A suppression of tunnelling ionization of deep impurities in terahertz
frequency electric fields by a magnetic field is observed. It is shown that the
ionization probability at external magnetic field, B, oriented perpendicular to
the electric field of terahertz radiation, E, is substantially smaller than
that at B || E. The effect occurs at low temperatures and high magnetic fields

A.S. Moskalenko

C. Back

Ganichev

I.N. Yassievich

J. Zimmermann

Kotova

Landauer

M. Sollinger

Moskalenko

Perel

S.D. Ganichev

S.N. Danilov

V.I. Perel

W. Prettl

English

arXiv

Ganichev, Sergey

Danilov, Sergey

Sollinger, M.

Zimmermann, J.

Perel, V.

Yassievich, Irina

Prettl, Wilhelm

University of Regensburg Publication Server

Magnetic field effect on tunnel ionization of deep impurities by terahertz radiation

A suppression of tunnelling ionization of deep impurities in terahertz frequency electric fields by a magnetic field is observed. It is shown that the ionization probability at external magnetic field, B, oriented perpendicular to the electric field of terahertz radiation, E, is substantially smaller than that at B parallel to E. The effect occurs at low temperatures and high magnetic fields. (C) 2003 Elsevier B.V. All rights reserved.

Ganichev, SD

Danilov, SN

Sollinger, M

Zimmermann, J

Andrey, S. Moskalenko

Perel, VI

Yassievich, IN

Back, C

Prettl, W

KAIST Institutional Repository

Physica B Condensed Matter

Moskalenko, A.

Yassievich, I.

Back, Christian

Abstract A suppression of tunnelling ionization of deep impurities in terahertz frequency electric fields by a magnetic field is observed. It is shown that the ionization probability at external magnetic field, B; oriented perpendicular to the electric field of terahertz radiation, E; is substantially smaller than that at B jj E: The effect occurs at low temperatures and high magnetic fields. 

