Impact ionization in InP and GaAs

Physica 134B (1985) 241-246 North-Holland,Amsterdam

241

IMPACT IONIZATION IN InP AND GaAs

G.E. STILLMAN, V.M. ROBBINS and K. HESS Electrical Engineering Research Laboratory, Materials Research Laboratory and Coordinated Science Laboratory, University of I l l i n o i s at Urbana-Champaign, Urbana, I l l i n o i s 61801

The experimental techniques that are c r i t i c a l in the determination of impact ionization coefficients in semiconductors are reviewed. The experimental results for the electron and hole ionization coefficients in InP and GaAs w i l l be given. A discussion of Monte Carlo calculations of the ionization coefficients in these materials is included.

1.

In

INTRODUCTION

this

paper we review

the

experimental

techniques which permit the reliable determinaRecently there have been many advances in the

tion of the impact ionization coefficients and

theory of impact ionization phenomena and in the

give the experimental results for electron and

a b i l i t y to calculate these effects including the

hole impact ionization in GaAs and InP.

details

of

the

energy band structure.

The

experimental determination of the impact ionization coefficients is important for the evalua-

2.

EXPERIMENTALTECHNIQUES The

accurate

determination

of

the

impact

tion of the physical parameters used in these

ionization coefficients

theoretical calculations, as well as to evaluate

experimental conditions be met.

the v a l i d i t y of the theoretical approach.

that is usually experimentally measured in order

measurement

of

the

impact

The

requires that certain The quantity

ionization

to determine the ionization coefficients is the

coefficients is also important for the evalua-

variation of the photocurrent in a diode with

tion of the ultimate performance capability of

reverse bias.

From this data the current multi-

hot electron devices such as avalanche photo-

plication and ultimately the ionization coeffi-

diodes.

cients are calculated.

The experimental determination of the

Careful

electron ahd hole impact ionization coefficients

experiment can f a c i l i t a t e

is not an easy task as is evident from the wide

Some

discrepancies in the l i t e r a t u r e .

considerations are detailed below.

semiconductor

materials

there

In compound is

not

the

these calculations.

m o s t important

experimental

even

general agreement on which carrier type has the higher ionization coefficient and in

of

design of the

silicon

To calculate the ionization coefficients from the experimental photocurrent vs. voltage data,

there is only poor agreement between the results

the multiplication for both pure hole and pure

of different investigators.

electron

injection

must be determined. This

This work was supported by the National Science Foundation under Contract NSF-ECS-82-09090 and by the Office of Naval Research under Contract N00014-76-C-0806. 0378-4363/85/$03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

G.E. Stillman et aL / Impact ionization in lnP and GaAs

242

requires

that

permits

a device be fabricated which

illumination of

junction separately. matter

to

shining

b o t h sides of

It

obtain one type

strongly

the

is generally a simple of

injection

absorbed l i g h t

To do t h i s ,

the primary photo-

current in the absence of m u l t i p l i c a t i o n must be known.

Since the m u l t i p l i c a t i o n process cannot

be turned o f f ,

the primary photocurrent a f t e r

top

the onset of m u l t i p l i c a t i o n must be calculated

contact layer of the diode.

There are several

based on the photocurrent at low bias voltage

methods for

photocurrent

and on the device structure.

obtaining

the

on the

by

of i n j e c t i o n .

injection of the other type of carrier.

for

One of

have been used to do t h i s .

Several methods

The simplest method

these is to illuminate the side of the mesa with

is to assume that the primary photocurrent does

strongly absorbed l i g h t .

not change with bias.

