Angular distribution of emitted electrons from wire by magnetic electron focusing effect and low field magnetoresistance

Pergamon

Vol. 92, No. 5, pp. 413-417, 1994 Elsevier Science Ltd Printed in Great Britain 0038-1098(94)$7.00+ .OO

Solid State Communications,

003X- 109X(94)005X2-6

ANGULAR

DISTRIBUTION

OF EMITTED

FOCUSING

EFFECT

S.Wakayama,

ELECTRONS

of Physics,

l-l

ELECTRON

AND LOW FIELD MAGNETORESISTANCE

I<.Tsukagoshi,

Department

FROM WIRE BY MAGNETIC

I<.Oto, S.Takaoka,

Faculty of Science,

Machikaneyama,

Toyonaka,

and K.Murase

Osaka

University

560, Japan

K.Gamo Department and

of Electrical

Research

Center

l-l

Engineering,

Faculty

for Extreme

Materials,

Machikaneyama,

( Received

Angular tron

distribution

focusing

dimensional with

distribution

In the two-dimensional

path

of electrons

ometry

PDEG

is comparable

has been

useful

properties(2-41. determined

6 is a tilted

vertical

direction

distribution

angle

has

magnetoresistance ter and 2DEG

The

a 2DEG

point

contacts

by varying

the width

which

is gradually

broadened

travel

adiabatically

forward,

the transversal formed

motion

to that

a collector

by using

the magnetic

or vertically

point

structure

connected

just

elec-

to a two

of the other

contact.

It is found

at the outlet

of the

device that

wire

the

rather

two

facing

at the outlet,

of longitudinal

f(B) of emitted

longitudinal

direction

(this

is called

Thus

collimation

effect)

The

confinement

tron

channels

represent

[9.

413

are 4.3

data

was formed

bridge

which

operated

Schottky

inset gates.

x

10”

cm-‘, patand metof elec-

potential

from

at 1.5 K by an AC

at 15 Hz with structure

of Fig. The

a mean

of Ti/Au

by electrostatic

3 PA. The schematic

in the upper

and

at the boundary

was measured

in-

dimen-

lithography,

by evaporation

potential

mobility Two

The device

electron-beam

were made

Resistance

current

high

mobility

illumination

by using

als.

tation

shift probes

ones by a clas-

and 7 pm, respectively.

gates

is shown

in the

would

experimental

on the

an electron

at 1.5 K under

was drawn

resistance

trans-

The

heterostructure.

density,

Schottky

the gates.

the angular

is collimated

electron

tern

of

positions

pair of oblique

the calculated

A is fabricated

of emit-

the electrons

wire is partly

device

6.4 x lo5 cm’/Vs

across

peak with

occurs.

with

of a GaAs/AlGaAs

free path

The

energy

effect

distribution

model.

low field

In a wire

the kinetic

motion. electrons

The

sional

other

the MEFE

collimation

billiard

from the

of the contact[5].

where

sical

terface

pairs

each

that

will also be compared

in

the angular

low field magnetoresistance.

field in a device

position

by the

we investigate and by using

It is expected

at 0 = O”,

boundary[5-7).

MEFE

transport

in a magnetic if the

trans-

the ballis-

direction

with

by using

the ge-

peak

D. c‘lrc1.ronic

10). In this letter,

free

(MEFE)

emitted

in a narrow

distribution

effect

determined

of a device

collector

)

low field magnetoresistance

size at low

regime,

MEFE

of the emission

been

mean

to understand

by electrons

against

f(0)

obliquely

A. nanostructures,

the electron

focusing

method

is apparently

electron

influences

electron

tic transport

where

is investigated

in a high

the

to a sample

a ballistic

strongly

The magnetic

on the

gas (2DEG)

heterostructure,

In such

of a sample

port(l].

depends

A. heterojunct.ions,

electron

GaAs/AlGaAs

temperatures.

wire and

University

560, Japan

1994 by A. Okiji

probes

and by using

of an emitter

strongly

with

Osaka

Science

the wire direct,ion.

Keywords:

mobility

gas,

20 April

electrons

in a device

electron

two pairs

than

of emitted

effect

Toyonaka,

of Engineering

of a sample

1. The shaded

separation

an exci-

AL

regions between

414

ANGULAR

DISTRIBUTION

OF EMITTED

ELECTRONS

Vol. 92, No. 5

4

.I

l.Opm

0’ -4’

I

1

I

I

-2

,

0

Gate Voltage ( V ) Fig.

