JFETs, MESFETs, and MODFETs 2013.01.26 SD Lab. SOGANG Univ. Gil Yong Song

Contents 1. JFET and MESFET 2. MODFET I-V characteristics Microwave performance Device structures 2. MODFET Equivalent circuit and microwave performance

JFET and MESFET I-V characteristics - two ohmic conatct : source, drain - positive 𝑉 𝐷 : electrons flow from source to drain - gate controls the net opening of the channel by varying the depletion width. - JFET : p-n junction, MESFET : Schottky junction - voltage controlled register - depletion mode : normally on with 𝑉 𝐺 =0, 𝑉 𝑇 is negative. - channel current increases with the drain voltage → saturate - assumption : uniform channel doping gradual-channel approximation abrupt depletion layer negligible gate current L : channel length a : channel depth 𝑊 𝐷 : depletion depth b : net channel opening

JFET and MESFET Channel-charge distribution - The depletion width 𝑊 𝐷 varies along the channel(x-direction) - By using Poisson’s equation, - one-sided abrupt-junction, - built-in potential for JFET is, for MESFET,

JFET and MESFET Channel-charge distribution - Potential difference between source and drain in neutral channel - The depletion width at the source and drain ends : - When , 𝑊 𝐷𝑠 =0 (flat band). The maximum value of 𝑊 𝐷𝑑 is equal to a (pinch off potential) - Current : - Current saturation mechanism 1. long channel(channel pinch off) : mobility is constant 2. short channel : At high field, mobility is no longer constant

JFET and MESFET Constant mobility - is assumed to hold without limit. Then, where - In the linear region, 𝑉 𝐷 ≪ 𝑉 𝐺 𝑎𝑛𝑑 𝑉 𝐷 ≪ - For more simple equation around 𝑉 𝐺 = 𝑉 𝑇 with - For non-linear condition(when drain bias continues to increase), 𝑉 𝐷𝑠𝑎𝑡 = 𝑉 𝐺 − 𝑉 𝑇 pinch-off condition when 𝑊 𝐷𝑑 =𝑎

JFET and MESFET Constant mobility - transconductance is given by - For drain bias higher than 𝑉 𝐷𝑠𝑎𝑡 , the pinch-off starts to migrate toward the source. However, potential remains 𝑉 𝐷𝑠𝑎𝑡 independent of 𝑉 𝐷 . Thus field remains constant too. - Practical devices show that 𝐼 𝐷𝑠𝑎𝑡 doesn’t saturate with 𝑉 𝐷 due to the reduction in the effective channel length. - 𝐼 𝐷𝑠𝑎𝑡 , 𝑔 𝑚 can be simplified to be(when 𝑉 𝐺 = 𝑉 𝑇 )

JFET and MESFET Long channel Velocity-Field Relationship - Long channel device : constant mobility - Short channel device : At higher fields, the carrier velocity saturates to a value called saturation velocity 𝑣 𝑠 . Field dependent Mobility : Two-Piece Linear Approximation - constant mobility (maximum field reaches critical field) - current saturates as 𝑉 𝐷 approaches Long channel Long channel과 short channel 길이에 대한 기준은 책에 안나와있음

JFET and MESFET Empirical formula Field-Dependent Mobility : Empirical Formula - current is reduced by a factor of from that of constant mobility model. - In order to obtain 𝑉 𝐷𝑠𝑎𝑡 , we set 𝑑 𝐼 𝐷 𝑑 𝑉 𝐷 =0, the transcendental equation for 𝑉 𝐷𝑠𝑎𝑡 as - saturation current(transcendental equation into 𝐼 𝐷 ) Empirical formula

JFET and MESFET Velocity Saturation - velocity saturation model : short gates where - transferred-electron effect - ballistic effect (a) constant mobility model (b) velocity saturation

JFET and MESFET Dipole-Layer Formation - Before the saturation drain bias 𝑉 𝐷𝑠𝑎𝑡 , the potential along the channel is increases from 0(source) to 𝑉 𝐷 (drain) → depletion width becomes wider and channel width decreases. - fig 8(a) 𝑉 𝐷 = 𝑉 𝐷𝑠𝑎𝑡 - fig 8(b) 𝑉 𝐷 > 𝑉 𝐷𝑠𝑎𝑡 𝑥 1 ~ 𝑥 2 : channel width decreases as depletion region increases 𝑛> 𝑁 𝐷 𝑥 2 ~ : negative charge changes to positive space charge 𝑛< 𝑁 𝐷

