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RESONANT ZENER TUNNELING OF ELECTRONS ACROSS THE BAND-GAP BETWEEN BOUND
STATES IN THE VALENCE- AND
CONDUCTION-BAND QUANTUM WELLS IN A MULTIPLE QUANTUM-WELL STRUCTURE
J. Allam, F. Beltram, F. Capasso, A. Cho
To cite this version:
J. Allam, F. Beltram, F. Capasso, A. Cho. RESONANT ZENER TUNNELING OF ELEC- TRONS ACROSS THE BAND-GAP BETWEEN BOUND STATES IN THE VALENCE- AND CONDUCTION-BAND QUANTUM WELLS IN A MULTIPLE QUANTUM-WELL STRUCTURE.
Journal de Physique Colloques, 1987, 48 (C5), pp.C5-439-C5-442. �10.1051/jphyscol:1987593�. �jpa-
00226797�
JOURNAL DE PHYSIQUE
Colloque C5, supplement au noll, Tome 48, novembre 1987
RESONANT ZENER TUNNELING OF ELECTRONS ACROSS THE BAND-GAP BETWEEN BOUND STATES I N T H E VALENCE- AND CONDUCTION-BAND QUANTUM WELLS IN A MULTIPLE QUANTUM-WELL STRUCTURE
J. ALLAM( )
,
F. BELTRAM, F. CAPASSO and A.Y. CHOAT and T Bell Laboratories, Murray Hill, NJ 07974, U.S.A.
Abstract. We report the observation of resonant tunneling effects a t high applied fields i n a multiple quantum-well P-I-N diode. T h e A10,81no,5,As/Gao,4,1no,53As structure shows features in the d a r k current due to Zener tunneling of electrons from the lowest sub-band i n a valence-band quantum well to t h e first a n d second sub-bands of a n adjacent conduction-band well.
1. Introduction. Since the original work of Esaki e t al.['I, resonant tunneling (RT) of electrons within t h e conduction band of heterojunction semiconductors has been investigated in a variety of double barrier, superlattice a n d multiple quantum-well (MQW) structures (see references i n [2]). Resonant tunneling of holes i n the valence band has also been reported13]. I n the present work, we report a new R T effect, resonant Zener tunneling (RZT) of electrons across the band-gap between bound states i n adjacent valence- and conduction-band q u a n t u m wells.
Narrow band-gap semiconductor P-N junctions exhibit large leakage currents a t high reverse-bias d u e to band-to-band ~ ~ n n e l i n g [ ~ ] . I n a MQW, the tunneling current will be modified b y t h e quantization of the energy levels i n the wells. T h u s significant tunneling current is expected only when a bound state in a conduction-band well is coincident in energy with a bound state i n a n adjacent valence-band well.
2. Experimental details and results. The MQW's studied consisted of 35 periods of 139 A A10,4,1no~,2As barriers a n d 139 A Gao,,71no,53As wells. This structure was grown within the undoped region of a P+-I-N+ diode, on top of a n N+ A10,481n0,52A~ b u f f e r layer on a
<100>InP substrate. T h e top A10,4,1n0,52As P+ layer is 1 pm thick a n d is capped with a 150 A highly-doped Gao.471no,53A_S, layer f o r p-type contact. T h e wafer was fabricated into mesa devices of area 1.3 x 10 c m 2 and ohmic contacts were applied to the P+ a n d N+
layers. Capacitance-voltage measurements indicate t h a t the I layer is completely depleted near zero bias with a capacitance of 1.5 pF, f o r temperatures beteween 4 K a n d room temperature.
("present address : Department of Physics. University of Surrey, GB-Guildford GU2 5XH. Great-Britain
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987593
JOURNAL
DE
PHYSIQUEFigure 1. Reverse bias characteristics of the M Q W P-I-N diode a t various temperatures, showing steps i n the 4 K tunneling current a t 24.0 and 28.5 V.
REVERSE BIAS ( V )
T h e diodes were mounted in a Janis He-immersion cryostat to allow continuous temperature variation between room temperature a n d s 4 K. T h e reverse-bias current-voltage (I-V) characteristics were measured using a n HP4145A parameter analyser. T h e background current d u e t o stray leakage paths i n t h e experimental set-up was s 1 PA. Figure 1 shows the characteristics a t temperatures between 4 K and 240 K. At high temperatures, thermally-generated electron-hole pairs dominate the d a r k current a t low bias. Above a reverse bias of about 20 V t h e current increases strongly d u e to tunneling of electrons across the band-gap. At a reverse bias of s 35 V, avalanche breakdown occurs. As the temperature decreases, the rate of thermally-generated electron-hole pairs decreases strongly, whereas t h e tunneling component is only weakly temperature dependent. T w o inflections a r e observed i n the tunneling current a t reverse biases of 24 V and a 28.5 V a t the lowest temperatures, a n d a t slightly higher bias as the temperature increases.
