Solid State Device Fundamentals 4.4. Field Effect Transistor (MOSFET) ENS 463 Lecture Course by Alexander M. Zaitsev alexander.zaitsev@csi.cuny.edu Tel: 718 982 2812 4N101b 1
Field-effect transistor (FET) Field effect devices are those in which current is controlled by external electric field, rather than via carrier injection. Field effect transistor is a metal-insulator-semiconductor capacitor, in which the charge induced in semiconductor is used for output current. 2
Principle of FET FETs are unipolar transistors. The term refers to the fact that current is transported by carriers of one polarity (majority), whereas in the conventional bipolar transistor the carriers of both polarities (majority and minority) are involved. The most common type of FET is MOSFET, the internal structure of which is that of Metal-Oxide-Semiconductor capacitor. 3
JFET and MOSFET JFET Junction Field Effect Transistor MOSFET - Metal Oxide Semiconductor Field Effect Transistor t ox L W L=0.1-10mm, W=0.5-500mm t ox =0.001-0.1mm 4
Fabrication of MOSFET Deposition of insulator Formation of gate insulator Deposition of metal (polysilicon) Formation of gate Doping of source and drain 5
Device operation V t = V + ± fb en 2ε 2φ sub s B 2 φb ± = Cox t ox en sub ε ox 2ε 2φ s B 6
Low drain voltage 7
Saturation region 8
V Channel depth versus drain voltage V SG V ch VSD V t x 9
Current-voltage characteristics 10
Current-voltage characteristics 11
Output characteristics 12
Input (transfer) characteristic Transconductance g m = di ds / dv gs g msat W = Coxeµ ml ns ( Vgs Vt ) 13
Homework: I-V characteristics Figures below show I-V characteristics of two NMOSFETs with t ox = 10 nm, W = 10 μm, and L = 2 μm. Assume m = 1. (a) Estimate V t from the plots. (b) Estimate μ ns in the inversion layer. (c) Add the I d V sd curve corresponding to V gs = 3 V to the plot. (d) Find transconductance for these transistors. 14
Channel length modulation 15
Early voltage and output resistance 16
Homework: Effective channel length The total resistance across the source and drain contacts of a MOSFET is (R s + R d + R channel ), where R s and R d are source and drain series resistances, respectively, and R channel is the channel resistance. Assume that V ds is very small in this problem. (a) Write down an expression for R channel, which depends on V gs (Hint: R channel = Vds/Ids). (c) Given t ox = 3 nm, W/L = 1/0.1 μm, V gs = 1.5V and V t = 0.4 V, what is I dsat for R s,d = 0, 100, and 1,000 Ω? 17
Body effect So far, the voltage on the source has been assumed to be equal to that on the body. However, it is not the case for FETs in integrated circuits. The voltage between source and body, V sb, changes V t. The fact that V t is a function of the body bias is called the body effect. For some transistors, the source body junctions are reversed biased. This raises their V t and reduces I ds and the circuit speed. Circuits therefore perform best when V t is as insensitive to V sb as possible, i.e., the body effect should be minimized. V BS =0 V BS <0 18
Inversion layer charge and the body effect C dep = ε s W d max Q = C ( V V ) + C V ( )] inv ox gs t dep sb = C dep ox[ Vgs Vt Vsb Cox C + 19
Threshold voltage and the body effect Due to body effect V t is a function of V sb. When the source-body junction is reverse-biased, V t increases: V Body effect coefficient a : a = C dep /C ox = 3t ox / W dep t ( V sb dep = Vt 0 + Vsb = Vt 0 Cox m = 1 + a = 1 + 3t ox / W dmax m is called the body-effect factor, or bulk-charge factor m + αv Body effect adds capacitance and slows down operation of FET ) = dmax C 1+ 3t oxe / W 1.2 sb 20
Uniform body doping Reverse bias widens the depletion region and reduces channel depth. This can be modeled as changing threshold voltage. When the source/body junction is reverse-biased, there are two quasi-fermi levels (E fn and E fp ) which are separated by ev sb. An NMOSFET reaches threshold of inversion when E c is close to E fn, not E fp. This requires the bandbending to be 2φ B + V sb, not 2φ B. V t = V t0 + en C a ox 2ε s ( 2φ B + V sb 2φ B ) V t0 + γ ( 2φ B + V sb 2φ B ) ϒ is the body-effect parameter (fabrication-process parameter). 21
Homework: Body effect P-channel MOSFET with heavily doped p-type poly-si gate has a threshold voltage of 1.5 V with V sb = 0 V. When a 5 V reverse bias is applied to the substrate, the threshold voltage changes to 2.3 V. (a) What is the dopant concentration in the substrate if the oxide thickness is 100 nm? (b) What is the threshold voltage if V sb is 2.5 V? 22
FET Summary I = µ C d s ox W L V V V 1 V 2 2 ( gs t ) ds ds IV characteristics can be divided into a linear region and a saturation region. I d saturates at V I dsat dsat = = V gs V t m W C 2mL ox µ ( V s gs V t 2 ) Transconductance g msat W = Coxµ ml V V s ( gs t ) 23