However, this method

This may be a reasonable

has several potential problems. One of these is

assumption when the depletion region edge is in

that i t

heavily

is possible for stray l i g h t to h i t the

top layer and thereby cause mixed injection.

doped material

and so does not move

toward the illu minat ed surface as the bias is

Another problem is that the mesa edge is beveled

increased.

and so

the width of the depletion region w i l l

the

different

electric

from

the

field field

at

the

in

edge is

the

bulk.

with

bias

However, for l i g h t l y doped material and the

collection

increase

efficiency

will

Therefore, i f the carriers stay at the surface

increase

of the device they w i l l multiply in a way that

diffuse is reduced. When such an increase in

is

not

typical

method for

of

the b u l k f i e l d .

obtaining carrier

Another

injection is

illuminate the device through the

as the

distance

the

carriers

must

the primary photocurrent is observed at low bias

to

voltages, a linear extrapolation of the low bias

substrate.

photocurrent to voltages higher than the onset

For direct bandgap compound semiconductors, i t

of multiplication is

has been shown that the material where the l i g h t

more accurate procedure is to use a model that

often used.

However, a

is absorbed must be no more than a few diffusion

takes into account the physical processes that

lengths

f r o m the

are responsible for the increase in the collec-

region.

This is because the sub-handgap l i g h t

edge of

the

high

field

tion efficiency.

This requires a knowledge of

generated by the radiative recombination of the

the doping levels in the device as well as the

carriers

layer thicknesses.

can be absorbed through the Franz-

Keldysh effect in the high f i e l d region at the

The movement of the deple-

tion edge toward the illuminated surface with

junction and therefore result in mixed carrier

increasing

injection. I

treating the minority carrier diffusion length

substrate

This can be avoided by thinning the underneath the

junction

to

a

few

voltage can be calculated and by

as an adjustable parameter, a least squares f i t

diffusion lenghts.

The only way to do this

to the experimental data can be obtained.

reproducibly is

grow a thin

model can then be extrapolated to calculate the

to

layer of

a

material with different etching characteristics

primary

on top of the substrate to act as an etch-stop

avalanche process is taking place.

photocurrent

at

voltages

This

where the

layer. For the calculations of the electron and hole impact

ionization

coefficients,

the

actual

After the multiplication has been calculated, this data is then used to calculate the ioniza-

carrier multiplication must be determined from

tion coefficients.

the variation of the photocurrent for both types

the electric f i e l d is known at each reverse bias

I f the spatial variation of

G.E. Stillman e( aL / Impact ionization in InP and GaAs voltage,

the

ionization coefficients

can be

that

operate

in

243

overlapping

electric

field

calculated from the variation of the electron

ranges must be measured and the data from these

and hole multiplication with reverse bias vol-

devices

tage for

coefficients over a large range of

any

type

of

numerical techniques.

structure

by

using

However, i f the electric

combined

to

obtain

ionization electric

field.

f i e l d variation has a simple form, such as a constant f i e l d or a l i n e a r l y varying f i e l d , then analytical expressions can be used to calculate the ionization coefficients. advantageous to

fabricate

Therefore, i t diodes that

is

have

After the ionization coefficients have been determined for a particular device structure or for

a

set

of

structures,

it

is

common to

calculate the breakdown voltage for those struc-

abrupt junctions and constant doping profiles in

tures from the experimental ionization coeffi-

the layers.

cients and then compare the calculated voltage

if

Punchthroughstructures may be used

the punchthrough occurs before the onset of

multiplication.

If

the electric f i e l d has a

rapid spatial variation, such as in a heavily

to

the

experimentally

voltage.

measured breakdown

While this serves as a check on the

self-consistency of the calculations, i t is not

doped depletion region, the carrier may travel

an independent v e r i f i c a t i o n of the correctness

through a significant part of the high f i e l d

of the results.

region

without

ionization.

reaching

the

threshold

An independent check of the

for

results for ~ and ~ can be obtained from excess

This results in a 'dead space' that

noise measurements for both pure electron and

must be taken into account in the calculations.

pure hole injection on the same devices that were used for the photocurrent multiplication

Even when all of the above mentioned factors are

taken into

introduced

consideration, errors

into

determination.

the

ionization

determination

of

the ionization coefficients.

can be

Comparison of experimentally determined excess

coefficient

noise factors with the noise factors calculated

I t is important that the device

from

Mclntyre's

have a spatially unifom photoresponse so the

ionization

measured photocurrent is characteristic of the

photocurrent

noise

coefficients

theory2

using

the

determined f r o m the

multiplication

measurements can

structure and the electric f i e l d p r o f i l e of the

indicate whether p u r e carrier

device.

obtained and whether the relative magnitudes of

avoid

This means that care must be taken to illuminating the edge of a mesa diode

where the electric f i e l d is not typical of the bulk f i e l d .

injection

was

the electron and hole ionization coefficients were correctly determined.

