U.S. Patent Oct. 18, 2022 Sheet 18 of 59 US 11,474,134 B2

O Contact pads

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FIG. 18


U.S. Patent Oct. 18, 2022 Sheet 39 of 59 US 11,474,134 B2

Pyx (Q}

0 70000 «= 20000» 30000 40000 ©= 50000 »=— 80000
Time (s)

FIG. 39


US 11,474,134 B2

Sheet 35 of 59

Oct. 18, 2022

U.S. Patent

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US 11,474,134 B2

Sheet 44 of 59

Oct. 18, 2022

U.S. Patent

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U.S. Patent Oct. 18, 2022 Sheet 12 of 59 US 11,474,134 B2

200

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US 11,474,134 B2

Feu

where a and b are integers. As seen in a previous experi-
mental work, a and b formed several measurable coefficients
of R, Since those observations, an explanation for why
those values appeared was not fully understood, let alone
formulated into a theoretical framework. The latter frame-
work is important to understand and may provide insights on
device functionality in the quantum Hall regime. Further-
more, this new framework provides an easily implementable
algorithm for the calculation of the quantized resistances
when specific experimental outputs are desired, an approach
that cannot be granted by simulations alone. Given that this
formulation is independent of material properties, applica-
tions to other material systems that exhibit quantum Hall
behavior are to be expected.

The use of source and drain is not used in the following
description in this Example to prevent confusion regarding
electron flow within the device and will be replaced by
electron entry or exit terminals, with entry and exit terminals
being representing by negative and positive symbol icons,

respectively. Many simulations were performed to deter- 2

mine a generalized behavior of how the overall effective
resistance of the circuit shown in FIG. 47 changes with
terminal configuration. These simulations were performed
with the analog electronic circuit simulator LTspice.

The overall circuit comprises quantized regions of both
p-type and n-type variety, with both regions being modeled
as either ideal counterclockwise (CCW) or clockwise (CW)
k-terminal quantum Hall effect (QHE) elements and shown
as gray or blue regions in FIG. 47, respectively. The terminal
voltages e,, are related to the currents j,, by Ryiin=@n-@mn-1
(m=, ...,k) for CW elements and Ryj,,-C,-C 4, for CCW
elements. To determine the circuit’s behavior at the external
terminals (labeled as A and B in FIG. 47), only a single
magnetic field (B-field) direction was simulated at a time.
For a positive B-field, an n-type (p-type) device (experi-
mentally represented as a graphene-based device) was mod-
eled by a CW (CCW) QHE element, whereas, when B is
negative, a CWW (CW) QHE element was used.

To test some of the simulations, graphene pnJ devices
were fabricated from epitaxially grown graphene (EG).
When at the high temperature of 1900° C., Si atoms subli-
mate from SiC samples, leaving behind an excess of carbon
that arranges itself into a honeycomb lattice. Samples were
diced from on-axis 4H—SiC(0001) semi-insulating wafers.
After a chemical cleaning with a 5:1 diluted solution of
hydrofluoric acid and deionized water, the samples were
processed with AZ5214E for polymer-assisted sublimation.
Next, samples were placed silicon-face down on a polished

graphite substrate. The growth was performed in an ambient

argon environment at 1900° C. with a graphite-lined resis-
tive-element furnace, with heating and cooling rates of about
15° C/s.

‘After growth, the quality of the EG was assessed with
confocal laser scanning and optical microscopy for effi-
ciency. Protective layers of Pd and Au were deposited on the
BG to prevent organic contamination during the subsequent
photolithography processes. The required functionalization
with Cr(CO), to reduce the electron density to the order of
10° cmr?, as well as the deposition of a $1813 photoresist
spacer layer and photoactive ZEPS20A layer, was also
followed as previously described.

&

&

26

As the theoretical framework for determining the effective
quantized resistance of the circuit exemplified in FIG. 47 is
explained, certain parameters will be frequently mentioned.
The total number of terminals, regardless of polarity and
position, is defined as N. For instance, the device in FIG. 47
has a total of 4 terminals. Direct current measurements were
set up such that a voltage was always measured between
points A and B in FIG. 47, yielding a resistance of the form
R,B=qy.,R,, Where R,; is the Hall resistance at the v=2
plateau (R,~12906Q) and qy., is defined as the coefficient
of effective resistance (CER). The CER, based on the efforts
reported here, appears to be restricted to the set of rational
numbers, with all simulated results being expressed as a
either a fraction or an integer.

For N terminals, the number n, is defined as the number
of junctions between two adjacent terminals, thereby limit-
ing j to N-1. In the example case of FIG. 47 (where N=4),
there are three n, terms: n,=1, n,=2, n,=2 (rectangles in FIG.
47). Assignment of numerical subscripts to n, must also be
defined. One of the conditions upon which the forthcoming
theory correctly predicts the CER is that the greater of the
two outermost adjacent terminal pairs in any given configu-
ration is assigned as ny.,. The second outermost is then
assigned as ny.» (if both pairs are equal, then the assignment
is arbitrary and will yield the same calculated result for both
selections). This alternation continues until n, has been
assigned. As one goes from region to region on the device
from left to right, terminals alternate in polarity like in FIG.
47 (negative, positive, negative, positive).

Terminals can be treated like point charges in electrostat-
ics (though confined to the Hall bar geometry), and this
analogy of bringing a new charge from infinity to a pre-
existing configuration will be useful to visualize many of the
results. One assumption is that for a given terminal configu-
ration, using either magnetic field polarity will yield the
same quantized resistance.

The case of two terminals is considered in FIGS. 48(a)
and (5). A positive terminal is first arbitrarily placed and kept
fixed while a negative terminal nearby is moved to deter-
mine q, as a function of n,. FIG. 48(a) shows the negative
terminal being moved one junction at a time (from n,=1 to
n,=6), with the corresponding result of simulation plotted in
FIG. 48(6). The simulations reveal that the CER (q,) is a
linear function of n, and should approach infinity as n, does.
This is an intuitive result since it essentially reflects a
traditional two-terminal measurement across an increasing
number of Hall bar regions. Furthermore, the case of n,=0
yields a CER of one and represents the traditional measure-
ment across a single region. The cases where both a positive
and negative terminal occupy the same region will play a
role.

Next, the three-terminal configuration is considered in
FIGS. 48(c) and (d), with each terminal alternating in
polarity going from left to right. The alternating polarities
will make generalizing behaviors easier. By performing
simulations for q, as a function of n., the non-linear behavior
begins to emerge. Two example sets of simulations are
shown in FIG. 48(c) while keeping n, fixed. In all cases of
n,, the resulting dependence of q2 on ny is sigmoidal,
warranting the use of the following ansatz:

Ai~ Az w

qx) = Ar + ¥
rere



U.S. Patent Oct. 18, 2022 Sheet 54 of 59 US 11,474,134 B2

FIG. 54

{7,0



U.S. Patent Oct. 18, 2022 Sheet 52 of 59 US 11,474,134 B2
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Magnetic rield cr)

FIG. 52


US 11,474,134 B2

Sheet 58 of 59

Oct. 18, 2022

U.S. Patent

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US 11,474,134 B2

1

wherein a, b, and c are fit parameters;

FIG. 43 shows a capacitance model;

FIG. 44 shows details of circuit simulations and experi-
mental data for resistance measured across points A and B
(left) and C and D (right);

FIG. 45 shows Hall resistance and electron density for
thicknesses of the $1813, a spacer for stability of the n
region. To approximate the size of the pnJ width, a spacer
layer thickness of 42.4 nm was measured with atomic force
microscopy, and when that device was exposed to UV light,
regions were maintained as n-type and had a change in
electron density. Electron density decreased from about
1.7x10!° cm? to 0.98x10"° cmTM. The Hall plateau for after
UV (in black) was still quantized at 9 T because the pnJ
width had an upper bound of 200 nm;

FIG. 46 shows a longitudinal resistivity of a gateless P-N
junction metrolog with 42.4 nm thick $1813 at room tem-
perature;

FIG. 47 shows a gateless P-N junction metrolog repre-

sented by a schematic from a circuit simulator that included 2

counterclockwise (CCW) and clockwise (CW) edge cur-
rents, as predicted in a positive magnetic field for p-type and
n-type doping, respectively. There is a total of 4 entry/exit
terminals in this depiction (two entries and two exits,
totaling N), with the various n, values labeled in dashed
rectangles. The effective resistance of the gateless P-N
junction metrolog is found from its corresponding voltage
measurement between points A and B (green squares);

FIG. 48 shows: (a) a two-terminal gateless P-N junction
metrolog, wherein a negative terminal is moved along the
gateless P-N junction metrolog. At each value of n, a
simulation is performed to get the behavior of the CER (q,);
(b) corresponding simulations for (a), wherein if ny
increases, q, increases linearly; (c) a three-terminal configu-
ration of gateless P-N junction metrolog with alternating
polarities with fixed n, and varying nj; and (d) for n,=1,
simulations;

FIG. 49 shows: (a) a four-terminal configuration of a
gateless P-N junction metrolog; (b) that CER has a value
based on a parallel resistance configuration, wherein edge
currents for central regions cancel and provide CER for two
parallel N=2 configurations;

FIG. 50 shows: (a) a self-interacting four-terminal con-
figuration of a gateless P-N junction metrolog, wherein two

outermost adjacent pairs were inspected with the larger of 5

the two being selected as n,. The assignment of n, and n,.
indicated as arrows, followed an alternating succession; (b)
once n, terms were assigned, CER was calculated as a
function of n,:

FIG. 51 shows (a) a self-interacting configuration of a s

gateless P-N junction metrolog with a non-alternating
sequence of inals; (b) data from simulations as squares.
The two limiting cases are shown for n,+0 and n,—>%. CER
in those limits are based on the corresponding limit. The
limited-case CERs are used to construct the for all n,; and (c)
and (d) using unit terminals, symmetry of odd and even
cases of n,. When part of the configuration is reflected about
the horizontal, the edge state picture dictates that the con-
figuration will switch its self-interaction condition;

FIG. 52 shows (a) experimental data for a non-altemating,
non-self-interacting, N=4 configuration of a gateless P-N
junction metrolog. The configuration includes two isolated

20

&

&

6

N=2 configurations, one of them being a unit terminal. The
calculation and simulation are together represented by the
dotted line at a resistance value of *AR,;; and (b) experi-
mental data for a non-alternating, non-self-interacting, N=5
configuration of a gateless P-N junction metrolog. The
configuration includes an N=2 unit terminal and an N=3
alternating, self-interacting terminal. The calculation and
simulation are together represented by the dotted line at the
resistance value of “Ry:

FIG. 53 shows a configuration of a gateless P-N junction
metrolog, wherein an N=11 alternating configuration has n,
terms assigned starting with the larger of the two outermost
pairs of adjacent terminals;

FIG. 54 shows a sub-calculation of the gateless P-N
junction metrolog shown in FIG. 53. To solve for the q3
term, which is the case where n,—>0, the gateless P-N
junction metrolog has total CER calculated;

FIG. 55 shows a sub-calculation of the gateless P-N
junction metrolog shown in FIG. 53. To solve for the q,(°
term, which is the case where n,->0, the gateless P-N
junction metrolog has total CER calculated;

FIG. 56 shows a sub-sub-calculation of the gateless P-N
junction metrolog configuration from FIG, 55, wherein
every additional terminal affects the calculation that
involves sub-calculations of other configurations;

FIG. 57 shows: a self-interacting, non-alternating termi-
nal at (a) positive and (b) negative B-fields. The difference
in electron flow does not change the configuration’s status,
and CER remains the same; and for (c) and (d) a similar set
of configurations that is not self-interacting;

FIG. 58 shows: (a) CER for a unit terminal is unaffected
when a third terminal is introduced, and the formula sim-
plifies to a constant function of n,; (b) the same result as (a)
for a configuration that has two like-polar terminals at its
endpoint; and (c) and (d) even and odd application of a
formula for n, to switch depending on the orientation of two
like-polar, adjacent terminals; and

FIG. 59 shows a semiclassical visualization of edge
currents canceling at junction crossing points, wherein for
i,>i,, a portion of i, do not cross the junction (i") due to the
difference in electric potential. The portion that crosses the
junction, i’, will approach the value of ij, and in the
steady-state, the two values will match.

DETAILED DESCRIPTION

A detailed description of one or more embodiments is
presented herein by way of exemplification and not limita-
tion.

It has been discovered that a gateless P-N junction
metrolog and processes herein provide p-n junctions work-
ing in a quantum Hall regime for resistance scaling and a
plurality of resistance traceable to the quantum Hall effect.
The gateless P-N junction metrolog provides values of
quantized resistance that overcomes problems of conven-
tional technology for dissemination of the ohm and reduces
a chain of calibration.

Gateless P-N junction metrolog 200 and processes herein
lyses cell 236. In an embodiment, with reference to FIG. 1.
FIG. 2, FIG. 3, FIG. 4, and FIG. 5, gateless P-N junction
metrolog 200 includes: junction member 218 including:
p-interface 228; and n-interface 230 disposed laterally and
adjacent to p-interface 228; and p-n junction 232 disposed at
where p-interface 228 and n-interface 230 contact; drain
electrode 220 disposed on junction member 218; source
electrode 222 disposed on junction member 218 such that
source electrode 222 is spaced apart from and opposing



U.S. Patent Oct. 18, 2022 Sheet 50 of 59 US 11,474,134 B2

(A)

(B)
M@ Simulation |
4.6 L| =~ First Prediction ]
we With Correction
14} ems
o 12+
10} \ [, =D
3 q,+n,+6, |
0.8 | 1
06 4 rl l L . : j . j
0 2 4 6 8 10 12 14 16 18
ns

FIG. 50


U.S. Patent Oct. 18, 2022 Sheet 22 of 59 US 11,474,134 B2

FIG, 22


U.S. Patent Oct. 18, 2022 Sheet 40 of 59 US 11,474,134 B2

8000 1 : :
|
7500 4
7000 + Z
e 4
z 6500 + 4
6000 + 4
Device 2 4
5500 + : omen Device 3 |
: 4

5000 L A n L

r) 40000 20000
Time (s)

FIG. 40


US 11,474,134 B2

23

negative B-fields, respectively. Lastly, the values of 2R,, and
3R,, emerge from measuring the opposing corners. These
measurements fully verify the functionality of the millime-
ter-scale pnJ device.

