"Study of Indium Tin Oxide (ITO) for Novel Optoelectronic Devices"
Ph.D. thesis by Shabbir A Bashar


4. Measurement and Analysis Techniques



4.1 Transmission Line Model - TLM

Transmission Line Model (TLM) theory was used for accessing the quality of ohmic contacts as well as electrical properties of ITO films used in this study. This technique was proposed by Reeves and Harrison. A detailed analysis is available in their published work [119,120].


4.1.1 Theory

A schematic diagram of a semiconductor material with ohmic contact pads prepared for TLM analysis is shown in Figure 4.1. It can be seen that the sample is first mesa etched usually to a semi-insulating substrate or to a depth where there is a natural depletion layer such as between n+ and p+ material. This is done in order to isolate columns of the conductive epitaxial layer there by restricting current flow within the mesa height, d. Metal pads, of finite width, w, and length, s, are then deposited on the mesa at a linearly increasing pad spacing, L, such that L1 < L2 < L3.

Figure 4.1: Schematic diagram of a semiconductor material with ohmic contact pads prepared for TLM analysis

A constant current is passed between two adjacent pads through two probes; a second set of probes are then used to measure the voltage drop using a digital volt meter (DVM) enabling the total resistance between the pads to be obtained. Separate current source and DVM are preferred to a single ohm meter because of the latter's relatively low impedence which may give rise to inaccuracies. The process is repeated and the total resistance is plotted on a linear graph as a function of pad spacing; an example is shown in Figure 4.2.

Figure 4.2: An example of a plot of total resistance as a function of TLM pad spacing

From Figure 4.1, it is seen that the resistance, r, between two adjacent pads, is given by:

r = 2Rc + Rs (eqn. 4.1)

where,
Rc = resistance due to the contact
Rs = resistance due to the semiconductor material

Rs is given by:

Rs = rL/dw (eqn. 4.2)

where,
r = resistivity of the semiconductor material

But, since the sheet resistance, Rsh, of the semiconductor is given by r/d, we can re-write (eqn. 4.1) as:

r = 2Rc + Rsh(L/w) (eqn. 4.3)

Thus, (eqn. 4.3) has a gradient of Rsh/w and x and y axis intercepts at Lx and 2Rc respectively. Reeves et al [119] have shown that Rc can be expressed as:

2Rc = 2RskLT/w (eqn. 4.4)

where,
Rsk = modified sheet resistance of the material directly underneath the pads
LT = the transfer length related to the distance required for current to flow into or out of the ohmic contact:

and,

LT = Ö(rc/Rsk) (eqn. 4.5)

where,
rc = specific contact resistance

Using (eqn. 4.3) and (eqn. 4.4), the relationship between Lx and LT is given by:

Lx = 2RskLT/Rsh (eqn. 4.6)

Rearranging (eqn. 4.4),

LT = Rcw/Rsk (eqn. 4.7)

Rearranging (eqn. 4.5),

rc = LT2.Rsk (eqn. 4.8)

Substituting (eqn. 4.7) in (eqn. 4.8),

rc = (Rc.w)2/Rsk (eqn. 4.9)

In practice, Rsk is determined using the "end contact resistance" analysis. Referring back to Figure 4.1, let us consider three resistances between pads 1 and 2, 2 and 3 as well as 1 and 3, denoted by R12, R23 and R13 respectively. Using, (eqn. 4.3), these can be expressed as:

R12 = Rc1 + Rc2 + Rsh(L1/w) (eqn. 4.10)

R23 = Rc2 + Rc3 + Rsh(L2/w) (eqn. 4.11)

R13 = Rc1 + Rc3 + Rsh({L1+L2}/w) + Rsk(s/w) (eqn. 4.12)

where,
s = length of the contact pad

Thus, the end contact resistance, Re is defined as follows:

Re = (R12 + R23 -R13)/2 (eqn. 4.13)

Substituting (eqn. 4.10), (eqn. 4.11), and (eqn. 4.12) in (eqn. 4.13) we obtain:

Re = Rc - Rsk.s/2w (eqn. 4.14)

Hence,

Rsk = (2w/s).(Rc - Re) (eqn. 4.15)

Substituting (eqn. 4.15) in (eqn. 4.9), the specific contact resistance, rc, can now be expressed as:

rc = Rc2.ws/2(Rc - Re) (eqn. 4.16)

In addition to these parameters, the transfer resistance, Rt, is often used as a figure of merit in the related literature. Rt is given by:

Rt = Rc.w (eqn. 4.17)


4.1.2 Experimental Set-up

In this study, the TLM pattern consisted of a rectangular mesa and eight rectangular contact pads. The mesa dimension was 300mm x 120mm; the metal pads were 100mm x 50mm (corresponding to w and s respectively); and the pad spacings were 10mm, 20mm, ...60mm, and 70mm (corresponding to L1, L2, ...L6 and L7 respectively). Once the sample to be tested was fully prepared, the "Auto TLM" system was used for taking the measurements [121]; this consists of a 16 fingered (8 x 2) probe card connected to a current source, DVM, controller card and a PC. Once the probe card is aligned and lowered over the mesa, all resistance values are measured automatically and transferred to the PC; generally, a 10mA source current was used for these measurements. The acquired data was then plotted and analysed to access the ohmic contacts or the ITO films.

From a purely experimental point of view, one has to be very careful about deformation to metal pad shape especially after anneal treatments where AuGe based contacts tend to flow. Deformed pads alter many of the vital dimensions which are pre-set in the analysis program; hence, in such cases, inspection under the microscope is required to obtain more realistic values for these dimensions and they need to be re-entered in order to obtain accurate values.


© 1998: Shabbir A. Bashar (in accordance with paragraph 8.2d, University of London Regulations for the Degrees of M.Phil. and Ph.D., October 1997). The Copyright of this thesis rests with the author, and no quotation from it or information derived from it may be published without the prior written consent of the author.
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