S D Ganichev

S N Danilov

M Sollinger

J Zimmermann

A S Moskalenko

V I Perel

I N Yassievich

C Back

W Prettl

CiteSeerX

ARTICLE IN PRESSPhysica B 340–342 (2003) 1155–1158*Corresp
941-943-422
E-mail
(S.D. Gani
0921-4526/$
doi:10.1016Magnetic field effect on tunnel ionization of deep impurities by
terahertz radiation
S.D. Ganicheva,b,*, S.N. Danilova, M. Sollingerb, J. Zimmermanna,
A.S. Moskalenkob, V.I. Perelb, I.N. Yassievichb, C. Backa, W. Prettla
a Institut f .ur Exp. und Angew. Physik, Universit .at Regensburg, D 93040 Regensburg, Germany
bA.F.Ioffe Physico-Technical Institute, St. Petersburg, RussiaAbstract
A suppression of tunnelling ionization of deep impurities in terahertz frequency electric fields by a magnetic field is
observed. It is shown that the ionization probability at external magnetic field, B; oriented perpendicular to the electric
field of terahertz radiation, E; is substantially smaller than that at B jj E: The effect occurs at low temperatures and high
magnetic fields.
r 2003 Elsevier B.V. All rights reserved.
PACS: 71.55.Eq; 72.10.Fk; 73.40.Gk
Keywords: Tunnel ionization; Terahertz radiation; Deep centers; Magnetic field1. Overview
Tunneling ionization of deep centers in a
terahertz field of high-intensity far-infrared laser
radiation, with photon energies tens of times lower
than the impurity binding energies has been in-
vestigated in great detail during the last decade [1].
In contrast to tunneling ionization of atoms, where
only electron tunneling takes place, ionization of
impurities in solids is accomplished by two
simultaneous processes: electron tunneling
through the potential well formed by the attractive
force of the impurity and the externally applied
electric field and the redistribution of the vibra-onding author. Tel.: +49-941-943-2050; fax: +49-
3.
address: sergey.ganichev@physik.uni-regensburg.de
chev).
- see front matter r 2003 Elsevier B.V. All rights reserve
/j.physb.2003.09.102tional system by defect tunneling. At very high
radiation electric field strengths direct tunneling
may occur without involving phonons.
The tunneling probability is independent on the
radiation frequency up to very high frequencies. In
this quasi-static regime, electrons tunnel at con-
stant energy in a time much shorter than the
reciprocal radiation frequency o1: At higher
frequencies, however, tunneling probability dras-
tically increases in comparison to the tunneling in
DC field of the same field strength. In such a high-
frequency regime electrons can absorb energy from
the radiation field during tunneling leaving the
barrier at higher energy. By this the effective width
of the tunneling barrier is reduced and, thus, the
tunneling probability enhanced.
In a semiclassical approach defect tunneling
takes place from the adiabatic potential corre-
sponding to the impurity bound state to the stated.
ARTICLE IN PRESS
S.D. Ganichev et al. / Physica B 340–342 (2003) 1155–11581156where the carrier is detached from the impurity.
The tunneling probability is controlled by the
B .uttiker–Landauer tunneling time [2] t which is a
function of temperature. The transition from
frequency-independent tunneling in a classical
electric field to fully quantized multi-photon
transitions occurs in the terahertz range and may
be explored applying high-power far-infrared
lasers. The borderline is given by ot ¼ 1 where
o is the radiation frequency.
These considerations are based on semiclassical
theory where the carriers have a classical trajec-
tory. In this case the tunneling probability is
expected to be affected by the strength and the
orientation of an external magnetic field. For
electron tunneling through static potential barriers
this effect was theoretically investigated in Ref. [3]
and observed in quantum well structures [4]. The
theory has been extended for phonon-assisted
tunneling ionization of deep impurities in DC
electric fields [5] and in high-frequency alternating
fields [6,7] showing that also in the case of phonon-
assisted tunneling, even in the high-frequency
regime, the carrier emission is suppressed by an
external magnetic field ðB>EÞ: In this work, we
give evidence for the applicability of the semi-
classical model to tunneling assisted by phonons
which is concluded from the experimental obser-
vation of the suppression of tunneling probability
by an external magnetic field oriented perpendi-
cular to the carrier trajectory.2. Tunneling in alternating fields
We have shown in Ref. [1] that the probability
of phonon assisted tunneling depends on the
strength of E; an oscillating electric field of
frequency o:
eðEÞpexp
E2
ðEc Þ
2
" #
with ðEc Þ
2 ¼
3m_
e2ðtÞ3
; ð1Þ
with electron effective mass m and
ðtÞ3 ¼
3
4o3
ð sinhð2otÞ  2otÞ: ð2Þ
The frequency dependence of the tunneling process
is controlled by ot where the tunneling time tdepends on temperature: t ¼ _=2kT7t1:Here t1 is
of the order of the period of the impurity vibration
and plus and minus correspond to substitutional
and auto-localized impurities, respectively [8]. It
follows from Eq. (2) that for ot51 the effective
time t gets equal to the tunneling time t yielding a
well known formula of phonon assisted tunneling
in the quasi-static regime [1].
In the presence of an external magnetic field
oriented perpendicular to the electric field of
radiation, the functional dependence of the prob-
ability on the electric field strength remains
unchanged, however the value of the effective time
t becomes dependent on the magnetic field
strength. An increase of the cyclotron frequency
oc ¼ eB=m over the reciprocal tunneling time
results in the decrease of the tunneling probability.
The suppression of the tunneling probability
occurs in both frequency ranges, at low frequen-
cies, when tunneling is independent of radiation
frequency, at high frequencies when the tunneling
probability increases drastically with rising fre-
quency. The effect of a magnetic field B on
tunneling is strongest if it is oriented normal to
the radiation electric field E and vanishes if B jj E:
For the ionization probability we again obtain an
exponential dependence on the square of the
electric field strength in the form of Eq. (1),
however, now the effective time t depends on
the magnetic field strength:
ðtÞ3 ¼
3o2c
ðo2  o2cÞ
2