1. Two terminal

resistance

sus applied

even voltage

Estimated

width

shown

at each

Schematic vertical

of an oblique

of both

voltage

and

collector show

peak

appears

Separation (V+,V-)

probe

with oblique

at oblique

and

probes

Fig.

2. Magnetic

gate

voltages.

dicate and

the

electron The

position

oblique

probes,

and

probes,

feet

respec-

with

and the collector with

oblique probes, while probes

. When

separation

negative

probes,

the

served.

of f45”

the upper

probes

are called

vertical

is comparable

to the

an emitter

electrons

the collector,

and

from

a peak

The electron

estimated

angles

diameter

emission

1 shows

the

oblique

wire

as a function

voltage

Vg=

-0.6

and

the wire

the

wire

gap

width

tance

-1.0,

The

and

Fig.

there

2.

resistance

The

voltage.

the gates

At gate

probes

magnetic

photograph.

1.0 pm) Since

the

fields.

is much

are dozens

larger of modes

for various magnetic

gate

electron

that

which

is

conducto its voltages

0.4 pm,

than

tiple

vertical

probes

peaks,

has

is observed

arrows

indicate

positions

in Fig.

re-

the Fermi

in the wire.

the

due

to mul-

The

The

of intensity

hand,

with

fields.

oblique

positions

oblique The right

probes.

against are

within

bound-

0.7 for vertical

magnetic

voltage

col-

of adjacent,

MEFE

with

and

specular

at the sample

are plotted

peak

by the gate

density

observed.

peak

the peaks

3.

and

to be about

in positive

=

emitter

by the ratio

the first

Jrst

of MEFE

are

of both

the

at B,,,,,

the

p of electrons

estimated

probes,

of

electron

reflections

been

region

is the

peaks

121. On the other

probes

age

n,

in the

is observed

between

is defined

probes[ll,

vertical

2, several

coefficient

which

At

where

boundary

reflection

The

gate

not

volt-

apparently

an experimental

er-

ror.

to the

to be proportional of the wire at gate

V are 1.0, 0.5 and

with

is observed

by the left arrow

In Fig.

affected

is depleted

V is equal

(about

be

of an

It is assumed -0.6

gates

-3.5

magnetoresistances in

terminal

widths

and

would

two

at Vg=

The wire width

wavelength,

rhown

-2.5

f(0) of MEFE.

under

into is ob-

position

is assumed

the estimated

spectively.

distribution

lector.

ary,

of vertical

are focused

of the gate

both

by a SEM wire

emitter

is constructed.

width

between

of the

width, Vg=

channel

a collector

peak

V, 2DEG

channel

determined

the

are called

of the magnetoresistance

by the shifted

Figure

and

peak

various

B > 0 in-

respectively.

AL is the separation

The lower probes

tilted

a cyclotron

between

is 7.5 pm.

of first

vertical

peak indicated

are connected

with

broken the first

-2fiJ2fm,/eAL,

which

effect

at B < 0 and

and

tively.

the emitter

focusing

arrows

(I+,I-)

for which

vertical

is

inset:

emitter Solid

trajectory

inset)

). Upper

between

is 7.5 pm.

the electron

wire ver-

of the wire.

(lower

( see text

view of the sample probes.

lines

side gates

of an oblique

gate

Magnetic Field ( kG )

To study tion

f(0)

electron which

boundary

motions

by

the

peak

position,

using

scattering

a classical within

141 are

conditions

and

between

MEFE

boundary[l3,

structure

emitter

relation

the

diffusive

sample

the

the

and

used

of device a collector

voltages

are

probes

is 1.0 pm,

the

focusing

ef-

( from

I+ to I-,

from

angular

billiard

the sample

taken

into

the

distance V+

between

to V-

in

and

at the The

separation

is 7.5 pm, the

model

account.

in the calculation A,

distribu-

we simulated

is based between

width

of wire

opposite

) is 20.0 pm,

on an of

probes and

an

ANGULAR

Vol. 92, No. 5

I ’

DISTRIBUTION

,

1

OF EMITTED ELECTRONS

I

1.5K

ns--4 -3x10” cme2

0 : oblique probes A : vertical probes 1 I

I

-3

-2

I

-1

Gate Voltage ( V )

Magnetic Field ( kG ) q--l-

Fig. 3. Gate voltage dependence of the position of the first peak. Both peak positions with oblique and vertical probes are not appreciably affected by the gate voltage.

density is 4.3 x 10” cm-*.

electron performed

(1) An electron angular

distribution

is ejected

was

from an emitter

with the

f(0).