Even i f the multiplication has been

carefully calculated using a physical model, the

3.

GaAs IONIZATION COEFFICIENTS

ionization coefficient values calculated from

The impact ionization coefficients in

multiplication values very close to unity must

GaAs have been determined experimentally.3

be viewed with suspicion.

this

Also, for values of

study,

devices f r o m eight

(100) In

wafers with

voltage that are close to the breakdown voltage

different doping concentrations

of a particular device, the multiplication may

Typically, six devices per wafer were measur-

increase so rapidly with voltage that

it

is

impossible to accurately calculate the deriva-

ed.

Five of these wafers have heavily doped p+

layers and the data from these devices therefore

tive needed for the evaluation of the ionization

had

coefficients.

mentioned previously.

Therefore, a number of devices

were studied.

to

be

corrected

for

the

' d e a d space'

The other three wafers

G.E. Stillman et al. / Impact ionization in InP and GaAs

244

had more l i g h t l y doped p-type regions and did not

require

this

correction.

The combined

T

,

There is excellent agreement between

10~~:

~

~-

~

L 2OFm

E 10~

6.0 5.0 ;

q

4.0 i

2.5

~

i,,,,,

I

,

,

, ,,..r

Caiculated Breakdown Voltage

\

%",,

'\.

{3 E x p e r i"m e n t a l

'%.

106

" Breakdown Field

..~."

"E

.....

...............

o

00"%, "~.~

g

i0

1014

L)

I

.......... . . , k . , ~ ,

~2~m

10 4

,

............ Calculated Breakdown Field % . . . . . . . Empirical Breakdown Expression ',,. o Experimental BreokdownVoltoge

o~0~F

xlO ~

r

i

B~m. . . . . . . .

:

(V/cm) 3.0

I

.....

results of all of these measurements are shown in Fig. i .

. r,,,,

1015 1016 Carrier Concentration, N B (cm ~)

o,~. 1017

Ii05

~o ~

FIGURE 2 used for the ionization coefficient determina-

~ 10 ~

tion

were used for

noise measurements.

calculated and the experimental

The

excess noise

factors were in excellent agreement with each

o

other. 1.5

2.0

2.5

&o 3.5 1/E (cm/V)

4.0

4.5

5,0 x l o -6 G# 525

4.

InP IONIZATION COEFFICIENTS Impact ionization in (100) InP has also been

characterized. 4 the

devices

FIGURE 1 on a single wafer

devices from different wafers. show that c is

and between These results

greater than ~, with the two

becoming almost equal at high fields.

The solid

lines are least squares f i t s to the data given

measured to obtain the ionization coefficients over a wide range of electric fields.

The more

heavily doped side of the junction

in

these

devices was not so highly doped that dead space correction was necessary for these devices. results

by

In this case three wafers were

Fig. 3.

of

these measurements are

The

given

in

In this material, ~ is greater than

~=1.gxloSexp(-(5.75x105/E) 1.82) (cm- I )

over the range of electric fields measured, but

~=2.2x105exp(-(6.57xlO5/E) 1.75) (cm-1).

electric fields. The parameterization obtained by a least squares f i t is given by

again the two become nearly equal at very high

The breakdown voltages and electric f i e l d values calculated using these f i t s ,

as well

as the

experimentally observed breakdown voltages are shown in Fig. 2.

Several of the same devices

:=3.5x105exp(-(1.04x106/E) 1-54) (cm- I ) ~=3.8x105exp(-(1.01x106/E)1-46) (cm-l).

