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NBSIh 78-1553

Theory and Application

of a Two-Layer Hall Technique

R. D. Larrabee and W. R. Thurber

Electron Devices Division

Center for Electronics and Electrical

Engineering

National Bureau of Standards

Washington, D.C. 20234

October 1978

Final

Prepared for U.S. Army ERADCOM

QC ~ Night Vision and Electro-optics Laboratory

100 Ft. Belvoir, VA 22060

U56

78-1553

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A

NBSIR 78-1553

THEORY AND APPLICATION

OF A TWO-LAYER HALL TECHNIQUE

R. D. Larrabee and W. R. Thurber

Electron Devices Division

Center for Electronics and Electrical

Engineering

National Bureau of Standards

Washington, DC 20234

October 1 978

Final

Prepared for U S. Army ERADCOM

Night Vision and Electro-optics Laboratory

Ft. Belvoir, VA 22060

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr. Sidney Harman, Under Secretary

Jordan J. Baruch. Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Director
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TABLE OF CONTENTS

Page

Abstract 1

1. Introduction 1

2. Summary of the Two- Layer Hall Technique . 3 A. Measurement of Resistivity 3

B. Measurement of Hall Coefficient 6

3. Illustrations of the Use of the Two-Layer Technique 13

A. For Making Measurements on Structures with Poor Interface p-n Junctions 13

B. For Demonstrating that the Interaction Between the Two

Layers is Negligible 18

4. Conclusions 20

5. References 21

Distribution 23

iii
LIST OF FIGURES

Page

1. Conventional measurement of resistivity using the van

der Pauw technique 4

2. Simultaneous measurement of resistivity in two distinct

van der Pauw specimens situated back-to-back with respect

to each other 5

3. Simultaneous measurement of resistivity when the two specimens of figure 2 are brought into contact with each other

to form a two-layer structure 7

4. Simultaneous measurement of Hall coefficient in two-layer

structures . 8

5. Equivalent circuits of the specimen of figure 4 in the

plane of the Hall contacts D-B and H-F > . . 10

6. Electron density in the epitaxial layer of Specimen 10-SYS1-

In deduced from conventional Hall measurements performed

at reduced temperature (circular points) fitted with a theoretical curve over the interval from 1000/T = 8 to

1000/T = 20 16

7. Electron density in the epitaxial layer of Specimen 8-SYS2-

In obtained by conventional Hall measurements (points) and

a theoretical fit to the data 19

IV
Theory and Application of a Two-Layer Hall Technique

R. D. Larrabee and W. R. Thurber

Electron Devices Division

National Bureau of Standards

Washington, DC 20234

ABSTRACT

The electrical characterization of epitaxial layers

of silicon on substrates of the opposite conductivity

type presents serious problems if the p-n junction at

the interface has significant leakage current such

that it cannot be used to effectively electrically

isolate the two regions. In order to meet the need

for nondestructively characterizing such structures,

a modification of the conventional Hall technique was developed in which the Hall measurements are made simultaneously on both the epitaxial layer and its substrate, the interface impedance is measured, and the

interaction between the two regions is modeled and

taken into account. This technique can be used not

only to measure the resistivity and Hall coefficient

of each layer separately, but also to verify those cases in which the perturbing effects of a high re- sistivity substrate are negligible, thus justifying

conventional measurements on the epitaxial layer.

This technique was used to measure the parameters of

an n-type indium-doped silicon epitaxial layer on a bulk-grown p-type indium-doped substrate. The results

suggest that the major n-type dopant in this specimen

has a density of about 1 x 10^^ cm ^ and an apparent

activation energy of about 45 meV. Similar data were obtained on a second epitaxial layer grown on a high

resistivity undoped substrate. These results argue

strongly for the presence of one or more undesired

sources of shallow donor contamination in the epitaxial growth system used to produce these specimens.

Key Words: Epitaxial growth; Hall measurements;

indium-doped silicon; p-n junction isolation; twolayer structures.

