CONTRIBUTEDP A P E R

Resonant Tunnelingin III-NitridesRising interest in applications of optoelectronic devices motivates this report on

nitride-based lasers that seem to exhibit capabilities like those formerly

attributed to gallium-based devices.

By Vladimir I. Litvinov, Member IEEE

ABSTRACT | Wide-bandgap semiconductors can sustain high

temperatures and high power operation in various important

applications such as transistors, light-emitting diodes, and

lasers. Although in embryonic stage, one can expect such a

resilience in GaN resonant tunneling diodes (RTDs) and super-

lattices as well with distinct applications. Because of the

negative differential conduction, the double barrier resonant

tunneling structures could be the basis for new high-power

coherent microwave sources operating in W-band and tera-

hertz. In this paper, recent progress in wide-bandgap semi-

conductor RTDs is discussed.

KEYWORDS | Resonant tunneling devices; resonant tunneling

diodes; wide-bandgap semiconductors

I . INTRODUCTION

Even at the time of its first observation in GaAs-based

heterostructures [1], resonant tunneling was recognized as

an important mechanism that could be harnessed for

oscillating devices capable of operation in the range ofW-band to terahertz. The operating principles of these

devices is based on the nonlinear electron transport

properties of the structures, namely, the negative differential

conductance (NDC) that is the basis of self-sustained current

oscillations. Resonant tunneling diodes (RTDs) have been

fabricated and intensively studied for many decades [2]–[9].

NDC in III–V double-barrier RTD persists up to room

temperature [2], [3], [10], which makes the structurescompetitive among other solid state coherent high-frequency

sources. NDC has also been observed in semiconductor

superlattices (SLs), and SL-based oscillating devices operate

up to 147 GHz [11], [12].

Since GaAs RTD-based oscillators produce microwave

output powers only at a microwatt level, it is imperative

that we explore wide-bandgap semiconductors such as

GaN-InN-AlN alloys, as they can sustain high temperatureand high power operation, as has been the case in several

important applications such as transistors, light-emitting

diodes, and lasers [13]–[15]. Shallow RTD-type structures

grown close to the surface may play an important role in

field emission applications where GaN-coated tips serve as

the large-area and low turn-on voltage electron emitters

[16]. Owing to large conduction band offsets available in

the GaN-based heterostructures, this system would pro-vide much more flexible tuning of resonant tunneling

compared to their GaAs-based counterparts.

Below we review vertical transport properties of

GaN-based RTD-like structures as a first-level attempt with

respect to electrical instabilities that can be used in oscil-

lating device applications. What distinguishes GaN-based

RTDs from those of the GaAs system, in addition to the

former being wide bandgap, is the presence of polarizationcharge and associated electric field with substantial impact

on the expected results. Fittingly, the discussion here will

begin analyzing the band structure with polarization effects

figured in.

II . RESONANT TUNNELING ANDPOLARIZATION FIELDS

Device modeling [17]–[19] has been performed taking into

account the piezoelectric and spontaneous polarizations and

resulted in pretty much standard tunneling I–V character-

istics with a well-defined NDC region, similar to those in

GaAs-based devices but distorted by electrical polarization.

The conduction band profile and electron wave

functions in a double barrier resonant tunneling (DBRT)

Manuscript received March 21, 2009; revised July 22, 2009; accepted July 31, 2009.

Date of publication February 25, 2010; date of current version June 18, 2010. This work

has been supported by the Air Force Office of Scientific Research under a Grant.

The author is with the Sierra Nevada Corporation, Irvine, CA 92618 USA

(e-mail: vlitvinov@earthlink.net; vladimir.litvinov@sncorp.com).

Digital Object Identifier: 10.1109/JPROC.2009.2039027

Vol. 98, No. 7, July 2010 | Proceedings of the IEEE 12490018-9219/$26.00 �2010 IEEE

diode AlN/GaN/AlN are shown in Fig. 1. Band offsets and

polarization-induced internal electric fields in all three

layers have been calculated with the method of [20] and

[32]. The reference energy is the conduction band edge of

the left GaN contact.