Observations in these pnJ devices motivated exploration
‘of how overall resistance of the pnJ devices can be quantized
at other values of R,, under the appropriate conditions.
Resistance simulations across points A and B using the
circuit simulator (FIG. 37(a)) yielded nonconventional frac-
tions of Rj, warranting experimental verification (FIG.
37(b)). Currents were injected at up to three distinct sites on
the device, with all currents summing to 1 WA. For general
notation, assume that I), I, and 1, are positive if they flow
from the top to the bottom of the device. If a current is
negative, assume that its source has been applied to the
bottom of a region, with flow to the top, much like 1,
pictured in FIG. 37(a). If one of the three currents is zero,
then only two branches are utilized. After the measurement,
the overall device resistance is determined from R,,-qR,,-

For the configuration 0<I, , Ip, I, in FIG. 4 (6), q=", which
may appear to be an intuitive behavior since there are
essentially three regions with Hall resistances, albeit with
‘one region having an opposite polarity. Results rapidly
become unintuitive when current directions are changed and

branches eliminated. The configuration 1,<0<I,, 1, which is 2

pictured in FIG. 37(a), yields q~%, revealing that electric
equipotentials are redistributed for reversing a single cur-
rent. Furthermore, when 1,<0<I, and 1,=0, a value of *ARyy
is obtained, and for the final displayed configuration of 0<I,,
1, and I,=0 occurs, R,,—%R,,. The simulations provide
insight on how the effective resistance can switch sign with
the polarity of the B-field. This antisymmetric behavior can
be measured with points C and D, with one example being
shown in FIG. 37(5) in the 0<1,, I,, I, configuration. Accu-
racy of the deviation of these measurements from their
expected values is limited to approximately 1% due to the
elements of the experiment whose uncertainties may also be
on that order. Other considerations to make are those of
possibly imperfect junctions of insufficient sharpness, whose
presence would result in local longitudinal resistances that
are unrelated to the propagation of edge states.

When every region of a pnJ device displays quantized
Hall resistances, but has a different carrier concentration and
polarity, the measured resistivity across one or several sets
of pnJs depends on Landauer-Biittiker edge state equilibra-
tion at the junction. In the case of EG, where the Fermi level
s typically pinned due to the buffer layer, and where the
carrier densities take on values on the order of 10'' em”,
v=2 equilibration becomes relevant, unlike exfoliated gra-

phene p-n-p devices. With this knowledge, one can construct 5

devices with more regions having opposite polarity, like the
one shown in FIG. 38(a). Though it can be speculated that
these atypical fractions arise from the redistribution of the
electric potential throughout the device, this phenomenon is

not intuitive with multiple currents in the quantum Hall

regime. Because of this difficulty, using a circuit simulator
including quantum Hall elements becomes vital for predict-
ing which fractions of R,, are measurable while each region
displays the v=2 plateau.

In FIG. 38(4), two examples are shown to provide further
validation of using the spice circuit simulator for pnJ
devices. Among the many combinations of input and output
currents on the device, the fractional values #R,, and !%/iR,,
are possible results. In the simpler case of q="%/1, only two
current sources are injected at opposite ends, with the drains
exiting from the pair of regions with reverse polarity (see
FIG. 38(a)). The data match within 3%, but more experi-

20

&

&

24

ments are called for to examine the offset errors, possibly a
result of the contact resistances and the lock-in amplifiers
used to measure points A and B. Furthermore, an analytical
way to determine fractional values for a given configuration
warranted. New pnJ devices with many regions in series
can now be constructed and explored to find more noncon-
ventional fractions of R,,.

For millimeter-scale epitaxial graphene p-n junctions.
FIG. 39, FIG. 40, and FIG. 41 show UV exposure details,

Modeling and simulation details are shown in FIG. 42 and
FIG. 43, wherein a capacitance model is given by:

The charge transferred from EG to ZEPS20A is desig-
nated as Aq. The top panels show how Aq varies with the
thickness of the $1813 layer while keeping the final carrier
density in EG constant at 2x10!° cm7. The bottom panel
shows Aq as a function of ng while keeping the $1813
thickness fixed at zero. These trends are shown to elucidate
the heavier influence of the final carrier density in EG on Aq
than the thickness of the $1813 layer. FIG. 44 shows aspects
of model circuitry and responses for gateless P-N junction
metrolog 200.

Spacer layer behavior is shown in FIG. 45 and FIG. 46.

Example 3. Analytical Determination of Atypical
Quantized Resistances in Graphene p-n Junctions

Graphene devices can display quantized Hall resistance
values of

1h
Gur 2

where m is an integer, h is the Planck constant, and e is the
elementary charge. When configured as p-n junctions (pnJs),
.g., for transport in the quantum Hall effect (QHE), these
graphene-based devices become a foundation for exploring
two-dimensional physics. Concordantly, such devices can be
applied towards photodetection, electron optics, and quan-
tum Hall resistance standards.

Of the applications listed, the latter can benefit from pnJs
for quantum transport to access different quantized values of
resistance. The behavior of those pnJs depend heavily on
which Landauer-Biittiker edge states equilibrate at the rel-
evant junctions and an extensive analysis of these behaviors
was explained in previous reports, many involving tunable
gates used to adjust the pnJ. To date, most of these studies
have only used single source and drain, and though this has
been useful for many fundamental device measurements,
this limit on how the current is permitted to flow confines the
parameter space within which a device may be operated.

This work introduces a new mathematical approach to
predicting quantized resistances in pnJ devices utilizing
more than a single entry and exit point for electron flow. The
introduction of multiple electron entry or exit terminals
appears to contribute to a nonintuitive effect on the measur-
able effective resistance of the device. For different numbers
and configurations of terminals, electrical measurements
yield a variety of nonconventional, fractional multiples of
the typical quantized Hall resistance at the v=2 plateau
(R,-12906Q) and take the form:



U.S. Patent

Oct. 18, 2022

Sheet 3 of 59

US 11,474,134 B2

v4

is
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Is : La |
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US 11,474,134 B2

29

to the CER as if both pairs were connected in parallel, and
this value is (4+14)"'=9. In FIG. 51(5), the isolated-case
CER manifests itself as the asymptotic value for q; (dotted
line), with its hypothetical device depicted in the outlined
box. For n,=0, the whole configuration effectively becomes
the one shown in the other outlined box, which is an
alternating terminal configuration that obeys Eg. (2). The
CER for this limiting case is q,=¥4, and this implies that, by
taking the lowest common factors, x=6, y-5, and z=4, the
final expression for this configuration for all n, is

6n, +6

ang) =

Ergo, for the exact configuration in FIG. S1(a), shown as the
data point in (b), q3=9%.

‘The final two conditions to mention are those of the “unit”
terminal, in which a positive and negative terminal both
occupy the same region, and the existing symmetry of the
formulas for non-alternating terminal configurations. First,
the unit terminal has the obvious CER value of 1 when

isolated. Once incorporated into a larger configuration, like >

the one shown in FIG. 51(c), the edge state picture is needed
to determine whether the unit terminal will remain isolated
or interact with the other terminals. For the graph in FIG.
§1(c), full self-interaction is expected only for even n,, and
for all odd n,, the CER is ¥4. The unit terminal immediately
renders the configuration as one that is non-altemating,
warranting the approach taken for Eq.s (4) and (5). By
repeating the analysis, one arrives at

Bn, +3
ng +3

asin)

for even n, (but for cases when the unit terminal is near
another single terminal of either polarity, the total CER
remains unaffected and at 1). With the formula for even n,.
one finds 5% (data point in FIG. 51(c)).

To address the second condition, if the two, adjacent,
like-polar terminals are on opposite sides of the device
shown in FIG. 51(d), then this reflection about the horizontal
must then be described by the same equations, with the
conditions on even and odd n, being switched. The repeated
simulations and mathematical analysis are plotted, and as

expected, the CER, still being based on n,=2, now describes 5

the parallel combination of two isolated configurations
(qs).

To begin generalizing behavior for alternating configura-
tions with any N, it will help to go through one additional

analysis of limiting cases. Recall Eq. (3), with appropriate 5

subscripts for the arbitrary N=5 case:

asing +1)
em tos

6
gals) = o

One note to make is t at 8, does not depend on n,, but
rather the remaining n, terms, and that independence allows
for an easier inspection of the limiting case when n,=0. By
applying this case to Eq. (6), the relation for the corrective
term becomes cl

0

38

&

&

at

30

5s = @5|

(i
z

By substituting this back into Eq. (6), the following result is
obtained:

a

In Eq. (7), the term q,© is a CER that characterizes a
similar N=5 configuration as above, with the substantial
difference that one of its outermost adjacent terminal pairs
(parameterized by n,) has been reduced to a unit terminal. A
unit terminal renders a configuration non-alternating, and so
a new calculation must be performed to obtain q,?. After
that calculation or simulation, q,(n,) is fully known and can
be predicted. The final result is one where Eq. (7) has been
generalized for any alternating configurations containing N
terminals:

(8)
gy -1lty a) =

Combining al the presented mathematical techniques
enables one to predict the CER for an arbitrary configuration
of large N despite the increasing complexity of both the
configurations and the corresponding calculations.

Two functioning devices were fabricated to test this
theoretical framework. They were inherently limited by the
number of allowable electrical contacts and the good per-
formance of a subset of those contacts. Nonetheless, experi-
mental data were acquired at +9 T, 1.6 K, and ona transistor
outline (TO-8) package. Two relatively complex configura-
tions that fit within the useable contacts were measured and
plotted in FIG. 52. The first configuration was a non-
alternating one that was not self-interacting (since n,=1). It
essentially contained a unit terminal on one isolated branch
and a CER of 2 on the other. A quick parallel resistance
calculation would reveal an expected value of q3—%4, and
this comparison is made on FIG. 52(a) between the data and
dashed line for the theory.

FIG. 52(6) has an additional terminal, but because n,=1
(odd) and the two like-polar terminals are on the same side
of the device, the unit terminal on the left is still isolated
from the rest of the configuration. The right side of n, may
be treated as an isolated N=3 configuration (with subsequent
assignments of n, and n,). The right side has a CER of % per
Eq. (2), and when this value is placed in parallel with the left
side’s CER of 1, the expected value is q,=%. In both cases,
there is a small offset from the plat most likely due to
instrument errors and device imperfections. Any simulations
performed henceforth may now be trusted and understood,
seeing as its analytical counterpart has been explained and
expressed.

‘A complex configuration, along with some of its sub-
configurations with main configuration (N=11) is shown in
FIG. 53. The calculations are done step-by-step for the first
few components of the configuration.

Once the n, terms have been assigned, the calculation can
begin. As described in the main text, selection of the larger



US 11,474,134 B2

27
Equation (1) is the Hill-Langmuir equation and also
known as Logistic fit curve. Using this sigmoidal fit fune-
tion, as opposed to others like the Fermi-Dirac distribution
or the Verhulst growth model, yields zero error when fitted
to the simulation data. Furthermore, the parameters of Eq.
(1) take on meaningful quantities (p=1):

2

Equation (2) establishes the general behavior for the
three-terminal configuration (recall that q,=n,+1). This
includes configuration conditions that have not yet been
fully elaborated, such as the case where two adjacent ter-
minals are of the same polarity or if two terminals of
opposite polarity occupy the same region (again, the latter
case gives a well-known quantized resistance of R,, and
CER of q,=1).

Electron flow can be restricted to regions along the entire
length of the device, as defined by the endpoint terminals.
For instance, in FIG. 48(c), electrons flow from the two
negative terminals to the single positive one, effectively
uniting the device as a single quantized resistor with a span
of n, +n, junctions, In these cases, the terminal configuration
is said to be fully self-interacting. However, there are cases
where configurations, like the one shown in FIG. 49 with
non-alternating terminals, involve a semiclassical edge state
picture to assist with visual understanding of the theoretical
framework.

FIG. 49(a) shows a self-interacting, four-terminal con-
figuration whose simulations reveal that the CER holds a
similar dependence on n, as it does in FIG. 48(d) for n. As
shown in FIG. 49(a) (n,~2), the corresponding simulation
yields q3=!2/1, and the reason for using n, instead of the
outermost adjacent pair will be explained later along with
the formula for N=4 configurations. When simulating the
CER for increasing n,, the sigmoidal trend only holds true
for even values of n,. For simulations of this configuration
when n, is any odd number, qy=1. This behavior can be
explained by FIG. 49(6), where the edge current picture
provides a possible answer. Both electron paths cross in
‘opposite directions at the same points in each junction.
Furthermore, within each of the central opaque regions, the
currents are expected to equilibrate since there is an appro-
priate, but temporary, potential difference at the n, junctions
(see Supplemental Material). This leads us to the justifica-

tion of treating the whole configuration like a pair of isolated 5

two-terminal configurations. And in the case of FIG. 49(6),
each two-terminal configuration has a CER of 2, thus
yielding our simulation result of q=1. Drawing a similar
diagram for other odd values will only validate this edge
state visualization, The latter configuration is said to not be
self-interacting, but rather is a simpler arrangement of two
configurations in parallel.

