Operation Bi-stable switch Oscillator Fundamental Bi-stable switch •Oscillator...
Transcript of Operation Bi-stable switch Oscillator Fundamental Bi-stable switch •Oscillator...
Lecture 15: Resonant Tunneling Diode
2011-02-28 1Lecture 15, High Speed Devices 2011
• Operation
• Bi-stable switch
• Oscillator
• Fundamental Physics
• Application Example
Resonant Tunneling Diode
2011-02-28 2Lecture 15, High Speed Devices 2011
E1
E2
An RTD consists of two large bandgap material forming a quantum well with quasi-bound states (in z-direction):
V
I
V
I
V
I
Energy and k conserved during tunneling – negative differential resistance
z
E
Resonant Tunneling Diode
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I
80
60
40
20
0
Cu
rren
t (k
A/c
m2)
1.61.20.80.40.0
Collector Voltage (V)
Experimental Data (T=300K)
Ideal device, T=0K
•Important DC figure of merits:•Peak current density (Jp)•Peak Voltage (Vp)•Valley current density (Jv)•Valley Voltage (Vv)• Peak-to-valley ratio: Jp/Jv
Jp
Jv
Vp Vv
Valley current is larger than 0 in a real device:
Thermionic emmision
Field-assisted tunneling
Transport through 2nd subband
Elastic/inelastic scattering
V
Plateau is an artifact from oscillations in the bias network
Application: Bistable Switch
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80
60
40
20
0
Cu
rren
t (k
A/c
m2)
1.61.20.80.40.0
Collector Voltage (V)
The two stable bias-points:Associated with the double barrier is a capacitance:
tb tw tb
wb
s
ttC
2
Vp,Ip
Vf,If
Vs
RL V1
IRTD(V1)
IRL(V1)
Assume RTD biased at V1=Vp – small increase in Vs forces new biasing point Vf
Charge stored over C will increase:
pf VVCQ
Speed Index
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80
60
40
20
0
Cu
rren
t (k
A/c
m2)
1.61.20.80.40.0
Collector Voltage (V)
Vp,Ip
Vf,If
Vs
RL V1
IRTD(V1)IRL
(V1)
pf VVCQ
1
11 )()(dV
VJVJ
Cf
p L
V
V RTDR
This charge has to be supplied through RL – delay in V1
Switching time:
IRL
Area inbetween curves gives current to charge C with Q
pv
pf
pvp
pf
V
V vp JJ
VV
J
C
JJ
VVCdV
JJ
Cf
p/1
1
Speed Index 1/PVR
Fast switching requires a large Jp!
AlSb/InAs/AlSb Switch Transition
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E. Özbay, EDL 1993
1.7 pS switching of ~ 0.7V
Slew-rate of 300mV/pS
1.7 pS
tb=1.8nmtw=7.5 nm10 nm drift region after RTD
~ 1.5 pS
Application: Negative resistance oscillator
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V
I The RTD has negative differential resistance (NDR):
0 NDRVVdv
dir
Rs
-gd
L
C
t
LCjt
C
gd
eiti
1
0
If Rs (series resistance in diode) ~0, the equivivalent circuit is a simple RLC:
VNDR
i(t)
If gd is negative, the oscillations amplitude grows instead of decaysAn RTD biased in the NDR region will oscillate between Ip and Iv
80
60
40
20
0
Cu
rren
t (k
A/c
m2)
1.61.20.80.40.0
Collector Voltage (V)
Some inductance in the biasing circuit.DC measurment averages over oscillations
High Frequency Oscillators
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Rs
-gdjwC
LCfosc
2
1
Zin
The oscillation frequency is essentially set by the effectiv LC-networkCan oscillate as long as Re(Zin)<0
gd=di/dv
2
max,2
1d
s
dosc g
R
g
Cf
vp
vp
dVV
IIg
For a high fmax, we want small Rs, small C and large gd
Highest RTD fmax ~ 850 GHz, which is the highest fundamental mode oscillator made as of today
2
1
woutP Low output power limits applications
Calculation of current
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dkkTkvkEEfq
kTkEEfkvqvqnIxk
sFsF
0
,, ,,2
Assume fully coherent transport:
1D-0D-1D-system
Ef,l Ef,l-qVsd
T(Ez,Vsd)
Transmission probability
Where T(Ez,Vsd) is the transmission probability of the quantum system
0, 0
,3, exp1ln)(2
,2zyx kkk
zzlfzsFz dEEEETqmkT
kTkEEfkvqvqnJ
3D-2D-3D
T(Ez)
z
E
m
kE z
z2
22
qVds
Transmission Probability
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Assuming plane waves
I II III IV V
V
III
II
I
Ie
FeEe
DeCe
BeAe
z
ikz
ikzikz
zz
ikzikz
......
EVm
Emk
0
*
*
2
2
E=0
E=V0
Match wavefunction and its derivative at all interfaces:
az
II
IIaz
I
I
III
z
z
mz
z
m
aa
**
11
z=a
2
2
A
IET
Solve for A ... I (e.g. Using the transfer matrix
method)
real kimag K
E
Should use complex bandstructure..
EC
Ev
Transmission Probability II
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10-5
10-4
10-3
10-2
10-1
100
Transmission Probability
0.6
0.4
0.2
En
erg
y (
eV
)
At resonance for a symmetric systemT=1Finite lifetime in well gives rise to a broadening of the state
Gt=FWHM
22 4/
2/
nzn
nz
EEET
G
G
Around the transmission peak, T(Ez) is essentially Lorenzian.
G
1
2*
2
1
22
Rbm
TEnn
b
T1 is the transmission probability through a single barrier
0
,3exp1ln)(
2zzlfz dEEEET
qmkTJ
If we want J+ to be large – T(Ez) should be ’wide’ in energy!
Build RTD with thin barriers and a thin well!
Design example: AlGaAs/GaAs/InGaAs RTD
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80
60
40
20
0
Cu
rren
t (k
A/c
m2)
1.61.20.80.40.0
Collector Voltage (V)
102
103
104
105
Cu
rren
t D
ensi
ty (
kA
/cm
2)
4.03.53.02.52.01.51.0
Barrier Thickness (nm)
Calculated
Exponential Fit
J=4.6910610
(-1.194x)
0.6
0.5
0.4
0.3
0.2
0.1
0.0
Qu
antu
m w
ell
ener
gy
(eV
)
3020100
In (%) in notch
50
40
30
20
10
0Pea
k C
urr
ent
Den
sity
(kA
/cm
2)
3020100
In (%) in notch
E
z InxGa1-xAs
Al0.8Ga0.2As
b
GaAs
4nm
An indium-rich notch lowers 1st subband, and increases 2nd – higher peak to valley ratio
Strong dependency on barrier thickness
T=300K
Startup Decay
Application Example: Ultra Wideband Source
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Very quick turn on/off due to the high slew-rate
Application Example: Ultra Wideband Source
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Gated Resonant Tunnel diode
Inductor
2 Gpulses/s On-Off Keying at 60 GHz
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Potential applications:UWB communication systems (Gbit/s over short ranges)Pulse-based radar systems THz spectroscopy (short pulse – large bandwidth)
RTD Conclusions
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Large research effort at universities and industry during 1990-2000At that time: ft,fmax of HEMT/HBTs were ~ 100 GHz, RTD had fmax ~ 700 GHz!
RTD – unipolar two-terminal component, with added functionality due to the NDRSimple design gives small capacitance fast switching, high oscillation frequency
Today – ft, fmax of transistors are approaching THz, limited usage for RTDs
Unique IV – can lead to simpler circuit solutions, e.g. oscillators as compared with traditional transistor technology.