J. B. Gunn, "Microwave Oscillation of Current in III-V Semiconductors",

Solid State Commun., 1 88 (1963)

Gunn Diodes

n-type GaAsMetal

Metal

In 1960’s GaAs was a new emerging semiconductor materialJohn Gunn research objective was to study the ohmic contacts to GaAs

V

I

GaAs sample I-V characteristic in Gunn experiments

n-type GaAsMetal

Metal

5V

V

I

GaAs sample I-V characteristic in Gunn experiments

n-type GaAsMetal

Metal

15V

V

I

GaAs sample I-V characteristic in Gunn experiments

30V

n-type GaAsMetal

Metal

.

0

4

8

12

16

20

0 20 40 60 80 100 120 140 160

Cur

rent

(mA

)

Time (ps)

js = qnovs

jp = qnovp

Short-pulse current waveform in Gunn experiment

Electron drift velocity – Electric field dependence in GaAs

2 4 6 8 10 12 14

0.5

1

1.5

2

Electric field (kV/cm)

μ = 0.85 m2/Vs

μ = 0.5 m2/Vs

Physical mechanism of the Gunn effect

Si

GaAs

Such an assumption is wrong.

2 4 6 8 10 12 14

0.5

1

1.5

2

Electric field (kV/cm)

μ = 0.85 m2/Vs

μ = 0.5 m2/Vs

Current voltage characteristic of GaAs samplein strong electric fields

I = q × n ×v(F) × AreaSince F = V/L, one can expect that I-V characteristic would besimilar in shape to the v(F) curve

2 4 6 8 10 12 14

0.5

1

1.5

2

Electric field (kV/cm)

μ = 0.85 m2/Vs

μ = 0.5 m2/VsCur

rent

Voltage

2 4 6 8 10 12 14

0.5

1

1.5

2

Electric field (kV/cm)

μ = 0.85 m2/Vs

μ = 0.5 m2/Vs

Space charge instability in semiconductors with negative differential mobility (NDM)

FC

In GaAs, at electric fields exceeding the critical value of FC ≈ 3.2 kV/cmthe differential mobility is negative.When the field exceeds FC and further increases, the electron drift velocity decreases.

x

x

F0 ≈ Fc

v0 = vm

x

n0 = ND

F

v

Fc

vm

- +F

v

n

Space charge instability in semiconductors with NDM

Initially uniform electric field and concentrationdistribution in the sample.

x

F0 ≈ Fc

F

v

Fc

vm

- +F

x

v0 = vm

v

x

n0 = ND

n

0 0

DF n Nqx

ρε ε ε ε

∂ −=− =

∂

x

F

x

v

F0 ≈ Fc

v0 = vm

x

nn0 = ND

F

v

Fc

vm

- +

x

F

x

v

F0 ≈ Fc

v0 = vm

x

nn0 = ND

F

v

Fc

vm

- +

x

F

x

v

F0 ≈ Fc

v0 = vm

x

nn0 = ND

F

v

Fc

vm

- +vs

vs

High-field, orGunn domain

x

F

x

v

F0 ≈ Fc

v0 = vm

x

nn0 = ND

F

v

Fc

vm

- +vs

vs

x

F

x

v

F0 ≈ Fc

v0 = vm

x

nn0 = ND

F

v

Fc

vm

- +vs

vs

x

F

v

F0 ≈ Fc

F

v

Fc

vm

- +vs

Current – time dependence in the sample with high-filed domain

Current at the device electrodes:IV= q n vs

When the domain is moving between the cathode and anode:

F

v

Fc

vm

- +vs

Current – time dependence in the sample with high-filed domain

Current at the device electrodes:Im = q n vm

When the domain dissipates in the anode and new domain did not form yet:

x

x

F0 ≈ Fc

v0 = vm

F

v

v

Fc

vm

vs

Current – time dependence in the sample with high-filed domain

Im = q n vm

.

0

4

8

12

16

20

0 20 40 60 80 100 120 140 160

Cur

rent

(mA

)

Time (ps)

js = qnovs

jp = qnovp

IV = q n vs

Transit-time oscillations in Gunn diodes

.