When examining self-interacting, four-terminal configu-
rations, an attempt can be made to posit a formula that
describes the CER. Since it is safe to assume that configu-
rations with alternating terminals are fully self-interacting,
that is the model upon which this next analysis will depend,
and the exact model is illustrated in FIG. 50(a). As before,
the two outermost adjacent pairs are inspected and the larger
of the two is selected as n,. The assignment of n, and n,
follows thereafter in alternating succession. With all three n,
terms assigned, calculating the CER becomes straightfor~

28

ward and starts with q,. Based on the previous two formulas
shown in FIG. 48, q,—3 and q,=34. The full formula for qs
has not been fully uncovered at this point, but an educated
prediction can be made in the form of Eq. (2), but iteratively
5 transformed:

This first prediction is shown in FIG. 50(6) as a red curve,
incorrectly yielding the CER of this configuration to be
q3~%. Extending the simulation for qs for ng:{0, ... , 16}
(black squares) shows that there is a consistent deviation

5 from the first prediction, but not one that is solvable by a
simple vertical translation. Adding a corrective term in the
Hill-Langmuir equation enabled the finding of that correc-
tive term, 5,, as a numerical value. The next question
regarded the origin of the term 6,. For this configuration,

29 8;-¥ for all values of ny, and the corrected formula was

plotted in blue, matching the simulations with zero error:

grits +1) @)

03) = eos

Describing other configurations that do not alternate in
polarity is beneficial tool to simplify complex configu-
rations. The edge state picture and FIG. 49 were presented

30 under the condition that a term n, was used to describe the
junctions between two adjacent terminals of similar polarity.
Since treating a self-interacting, non-alternating terminal
configuration did not obey the same formula as its alternat-
ing counterpart, using n, was the simplest way to charac-
terize the configuration. A similar configuration to FIG. 49
was used in FIG. 51(a), and prior to its analysis, self-
interaction was verified with the edge state picture. The
following formula was used as an ansatz with the intention
of analyzing the limits of n,:
0

38

&

galt) = @

Equation (4) (which for this configuration is only valid for
even n,) takes on the form of Eq. (3), with the numerator
fully distributed and the denominator containing two terms.
As seen in FIG. 51(a), if the limits of n, are evaluated, these
variables can be found:

(6)

35 lim,
nsdn, FE

Equation (5) yields two ratios that need to be determined
to obtain a formula for this configuration. For n>, the left

60 and right pairs of terminals are considered isolated, thus
equating


US 11,474,134 B2

33

more substantial, both cases still feature central opaque
regions that effectively isolate the two pairs of terminals
The mechanism for edge state “cancellation” in FIG. 57 (c)
is shown below. Alternating configurations are easier to
justify as having this CER symmetry with positive and
negative B-field because no matter which region electrons
begin to flow from, the first junction will split the current
such that they flow towards both positive, adjacent termi-
nals.

With q,(=1, if one considers where a unit terminal has a
third terminal adjacent to it (see FIG. 58(a)), we arrive at
that result by performing the limiting case analysis.

Xing +
yn +e

sin)

If n,0, the ratio

is 1 since all that remains is a single unit terminal. When
1, >, the lone negative terminal at infinity will provide no
current due to the infinite resistance that path would offer to
an electron. Ergo, the ratio

which is the case where current only flows through the unit
terminal. It is implied that y=z, and the final result for this
configuration is that q;‘°(n,)=1, independent of n,. Since
FIGS. 58(a) and (6) are both non-alternating cases with the
two negative terminals separated by n,, a similar result will
hold true: q,(n,)=2.

Like-polar terminals can be on the same side of the
configuration or on opposite sides. The former case is
presented in FIG. 58(c), where if n,0, the ratio

is 1 again. When n,—>, the ratio

is equal to the CER of two parallel unit terminals. Therefore,
we get

and the two ratios give us our final result for even n,:

ny +1

nits

20

3

&

4

s

at

6:

34

When the like-polar terminals are on opposite sides, the
formula remains true for odd n,.

For visual representation when portions of a configuration
are isolated from one another, two methods can be used for
a configuration that has isolated components. Electrons may
be unable to flow through portions of the configuration
because the electric potential extremum has been reached,
i.e., the electron has reached the positive terminal along its
path leading out of the circuit (FIG. 57(d))

With reference to FIG. 59, the second case is a magnifi-
cation of part of FIG. 57(c). If one current is larger than the
other, at every junction crossing point, then a portion of the
larger current Will split off to return toward the positive
terminal it had already passed. This further reduction of the
larger current continues to the point that both currents within
the middle regions are equal at the junction crossing points.
The net current flow is zero, and those central regions do not
contribute to the CER. This situation is equivalent to having
the two branches in the circuit in parallel.

While one or more embodiments have been shown and
described, modifications and substitutions may be made
thereto without departing from the spirit and scope of the
invention. Accordingly, it is to be understood that the present
invention has been described by way of illustrations and not
imitation. Embodiments herein can be used independently or
can be combined.

All ranges disclosed herein are inclusive of the endpoints,
and the endpoints are independently combinable with each
other. The ranges are continuous and thus contain every
value and subset thereof in the range. Unless otherwise
stated or contextually inapplicable, all percentages, when
expressing a quantity, are weight percentages. The suflix
“(s)” as used herein is intended to include both the singular
and the plural of the term that it modifies, thereby including
at least one of that term (¢.g., the colorant(s) includes at least
‘one colorants). “Optional” or “optionally” means that the
subsequently described event or circumstance can or cannot
occur, and that the description includes instances where the
event occurs and instances where it does not. As used herein,
“combination” is inclusive of blends, mixtures, alloys, reac-
tion products, and the like.

As used herein, “a combination thereof” refers to a
combination comprising at least one of the named constitu-
ents, components, compounds, or elements, optionally
together with one or more of the same class of constituents,
components, compounds, or elements

All references are incorporated herein by reference.

The use of the terms “a” and “an” and “the” and similar
referents in the context of describing the invention (espe-
cially in the context of the following claims) are to be
construed to cover both the singular and the plural, unless
otherwise indicated herein or clearly contradicted by con-
text. “Or” means “and/or.” It should further be noted that the
terms “first,” “second,” “primary,” “secondary,” and the like
herein do not denote any order, quantity, or importance, but
rather are used to distinguish one element from another. The
modifier “about” used in connection with a quantity is
inclusive of the stated value and has the meaning dictated by
the context (e.g., it includes the degree of error associated
with measurement of the particular quantity). The conjune-
tion “or” is used to link objects of a list or alternatives and.
is not disjunctive; rather the elements can be used separately
or can be combined together under appropriate circum-
stances

What is claimed is:

1. A process for performing resistance metrology with a
gateless P-N junction metrolog, the process comprising:



U.S. Patent Oct. 18, 2022 Sheet 33 of 59 US 11,474,134 B2

(A)
i j—a
_—_— =
S i oS
ee woth m
i AG

as

Boa

Boo t se
Boz t

i ‘

é

BB.

18

&

2

__ Gombined mean {ri}
3 3
ae

° i
10 150 260 259 300 360 400
Curent gud)

&
ws
o
~
oe
e

Magnetic flux density B (1)

FIG. 33


U.S. Patent Oct. 18, 2022 Sheet 19 of 59 US 11,474,134 B2

i R
a4 06126 be Ra
4

=

114,2,43 {16,10,6} 7° Ru

FIG. 19


U.S. Patent Oct. 18, 2022 Sheet 25 of 59 US 11,474,134 B2

222

210

230 234.11 230
289.7 234.8 234.9 228 234.10 234.12

FIG. 25


U.S. Patent Oct. 18, 2022 Sheet 21 of 59 US 11,474,134 B2

FIG. 21


US 11,474,134 B2

Sheet 34 of 59

Oct. 18, 2022

U.S. Patent

{unl} uonisod

VE “DL

=.

ee

< -
2 cerrerrensrnernrernensrnel
4 oe

1 * 4. te

—

2
8

3
(uu) Wy Bie}

8
3

(.4ua} wus uewiey

sexe Sereooeny IS,

eine PROTETE

KEGRAGIONS TEUES SPITE

@

(@)

unl oc



U.S. Patent

Oct. 18, 2022

Sheet 16 of 59

US 11,474,134 B2

 .

—

__

=

ee

|

FIG. 16


US 11,474,134 B2

31
of the two outermost pairs of adjacent terminals to be nyo.
When assigning the lower numerical subscripts, take care to
g0 from one side of the device to the other. This will result
in the even subscripts being on one side and the odd
subscripts being on the other. This condition is necessary to
ensure the exactness of Eq. (A1) (also in FIG. 53):

(AD
gy -alty.

With n,=1, we use the linear form of Eq. (Al), which is
q2—(n,+1). Note that this is the only case when Eq. (Al)
“breaks down”, mainly because of the ill-defined qo. q,=2.
and that brings us to n,=2. If we apply Eq. (Al) again:

my M*D 204 6 3
going) = BEAD 22D 6 3
Ti T7475
met 247
36
30+) 6
75
3+
a

To calculate the q;‘° term, n,—>0, and resulting configu-
ration must be solved as though it was a new configuration.
This resembles the configuration in FIG. 52(a) of the main
text. The edge state picture suggests that the electron flow
from each of the two negative terminals cross in opposite
directions at the single n, junction. Now we know that this
new q,° configuration in FIG. 54 has two isolated branches.
The left branch (a unit terminal) has a CER of 1, and the
right branch has a CER of 3. Taking the parallel addition of
the two yields qs=%4. Using this value gives q.-%.

6
34+) 30

sly #1) _
5 29

a(n) =

nye
a

Moving on to qq, we repeat the calculation, knowing all
the terms except for q,°. To get this value, we must repeat
the previous analysis of taking the limiting case of n,->0,
giving us q,=q,(n,=0). The relevant portion of the con-
figuration from FIG. 53 is used for FIG. 55.

‘The corresponding configuration for q,° is on the right
side of the arrow in FIG. 55. The edge state picture suggests
that the unit terminal on the right interacts with the other
terminals, making this configuration self-interacting, and

ng +X
nee

ging =

When

20

&

45

50

at

0

6:

32

is equal to the total CER of two independent branches in
parallel, with the left branch having a CER of % (in this new
configuration’s left branch, n,=1 and n,=3) and the right
branch having a CER of 1 (unit terminal). Therefore,

Now let’s consider the n,-+0 case. The ratio

is equal to the CER of the configuration shown in FIG. 56.
‘To make matters slightly easier, the CER of FIG. 56 is the
parallel combination of njei~4 and Nyjg, 1, giving

For determining q,,
the ratios yields:

plug in the lowest common factors for

Now that qq(n.-4)=3%e has been established, the calcu-
lation may continue with n,=4. At this point, the remaining
calculations are left as an exercise to the reader, and they
will find that the simulations match the resulting calculated
values:

g3(015-4)=9/7,g5—9
qoltteS)-!9i9.gg-"929

(15,
m5

goes
qs(t'g-6) V2.5

gohtg6)"9Ar.g—551

Grol? p= 7997.95

Having such a device at the v=2 plateau (R,~12906Q)
would result in a quantized effective resistance of:
Rasa 5152.75.

Terminal configurations yield the same CER for both
polarities of magnetic field. The support will stem mostly
from a visual representation of the edge state picture. In FIG.
57, non-alternating configurations are placed in both polari-
ties of magnetic field. A self-interacting configuration Is
shown in FIGS. 57 (a) and (6), with positive and negative
B-field, respectively. The difference in how the currents are
permitted to travel does not alter the configuration’s status as
one that is self-interacting.

‘A configuration that is not self-interacting is shown in
FIGS. 57 (c) and (d), with positive and negative B-field,
respectively. Though the differences in electron flow are



US 11,474,134 B2

1

GATELESS P-N JUNCTION METROLOG

CROSS REFERENCE TO REI
APPLICATIONS

PED

‘The application claims priority to U.S, Provisional Patent
Application Ser. No. 62/757,274 filed Nov. 8, 2018, and U.S.
Provisional Patent Application Ser. No. 62/823,148 filed
Mar. 25, 2019, the disclosures of which are incorporated
herein by reference in their entirety.

STATEMENT REGARDING FEDERALLY,
SPONSORED RESEARCH

This invention was made with United States Government
support from the National Institute of Standards and Tech-
nology (NIST), an agency of the United States Department
of Commerce. The Government has certain rights in the

invention. Licensing inquiries may be directed to the Tech- >,

nology Partnerships Office, NIST, Gaithersburg, Md.,
20899; voice (301) 301-975-2573; email tpo@nist. gov; re!
erence NIST Docket Number 18-070USI.

BRIEF DESCRIPTION

Disclosed is a gateless P-N junction metrolog comprising:
a junction member comprising: a p-interface; and an n-in-
terface disposed laterally and adjacent to the p-interface; and
‘a p-n junction disposed at where the p-interface and n-in-
terface contact; a drain electrode disposed on the junction
member; a source electrode disposed on the junction mem-
ber such that the source electrode is spaced apart from and
‘opposing the drain electrode; an n-polymer disposed on the
n-interface of the junction member; a p-polymer disposed on
the p-interface of the junction member such that the n-poly-
mer is interposed between the p-polymer and the n-interface:
a mediation polymer disposed on the p-polymer such that
the p-polymer is interposed between the mediation polymer
and the junction member; and a mediator disposed in the
mediation polymer and that receives electrons from the
junction member in forming the p-interface.

Disclosed is a process for performing resistance metrol-
ogy with the gateless P-N junction metrolog, the process
comprising: connecting a first electrode to the p-interface;
connecting a second electrode to the n-interface; communi-
cating voltage across through the drain electrode and the
source electrode; and acquiring a resistance value across the
p-n junction from the first electrode and the second electrode
to perform resistance metrology.

BRIEF DESCRIPTION OF THE DRAWINGS.

The following description should not be considered lim-

iting in any way. With reference to the accompanying 5

drawings, like elements are numbered alike.

