CHARGE TRANSPORT AND INTRINSIC BISTABILITY IN RESONANT TUNNELING STRUCTURES

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CHARGE TRANSPORT AND INTRINSIC BISTABILITY IN RESONANT TUNNELING

STRUCTURES

V. Goldman, D. Tsui, J. Cunningham

To cite this version:

V. Goldman, D. Tsui, J. Cunningham. CHARGE TRANSPORT AND INTRINSIC BISTABILITY IN

RESONANT TUNNELING STRUCTURES. Journal de Physique Colloques, 1987, 48 (C5), pp.C5-

463-C5-466. �10.1051/jphyscol:1987597�. �jpa-00226801�

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JOURNAL DE PHYSIQUE

Colloque C5, supplement au n0ll, Tome 48, novembre 1987

CHARGE TRANSPORT AND INTRINSIC BISTABILITY IN RESONANT TUNNELING STRUCTURES

V.J. GOLDMAN, D.C. TSUI and J.E. CUNNINGHAM*

Princeton University, Princeton, NJ 08544, U.S:A.

* A T and T Bell Laboratories, Holrndel, NJ 07733, U.S.A.

Nous rapportons des mesures de caractiristiques courant-tension s u r des structures tunnel risonantes & double barriere (DBRTS), demontrant une bistabilite intrinskque. Nous interpretons les donnees dans le cadre d'un mod6le auto-consistant, qui tient cornpte de l a formation de la zone de charge dans l a DBRTS, e t dernontre que la bistabilite intrimeque est due & l a contre-reaction d u champ electrique des electrons dans le puits s u r la densite de courant tunnel.

M'e report measurements of current-voltage characteristics of AIG&/Gaks double-barrier resonant tunneling structures (DBRTS) which exhibit intrinsic bistability. W e interpret the d a t a with a self-consistent model which takes into account t h e space-charge formation in DBRTS and show t h a t the intrinsic bistability is due t o the feedback of t h e electrostatic field of the electrons in the well on the tunneling current density.

Presently, there is substantial interest in the physics and device applications of semiconductor-based double-barrier resonant tunneling structures (DBRTS) 11-51. This interest is motivated, in part, by the prospects of using DBRTS in high-speed electronics as oscillators [I], switches and memory units. DBRTS are of interest also from the point of view of physics providing an' experimentally realizable macroscopic quantum system. In this paper we present the steady-state electrical transport data for high-quality DBRTS and interpret these data sys- tematically within the sequential resonant tunneling picture [2,4].

Our DBRTS were grown in a VG-80 molecular beam epitaxy system. A relatively low substrate temperature of 620" C was employed t o limit Si diffusion into the barriers. Epitaxial layers were grown on an n+

<loo>

GaAs substrate. In order of growth the layers are: (i) O.lpm of n+ = 1 . 5 ~ 1 0 ' ~ c m - ~ ; (ii) 0.4pm of n = 2 ~ 1 0 ' ~ c m - ~ GaAs; (iii) 8 5 i of undoped Alo,40G~,s&; (iv) 5 6 i of undoped GaAs; (v) 8 5 i of undoped A l o , 4 0 G ~ , & ; (vi) 0.4pm of n

= 2 ~ 1 0 " c m - ~ GaAs; and O.l,um of n+ = 1 . 5 ~ 1 0 ' ~ c m - ~ GaAs. The A1 content in AlGaAs was calibrated using X-ray diffraction and photoluminescence measurements and is believed to be accurate to within 3%. The devices were defined by a shadow-mask evaporation of AuNiGe film

IOOOA

thick and 20 t o 150 ,tm in diameter, and subsequent mesa etching. Good Ohmic contacts were formed by alloying a t 350 " C in Hz atmosphere for 30 sec.

The current-voltage (I-V) characteristics of a DBRTS device a t several temperatures are shown in Fig. 1. The negative differential resistance (NDR) is present but small a t room temperature since most of the current is transported by electrons thermally excited t o energies near the E, subband or the top of the barrier in this thick-barrier structur.9. The current peak-to- valley (PTV) ratio increases rapidly upon cooling and exceeds 13:l at 77K. This is, to our knowledge, the highest reported value for a DBRTS. Upon further cooling PTV ratio continues to increase somewhat and reaches 17:l a t 4.2K.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987597

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C5-464 JOURNAL DE PHYSIQUE

i

Fig. 1:

I-V curves of a DBRTS device (11Opm diam) a t several temperatures.