JFET and MESFET Breakdown - As the drain voltage increases further, breakdown occurs. - The fundamental mechanism of breakdown : impact ionization - one dimension, treating the gate-drain structure as reverse-biased diode, the drain breakdown voltage 𝑉 𝐷𝐵 is 𝑉 𝐷𝐵 = 𝑉 𝐵 − 𝑉 𝐺 - fig 9(a) : for higher 𝑉 𝐺 , the drain breakdown voltage becomes higher. → Bur for MESFETS on GaAs, the breakdown mechanisms are changed. - MESFETs have a gap between the gate and the source/drain contacts. In gate-drain distance 𝐿 𝐺𝐷 region, the doping level is the same as the channel. → surface effect could be occurred and affect the field distribution. - tunneling current associated with the Schottky-barrier gate contact. Surface potential created by surface traps.

Microwave Performance Small-Signal Equivalent circuit - total gate-channel capacitance : 𝐶 𝐺𝑆 ′ + 𝐶 𝐺𝐷 ′ - channel resistance : 𝑅 𝑐ℎ - series resistance(source,drain,gate) : 𝑅 𝑆 , 𝑅 𝐷 , 𝑅 𝐺 - parasitic input capacitance : 𝐶 𝑝𝑎𝑟 ′ - output capacitance : 𝐶 𝐷𝑆 ′ - leakage current in the gate-to-channel junction : - Input resistance : - In the linear region, effective 𝑉 𝐺 , 𝑉 𝐷 are 𝑉 𝐺 − 𝐼 𝐷 𝑅 𝑆 + 𝑅 𝐷 , 𝑉 𝐷 − 𝐼 𝐷 𝑅 𝑆 - In saturation region, measured extrinsic transconductance is equal to

Microwave Performance Cutoff Frequency - For a measure of the high-speed capability, 𝑓 𝑇 is used. - 𝑓 𝑇 is defined as the frequency of unity gain, - total input capacitance 𝐶 𝑖𝑛 ′ = C G ′ + C par ′ - for ideal case of zero input capacitance, → L/v : the transit time for a carrier to travel from source to drain. - more complete equation containing series components, - Geometry affects the cutoff frequency. Decreasing gate length(L) will decrease gate capacitance and increase transconductance. consequently, f T increases 𝐶 𝐺 ′ ∝𝑍×𝐿;

Microwave Performance Maximum Frequency of Oscillation. - for measure of the high-speed capability, 𝑓 𝑚𝑎𝑥 is used. - definition : maximum frequency at which the device can provide power gain. - To maximize 𝑓 𝑚𝑎𝑥 , 𝑓 𝑇 must be optimized in the intrinsic FET and 𝑅 𝐺 , 𝑅 𝑆 𝑎𝑛𝑑 𝐶 𝐺𝐷 ′ must be minimized. Power-Frequency Limitations - For power applications, both high voltage and high current are required. - For high current, the total channel dose has to be high. - For high BV, doping level cannot to be high and L cannot be small. - For a high 𝑓 𝑇 , L has to be minimized and as a consequence, 𝑁 𝐷 has to increase. - - In high power operation, the device temperature increases → reduction of the mobility(∝1/ 𝑇 2 ), saturation velocity(∝1/𝑇). 마지막식 설명 : channel을 지나는 전류를 조절하려면 gate length가 channel depth보다 어느정도커야 한다.L이 줄면 a도 줄어야 하는데, 이는 doping level을 높여서 전류를 유지해야 함을 의미한다