FIG. 1 shows a perspective view of a gatel
junction metrolog;

FIG. 2 shows an exploded view of the gateless P-N
junction metrolog shown in FIG. 1;

FIG. 3 shows a cross-section along line
gateless P-N junction metrolog shown in FIG. 4;

FIG. 4 shows a plan view of the gateless P-N junction
metrolog shown in FIG. 1;

FIG. 5 shows a junction member for the gateless P-N
junction metrolog shown in FIG. 1;

FIG. 6 shows a gateless P-N junction metrolog;

s P-N

of the

&

&

2

FIG. 7 shows a cross-section of the gateless P-N junetion
metrolog shown in FIG. 6;

FIG. 8 shows a gateless P-N junction metrolog:

FIG. 9 shows a cross-section of the gateless P-N junetion
metrolog shown in FIG. 8;

FIG. 10 shows a perspective view of a gateless P-N
junction metrolog:

FIG. 11 shows an exploded view of the gateless P-N
junction metrolog shown in FIG. 10;

FIG. 12 shows a plan view of the gateless P-N junction
metrolog shown in FIG. 10;

FIG. 13 shows a bottom view of the gateless P-N junetion
metrolog shown in FIG. 10;

FIG. 14 shows a perspective view of a gateless P-N
junction metrolog:

FIG. 15 shows an exploded view of the gateless P-N
junction metrolog shown in FIG. 14:

FIG. 16 shows a plan view of the gateless P-N junction
metrolog shown in FIG, 14;

FIG. 17 shows a bottom view of the gateless P-N junetion
metrolog shown in FIG. 14;

FIG. 18 shows a layout of electrodes, n-interfaces, and
p-interfaces of a gateless P-N junction metrolog and source
connections, drain connections, and corresponding resis-

5 tance thereof for the gateless P-N junction metrolog;

FIG. 19 shows a layout of electrodes, n-interfaces, and
p-interfaces of a gateless P-N junction metrolog and source
connections, drain connections, and corresponding resis-
tance thereof for the gateless P-N junction metrolog:

FIG. 20 shows a layout of electrodes, n-interfaces, and
p-interfaces of a gateless P-N junction metrolog and source
connections, drain connections, and corresponding resis-
tance thereof for the gateless P-N junction metrolog;

FIG. 21 shows a layout of electrodes, n-interfaces, and
p-interfaces of a gateless P-N junction metrolog and source
connections, drain connections, and corresponding resis-
tance thereof for the gateless P-N junction metrolog;

FIG. 22 shows a layout of electrodes, n-interfaces, and
p-interfaces of a gateless P-N junction metrolog and source
connections, drain connections, and corresponding resis-
tance thereof for the gateless P-N junction metrolog;

FIG. 23 shows, for making a gateless P-N junction
metrolog, a photomask for forming a junction member in
panel A; a photomask for forming a drain electrode, source
electrode, and electrodes; and a gateless P-N junction
metrolog that includes a substrate in panel C that is formed
from the photomask;

FIG. 24 shows a photomask for exposing a central region,
labelled p, to ultraviolet light, wherein S and D indicate
source and drain electrodes;

FIG. 25 shows a gateless P-N junction metrolog formed
from the photomask shown in FIG. 24;

FIG. 26 shows connections in a configuration for mea-
surement of resistance of the gateless P-N junction metrolog
shown in FIG. 25;

FIG. 27 shows a gateless P-N junction metrolog;

FIG. 28 shows a gateless P-N junction metrolog that
provides a fractional multiple of Hall resistance Ry
(12906.4035Q);

FIG. 29 shows a gateless P-N junction metrolog;

FIG. 30 shows: (a) a furnace for functionalizing and
forming graphene crystal structure functionalized with
Cr(CO),; (b) an image of a gateless P-N junction metrolog,
taken at 5x and 20x (inset) magnification with a confocal
laser scanning microscope, after functionalization. The inset
uses a dashed line to mark the EG edge. Black dots appear
on the surface which are clusters of CrO, from XPS mea-



U.S. Patent Oct. 18, 2022 Sheet 8 of 59 US 11,474,134 B2

FIG. 8


US 11,474,134 B2

Sheet 31 of 59

Oct. 18, 2022

U.S. Patent

Té ‘Dla

(s) euit,
ah x é 1 0
(8) aun ~ ;
PO eee’ bie)

(1) Aisueq xnj4 oneubepy

v

z

G

oC Fr oF Be

g
» F c
z 2a Sho
." 3
| EO as
S E 4g
= 3 i
he dog E ee
“o LunUIDE ee 3 a>
. __ fusued JeuleD OT 2 < c
« : aa
(4) Aisueq xnj4 oneuBbeyy E om 4;
fm Ge Ge E : 3°
OC ape 3 xg 0 Gs
nw Of i 2 } x ae
ie) 4 E E ia
=o F suez=@) 3 a re
zx £E AP LV'y | =e ae
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el eee
ra rr a POOH AOYY wemsrnne
[einsodxs diy Joy JOH Gu0jog

(oy) “y

(vy)


US 11,474,134 B2

15

the load lock slightly open to remove any lingering adsor-
bates on the surface of the EG device. After placing approxi-
mately 100 mg of crystalline Cr(CO), (chromium hexacar-
bonyl) in a separate section of the Ph-Br sample boat, the
system was closed, and nitrogen flow was stopped. The
furnace temperature was then raised to 130° C. The Cr(CO),
sublimates and reacts with the surface of EG, resulting in the
ring-centered Cr(CO), functionalization. An illustration of
this mechanism is provided in FIG. 30(a), as well as an
optical image of one of the devices in FIG. 30(5). The
sample space was then evacuated using a liquid nitrogen
cold trap for about 30 minutes before the chamber was
cooled down and opened. Out of seven fabricated devices
used in this study, six were functionalized using the vacuum
furnace method.

Raman spectroscopy monitored behavior of the 2D (G’)
peak of the EG before and after the functionalization pro-
cess. Spectra were collected with a micro-Raman spectrom-
eter using a 633 nm wavelength excitation laser source and
‘a backscattering configuration. The spot size was about 1
jun, the acquisition times were 300 s, the laser power was 1.7
mW power, and the optical path included a 50x objective
and 1200 mm° grating. Rectangular Raman maps were
collected with step sizes of 20 um in a 5 by 3 raster-style
grid. The presence of Cr(CO), on the EG surface yielded a
modified 2D (G’) peak with a smaller intensity, redshifted
position, and larger width. The average changes in intensity,
position, and width for the case before and afier function-
alization corresponded to a factor of 0.680.05, a redshift of
4 cmTM'+0.5 cmTM', and a broadening of 51.3 cmTM'+10.5
cmTM', as shown in FIG. 30(c) using two examples (all
uncertainties represent 1o deviations). The effects have been
observed with other amorphous materials deposited on EG.
The 2D (G') peak was used to assess the changes of the EG
surface due to the overwhelmingly large SiC response in the
G peak region.

X-ray photoelectron spectroscopy (XPS) measurements
on functionalized EG devices were performed in a commer-
cial instrument equipped with a monochromatic Al Ka.
excitation photon source and a hemispherical electron ana-
lyzer. All XPS measurements were performed at a base
pressure of 2.7x1077 Pa or less, electron take-off angle of 0°
with respect to the surface normal, and an energy resolution
of 0.1 eV. The spectra in FIG. 30(d) show the fittings done
for the spectral regions relevant to C Is in the top panel and
Cr 2p in the bottom panel. For binding energies near the
carbon region, EG and SiC show contributions of carbon
around 283 eV, C—O at 285 eV, and C=O at 287 eV.
Analyzing the Cr 2p peaks required the fitting to include

chromium oxide compounds. The Cr 2ps,2 peak can be 5

deconvoluted into two peaks at binding energies of 576 eV
and 577 eV, assigned to graphene bonded Cr(CO); and
CrO,, respectively. The observed components of the func-
tionalization process have relative intensities that were much
higher compared to adjacent atoms like carbon.

Six functionalized devices and one control device were
tested for carrier density stability. By annealing the device at
a fixed temperature for a prolonged time in vacuum and
within the cryogenic measuring system, ranging from 5 min
to 90 min, the carrier density becomes more n-type. The
integrated heat exposure (IHE) is a figure of merit used to
quantify the applied changes to the device caused by anneal-
ing:

THEAfolko Tappa Tent! a

Ter is taken to be 300 K, ky is the Boltzmann constant,
and the integral is evaluated over time in seconds. Repeat-

&

&

s

65

16

able annealing was achieved using proportional-integral-
derivative (PID) controllers that require some time to reach
temperatures as high as 360 K, and so the effects of
annealing between room temperature and the desired tem-
perature must be accounted for. While annealing, only the
longitudinal resistivity, a quantity that is correlated with the
carrier density, was monitored. At room temperature while
in vacuum or inert gases such as helium, the longitudinal
resistivity shifted by less than 1002 overnight, compared to
the typical value of up to 10 kQ, making it a negligible shift
compared with that above room temperature. After anneal-
ing, the carrier density and mobility were derived from
cryogenic transport measurements in a 9 T superconducting
magnet system.

To evaluate a device’s carrier density, one can use the
relation

where n, is the carrier density, e is the elementary charge, B
is the magnetic flux density, and R,,, is the Hall resistance,

5 using SI units for all quantities. As shown in the gray curves

in FIG. 31(a), before the device was annealed, the Hall
resistance data indicated low carrier densities, on the order
of 10'° cm”?. The carrier density increased as a consequence
of annealing at a temperature between 300 K and 360 K for
varying periods of time, resulting in an THE (or x, as shown
abstractly in each panel) on the order of 107'* J-s. The device
was able to retain this carrier density in vacuum or helium.
at 300 K, before its exposure to air. Once the device was in
air, the carrier density returned to its low value as before
within roughly 24 hr. During this process, the longitudinal
resistivity was monitored with time, and is plotted in FIG.
31(4). Two exponential decay terms were used to describe
the device’s asymptotic approach to 15.5 k@ for reasons that
will be explained next. The corresponding time constants, 7,
and t,, were 7600 s and 6.97x10* s, respectively.

The physical interpretation of this behavior can best be
described by the Langmuir adsorption model for competing
species. To convert the longitudinal resistivity in FIG. 31(6)
to a corresponding device carrier density in the inset, the two
quantities’ relationship was determined for each device and
averaged, as shown in FIG. 32. Since the devices were
presumed to have a significantly lower population of physi-
cal adsorbates (but not of chemically bonded Cr(CO)) due to
prolonged annealing, the gas species to which the devices
presumably were exposed included atmospheric dopants,
namely N, (78.1%), O, (20.9%), and Ar (0.93%) as well as
water vapor. Other constituents are several orders of mag-
nitude lower in concentration. Argon and nitrogen were
neglected due to weak interactions with graphene compared
to other constituents. This leaves O,, but H,O must also be
added in the appropriate amount. At 25° C. and 35% to 40%
relative humidity, the expected percentage contribution of
water vapor to the ambient environment, in terms of mass,
is between 0.8% and 0.9%. The time-dependent function for
the occupancy of one of two competing gaseous species (in
this case, oxygen) is:

480 2)

oy AP0x(1 ~ 49 (0) ~ 8,010) ~ ko» D803)


US 11,474,134 B2

19

ment furnace. The heating and cooling rates were about 1.5°
C/Js, with the growth performed in an ambient argon envi-
ronment at 1900° C.

The grown EG was evaluated with confocal laser scan-
ning and optical microscopy as an efficient way to identify
large areas of successfull growth. Protective layers of Pd and
Au are deposited on the EG to prevent organic contamina-
tion. While protected, the EG is etched into the desired
device shape, with the final step being the removal of the
protective layers from the Hall bar using a solution of 1:1
aqua regia to deionized water. To fabricate the pnJs, com-
pleted Hall bars were functionalized with Cr(CO), to reduce
the electron density to a value close to the Dirac point and
on the order of 10'° cm~?. An $1813 photoresist spacer layer
was then deposited on a region intended to be preserved as
ann region. Finally, a 100 nm layer of PMMA/MMA and an
approximately 350 nm layer of ZEP520A were deposited.
The 100 nm layer was intended to be a mild protectant for

EG since ZEP520A is very photoactive and known to reduce >

the mobility of EG when in direct contact with it.

Raman spectroscopy was used to verify the behavior of
the 2D (G') peak of the EG before and after the function-
alization process and polymer photogating development.
Spectra were collected with a micro-Raman spectrometer
using a 633 nm wavelength excitation laser source. The spot
size was about 1 jum, the acquisition times were 30 s, the
laser power was 1.7 mW power, and the optical path
included a 50x objective and 1200 mm”! grating. Rectan-
gular Raman maps were collected in a backscattering con-
figuration with step sizes of 20 um in a 5 by 3 raster-style
grid. To avoid the eflects of polymer interference, spectra
were collected through the backside of the SiC chip.

The analog electronic circuit simulator LTspice was
employed to predict the electrical behavior of the pnJ
devices in several measurement configurations. Intercon-
nected p-type and n-type quantized regions compose the
circuit and were modeied either as ideal clockwise (CW) or
counterclockwise (CCW) k-terminal quantum Hall effect
(QHE) elements. The terminal voltages e,, and currents j,,
are related by Ryjj (o ~. .k) for CW elements
and Ryjiy-@,-@,,,, for CCW elements. To determine the
circuit’s behavior at the external terminals (to be labeled as
A and B), only one polarity of magnetic flux density was
simulated at a time. For a positive B-field, an n-doped
(p-doped) graphene device was modeled by a CW (CCW)
QUE element, whereas, when B is negative, a CWW (CW)
QUE element was used.

An optical image of the EG device, fabricated into a Hall
bar geometry and processed with Cr(CO), and ZEP520A to
establish two pnJs, is shown in FIG. 34(a). The first and third
regions separated by the UVP-obtained junctions were
intended to be p-type regions, as indicated by the gray
letters, whereas the n region is preserved by a thick $1813

photoresist spacer layer. Raman spectra of the device’s 2D

(G) peak were acquired and shown for the n and p regions
immediately after transport measurements to verify the
polarity of the regions. Since the thick photoresist layers
prevented spectra acquired in the usual backscattering
geometry, the setup was modified such that the excitation
laser was shown through the backside of the SiC chip to
enhance the quality of the 2D (G’) peak. For the data in FIG.
34(b), the p and n region spectra, which are averages of the
map acquisitions, show 2D (G') peaks positioned at 2668.2
cmTM'#2.3 cmTM! and 2664.9 cmTM!+4.1 cmTM!, respectively
with corresponding full-widths at half-maxima of 79.1
omTM'+11.5 cm”! and 64.9 cmTM!+9.3 cm”

&

50

20

Atomic force microscope (AFM) images, one of which is
shown in FIG. 34(c), were used to determine the device’s
final thickness profile. The example profile in FIG. 34(d)
was averaged over 1.1 jim and shows a height difference of
about 1.4 jum between the n and p region. What became
evident was that the pnJ width was not guaranteed to be
sharp enough for dissipationless edge state equilibration.
Therefore, careful treatment and analysis of the device's
charge configuration was required to assess the viability of
pnJs created with UVP.