1 . INTRODUCTION

There are two well-established techniques for making Hall measurements

on two-layer structures. If the two layers are of the same conductivity

type. Hall measurements made before and after the removal of one of the

1
layers will provide the information necessary to characterize both

layers [1]. If the two layers have opposite conductivity types, the

p-n junction at the interface can often be used to electrically isolate

the two regions and allow Hall measurements to be made on each layer

separately. Frequently, the p-n junction at the interface has a large

leakage current and the desired degree of isolation cannot be obtained.

To handle this high leakage current case, a new technique was developed

in which the interaction between the layers is modeled and equations are developed for obtaining the properties of each layer separately. In the

special case of infinite interface impedance, this technique reduces to

the case of complete isolation. In the other extreme of zero interface

impedance, this technique reduces to the case of the intimate contact of

the two layers of the same conductivity type. Therefore, the present

technique bridges the gap between these two extremes and thus permits

Hall measurements to be made on samples with arbitrary interface impedance.

The epitaxial silicon specimens that motivated the development of this

technique were grown from indium solution with no other dopants intentionally added to the system. One would expect the epitaxial layer to

be saturated with indium and, as a result, to be p-type. However, the

layers were n-type. Actually, this behavior is not without precedent

since alloyed indium contacts have been observed to be rectifying to

p-type silicon and "ohmic" to n-type silicon [2,3]. One possible ex- planation is that interstitial indium is present and acting as a donor

in the recrystallized regions of these contacts [4]

.

Another possibility is that some contamination, or other unidentified source of donor

impurity, is present that overcompensates the indium acceptors that are incorporated into the regrown contact region. The search for the cause

of this n-type behavior generated an interest in making Hall measurements on the epitaxial material. The high leakage current at the epitaxial layer-substrate p-n junction interface made it impossible to use conventional Hall techniques and necessitated the development of the

two-layer Hall technique.

2
This report briefly outlines the details of this new two-layer technique and discusses the results obtained when using it to determine the

nature of the n-type dopants in these specimens of indiiam-doped silicon

2. SUMMARY OF THE TWO-LAYER HALL TECHNIQUE

A. Measurement of Resistivity

Figure 1 is a schematic diagram of a symmetrical van der Pauw specimen

cut from a homogeneous slice of silicon and provided with low impedance

"ohmic" contacts at the end of each arm. This configuration is ideally

suited for measurements of resistivity and Hall coefficient [5,6]. Resistivity is measured by passing a known current through two adjacent

arms and measuring the voltage developed across the remaining two arms. The resistivity is computed by substituting this voltage and current,

along with the specimen thickness, d, into the following equation:

Figure 2 shows two symmetrical van der Pauw specimens of different re- sistivity arranged back-to-back but separated, each provided with its own current, and each with its corresponding voltage measured separately.

If the two specimens of figure 2 were each homogeneous in geometry and

resistivity, and had negligible (or the same) resistance at the current

carrying contacts and Vj = V2 , the voltage distribution over the backto-back surfaces would be the same. In this case, the two specimens

could be brought together to form a two-layer composite structure without any current crossing the interface. The currents Ii and 1 2 would be

unchanged, the voltages Vj and V2 would be equal, and the resistivities

of each layer would be given by the following expressions:

( 1 )

( 2 )

and

( 3 )

3
Figure

1.

Conventional

measurement

of

resistivity

using

the

van

der

Pauw

technique.
4J •H • s

(N

(U

u

nj 3 X)

tj' I •rH O

IX -P 5

Simultaneous

measurement

of

resistivity

in

two

distinct

van

der

Pauw

specimens

situated

back-
Since the contact resistances may not be equal or negligible, external

compensating resistors are placed in series with each of the four current leads as shown in figure 3. In addition, the current in each of

the four arms is separately monitored. The resistors are adjusted to

give zero voltage across the interface (i.e., V = V = 0) at the same

DH CG

time that I = I and

A B E F

Violation of the assumption of uniformity of resistivity in either or both layers may show up at this point

as the inability to achieve these conditions by varying R^, R^, R^

,

and/or R^. However, when these conditions can be achieved, or reasonably well approximated, a negligible amount of current crosses the interface and the resistivities of each layer are given by:

