Typical example of the FET: MEtal Semiconductor FET (MESFET) Conducting channel (RED) is made of highly doped material. The electron concentration in the channel n = the donor impurity concentration N D
Fundamental performance limitations in FETs Any type of FET using channel doping to provide high channel currents suffers from transconductance/speed of response degradation Doping increases n S and channel current increase Electron mobility and velocity decrease g m and f T increase slowly or decrease
Heterostructure FET (HFET) concept: Band diagram of AlGaAs GaAs junction The bandgap of AlGaAs is larger than that of GaAs. Free electrons in AlGaAs have higher energy than in GaAs In Type I heterostructures, illustrated in the Figure above, the band gap of one material overlaps that of the other and the potential discontinuities for the conduction band, Ec, and for the valence band, Ev, may be expressed as, Ec = Ec1 Ec = f (Eg1 Eg) = f Eg, Ev = Ev1 Ev = (1 f )(Eg1 Eg) = (1 f ) Eg,
Heterostructure FET (HFET) concept: Formation of D electron gas at the heterojunction Positive charge ionized donors Negative charge of electrons induced by modulation doping Energy + + + + + AlGaAs GaAs + + + + AlGaAs GaAs - - - -
Concentration dependence of electron mobility comparison 3D (bulk electron gas) D electron gas (HFET) No impurity scattering in the D channel high electron mobility
Heterostructure FET (HFET) concept: D electron gas at the AlGaAs/GaAs interface The idea behind the HFET design is to use THIN wide bandgap layer (AlGaAs in this example), which is fully depleted by the electrons transferred into the D layer
The HFET design The channel is formed by doping The channel is formed by D electron gas (DEG) in the UNDOPED material Channel induced channel (DEG) electrons JFET, MOSFET, MESFET HFET
The HFET history The channel of HFETs is formed by D electron gas (DEG) electrons induced channel (DEG) after T.A. Fjeldly, T. Ytterdal and M. Shur, 1998 Undoped active layer Very high N S ; very high µ; very high v S (in sub-µ HFETs) 1960 - Accumulation layer prediction (Anderson) 1969 - Enhanced mobility of DEG prediction (Esaki & Tsu) 1978 Enhanced mobility observed (Dingle et. al.) 1980 The first Heterojunction FET (HFET) 1991 The first GaN based HFET (A. Khan)
The D channel formation in HFETs All the electrons are frozen
The D electron gas formation at the AlGaAs/GaAs interface Electrons are allowed to diffuse
The D electron concentration control by the bias: N + - p heterojunction example
The HFET basics qv N Potential energy balance equation: E f E f E f qv G + qϕ B = E C + qv N qv G = qϕ B E C qv N + E f Band diagram V G = ϕ B E q C V N + E q f D electron gas exists if the last term is >0
HFET threshold voltage V G = ϕ B E q C V N + E q f where V N = qnd d ε i i When n s is close to zero, the Fermi level in the GaAs is close to the bottom of the conductance band. Therefore, qn d V d i T φb Ec / q ε i For non-uniform doping profile, For the delta-doped barrier layer, V N = q d i 0 N d (x) ε i (x) xdx V T φ b qn δ d δ / ε i E c / q
The HFET basics HFET I-V characteristics Above the threshold the HFET is similar to MOSFET. n S = (C 1 /q) (V G V T ) = (C 1 /q) V GT Here we defined V GT as the gate bias offset: V GT = V G V T I = q n S v = v C 1 V GT At low drain bias, the electric field in the channel is low and the mobility approximation is valid: v = µ E ~ µ V D /L G Substituting v, we obtain the HFET I-V characteristic at low drain bias: I W C = µ L 1 G V GT V D W is the HFET width
Effect of high drain bias on the HFET I-V Due to the voltage drop along the channel, the channel potential is a function of a distance: V(x). The expression for n S : Must be replaced with n S = (C 1 /q) V GT n S = (C 1 /q) [V GT V(x)] The drain current: I d = Wµ n qn s F = Wµ n c i ( V GT V) dv dx The solution of this differential equation: I d = Wµ nc i L [ V GT V DS V DS / ], forv DS V SAT /, forvds > V SAT V GT where V SAT = V GT
HFET transconductance The transconductance, g m = di d dv GS V DS The expression of g m can be obtained from the I D V G dependence I d = Wµ nc i L [ V GT V DS V DS / ], forv DS V SAT /, forvds > V SAT V GT g m = βv DS, for V DS V SAT βv GT, for V DS > V SAT where β = Wµ n c i /L is called the transconductance parameter.
Velocity saturation in HFETs A two-piece model is a simple, first approximation to a realistic velocity-field relationship: vf ( ) = µf, F < F s v s, F F s More realistic velocity-field relationships : vf ( ) = µf [ 1+ ( µf / v s ) m ] 1/m 1. 0.8 0.4 m = m = m = 1 where m = 1. 0.0 0 1 Normalized Field 3
Velocity saturation in HFETs The I-V characteristics in a mobility approximation can be modified to account for the velocity saturation by introducing the characteristic velocity saturation voltage V L V L = F s L, where F S is the characteristic field for velocity saturation I d = Wµ nc i L V GT V DS V [ DS / ], for V DS V SAT V L 1 + ( V GT V L ) 1, for V DS > V SAT V SAT = V GT V L ( ) 1 1+ V GT / V L Compare to the long-gate I-Vs: I d = Wµ nc i L [ V GT V DS V DS / ], forv DS V SAT /, forvds > V SAT V GT
Velocity saturation in HFETs This approximation describes both the long gate (mobility limit) and the short gate (velocity saturation limit) cases. For long gate devices, V L = F s L >> V GT at any gate voltage. The maximum value of V GT is V T (when the gate voltage is zero) For V L >> V GT, (V GT /V L ) << 1 and the saturation voltage V becomes: V SAT = V GT V L ( ) 1 1+ V GT / V L For x << 1, ( 1+ x) 1+ x VGT The expression for I D transforms into: I d = Wµ nc i L [ V GT V DS V DS / ], forv DS V SAT /, forvds > V SAT V GT
Velocity saturation in HFETs In the opposite limit, when V L << V GT, we obtain V SAT = V GT V L ( ) 1 1+ V GT / V L VL The expression for the I D transforms into: I d = Wµ nc i L [ V GT V DS V DS / ], forv DS V SAT V GT L V GT /, forvds > V SAT