To assess device quality, the charge configuration of the
device needed to be known and the width of the pins needed.
to be estimated. It is also important to approximate how the
carrier densities in the regions change with exposure to 254
nm, 17 000 u.Wem"? UV light (distinct from the UV light
used in UVP), and this is primarily done by monitoring the
longitudinal resistivity in all three regions of a p-n-p device
during a room temperature exposure, with two polarities
shown in the upper panel of FIG. 35(a). For the p region, the
expected p-type doping mechanism resulting from the depo-
sition of a ZEPS20A layer on the whole device persists to the
point where the carrier density crosses the Dirac point. This
crossing is most evident during the room temperature UV
exposure when the longitudinal resistivity of the device
exhibits a similar value to when the exposure was started,
but instead with a negative time derivative. The $1813
successfully prevents the n region from becoming a p region,
as exhibited by the flat resistivity (and electron density). For
varying distances between the device and the UV lamp, as
weil as how the devices behave after UV exposure and
without functionalization. Though the idea of using
ZEP5S20A as a dopant for EG has been demonstrated,
accessing the p region with that mechanism is challenging
due to the intrinsic EG Fermi level pinning from the buffer
layer below. However, the reduction of the electron density
from the order of 10"? cm? to the order of 10'° em~? by the
presence of Cr(CO), considerably assists the p region to
undergo its transition. It should be briefly noted that the
temporary dip in resistivity near t-30 000 s arises from
another competing process to shift the carrier density,
namely that of the applied heat, which as prescribed by other
work, causes n-type doping in EG devices.

Transport measurements were performed at 4 K, allowing
us to determine the low-temperature longitudinal resistivity
(Px) mobility (j1), and electron density in EG (ng), where
the latter two parameters are calculated by the following
respective formulas:

with e as the elementary charge, B as the magnetic flux
density, and R,,, as the Hall resistance, using SI units for all
quantities. The derivative term in the denominator is calcu-
lated for magnetic flux densities under 1 T due to the linear
behavior of the Hall resistance. Mobilities were measured to
be on the high range of the order 10° cm?V~'s~! and low
range of the order 10* cm?V-!s"!. By mapping the change
of the room temperature resistivity to that measured at 4 K,
the time-dependent shift of the carrier density with UV
exposure can be approximated. These trends are plotted in
the lower panel of FIG. 35(a) for both polarities.

Viability of pnJ creation has focused on how regions’
polarities can be converted from n-type to p-type, and how



US 11,474,134 B2

21

these devices respond to the conversion process. More
crucially, to determine the width of the pnJ, a capacitance
model was implemented using parameters from a magnified
AFM profile in FIG. 35(6) to gain insight on the amount of
expected charge transfer from EG to ZEP520A in the p and
n regions. For the model, we must consider the quantum
capacitance of the charge transfer layers which includes EG,
the buffer layer beneath, and the residual chemical doping
between graphene and polymer layers above it. The general
properties of the interfacial buffer layer are well-known,
with its presence leading to n-type doping in EG. E,- is the
Fermi level of the EG layer, respectively, with E,-hv,
Vainglsign(ng). The relationship between those two param-
eters and the amount of charge transferred from graphene to
ZEPS20A is given by:

eaq w

Crow

(

In equation (1),

Ag

Coots

replaces the term that typically represents an electrostatic
gate (V), where Aq is the amount of charge transferred. The
polymer gate geometric capacitance (all capacitances are per
unit area) is

Cos = Ee
where ¢,,,,,and d,,,,,are the dielectric constant and thickness

of the used polymer (either $1813 or PMMA/MMA or a
combination in series), respectively. Vu is the voltage cor-
responding to the Dirac point, which is approximately 16.5
meV (ng=2x10'° cm), as per the expected behavior of
functionalized EG. The summed capacitance, taking on the
subscript i=1 for the buffer layer and i=2 for residual
chemical doping, is

Within that sum, the contribution from quantum capacitance
is C,=y° and that from the geometrical capacitance is

with d-0.3 nm as the distance for both cases. The following
dielectric constants are used: €s,9:372-54€o, €prenca
aMa-4éo, €,-9.7€p, and €,-3€9, Where €, is the vacuum
permittivity.

This charge transfer calculation depends on the quantum
capacitance parameters y, and y3, which have been roughly
determined for EG devices as y,=5x10'? eV-' cmTM? and
yor 1.5x10* eV-'cmTM?.® *! For the p region, we only need
to use a PMMA/MMA spacer layer thickness of 100 nm,

3

3

&

4

5

s

22

yielding a predicted transfer of Aq=5.9x10'° em? for the
corresponding measured hole density of 1.22x10" cm~,
Subsequently, we repeat the calculation for the n region,
bearing in mind that the two polymer spacer layers must be
summed in series. The $1813 thickness was 1.2 um, as per
the example AFM images, and the PMMA/MMA thickness
slightly increased along the $1813 wall due to the changes
in flow during spin coating. The expected charge transfer is
Aq=2.2x10® cm, a couple of orders of magnitude lower,
which makes sense because the observed electron density
does not change very much with UV exposure.

Though the capacitance model gave us insight into what
charge dynamics to expect in the device, additional infor-
mation was needed to determine how the charge transfer and
total carrier density changed across the junction as a result
of the dielectric spacer thickness. For this, we performed
similar coating methods on an example device to gauge
whether an identical UV exposure will change the carrier
density. For a device having a 300 nm-thick $1813 layer, the
electron density remained the same. However, for a device
having an approximate $1813 thickness of 41 nm, from
reactive ion etching the $1813 layer, the n region changed by
nearly one part in 10'° cm~2, but still had a region providing
quantized plateaus. This small shift corresponds to a calcu-

5 lated charge transfer of 1.9x10° cm”, an order of magnitude

lower than that of the p region. In other work, a polymeth-
ylglutarimide spacer layer of around 200 nm yielded similar
results. From these factors, and combining the information
obtained from the AFM profile, one can claim that the
junction width in these devices have an upper bound of 200
nm, well within the range of junction widths enabling v=2
edge state equilibration. With the knowledge of an upper
bound, one can predict the spatial dependence of the carrier
density along the pnJ by using the charge transfer model.
The resulting behavior is shown in FIG. 35(c).

With regard to measuring nonconventional fractions of
the v=2 Hall resistance and determination that UVP creates
large-scale pnJs, we verify expected electrical behavior in a
p-n-p device. Circuit simulations were implemented to assist
in predicting varied configurations, but first started with the
well-known case of injecting a current along the length of
the device and measuring various resistances, Hall and
otherwise. This verification procedure is presented in FIG.
36. The device and its corresponding circuit simulation
model are shown in FIG. 36(a). Three voltage measurements
are indicated on the device: a single Hall, a pnJ, and
opposing corners. An injected current of 1 A is used. The
circuit simulator drawing, on the other hand, elaborates on
how the software interprets the problem of current flow. It
first assumes that each box represents either a counterclock-
wise (p region) or clockwise (n region) edge current, strictly
for B>0. The simulations can only be performed for a single
polarity of magnetic flux density, so to predict the expected
resistive behavior for B<0, one may reverse the polarity of
the edge current (pink-gray-pink circuit). Equipotential lines
are shown to clarify how the potential is expected to behave
in the shown orientation.

Dividing current from voltage measurements yields final
resistance data shown in FIG. 36(6). According to the model,
for positive B-field, if one was to measure the resistance
from the top to the bottom of the device, one could see a
negative Hall resistance. This result is confirmed in the top
panel, with a dotted line showing the experimental result for
a Hall measurement in the center of the device, maintaining
the positive and negative voltage terminals as the top and
bottom, respectively. For another measurement, one con-
firms the resistance values of 2R,, and 0 for positive and



U.S. Patent Oct. 18, 2022 Sheet 28 of 59 US 11,474,134 B2

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United States Patent

U!

'S011474134B2

(12) (0) Patent No: US 11,474,134 B2
Rigosi (45) Date of Patent: Oct. 18, 2022
(54) GATELESS P-N JUNCTION METROLOG (58) Field of Classification Search
CPC ..... GOIR 27/14; GOIR 33/07; HOIL 29/1606;
(71) Applicant: Government of the United States of HOIL 29/24; HOIL 29/6697:
America, as represented by the (Continued)
Secretary of Commerce, Gaithersburg, (56) References Cited
(72) Inventor: Albert Felix Rigosi, Rockville, MD U.S, PATENT DOCUMENTS
(US) 9,647,098 B2* 5/2017 Obradovie HOIL 27/088
2006/0009872 Al” 1/2006 Prager ... GOIB 11/24
(73) Assignee: GOVERNMENT OF THE UNITED 700/121
TATES OF AMERICA, AS (Continued)
REPRESENTED BY THE
SECRETARY OF COMMERCE, OTHER PUBLICATIONS
Gaithersburg, MD (US)
M., et al., “Graphene p-n junction arrays as quantum-
(*) Notice: Subject to any disclaimer, the term of this Hall resistance standards”, Applied Physics Letters, 2011, p. 022112,
patent is extended or adjusted under 35. vol. 99.
U.S.C. 154(b) by 436 days. (Continued)
(21) Appl. No.: 16/672,613 Primary Examiner — Giovanni Astacio-Oquendo
(74) Attorney, Agent, or Firm — Office of Chief Counsel
(22) Filed: Nov. 4, 2019 for National Institute of Standards and Technology
(65) Prior Publication Data 6) _ ABSTRACT .
A gateless P-N junction metrolog includes: a junction mem-
US 2020/0150165 Al May 14, 2020 ber including: a p-interface; and an n-interface disposed
laterally and adjacent to the p-interface; and a p-n junction
en disposed at where the p-interface and n-interface contact; a
Related U.S. Application Data drain electrode disposed on the junction member; a source
(60) Provisional application No. 62/823.148, filed on Mar. electrode disposed on the junction member such that the
25, 2019, provisional application No. 62/757.274, _ source electrode is spaced apart from and opposing the drain
filed on Nov. 8, 2018. electrode; an n-polymer disposed on the n-interface of the
junction member; a p-polymer disposed on the p-interface of
(51) Int. CL the junction member such that the n-polymer is interposed
GOIR 27/14 (2006.01) between the p-polymer and the n-interface; a mediation
HOLL 29/66 (2006.01) polymer disposed on the p-polymer such that the p-polymer
(Continued) is interposed between the mediation polymer and the junc-
(52) US.Ch tion member; and a mediator disposed in the mediation
CPC GOIR 27/14 (2013.01); HOIL 29/1606 polymer and that receives electrons from the junction mem-

(2013.01); HOIL 29/24 (2013.01):
(Continued)

ber in forming the p-interface.
1 Claim, 59 Drawing Sheets



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density control renders the process highly advantageous due
to its quicker fabrication processing time.

Gateless P-N junction metrolog 200 and processes herein
unexpectedly accommodates sufficiently narrow p-n junc-
tion formation by use of ultraviolet photolithography. More-
over, gateless P-N junction metrolog 200 provides access to
fractional values of the quantum Hall resistances as
described by Example 3.

The articles and processes herein are illustrated further by
the following Examples, which are non-limiting.

EXAMPLES
Example 1

Gateless and reversible carrier density tunability in epi-
taxial graphene devices functionalized with chromium tri-
carbonyl

Monolayer epitaxial graphene (EG) can provide quan-

tized Hall resistance (QHR). One major difficulty with 2

conventional QHR devices based on EG is that their elec-
trical properties drift over time, e.g., due to adsorption of
atmospheric molecular dopants. A parameter for device
stability is charge carrier density, which helps determine the
magnetic flux density required for precise QHR measure-
ments. Gateless P-N junction metrolog 200 overcomes this
problem of instability in air by functionalizing the surface of
gateless P-N junction metrolog 200 with chromium tri
bonyl, Cr(CO)s. Observations of carrier densi
air over the course of one year occurred, as well as the ability
to tune the carrier density by annealing the devices. For low
temperature annealing, the presence of Cr(CO), stabilized
electrical properties and provided reversible tuning of carrier
density in millimeter-scale graphene devices close to the
Dirac point. Precision measurements in the quantum Hall
regime showed no detrimental effect on the carrier mobility.

Developing highly efficient standards using EG involves
long-term stability of electrical properties of millimeter-
scale EG devices in ambient conditions, to equal the long-
term stability and precision of GaAs—AIGaAs heterostruc-
ture QHR devices. These properties include the longitudinal
conductivity 6,,,, carrier density n, and mobility 1, which are
related by the equation oxx=new.

Flectrostatic gating for devices is difficult. One early and
successful process used to reduce the carrier density for
QHR devices was photochemical gating, using methyl sty-
rene/chloromethyl acrylate copolymer (available under the
tradename ZEP-520A) electron beam positive tone resist as
an electron acceptor, but the process reversibility has inher-

ent limitations based on number of thermal cycles to which 5

a device is exposed. Other methods for carrier density
control and conservation have been explored such as the use
of poly-methyl methacrylate (PMMA), atomically layered
dielectrics, perylene, amorphous boron nitride, and hexago-

nal boron nitride but were either unable to achieve metro-

logical usefulness or are irreversible processes.

When EG is exposed to ambient atmospheric conditions,
it experiences a drift in the carrier density and conductivity
because of the physisorption of HO and O,, which are
found to be p-doping species because of their oxidizing
characteristic. Achieving electrical stability is critical for
device applications including mass-produced electronics,
chemical and biological sensors, and functionalized mate-
rials. This motivation holds particularly true for resistance
metrology, where a narrow range of carrier densities
between 1x10"! cm”? and 3x10! cm”? is needed to produce
a resistance plateau of

1

&

&

14

at easily accessible magnetic flux densities (B). Generally,
lower carrier densities will yield unreliable plateaus and
higher carrier densities correlate to a plateau onset at higher
magnetic flux densities. Thus, gateless control of the carrier
density is crucial to improving accessibility of resistance
metrology using EG, where this v-2 plateau can exhibit
precise quantization at low magnetic fields (between 2. 5. T
and 7 T) for carrier densities in the vicinity of 10"' cmTM>.