... _{4.2 K}

-

⁷⁷^K

---

³⁰⁰^K

I , I / / , , , , , I , , ,

-0.6 -0.4 -0.2 0 0.2 0.4 0.6 BIAS (V)

d w d

I I " ' _ ^E~

-

₄

-

^-

K

-

K

Schematic CB energy

0 ' I 1 ' ' -

o 0.2 0.4 0.6 0.22 0.30 0 . 3 6 diagram of a DBRTS

BIAS ( V ) B I A S ( V l

under bias V. The Fig. 2: I-V curves of the undamped and damped DBRTS inset shows the aecu- (area 4 . 5 ~ 1 0 - ~ c m ~ ) a t 4.21IC. The dashed vertical mulation layer in the lines show the switching between the high and low emitter.

current states.

Fig. 2a shows he I-V characteristics of another DBRTS device (area 4 . 5 ~ 1 0 - ~ c ~ ~ ) meas- ured at 4.21K with a n d without a capacitor. The equivalent experimental circuit consists of a voltage source, series resistance R , inductance of the connecting wires L and t h e DBRTS. T h e bias applied t o the DBRTS is swept a t

--

0.1 mV/sec and is measured using t h e pseudo-four- terminal technique in order t o eliminate t h e voltage drop IR. T h e series impedance wL, however, does not allow us t o maintain a constant bias across t h e DBRTS on a short time scale w-' a t t h e NDR region of t h e I-V curve, and the biasing circuit oscillates [I]. We, however, can maintain V constant o n a time scale LC b y connecting a capacitor C i n ~ a r a l l e l t o the DBRTS;

on a longer time scale t h e impedance wL is small enough not t o cause oscillations. The "real"

I-V curve displays t w o bistable regions of V, shown in detail in Fig. 2b. T h e I-V curve does not change appreciably as t h e temperature is lowered t o 1.6K.

In Ref. 4 we have shown t h a t t w o previously neglected effects are quite substantial in prac- tically all experimentally studied DBRTS. The first is the formation of the accumulation and depletion layers in t h e emitter and t h e collector electrodes, respectively, i n a biased device (Fig.

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3). The areal concentration of electrons and ionized donors is - 5 ~ 1 0 ~ ' c m - ~ . The depletion layer reduces the electric field in the barriers and the well thus increasing the bias required t o align the energy of the bottom of the subband in the well, EBsB, and EF. The accumulation layer lowers the CB edge in the emitter close t o the barrier, thus lowering EBSB, relative to EF, in contrast to the depletion layer, and also extends the range of energies from which the electrons can tunnel (see below).

The second effect is the formation of the space-charge created by the tunneling electrons in the well. Once an electron has tunneled into the well it occupies a resonant state with the kinetic energy of just above E,. If we denote the transmission coefficient of the collector barrier as T2, then the lifetime in the well is T rr. ii/(T2Eo). Since the number flux of electrons passing through the well in the steady state is -J/e, where J is the tunneling current density, the areal concentration of the electrons in the well is n, rr liJ/(eT2Eo). Consequently, the electric field in the collector barrier, Vz/d, can be appreciably greater than Vl/d (see Fig. 3). A simple estimate gives n,

-

¹X 10"crn-~ a t the peak current.

The origin of the intrinsic bistability in the DBRTS is quite simple and basic 15). The voltage drops across the different regions of the structure must add up t o V; therefore, both V1 and Al decrease (at a fixed V) as J increases (both V2 and

4

increase). That is, the energy separation between the EF in the emitter and the bottom of the subband in the well, AE, depends on J through this electrostatic feedback mechanism. Since J is determined by AE, two stable states of the DBRTS occur at certain biases (cf. inset in Fig. 2b).