Pi = (4)

and

p2 = (5)

B. Measurement of Hall Coefficient

The van der Pauw specimen of figure 3 can also be used to measure the

Hall coefficient of each layer. For this measurement, the current is

passed through a pair of opposite contacts on each layer as shown in

figure 4, instead of adjacent contacts as shown in figure 3. This

change in current configuration does not alter the argument presented

above leading to the conclusion that settings can be found for the re- sistances in series with each carrying arm that will cause the voltage

distributions in the two layers to be the same and result in zero voltage across the interface (i.e., = 0) at the same time that

I,AC= and EG= I^.

If a magnetic field is now applied perpendicularly to the plane of the

interface between the two layers. Hall fields will be developed in the

vertical direction of figure 4. If the two layers have different re- sistivities or different conductivity types, the Hall voltages developed within each layer will be different, thus upsetting the pre6
:?Vs

;.V-* *

f4

ri

V”

• s m

+J

CD O

U td 3 -P tr C

•H O

Pn U

7

Simultaneous

measurement

of

resistivity

when

the

two

specimens

of

figure

2

are

brought

into

h

each

other

to

form

a

two-layer

structure.
8

Figure

4.

Simultaneous

measurement

of

Hall

coefficient

in

two-layer

structures.
viously established equality of voltage distribution of the two layers.

This will result in a difference in potential across the interface impedance, and currents will cross the interface between the two layers.

Figure 5A is a schematic diagram of an equivalent circuit for this situa

tion. The internally developed Hall voltages to be determined are desig

nated and V2. For layers of opposite conductivity type, Vi and V2

have the relative polarities indicated. The series resistances of the

active region of each layer (i.e., the Thevenin equivalent resistances

of the Hall voltage sources) are represented by and R2. The series

resistances of each layer in the arms of the van der Pauw structure

correspond to R5 through R3. The resistors R3 and R4 represent the interface impedance coupling the two layers together.

High values of R3 and R4 (compared to the larger of R^ or R2) correspond

to the case of good isolation by a nonleaky p-n junction at the interface. In this case, the loop current I in figure 5A is small, and the

internally developed Hall voltages Vj and V2 can be directly measured

at the arm contacts D-B and H-F with a high impedance voltmeter (to

avoid potential drops in R5 through Rg)

.

Low values of R3 and R4 correspond to the case of intimate contact of

two layers of different resistivity, but the same conductivity type.

In this case, the resulting loop current will produce potential drops across Rj and R2 which prevent the direct measurement of and V2 at

the arm contacts.

Between these two extremes, there is an intermediate case of a leaky

p-n junction at the interface that corresponds to intermediate values of

R3 and R4. The interface p-n junction can be modeled in terms of linear

resistors if the voltage across the junction is less than kT/q (=25 mV

at room temperature) . The circuit in figure 5A is not the most general

equivalent circuit one could imagine for this situation, but it is one that appears to contain elements representing all of the essential interactions of this problem and, as will be shown below, is simple enough

to lead to a practical measurement technique. It remains to be shown

that this circuit is capable of modeling the situation with sufficient

accuracy to produce a meaningful result.

9
A) EQUIVALENT CIRCUIT IN PLANE OF HALL FIELD

B) EQUIVALENT CIRCUIT OF A) IN ZERO MAGNETIC FIELD

Figure 5. Equivalent circuits of the specimen of figure 4 in the plane

of the Hall contacts D-B and H-F

.