3. Identification of transitions. At these fields t h e potential d r o p across one period of the M Q W is of the order of the band-gap, which suggests R T across the band-gap between bound states i n the valence- a n d conduction-band quantum wells. These states are coincident i n energy when the potential drof across a period (eFa) is equal to the separation of th electron sub-band ( E , ( ~ ) a n d the hole sub-band E,(~)x i.e.
eFa=Eg+Em(h)+Ente5, where Eg is the band-gap of Gao,,,lno~53As. The sub-band energies arc measured a t t h e center of the wells. This tunneling process will occur simultaneously i n all 35 periods of the MQW. The electron-hole pair created escape f r o m the wells by thermal emission (tunnel-assisted f o r electrons) a n d a r e collected by the contacts, giving rise to the measured current.
In order to identify the tunneling transitions, the energy levels i n the q u a n t u m wells were calculated a t field corresponding t o the experimental data. T h e electron sub-band energies were calculated numerically from the t r nsmissivity of a double barrier, using a n envelope
8
function approach[5], with AEc = 0.5 e ~ [
I,
(me/m0)=0.076 (AIo~,,Ino,5,As) a n d (me/m0)=0.0427 (Gao~4,1n,~53As). T h e energy level of the lowest heavy-hole sub-band ( ~ ~ ( ~ 1 ) was estimated using a n i n f i n i t e triangular well a p p r ~ x i m a ? i o n [ ~ ] , with a heavy-hole mass of 0.465 mo. The band-gap of Gao,,,In,.53As a t 4 K i taken as 0.821 eV. The calculated values of the field f o r tunneling f r o m E , ( ~ ) into E,te) (shown in f i g u r e 2(a)) a n d f r o m E ~ ( ~ ) into E,(s)(figure 2(b)) a r e 2.56 a n d 2.99 x 10' Vcm-', respectively. This is i n excellent agreement with the experimental position of the current steps a t 2.6 x l o 5 Vcm-' (at 24 V) and 3 . 0 ~ 1 0 ~ ~ c m - ' (at 28.5 V). Observation of tunneling i n t o higher sub-bands is obscured by avalance breakdown.
T h e temperature-dependence of the bias f o r R Z T is d u e to t h e temperature-dependence of the band-gap, given by E (T) = Eg(0)-wT, where E ( 0 ) = 0.825 eV and w = 3 . 0 0 ~ 1 0 ~ ~ ~ v K - ' [ ~ ] . T h i s i s i n reasonable agreement with the experimental behaviour. T h e R Z T features become less clear a t high temperatures d u e t o t h e increasing contribution f r o m thermally- generated electron-hole pairs. T h e tunneling is
over thus a i n barrier competition of Eg+El(e)+Ei(hy, with therm 1 emission or 3 . 7
(b)\
eV. Note t h a t sequential R T between conduction- band wells[2], which occurs i n
these same samples a t lower bias, is observed (h) El only a t temperatures below *50K, due to the
lower v a j r i e r f o r thermal emission, which is AEc-El 3 . 4 eV.
\ 4. Comparison with Sequential R T i n t h e
conduction band. Sequential RT is not observed i n the reverse-bias dark-current since carriers cannot be injected f r o m t h e contacts. T h e dark-current arising f r o m electron-hole pair generation within the depletion region is below t h e detection capabilities of the experimental measurement i n the bias region (Vr<10 V) a n d temperature region ( T 4 0 K) in which sequential R T occurs. (Note t h a t i n
band wells.)
forward-bias the contacts a r e injecting a n d Figure 2. Zener tunneling f r o m the peaks a r e observed in the d a r k current d u e lowest valence sub-band into:
to sequential R T between the conduction- (a) the n = l conduction sub-band, (b) t h e , n=2 conduction sub-band.
T h e conditions f o r resonant tunneling a r e
conservation of energy a n d of lateral momentum (perpendicular to the electric field). Note t h a t a coherent (Fabry-Perot) resonant enhancement will not occur i n R Z T since the wide tunneling barrier (s 300 A) causes the build-up time of t h e electron wave f u n c t i o n i n the well t o b e - m u c h longer than the momentum relaxation time. ~ u r ~ i [ ~ ] h a s pointed out that negative d i f f e r e n t i a l resistance can occur i n incoherent R T solely through the conditions of conservation of energy a n d momentum. I n the case of sequential R T between conduction band wells i n a MQW [2], R T can only occur a t particular fields when sub-bands for adjacent wells a r e coincident i n energy. However, i n RZT, lateral momentum can be conserved a t all values of the field higher than t h a t required f o r the f i r s t resonance (figure 2a). This is d u e to the d i f f e r e n t dispersion relations f o r the conduction- a n d valence-band bound states, as shown i n f i g u r e 3. T h e left side of the f i g u r e shows the dispersion relations f o r heavy holes i n t h e n = l sub-band, a n d f o r the conduction-band barrier layer.
