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

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

3. 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

4. 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,

5. 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

6. 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

7. 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 )

8. 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

9. 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

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

11. 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

12. 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.

13. 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

14. 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;

15. 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

16. 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

17. 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!!

18. 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

19. 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,

20. 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,

21. 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 :

22. 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.

23. 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

24. 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.