(2) Each electron cyclotron

The calculation

as follows:

trajectory,

moves by the length

6 along the

where 6 is equal to 0.1 pm which is

small enough compared (3) After a cyclotron

motion by 6, the electron

elas-

tically scattered

in random directions

1 - exp(-6/l).

The mean free path (7 pm) which was

estimated

by the electron

is tentatively boundary,

density

and electron

mobility

a probability,

is either randomly

1 - p, or specularly

scattered

reflected

with

with a prob-

ability, p. The experimental

value 0.7 is adopted

specularity

enters any probes or moves

p. If the electron

for the

over ten times as long as the decay length, the calculation of the trajectory These

is stopped.

calculations

have been performed

5 x lo3 times for each magnetic the calculated ference

between

the number

4 shows

of electrons

are emitted

entering

for various function

The broken lines indicate

first peak Bfocus estimated electrons

Figure

0.5 Magnetic Field ( kG )

Fig. 4. Calculated MEFE with various f(0) at an emitter. Broken lines show the position of the first peak (B,,,,,) on the assumption that all electrons are emitted at a tilted angle 0 to vertical direction against the sample boundary. (a) If f(0) is cos(0) or cos(0 45”), the collimation effect is practically absent. The MEFE first peak position with f(6) = cos(0) is the almost the same with cos(0 - 45”). (b) If f(0) is COS’~(~) or COS’~(~- 45”), a strong collimation effect occurs. The ratio of the MEFE first peak position with f(0) = COS’~(~) to that with cosi”(B - 45”) is about 0.8.

result of the voltage difference from a dif-

probe V+ and the probe Vof f(0).

field.

more than

,cqS’O(y-457

0

with a probability,

used for the decay length I. At the sample

the electron

I-4”)

with a probe width 1 pm.

the positions

the forms

the same as those for f(0) = cos(0 - 45”) (Fig. 4(a)).

of the

a collimation

on the assumption

that all

in the vertical direction.

The po-

function shape f(0)

responding

contrast

distribution,

are almost

according

different

and

from those with

= COS’~(~- 45’) as shown in Fig. 4(b). to our observation

If

to a highly collimated

like f(0) = cosi”(0), the first peak position would be significantly

sition and shape of the first peak for f(B) = cos(Q), corto a usual classical

occurred

This is in

that the first peak positions

416

ANGULAR

DISTRZBU-I’ION

OF EMITTED

ELECTRONS

Or -90

( degree )

Angle of Emission

Fig. 5. The angular (a)The

angular

gate voltage the emitter

Vg=

-2.OV

which is determined

angular

distribution

of a point contact.

-2.0,

-3.OV

electrons

to measure

and vertical

resistance 0”).

are almost

the

10” from

-2.OV

of emitted

electrons,

magnetoresistance

with two pairs of an emitter other

across

2DEG

fields[8,15-171. electron

mobility

was measured

tation

cm-*,

Resistance

current

E2 is an oblique

probe

point

The

contacts.

1.4 x IO6 cm’/Vs

and 13 pm,

with a low exci-

probe,

between

the emitter

Cl and C2 are the emitter

and

( from El to Cl, or from E2 to C2 ) is 4 pm than a mean free path.

>f each channel

of the probes

minal resistances

and SEM

hgure captions m-&ted

an

shown in the inset of

is a vertical

distance

density,

at 0.4 K in the

and the collectors

which is much shorter

vestigated

electron

was measured

El

facing each

at very low magnetic

30 nA in a sample

The emitter

the collector

in the device B

and a mean free path

dark are 3.2 x IO”

distribution

and a collector

The two-dimensional

respectively.

Fig. 5.

the angular

electrons

of Fig. from

5.

was estimated photograph

The

probe

is fitted

of emitted

defining

the vertical

tges were independently

The width by two ter-

to measure

of

the electron

direction

relation

between

probe 0”).

electron

detected

Another

by Cl.

an emitter

5(a).

were fitted

becomes

grow around

collector

fluctuation,

was plot-

magnetoresisby cosN(8 + a) almost

slightly

6’ = 0”. appear

width,

the

are similar

the fine structures

wave interference

for instance,

sharper Since

effect by

due to uninten-

of gates and/or inhomogeneity

density[l8-201.

Similarly

the angular

of

distribu-

was in-

tion from theoblique

emitter

with a configuration

shown in the inset of Fig. 5(b).

corresponding

sym-

gate voltage of the emit-

the fine structures

shape

The

The volt-

applied to two pairs of side gates

The

and a collec-

The peaks appear

might be come from electron

of

(El)

of 6 in Fig.

to those at different

distribution

3”).

