Download Characterization of Gallium Antimonide Grown on Semi

ACTIVITIES
Characterization of Gallium Antimonide Grown on Semi-Insulating Gallium Arsenide
Using Interfacial Misfit Technique
REU Student: Daniel Kim
Graduate Student Mentor: Orlando S. Romero, Nassim Rahimi
Faculty Mentor: Dr. Luke F. Lester, Dr. Sayan D. Mukherjee
A. Introduction
The determination of semiconductor characteristics is an essential part of the process
of understanding particular properties of the material. The actual process of
characterization can involve different methods depending on the context but
consistent to all contexts is the idea that one uses particular methods in order to
obtain measurable quantities that relate to the material’s properties. The context here
is that of the determination of three characteristic values related to the material being
studied, gallium antimonide. The characteristic values are carrier type, carrier
concentration, and carrier mobility. Consistently associating the word carrier with all
three of these characteristic quantities is not without reason. The word carrier simply
refers to the particles that carry charge throughout the material. Though it is worth
mentioning that implicit in the word carrier is the idea that these charges are free to
move and contribute to a current, which will be elaborated on later. There are two
possible charged particles to be considered which are electrons and holes, holes being
virtual particles that result from the absence of an electron. Both particles may be
referred to synonymously as carriers. The method that is utilized here to obtain the
characteristic values mentioned above, and that will be elaborated on in a later
portion of this paper, is that of Hall measurements. While the prevalence of material
characterization may make Hall measurements made on gallium antimonide seem
unexceptional, there are aspects of the characterization of gallium antimonide that
make this project particularly deserving of attention. This is especially so when
considering the inability to obtain a semi-insulating substrate of gallium antimonide
and the reason why this is necessary will be elaborated on and hopefully made clear
in the discussion of the method of Hall measurements in the following section. This
introduces the added intrigue to an otherwise routine experimental process of
studying how the growth technique used to grow the gallium antimonide will affect
the characteristic values obtained through Hall measurements.
B. Background
Essential to the understanding of the experimental process involved in this project is
knowledge of what is called the Hall effect. Diagramed in Figure 1 (NIST) below is
what is known as a Hall bar. What is to be imagined is a conducting material through
which a current is passing (in the direction of I in Figure 1). The magnetic field
applied perpendicular to the surface of the Hall bar results in the charges flowing in
the current experiencing a force known as the Lorentz force. The direction of this
force experienced by the charges is governed by what is known as the right-hand rule
and is determined by pointing the fingers of the right hand along the direction of the
velocity of these charges, curling them toward the direction in which the magnetic
field is pointing, the resulting direction in which the thumb points being the direction
of the Lorentz force (where the absence of an applied electric field is assumed). The
force experienced thus results in the deflection of the charges to the edges of the Hall
bar creating an electric field across the Hall bar called the Hall field. The deflection of
these charges due to the Hall field leads to an electric potential difference across this
Hall bar, which is measurable and which is called the Hall voltage.
This is one of the essential quantities that is measured in Hall measurements. The
polarity of this measurement determines the carrier type. That is, the Hall voltage
being positive or negative will indicate whether the carriers, of which the current is
composed, are either holes or electrons, respectively. Defining the other characteristic
values mentioned in the introduction will necessitate an understanding of some basic
knowledge of where these carriers come from and how they move throughout the
semiconductor material. The idea of a pure semiconductor material is an idealization
wherein it is assumed that there are no defects or impurity atoms (Neaman). Defects
refer to the variety of different structural imperfections that may be present in the
crystal structure of the semiconductor material. These defects vary in type from the
absence of entire rows of atoms to the presence of atoms in between lattice points in
the crystal structure of the material. Impurity atoms are atoms of a foreign material
present in the crystal structure of another. Impurity atoms are added in order to
influence the conductivity of the material and they do so by contributing to the carrier
concentration. Carrier concentration then is the number of free carriers that are
present in every cubic centimeter of the semiconductor. While the definition of the
carrier type was simple enough to be incorporated into the discussion of how it is
obtained through the process of Hall measurements, the definition of Hall mobility
requires a slightly more detailed elaboration. One way these free carriers move
throughout the material is under the influence of an externally applied electric field
and this resultant movement is what is known as drift. The net drift of these free
carriers is what is defined as the drift current and the speed at which these free
carriers move is called the drift velocity. The drift velocity is proportional to the
applied electric field for sufficiently low applied electric fields. The proportionality
constant between the drift velocity and the applied electric field is what is known as
the mobility. Intuitively defined, the mobility can be thought of as how well these free
carriers are able to move throughout the material. A plot of the relationship between
the drift velocity and the applied electric field for silicon is shown below (GlobalSino).
