The document discusses the characteristics and operational principles of Gunn diodes using n-type GaAs as a semiconductor, focusing on the Gunn effect and its relation to current and electric field behavior. It examines important parameters such as electron drift velocity, transit-time oscillations, and conditions for stable operation versus oscillation modes. The analysis includes the influence of sample length on frequency and the significance of the Kroemer criterion for domain formation in Gunn diodes.

1. J. B. Gunn, "Microwave Oscillation of Current in III-V Semiconductors",
Solid State Commun., 1 88 (1963)
Gunn Diodes
n-type GaAs
Metal
Metal
In 1960’s GaAs was a new emerging semiconductor material
John Gunn research objective was to study the ohmic contacts to GaAs

2. V
I
GaAs sample I-V characteristic in Gunn experiments
n-type GaAs
Metal
Metal
5V

3. V
I
GaAs sample I-V characteristic in Gunn experiments
n-type GaAs
Metal
Metal
15V

4. V
I
GaAs sample I-V characteristic in Gunn experiments
30V
n-type GaAs
Metal
Metal

5. .
0
4
8
12
16
20
0 20 40 60 80 100 120 140 160
Current
(mA)
Time (ps)
js = qnovs
jp = qnovp
Short-pulse current waveform in Gunn experiment

6. 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 m
2
/Vs
Physical mechanism of the Gunn effect
Si
GaAs

7. 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 m
2
/Vs
μ = 0.5 m2
/Vs
Current voltage characteristic of GaAs sample
in strong electric fields
I = q × n ×v(F) × Area
Since F = V/L, one can expect that I-V characteristic would be
similar 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 m
2
/Vs
μ = 0.5 m2
/Vs
Current
Voltage

8. 2 4 6 8 10 12 14
0.5
1
1.5
2
Electric field (kV/cm)
μ = 0.85 m
2
/Vs
μ = 0.5 m
2
/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/cm
the differential mobility is negative.
When the field exceeds FC and further increases, the electron drift velocity decreases.

9. 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
concentration
distribution in
the sample.

10. x
F0 ≈ Fc
F
v
Fc
vm
- +
F
x
v0 = vm
v
x
n0 = ND
n
0 0
D
F n N
q
x
ρ
ε ε ε ε
∂ −
=− =
∂

11. x
F
x
v
F0 ≈ Fc
v0 = vm
x
n
n0 = ND
F
v
Fc
vm
- +

12. x
F
x
v
F0 ≈ Fc
v0 = vm
x
n
n0 = ND
F
v
Fc
vm
- +

13. x
F
x
v
F0 ≈ Fc
v0 = vm
x
n
n0 = ND
F
v
Fc
vm
- +
vs
vs
High-field, or
Gunn domain

14. x
F
x
v
F0 ≈ Fc
v0 = vm
x
n
n0 = ND
F
v
Fc
vm
- +
vs
vs

15. x
F
x
v
F0 ≈ Fc
v0 = vm
x
n
n0 = ND
F
v
Fc
vm
- +
vs
vs

16. 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:

17. 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

18. 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
Current
(mA)
Time (ps)
js = qnovs
jp = qnovp
IV = q n vs

19. Transit-time oscillations in Gunn diodes
.
0
4
8
12
16
20
0 20 40 60 80 100 120 140 160
Current
(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/s
For the sample with the length L = 100 μm,
ttr = 100 ×10-4 cm / 107 cm/s = 10-9 s
The frequency of transit –time oscillations:
ftr = 1/ttr = 109 1/s = 1 GHz
For L=10 μm, ftr = 10 GHz

20. .
0
4
8
12
16
20
0 20 40 60 80 100 120 140 160
Current
(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:

21. 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

22. 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

23. Highly-efficient Limited –Space charge- Accumulation mode
Achieved frequencies: up to 100 GHz

24. Kroemer criterion in the Gunn effect
Concentration
Distance
Cathode Anode
Field
Characteristic time of the domain formation can
be evaluated by effective RC- circuit charging
time:
0
0 | |
d d d
d
t R C
qn
ε 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 =
εS
L
Rd =
L
qμd noS
0
d
d
S
C
L
ε ε
=
0
d
d
d
L
R
q n S
μ
=

25. Kroemer criterion in the Gunn effect
Characteristic domain transit time in the sample of the length L:
tr
s
L
t
v
≈
If domain formation time td is greater
than 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
Concentration
Depletion
Layer
Accumulation
Layer
Distance
Field
Anode
Cathode
L
( )
( ) 0
,
| |
o o CR
s
o CR
d
n L n L
v
where n L
q
εε
μ
>
=
0
0
d d d
d
t R C
qn
ε ε
μ
≈ =
Kroemer criterion for
domain formation:

26. Stable Gunn diodes - amplifiers
Field/concentration distributions and impedance –frequency
dependence in stable Gunn diode
If the Kroemer criterion is not met:
0
| |
s
o
d
v
n L
q
εε
μ
<
High-field domains do not form and Gunn diodes are stable.

27. 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

28. Stable Gunn diodes – travelling space-charge
wave amplifiers
Space-charge amplitude increases from cathode to anode: unidirectional
amplification.

29. Gunn diode mode of operation – parameter map
0
| |
s
o
d
v
n L
q
εε
μ
>= 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
o
d
v
n L
q
εε
μ
< Gunn diode works as a stable amplifier. No Gunn
domain or LSA oscillations
0
0
d
d
t
qn
ε ε
μ
=
The mode of operation depends on the relationship between
the resonant frequency of the attached resonant circuit f0
and the domain formation time:
I.
II.