Current degradation due to electromechanical coupling in GaN HEMT’s

Balaji Padmanabhan, Dragica Vasileska and Stephen M. Goodnick

Arizona State University, Tempe, AZ 85287-5706

balajipad@gmail.com; vasileska@asu.edu; goodnick@asu.edu

ABSTRACT

In this work we first report on a theoretical model which

provides the gate voltage dependence of the piezoelectric

polarization charge in GaN HEMT devices. The model

utilizes a generalization of Gauss’ law, imposing

constraints on the electric displacement vector D. The

constraint on D is given by the continuity of the

perpendicular component of the displacement vector across

an interface. Poisson’s equation is then solved across

various layers under proper boundary conditions for the

applied bias. The piezoelectric polarization charge is

reduced due to the electromechanical coupling compared to

the uncoupled case. Under high sheet electron densities, the

correction in the piezoelectric polarization charge is also

lower due to smaller electric fields. The theoretical model is

then incorporated in the particle-based device simulator and

device transfer and output characteristics are calculated

without and with the bias dependent polarization charge.

We find that percentage change in drain current increases

with larger negative bias on the gate, due to the larger

vertical electric fields.

Keywords: Electro-Mechanical Coupling, GaN HEMTs,

polarization charges.

1 INTRODUCTION

AlGaN/GaN high-electron mobility transistors

(HEMTs) are a very promising technology for switching

and radio frequency power applications due to the high

saturation velocity and large breakdown field of the GaN

material [1]. However, the electrical reliability of this

material system is still a fundamental problem to be solved

before the widespread use of this technology can be made.

Reports of reliability that have appeared in the last few

years include both the on and the off-state operation

regimes.

The major concerns in these device structures are proper

understanding of the physics of the underlying relevant

mechanisms that lead to reliability concerns. One such

concern is the electric-field induced strain degradation, also

known as electro-mechanical coupling. The polarization

charge which is responsible for inducing carriers in the

channel comprises of two components, spontaneous and

piezoelectric polarization charge. The piezoelectric

polarization charge which is due to the stress between the

layers varies with the applied gate voltage and therefore

alters the channel carrier density.

In previous work, a theoretical model was developed [2]

to model the physics behind electro-mechanical coupling in

GaN HEMT structures. A relation between the piezoelectric

polarization and the vertical component of the electric field

in each layer comprising the device structure was derived

from the generalization of Gauss’s law, imposing

constraints on the electric displacement vector.

In the present work, the electro-mechanical coupling has

been implemented into a particle based Monte Carlo device

simulator. Simulation results have been obtained for the

transfer, output characteristics and percentage change in the

drain current given the drain voltage and various gate

voltages.

The paper is organized as follows. In Section 2, the

theoretical model with which we account for the electro-

mechanical coupling is briefly described. Afterwards, the

particle-based device simulator, that in a self-consistent

manner accounts for the electro-mechanical coupling, is

discussed. Simulation results are presented in Section 3.

These results illustrate the importance of the electro-

mechanical coupling and its impact on the magnitude of the

drain current. Conclusions from this work are presented in

Section 4.

2 THEORETICAL MODEL

In bulk GaN the 1D Poisson equation may be written,

far from the GaN/AlN interface, as follows

3

2

2

εDqN

dx

d −=

Ψ (1)

where ψ represents the electrostatic potential, ND is the

donor concentration, and ε3 is the bulk GaN permittivity. The solution of the 1D Poisson equation for a bulk GaN

slab of thickness W (see Figure 1), ignoring for the moment

the sheet electron density in the triangular potential well,

and assuming that )( Wxb =Ψ=Φ and 0)0( ==Ψ x ,

gives using simple algebra

)2

()(2

3

xWx

qNx D −=Ψ

ε, (2)

or

Db

qN

E

2

)0(2

33ε=Φ . (3)

NSTI-Nanotech 2012, www.nsti.org, ISBN 978-1-4665-6275-2 Vol. 2, 2012 17

(3)

where )0(3E is the electric field at the GaN interface (x =

0). The Fermi potential in the bulk GaN region is given by

)ln(D

CF

N

N

q

KT=Φ . (4)

(4)

At the AlN/GaN interface, using Gauss’ law one arrives

at the following expression for the field in the AlN layer

[2],

2

22332

)0(

ε

σε DqnqEE+−

= , (5)

(5)

where the various terms appearing in (5) are defined in Fig.

1. At the AlGaN/AlN interface the field is given by

1

21331

)0(

ε

σε DqnqEE+−

= (6)

For the entire structure (Fig. 1) one has that

0222111 =Φ−Φ+∆−+∆++Φ Fbs dEdE (7)

Substituting (3), (5), and (6) into (7) leads to a quadratic

equation for )0(3E of the form

))(

)(((

))(0(2

)0(

222

2

211

121

2

32

1

313

233

D

DFs

D

nqd

nqd

ddE

qN

E

−+

−−∆−∆+Φ−Φ

+++

σε

σε

ε

ε

ε

εε

(8)

The solution for )0(3E is used in the expressions for the

field in the AlN, E2, and the field in the AlGaN, E1. Having

calculated the fields in the various domains allows us to

proceed with the calculation of the piezoelectric

polarization charges at various interfaces using [3]

α

ααα

α

αααα

33

2

3333

33

1331 )(2

c

eEe

c

ceP zxPE +−Ξ= (9)

where α represents the layers, αzE represents the electric

field normal to each layer which is calculated using the

theoretical model described above, α31e and α33e are the

piezoelectric constants, α13c and α33c are the elastic constants

and αxΞ represents the strain at the surface given by

toplayer

toplayerrbottomlaye

a

aa − (10)

where a represents the c-plane lattice constant of the

material.

n2D

2σ

2σ−

1σ

sΦ

2∆

FΦbΦ

1d 2d

Figure 1. The conduction Band profile under zero gate bias in an

AlxGa1-xN/AlN/GaN structure, defining the various terms

appearing in Eqs. (3-8). The top panel is the conduction band

profile and the bottom panel describes the charge densities in the

system; d1 is the thickness of the AlGaN layer and d2 is the

thickness of the AlN layer.