The total height of the tunneling barrier (B(kl)) is the vertical height.between these curves.
The right-hand side shows the n=l a n d n=2 conduction sub-bands i n a n adjacent well. The heavy-hole sub-band of the adjacent well is superimposed (dashed line) f o r clarity. In (a), the applied f i e l d causes the heavy-hole n = l energy level to line u p with the n = l electron level. Lateral momentum is conserved a t the zone centre and tunneling c a n occur. The
C5-442 JOURNAL DE PHYSIQUE
barrier height is shown by B(kl=O). At a higher bias (b), lateral momentum can be conserved a t a particular value of kl#O. The barrier height is increased to B(kl=O)
+
(fi2kl2/2m*), where (I/m*)=l/mhh)+(l/me). A t higher bias, tunneling is possible into both the n = l and n=2 sub-bands.
Although R Z T c a n occur a t all values of k l , t h e tunneling probability away f r o m the zone centre is greatly reduced by the increase i n t h e effective barrier height, by a factor [I0] xpt-el/?), where ? =
@eFti/2nm*%Zg5. T h e tunneling current is thus dominated by zone-centre tunneling which c a n occur only when t h e extrema of the hole a n d electron sub-bands a r e coincident i n energy. Thus, t h e tunneling
current i s expected to consist of peaks a t
-.
k~fields such that zone-centre tunneling can occur. T h e peak's will b e strongly assymetric due to the decreasing barrier width with
increasing field. This explains the higher (b) tunneling current f o r t h e second
experimental feature, sinze the barrier width (E /(eF)) decreases f r o m 342 A (n=l) to 283 A $n=2) while the barrier height is roughly constant.
5. Origin of background tunneling current.
The detailed shape of the R Z T resonances is hh I masked i n the experimental d a t a by a
significant background tunneling current.
This may arise f r o m two sources, both due
to the small valence band offset F i ure 3. Conservation of lateral (AEv=0.2 ev)r61. R Z T may occur from mfmeotum f o r RZT. On the l e f t is the higher energy valence sub-bands (light-hole in-plane dispersion relation f o r the n = l a n d heavy-hole n=2) i n t o the n = l heavy-hole sub-band i n t h e well, a n d conduction sub-band. These levels a r e close the conduction band in the barrier.
i n energy t o the valence band offset a n d T h e right h a n d side shows t h e f i r s t thus a r e weakly bound and considerably two conduction sub-bands of the well, broadened d u e t o penetration of the a t d i f f e r e n t fields.
wavefunction into the narrow confining
triangular barrier (of t h e order of QO A). This will give rise t o broad resonances.
Secondly, when the potential d r o p across one layer exceeds AEv, there a r e regions close to the band-edge i n the valence band "quantum wells" whic a r e not confined by the valence-band barrier. Tunneling f r o m these regions into E , k ) can occur a t reverse bias greater than
"
26 V, giving rise to a bulk-like background tunneling current.Acknowledgements. I t is a pleasure to acknowledge A.R.Adams a n d E.P.O'Reilly f o r valuable discussions, a n d A.L.Hutchinson f o r processing the samples. J.A. acknowledges financial assistance f r o m the U K Science and Engineering Research Council. F.B.
acknowledges financial support f r o m the Italian G r l ~ p p o Nazionale Struttura della Materia-Comitato Interuniversitario S t r u t t u r a della Materia.
References.
L.L.Chang, L.Esaki a n d R.Tsu, Appl. Phys. Lett. 24, 593 (1974)
F.Capasso, K.Mohammed and A.Y.Cho, IEEE J. Quantum Electronics QE-22, 1853 (1986) E.E.Mendez, W.I.Wang, B.Ricco and L.Esaki, Appl. Phys. Lett. 47, 415 (1985)
S.R.Forrest, R.F.Leheny, R.E.Nahory and M.A.Pollack, Appl. Phys. Lett. 37, 322 (1980) G.Bastard and J.A.Brum, IEEE J. Quantum Electronics QE-22, 1625, (1986)
R.People, K.W.Wecht, K.Alavi a n d A.Y.Cho, Appl. Phys. Lett. 43, 118 (1983) G.Bastard, E.E.Mendez, L.L.Chang and L.Esaki, Phys. Rev. B28, 3241 (1983) S.R.Forrest, 0.K.Kim a n d R.G.Smith, Solid-State Electronics 26, 951 (1983) S.Luryi, Appl. Phys. Lett. 47, 490 (1985)
J.L.Mol1, Physics of Semiconductors (McGraw-Hill, New York, 1964)
