Parametric Instability of Mobile Elastic Gate in Tera- and Nano-

High Electron Mobility Transistor

V.L. Semenenko, V.G. Leiman, A.V. Arsenin,

A.D. Gladun and V.I Ryzhii

Outline

• Introduction• Modulated THz radiation detector• Reduction the model to the capacitance transducer equations• Calculation for the threshold signal amplitude and power

Motivation

Expected roadmap for some THz applications, 2007*)

* Masayoshi Tonouchi, “Cutting-edge terahertz technology”, Nature Photonics 1, 97 - 105 (2007)

Mod

ulat

ed T

Hz

radi

ation

de

tect

ors

are

requ

ired

The first resonant gate transistor

H. C. Nathanson, W. E. Newell, R. A. Wickstorm, and J. R. Davis, IEEE Trans. Electron Devices 14, 117, 1967.

Recent modulated THz detectors

V. Ryzhii, M. Ryzhii, Y. Hu, et al., Appl. Phys. Lett. 90, 203503 (2007).

V. G. Leiman, et al., J. Appl. Phys. 104, 024514 (2008).

Parametric instability in capacitance transducer

2 2

1 12

2 2 0

2 =

2 1 = cos ,

22

m m 2S

2 0e e 0

2e e 0

0

2

1 cos ,

1, , .

4

qx x x

S M

x Uq q q t

d L

R SC

L LC d

(0)(0)

m m e e1 1 2 2

03

= , = , = , = ,2

= , = , = , = ,2 2

2

S

S

x q M dt q S

d q

U

SL M d

2 1 1m m S S S S 0

simple analisys:

x x x M F x t M F x x

Dimensionless equations

Calculations for threshold Λ

Device scheme & modelFront view Top view

= 0

= ,xe

u

t xu u e

u u Et x m

/2

/2

1 2

under the conditions:

, = 0,

= .

L

l

L

x t dx t

t

S

where

, ,x t en x t

/2

2 20/2

and

2 , 2Ll

x

L

t t xE d

x z x

0~1 um, ~1 um, ~ 50 nm, ~1 5 nmL l z a

Gate charge field component

Hydrodynamic model of electron transport in 2DEG

Solution of the linearized equations

for the harmonic incoming signal c.c.,2

response of the charge on the gate will be c.c.2

i t

i t

l l

et V

et q

2 20

0

2= , = .S

e

e nQ

m L

/2

2 20/2

/2

1 2

/2

= 0

2 , 2=

under the conditions:

, = 0, = .

S

Ll

e eL

L

l

L

uen

t x

t t xu e eu d

t m x m z x

x t dx t t

lq C V Because of the

linear equations

Characteristic frequency & quality factor of the 2DEG oscillations

Power consumption & linear force acting on the gate

2

src 0= .2lP

2

0

0

= .lF z

Equivalent system of ODEs

22

0

2 2res 0 0 0 0

0

lets try to find the equivalent equations system

in the following form:

2 =

1 = cos ,

m ml

qDM z

q q z A q B tz

2

res

0

= 0

where

2= , .

ln

z z

zd

zA

d L

… As it would be if the device was the

following:

Fitting the parameters C & D

0res res 2 2

2 2res

0 0

,

Q

;

2res res

22 2

2 2res

0 0

,

Q

; res 0

res0

.z

2 resres 2

res

= 2D

resres= ,BQ

Dimensionless equations system

2 22 res res

2res 0

2 2 2res0 res res 0 0 0

0

ODEs system with dimensional paremeters:

2 = 2

= cos .

m ml

q

M z

q q q A tz Q

(0)res 02 (0)

res 0 res

2resm m res 0 res 0 0

1 1 2 2 30

after the following substitution:

= , = , = , = ,2

2= , = , = , = , = ,

2

l

l

A q Mt q z

z q A

A

Q M z

2 2

1 12

2 2 0

we obtain already known equation system:

2 =

2 1 = cos ,

Results & conclusion

3min 00 min 2

res 0 res2lQ z M

A

2minmin 0

res=2lP

* Huttel A.K. et al // Nano Lett., Vol. 9, No. 7, P. 2547, 2009.** Arsenin A.V. et al // J. of Comm. Tech. and Electronics,Vol. 54, No. 11, P. 1319, 2009.

5 *) 40 m 0m

m

we used the following parameters:

~ 1 THz, ~ 10, 100MHz, ~ 10 , 10 ,2 2

material of cantilever: single-wall carbon nanotube.

Q Q

According to our previous work**), in the case of plain metallic cantilever gate: min

0 0.5 1V can be 2-3 orders lower in the case of SWCNT gate

Thank you very muchfor your attention!

Calculation for the values Θres & Ψres