10
It will be assumed throughout this discussion that high impedance voltmeters are used to measure differences in potentials between the con- tacts on the arms of the van der Pauw structure, so that the potential

drops in the series resistances R5 through Rs can be neglected. In this

case, the equivalent circuit of figure 5A can be used to show that:

and

V

DB

Vj [R2 + R3 + R4] - V2 [Ri]

Rl + R2 + R3 + R4 ( 6 )

V

FH

V2[Ri + R3 + R4 ] - Vi [R2 ]

Rl + R2 + R3 + R4

(7)

A parameter U which is a measiare of uniformity of the interface impedance can be defined by:

U

''fb

( 8)

For a perfectly uniform p-n junction at the interface, U would be unity.

Since Ri and R2 represent the series resistances within each layer separately, their ratio N is given by

Rl Pl^2

R2 P2^1

" (9)

where Pi and p 2 are the resistivities of the two layers as measured by

the technique discussed above.

If the applied magnetic field is now removed from the specimen of figure

4, the internally developed Hall voltages Vi and V2 disappear and the

equivalent circuit can be redrawn as shown in figure 5B. If magnetoresistance effects can be neglected, the resistance values in figure 5B are equal to the corresponding resistance values in figure 5A. Two

transfer impedances, R^ and R^, can be defined and measured as follows:

R

X

R3 R4V,BF

Rl + R2 + R3 + R4 Ij^jj

( 10 )

and

11
Rl R2

( 11 ) V

— -------- - -- y R]^ + R2 + R3 + R4

DB

HF

Equations ( 8 ) through (11) can be solved simultaneously for Rj , R2 , R3 , and Ru^ in terms of the measured Quantities U, N, R , and R . The re- " X y

suits are substituted into eqs ( 6 ) and (7) which can then be solved

simultaneously for Vi and V2

:

1/2 1/2

V_DB

Vi =

UNR

R

X .

+ U + 1

DENOM

UNR

-t- V

y

FH R

L X J

( 12 )

and

V

FH

Vo =

- -. 1/2

UR

NR

X.

-t- U -t- 1

DENOM

+ V.DB

UR

NR

X,

1/2

(13)

where

DENOM =

UNR

I

R

X .

1/2

-I- U + 1 UR

NR

X

-. 1/2

-I- U + 1

r 1 1/2 - -| UNR UR

Z + __Z

R NR

X J L X J

1/2

-I- U 1

UR

R

(14)

The Hall coefficient of each layer is then computed for these values of

Vi and V2 in the conventional way [5,6]:

and

RHi =

RH 2 =

Vi di

II B

V2 d2

lo B

where all quantities in the equations are in SI units.

Two examples of the use of this technique to characterize a thin n-type

epitaxial silicon layer on top of a thicker p-type bulk-grown substrate

are presented in the following section. These specimens were prepared

12
by Dr. Barbara E. Sumner at the Night Vision and Electro-optics Laboratory, Ft. Belvoir, Virginia.

3. ILLUSTRATIONS OF THE USE OF THE TWO-LAYER TECHNIQUE

A. For Making Measurements on Structures with Poor Interface p-n

Junctions

The material that motivated the development of the above two- layer technique consisted of a 1.0-mil (0.025-mm) thick layer of n-type epitaxial

silicon grown by liquid phase epitaxial techniques on top of a 14-mil

(0.36-mm) thick substrate of bulk-grown p-type indivun-doped silicon.

The n-type conductivity of the epitaxial layer, which was initially

demonstrated by thermal probe techniques, was completely unexpected be- cause the layer was grown from indium solution, but otherwise not intentionally doped. Since these growth conditions would be expected to produce a layer saturated with. indium, the question immediately arose re- garding the nature and cause of the observed n-type conductivity. In an experiment designed to answer this question, a van der Pauw specimen was ultrasonically cut from this material, and metallic contacts were evaporated on each side of the four arms. Aluminum was used to contact the

p-type substrate and gold-antimony was used to contact the n-type epitaxial layer. The current-voltage characteristic of this structure was linear between any two aluminum or any two gold-antimony contacts. It