The regime wherein the relationship between the drift velocity and the applied
electric field can be considered to be linear is for very low applied electric field, which
is apparent when considering the lower end of the horizontal axis. The line that
highlights this relationship is extended using the dotted lines for both electrons and
holes. The solid line starts to deviate and become sub-linear and only remains an
accurate approximation for a small portion of the electric field values shown on the
graph. This behavior is not exclusive to silicon and is due to what is known as velocity
saturation, the definition of which is not pertinent to the project discussion and is
thus omitted.
The concept of the lattice mismatch between the two materials, that of the substrate
GaAs and that of the epitaxial layer under study GaSb, is important to acknowledge.
Unit cells are the “small volumes of the crystal that can be used to reproduce the
entire crystal” (Neaman, p. 3). The intrinsic crystal structures of the materials under
study are comprised of regularly reproduced unit cells in periodic fashion and the
space between these unit cells is what is known as the lattice constant (Neaman, p. 3).
The lattice constant of GaAs is ~6 Angstrom and of GaSb is ~5.6 Angstrom (Ioffe
Institute). This mismatch results in a high concentration of dislocation defects. These
dislocation defects can trap carriers thus degrading the characteristic values
considered in this project. The growth technique has an effect on this concentration.
The growth technique used in this project is that of interfacial misfit (IMF) technique
with the growth method being molecular beam epitaxy (MBE). Without this growth
technique the dislocation densities, meaning the number of dislocations found per
square centimeter, is ~108cm-2 while the density with the IMF technique is ~106cm-2.
The method and technique of MBE and IMF will not be explained because the relevant
information to be considered is the comparison of the dislocation densities with and
without the IMF technique in order to highlight the likelihood of degradation.
C. Research Objective
Objectives as my professor mentor outlined them are as follows (Dr. Luke F. Lester,
Center for High Technology Materials, personal communication)
(1) Compare the carrier concentration of n-type (Te-doped) and p-type (Be-doped)
GaAs grown on SI-GaAs with n- and p-type GaSb grown with the Interfacial Misfit
Dislocation (IMF) technique on SI-GaAs. Orlando Romero will grow these wafers
targeting 3 different doping concentrations each for the four sets. There are a total
of 12 growths. It is anticipated that these growths will be completed by June 15th.
(2) Learn Hall setup and theory. Measure the samples grown by Orlando in (1). Learn
how to interpret Hall data as to its quality and reproducibility.
(3) Assist Orlando in photoluminescence and x-ray diffraction characterization of the
structures grown in (1) whenever practical. Observe Molecular Beam Epitaxy
(MBE) growth with Orlando.
The primary objective explicitly stated is to obtain the characteristic values of the
samples of GaSb grown on SI-GaAs. Acquiring an understanding of Hall setup and
theory is essential to this primary objective in that the method utilized to ascertain
these characteristic values is that of Hall measurements. An understanding of the
relations between the characteristic values and the interfacial misfit (IMF) growth
technique is a natural extension outlined in the objectives written by Dr. Luke F.
Lester. An assessment of the magnitudes of degradation in the mobility values
obtained by Hall measurements of GaSb on SI-GaAs with IMF as compared to GaSb
grown on its native substrate will be made possible provided the possibility of making
Hall measurements of GaSb when grown on its native substrate. The hypothesized
outcome is that the mobility values will be degraded due to the large concentration of
dislocation defects that arise from the mismatch of the lattice constants of GaSb and
GaAs.
