HWS11 - SOiQHQmS 0C H.3on 395;: k. Vmblam & 16.1 ....

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Unformatted text preview: SOiQHQmS 0C H.3on 395;: k. Vmblam & 16.1 . Biasing Pan Doping Con :1“. (a) P depletion (b) n flat band (C) p depl/inv transmon (d) ’1 accumulation (e) p inversion Energy Band Diagam EF Block Charge M Jr? ii. ‘%OHS fiom ‘qa—Erecmns MOS Problf m 2 16.9 (a) . The Fermi level inside the semiconducmr is position independent. (b)... (c)... (d)... (PF = (1/(1)[Ei(bulk) — EF] = 0.3 V abs = (l/q)[Ei(bulk) — Ei(surface)] = «pp = 0.3 V EF(metal) — EF(semi) = —qVG ...Eq. (2.1) VG = (1/q)[EF(semi) — EF(meta1)] = 0.6 V (e) Based on the delta—depletion approximation, 241V A VG = ¢S+E§£Q K580 K0 (pg <2: Eq.(16.28) where from prior parts of the problem VG = 0.6V and (1)5 = 0.3V.~? Also, ¢F = (kT/q) 1n(NA/ni) or NA = “Rem/(kT/q) = (1010)e0.3/0.0259 : 1.073x 1015/Cm3 Thus xO _ VG—¢s = 0.6—0.3 E; ZQNA (p8 (£471)[(2)(1.6><10-19)(1.073><1015)(0.3)]”2 K0 K550 3.9 (11.8)(8.85X10’14) (f) = 0.10um V“f)«eL VWB i€ifl g 16.11 ' Part(a) 1 Part (b) J, No charge anywhere S O S (ii) VG >0 but small ionized donors \ — _ _ — — W acc layer of electrons holes (1h) VG > O and large (inv layer)\ ionized donors WT (iv) VG < 0 but small — (ii) answer with semiconductor regions interchanged. (v) VG < O and large —— (iii) answer with semiconductor regions interchanged. (c) e3 ‘ l7fis5l8rnsL-‘g 17.19 10 M 15 0 ' 5 y . VG -— VT (volts) The above 1]) versus V5~VT characteristics were arrived at as follows: (i) Suppose we systematically increase Vg—VT from zero with VD held constant. Initially VD is greater than Vg-VT and the device is in saturation. (Use is being made of the square- law theory.) Thus initially ZfinCo 1D = IDsat = (VG—VT)2 and we conclude ID varies as the square of Vg—VT if Vg—VT < VD. (ii) When Vg~VT becomes equal to V1), the device moves into the linear region of operation. In the linear region = zinco ID tth—vaD— vii/21 and [D varies linearly with Vg—VT. (iii) With increased VD, one stays on the voltage-squared part of the curve for a longer and longer range of voltages. Once VG—VT > VD, a linear region whose slope increases with increasing VD is observed. 3§mhl€m ( $3439 ET 1 2.2!) (a) Since the applied VD is greater than zero, we infer the given MOSFET is an n-channe device. Also, at point (1) the MOSFET is biased below saturation. Thus the channel narrows near the drain but is not pinched-off. inversion layer (rt-channel) .- o . / Z’depl‘eLion region outline (b) In the squaredaw theory V1351“: Vg—VT. 'l‘hus VG = VDSat+VT = 6V (c) The point (2) bias corresponds to the pinch-off point. At the pinch-off point, and based on the square-law theory, the charge in the MOSFET Channel goes to zero at the drain. QN(L) = 0 (d) With VD = 4v and Vg—VT = 3v, VD > VIM = VG-VT. Consequently, for the readjusted gate voltage, the MOSFET is being operated in the saturation region. Since 113mm (VG—VT)2, it follows that m = (M)2 IDsatZ VGZ—VT Here identifying the desired 1;) = IDsau (Val—VT = 3V) and [135319 = 10‘3A (VGz—VT = 5V) from the given characteristics, we conclude 1D =(10'3)(%)2 = 3.6x10'4 A (6) By definition gd = BID/W1) with VG held constant. Inspecting the given characteristic, we conclude BID/8V1) = O at bias point (3) and gd = 0. Alternatively, in the saturation region of operation, [mat is not a function of VD. Consequently 81133”an = O and gd : 0. (0 At bias point (3) the MOSFET is in the above pinch-off region of operation and from Table 17.1 zfinCO 21D (2)003) . = V~V =~—Sa‘—=——=4x104 L ( G T) VG_VT 5 S gm ...
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HWS11 - SOiQHQmS 0C H.3on 395;: k. Vmblam &amp;amp; 16.1 ....

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