The electrons

magnetoresistance

the magnetoresistance

irregular

-

(E2).

of an angle 0 from the

L between

in 0. With increasing

the potential

probe

to the ground.

The observed

at which

are 0.4, 0.3,

and the collector(C1).

and the fine structures angles

-2.OV

would be directly

of the vertical

ter (El),

-1.5,

8 and B is 0 = arcsin[eB1/2fi,,!Z%J,

(12 < N 5 13,(~ metrically

estimated resistance

in the direction

ted as a function tances

direction.

from the oblique

where the separation tor is 4 pm.

The

by two terminal

-1.0,

were connected

vertical

tional

probe

Vg=

the emitter(E1)

from El

in

as shown in the inset of Fig. 5(a).

widths distribution

by cosN(6’ + p) {7 < N 5 9,p

electrons

emitted

as described

angular

The estimated The angular

the vertical

which is determined

two gates directly

probe(b).

Cl is 0.05 pm at the

The configuration

E2 at the gate voltage

distribution

same. In order to observe

of a point contact.

Inset:

about

Vg=

from the oblique

the angular

probes

and from the oblique

width of the collector

are 0.7, 0.6, 0.2 pm, respectively.

shifts

widths of the emitter

The magnetoresistance

The configuration

probe(a),

90

( degree )

(El).

of the emitted

The estimated

probes

from the vertical

{ 12 5 N < 13, cr -

probe

45

Angle of Emission

by two terminal

-1.0,

-1 .ov

I 0

-45

in 6’. The estimated

C2 is 0.05 pm at the gate voltage

0.2 pm, respectively.

with oblique

Vg=

from the vertical

widths of the collector

Inset:

emitted

symmetrically

probe is fitted by cosN(B +a)

distribution

(b)The

of electrons

appears

El at the gate voltage

of the vertical emission

distribution

distribution

Vol. 92, No. 5

probe (E2) was investigated

magnetoresistance

The

is shown in Fig. 5(b).

ANGULAR

Vol. 92, No. 5 The magnetoresistance

DISTRIBUTION

from the oblique probe was fitted

by cosN(O + p) {7 5 N 5 9,p N 3”}. ejected

from the emitter

enters the collector

If an electron

(E2) along the wire direction

(C2), the angular distribution

of the

by t,he replacement

low field magnetoresistance emitter

probe appeared

might shift by 45” from the vertical di-

). This suggests

rection.

Actually

the peak shifted by 6’ N 10” from the

electrons

vertical

direction.

lar distribution

The fact suggests

us that the angu-

is not decided only by the wire direction.

of the sharp distribution

COS’~(B- 45”) to COS’~(~). Moreover,

electrons

emitted

417

OF EMITTED ELECTRONS

outlet

measured

at 0 ‘v 10” (insted

strongly

depends

on the structure

wave character

of electrons

derstand

When the angles of emission

same. The angular distribution

are almost the

may depend on the struc-

ture just at the outlet of the wire. It should be noted that at the outlet of the oblique probes the escaping electron waves feels asymmetric In conclusion, tion of emitted MEFE

electrons

angular distribu-

in two kinds of devices by using

are almost

the same.

MEFE with a classical sive scattering.

The position

first peak for both oblique billiard

The calculated

is not shifted by the replacement

and vertical

We have calculated model considering position

also diffu-

of the first peak

of the broad distribution

f(0) from cos(8) to cos(t) - 45”), but it is shifted by 20%

just at the

of escaping electron

The to un-

at the outlet.

is lowered, the observation

of the peak shift becomes difficult with the oblique probe in MEFE experiments. The authors

would like to thank O.Matsuda

ful advice about computer

of the wire.

and low field magnetoresistance.

of the MEFE probes

termination

we have investigated

the behavior

of emitted

might be important

with oblique probes

probes

of 0 = 45”

than the wire direction.

This is the reason why the MEFE first peak positions and vertical

with the oblique

that the angular distribution

of the wire rather

f(0) from

the peak of the

NEC Co.,Ltd. try Co.,Ltd.

for providing

Research

supported

The authors

for supporting

for Young Scientists. edge the support

of

Electric Indus-

high mobility heterostructure. by a Grant-in-Aid

(B) from the Ministry

Science and Culture. knowledge

and K.Kasahara

and H.Okada of Sumitomo

The work is partially Scientific

simulation,

for use-

for

of Education,

(K.T. and K.O.) ac-

by JSPS Research

One of the authors

Fellowships

(S.T.) acknowl-

by Casio Science Promotion

and Shi-

mazu Science Foundation.

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