Optical nonlinearities due to carrier transport in semiconductors

Garmireet al.

Vol. 6, No. 4/April 1989/J. Opt. Soc. Am. B

579

Optical nonlinearities due to carrier transport in semiconductors Elsa Garmire, N. M. Jokerst, A. Kost, A. Danner, and P. D. Dapkus Department of Electrical Engineering, University of Southern California,Los Angeles, California 90089-1112 Received October 4, 1988; accepted December 28, 1988 A nonlocal nonlinearity results when optically excited carriers move within the internal electric fields of depletion regions, causing field-dependent changes in absorption and/or refractive index. We review some recent experimen-

tal results and use these concepts in hetero-Schottky barriers and hetero-n-i-p-i structures. We show that extremely sensitive, rather large nonlinearities result.

INTRODUCTION Semiconductor nonlinearities can generally be grouped into three basic classes, as shown in Table 1. These include the intrinsic, local nonlinearities that have been explored for

many years. Nonlinear mechanisms include saturable absorption and its resulting nonlinear refractive indices that are due to band filling and band-gap renormalization, as well as plasma-induced index changes, in bulk materials 1' 2 and in thin films.3 In multiple quantum wells, all the above non-

linearities are present but are altered by quantum confinement, which enhances the exciton nonlinearities.4 At the other end of the scale, hybrid nonlinearities have been proposed that use photogenerated currents in an external circuit to alter electrical biases, causing photoactivated modulation, such as the quantum-well self-electro-optic-effect device12 (SEED) and its counterpart in thin-film devices.1 1 These hybrid nonlinearities represent specific examples of the class of hybrid optical nonlinearity first suggested by Garmire et al.10 for use with a modulator-detector

combina-

acteristic lifetime. The result is a net bound charge distribution centered in the dark areas, since after carrier transport these carriers cannot be reexcited. This periodic charge distribution induces a periodic electric-field distribution. In photorefractive materials, the spatially varying electric field gives rise to a spatially varying refractive index through the electro-optic effect. It can be seen that the photorefractive effect utilizes carrier transport to create an optical "nonlinearity." It is not an intrinsic nonlinearity in the usual X3 sense, since refractiveindex changes are created through x2, the electro-optic effect. That is, the optically induced index changes occur because the carrier transport causes charge separation, which introduces an internal electric field. The result is a highly sensitive optical nonlinearity, occurring at milliwatt power levels, but that, for the photorefractive effect, results in small index changes (10-6). This is because the nonresonant electro-optic effect is employed and the electric fields are relatively small. The carrier-transport nonlinearities that we shall describe here use resonant nonlinearities and the large internal electric fields that exist within depletion

tion. In this paper we discuss a different class of optical nonlinearity, namely, those due to photoinduced carrier transport. This phenomenon is well known in photorefractive materi-

regions, resulting in enhanced index changes for comparable

als and has been explored recently in n-i-p-i (doping superlattice) materials. 8 We describe how these concepts can be

Concept of Our Work

sensitivity.

5

generalized and optimized and introduce three new classes of material: the hetero-Schottky barrier,6 the hetero-n-i-p7 9 i, and the multiple-quantum-well (MQW) hetero-n-i-p-i. Photorefractive Effect

The best known example of an optical nonlinearity due to carrier transport is the photorefractive effect. This phenomenon uses carrier transport by either diffusion or drift to create a refractive-index grating that is phase shifted relative to an incident optical interference pattern, giving rise to the possibility of two-wave mixing.

In a photorefractive

medium, light from a sinusoidal intensity pattern excites carriers from deep traps into the conduction band. These

In this paper we explore several new nonlinear media, which extend the concept of carrier-transport nonlinearities beyond the photorefractive effect of including three additional features: 1. Depletion regions to enhance internal electric fields. 2. Carrier confinement by use of heterobarriers. 3. Enhanced resonant index and absorption changes by operation near the band edge. The principles of these enhanced carrier-transport nonlinearities will be demonstrated 1.

