Uversty of Clfor t Berkeley College of Egeerg et. of Electrcl Egeerg Comuter Sceces EE 5 Mterm I Srg 6 Prof. Mg C. u Feb. 3, 6 Gueles Close book otes. Oe-ge formto sheet llowe. There re some useful formuls the e of the exm. The vlues of commo rmeters re lste t the begg of ext ge.
Plese use the followg rmeters for ll roblems uless secfe otherwse: 55 m, -55 m, th 6 m ε S.7, ε SO 3.9, ε 8.854-4 F/cm, q.6x -9 C, cm -3. () Coser slco P jucto oe wth -og cocetrto of 6 cm -3 P-og cocetrto of 8 cm -3. Ther cross-sectol re of the oe s μm. Assume the reverse sturto curret of the oe s -4 Am. The oe s forwr se t.7. ) [ t] F the ymc resstce t ths s. b) [ t] F the eleto cctce t ths s. () Coser MOS cctor wth P olyslco gte -oe substrte wth og cocetrto of 6 cm -3. The thckess of the oxe s m. ) [ t] F the threshol voltge. b) [ t] hch moe s the MOS cctor whe ts gte s se t? c) [ t] ht s the mxmum cctce er ut re? ) [ t] ht s the mmum cctce er ut re? (3) [ t] For the MOS cctor Problem (), lot the chrge esty strbuto s fucto of osto whe the gte s se t -. Plese be s qutttve s ossble. Show the ostos of ll chrges, show the mgtue olrty of the chrges. (4) [ t] If the P gte of the MOS cctor Problem () s relce by metl whose electrosttc otetl s. ht s the threshol voltge of the ew MOS cctor? (5) Coser -MOSFET wth olyslco gte o P-tye substrte ( 7 cm -3 ). The source s groue, the r s se t 5. The trsstor hs gte legth of μm, wth of μm. The thckess of gte oxe s m. For smlcty, ssume the chel-legth moulto rmeter λ. S G gte P-substrte ) [ t] At wht gte voltge oes the trsstor tur o,.e., strt to hve sgfct curret flowg betwee source r? b) [ t] F the r curret whe the gte s se t.
3 Some equtos Mss-cto lw ) ( T Resstvty: Resstce: Totl curret (e - ): Guss s lw: eleto lyer: eleto lyer cctce: ffuso curret kt qv ff e q kt qv S e I ffuso cctce: τ kt qi C eff q, μ σ ρ ρ ρ R t t R sq x q E q ff rft μ ε Q S E C Q x E ε s q x x X X X ) ( j j C x q C
Threshol voltge (MOS) T FB qεs Cox γ T T ( ) ( ) SB kt l q MOS equtos: I, < μc μc ox ox v T T v S v S ( v ) ( λ ), T S ( λ ), S > T, S > T, S < > T T MOS cctces sturto C C C gs ( / 3) Cox Cov ov ox MOS sgl rmeters: gm μcox v T λ, S ( )( ) μc ( ) S ox T r o v S, S λi S gmb v BS Q γgm BS 4
EE 5 Mterm- Soluto Prof. Mg C. u Srg 6 q :.6 9 : th :.6 ε : 8.854 4 εs :.7 ε εox : 3.9 ε μm: 4 m : 7 m : 3 μ_ : 45 cm /-sec () () Is : 4 I( ) : Is ex th I(.7) 4.97 3 th r_ : r_ 5.78 Ω I(.7) (b) : 6 : 8 Are : μm : 6 m log.36 : 6 m log.48 b : b.84 x( ) ( ) εs b : x(.7).353 5 q εs Cj : x(.7) Are 4 Cj 7.656 F () : 6 tox : m () : 6 m log.36 : 55 m _FB : _FB.9 ( ) εs X_mx : X_mx 3.53 5 q Qb_mx : q X_mx εox Cox : tox Qb_mx _T : _FB _T.93 Cox
(b) s greter th fltb voltge --> the MOS s ccumulto moe (c) Mxmum cctce s smly Cox: Cmx : Cox Cmx.77 7 F/cm () Cb_m : Cm : εs X_mx Cox Cb_m Cox Cb_m Cm.835 8 F/cm (3) - s more egtve th threshol (-.93), so t s verso. The chrge o the semcouctor se clue fxe oor chrges from the semcouctor-oxe terfce to the mxmum eleto wth, X_mx the verso hole chrges t the terfce, Q. The gte chrge s equl to the totl chrge wth ooste sg. _GB : Q : Cox ( _GB _T) ρ_b : q Qg : Q ρ_b X_mx X_mx 3.53 5 Q 3.93 7 ρ_b.6 3 Qg 3.78 7 C/cm^ C/cm^3 C/cm^ Chrge esty 3.9x -7 C/cm.6x -3 C/cm 3 t ox Posto, x X,mx 3x -5 cm -3.78x -7 C/cm (4) Fltb voltge threshol voltge s shfte by the sme mout: m: _FB_m : m Δ_FB : _FB_m _FB _T_m : _T Δ_FB _FB_m.36 Δ_FB.55 _T_m.643
(5) : 7 tox : m : μm : μm : 6 m log : 55 m.4 _FB : εs X_mx : q Qb_mx : q X_mx εox Cox : tox Qb_mx _T : _FB Cox () The MOS FET s ture o whe the gte voltge s equl to the thresol voltge _T.353 ( ) _FB.97 X_mx.43 5 _T.353 (b) _ : _S : 5 _S_st : T Sce _S s greter th _S_st, the FET s sturto I_S( ) μ_ Cox : ( T) _S_st.647 I_S( 5) 6.789 3 Am