Design and sketch a photoconductor using a 5-μm -thick film of CdS, assuming that τn=τp=10^-6 s

step 1 So since the resistivity changes according to the length of the resistor, we need to find the to

Design and sketch a photoconductor using a 5-μm -thick film...

Design and sketch a photoconductor using a $5-\mu \mathrm{m}$ -thick film of $\mathrm{CdS}$, assuming that $\tau_{n}=\tau_{p}=10^{-6} \mathrm{~s}$ and $N_{d}=10^{14} \mathrm{~cm}^{-3}$. The dark resistance (with $g_{\text {op }}=0$ ) should be $10 \mathrm{M} \Omega$, and the device must fit in a square $0.5 \mathrm{~cm}$ on a side; therefore, some sort of folded or zigzag pattern is in order. With an excitation of $g_{\text {op }}=10^{21} \mathrm{EHP} / \mathrm{cm}^{3}-\mathrm{s}$, what is the resistance change?

Key Concepts

Photoconductivity

Photoconductivity refers to the increase in electrical conductivity of a material when it is exposed to light. In semiconductor devices, absorbed photons generate electron–hole pairs (EHPs), which contribute to current flow, thereby reducing the material's resistance. This photoresponse is fundamental to the operation of photoconductors.

Carrier Generation and Recombination Dynamics

The behavior of photoconductors is governed by the processes of carrier generation and recombination. When light shines on the material, electron–hole pairs are generated at a rate determined by the optical generation rate. These carriers have a finite lifetime before they recombine, which is quantified by the carrier lifetime. The balance of these processes determines the steady-state carrier concentration and, consequently, the conductivity under illumination.

Semiconductor Material Properties and Doping

The intrinsic properties of the semiconductor material, such as its bandgap, mobility, and thickness, play a crucial role in device performance. Doping—the intentional introduction of impurities—sets the baseline carrier concentration in the dark, affecting the dark resistance. Understanding the interplay between doping concentration, material thickness, and carrier mobility is essential for designing devices with specific resistance characteristics.

Resistance and Conductivity Relationships

The resistance of a semiconductor is inversely related to its conductivity, which depends on the carrier concentration and mobility. In the dark state, the material exhibits a high resistance when the carrier concentration is low due to doping levels. Under optical excitation, the increase in free carriers leads to a decrease in resistance. This relationship is fundamental in quantifying the resistance change in photoconductive devices.

Device Geometry and Patterning

Due to practical device size constraints, innovative design approaches such as folded or zigzag patterns are used to maximize the effective conduction path within a limited area. The geometry of the device directly impacts the measured resistance because it determines the length and cross-sectional area of the conductive channel. Optimizing the device layout is crucial to achieve the desired electrical characteristics while fitting within specified spatial dimensions.

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