D. Methodology
There is a specific method utilized in making Hall measurements. The method is called
the Van der Pauw method and is diagramed below in the figures labeled Figure 2 and
Figure 3 (NIST). Both figures show squares (rectangular prisms) that represent the
sample to be measured. In this case, the sample is an epitaxial layer of gallium
antimonide grown on a substrate of semi-insulating gallium arsenide using molecular
beam epitaxy that has a square centimeter dimension. The shaded corners of the
squares represent contacts, in this case dots of melted indium, to which wires are
soldered through which current is passed and voltages measured. Figure 2 depicts the
method in measuring what is known as the Hall resistivity. Working backwards,
resistivity is defined as the inverse of conductivity. The conductivity is a quantity that
is related to the mobility through the electronic charge and carrier concentration.
Thus, passing current in the direction of the arrows diagramed in Figure 2, measuring
the values of the voltages across the points to which the voltmeter is attached, allows
one to calculate this resistivity. This process of measurement is repeated for all
possible configurations around the Hall sample. That is, for example, after the
measurement made in the configuration depicted in the figure is made, the
configuration of the setup would change such that current is passed into point 4 and
out of point 1 and voltages would be measured across points 2 and 3 continuing for all
possible configurations of current and voltage arrangements. Figure 3 is a depiction of
the measurement of the Hall voltage. Current is passed in the direction of the arrows
diagramed in the figure. How this process of measurement is accomplished and what
sorts of machines are involved will be described in greater detail in the section that
provides the descriptions of the experiments.
(Above: Depiction of Van der Pauw method in measuring Hall resistivity)
(Above: Depiction of Van der Pauw method in measuring Hall voltage)
The mathematical relations between the measured quantities and the calculated
quantities are as follows (Neaman, 2012, p. 181):
Where VHall represents the Hall voltage, I the magnitude of the current, B the
magnitude of the magnetic field, d the thickness of the grown layer, W and L
representing dimensions of width and length of the sample.
E. Description of Experiments
General information of the four samples of GaSb grown on SI-GaAs using MBE and the
IMF technique are as follows:
(1) R12-53: SI-GaAs/GaSb (n~1E19)/Surface
Ga Cell/Ga Tip Temp: 821.9oC/1035oC
Sb Cell Temp: 447oC
Growth Rate: GaAs: .3313 µm/hr
GaSb: .4154 µm/hr
Thickness: 300 nm
GaTe Temp: 503oC
(2) R12-54: SI-GaAs/GaSb (n~5E18)/Surface
Ga Cell/Ga Tip Temp: 821.9oC/1035oC
Sb Cell Temp: 447oC
Growth Rate: GaAs: .3313 µm/hr
GaSb: .4154 µm/hr
Thickness: 500 nm
GaTe Temp: 484oC
(3) R12-55: SI-GaAs/GaSb (n~1E18)/Surface
Ga Cell/Ga Tip Temp: 821.9oC/1035oC
Sb Cell Temp: 447oC
Growth Rate: GaAs: .3313 µm/hr
GaSb: .4154 µm/hr
Thickness: 1 µm
GaTe Temp: 444oC
(4) R12-56: SI-GaAs/GaSb (n~5E17)/Surface
Ga Cell/Ga Tip Temp: 821.9oC/1035oC
Sb Cell Temp: 445oC
Growth Rate: GaAs: .3313 µm/hr
GaSb: .4154 µm/hr
Thickness: 1 µm
GaTe Temp: 428oC
These samples were grown on 3-inch SEMI-A standard wafers. The SEMI-A standard
wafers are depicted below along with the convention that was used in order to label
and organize the square centimeter samples that were cleaved for Hall
measurements. Exactly which samples were used in accordance with this convention
will be mentioned in the findings section under the results heading. The red lines on
the bottom and the right of the sample represent the major and minor flats,
respectively.
