25:
82:
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wafers, flat panel displays, polymer foils, OLED, ceramics, etc. The contacting four-point probe is often applied for single-point measurements of hard or coarse materials. Non-contact eddy current systems are applied for sensitive or encapsulated coatings, for inline measurements and for high-resolution mapping.
575:"), which is dimensionally equal to an ohm, but is exclusively used for sheet resistance. This is an advantage, because sheet resistance of 1 Ω could be taken out of context and misinterpreted as bulk resistance of 1 ohm, whereas sheet resistance of 1 Ω/sq cannot thus be misinterpreted.
641:". Example: A 3-unit long by 1-unit wide (aspect ratio = 3) sheet made of material having a sheet resistance of 21 Ω/sq would measure 63 Ω (since it is composed of three 1-unit by 1-unit squares), if the 1-unit edges were attached to an ohmmeter that made contact entirely over each edge.
1151:
Sheet resistance measurements are very common to characterize the uniformity of conductive or semiconductive coatings and materials, e.g. for quality assurance. Typical applications include the inline process control of metal, TCO, conductive nanomaterials, or other coatings on architectural glass,
519:
Sheet resistance is a special case of resistivity for a uniform sheet thickness. Commonly, resistivity (also known as bulk resistivity, specific electrical resistivity, or volume resistivity) is in units of Ω·m, which is more completely stated in units of Ω·m/m (Ω·area/length). When divided by the
845:
138:
measurement (also known as a four-point probe measurement) or indirectly by using a non-contact eddy-current-based testing device. Sheet resistance is invariable under scaling of the film contact and therefore can be used to compare the electrical properties of devices that are significantly
1127:
Measurement may also be made by applying high-conductivity bus bars to opposite edges of a square (or rectangular) sample. Resistance across a square area will be measured in Ω/sq (often written as Ω/◻). For a rectangle, an appropriate geometric factor is added. Bus bars must make
159:
Sheet resistance is applicable to two-dimensional systems in which thin films are considered two-dimensional entities. When the term sheet resistance is used, it is implied that the current is along the plane of the sheet, not perpendicular to it.
1142:
A very crude two-point probe method is to measure resistance with the probes close together and the resistance with the probes far apart. The difference between these two resistances will be of the order of magnitude of the sheet resistance.
700:
1139:. In one version of this technique a conductive sheet under test is placed between two coils. This non-contact sheet resistance measurement method also allows to characterize encapsulated thin-films or films with rough surfaces.
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417:
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225:
578:
The reason for the name "ohms per square" is that a square sheet with sheet resistance 10 ohm/square has an actual resistance of 10 ohm, regardless of the size of the square. (For a square,
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510:
635:
573:
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of thin films that are uniform in thickness. It is commonly used to characterize materials made by semiconductor doping, metal deposition, resistive paste printing, and
850:
464:
353:
248:
1030:
981:
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602:
1001:
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840:{\displaystyle R_{\text{s}}={\overline {\rho }}/x_{\text{j}}=({\overline {\sigma }}x_{\text{j}})^{-1}={\frac {1}{\int _{0}^{x_{\text{j}}}\sigma (x)\,dx}},}
1120:. A geometry factor needs to be applied according to the shape of the four-point array. Two common arrays are square and in-line. For more details see
170:
520:
sheet thickness (m), the units are Ω·m·(m/m)/m = Ω. The term "(m/m)" cancels, but represents a special "square" situation yielding an answer in
92:
is the resistance of a square piece of a thin material with contacts made to two opposite sides of the square. It is usually a measurement of
1194:
649:
For semiconductors doped through diffusion or surface peaked ion implantation we define the sheet resistance using the average resistivity
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is used to avoid contact resistance, which can often have the same magnitude as the sheet resistance. Typically a constant
473:
151:
Geometry for defining resistivity (left) and sheet resistance (right). In both cases, the current is parallel to the
39:
33:
847:
which in materials with majority-carrier properties can be approximated by (neglecting intrinsic charge carriers):
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50:
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1342:
1327:
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is applied to two probes, and the potential on the other two probes is measured with a high-impedance
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is the net impurity concentration in terms of depth. Knowing the background carrier concentration
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Inductive measurement is used as well. This method measures the shielding effect created by
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Overview on non-contact eddy current sheet resistance measurement techniques and benefits
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can be found using Irvin's curves, which are numerical solutions to the above equation.
350:
Upon combining the resistivity with the thickness, the resistance can then be written as
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281:
259:
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1301:
1272:
1161:
1136:
1129:
470:·m) can be calculated by multiplying the sheet resistance by the film thickness in m:
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638:
929:{\displaystyle R_{\text{s}}={\frac {1}{\int _{0}^{x_{\text{j}}}\mu qN(x)\,dx}},}
251:
131:
112:
1214:
147:
446:
is the sheet resistance. If the film thickness is known, the bulk resistivity
412:{\displaystyle R={\frac {\rho }{t}}{\frac {L}{W}}=R_{\text{s}}{\frac {L}{W}},}
1117:
108:
146:
80:
521:
467:
18:
690:{\displaystyle {\overline {\rho }}=1/{\overline {\sigma }}}
220:{\displaystyle R=\rho {\frac {L}{A}}=\rho {\frac {L}{Wt}},}
1181:
Dobkin, Daniel M. (2013-01-01), Dobkin, Daniel M. (ed.),
524:. An alternative, common unit is "ohms square" (denoted "
298:
is the cross-sectional area, which can be split into:
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Resistor based on the sheet resistance of carbon film
1278:(2nd ed.). New Jersey: Prentice Hall. pp.
