Direct verification of heterojunction rules

0038-1101/82/121201~)4$03.00/0 Pergamon Press Ltd

Solid-SroteElecfronics Vol. 25, No. 12, pp. 1201-1204. 1982 Pnnted in Great Bntain.

DIRECT

VERIFICATION

OF

HETEROJUNCTION

Allen Electrical

Nussbaum

Engineering

University

being

with

unequal

forbidden

discontinuities of these present

since

via

to examine

this

the most

(l-3)

measurements

recent

The

prior

attempts

analysis

to compare

of measurements

and the interpretation experimental point

data

directly

in these continuity

lies

The three

lies in the fact have

in the way

involved

characteristics

The fundamental

that the requirement potential

possibilities

been

(4)

,

The possibly

difference for the

at the junction

that have

of

that

or straightforward.

model.

of

AEV obtained

below (5) can, in some instances,

of the electrostatic

satisfied.

df this Note consisting

as voltage-current

to the correct

models

have been

at the University

and experiment

simple

and magnitude

discontinuity

radiation

theory

is not

cited

band

of this work

such

models

evidence,

have

at the

It is the purpose

of the valence

importance

The nature

of controversy

experimental

semiconductors

automatically

exclusive

.

by the use of 22 eV synchrotron Wisconsin.

will

structure.

mutually

journal

55455

from two different

is a matter

three

MN

energies,

band

discontinuities

proposed

direct

in their

time,

formed

band

Department

of Minnesota

Minneapolis,

Heterojunctions,

RULES

is

proposed

are as follows:

where

(1)

A continuous

vacuum

(2)

A continuous

intrinsic

(3)

A continuous

conduction

the order

The outcome is a two-part and valence

given

band,

level

corresponds

of the first

affinity

level

rule.

respectively,

band

edge

to the numbering

alternative

(the Anderson

The discontinuities are 1201

of References

model'

in conduction

l))

l-3.

A.NUSSBAUM

1202

AEc = x1 where

xl8

widths,

-

with

(EG2 - EGl)

the subscripts

rule with

and

distinguishing

a continuous

(1)

- (xl - x2)

EG2 are the affinities

involving

affinity

=

A%

EGlr

x2’

The model

x2

the energy

gap

the two materials. level (2) replaces

intrinsic

this

the relations

AEC = icEG2

- EG1 ) - (3/4)kT

log(c2/cl)

AEV = ;(SG2

- EG1 1 + (3/4)kT

log(c2/cl)

(2) i where

cl, c2 are the mobility

and the third

by the continuity

spectroscopy,

have measured Ge overlayers

involving

results(6) The table

condition.

compares

soft

these

onto

as shown.

values should

from the literature

mobility

ratios

SnSe and CdSe, we have both

are different

involve

a similar

for which

mobility

assumed

The most

table

a virtually

perfect

criterion

gives

The same

is true

a significantly

about

the natural

logarithm,

excellent

from one

the mobility

example

has

ratios

where

better

is

since

the material

values,

conclusion the

lattice

match

effect

reliability

to another

are completely

and

than

and quoted emerges

match

implies level

the other

ZnSe/Ge.

two.

The

in the argument

on this

for which

unknown,

which

intrinsic

combination,

Si/Ge,

equations

(For the compounds

ratios,.being

little

using

source

problem.

for the next best

shown.

(7,S) are of unknown

The continuous

crystal.

uncertainty

A third

0.1 eV and

definite

is for Ge/GaAs,

are also

to skepticism,

10 and 100 as two reasonable

calculations.)

from this

to/

in

some previous

computations

be subject

by

listed

material

with

parameters

affinities

obtained

In addition,

are good only

electron

photoemission

the semiconductors

the measurements taken

X-ray

AEV for interfaces

Si as the common

All comparisons

(l-3).

(3)

et al. (5) , using

I, and with results

Table

of the two materials,

AEV = EG2 - EG1

Margaritondo

evaporating

in each

(3) is

possibility

AEC = 0

as required

ratios

situation.

the affinities

of

Direct

verification

of heterojunction

rules

A.NUSSBAUM

1204 and mobility mismatch

ratios

should

of 4% would

the three models

be expected

than the others.

with

but

We may tentatively

The lattice

comparison

with

(2), although

On the other

we see for ZnSe/Ge,

to make

For GaAs/Si,

the agreement

known.

so that the agreement

difficult,

(2) may be coincidence. mismatch,

be accurately

it does

summarize

not good, does

not completely

by saying

that

good

the predictions

of the continuous

level

correspondence

and for making

intrinsic

to Prof.

is better

not confirm

the direct

of Margaritondo

is expressed

his

what

it, either

measurements

correlation

with

rule.

G. Margaritondo

available

equations

contradict

et al. (5) show a reasonably

Appreciation

with

any of

the same kind of

ZnSe/Si

hand,

with

results

for

prior

to

publication.

References (1)

R. L. Anderson,

(2)

M. J. Adams

(3)

0. von ROOS,

Solid

(4)

A. Nussbaum,

"Theory

(5)

Zhao,

G. Margaritondo,

(7)

B. L. Sharma

(8)

State

Academic

(6)

Pergamon

Elec.

Elec.

State

e,

1069

of Semiconducting

Press

15, ed.

State

Personal

Elec.

2,

783

(1979).

(1980). Junctions,"

in

R. A.) Willardson

&

(1981).

A. D. Katnani, Solid

2, 341' (1962).

Solid

and Semimetals

G. Margaritondo, and T.-X.

State

and A. Nussbaum,

Semiconductors A. C. Beer,

Solid

N. G. Stoffel,

Commns.

(to be published).

Communication,

and R. D. Purohit,

P. R. Daniels,

19 Oct.

Semiconductor

1981.

Heterojunctions,

(1974).

A. G. Milnes Semiconductor

and D. L. Feucht Junctions,

, Heterojunctions

Academic

Press

(1972).

and Metal-