A hetero-Schottky

in three devices:

barrier, a depletion-region

elec-

mobile carriers are transported from regions of high concentration into regions of low concentration, either by diffusion owing to concentration gradients or by drift in an applied

troabsorption modulator, which we call the DREAM. 2. A hetero-n-i-p-i structure (h-nipi). 3. An h-nipi structure that includes multiple quantum

field. The mobile carriers are then recaptured after a char-

wells within the i layers (MQW h-nipi).

0740-3224/89/040579-09$02.00

©)1989 Optical Society of America

Garmireet al.

J. Opt. Soc. Am. B/Vol. 6, No. 4/April 1989

580

Table 1. Classification of Optical Nonlinearities

this absorption change causes a related refractive-index

Quantum

change. 4. Changes in transmitted or reflected light owing to changes in depletion region thickness.

Thin Film

Bulk

Classification

2

GaAs

3

MQW

Intrinsic

InSb,l InAs

Carrier transport

Photorefractive 5 effect

DREAM 7 n-i-p-i

Hybrid

Hybrid BOD'0

p-i-n"i

6

4 8

n-i-p-i MQW-h-nipiP

SEED' 2

Electroabsorption and Electrorefraction in Bulk Semiconductors When an electric field is applied to a semiconductor, the absorption must be recalculated, as originally suggested by

Franz and Keldysh. As an example, the calculated fieldWe shall show that these materials may have half-satura2 tion intensities as small as 700 ,uW/cm , optically induced refractive-index changes as much as 0.02, and optically induced absorption changes as much as 50%. An important

feature of these materials, different from traditional nonlinearities, is that the response time is strongly intensity dependent.

In some ways the nonlinearities

that we suggest here

dependent absorption as a function of energy for the simplest model' 4 is shown in Fig. 2. Increasing electric field causes an increase in absorption below the band gap, com-

monly referred to as photon-assisted tunneling. There is a corresponding decrease in absorption above the band edge. To calculate a change in index of refraction from a change

in absorption, the Kramers-Kronig relation is applied:

are similar to those of the SEED" but without the use of external feedback. That is, we optically modulate the internal fields within depletion regions rather than using external feedback currents to modulate internal fields.

Aa(E)dE

An(hp) =7r

LIGHT APPLIED

WITH NO LIGHT

UNDERSTANDING NONLINEARITIES

(1)

E2 - (hV)'

CARRIER-TRANSPORT

Figure 1 shows an example of a carrier-transport nonlinearity in a hetero-Schottky barrier, that is, in a narrow-bandgap epilayer grown upon a wider-band-gap substrate and

covered by a metal Schottky barrier. The left-hand side shows the spatial dependence of the device parameters in the dark. The metal-semiconductor energy band diagram

ND+ ND

shows the potential well in which carriers reside and shows

the potential barrier between the well and the metal in which carriers are excluded. With a semi-insulating substrate, band bending at the hetero barrier can be neglected. The

L

uncovered bound charge distribution, ND+, is shown as a function of position as well as the internal electric field that

,J

3 results from this bound charge distribution.' When light is applied near the band gap of the epilayer,

the characteristics of the depletion region change, as shown in Fig. 1. Light creates carriers that flow so as to create an effective forward bias. The results of this optical forward bias, Vopt, are a much smaller potential barrier, a much

smaller depletion region, and a much smaller internal electric field. The optically induced changes in the internal

I

A

z Fig. 1.

i

|E|

JE|

Example of carrier-transport

nonlinearity

I-

as it occurs in a

hetero-Schottky barrier. The energies for the conduction band, E,

and the valence band, E, are shown as a function of depth z in the top diagrams. The ionized donor distributions ND+ are shown in

the middle, and the magnitudes of the internal electric field, E, in the lower diagrams. Caseswith and without applied light are shown as the right-hand side and the left-hand side, respectively.

electric field cause changes to the incident light. While pho-

torefractivty uses the nonresonant electro-optic effect, here we consider resonant effects. Four phenomena predomi-