exhibited a very leaky p-n junction characteristic between any aluminxim

and gold-antimony contact. These results, plus the initial thermal

probe result, leave little doubt that the epitaxial layer is n-type and

the svibstrate is p-type. It was found that some of the apparent leakage

of the interface p-n junction was due to the exposed regions of this

junction around the edges of the van der Pauw specimen. This component

of leakage was reduced significantly by etching the edge of the specimen

to remove the damage caused by the ultrasonic cutting. However, at room

temperature, the leakage current was still too large to permit the p-n

junction at the interface to be used to electrically isolate the two

regions of this specimen. The room temperature results given in table

1 were obtained by the above two-layer modified Hall technique on this

edge-etched van der Pauw specimen.

13
Table 1. Results on Specimen 10-SYS-l-In Obtained by Two-Layer

Technique at Room Temperature.

Layer Parameter Value

Epitaxial Resistivity 0.085 fi*cm

(n-type) Hall coefficient -65 cm^/C

Carrier density 9.6 X 10^^ cm"^

Hall mobility 760 cm^/V*s

Substrate Resistivity 0.818 fi*cm

(p-type) Hall coefficient +172 cmVc

Carrier density 2.6 X 10 IS cm“S

Hall mobility 210 cm^/V*s

Since the interface between the two layers was visible on the cut edges

of the specimen, the thickness of each layer was measured optically with

a microscope. Instrumental problems, specimen symmetry, and specimen inhomogeneity can often be determined by the change in resistivity or Hall

coefficient with current reversal or contact rotation. The resistivity

values quoted in table 1 represent the average of measurements made with

current reversals and with 90-deg contact rotation. The small deviations of the individual measurements about this average (5 percent for

the epitaxial layer and 6 percent for the substrate) indicate that this

specimen was fairly homogeneous. In addition, the resistivity was observed to change less than 2 percent with a sevenfold increase in cur- rent and is thus considered to be independent of the magnitude of the

measuring current used.

The Hall coefficient data in table 1 represent the average of values

obtained with current reversals, magnetic field reversals, and 90-deg

contact rotation. For contact rotation, the deviation of the two measurements from the average was 6 percent for the epitaxial layer and

1 percent for the substrate. This good agreement for the two configurations is another indication that the specimen was fairly homogeneous.

The carrier density was computed from the resistivity and Hall coefficient (assuming equal drift and Hall mobility) . The measured value of

Hall mobility for the electrons in the epitaxial layer is a very rea14
sonable one for silicon doped with approximately 10^^ donors per ciobic

centimeter. Likewise, the mobility and carrier density in the substrate

are very reasonable values for indium-doped silicon at room temperature.

The bulk-grown indium-doped p-type substrate of this specimen rapidly deionizes as the temperature is lowered below room temperature. Therefore,

if the n-type epitaxial layer does not deionize too rapidly, a temperature can be reached where the resistivity of the substrate becomes so large relative to the epitaxial layer that its perturbing effects can be

neglected. In this temperature regime, the epitaxial layer can be characterized by conventional Hall techniques without making any connection

to, or correction for, the substrate.

Figure 6 shows the results of such Hall measurements in which the apparent density of electrons in the epitaxial layer is plotted as a function

of 1000/T. In the vicinity of liquid nitrogen temperature (1000/T = 13)

where substrate effects can be neglected, the measured points have been

fitted by a theoretical curve generated by a computer solution of the

charge balance equation [7]

.

The dopant parameters so obtained are listed in table 2. The value of acceptor density was estimated from

the solubility of indium at the 900 °C growth temperature of this layer.

Table 2. Dopant Parameters Deduced from an Analysis

of the Data Presented in Figure 6.

Dopant Density

-3 cm Activation Energy

meV

Donor 1 9 X 10^^ 45

Donor 2 2 X 10^^ 10

Acceptor 1.5 X 10^^ ?