Polarization fields shift confinement energy levels in

DBRT diode as compared to those calculated in a flat-band

approximation. Obviously, both polarization fields andapplied voltage distort the band profile, and thus change

the resonant energies with impact on any tunneling

process. The role of applied voltage Vext is seen from a

simple example of tunnel transmission. Biased flat-band

DBRT shown in Fig. 2 reveals a bias-dependent transmis-

sion coefficient, illustrated in Fig. 3.

The transmission coefficient has been calculated by a

transfer matrix method using Airy functions as a basis set.The results shown in Fig. 3 clearly indicate that one

should not expect resonances in the I–V characteristics to

be concomitant with the energy levels in an unbiased

DBRT structure since the applied voltage also distorts the

band profile thus shifting the resonances.

As stated earlier, the polarization-induced internal

electric fields are expected to make the I–V characteristics

asymmetric with respect to the polarity of applied voltage.However, this is not the only reason for the asymmetric

I–V traces to occur. The structure can be highly asymmetric

because of a depletion region formed on the right (top) GaN

contact [21]. In this context, the depletion region at doping

level of Nd ¼ 1018 cm�3 is shown in Fig. 4.

In order to single out the role of polarization fields, we

present in Figs. 5 and 6 the transmission coefficient in a

highly doped structure where the depletion region is shortand somewhat irrelevant.

Figs. 5 and 6 compare and contrast tunneling with and

without polarization fields taken into account. It is,

therefore, clear that the polarization fields influence the

tunneling characteristics considerably and have notable

implications on the I–V characteristics of the GaN-based

RTDs.

Fig. 1. Band profile (eV) along the growth axis (A) and an electron

wave function in 20/20/20 A DBRT: E1 ¼ 0:136 eV, E2 ¼ 0:952 eV.

Fig. 2. Biased DBRT conduction band profile in flat band

approximation. 1) Vext ¼ 0, 2) Vext ¼ 1 V, and 3) Vext ¼ 2 V.

Fig. 3. Transmission coefficient ðLog10ðTÞÞ versus energy (eV)

calculated by a transfer matrix method. 1) Vext ¼ 0:005 V,

2) Vext ¼ 1 V, and 3) Vext ¼ 2 V.

Fig. 4. Band profile (eV) versus distance in the structure

20 A/20 A/20 A studied in [21]; Nd ¼ 1018 cm�3. 1) Vext ¼ �2 V;

2) Vext ¼ 0; and 3) Vext ¼ 2 V.

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1250 Proceedings of the IEEE | Vol. 98, No. 7, July 2010

The tunneling current through the structure can be

written as

J ¼ 2q

ð2��hÞ3Zð fe � fcÞT dEz d~pk (1)

where T is the transmission coefficient and fe;c are the

electron distribution functions in bulk GaN emitter and

collector, respectively. After integration over the direc-tions of the in-plane momentum, the current takes

the form

J ¼mkqkBT

2�2�h3

Z1

0

dEz

ZymaxðEzÞ

0

dyTðEz; yÞ�ðEz; yÞ

� ¼ expðvÞ � 1

1þ expð�x� yÞ þ expðxþ yþ vÞ þ expðvÞ

x ¼ Ez � Ef

kBT; y ¼

p2k

2mkkBT; v ¼ qVext

kBT: (2)

The limits of the in-plane momentum integration ymaxðEzÞare determined by the regions where both incident and

outgoing electron moments are real.

Large depletion region shown in Fig. 4 preventstunneling from the right to the left contacts and results

in the asymmetric I–V curve as illustrated in Fig. 7.

If the top contact is doped to 5 � 1018 cm�3, the deple-

tion region becomes narrower and less relevant, polariza-

tion fields are pretty much screened, so the I–V curve

becomes almost symmetric as shown in Fig. 8.