4
3
SEMI-A Standard Wafer Orientation
1cm
A
2
B
C
1
After cleaving the entire 3-inch wafer in quarters, a quarter was selected (which one,
will again be specified in the results section of the paper). The quarter was then
cleaved separating a triangular piece and a strip; the strip is where the Hall
measurements were taken from. Three square centimeter pieces were taken from the
strip and labeled A, B, and C in the convention diagrammed above. Contacts were then
made to the square centimeter samples by thermally annealing dots of indium on the
order of half to one square millimeter. The temperature at which these contacts were
annealed was just above the melting temperature of indium (~156oC) at ~160oC. The
samples were removed from the annealing surface as soon as the indium had melted.
The reason for the low temperature short time annealing is explained in accordance
with the following diagram. The diagram below depicts the sample viewed from the
side. The necessity of a semi-insulating substrate was mentioned in the introduction
and can also be explained with the diagram.
GaAs
SI-GaAs
GaSb
GaSb
GaSb
SI-GaAs
The top figure shows the indium contacts as two vertically oriented silver bars
penetrating through to the substrate material. Supposing that this material is GaAs
grown on its native substrate, current is only allowed to flow in the epitaxial layer due
to the semi-insulating nature of the substrate as indicated by the blue arrows. Thus, it
would be possible to obtain characteristic values using Hall measurements on this
sample. Though, the material under study is GaSb grown on SI-GaAs. This is because
GaSb cannot be had in a semi-insulating form. Thus, if GaSb were to be grown on its
native substrate, it would be impossible to determine which layer you were
characterizing with Hall measurements if you penetrated both layers because current
would be liable to flow in either of the conducting layers as shown in the middle
figure. Thus, GaSb was grown on the semi-insulating substrate of GaAs with MBE
using the IMF technique. The reason for the low temperature short time annealing is
due to the IMF layer. The IMF layer is highly conductive, and when penetrated by the
indium contacts, renders the Hall measurements useless. Thus, low temperatures and
short annealing times were utilized such that the indium only penetrates to
sufficiently shallow depths in order to avoid penetrating the IMF interface shown in
the bottom figure. Wires were soldered to these indium contacts and current was
passed and voltages were measured in the fashion diagramed in the figures in the
methodology section. Before making actual measurements, the resistances between
the contacts were made using a multi-meter to ensure that relatively consistent
resistance values were obtained. This was done as a way of checking the wire
connections to the contacts and the contacts themselves. An example of the
measurements page is shown below.
The current passed through was varied until self-consistent values were obtained for the
concentrations and mobility values. The thickness was entered in accordance with the
sample and the rest of the variable values remained as depicted in the above figure. This
process was repeated for the four samples described above and the results will be
summarized in the results section.
FINDINGS
REU Student: Daniel Kim
Graduate Student Mentor: Orlando S. Romero
Faculty Mentor: Dr. Luke F Lester
A. Results
The results for the four samples given in the experimental description section of the
activities portion of the paper are summarized in the following table:
Hall
Sample
Average
Carrier
Concentration
(cm-3)
Average
Mobility
(cm2/Vs)
Resistivity
Without
B-Field
(-cm)
Sheet
Resistivity
Without Bfield
(/square)
Resistivity
With B-Field
(-cm)
Sheet
Resistivity
With BField
(/square)
Test
Current
(A)
R12-53
9.69E17
1203.84
5.379E-3
1.793E2
4.777E-3
1.592E2
120.0
R12-54
6.95E17
1908.86
4.712E-3
9.423E1
3.982E-3
7.964E1
150.0
R12-55
2.16E17
3648.26
7.933E-3
7.933E1
6.010E-3
6.010E1
100.0
R12-56
9.25E16
4562.04
1.482E-2
1.482E2
1.301E-2
1.301E2
100.0
Each sample was taken from quarter 1 in the SEMI-A standard. With the exception of
sample R12-56, each sample was section A in accordance with the convention
diagramed in the experimental description section of the activities portion above.
