12 NDR and Gunn Devices

8/19/2019 12 NDR and Gunn Devices

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11 NDR and Gunn Effect (Transferred Electron) devices

Gunn Diodes represent an example of negative differential resistance (NDR) devices

Why achieving the NDR is so attractive?

NDR Load

Power dissipated in the diode = I2 x R d

< 0

The NDR diode can serve as an amplifier or oscillator

without any external circuits providing a feedback



The NDR can be easily achieved in ANY semiconductor diode

kT

E

cv

G

e N N n 2

−

=

S

L

N N q Bwheree Be

S

L

N N qS

L

qn R

cvkT

E

kT

E

cv

GG

µ µ µ )(

1;

)(

1122 ====

When the current flows through the sample, the sample

temperature increases due to Joule heating

∆T = RT P = RT I .V;

T = T 0 + ∆T = T 0 + RT I .V;

Therefore,

)(2)(22 00 IV RT k

E

T T k

E

kT

E

T

GGG

e Be Be B R +∆+

===

)()(2 00 IV RT IV RT k E

T T

G

e IBe B I IRV ++

===α



The NDR due to a self-heating

0

5000

10000

15000

2000025000

30000

35000

40000

4500050000

0 0. 0001 0 .0002 0. 0003 0 .0004 0.0005 0 .0006

P (a.u.)

R ( a

. u . )

)(2)(22 00 IV RT k E

T T k E

kT

E

T

GGG

e Be Be B R +∆+

===

At low powers the resistance does not depend on the power



)()(2 00 IV RT IV RT k

E

T T

G

e IBe B I IRV ++ ===

α

The NDR due to a self-heating

0

5000

10000

15000

20000

25000

0 0.5 1 1.5 2

IV (a.u.)

R ( a . u . )

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0 10 20 30 40

V (a.u)

I ( a . u . )

At high powers the temperature rise increases the concentration and the resistancedecreases

NDR



0 5 10 15 20 250

0.05

0.1

0.15

0.2

0.25Current - Voltage

Volta e, V

C u r

r e n t , A

t=27 C

Load-line method for electric circuit with NDR

Solution: the

lowest current

after turn on



0 5 10 15 20 250

0.05

0.1

0.15

0.2

0.25

Current - Voltage

Volta e V

C u r r e

n t , A

t=27 Ct=77 C

t=127 C

Thermistor with NDR as a temperature sensitive switch

(Fire Alarm)

Solution at 27 C – very

low current (<1 mA)

Solution at 77 C VERY HIGH

CURRENT – FIRE ALARM!



Gunn Effect (Transferred Electron) NDR devices

First Observation

n-GaAs

+-

J. B. Gunn, 1963

I

V

2 mm

“Noisy” current



11 Gunn Effect (Transferred Electron) devices

First Observation

n-GaAs

+-

J. B. Gunn, 1963

I

V

t

I ~20 ns

2 mm

v = 0.2 cm/20 ns

= 107 cm/s



Ridley-Watkins-Hilsum-Gunn Effect

B.K. Ridley, 1963:“Domain instability should occur in a semiconductor sample with a

negative differential resistance”

0<∂

∂

= F

v

d µ

σd = qnµd < 0

In GaAs, InP and other III-V compounds, the differentialmobility may become negative at high electric fields

So does the differential conductivity:



The negative slope of the v vs. F characteristic develops as a

consequence of the intervalley transition of electrons from thecentral Γ valley of the conduction band into the satellite valleys.

When the electric field is low, electrons are primarily located in the central valley of the

conduction band. As the electric field increases, many electrons gain enough energy

from the electric field for the intervalley transition into the satellite valleys.



The electron effective mass in the L and X valleys of the conduction band is much greater

than in the Γ valley. Also, the intervalley transition is accompanied by an increased

intervalley scattering.These factors result in the decrease of the electron velocity in high electric fields

m2 >> m1

m1





The mechanism of negative differential mobility in GaAs and other III-Vs

We can define an average drift velocity of all the electrons, vs as

or

In order to find the electric field dependence of v, we need to know

the n2(F) dependence



The fraction of electrons in the upper valleys p = n2/no can be approximate as

t S

t S

F F

F F A

p )/(1

)/(

+=

where Fs = vs/µ , A ~ 0.6 and t ~ 4 for GaAs

The exact expressions for GaAs are:



An important results that follows from v(F) dependence:

is that the differential mobility,

becomes NEGATIVE if:

This occurs if the electric field exceeds the critical value FP ~ FS.

For GaAs, FP ~ 3.5 kV/cm



This approximation gives a good agreement with Monte Carlo

simulations and experimental data

µ



Instabilities in the samples with bulk NDR

The negative differential resistance may lead to a growth of smallfluctuations in the space charge in a sample.

A simplified equivalent circuit may be presented as a parallel combination

of the differential resistance

Sqnµd L Rd =

L

Sε

=d C and the differential capacitance:

d d µqN

ε τ == d d d C RThe RC time constant:

This time constant is called the Maxwell differential dielectric relaxation time.

Remember, ε = εε0 here!



Instabilities in the samples with bulk NDR

d d µqN

ε τ == d d d C R

In a material with a positive differential conductivity a space

charge fluctuation, ∆Q, decays exponentially with time:

∆Q = ∆Q(0).exp(-t/τd)

where ∆Q(0) is the magnitude of the fluctuation at t = 0.

When the differential conductivity is negative the space charge

fluctuation may actually grow with time

∆Q = ∆Q(0)exp(t/τd)

Let the a erage field in the sample be greater than F :



2

1

3

4

1. The sample has a fluctuation of electron concentration;

2. This fluctuation leads to an electric field fluctuation:

ε

)(0

nnq

x

F −=∂

∂

3. In the higher-filed region the electrons “slow down”

4. These slow electrons INCREASE the original concentration fluctuation


Let the average field in the sample be greater than FP:



The fluctuation develops in such a way that the accumulation layer remains “behind”

and the “front edge” is depleted with electrons

>

2

1

3

4



At the same time the entire fluctuation drifts towards the positive contact (the anode)

with the velocity of the “slow” electrons, i.e. vs

If the sample is long enough, the fluctuation develops into a “high-field domain”



What time is needed to develop a high-field domain?

d d µqN

ε τ == d d d C R

The characteristic time of the space charge growing is ~ 3τd :

During the time of 3τd the domain travels the distance:

Ltr ~ vs.3τd

This leads to the so-called Kroemer criterion for the Gunn instabilities:

L> 3vs. τd

Therefore the instability occurs if

For GaAs µd

~ 0.07 m2 /V-s


Derive the Kroemer criterion

Wh h l h K i i hi h fi ld d i



When the sample parameters meet the Kroemer criterion, a high-field domain

periodically develops at the cathode side, drifts towards the anode and

dissolves there.

• There is always ONE and ONLY ONE domain propagating in the sample if

the applied voltage is above the threshold and constant.

• The current decreases with the domain formation and increases when the

domain dissipates.• The oscillation frequency (the “transit time” frequency), f T ~ vs/L



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12 NDR and Gunn Devices