We interpret the experimental I-V curve as follows. At low biases, V s 160mV, the bottom of the subband in the well (EBSB) is higher in energy than the emitter EF and no resonantly enhanced tunneling is possible. I starts to rise when EBsB is aligned with the emitter EF, and, as the energy separation between the two,

aE,

increases, I continues t o rise. As illustrated schematically in the inset in Fig. 3, the electric field in the accumulation layer leads t o 2D quantization of the electronic states in the emitter, near the barrier. The higher lying subbands overlap strongly, however, due, mostly, t o the energy broadening produced by the ionized donors. These subbands are not resolved and can be treated collectively as 3D states. When V is such that EBsB is just below these 3D states in the emitter, resonantly enhanced tunneling is no longer possible since the component of the electron wave-vector transverse to I, kl cannot be conserved in an elastic process, and I drops. The energy separation between the bottoms of the lowest subhands in the accumulation layer is substantial, and one of them is clearly resolved so that there are two bistable regions in the I-V curve in Fig. 2.

It is evident from the data shown in Fig. 1 that the valley current is essentially temperature-independent below 77K. This independence implies that the valley current is due to a tunneling process. Fig. 4 shows the blown-up I-V and the dI/dV-V curves of the valley region of Fig. 2. An interesting, previously unreported feature is a replica peak seen clearly in these data a t V

---

^0.35V^161. The LO-phonon-emission-assisted tunneling becomes possible a t AE = kw,, the LO-phonon energy, and the probability of such process peaks a t AE

=

kc^,

+

^EF

[7]. In general there are three types of LO-phonons which could be emitted in an inelastic tunneling event in DBRTS. First is the GaAs LO-phonons (hw,

--

36 meV); the other two are the GaAs-like and the AlAs-like LO-phonons in Alo4G%& barrier ( z 35meV and

--

^{47 meV,}

respectively). The replica peak is shifted by

--

45 meV (in &3) from the elastic peak; however,

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C5-466 J O U R N A L D E PHYSIQUE

there is no evidence for a similar structure shifted by

--

35meV. This indicates that the inelastic tunneling is accompanied by emission of the AlAs-like LO-phonons in the barrier with no appreciable contribution from the two other possibilities. The magnitude of the inelastic tunneling current peak is

--

0.04 of the elastic one.

Also shown in Fig. 4 is the dI/dV-V curve taken in the magnetic field B = 8.5 Tesla (parallel t o the direction of tunneling). The most striking feature of the magnetoconductance curve is the oscillations which become observable a t B 2: 2.5T. Since these oscillations extend through the whole bias range between the E, and the E l tunneling peaks, we conclude that they are due t o a kl-nonconserving, but elastic tunneling from the occupied states in the emitter elec- trode t o the Landau-quantized states of the lowest (E,) subband in the well [3,4]. The ionized impurity scattering appears to be the most likely mechanism which lifts the kl conservation rule in this DBRTS. This interpretation is supported by the general shape of the valley region of the I-V curve which, except for the inelastic tunneling peak, appears to be composed of the tails of the E, and E l tunneling peaks.

The work at Princeton is supported in part by the U.S. Army Research Office under Grant NO. DAAG29-85-K0098.

Fig. 4: The I-V and dI/dV-V curves in the valley region of Fig. 2. Inset shows schematically a LO-phonon-emission-assisted tunneling event. The dotted line (drawn by hand) indicates the background current in the replica peak region. The

aE

scale was calcu- lated as described in Ref. 4.

I

'

Î Î Î

References

1. T.C.L.G. Sollner, et al, Appl. Phys. Lett. 45 (1984) 1319; T.J. Schewchuk, et al, ibid 46 (1985) 508.

2. S. Luryi, Appl. Phys. Lett. 47 (1985) 490 and references therein.

3. E.E. Mendez, L. Esaki, and W.I. Wang, Phys.

Rev. B33 (1986) 2893 and references therein.

4. V.J. Goldman, D.C. Tsui, and J.E. Cunningham, Phys. Rev. B35 (1987)

5. V.J. Goldman, D.C. Tsui, and J.E. Cunningham, Phys. Rev. Lett. 58 (1987) 1256; also S.

Wingreen and J.W. Wilkins, Bull. Am. Phys.

SOC. 32 (1987).833.

6. V.J. Goldman, D.C. Tsui, and J.E. Cunningham,

100 AE(meV)

t o be published in Phys. Rev. B15.

7. The electrons do not couple t o the TO-phonons 0.4 0.5 0.6

[e.g., D.C. Tsui, Phys. Rev. Lett. 21 (1968) 9941.

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