**Ohmic Contacts to Photoconducting Semiconductors**

Uri Lachish, *guma* science

**Abstract: **Ohmic contacts of dark leakage current in semiconductors support higher orders of magnitude photocurrents. See why.

Light illumination of variety of semiconductors may enhance the electrical current through them by orders of magnitude. The spectral sensitivity of the photocurrent depends on the semiconductor's band gap, and it shifts from shorter to longer wavelength with gap reduction. For example, in the series, GaN GaAlAs CdZnTe CdTe GaAs Si InSb HgCdTe.

Semiconductors equipped with ohmic contacts yield linear Current Voltage (I-V) dependence presented in figure-1.

Figure-1: Linear I-V curve of a semiconductor equipped with ohmic contacts.

Will ohmic contacts, operating in the dark, supply also higher orders of magnitude photocurrents? The answer is, yes they will.

Figure-2 models an ohmic contact by two conductors, *r* and *R*, connected back to back and biased by a voltage *V*. *R* is a semiconductor of high dark resistance, and *r* << *R* is a bulk contact material of very low but finite resistance. The other contact is omitted for reasons of symmetry. *x* is the thickness of each conductor.

Figure-2: Two conductors, *r* and *R*, model an ohmic contact to semiconductor. The contact resistance *r* is lower by many orders of magnitude than the semiconductor resistance *R*. However, it is finite and not zero.

The bias voltage *V* = *V*_{r} + *V*_{R} is distributed between the two conductors:

*V*_{r} = *V*∙*r*/(r + *R*) ≈ *V*∙*r*/*R* (1)

*V*_{R} = *V*∙*R*/(*r* + *R*) ≈ *V* (2)

Practically, almost all the voltage falls on the semiconductor bulk and the voltage falling on the contact bulk is very small, but not zero. Equations (1) - (2) are simple application of Kirchoff's law.

The current through the two conductors is:

*I* = *V*_{R}/*R* = *V*_{r}/*r * (3)

and the electric fields in the contact and semiconductor bulks are:

*E*_{r} = *V*_{r}/*x* ≈ (*r*/*R*)*V*/*x * (4)

*E*_{R} = *V*_{R}/*x* ≈ *V*/*x* (5)

The current density is:

*J* = *env* = *enμE* (6)

where *e* is the unit charge, *n* is the charge carrier density, and *v* is the drift velocity. *μ* is the mobility and *E* the electric field. The electric field *E*_{r} within contact bulk is very small, but it is important since it drives the electric current in it. Doubling the bias *V*, for example, doubles the electric field in both the contact and semiconductor bulks, and doubles also the drift velocity within them.

Light illumination of the semiconductor bulk increases the density of charge carriers within it, and decreases its electrical resistance by the same ratio. For example, assume that the light induced resistance reduces ten times, *R*_{L} = *R*/10. Then *r* and *R*_{L} will redistribute the voltage *V* according to equations (1)-(2). Since *R*_{L} is still far higher than *r*, almost all the bias voltage will fall on the semiconductor bulk, and the electric field within it will be the same as in the dark. The current increases ten times by the same increase of charge carrier density.

However, according to equation (1), the voltage on the contact bulk increases ten times, and therefore, the electric field within it increases by the same ratio (equation (4)). Then the charge carriers in the contact bulk will move ten times faster (equation (6)), in proportion to the stronger electric field.

The charge carriers' density in the contact bulk is the same as in the dark, and the current increases by their faster drift velocity. Therefore, the charge carriers in the contact bulk flow ten time faster into the semiconductor bulk, and support the ten times higher photocurrent.

Conclusion:

Simple application of the macroscopic Kirchhoff's law shows:

If a contact is ohmic to the dark leakage current, then it will be automatically ohmic to many orders of magnitude higher photocurrents.

The mechanism of contact operation is increase of the drift velocity of the charge carriers within the contact bulk. The velocity is proportional to the electric field in the contact bulk. The field increases by the same ratio as the photo-induced increase of charge carrier density in the semiconductor bulk.

on the net: March 2000.

by the author:

- "CdTe and CdZnTe semiconductor gamma detectors equipped with ohmic contacts", Nucl. Instr. and Meth.
**A436**, 146 - 149 (1999). - "Ohmic Contact Gamma Radiation Detectors", in R.B. James and R.C. Schirato Eds. "Hard X-Ray, Gamma Ray, and Neutron Detector Physics", SPIE Proc.
**3768**, Denver Colorado, July (1999). - "The role of semiconductors in digital x-ray medical imaging ", http://urila.tripod.com/xray.htm, April (1999).
- "CdTe and CdZnTe Gamma Detectors - Model of an Ohmic Contact", http://urila.tripod.com/ohmic.htm, July (1998).
- "CdTe and CdZnTe Crystal Growth and Fabrication of Gamma Radiation Detectors", http://urila.tripod.com/crystal.htm, March (1998).
- "CdTe Semiconductor Gamma Radiation Detectors equipped with ohmic contacts", http://urila.tripod.com/cdte.htm, February (1998).
- "The role of contacts in semiconductor gamma radiation detectors", Nucl. Instr. and Meth.
**A403**, 417 - 424 (1998)