The Ensemble Monte Carlo transport kernel

incorporates a 3 valley non parabolic band model (see

Figure 2 for the case of GaN) and various scattering

mechanisms such as acoustic, polar optical phonon, ionized

impurity, inter valley and piezoelectric scattering were

included.

k=0

k

ΓΓΓΓ1

ΓΓΓΓ2

L-M

Figure 2. Graphical description of the conduction bands in GaN

used in our theoretical model. Similar model has been used for

AlN.

Device simulations were performed using our in-house 2D

particle-based device simulator to generate the ID – VD and

ID – VG characteristics using the two polarization models –

“uncoupled” and “coupled” formulations to study the

importance of the gate bias induced strain in these

NSTI-Nanotech 2012, www.nsti.org, ISBN 978-1-4665-6275-2 Vol. 2, 201218

heterostructures. The flow-chart of the device simulator,

which in a self-consistent manner incorporates the electro-

mechanical coupling, is shown in Figure 3.

Initialize Material Parameters

and Device Structure

Monte Carlo Kernel:

free-flight-scatter

Solve Poisson Equation

Molecular Dynamics

Collect Results

Bias polarization

Perform

Particle-Mesh

Coupling

Figure 3. Flow-chart of the particle-based device simulator that in

the self-consistent manner takes into account the bias polarization

charge.

3 SIMULATION RESULTS

The dimensions of the actual structure being simulated

are given in Figure 4. Briefly, it consists of bulk GaN on

top of which is grown 1 nm of AlN, which is used to

prevent the spillover of the carriers from the channel in the

AlGaN layer where alloy disorder scatering dominates the

mobility and drift velocity. The thickness of the AlGaN

layer is 16 nm. On top of the AlGaN layer, a layer of

unintentionaly doped GaN of thickness of 3 nm is grown.

This layer is supposed to lead to less surface states which

can trap the carriers. Shielding electrodes are not being

considered in this structure. In the present work we also do

not account for self-heating, even though we have the

capability to do so, because of simple reason that we want

to isolate the effect of electro-mechanical coupling on the

device drain current for various gate and drain voltages.

The device transfer characteristics for the case of the

“uncoupled” and “coupled” formulation are shown in

Figure 5. From the results presented in this figure one

clearly sees that the coupled formulation leads to

degradation in the drain current that varies from 2 to 18%

(see Figure 6). The degradation in the drain current is the

largest near the threshold voltage and reduces for more

positive gate voltages. This behavior can be easily

explained using the charge argument. Namely for large

negative bias, there is almost no inversion charge density in

the channel and the vertical fields are high. For zero bias on

the gate the inversion charge is the highest and it balances

the net positive spontaneous and polarization charge

density, hence the vertical field is the smallest.

UID GaN 3nm

UID Al0.28Ga0.72N 16nm

UID AlN 1nm

UID GaN Channel 100nm

GaN

Source

1018cm-3

n-doped

GaN

Drain

1018cm-3

n-doped

1.0 um

0.25 um0.1 um 0.1 um

GATE

DR

AIN

SO

UR

CE

Y

X

Figure 4. GaN/AlN/AlGaN structure being considered in this

study.

Figure 5. Transfer characteristics of the device structure depicted

in Figure 4.

Figure 6. % change in drain current due to the incorporation of the

electro-mechanical coupling.

NSTI-Nanotech 2012, www.nsti.org, ISBN 978-1-4665-6275-2 Vol. 2, 2012 19

Figure 7. Device output characteristics for VG = 0, -1, and -2 V.

The same trends are clearly seen in the device output

characteristics shown in Figure 7. Namely, the on-current is

smaller when the electromechanical coupling is

incorporated in the model and the difference is the largest

for VG= - 2 V. For applied gate bias of 0V there is much

smaller current degradation on the order of 2-3 %. More

work needs to be done to better match the experimental

data and that is currently being pursued. Namely, we have

to account for the partial relaxation of the lattice and the

modification of the theoretical values of the polarization

charges. The results of these investigations will be

published elsewhere.

4 CONCLUSIONS

In summary, we have presented a theoretical

model and its numerical implementation for the

incorporation of the electromechanical coupling when

modeling GaN/AlN/AlGaN HEMTs. We find that

electromechanical coupling is important near threshold

regime of device operation. In the on-state, the corrections

due to electromechanical coupling are on the order of 2%.

ACKNOWLEDGMENT

This work was supported by a grant from the Army

Research Laboratory. Program coordinator is Tsvetanka

Zheleva. We also acknowledge the financial support from

the NSF under contract No. ECCS 0901251.

REFERENCES [1] W. Saito, I. Omura, K. Tsuda, “High-Voltage GaN-HEMTs

for Power Electronics Applications and Current Collapse

Phenomena under High Applied Voltage”, CS Mantech

Conference, 2007.

[2] B. Padmanabhan, D. Vasileska and S. M. Goodnick,

Electromechanical Coupling in AlGaN/AlN/GaN HEMT's, in

Proceedings of the 2011 Nanotech, pp. 679 - 681, 2011.

[3] A. F. M. Anwar, R. T. Webster and K. V. Smith, “Bias

induced strain in AlGaN/GaN heterojunction field effect

transistors and its implications”, Appl. Phys. Lett., vol. 88, p.

203510, 2006.

NSTI-Nanotech 2012, www.nsti.org, ISBN 978-1-4665-6275-2 Vol. 2, 201220