Here, gateless and reversible carrier density tunability in
EG devices functionalized with chromium tricarbonyl [Cr
(CO),] were obtained with carrier density stability in air
over the course of one year with shifts less than 10'' em7*,
and by controllable and reversible tuning, achieved metro-
logically useful values of the QHR, rendering Cr(CO), as a
suitable compound for stabilizing electrical devices based on
EG. Controllable tuning was demonstrated by annealing the
device in vacuum to the desired carrier density while moni-
toring the device’s room-temperature longitudinal resistiv-
ity. Despite exposure to heating in vacuum at up to 363 K

5 (90° C.), EG devices retained full functionalization, and

when stored in air for typically 24 h to 36 h following the
anneal and measurement, the device’s carrier density drifted
back to a low value, on the order of 10'° cm”?, with respect
to inherent EG doping above 10° These results
demonstrated that this functionalization method can be used
to stabilize and reversibly tune the carrier density in milli-
meter-scale EG devices without the need of electrostatic
gating, reducing the level of processing required for useful
devices. Furthermore, these devices exhibited properties
suitable for resistance metrology with proper tuning.

EG is formed during thermal decomposition of the SiC
substrate causing an enrichment of the surface with carbon
atoms due to the preferential sublimation of silicon atoms.
Samples used for this study were grown using 4H—SiC
(0001) semi-insulating substrates with a mis-cut of <0.10°.
Before growth, the substrates were first cleaned by piranha
etch, followed by a dip into diluted hydrofluoric acid and a
surface treatment with polymer adsorbates for polymer-
assisted sublimation growth (PASG) by spin coating a weak
solution (approximately 2 mlr42s>142y/Tisoprepanon) Eor gra
phene growth, the resulting SiC(0001) samples were placed
ona polished disk of glassy carbon with the Si face in direct
contact with the disk for face-to-graphite growth. Combin-
ing the PASG and face-to-graphite growth methods sup-
presses the formation of etch pits and high substrate steps as
well as related bilayer domains. The annealing process at
1900° C. was performed in argon at atmospheric pressure
with a graphite-lined resistive-element furnace. After
growth, EG was inspected with confocal laser scanning and
optical microscopy to rapidly identify successful growths
over large areas.

The concept of functionalizing EG with C(CO), was
motivated, in part, by pursuits to alter the electronic struc-
ture of graphene without drastically modifying the in-plane
transport properties. Covalent functionalization by this
method does not fully passivate the EG surface but reduces
the level of electron doping in EG devices and helps to limit
the long-term drift in carrier density levels. The completed
EG device was placed in a phosphor-bronze (Ph-Br) boat
and loaded into a small homemade vacuum furnace shown,
in FIG. 30(a). The chamber was then purged with nitrogen
gas and heated slightly above 130° C. for 2h while keeping



US 11,474,134 B2

Sheet 6 of 59

Oct. 18, 2022

U.S. Patent

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U.S. Patent Oct. 18, 2022 Sheet 20 of 59

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US 11,474,134 B2

Sheet 57 of 59

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US 11,474,134 B2

9

length, e.g., UV, of light to junction member 218 to form
p-interface 228 via extraction of electrons 226 in a region
that becomes p-interface 228 of junction member 218 so that
electrons 226 are communicated from junction member 218,
through p-polymer 214, and received by mediator 212 in
mediation polymer 210. Exemplary mediation polymer 210
include methyl styrene, chloromethyl acrylate copolymer,
and the like. A thickness of mediation polymer 210 can be
from 50 nm to 1000 nm, specifically from 100 nm to 500
nm, and more specifically from 300 nm to 400 nm. In an.
embodiment, mediation polymer 210 includes anisole,
methyl styrene, chloromethyl acrylate copolymer, and the
like.

Mediator 212 can include supplementary additives to
attract or repel charges and can be a compound that has high
electronegativity. Here, mediator 212 receives electrons 226
from junction member 218 to form p-interface 228. Exem-
plary mediator 212 include halogens, chalcogens, and the
like. Mediator 212 has an optical absorption from 100 nm to
1000 nm, specifically from 200 nm to 700 nm, and more
specifically from 230 nm to 400 nm. In an embodiment,
mediator 212 includes Cl atoms from chloromethyl acrylate
copolymers

With reference to FIG. 5. FIG. 6, FIG. 7, FIG. 8, and FIG.

9, a number of p-interface 228 and n-interface 230 indepen- 2:

dently can have a minimum value of 1. Moreover, a shape
of p-interface 228 and n-interface 230 independently can be
: ion, eg., polygonal a

8 or FIG. 9.

Gateless P-N junction metrolog 200 can include wire 236
in electrical communication independently with drain elec-
trode 220, source electrode 222, or electrode 234. Wire 236
can include a metallic composition that enhances conduc-
tivity and can be metals for typical semiconductor wire
bonding. Exemplary wires 236 include Au, Al, and the like.
A thickness of wire 236 can be from 15 jum to 100 jum and
specifically from 15 pm to 50 um. Moreover, wire 236
allows current to flow within the gateless p-n junction
metrolog 200. Wire 236 has a minimum electrical conduc-
tivity of 1000 S/mm.

In an embodiment, with reference to FIG. 10, FIG. 11
FIG. 12, FIG. 13, FIG. 14, FIG. 15, FIG. 16, and FIG. 17,
gateless p-n junction metrolog 200 can be packaged with
various formats, shapes, numbers, and sizes of elements.
According to an embodiment, gateless P-N junction
metrolog 200 is a quantum Hall resistor that includes a
plurality of discrete fractional resistance values provided by
the p-n junction 232. With reference to FIG. 18, gateless P-N

junction metrolog 200 can include alternatingly disposed 5

p-interface 228 and n-interface 230 with independent elec-
trode 234 connected thereto. Selected electrodes 234 can be
connected together as drain electrodes 220 (indicated as
“I#”) or connected as source electrodes 222 (indicated a

“J-") to provide a plurality of resistances that have a value s

that is (a/b)R,,, wherein a and b are integers, and R,, (h/2e?,
h being Planck’s constant) is one-half of the von Klitzing
constant, Ry=h/e*=25812.80745 .. . Q.

Gateless P-N junction metrolog 200 can be made in
various ways. In an embodiment, a process for making
gateless P-N junction metrolog 200 includes forming sub-
strate 224 by dicing a silicon carbide (SiC) wafer; cleaning
substrate 224 with a piranha etching composition; contacting
substrate 224 with a graphitic slab that promotes homoge-
neous epitaxial graphene (EG) growth; growing graphene on
substrate 224; disposing substrate 224 in a furnace and
purging with argon; heating substrate 224 in a gas compo-

20

3

&

&

10

sition that includes argon and Hy (e.g., 3% Hy in a balance
of Art by volume) at a heating rate of about 3° C./s to 500°
".; maintaining substrate 224 at 500° C. for a selected
period, e.g., 5 min; increasing the temperature of substrate
224 at the heating rate to 1050° C.; maintaining substrate
224 at 1050° C. fora selected period, e.g., 1 h; purifying the
gas composition to remove hydrogen from the furnace so
that argon solely is in the furnace; maintaining, after puri-
fying the gas composition, substrate 224 at 1050° C. for a
selected period, e.g., 2 h in the argon; heating substrate 224
at the heating rate to 1300° C.; maintaining substrate 224 at
1300° C. for a selected period, e.g., 1 min; heating substrate
224 at the heating rate to 1850° maintaining substrate
224 at 1850° C. for a selected period, e.g., 4.5 min; and
cooling substrate 224 to room temperature at a selected
cooling rate, e.g. (1850° C.-20° C)/12 hrs to produce
junction member 218 on substrate 224.

The process for forming gateless P-N junction metrolog
200 also includes subjecting the substrate 224 to lithography
to obtain gateless P-N junction metrolog 200 by: depositing
20 nm of gold onto substrate 224 by electron beam depo-
sition (e.g., at an initial pressure of 10-7 Torr); disposing, by
spinning onto substrate 224, a lift-off photoresist at 4000
rpm for 45 s (e.g., at acceleration: 5000 rpm/s), the lift-off
photoresist including, e.g., 75 vol. % cyclopentanone, 15
vol. % propylene glycol monomethyl ether, and 10 vol. %
polyaliphatic imide copolymer, based on a total volume of a
composition for forming the lifi-off photoresists; maintain-
ing substrate 224 at 170° C. for 5 min after spinning the
lift-off photoresist; disposing, by spinning onto substrate
224, a capping photoresist at 4500 rpm for 45 s (e.g., at
acceleration: 5000 rpm/s, the capping photoresist including
75 vol. % electronic-grade propylene glycol monomethy!
ether acetate, 15 vol. % mixed cresol novolak resin and 10
vol. % diazo photoactive compound, based ona total volume
of capping photoresist composition; maintaining substrate
224 at 115° C. for 1 min after spinning the capping photo-
resist; exposing, to ultraviolet light (e.g., 365 nm), the
photoresists on substrate 224 for 5 seconds with a photo-
mask that has a selected shape, e.g., as shown in FIG. 23A;
removing the photoresists from by washing substrate 224
with a wash composition that included 97 vol. % water and
3 vol. % tetramethylammonium hydroxide, based on a total
volume of the wash composition, for 1 min to remove
photoresists exposed to ultraviolet light, to form a region of
20-nm-gold-coated graphene exposed to air in the shape
shown in FIG. 23B; washing substrate 224 in deionized
H,0; depositing 50 nm of gold onto substrate 224; disposing
substrate 224 in N-methyl-2-pyrrolidone for 1 h at 75° C. to
remove remaining photoresists by lift off from substrate 224;
dry etching substrate 224 with argon at 4 Pa and power of
150 W, for 3 min; repeating earlier lithography steps with a
photomask in a shape of electrode 234, drain electrode 220,
and source electrode 222 as shown in FIG. 23B; dry etching
substrate 224 with argon at 4 Pa and power of 150 W, for 30
s; depositing 50 nm of titanium and then 150 nm of gold
onto substrate 224 with electron beam deposition at initial
pressure 10-7 Torr; disposing substrate 224 N-ethyl-2-pyr-
rolidone for 1 h at 75° C. to remove remaining photoresists
by lift off from substrate 224; repeating earlier lithography
steps with a photomask having rectangles that can be 2400
jim by 450 um for the eventual UV exposure treatment;
aligning the rectangles to be geometrically arranged to the
shape shown in FIG. 23A such that a rectangular structure
has its perimeter (excluding the trident features) enclosed
within a larger, rectangle, wherein electrical contacts (220,
222, 234) are not present within the rectangular window;



U.S. Patent Oct. 18, 2022 Sheet 37 of 59 US 11,474,134 B2

(B)

Resistance (kQ)}

19

10

8 4 o 4 8 8 4 0 4 8

Magnetic Flux Density (T)

FIG. 37


US 11,474,134 B2

35

connecting a first electrode to a p-interface;

connecting a second electrode to an n-interface;

communicating voltage across through a drain electrode
and a source electrode; and

acquiring a resistance value across a p-n junction from the
first electrode and the second electrode to perform
resistance metrology,

wherein the gateless P-N junction metrolog comprises:

a junction member comprising:
the p-interface; and
the n-interface disposed laterally and adjacent to the

p-interface: and
the p-n junction disposed at where the p-interface
and n-interface contact;

the drain electrode disposed on the junction member;

the source electrode disposed on the junction member
such that the source electrode is spaced apart from
and opposing the drain electrode;

an n-polymer disposed on the n-interface of the junc-
tion member;

a p-polymer disposed on the p-interface of the junction
member such that the n-polymer is interposed
between the p-polymer and the n-interface;

a mediation polymer disposed on the p-polymer such
that the p-polymer is interposed between the media-
tion polymer and the junction member; and

a mediator disposed in the mediation polymer and that
receives electrons from the junction member in
forming the p-interface.

ee Ree

30

36


U.S. Patent Oct. 18, 2022 Sheet 38 of 59 US 11,474,134 B2

(A)

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Resistance (kQ)

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Magnetic Flux Density (T)

FIG. 38


US 11,474,134 B2

Sheet 53 of 59

Oct. 18, 2022

U.S. Patent

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US 11,474,134 B2

Sheet 26 of 59

Oct. 18, 2022

U.S. Patent

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U.S. Patent Oct. 18, 2022 Sheet 56 of 59 US 11,474,134 B2

FIG. 56


US 11,474,134 B2

11

disposing substrate 224 in aqua regia (e.g., 1:1 deionized
H,O to aqua regia) for 45 s; disposing substrate 224 in
acetone for 10 min; disposing substrate 224 in isopropanol
for 5 min; and substrate 224 to provide gateless P-N junction
metrolog 200, e.g., as shown in FIG. 23C.

The process for forming gateless P-N junction metrolog
200 also can include providing a low electron density for
gateless P-N junction metrolog 200 that includes function-
alizing substrate 224 with chromium tricarbonyl with a
deposition furnace, e.g., from chromium hexacarbonyl by:
disposing substrate 224 in inert gas environment (e.g. under
N, gas); heating substrate 224 at 130° C. for 1 h at a
temperature tolerance, e.g., 130° C.£10° C.; introducing
chromium hexacarbonyl Cr(CO), in the inert gas environ-
ment; reducing a pressure in which substrate 224 and the
chromium hexacarbonyl are disposed to 10-? Torr; main-
taining for a period, e.g., 40 minutes, at 130° C. and 107?
Torr in a presence of the chromium hexacarbonyl for
completion of deposition of chromium tricarbonyl on sub-
strate 224; and cooling substrate 224 to room temperature.

