Download Towards resonant-state THz laser based on strained p

NONRESONANT TUNNELING IN SHORT-PERIOD SUPERLATTICES
WITH OPTICAL CAVITIES
M.S. Kagan1, I.V. Altukhov1, S.K. Paprotskiy1,
A.N. Baranov2, R. Teissier2,
A. A. Usikova3, N.D. Il’inskaya3, A.D. Buravlev3, V.M. Ustinov3
1V.A. Kotel’nikov Institute of Radio Engineering and Electronics, Russian Ac. Sci., Moscow, Russia;
[email protected]
2IES, Université Montpellier 2, CNRS, Montpellier, France
3 A.F. Ioffe Physico-Technical Institute, Russian Ac. Sci., St. Petersburg, Russia
OUTLINE
1. Motivation
2. Superlattices
3. Measurements
4. Current-voltage characteristics
5. Nonresonant tunneling
6. Effect of resonant cavity
Emission power vs frequency
Superlattices
Note, that all semiconductor THz lasers operate
at cryogenic temperatures and can not work
at room temperature (kT=25 meV) because
the energies of quanta in THz range are around
10 meV and to obtain the population inversion is
practically impossible.
So, we need to reject the laser scheme and to look
for another way to get THz generation at room T.
The reasonable idea seems to look for a
semiconductor system with a fast negative
differential conductivity (NDC), which can
produce THz oscillations in a suitable resonant
cavity.
L. Esaki and R. Tsu,
IBM J. Res. Devel. 14, 61 (1970).
Superlattices
wave propagation
1100
E
1000
900
Whispering gallery mode
E (meV)
800
Resonant cavity with the current lead
InAs/AlSb superlattices:
Cap layer: n+-InAs<Si> (n = 1x1019 cm-3) - 1
µm, 60 periods of 4.5 nm InAs/3.5 nm AlSb
InAs(Si) QWs: n = (0.5 - 2) 1017 см-3
Substrate: n+-InAs<Si>, n = 1x1019 cm-3
GaAs/AlAs superlattices:
100 periods of 4 nm GaAs/2 nm AlAs
Cavities: ring-shaped gold contacts formed THz
optical cavities for free space l ~ 110 to 160 mm.
700
600
500
400
300
200
100
500
600
700
800
0
x (A )
Energy spectrum and wave functions.
40 kV/cm. T = 300 K
3
Current, A
2
1
0
0
0,5
1,0
1,5
2,0
Voltage, V
Current-voltage characteristics of InAs/AlSb SLs without cavity.
T = 77 K. Rectangular pulse, matched load resistance.
At low voltages, the current saturation or negative differential conductivity (NDC) were observed
caused by Esaki-Tsu mechanism of miniband transport at overlapping broadened confined states
in periodic QWs.
Time dependences of voltage and current
12
2,0
10
1,5
6
I, A
U, V
8
1,0
4
0,5
2
0
0,0
-5
3,3x10
-5
3,4x10
time, s
-5
3,5x10
-5
3,3x10
-5
3,4x10
time, s
InAs/AlSb superlattices.
Т=300 К, matched load resistance.
Current oscillations are due to NDC of the sample exciting parasitic resonant circuits.
-5
3,5x10
InAs/AlSb SLs with optical cavities
D-324 n 11
1.0x10
I, A
5.0x10
-2
-3
0.0
-5.0x10
-1.0x10
-3
-2
-2
-1
0
1
2
U, V
Time dependences of current and voltage.
I-V characteristics in two polarities.
Т = 300 К. Triangular pulse, small load resistance.
The current saturation on initial part of I-V curve is connected with static domain formation
resulted from NDC.
Nonresonant tunneling and the influence of optical cavity (Purcell effect)
Purcell factor
-3
6x10
D-324-I n9
-3
5x10
lc/n is the wavelength
within the material,
Q is the quality factor,
-3
I, A
4x10
-3
3x10
V is the mode volume
of the cavity.
8 мВ
-3
2x10
8 мВ
(E.M. Purcell, Phys. Rev. 69, 681,
1946.)
-3
1x10
8 мВ
0
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
U, V
4
The Purcell’s paper, where he first
entered this factor is one of the
shortest (one paragraph) and at
the same time one of the most
cited in the modern physics.
E.g., in 2011 there were 1681
citings.
Current-voltage characteristics of InAs/AlSb SL.
T = 300 K. Triangular pulses, small load resistance (1 Ohm).
Inset: scheme of nonresonant tunneling
Using for estimation Q=100
we get in our case Fp ~ 1000.
Measurements.
GaAs/AlAs
st D-311
st D-311
3,5
0,035
3,0
0,030
2,5
0,025
2,0
0,020
1,5
0,015
1,0
0,010
0,5
0,005
Current, A
0,025
Current, A
Voltage, V
0,030
0,020
0,015
0,010
0,0
1,0x10-5
1,5x10-5
2,0x10-5
2,5x10-5
0,000
3,0x10-5
0,005
0,5
1,0
1,5
2,0
Voltage, V
time, s
Time dependences of current and voltage.
I-V curves.
Т = 300 К. Triangular pulse, small load resistance.
2,5
Measurements.
GaAs/AlAs
st D-311
2,5
0,030
0,030
0,025
0,025
2,0
0,020
0,020
1,5
0,015
1,0
0,010
0,5
0,0
-5
1,1x10
-5
1,2x10
time (s)
-5
1,3x10
Time dependences of current and voltage.
Т = 300 К.
Current, A
Voltage (V)
st D-311
0,035
Current, A
3,0
0,015
0,010
0,005
0,005
0,000
0,000
0,0
0,5
1,0
1,5
Voltage, V
I-V curves.
2,0
2,5
3,0
GaAs/AlAs superlattices with optical cavities
100 periods of 4 nm GaAs (QW)/2 nm AlAs on heavily doped GaAs substrate.
8-414
Current-voltage characteristics of GaAs/AlAs SL.
T = 300 K. Triangular pulses, small load resistance (1 Ohm).
Conclusion
Vertical transport in short-period InAs/AlSb and GaAs/AlAs superlattices (SLs)
was studied. The periodic maxima observed in the current-voltage characteristics
of these SLs in the nonresonant tunneling regime were attributed to the influence
of optical cavity on optical transitions within quantum wells (Purcell effect).
Certainly, the additional confirmation is desirable for this explanation, both
theoretical and experimental.
In particular, it is necessary to calculate the probabilities of phonon-assisted and
radiative transitions between the confined states in the neighboring QWs.
It would be useful, as well, to study the current-voltage characteristics
of resonant-cavity samples with different frequencies.