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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.