Z t
0
 
 coshot0
(
þ
oc
o
sinhot
sinhoct
coshoct0
!2
dt0
þ
Z t
0
o
oc
sinhot0
 

oc
o
sinhot
sinhoct
sinhoct0
!2
dt0
)
: ð3Þ
In Fig. 1, the calculated impurity ionization
probability is plotted as a function of E2 for
various magnetic field strengths showing the drop
ARTICLE IN PRESS
S.D. Ganichev et al. / Physica B 340–342 (2003) 1155–1158 1157of the carrier emission rate with increasing B: The
data are presented for two different values of
ot representing the quasi-static and the high-
frequency regimes.105 106 107 108
1
10
Ge:Hg
λ = 148 µm
T = 15 K
S
ig
na
l (
a.
u.
)
2 2
 E || x;
 E ⊥  x; Bx = 0
 E || x;
 E ⊥  x;
Bx = 0
Bx = 7.4 T
Bx = 7.4 T3. Experimental technique and results
The experiments were carried out on mercury
doped germanium in the temperature range of 10–
70 K: Tunneling ionization has been achieved by
far-infrared laser radiation with photon energies
much smaller than the thermal impurity ionization
energy eT ¼ 90 meV: The radiation source was a
pulsed far-infrared molecular laser optically
pumped by a TEA–CO2 laser. Operating the
optically pumped laser with NH3 and CH3F as
active gases, 40 ns pulses with intensity up to
2 MW=cm2 have been obtained at wavelengths of
148 and 496 mm: The ionization probability has
been measured by detecting photoconductivity [1].
To apply a small probe voltage to the sample two
ohmic contacts along x direction were prepared.
An external magnetic field B up to 7:5 T has been
applied along x: The ionization probability as a
function of the radiation intensity IpE2 has been
obtained for E jj Bx and E>Bx for different
magnetic field strengths. In addition, the magnetic0 1 2 3 4 5
1
2
3
4
5
ωτ = 5
ωτ = 0
  ω
c
 τ = 0
  ω
c
 τ = 1
  ω
c
 τ = 4
ln
 [
e(
E
) 
/ e
(0
)]
E 2 /Ec
2*
Fig. 1. ln½eðEÞ=eð0Þ
 as a function of E2=E2c for different ot
and oct calculated after Eqs. (1)–(3) for a magnetic field normal
to the electric field; o and oc are the radiation frequency and
the cyclotron frequency, respectively. Here the parameter ot
controls the frequency dependence of tunneling while oct
reflects the influence of the magnetic field.field dependence of the signal has been determined
for constant intensity. The orientation between the
external magnetic field Bx and the electric field E
of linearly polarized terahertz radiation has been
changed by means of a l=2 crystal quartz plate.
In Fig. 2, the dependence of the photoconduc-
tive signal being proportional to the ionization
probability on the square of the electric field
strength of the radiation is plotted for B ¼ 0 and
7:4 T: Results are presented for a temperature of
15 K and l ¼ 148 mm: These measurements show
that at zero magnetic field the ionization prob-
ability is independent of the electric field orienta-
tion. At high magnetic fields, however, the signal
for E>Bx drops significantly below that of E jj Bx:E  (V/cm )
Fig. 2. Photoconductive signal for Ge:Hg as a function of E2
for different magnetic field strengths Bx and orientations.
0 2 4 6 8
0.4
0.8
 E || Bx
  
Ge:Hg
λ = 148 µm
T = 15 K
E 2 = 8.9⋅107 V2/cm2
S
ig
na
l  
(a
.u
.)
Bx (T)
E ⊥  Bx
Fig. 3. Photoconductive signal as a function of magnetic field
strength for two polarizations: E>Bx and E jj Bx in the high-
frequency limit ðot > 1Þ:
ARTICLE IN PRESS
Bx (T)
E || Bx
E ⊥  Bx
Fig. 4. Photoconductive signal as a function of magnetic field
strength for two polarizations: E>Bx and E jj Bx in the quasi-
static limit ðoto1Þ:
S.D. Ganichev et al. / Physica B 340–342 (2003) 1155–11581158This suppression of the tunneling probability can
also be seen in the magnetic field dependence of
the photoconductive signal shown in Figs. 3 and 4.
The effect of tunneling suppression occurs only at
low temperatures where, on one side, practically
all carriers are frozen out on the impurities and on
the other side the tunneling time assumes high
values [1]. At high temperatures the effect of free
carrier absorption interferes with the change of
conductivity by tunneling ionization. Therefore no
suppression of the signal could be observed.
Tunneling suppression has been observed in both
regimes, the quasi-static limit ðoto1Þ at 496 mm
(Fig. 3) and in the high-frequency limit ðot > 1Þobtained by the excitation with radiation of
148 mm (Fig. 4).
In summary, our present observation shows that
for B>E the magnetic field deflects the carriers,
which increases the length of the tunneling
trajectory. Thus, a magnetic field reduces the
ionization probability if the cyclotron frequency
becomes larger than the reciprocal tunneling time.
Experimental findings are in good agreement with
the developed theory of phonon-assisted tunneling
ionization of deep impurities in the presence of a
magnetic field.References
[1] S.D. Ganichev, I.N. Yassievich, W. Prettl, J. Phys.:
Condens. Matter 14 (2002) R1263.
[2] R. Landauer, Th. Martin, Rev. Mod. Phys. 66 (1994)
217.
[3] L.P. Kotova, A.M. Perelomov, V.S. Popov, Sov. JETP 27
(1968) 616.
[4] L. Eaves, K.W.H. Stevens, F.W. Sheard, in: M.J. Kelly,
C. Weisbuch (Eds.), The Physics and Fabrication of
Microstructures and Microdevices, Springer, Berlin, 1986,
pp. 343–349.
[5] V.I. Perel, I.N. Yassievich, JETP Lett. 68 (1998) 804.
[6] A.S. Moskalenko, S.D. Ganichev, V.I. Perel, I.N. Yassie-
vich, Physica B 273–274 (1999) 1007.
[7] A.S. Moskalenko, V.I. Perel, I.N. Yassievich, JETP 90
(2000) 217.
[8] S.D. Ganichev, J. Diener, I.N. Yassievich, W. Prettl, B.K.
Meyer, K.W. Benz, Phys. Rev. Lett. 75 (1995) 1590.


Magnetic field effect on tunnel ionization of deep impurities by
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Magnetic field effect on tunnel ionization of deep impurities by terahertz radiation

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