From the theory standpoint, nothing prevents the

resonant tunneling to be observed whether the polariza-tion fields are present or not. However, the depletion

region and polarization fields may shift the NDC region

toward the higher applied voltage (see Fig. 7) that might

result in a contacts breakdown.

Fig. 5. Transmission coefficient in an unbiased DBRT structure,

flat-band approximation. 1) 10 A/20 A/10 A; 2) 20 A/20 A/20 A; and

3) 30 A/20 A/30 A.

Fig. 6. Transmission coefficient in an unbiased DBRT structure,

polarization fields included. 1) 10 A/20 A/10 A; 2) 20 A/20 A/20 A;

and 3) 30 A/20 A/30 A.

Fig. 7. I–V characteristics at various doping levels of the top GaN

contact. Mesa diameter: 75 �m, 20 A/20 A/20 A.

Litvinov: Resonant Tunneling in III-Nitrides

Vol. 98, No. 7, July 2010 | Proceedings of the IEEE 1251

III . CURRENT–VOLTAGECHARACTERISTICS

On the experimental front, the structure and the I–V

characteristics of the first GaN-based RTD’s reported in

[22] and [33] are shown in Figs. 9 and 10, respectively.

Fig. 10. illustrates the I–V curve in the RTD structure

shown in Fig. 9.

The structure shown in Fig. 9 and those reported in

[23]–[25] and [34] have been grown by plasma-assisted

molecular beam epitaxy (MBE) with purported precautionstaken in order to prevent dislocation penetration from the

metal-organic chemical vapor deposited template.

An NDC region has been reported in an MBE-grown

structure on a bulk GaN substrate [25] (see Fig. 11). It was

anticipated that the low dislocation density might help an

NDC formation.

It should be noted that the results shown in Fig. 10have not been confirmed by any other group and may

represent anomalies in contacts. Results illustrated in

Fig. 11 (curves F1–F5) do not necessarily prove the

expected resonant tunneling was observed since the peak-

to-valley ratio could not be resolved. So, the very existence

of NDC as measured and its relation to the quality of

interfaces and contacts is still controversial. It is clear that

high-quality structures are needed to minimize or prefer-ably eliminate the extraneous current so that the tunneling

process would be dominant.

The main point of confusion is that although an NDC

region in I–V traces has already been reported [22], [24],

[25], [33], it is not the only unstable behavior observed. In

some instances, the hysteresis in the I–V curve when the

voltage sweeps in opposite directions [23], [26], [34] and

Fig. 8. I–V characteristics with no polarization fields and no depletion

region. Structure 20 A/20 A/20 A, mesa diameter: 75 �m,

Nd ¼ 5 � 1018 cm�3.

Fig. 9. RTD layout (from [22] and [33]).

Fig. 10. RTD tunneling I–V characteristics (from [22] and [33]).

Fig. 11. Room-temperature I–V traces (from [25]).

Litvinov: Resonant Tunneling in III-Nitrides

1252 Proceedings of the IEEE | Vol. 98, No. 7, July 2010

current jumps [21] were clearly observable in the I–V

characteristics (see Figs. 12 and 13).

Figs. 12 and 13 show I–V traces typical for the S-typecharacteristics where current instabilities mark the NDC

regions on the horizontal voltage scale. The origin of these

instabilities as well as the reported NDC in the literature

would need to be determined.

To date, the GaN-based RTDs demonstrate quite rich

behavior in terms of the type of I–V characteristics,

which has been attributed to resonant tunneling in

polarization-distorted DBRT diodes and strong electronscattering by defects of various types. As is widely

recognized, the interface quality, dislocations, and

electron traps in the barriers strongly influence the

tunneling process. Defects in the barriers that trap orrelease electrons as the voltage sweep changes in

amplitude and polarity are assumed to be responsible

for the hysteresis in the I–V characteristics.