The dominant donor state has an apparent activation energy of about 45

meV which is the activation energy of phosphorus in silicon. However,

for a phosphorus density close to 10^^ cm~^ and the compensation ratio

of 0.14 calculated from the densities in table 2, one would expect a decrease of the activation energy from its value at low phosphorus den15
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16
sities [8-11]. Neutron activation analysis measurements show that the

dominant donor is not arsenic (AE = 49 meV) or antimony (AE = 39 meV)

.

It was impossible with activation analysis to determine if phosphorus

was present at the level expected because of the large amount of indium

in the substrate (indium decays with the emission of a beta particle

with about the same energy as the beta particle from phosphorus) . Since

even a few millielectronvolts change in the activation energy gives a noticeably poorer fit to the data in figure 6, one must assume either

that the dominant donor in this specimen is not phosphorus or that the

compensation is less than that of table 2. The latter possibility is

consistent with the results of Penin [9] who showed that the decrease

in activation energy is more pronounced in highly compensated material.

The tendency of the electron density curve to level off below liquid

nitrogen temperature has been attributed to the presence of a second

donor state with an activation energy less than that of the dominant

donor state. The incorporation of this second donor state into the

theoretical model upon which the curves of figure 6 are based has ex- tended the range of agreement to 1000/T = 20. The tendency of the electron density curve to become completely level and then increase at still

lower temperatures is not understood at this time. At these lower temperatures, the measured values are erratic and, to some extent, nonreproducible as evidenced in figure 6 by the spread of points beyond 1000/T

= 20 .

The failure of the theoretical curve to fit the measured points at the

higher temperatures is understandable in view of the substrate effects

that enter the picture as the temperature approaches room temperature.

This is the region where the present two-layer technique is needed to

make meaningful measurements. The theoretical curve extrapolates to a value that is in good agreement with the room temperature result which

was obtained by the two-layer technique. This point is indicated by

the triangular point in figure 6. This agreement supports the results

of the room-temperature two- layer technique.

17
The following section deals with the same type of epitaxial layer on an undoped high resistivity substrate. In this case, the two-layer technique was used to demonstrate that the substrate effects were negligible

and thus validate the conventional Hall measuring technique.

B. For Demonstrating that the Interaction Between the Two Layers is

Negligible

This section discusses measurements on material which was also grown by

liquid epitaxy except that the substrate was high resistivity p-type

silicon rather than the indium-doped silicon used previously. As before

the epitaxial layer was n-type with a thickness of 1.0 mil (0.025 mm).

A van der Pauw specimen was ultrasonically cut from the material and con

tacts were evaporated and alloyed on each side of the four arms. The ex posed regions of the p-n junction were not etched. Measurements were

made by the two-layer technique at room temperature and 77 K in the manner discussed previously. Measurements were also made at these same tern peratures on both layers by the conventional technique in which no connections were made to the contacts on the layer not being measured. The

results are summarized in tables 3 and 4. The values obtained for the

epitaxial layer by the two techniques are in excellent agreement and sup

port the conclusion that the interaction between the two layers is small

enough that the epitaxial layer can be correctly measured by the conven-

* tional technxque. The conventional technique was then used to obtain

the electron density as a function of temperature; these results are shown in figure 7. These data were fitted by a theoretical curve with

a donor density of 1.7 x 10^^ cm“^ and an activation energy of 45 meV.

The measurements on this specimen do not extend to low enough temperatures to determine if a second donor and an acceptor level are present,

but since the growth conditions for this specimen were similar to those

for the first specimen, the parameters for donor two and the acceptor

'k The converse is not true. Conventional measurements on the high resistivity substrate may be seriously perturbed by the lower resistivity

epitaxial layer. Therefore, agreement between the two techniques is

not expected for the substrate as indicated in table 3.

18
were included in the fit of this specimen. However, these levels have

a negligible effect on the fit in the temperature range shown in figure

7. The 45-meV activation energy for the dominant donor state suggests

that the unknown impurity may be phosphorus. However, as before, this

conclusion is clouded by the fact that with significant compensation

the activation energy of phosphorus should be somewhat lower than 45 meV.

