Chapter 17. MOSFETs An Introduction Sung June Kim kimsj@snu.ac.kr http://helios.snu.ac.kr
CONTENTS Qualitative Theory of Operation Quantitative I Relationships Subthreshold Swing ac Response
Qualitative Theory of Operation Assumption Ideal Structure Long Channel EnhancementMode MOSFET=MOSCapacitor + 2 pn junctions n channel (ptype substrate)
= 0 Case When T, very few electrons in the channel. an open circuit between the n+ region When > T, Inversion layer is formed The conducting channel (induced ntype region, inversion layer) connects the & S the pile up of electrons conductance \ determines the maximum conductance Thermal equilibrium prevails, and I =0
The is increased in small steps starting from = 0 The channel acts like a simple resistor I µ The reverse bias junction current is negligible voltage drop from the drain to the source starts to negate the inverting effect of the gate epletion of the channel # of carriers conductance slopeover in the I
Pinch off ( = sat ) isappearance of the channel adjacent to the drain The slope of the I becomes approximately zero(point B)
Postpinchoff ( > sat ) The pinchedoff portion widens from just a point into a depleted channel section L The pinchedoff section absorbs most of the voltage drop in excess of sat For L << L, the shape of the conducting region and the potential across the region do not change Constant I For L ~ L, I will increase with > sat
eneral form of the I (L << L ) For T, I» 0 For > T, transistor action: I is modulated by > sat : saturation region < sat : linear(triode) region I Characteristics sat increases with The slope increases with
Quantitative I Relationships Effective Mobility : Impurity Scattering + Lattice Scattering + Surface Scattering
Effective Mobility m = n ò ( y ) xc 0 mn xc(y) ò0 (x,y)n(x,y)dx n(x,y)dx
more carriers closer to the interface higher electric field surface scattering m n
Square Law Theory < sat Q N A drift current is dominant (y) @ C o ( Q gate T = Q QN @ Co ( T At an arbitrary point y f ) semi I @ Q = WQ = Wm C n ) N (y) m E(y) o N ( n T df f ) dy
Integrating ú û ù ê ë é = 2 ) ( 2 T o n L C W I m f m ò f ò = T o L n d C W dy I 0 0 ) (
³ sat I is approximately constant ( ) 2 2 2 0 ) ( ) ( 2 ) ( T o n sat T sat sat T o N sat sat T o n sat L C W I C L Q L C W I = = = = ú û ù ê ë é = m m
Subthreshold transfer characteristics At weak inversion, diffusion current dominates I» I diff where where µ Q Q Q S Q L Q µ L S é ê 1 exp( ë q kt æ q ö =QS expç è kt ø is exponential function S In long channel MOSFETS the subthreshold current varies exponentially with and is independent of provided > a few kt/q of ù ) ú û
10 6 rain Current [A] 10 7 10 8 10 9 10 10 10 11 slope = 10 12 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 ate oltage [] 1 S t Subthreshold swing S t = 1 d log I d = change for [ m/dec] in a decade change in I
17.3 a.c. Response(skip) C gs (C gd ): The interaction between and the channel charge near S() C gsp,c gdp : parasitic or overlap capacitances
Smallsignal equivalent circuit S in MOSFET out S + + v g g m v gs g d v d S S
C gd + + C gs v g g m v gs g d v d S S A capacitor behaves like an open circuit at low frequencies.
I (, ) + i d = I ( + v d, +v g ) i d = I ( + v d, +v g ) I (, ) ( ) ( ) g d d g d g d v I v I i v I v I I v v I + = \ + + = + +,, ce conduc mutual ce or transconduc I g ce conduc channel drain or the I g t cons m t cons d tan tan tan tan tan L L = = = =
\ i = g v + d d d g m v g + i d + v g g m v gs g d v d S S
Table 17.1 Below pinchoff ( sat ) Above pinchoff ( > sat ) Z nco gd = m ( T ) L g d = 0 g m Z m C L Z C = m L n O n O = g ( ) m T
At the higher operational frequencies encountered in practical applications, the circuit must be modified to take into account capacitive coupling between the device terminals. The overlap capacitance is minimized by forming a thicker oxide in the overlap region or preferably through the use of self aligned gate procedures. è C gd is typically negligible. C gd + + C gs v g g m v gs g d v d S S
17.3.2. Cutoff Frequency The f T be defined as the frequency where the MOSFET is no longer amplifying the input signal under optimum conditions. à alue of the output current to input current ratio is unity i i in out i \ out = f» T i jw( C g in = m v g = 1 gs gm 2pC o + C = gd ) v mn 2pL g 2 @ j(2pf ) C if o v g sat
g d vs. ( =0) Small Signal Characteristics Extrapolating the linear portion of the g d characteristics into the axis and equating the voltage intercept to T educe the effective mobility from the slope WmnCo gd= (T ) (= 0) L
ate Capacitance vs. ( =0) iagnostic purposes in much the same manner as the MOSC C characteristics Unlike the MOSC, a lowfrequency characteristics is observed even for frequencies exceeding 1MHz Because the source and drain islands supply the minority carries