637:.) The unit can be thought of as, loosely, "ohms ·
1303:Semiconductor Material and Device Characterization
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163:In a regular three-dimensional conductor, the
126:The utility of sheet resistance as opposed to
8:
1059:and the surface impurity concentration, the
547:") or "ohms per square" (denoted "Ω/sq" or "
1274:Introduction to Microelectronic Fabrication
1307:. New York: J Wiley & Sons. pp.
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69:Learn how and when to remove this message
1093:{\displaystyle R_{\text{s}}x_{\text{j}}}
134:is that it is directly measured using a
32:This article includes a list of general
1173:
1348:Electrical resistance and conductance
7:
16:Electrical resistance of a thin film
505:{\displaystyle \rho =R_{s}\cdot t.}
100:. Examples of these processes are:
1249:. New York: McGraw-Hill. pp.
983:is the majority-carrier mobility,
554:
531:
38:it lacks sufficient corresponding
14:
23:
1187:The RF in RFID (Second Edition)
1061:sheet resistance-junction depth
121:thick-film hybrid microcircuits
1019:
1013:
910:
904:
821:
815:
769:
745:
630:{\displaystyle R_{\text{s}}=R}
115:), and the resistors that are
1:
1217:, retrieved 22 November 2013.
568:{\displaystyle \Omega /\Box }
1299:Schroder, Dieter K. (1998).
1189:, Newnes, pp. 189–237,
1052:{\displaystyle N_{\text{B}}}
956:{\displaystyle x_{\text{j}}}
753:
722:
682:
661:
540:{\displaystyle \Omega \Box }
439:{\displaystyle R_{\text{s}}}
1270:Jaeger, Richard C. (2002).
1183:"Chapter 5 - UHF RFID Tags"
1003:is the carrier charge, and
1364:
1328:Measuring Sheet Resistance
1226:Measuring Sheet Resistance
1241:Van Zant, Peter (2000).
963:is the junction depth,
119:onto the substrates of
53:more precise citations.
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1245:Microchip Fabrication
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459:{\displaystyle \rho }
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243:{\displaystyle \rho }
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136:four-terminal sensing
94:electrical resistance
84:
1147:Typical applications
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1036:
1025:{\displaystyle N(x)}
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987:
976:{\displaystyle \mu }
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1122:Van der Pauw method
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597:{\displaystyle L=W}
139:different in size.
1235:General references
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645:For semiconductors
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996:{\displaystyle q}
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337:{\displaystyle t}
314:{\displaystyle W}
291:{\displaystyle A}
269:{\displaystyle L}
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167:can be written as
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1110:four-point probe
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90:Sheet resistance
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1162:ESD materials
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1137:eddy currents
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1130:ohmic contact
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105:semiconductor
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98:glass coating
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42:
41:
35:
30:
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1200:, retrieved
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1176:
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1107:
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648:
639:aspect ratio
577:
518:
349:
250:is material
162:
158:
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143:Calculations
125:
89:
88:
65:
56:
37:
1104:Measurement
252:resistivity
132:resistivity
113:polysilicon
51:introducing
1337:Categories
1202:2023-02-23
1168:References
324:thickness
165:resistance
155:direction.
128:resistance
34:references
1118:voltmeter
971:μ
896:μ
875:∫
813:σ
792:∫
774:−
754:¯
751:σ
723:¯
720:ρ
683:¯
680:σ
662:¯
659:ρ
563:◻
555:Ω
535:◻
532:Ω
494:⋅
478:ρ
454:ρ
366:ρ
238:ρ
197:ρ
181:ρ
1156:See also
1063:product
1114:current
109:silicon
47:improve
1315:
1286:
1257:
1193:
936:where
419:where
301:width
227:where
36:, but
1311:–55.
1282:–88.
1251:431–2
604:, so
515:Units
102:doped
1313:ISBN
1284:ISBN
1255:ISBN
1191:ISBN
522:ohms
466:(in
130:or
111:or
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1280:81
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1132:.
1124:.
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123:.
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746:(
743:=
738:j
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729:/
715:=
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674:/
670:1
667:=
625:R
622:=
617:s
613:R
592:W
589:=
586:L
559:/
500:.
497:t
489:s
485:R
481:=
468:Ω
432:s
428:R
407:,
402:W
399:L
392:s
388:R
384:=
379:W
376:L
369:t
361:=
358:R
344:.
332:t
321:,
309:W
286:A
264:L
254:,
215:,
209:t
206:W
202:L
194:=
189:A
186:L
178:=
175:R
153:L
72:)
66:(
61:)
57:(
43:.
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