Technische Universität raz Institute of Solid State Physics JFETs - MESFETs - MOFETs
JFET n n-channel JFET S n-channel JFET x n 2 ( Vbi V) en S p-channel JFET 2 Pinch-off at h = x en n h Vp 2 V p = pinch-off voltage At Pinch-off, V = V bi -V p.
The drain is the side of the transistor that gets pinched off. JFET
http://lampx.tugraz.at/~hadley/psd/l9/gradual.php
JFET There is a long derivation to determine how the current depends on V and V. We will find a relatively simple formula (probably familiar to electrical engineers). Understanding the derivation is important for knowing when this formula is valid.
JFET dv I dr I dy Z( h x ( y)) n 1 1 1 ne N e dv I n n dy e N Z( h x ( y)) n n I is constant throughout the transistor I dy e N Z( h x ( y)) dv n n
JFET I dy e N Z( h x ( y)) dv n n V is a forward bias V(y) is a reverse bias. depletion width is a function of position x n 2 ( Vbi V( y) V ) ( y) en differentiate dx ( ) n y dv
JFET I dy e N Z( h x ( y)) dv n n V is a forward bias V(y) is a reverse bias. depletion width is a function of position x n 2 ( Vbi V( y) V ) ( y) en differentiate 1/2 dxn( y) 2 ( V ( ) ) 1 bi V y V 2 2 dv en en enxn( y) dv enx n dx n
JFET I dy e N Z( h x ( y)) dv n n from last slide dv enx n dx n dxn ( y) I dy en ennz( h xn( y)) xn( y) If I is known, this can be solved for x n (y).
JFET I dy e N Z( h x ( y)) dv n n dv enx I dy e N Z( hx ( y)) en xdx n n n n n dx n from a previous slide L xr en n ( n( )) n n 0 x I dy e N Z h x y xdx N Ze I h x x x x 2L 2 2 n R L R L L 2 2 2 3 3 3
JFET N Ze I h x x x x 2L 2 2 n R L R L 2 2 2 3 3 3 h 2Vp en x L 2 ( Vbi V ) en x R 2 ( Vbi V V ) en
JFET - drain current I V 2 Vbi V V 2Vbi V I p Vp 3 V p 3 V p 3/2 3/2 I p nn Ze h 2L 2 2 3 valid in the linear regime (until pinch-off)
JFET - Linear regime I V 2 Vbi V V 2Vbi V I p Vp 3 V p 3 V p 3/2 3/2 In the linear regime V << V sat. di dv
JFET - Linear regime I V 2 Vbi V V 2Vbi V I p Vp 3 V p 3 V p 3/2 3/2 In the linear regime V << V sat. di 1 1 Vbi V V I p dv Vp V p V p I p Vbi V I 1 V for V V Vp Vp sat variable resistor 1/2
JFET - Saturation regime I V 2 Vbi V V 2Vbi V I p Vp 3 V p 3 V p 3/2 3/2 set di /dv = 0 to find V sat 1/2 di 1 1 Vbi V V I p dv Vp V p V p 0 di /dv = 0 when Vbi V V 1 V Vsat Vp Vbi V p Substitute V sat into the equation at the top to find I sat
JFET - Saturation regime Vsat Vp Vbi V I V 2 Vbi V V 2Vbi V I p Vp 3 V p 3 V p 3/2 3/2 I sat 1 Vbi V 2Vbi V I p 3 Vp 3 V p 3/2 No V dependence Voltage controlled current source
JFET - transconductance In the saturation regime, I sat 1 Vbi V 2Vbi V I p 3 Vp 3 V p transconductance (describes how good the voltage controlled current source is) 3/2 g m di I p V V 1 dv V p Vp sat bi g m disat 2ZneN h Vbi V 1 dv L V p
JFET
High frequencies i in 2 fcv i out gmv for gain: i in i out average capacitance: f C gm 2C ZL x n f T f T is the frequency where the gain drops below 1 f T nenh 2 2 L 2
For velocity saturation, the approximation Ohm's law assumes v d = E f T vs L dv I dy Z( h x ( y)) n is not valid
JFET/MESFET JFET: small gate current (reverse leakage of the gate-to-channel junction) More gate leakage than MOSFET, less than bipolar. JFET has higher transconductance than the MOSFET. Used in low-noise, high input-impedance op-amps and sometimes used in switching applications. MESFET: usually constructed in compound semiconductor technologies lacking high quality surface passivation such as aas, InP, or SiC, and are faster but more expensive than silicon-based JFETs or MOSFETs. Production MESFETs are operated up to approximately 30 Hz, and are commonly used for microwave frequency communications and radar. Majority carrier device (like Schottky diode).
MOFET (HEMT) Modulation doped field effect transistor (MOFET) High electron mobility transistor (HEMT) Modulation doped field effect transistor High electron mobility transistor V T = Threshold voltage = voltage where charge is depleted
Heterostructure pn junction formed from two semiconductors with different band gaps
MOFET/HEMT undoped channel HEMT: HEMT devices are found in cell phones, electronic warfare systems, microwave and millimeter wave communications, radar, and radio astronomy. Ph Thesis Sergey Smirnov http://www.iue.tuwien.ac.at/phd/smirnov/node71.html
MOFET (HEMT) j nev ne E d n y I jzt Ze n E n s y t is the thickness of the 2E n s is the sheet charge at the interface in C/cm 2. n n s t V V( y) is the voltage between the gate and the 2E n s = 0 when V V( y) V T gate y 2E q CV en ( y) C V V ( y) V s g T
MOFET (HEMT) en ( y) C V V ( y) V s g B T The charge is zero when V V ( y) V is the charge on the 2E at point y B T solve for n s n s ( y) C V V ( y) V g B T e Substitute this in Ohm's law: I jzt Ze n E n s y
MOFET (HEMT) n s I jzt Ze n E ( y) n s y substitute n s in the top equation and substitute C V V( y) V g T e E y dv ( y) dy I Z C V V V( y) n T dv ( y) dy integrate along the length of the channel L V 0 0 Idy Z C V V V ( y) dv n T 2 Z V L I nc V VT V 2
MOFET (HEMT) 2 Z V n T L I C V V V di dv Z nc V VT V L 2 0 Set the derivative = 0 to find saturation voltage V V V sat T Substitute the saturation voltage into the formula at the top to find saturation current Z I C V V 2L 2 sat n T
MOFET/HEMT HEMT: HEMT devices are found in many types of equipment ranging from cell phones and BS receivers to electronic warfare systems, microwave and millimeter wave communications, radar, and radio astronomy. 600 Hz
an-hemt Source: Oliver Hilt, Bauteile aus an, ET Tagung Bad Nauheim 2011
Quantized conduction R K = h/e 2 = 25812.807557(18) Quantized conductance of point contacts in a two-dimensional electron gas, B. J. van Wees, H. van Houten, C. W. J. Beenakker, J.. Williamson, L. P. Kouwenhoven,. van der Marel, and C. T. Foxon, Phys. Rev. Lett. 60, 848-850 (1988).
Quantized conduction R K = h/e 2 = 25812.807557(18) Formation and Manipulation of a Metallic Wire of Single old Atoms, A. I. Yanson,. Rubio Bollinger, H.E. van den Brom, N. Agraït, J.M. van Ruitenbeek, Nature Oct. 1998.
Quantum Hall Effect Bz xy ne v 1, 2,3 h ve 2 Shubnikov-e Haas oscillations Resistance standard 25812.807557(18)
Technische Universität raz Institute of Solid State Physics MOSFETs functions as a switch ~ 1 billion /chip n - channel p - channel