The process for forming gateless P-N junction metrolog
200 also can include spinning a photoresist at 5000 rpm for
1 min with acceleration: 5000 rpm/s, wherein the photoresist
includes 75 vol. % electronic-grade propylene glycol
monomethyl ether acetate, 15 vol. % mixed cresol novolak
resin, and 10 vol. % diazo photoactive compound, based on
a total volume of a composition for the photoresist; heating
substrate 224 at 115° C. for 1 min; exposing, to ultraviolet
light (365 nm) for 5 seconds, substrate 224 with a photo-
mask that exposes a central region of substrate 224, as in
FIG. 24. Parameters were measured on a high-precision
mask and bond aligner with exemplary parameters being
1130 W; WEC=cont.; vacuum mode: 10 s/30 s/15 s; Al-
gap=15 um; and dosage=100 mJ. The process can further
include removing exposed regions by contacting substrate
224 with a removal composition that includes 97 vol. %
water, 2.3 vol. % tetramethylammonium hydroxide, and 0.7
vol. % polyglycol for 1 min to remove exposed region;
heating substrate 224 at 200° C. for 5 min; forming a spacer
layer on from a spacer composition that includes 95 vol. %
ethyl lactate and 5 vol. % poly(methy! methacrylate/meth-
acrylic acid), based on a total volume of the spacer compo-
sition, a thickness of this photoresist can be from 50 nm to
100 nm or less with a spin rate of 5000 rpm at an accelera-
tion of 5000 rpm/s; heating substrate 224 at 170° C. for 1
min; spinning another photoresist on substrate 224 at 4000
rpm for 1 min to a thickness from 300 nm and 400 nm to
form mediation polymer 210 and mediator 212, the photo-
resist composition including 89 vol. % anisole and 11 vol. %

methyl styrene/chloromethyl acrylate copolymer, based ona s

total of the photoresist composition; heating gateless P-N
junction metrolog 200 at 170° C. for 1 min; exposing
substrate 224 to 254 nm ultraviolet light for 15 hours to
activate the p-type regions p-interface 228; and forming

n-interface 230 in other regions of junction member 218 that

are inherently n-type; and optionally adjusting a level of
doping by annealing to form gate! -N junction metrolog
200, e.g., as shown in FIG. 25 that includes graphene p-n
junction 232 disposed on SiC substrate 224.

The process for making gateless P-N junction metrolog
200 also can include an annealing step prior to measurement,
with 350 K applied to gateless P-N junction metrolog 200
for 15 minutes.

Gateless P-N junction metrolog 200 has numerous advan-
tageous and unexpected benefits and uses. In an embodi-
ment, a process for performing resistance metrology with
gateless P-N junction metrolog 200 includes: connecting

&

&

12

first electrode 234.1 to p-interface 228; connecting second
electrode 234.2 to n-interface 230; communicating voltage
across through drain electrode 220 and source electrode 222;
and acquiring a resistance value across p-n junction 232
from first electrode 234.1 and second electrode 234.2 to
perform resistance metrology.

According to an embodiment, with reference to FIG. 26,
a process for measuring a resistance for p-interface 228 and
n-interface 230 of gateless P-N junction metrolog 200
includes measuring longitudinal resistance Rx, longitudi-
nal resistance Rx being a multiple of Hall resistance Ry
(12906.4035Q). Here, both longitudinal resistances R'xx
and R?xx are 2*Rx (25812.807Q).

According to an embodiment, with reference to FIG. 27,
a process for measuring a resistance for p-interface 228 and
n-interface 230 of gateless P-N junction metrolog 200
includes measuring resistance that is a multiple of Ry that
depends on a total number of p-n junction 232 between
adjacent p-interface 228 and n-interface 230 that are crossed
by the resistance measurement, with each p-n junction 232
contributing 2*Rx. It should be appreciated that the resis-
tance between the bottom left contact and the bottom right
contact yields 6*R,.. Moreover, to make gateless P-N junc-

5 tion metrolog 200 shown in FIG. 27 includes using a

photomask that includes this arrangement and number of
p-interfaces 228.

According to an embodiment, with reference to FIG. 28,
a process for measuring a resistance for p-interface 228 and
n-interface 230 of gateless P-N junction metrolog 200
includes measuring resistance that is a multiple of Rx that
depends on a total number of p-n junction 232 between
adjacent p-interface 228 and n-interface 230 that are crossed
by the resistance measurement, with each p-n junction 232
contributing 2*Rx, such that a checkerboard configuration
of p-interfaces 228 and n-interfaces 230 provide fractional
multiples of Hall resistance Rx (12906.4035Q). It should be
appreciated that to make gateless P-N junction metrolog 200
shown in FIG. 28 includes using a photomask that includes
this arrangement and number of p-interfaces 228.

According to an embodiment, with reference to FIG. 29,
a process for measuring a resistance for p-interface 228 and
n-interface 230 of gateless P-N junction metrolog 200
includes measuring resistance that is a multiple of Ry that
depends on a total number of p-n junction 232 between
adjacent p-interface 228 and n-interface 230 that are crossed.
by the resistance measurement. It should be appreciated that
to make gateless P-N junction metrolog 200 shown in FIG.
29 includes using a photomask that includes this arrange-
ment and number of p-interfaces 228.

In certain embodiments, with reference to FIG. 18, FIG.
19, FIG. 20, FIG. 21, and FIG. 22, gateless P-N junction
metrolog 200 includes a select arrangement of p-n junction
232 and a process of performing resistance metrology
includes injection of current through any simultaneously-
used combination of source electrode 222 and drain elec-
trode 220, as described in Example 3. Here, a current source
can be split among several branches with inputs labeled as
I+ and outputs labeled as I-.

Gateless P-N junction metrolog 200 and processes dis-
closed herein have numerous beneficial uses, including,
electron optics, photodetection, resistance metrology, and
edge state manipulation. Advantageously, gateless P-N junc-
tion metrolog 200 overcomes limitations of technical defi-
ciencies of conventional compositions such as fabrication
length scales, carrier density control, fabrication time scales,
and lifetime of functionality. Further, the gateless carrier



U.S. Patent Oct. 18, 2022 Sheet 2 of 59 US 11,474,134 B2

200

220



U.S. Patent Oct. 18, 2022 Sheet 45 of 59 US 11,474,134 B2

$1813 Thickness = 42.4 nm
Tb °c _ 44
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Magnetic Flux Density (1)

FIG. 45


US 11,474,134 B2

Sheet 43 of 59

Oct. 18, 2022

U.S. Patent

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US 11,474,134 B2

17

Go,(0) and 0,,,oft) are the fractional occupancies of oxygen
and water on EG’s available surface sites. The quantities ko,
and po, are the rate constants (A for adsorption and D for
desorption) and unitless ratio of oxygen’s partial pressure to
the total pressure. For the differential equation involving
8;,,0(t), the two molecule subscripts need to be swapped.
From these coupled first-order ordinary differential equa-
tions, one can determine both the final occupancy percent-
age for each species at equilibrium as well as the form taken
by 0,,,(t). Which includes two exponential decay terms. The
final predicted occupancies of oxygen and water are
approximately 90% and 10%, respectively.

When the carrier density is fit to the two decay terms from
the Langmuir model, the time constants listed earlier pro-
vide an optimized reduced chi-squared. Previously reported
work indicates that adsorption of oxygen and water on
graphene takes place on a similar order of magnitude, with
‘oxygen adsorption taking place at slightly slower times at
room temperature, assuming that the adsorption follows an
Arrhenius behavior. A more detailed analysis of the time-
dependency of water adsorption revealed a tj, of about 130
min. The second constant requires more careful treatment to
justify. With both species of gases occupying roughly equal
areas for times below 2 hr, water must undergo significant
desorption to accommodate for the equilibrium occupancies.
A different study on EG measured a time constant on the
same order of magnitude when the device was exposed to
room temperature air. We estimated based on the measured
water desorption energy of 360 meV and by use of the
formula

where E.,,, is the adsorption energy per molecule, v is an
attempt frequency (in this case, the attempt frequency is the
vibrational frequency of the molecule, usually approximated
as 10" s-'), k, is the Boltzmann constant, and T is tem-
perature (K), the estimated time constant is on the order of
10° s, which is about 15 times higher than our fit value.
Inaccuracies can arise from two factors: (1) the uncertainty
of the desorption energy on EG, which can contribute an
order-of-magnitude change to the time constant, and (2) the
significant increase of hydrophobicity found in BG versus
other forms of graphene, which would cause desorption to
occur on faster time scales.

The amount of IHE (shown as x, in FIG. 31) was quan-

tified in Equation 1 and used to shift the carrier density by 5

a desired amount. This correlation is shown in FIG. 32(a)
‘The two data point types indicate the two different types of
devices since some devices were older by a year compared
with the newer devices. Some data came from devices

mounted on a 12-pin package, whereas the data in green ;

were acquired with devices mounted on a 32-pin package
and allowed for more regions of the millimeter-scale EG to
be tested. The error bars correspond to the uncertainties
generated by the variation across the device, only present in
the 32-pin package since the 12-pin package was only used
to monitor one region’s carrier density. There is a clear linear
trend within the order of magnitude of carrier density that is
most suitable for resistance metrology. FIG. 32(b), as
described earlier, is a plot of the relationship between the
longitudinal resistivity and carrier density, both measured at
1.6 K using the length of the device as 640 um and the width
as 400 uum for the conversion from a measured resistance,

&

18

From this plot, we are also able to determine the mobilities
of the device regions which span two orders of magnitude,
from 10* em?V~'s~! to 10° em?V~!s~!.

Tunability and reversibility of functionalized EG were
explored, and long term stability was considered. FIG. 32(c)
shows an example device stored in air over the course of one
year and exhibits stability such that shifts are less than 10"*
cm”. Despite the appearance of the Hall plateau as flat at
this low carrier density, precision measurements suggest that
the plateau is not quantized to within parts in 10°. Thus,
some additional electrons are needed, but with this level of
stability in air coupled with the linear relationship between,
IHE and carrier density, we can develop resistance standards
that have a shelf life longer than one year.

With the knowledge that devices exposed to air retain a
stable, but low, carrier density (less than 10'' cm”), and the
method to apply a specific amount integrated heat, we are
now able to tune devices to a carrier density which enables
metrological access to the quantum Hall effect. Device
quantization was verified by measuring the longitudinal
resistivity p,,.=V,,/Isp*w/l where V,,, is the voltage drop
across the potential contacts, I<, is the source/drain current
and w and 1 are the width of the Hall bar and the distance
between the potential contacts, respectively. If p,,, becomes
negligibly small, the Hall resistance R,, becomes quantized,
for example, at the v=2 plateau with Ry-V,/Isp-Ry/2.
where Rx is the von Klitzing constant. Thus, clear indication
of a breakdown of resistance quantization can be identified
through changes in the resistivity that depend on the mag-
netic flux density, temperature, and current.

FIG. 33 shows resistivity measurements of an EG device
of dimensions 1.6 mmx0.4 mm (FIG. 33(a)) that were
collected using a nanovoltmeter and a ramping voltage
source that are both normally used in a two-terminal cryo-
genic current comparator bridge for high resistance mea-
surements. The voltage source was operated at voltages of
+0.5 V, +1.1 V and +5 V, allowing for currents up to about
387 A in the v=2 quantum Hall regime. Increasing the
temperature from 1.5 K to 4 K at a high current of 387 pA
had no measurable impact on the longitudinal resistivity at
magnetic flux densities greater than 6 T (FIG. 33(5), upper
panels) and reducing the current only increased measure-
ment noise (FIG. 33(4), lower panels). In all measurements,
an offset of about p,,-0.25 mQ (about 10-* Ry) was
observed, likely to be the result of circuit leakage or nano-
voltmeter input leakage in the measurement, since similar
offsets were also observed using many functionalized and
untreated samples. However, since there is no temperature or
current dependent behavior over a wide range of magnetic
flux densities, in agreement with the guidelines for reliable
dc measurements of the QHR, we expect the devices to be
well quantized despite the small offset.

Example 2

Atypical Quantized Resistances in Millimeter-Scale Epi-
taxial Graphene p-n Junctions.

Si atoms that sublimate from the silicon face of SiC.
Samples were grown on square SiC chips diced from on-axis
4H—SiC(0001) semi-insulating wafers. SiC chips were
submerged in a 5:1 diluted solution of hydrofluoric acid and
deionized water prior to the growth process. Chips were
placed, silicon face down, on a polished graphite substrate
and processed with AZ5214E to utilize polymer-assisted
sublimation growth techniques. The face-down configura-
tion promotes homogeneous growth, and the annealing
process was performed with a graphite-lined resistive-ele-


US 11,474,134 B2

Sheet 13 of 59

Oct. 18, 2022

U.S. Patent

8

S

FIG. 13


U.S. Patent Oct. 18, 2022 Sheet 55 of 59 US 11,474,134 B2

®

Of

FIG. 55



US 11,474,134 B2

3

surements; (c) Raman spectra for two devices, taken both
before and afier functionalization; and (d) XPS spectra for
the surface presence of carbon (C Is) and chromium (Cr 2p)
in the top and bottom panel, respectively

FIG. 31 shows: (a) Hall resistance for a gateless P-N
junction metrolog at 1.6 K, with all gray curves representing
data after the gateless P-N junction metrolog stabilized in air
before temperatures above 300 K were applied. The stacked
graphs show different measurements where the gateless P-N
junction metrolog chemically equilibrated with air and then
annealed in vacuum. Total THE increases in each panel.
When the gateless P-N junction metrolog was left in air,
carrier density of the gateless P-N junction metrolog
returned to a value of 10'° cm-?. (b) When the gateless P-N
junction metrolog was warmed to room temperature and
stored in air, longitudinal resistivity shifted and asymptoti-
cally reached a maximum with a Fermi level of EG near a
Dirac point. Two exponential decays included this behavior
as seen in the inset and were used to fit the data;

FIG. 32 shows: (a) a correlation between integrated heat
exposure and subsequently-measured carrier density at 1.6
K with data representing different packages onto which
gateless P-N junction metrologs were mounted, with Series
1 and 2 corresponding to the 12-pin and 32-pin packages,

respectively. Error bars represent 1o uncertainties of the 2

average of multiple measurable regions on the gateless P-N
junction metrolog; (b) The relationship between carrier
density and longitudinal resistivity, both measured at 1.6 K;
and (c) The stability of the carrier density is shown to be less
than 10!" cm” for the same gateless P-N junction metrolog
exposed to air for one year. Cr(CO), remained on the EG
surface as a material for metrological applications;