G.E. Stillman et al. / Impact ionization in InP and Ga.4s measurements is 7.0

6.0

5.0

not as great because of the

d i f f i c u l t i e s in device fabriation.

E (105 V/cm) 105

245

4.0

3.0

2.5

The ioniza-

tion rates for the two orientations d i f f e r only by a five percent uncertainty in the measured value of the peak electric f i e l d which causes a

104

slight s h i f t

along the horizontal coordinate.

There is essentially no difference in the ratio c ~'~

103

8

of ~ and ~ for these two orientations.

In a

separate

(100)

study

the

(110)

and

the

orientations were compared and there was also no difference between the ionization coefficients

10;

in these directions. 6

10

115

210

215

310

315

410

5,

4.5

MONTECARLOCALCULATIONS In addition to the experimental measurements,

1/E (10 6crn/V)

Monte Carlo

calculations

of

the

ionization

coefficients have been performed and the results FIGURE 3 In this material, excess noise measurements were also made with both types of carrier injection and

good agreement was

found between the

experimental and the calculated noise factors.

compared

to

calculated

the

experimental

values

experimental values. anisotropy

in

data. 7

a g r e e well

The

with

the

The calculations show no

the

electron

ionization

coefficients as a function of orientation. This The ionization coefficients have also been measured in (111) InP.5 These results are shown

is consistent with the experimental results in InP but

in contrast to the results of other

workers in GaAs.8

in Fig. 4 and are compared to the (100) InP

The Monte Carlo results also

indicate that the reversal of the ~ to ~ ratio between the two materials can be explained in 105

>

t

r

~

I

I

terms of the ionization threshold energies and

I

the densities of states in the two materials. ~IF~_~_ ' ~ I ~

Points: < I i i > Bonds:

The

threshold

energies

for

b o t h holes

and

electrons are the same in GaAs whereas in InP the hole threshold energy is smaller than the

o 10 3

electron threshold

8

energy.

The densities of

states in the valence and conduction bands of "6 N

both materials would tend to make the electron

102

rate

greater t h a n the

hole rate.

In GaAs,

because of the equal threshold energies, i t is I

1.5

results bands.

that

I

I

I

20

25

30

I/Ern (crn/V)

are

FIGURE 4 ~ndicated

3.5

I 40

:~

4.5

true that ~ is greater than 6.

Gp4o7

the

x10-~

smaller

threshold

However, in InP,

energy of

the

holes

overcomes the effects of the density of states by

the

shaded

The electric f i e l d range of the (111)

and

so

the

hole

ionization coefficient

greater than that for electrons.

is

G.E. Stillman et al. / Impact ionization in InP and GaAs

246

ACKNOWLEDGEMENTS The authors would like to thank B.L. Payne and R.T. Gladin for

assistance

in preparing

3. G.E. 8ulman, V.M. Robbins, K.F. Brennan, K. Hess, and GoE. Stillman, IEEE Electron Dev. Lett. EDL-4 (1983) 181.

this

manuscript.

4. L.W. Cook, G.E. Bulman, and G.E. Stillman, Appl. Phys. Lett. 40 (1982) 589.

REFERENCES

5. N. Tabatabaie, V.M. Robbins, N. Pan and G.E. Stillman, Appl. Phys. Lett. 46 (1985) 182.

I . G.E. Bulman, L.W. Cook, and G.E. Stillman, Appl. Phys. Lett. 39 (1981) 8 1 3 . 2. R.J. Mclntyre, IEEE Trans. Electron Dev. ED19 (1972) 703.

6. C.A. Armiento and S.H. Groves, Appl. Phys. Lett. 43 (1983) 198. 7. K. Brennan and K. (1984) 5581.

Hess, Phys. Rev. B 29

8. T.P. Pearsall, F. Capasso. R.E. Nahory, M.A. Pollack, and J.R. Chelikowsky, Solid-State Electronics 21 (1978) 197.