0

4

8

12

16

20

0 20 40 60 80 100 120 140 160

Cur

rent

(mA

)

Time (ps)

js = qnovs

jp = qnovp

GD

L

RL

Domain transit time: ttr = sample length /domain velocity ttr = L/vs

In GaAs, vs ≈107 cm/sFor the sample with the length L = 100 μm,

ttr = 100 ×10-4 cm / 107 cm/s = 10-9 sThe frequency of transit –time oscillations:

ftr = 1/ttr = 109 1/s = 1 GHzFor L=10 μm, ftr = 10 GHz

.

0

4

8

12

16

20

0 20 40 60 80 100 120 140 160

Cur

rent

(mA

)

Time (ps)

js = qnovs

jp = qnovp

GD

L

RL

1. Operating frequency controlled by the sample length:

no tuning, varies from sample to sample, sensitive to sample non-uniformities.

2. Current waveform consist of short pulses with the width << half-a-period:

low efficiency

Transit-time oscillation issues:

1. Resonator voltage controls the

domain nucleation and dissipation.

2. Current waveform pulses are wider

as compared to transit-time mode:

higher efficiency

Resonator-controlled oscillations in Gunn diodes

Gunn diode in the LC-resonator

Highly-efficient Limited –Space charge- Accumulation mode

Approach:

Domain formation requires certain time td.

If the resonator frequency fr >> (1/td), the domain cannot completely develop

The filed and concentration in the sample remain nearly uniform.

The “dynamic” I-V curve of the Gunn diode reproduces the v(F) dependence

Highly-efficient Limited –Space charge- Accumulation mode

Achieved frequencies: up to 100 GHz

Kroemer criterion in the Gunn effectC

once

ntra

tion

DistanceCathode Anode

Fiel

d

Characteristic time of the domain formation can be evaluated by effective RC- circuit charging time:

0

0 | |d d dd

t R Cq nε ε

μ≈ =

Domain formation time is equal to td (so-called Maxwell relaxation time);n0 is the equilibrium electron concentration,μd is the differential electron mobility.In GaAs, typically, |μd| ≈ 2000 сm2/(V×s)

Cd =εSL

Rd =L

qμd noS

0d

d

SCL

ε ε=

0

dd

d

LRq n Sμ

=

Kroemer criterion in the Gunn effectCharacteristic domain transit time in the sample of the length L:

trs

Ltv

≈

If domain formation time td is greaterthan the domain transit time ttr, the domain does not have enough time to develop – the diode is stable. Gunn diode is stable if td > ttr;Gunn diode may oscillate in one of the Gunn-domain modes if td < ttr

Con

cent

ratio

n DepletionLayer

AccumulationLayer

Distance

Fiel

d

AnodeCathode

L( )

( ) 0

,

| |

o o CR

so CR

d

n L n L

vwhere n L

qεεμ

>

=

0

0d d d

d

t R Cq nε εμ

≈ =

Kroemer criterion for domain formation:

Stable Gunn diodes - amplifiers

Field/concentration distributions and impedance –frequency dependence in stable Gunn diode

If the Kroemer criterion is not met: 0

| |s

od

vn Lqεεμ

<

High-field domains do not form and Gunn diodes are stable.

Stable Gunn diodes - amplifiers

Reflective type microwave diode amplifier:When the diode resistance Rd <0, the amplitude of reflected e/m wave Arefl is greater than that of incident wave Ainc

Stable Gunn diodes – travelling space-charge wave amplifiers

Space-charge amplitude increases from cathode to anode: unidirectionalamplification.

Gunn diode mode of operation – parameter map0

| |s

od

vn L

qεεμ

>= Gunn diode works as an oscillator

f0 < 1/td – Gunn diode operates in the Gunn domain mode.

f0 > 1/td – Gunn diode operates in the limited space charge accumulation (LSA) mode – no domains are formed. For the LSA mode, f0 > 3× 1/td

if f0 >1/td but f0 < 3 × 1/td, Gunn diode operates in a mixed Gunn domain/LSA mode

0

| |s

od

vn L

qεεμ

< Gunn diode works as a stable amplifier. No Gunn domain or LSA oscillations

0

0d

d

tq nε εμ

=

The mode of operation depends on the relationship between the resonant frequency of the attached resonant circuit f0and the domain formation time:

I.

II.