104

nate in such devices: -

1. Electroabsorption, which is a change in absorption with electric field. When the medium is a bulk semiconductor (or a thin film of thickness >-300 A),this is called the Franz-Keldysh effect. When the medium is a MQW, this is

2 I-

called the quantum-confined Stark effect (QCSE). 2. Electro-refraction,

which is the change in refractive

index created by a change in absorption and calculated through the Kramers-Kronig relation. Whenever there is electroabsorption, there is a resulting electrorefraction.

in2

0 0,02 0.04 0,06 -0.04 -0.02 EDGE EV FROMBAND Calculated absorption as a function of photon energy from -0.06

3. Band filling, also called the dynamic Burstein-Moss shift. This causes a change in absorption when the carrier

Fig. 2.

density changes. Through the Kramers-Kronig relation,

electric field using Ref. 14. This is the Franz-Keldysh

the band gap for GaAs, calculated with and without an applied effect.

Garmire et al.

Vol. 6, No. 4/April 1989/J. Opt. Soc. Am. B

581

From Fig. 4 we have determined the wavelength-dependent absorption change and calculated the resulting index change, using the Kramers-Kronig relation, Eq. (1). The result is shown in Fig. 5 and will be compared below with

4-

experimental MQW-h-nipi measurements. C

.

Band Filling

.0

Band filling occurs when incident light excites carriers into the conduction band near the band edge. States fill because of Fermi statistics, and the absorption saturates. This gives

U C CL

I

0

z 10,0000

E 0 V/CM

I=

0 01

'U

5,000-

F uS

C

6.5x10 1 /

cc 'U

0

V/CM,/ n U

-

-

-

=

. _

_

1.44

IK38 C

1.5

PHOTONENERGY (eV)

Fig. 4.

Measurements

of relative absorption of 94-A MQW's versus

photon energy with and without an applied electric field.'7

6000 -

0.02L-L

-0.12

-0.06

0

0.06

0.12

hw - Ec (eV) Fig. 3.

Electric-field induced changes in (a) absorption

0 E

(a)

4000

U

2000 and (b)

refractive index calculated for bulk GaAs by Seraphin and Bottka.5

0 -J

<

-2000

a

-4000

where A\a(E) is the absorption change in all possible photon

energies E and h is the photon energy at which the index change is being calculated. P denotes the principal value. Seraphin and Bottka15 have calculated field-induced absorption and index changes in bulk GaAs for a variety of

1.36

internal electric fields. We show two examples in Fig. 3. These results will be compared below with experimental

1.41

1.46

1.51

ENERGY(eV)

results in an h-nipi structure. 0.05

Quantum-Confined Stark Effect Chemla and Miller have shown that when a MQW is subject

(b) 0.04

to an electric field, there is an actual shift of the absorption

0.03

to a longer wavelength as well as a decrease in absorption on

the high-energy side of the band edge. While the net result looks qualitatively similar to the Franz-Keldysh effect, here the physical mehcanism arises from quantum confinement of the electrons and holes, which enhances the exciton resonance.16 Two effects predominate.

Z

Iw

0.02 0.01

First, the energy levels

0.00

of quantum-confined electrons and holes shift owing to the

-0.01

applied field (Stark effect).

Second, there is a decrease in

oscillator strength and total absorption because the spatial

-0.02 _

1.36

distribution of electron and hole wave functions is no longer the same and the overlap integral is reduced. An example of

experimental results on the QCSE, determined by measuring absorption as a function of photon energy with and

without an applied field,17 is shown in Fig. 4.

Fig. 5.

Electric-field-induced

1.41

1.46

1.51

ENERGY(eV) change in absorption and calculated

change in refractive index versus photon energy. The applied voltage is 6.5 X 104 V/cm.

Garmire et al.

J. Opt. Soc. Am. B/Vol. 6, No. 4/April 1989

582

O

8

I0 6

6

0

to

N

A = A(aL)= ad(I)Ld(I) + a,(I)L,(I) to

0

u)

X

thickness changes. The total effective absorption change at intensity I is therefore

_

/#1 I'll/

_2

-

4

'