It should be noted that the presence of traps is not

the only possible reason for the hysteresis. Even though

the NDC region has not been explicitly observed in the

structure characterized in Figs. 10 and 11, the S-type

behavior provides for hysteresis and also implies that NDCdoes exist in the bistable region. Under an applied voltage,

the total current is not fixed as various current channels

(including leakage through electrically active threading

dislocations) may contribute to the total current when

voltage changes. In the system with S-type characteristics,

providing that the current is not fixed, the system jumps

from one stable current state to another making the NDC

region unobservable [27]. The stable states presentinhomogeneous current distributions across the device

mesa. Recently, two stable current states have been found

in another AlN/Ga/AlN device [28]. The microscopic

origin of the S-type characteristics in GaN/AlGaN-RTDs

still remains to be explained but might be associated with

both tunneling and electron heating. Electron heating is

caused by a fast electron scattering by ionized defects

accompanied by a slow phonon-assisted energy relaxation.For further information, various mechanisms of S-type

behavior in homogeneous semiconductors have been

studied in [29].

It is reasonable to expect that as high-quality bulk GaN

substrates become available, further research would most

likely be undertaken and undoubtedly shed the much

needed light and perhaps lead to NDC, which is capable of

leading to microwave oscillations.Observation of NDC or other type of instability under

dc or pseudo-dc conditions alone may not be sufficient.

Attainment of high-frequency oscillations in a cavity, for

example, would go a long way to add the much needed

credence to the NDC observations. In the quest for the

current instability region, it would be useful to fabricate

the cubic or nonpolar GaN-based structures, where

polarization fields play no role that makes possible acomparison to I-V curves in (100) GaAs RTDs. Growth of

the free-standing cubic GaN structures for various

electronic devices is discussed in [30].

If the vertical transport in GaN/AlGaN RTD was

fully understood, it would create a background for

further development of superlattice-based semiconduc-

tor high-frequency sources. Preliminary modeling and

simulation of GaN-based oscillating superlattice struc-tures and devices have been performed in [20], [31],

and [32]. h

Acknowledgment

The author thanks Prof. H. Morkoc for valuable

discussions.

Fig. 12. S-type I–V characteristics of DBRT. (a) Temperature-dependent

I–V characteristics with a heavily doped (5� 1018 cm�3) top n-GaN

layer (from [21]).

Fig. 13. S-type I–V characteristics of Fig. 9. Curve tracer image of I–V

characteristics near 1.4 V (from [21]).

Litvinov: Resonant Tunneling in III-Nitrides

Vol. 98, No. 7, July 2010 | Proceedings of the IEEE 1253

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ABOUT THE AUT HOR

Vladimir I. Litvinov (Member, IEEE) received the Ph.D. degree in solid

state theory from Chernovtsy University, Ukraine, and the Habilitation

degree in physics and mathematics from the Institute of Physics, Estonian

Academy of Science, Tartu.

In 1978, he became Head of the Theoretical Laboratory, Institute of

Material Science Problems, Academy of Science of Ukraine. In 1996–

1999, he was a Senior Research Associate at the Department of

Electrical and Computer Engineering, Northwestern University, Evanston,

IL. He joined Sierra Nevada Corporation in 1999. His areas of

expertise include theory and modeling in semiconductor physics, III–V,

and IV–VI semiconductor optoelectronic devices, superlattices, metal-

lic magnetic multilayers, and millimeter-wave devices and antennas.

He has served as the Principal Investigator on projects supported by

the U.S. Air Force, SOCOM, U.S. Army, U.S. Navy, NASA, and MDA. He

has authored or coauthored over 150 publications and conference

papers.

Dr. Litvinov is a member of the American Physical Society and Material

Research Society.

Litvinov: Resonant Tunneling in III-Nitrides

1254 Proceedings of the IEEE | Vol. 98, No. 7, July 2010