizatio c v uelig caue large gate leakage ateral F breakdow i due to high ield i the gate-drai regio. he high ield caue impact ioizatio / tuelig breakdow. hi limit the maximum S o the device Scale with bad gap ( g,chael & g,barrier ) dg = d - g ecture 7, High Speed evice 04 0
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