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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><1019)(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 VgVT 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 voltagesquared 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 nchanne device. Also, at point (1) the MOSFET is biased below saturation. Thus the channel
narrows near the drain but is not pinchedoff. inversion layer
(rtchannel) .
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 pinchoff point. At the pinchoff point, and based
on the squarelaw 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 = VGVT. 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 pinchoff 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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 Fall '07
 HAMBLEN
 Vmblam

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