Sample R12-56 was section C in accordance with the same convention. The
concentrations are significantly lower from the expected concentrations. Before the
low temperature short time annealing methods were used, the values for the
concentrations were in the 1020-1021 range, which were even larger than the expected
concentration values and even less likely considering the expectation of seeing lower
concentrations due to the nature of the material. Current-Voltage (IV) characteristics
were taken of the indium contacts made on the sample and resulted in determining
the nature of the contacts to be indeed ohmic. It was then though that higher
annealing temperatures would help but after a brief discussion of the questionable
results it was determined that the unreliable measurements being taken was due to
the penetration of the contact through to the IMF layer. The concentrations when
compared with the mobility values also appeared counter-intuitive before the low
temperature annealing methods were used. After low temperature short time
annealing was used, the values given in the table were obtained and were considered
to be acceptable. The reasoning behind why this data set could be considered
acceptable will be elaborated on in the conclusions section.
General information for the samples of GaAs grown on SI GaAs in the same manner as
given for the samples of GaSb are as follows:
(1) R12-37: SI-GaAs/GaAs (n~1E18)/Surface
Ga Cell/Ga Tip Temp: 816oC/1032oC
Growth Rate: .3256 µm/hr
Thickness: 3 µm
GaTe Temp: 444oC
(2) R12-42: SI-GaAs/GaAs (n~5E18)/Surface
Ga Cell: 816.4oC
Growth Rate: .3256 µm/hr
Thickness: 700 nm
GaTe Temp: 484oC
(3) R12-43: SI-GaAs/GaAs (n~7E18)/Surface
Ga Cell/Ga Tip Temp: 816.4oC/1033oC
Growth Rate: GaAs: .3256 µm/hr
Thickness: 500 nm
GaTe Temp: 493oC
The results for the samples of GaAs grown on SI-GaAs outlined about are summarized
in the following table:
Hall
Sample
Average
Carrier
Concentration
(cm-3)
Average
Mobility
(cm2/Vs)
Resistivity
Without
B-Field
(-cm)
Sheet
Resistivity
Without Bfield
(/square)
Resistivity
With B-Field
(-cm)
Sheet
Resistivity
With BField
(/square)
Test
Current
(A)
R12-37
2.43E18
2312.42
1.113E-3
3.708
8.649E-4
2.883
3000.0
R12-42
3.66E18
2039.00
8.369E-4
1.196E1
6.532E-4
9.332
1000.0
R12-43
2.35E18
2280.46
1.164E-3
2.328E1
9.414E-4
1.883E1
500.0
There is an issue with the results for the sample R12-43. As compared to the values
measured for R12-37, there is a lower concentration; yet, there is also a lower
mobility. With a lower doping concentration one would expect that the mobility
values be higher. The reasoning for this will again be elaborated on in the conclusions
section, though it should be known that this error was expected. There was a
notification of the error during this sample’s growth where the temperature had been
raised for an appreciable amount of time (~10 minutes) and lowered back down to
the original value (listed in the information as the GaTe temperature). This
temperature fluctuation could possibly have had a significant impact on the quality of
the growth and consequentially the characteristics of the sample. Thus, there is less
reason for the sample R12-43 to be considered as having been measured with success.