Table 3. Results on Specimen 8-SYS-2-In at Room Temperature.

Layer Parameter

Conventional

Technique

Two-Layer

Technique

Epitaxial Resistivity 0.0605 S7*cm 0.0592 fl’cm

Hall coefficient -37.2 cm^/C -37.5 cm^/C

Carrier density 1.68 X lo^'^ cm"3 1.66 X 10^^ cm~^

Hall mobility 614 cm^/V*s 635 cm^/V*s

Substrate Resistivity 530 n*cm 69,000 J^*cm

Hall coefficient +4.82 X 10*+ cmVc - 2.3 X 10^ cm^/C

Carrier density 1.3 X 10^*+ cm" 3 2.7 X cm~3

Hall mobility 90.6 cm^/V*s 335 cm^/V*s

Table 4. Results on Specimen 8-SYS-2-In at 77 K.

Layer Parameter

Conventional

Technique

Two-Layer

Technique

Epitaxial Resistivity

Hall coefficient

Carrier density

Hall mobility

0.201 fi*cm

-2.96 X iq 2 cm^/C

2.11 X 10^^ cm"3

1472 cm^/V*s

0.197 Q*cm

-2.95 X iq 2 cm^/C

2.12 X cm"3

1495 cm^/V*s

Substrate Resistivity

Hall coefficient

Carrier density

Hall mobility

78.7 • cm

7.42 X 10^ cm^/C

8.41 X 10^2 ^^-3

9430 cm^/V*s

80.5 • cm

7.18 X 10^ cmVc

8.69 X 10^^ cm"3

8920 cm^/V*s

4. CONCLUSIONS

A technique was developed for characterizing epitaxial layers on substrates of opposite conductivity type for situations where the p-n junction does not effectively isolate the two layers. This two-layer tech19
10 '*

10'6l__l I I I I I I I I I I I 1—1

1 2 3 4 S 8 7 8 9 10 11 12 13 14

1000/T IKELVIN) '

Figure 7. Electron density in the epitaxial layer of Specimen 8-SYS-2-

In obtained by conventional Hall measurements (points) and a theoretical

fit to the data.

20
nique was used to determine the room temperature resistivity and Hall

coefficient in both layers of an epitaxial specimen, and the results

agreed well with those obtained from a theoretical fit based on low temperature measurements by the conventional technique. For another specimen, the two- layer technique demonstrated that substrate effects were negligible, thus validating the conventional technique. In both epitaxial specimens, an unknown n-type impurity was identified with an apparent activation energy of 45 meV and a density of about 10^^ cm“^.

The activation energy suggests that the impurity may be phosphorus. How

ever, since the activation energy of phosphorus should be somewhat lower

than 45 meV at a concentration of 10^^ cm“^ and with significant compensation, there is a possibility that this donor is some other species

with a low-density activation energy somewhat above 45 meV. Arsenic (AE = 49 meV) has been ruled out by neutron activation analysis. Other possibilities that may satisfy these criteria are bismuth (AE = 0.069 eV)

and interstitial indium (AE = ?) . (Note added in proof: The presence

of phosphorus at a density of about 10^^ cm"^ has been confirmed in Spec

imen 10-SYS-l-In by Dr. Te-Tse Chang of the National Bureau of Standards

using electron paramagnetic resonance.)

5 . REFERENCES

1. Petritz, R. L. , Theory of an Experiment for Measuring the Mobility

and Density of Carriers in the Space-Charge Region of a Semiconductor Surface, Phys. Rev. 110 , 1254-1262 (1958)

.

2. Migitaka, M. , Anomalous Properties of Silicon Recrystallized Layers

Containing Indium Atoms, J. Appl . Phys. 2139-2143 (1965).

3. McCaldin, J. 0., and Mayer, J. W. , Donor Behavior in Indium-Alloyed

Silicon, Appl. Phys. Letters'^, 365-366 (1970).