Microwave Performance Noise Behavior - MESFET, JFET : low-noise devices (only majority carriers participate in their operations) - In practical devices, parasitic resistances are responsible for the noise behavior. - 𝑖 𝑛𝑔 𝑖𝑛𝑑𝑢𝑐𝑒𝑑 𝑔𝑎𝑡𝑒 𝑛𝑜𝑖𝑠𝑒 , 𝑖 𝑛𝑑 𝑖𝑛𝑑𝑢𝑐𝑒𝑑 𝑑𝑟𝑎𝑖𝑛 𝑛𝑜𝑖𝑠𝑒 , 𝑒 𝑛𝑔 𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝑛𝑜𝑖𝑠𝑒𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑔𝑎𝑡𝑒 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 , 𝑒 𝑛𝑠 (𝑡ℎ𝑒𝑟𝑚𝑎𝑙 𝑛𝑜𝑖𝑠𝑒 𝑜𝑓 𝑠𝑜𝑢𝑟𝑐𝑒 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒) - The noise figure is defined as the ratio of the total noise power to the noise power generated from the source impedance. - minimum noise figure : - For low-noise performance, parasitic gate resistance and source resistance should be minimized. 마지막식 설명 : channel을 지나는 전류를 조절하려면 gate length가 channel depth보다 어느정도커야 한다.L이 줄면 a도 줄어야 하는데, 이는 doping level을 높여서 전류를 유지해야 함을 의미한다

Microwave Performance Device Structures - semiinsulating(SI) substrate : for compound semiconductors such as GaAs. - Fig 16(a) : Ion-implanted planar structure (1) self aligned process : the gate is formed first, and the source/drain ion implantation is self-alinged to the gate. (2) ohmic-priority : source/drain implantation and anneal are done before the gate formation - Fig 16(b) : recessed-channel structure. buffer layer : to eliminate defects duplicating from the SI substrate n+ layer : to reduce the source and drain contact resistance n+ layer is selectively removed for gate formation. advantage : surface is further away from the n-channel so that surface effects are minimized - T-gate shorter dimension of bottom : to optimize 𝑓 𝑇 and 𝑔 𝑚 wider dimension of top : to reduce the gate resistance cutoff frequency : L이 짧을수록 커지기 때문에 좋다!!

MODFET lattice scattering Modulated-doped field-effect transistor (also known as HEMT (high-electron mobility transistor)) Hetero structure : wide band gap material is doped and carriers diffuse to the undoped narrow bandgap layer at which heterointerface the channel is formed. channel carreirs in the undoped heterointerface are spatially separated from the doped region and have high mobilities because there is no impurity scattering. The main advantage of modulation doping is the superior mobility. (no scattering) - electron gas. lattice scattering Impurity scattering

MODFET Basic device structure - AlGaAs/GaAs heterointerface. - barrier layer AlGaAs under the gate is doped - channel layer GaAs is undoped - principle of modulation doping : Carriers from the doped barrier layer are transferred to reside at the heterointerface and are away from the doped region to avoid impurity scattering. I-V Characteristics - The impurities within the barrier layer are ionized and carriers depleted away. - potential variation within the depletion region : - For uniform doping profile,

MODFET Threshold voltage : when the 𝐸 𝐹 at the GaAs surface coincide with the conduction-band edge 𝐸 𝐶 . By choosing the doping profile and , 𝑉 𝑇 can be varied. With gate voltage larger than the threshold voltage, charge sheet in the channel is given by The channel has a variable potential with distance, Channel current is constant through out the channel,

MODFET → Constant mobility - drift velocity : - - In the linear region where 𝑉 𝐷 ≪ 𝑉 𝐺 − 𝑉 𝑇 , - At high 𝑉 𝐷 , pinch off is occurred and current saturates with 𝑉 𝐷 . saturation drain bias is ,then - transconductance :

MODFET → Field-Dependent mobility - current becomes saturated with 𝑉 𝐷 before the pinch-off occurs, due to the fact that carrier drift velocity no longer is linearly proportional to the electric field. In high fields, the mobility becomes field dependent. → Velocity Saturation - In the case of short-channel devices, velocity saturation is approached and simpler equations can be used.

MODFET Equivalent circuit and microwave performance - From the equivalent circuit, in the presence of parasitic source resistance, the extrinsic transconductance is degraded by - cutoff frequency 𝑓 𝑇 , maximum frequency 𝑓 𝑀𝑎𝑥 : - minimum noise figure : - Since gate-channel capacitance 𝐶 𝐺𝑆 ∝𝐿, shorter channels have better noise performance. - mobility : MODFET>MESFET so, speed : MODFET>MESFET

MODFET - Right side : identical(same amount of channel charge) Left side : 1. the threshold voltage of the MODFET is lowered 2. the built-in potential within the barrier layer increases the total barrier for carrier confinement. The higher barrier enables a higher gate bias before excessive gate current takes place.