B. Conclusions
The objectives of this project were not only to obtain the characteristic values of GaSb
epitaxially grown on semi-insulating GaAs but also to understand the affect that the
IMF growth technique would have on the mobility values. There are many factors that
are not taken into account when making Hall measurements. For example one does
not incorporate depletion widths into the calculated values. Thus, many of the
characteristic values taken from Hall measurements are considered as averages and
thus other methods may be used to obtain more precise measurements of
characteristic values like carrier concentration. However, carrier mobility is
unambiguous and reliable because the growth process determines the factors taken
into account in its calculation. It was expected that the characteristic values of GaSb
grown on semi-insulating GaAs would be degraded and that was observed in the
results section. The ideal mobility values can be calculated using the following
formula (Bett, 2001):
Tables summarizing the measured concentrations and the mobility values and the
plot of the carrier concentration versus mobility for both the expected values in
accordance with the formula and the measured values taken from Hall measurements
are as follows:
Carrier Concentration (cm-3)
Measured Mobility
(cm2/V-s)
Ideal Mobility (cm2/V-s)
9.69E+17
1203.84
6590.35
6.95E+17
1908.86
6590.35
2.16E+17
3648.26
6590.35
9.25E+16
4562.04
6590.35
Carrier Concentration vs. Mobility
7000
6000
Mobility (cm2/V-s)
5000
4000
Mobility (cm2/V-s)
3000
Ideal Mobility (cm2/V-s)
2000
1000
0
1.00E+16
1.00E+17
Carrier Concentration (cm-3)
1.00E+18
The concentration values of the GaSb were expected to be lower than GaAs because of
the intrinsic p-type nature of GaSb that needed to be compensated before becoming ntype. With this data one could determine the amount of p-doping that was being
compensated by the n-doping. A sample of un-doped GaSb grown on semi-insulating
GaAs using the IMF technique was measured also. On average, the difference in the
measured values and the ideal values is approximately 54 percent. The calculation of
the compensation could then be compared with this measured value for the un-doped
substrate and theoretically they should be comparable to each other. Qualitatively, the
outcome of the Hall measurements made on GaSb agrees with our expectations. The
natural extension of this agreement would be to determine quantitative relations that
the interfacial misfit growth technique has on the characteristic values of GaSb grown
on semi-insulating GaAs.
C. Future Work
Provided evaporated metal contacts can be connected to the Hall set up, it could be
possible to take Hall measurements on GaSb samples grown on its native substrate
and compare the values with the GaSb grown on the non-native substrate of GaAs.
These metal contacts would be shallow enough to ensure that the substrate layer is
not penetrated thus only passing current through the epitaxial layer. Diagramed
below is a crude depiction of what this would look like.
(n- or p-type)
GaSb
(p- or n-type)
GaSb
The shallow contacts would be wired to the Hall set up much in the same way that the
samples with the indium contacts were. This would aid in the characterization of GaSb
and could contribute to the research of thermal photovoltaic (TPV) generators. (Bett,
2003). This could also contribute to the study of utilizing GaSb in multi-junction solar
cell applications (Bett, 2001).
References
Neaman, Donald A., 2012, Semiconductor Physics and Devices, McGraw-Hill, New York City,
758 p.
NIST, December 2, 2011, National Institute of Standards and Technology, The Hall Effect,
http://www.nist.gov/pml/div683/hall_effect.cfm, July 23, 2012
GlabalSino, October 15, 2011, GlobalSino, Drift Velocity Versus Electric Field in Silicon,
http://www.globalsino.com/micro/1/1micro9938.html
Ioffe Institute, 1998-2001, Ioffe Physico-Technical Institute, New Semiconductor Materials.
Characteristics and Properties, Gallium Arsenide,
http://www.ioffe.ru/SVA/NSM/Semicond/GaAs/basic.html
Ioffe Institute, 1998-2001, Ioffe Physico-Technical Institute, New Semiconductor Materials.
Characteristics and Properties, Gallium Antimonide,
http://www.ioffe.rssi.ru/SVA/NSM/Semicond/GaSb/basic.html
Bett A. W., Sulima O. V., 2003, GaSb Photovoltaic Cells for Applications in TPV Generators, IOP
Science, http://iopscience.iop.org/0268-1242/18/5/307
Bett A. W., Adelhelm R., Agert C., Beckert R., Dimroth F., Shubert U., 2001, Advanced III-V
Solar Cell Structures Grown by MOVPE, Solar Energy Materials & Solar Cells
Bett, A. W., Sulima O. V., 2001, Fabrication and Simulation of GaSb Thermophotovoltaic Cells,
Solar Energy Materials & Solar Cells 66