FIG. 33 shows resistivity measurements in a QHE regime
at a low potentials, wherein (a) shows measurement con-
figuration of a gateless P-N junction metrolog (1600
j1mx400 jm) for determination of resistivity along the right
and the left side of the device with polarity reversal; (b)
shows vanishing of resistivity on both sides of the gateless
P-N junction metrolog at high fields indicates resistance
quantization at a current of 387 1A and temperatures up to
4K. Increasing current from 111 pA to 387 pA at 1.5 K
resulted in reduced noise but not correlated with increase in
resistivity. Scatterplots show corresponding resistivity mea-
surements for increasing temperatures (upper) and increas-
ing currents (lower) summarize the results by taking the
mean value of the left and the right side of the Hall bar for
Bz6 T and BeS T. Error bars represent 10 uncertainties of
the average of all measurements above the indicated mag-
netic flux density;

FIG. 34 shows: (a) an optical image of a gateless P-N 5

junction metrolog with labels indicating charge polarity. A
cross-section of the gateless P-N junction metrolog is shown
in the inset; (b) an illustration of Raman acquisition and a
map-averaged 2D (G') spectrum for the n and p regions; (c)

an atomic force microscope image of a boundary between p 5

and n regions formed; and (d) an extracted profile prior to
ZEP520A deposition;

FIG. 35 shows: (a) longitudinal resistivity p,,, and electron
density in EG ng asa function of time in the upper and lower
panel, respectively, while being exposed to 254 nm UV
light. Cr(CO), provided carrier density transition from
n-type to p-type. Charge neutrality point (CNP) is indicated
by a dashed line. Shading bands show a range where
electrical properties of the EG did not yield quantized
plateaus; (b) AFM profile and magnified image of the pnJ
after PMMA/MMA copolymer deposition (totaling 100 nm).
The curve is taken along the white line in the inset. To

&

&

4

validate the junction width, multiple gateless P-N junction
metrologs with various thicknesses were measured, as indi-
cated by dots along the profile representing two thicknesses
of 300 nm and 42.4 nm. The shaded region indicates bounds
within which the carrier density to switched polarity; and (©)
the profile and shaded region projected onto calculated
charge transfer Aq to the ZEP5S20A layer and profile of no as
a function of lateral distance;

FIG. 36 shows: (a) a gateless P-N junction metrolog and
model implemented in LTspice. Voltage measurements are
marked with lines connecting the positive and negative
terminals and an injected current of 1 tA. Below the gateless
P-N junction metrolog, the current simulator drawing shows
current flow with assumptions that each box is either a
counterclockwise (p region) or clockwise (n region) edge
current, for B>0. Contacts are shown and equipotential lines
are drawn; and (b) resistances of voltage measurements with
the curves matching voltage counterparts as a function of
magnetic flux density such that multiples of R,; are acces-
sible;

FIG. 37 shows: (a) a circuit model implemented by a
circuit simulator. A total current (1) of 1 A is used and split
among up to three injection points on the gateless P-N
junction metrolog, shown as I, I;, and I; and (b) measured
resistances of several configurations of current injection
plotted as a function of magnetic flux density for fractional
multiples of R,,, including ¥, 74, 4, and 34;

FIG. 38 shows: (a) a circuit model implemented by a
circuit simulator. A total current (I) of 1 1A is used and split
among up to injection points on the gateless P-N junction
metrolog. For obtaining '%iR,,, two currents are injected
into the gateless P-N junction metrolog. Other fractions,
¢.g., Rj, involve four injected currents, indicated by solid
(source) and dashed (drain) arrows; and (b) experimental
data for simulated fractions 171 and %, to within 97%
accuracy. Dotted lines are simulated values;

FIG. 39 shows a longitudinal resistivity p,, for several
gateless P-N junction metrologs exposed to 254 nm UV light
with some gateless P-N junction metrologs closer or farther
from the 17 000 W/cm? bulb source. The dip at 1.9x10* s
(18 mm), 3x10* s (35 mm for two cases), and 3.3x10* s (40
mm) is a start of transition of an n-type region to a p-type
region with Dirac point crossed after the local maximum
approximately 10* seconds after each major dip. Measuring
gateless P-N junction metrologs with a resistivity at the dip
(local minimum) yielded n-type behavior in Hall resistance
at OT;

FIG. 40 shows a longitudinal resistivity p,,, for gateless
P-N junction metrologs after exposure to 254 nm UV light.
Within 2x10* s, longitudinal resistivity increased because
the p-type region did not maintain its hole density at room
temperature under ambient laboratory conditions;

FIG. 41 shows a longitudinal resistivity p,, at room
temperature as a function of UV exposure time for a gateless
P-N junction metrolog not been functionalized with Cr(CO)
3. Four different regions were to remain as n-type regions.
‘Two measurements for the p region were in the middle of the
gateless P-N junction metrolog and had a transient effect
within 1.5x10* s, At the end of exposure, all regions main-
tained an electron density that provided a quantized Hall
resistance at 9 T and 4 K;

FIG. 42 shows a relationship between p,, to ng from a
modified Langmuir fit on historical data for gateless P-N
junction metrolog formed under similar conditions with



U.S. Patent Oct. 18, 2022 Sheet 15 of 59 US 11,474,134 B2

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Page 2
(51) Int. Cl.
HOLL 29/24 (2006.01)
HOIL 29/76 (2006.01)
HOLL 29/16 (2006.01)
HOLL 43/06 (2006.01)

(52). US. Cl.
CPC ..... HOLL 29/6697 (2013.01); HOLL 29/7606
(2013.01); HOIL 43/065 (2013.01)
(58) Field of Classification Search
CPC . HOIL 29/7606; HOIL 43/065; HOIL 5/0583:
HOIL 51/0034
USPC 324/713, 691, 649, 600
See application file for complete search history.

(56) References Cited
U.S. PATENT DOCUMENTS.
2016/0247927 AL* 8/2016 Nomura .. HOLL 29/78618

2017/0018584 AL* 1/2017 Ma HOLL 27/14643
2017/0365605 A1* 12/2017 Bedau ve HOLL 29/24

OTHER PUBLICATIONS

Lara-Avila, S., et al., “Non-volatile photochemical gating of an
epitaxial graphene/polymer heterostructure” Advanced Materials,
2011, p. 878-882, vol. 23

* cited by examiner


U.S. Patent

(A)

(B)

Oct. 18, 2022

N#=2

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US 11,474,134 B2

Sheet 27 of 59

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U.S. Patent Oct. 18, 2022 Sheet 11 of 59 US 11,474,134 B2

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US 11,474,134 B2

7

drain electrode 220; n-polymer 216 disposed on n-interface
230 of junction member 218; p-polymer 214 disposed on
p-interface 228 of junction member 218 such that n-polymer
216 is interposed between p-polymer 214 and n-interface
230; mediation polymer 210 disposed on p-polymer 214
such that p-polymer 214 is interposed between mediation
polymer 210 and junction member 218; and mediator 212
disposed in mediation polymer 210 and that receives elec-
trons 226 from junction member 218 in forming p-interface
228.

Gateless P-N junction metrolog 200 can include substrate
224 on which is disposed junction member 218. Substrate
224 can include a semiconducting wafer with a dielectric
spacer layer or an insulating support wafer to provide
physical stability for the gateless P-N junction metrolog 200.
Exemplary substrates include SiO,, SiC, and the like. A
thickness of substrate 224 can be from 2 mm to 0.2 mm,
specifically from 1 mm to 0.3 mm, and more specifically
from 0.5 mm to 0.4 mm. Moreover, substrate 224 should
exhibit insulating properties to prevent interaction with
junction member 218.

Junction member 218 can include a material that provides
electrical Hall conductivity and can be three- or two-dimen-
sional. Exemplary junction members 218 include graphene,
GaAs, and the like. A thickness of junction member 218 can
be from 100 um to 0.1 nm, specifically from 100 nm to 0.3
nm, and more specifically from 1 nm to 0.35 nm. Junction
member 218 has a minimum electrical conductivity of 0.1
mS/mm. In an embodiment, junction member 218 includes
a two-dimensional electrical conductor. According to an
embodiment, the two-dimensional electrical conductor is
graphene, molybdenum disulfide, or silicene. It is contem-
plated that the junction member 218 can be chemically
modified to include a functional group, oxidation state, and
the like. Exemplary functional groups that can be included
in junction member 218 include chromium tricarbonyl,
diazonium salts, nitrenes, carbenes, and the like.

Junction member 218 includes p-interface 228 disposed at
a surface adjacent to p-polymer 214 and n-interface 230
disposed at a surface adjacent to n-polymer 216 such that
p-interface 228 and n-interface 230 are laterally disposed
adjacent to one another in junction member 218. P-interface
228 can include aforementioned functional groups to enable
clockwise or counterclockwise electron flow in a magnetic
field and can be p-doped graphene. It is contemplated that
p-interface 228 has an electron density that can be from
10"? cmTM? to 0. cm”, specifically from -10!? emTM? to -10°
cm”, and more specifically -10'' cmr? to -10'° cm”,
where a negative sign indicates dominance of positive
charges. Moreover, p-interface 228 has an electron flow
opposite to n-interface 230. P-interface 228 has a minimum
electrical conductivity of 0.1 mS/mm. N-interface 230 can
include aforementioned functional groups to enable clock-
wise or counterclockwise electron flow in a magnetic field

and can be n-doped graphene. It is contemplated that n-in-

terface 230 has an electron density from 10'* cm-? to 0
pecifically from 10'? cmTM? to 10” cmTM?, and more
specifically 10'! cm? to 10'° cm”. Moreover, n-interface
230 has an electron flow opposite to p-interface 228. N-in-
terface 230 has a minimum electrical conductivity of 0.1
mS/mm.

Drain electrode 220 can include a metallic layer to
provide adhesion to substrate 224 and can be a metal or
superconducting metal. Exemplary junction members 220
include Au, Ti, NbTiN, and the like. A thickness of drain
electrode 220 can be from 50 nm to 500 nm, specifically
from 100 nm to 400 nm, and more specifically from 250 nm

20

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to 350 nm. Moreover, drain electrode 220 provides flow of
current, Drain electrode 220 has a minimum electrical
conductivity of 0.1 mS/mm. In an embodiment, drain elec-
trode 220 includes a two-dimensional electrical conductor.
According to an embodiment, the two-dimensional electrical
conductor is graphene, molybdenum disulfide, or silicene.

Source electrode 222 can include a metallic layer to
provide adhesion to substrate 224 and can be an ordinary
metal or superconducting metal. Exemplary junction mem-
bers 222 include Au, Ti, NbTiN, and the like. A thickness of
source electrode 222 can be from 50 nm to 500 nm,
specifically from 100 nm to 400 nm, and more specifically
from 250 nm to 350 nm. Moreover, source electrode 222
provides flow of current. Source electrode 222 has a mini-
mum electrical conductivity of 0.1 mS/mm. In an embodi-
ment, source electrode 222 includes a two-dimensional
electrical conductor. According to an embodiment, the two-
dimensional electrical conductor is graphene, molybdenum
disulfide, or silicene.

N-polymer 216 can include additives to enhance electrical
insulation and can be an insulating mineral. N-polymer
prevents the transfer of electrons 226 between junction
member 218 and mediation polymer 210. That is, n-polymer
216 may not communicate a selected wavelength, e.g.. UV,
of light, from mediation polymer 210 to junction member
218 to form n-interface 230 (relative to p-interface 228) by
blocking extraction of electrons 226 in a region that
becomes n-interface 230 of junction member 218, wherein
either the light of selected wavelength or electrons 226 are
not communicated from junction member 218 through
n-polymer 216. Exemplary n-polymer 216 include polym-
ethyl methacrylate, trinydroxybenzophenone, and the like. A
thickness of n-polymer 216 can be from 50 nm to 1000 nm,
specifically from 100 nm to 500 nm, and more specifically
from 300 nm to 400 nm. N-polymer 216 has a maximum
electrical conductivity of 0.001 mS/cm. In an embodiment,
n-polymer 216 includes electronic grade propylene glycol
monomethyl ether acetate, cresol novolak resin, fluoroali-
phatic polymer ester, a diazo photoactive compound, and the
like.

P-polymer 214 can include additives to prevent inter
tion between junction member 218 and mediation polymer
210 and can be chemically similar to compounds used for
photoresists. P-polymer 214 prevents direct physical inter-
action between the mediation polymer 210 and mediator
212. That is, p-polymer 214 communicates a selected wave-
length, e.g., UV, of light, from mediation polymer 210 to
junction member 218 to form p-interface 228 via extraction
of electrons 226 in a region that becomes p-interface 228 of
junction member 218, wherein electrons 226 are communi-
cated from junction member 218, through p-polymer 214,
and received by mediator 212 in mediation polymer 210.
Exemplary p-polymers 214 include polymethyl methacry-
late, acrylic resins, and the like. A thickness of p-polymer
214 can be from 50 nm to 1000 nm, specifically from 100
nm to 500 nm, and more specifically from 200 nm to 300
nm. P-polymer 214 has a maximum electrical conductivity
of 0.001 mS/cm. In an embodiment, p-polymer 214 includes
acomposition of ethyl lactate and poly(methyl methacrylate/
methacrylic acid).

Mediation polymer 210 can include additives to enhance
electron 226 acceptance from junction member 218 to
mediator polymer 210 and can be chemically similar to
compounds used for photoresist. Mediation polymer 210
includes mediator 212 and enables electron transfer from
junction member 218 through p-polymer 214. That is,
mediation polymer 210 communicates a selected wave-



U.S. Patent Oct. 18, 2022 Sheet 49 of 59 US 11,474,134 B2

(A)

N = 4, Self-Interacting @) B-field

(B)

N=2 Equivalent to N=2

two configurations
AW tee parallel ons_ A

FIG. 49


US 11,474,134 B2

Sheet 51 of 59

Oct. 18, 2022

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