4. Davies, J. A., Eriksson, L., and Mayer, J. W. , Experimental Evidence for Interstitial In and T1 in Ion-Implanted Silicon, Appl.

Phys. Letters I^, 255-256 (1968)

.

5. van der Pauw, L. J., A Method of Measuring the Resistivity and Hall

Coefficient on Lamellae of Arbitrary Shape, Philips Tech. Rev. 20,

220-224 (1958)

.

6. van der Pauw, L. J. , A Method of Measuring Specific Resistivity and

Hall Effect of Discs of Arbitrary Shape, Philips Res. Rep. 13, 1-9

(1958)

.

21
7. Larrabee, R. D. , Thurber, W. R. , and Bullis, W. M., A Fortran Program for Calculating the Electrical Properties of Extrinsic Silicon,

to be published.

8. Pearson, G. L. , and Bardeen, J. , Electrical Properties of Pure Silicon and Silicon Alloys Containing Boron and Phosphorus, Phys. Rev.

75, 865-883 (1949).

9. Penin, N. A., Zhurkin, B. G., and Volkov, B. A., Influence of the

Concentration of Donors and Acceptors on the Electrical Conductivity of Heavily Doped n-Type Silicon, Sov. Phys. - Solid State J7, 2580-2584 (1966)

.

10. Newmark, G. F., Comment on "Comparison of Experimental and Theoretical Carrier Concentrations in Heavily Doped n-Type Silicon," J.

Appl. Phys. 3618-3619 (1977).

11. Lee, T. F,, and McGill, T. C., Variation of Impurity-to-Band Activation Energies with Impurity Density, J. Appl. Phys. 46, 373-380

(1975)

.

22
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24
NBS-1 14A (REV. t 1-77)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBSIR 78-1553

2. Gov’t Accession

No.

3. Recipient’s Accession No.

4. TITLE AND SUBTITLE

Theory and Application of a Two-Layer Hall Technique

5. Publication Date

6. Performing Organization Code

7. AUTHOR(S)

R. D. Larrabee and W. R. Thurber

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Worlc Unit No. 7216458

11. Contract/Grant No. MERADCOM 28052

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

U.S. Army ERADCOM

Night Vision Laboratory

Fort Bel voir, VA 22060

13. Type of Report & Period Final

April 3“Sept. 30, 1978

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

Concducted as part of the NBS Semi coniductor Technology Program.

16. ABSTRACT (A 200-word or less factual summary of moat significant information. If document includes a significant

bibliography or literature survey, mention it here.)

The electrical characterization of epitaxial layers of silicon on substrates of the

opposite conductivity type presents serious problems if the p-n junction at the Interface

has significant leakage current such that It cannot be used to effectively isolate the two

regions. In order to meet the need for nondes truct i vel y characterizing such structures, a modification of the conventional Hall technique was developed In which the Hall measurements are made simultaneously on both the epitaxial layer and its substrate; the interface

impedance is measured; and the Interaction between the two regions Is modeled and taken

into account. This technique can be used not only to measure the unperturbed resistivity

and Hall coefficient of each layer separately, but also to verify those cases In which

the perturbing effects of a high resistivity substrate are negligible, thus justifying

conventional measurements on the epitaxial layer.

Th i s . techn i que was used to measure the parameters of an n-type Indium-doped silicon

epitaxial layer on a bulk-grown p-type indium-doped substrate. The results suggest that

the major n-type dopant in this specimen has a density of about 1 x 10^^ cm" ^ and an apparent activation energy of about 45 meV. Similar data were obtained on a second epitaxial layer grown on a high resistivity undoped substrate. These results argue strongly

for the presence of one or more undesired sources of shallow donor contamination in the

epitaxial growth system used to produce these specimens.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only die first letter of die first key word unless a proper name; separated by semicolons)

Epitaxial growth; Hall measurements; indium-doped silicon; p-n junction isolation;

two—layer structures.

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