SaM - Photoresistance

Remeber:

A “photoresisitve device” operates using the photoelectric effect. The photoelectric effect is based on the use of a semiconductor, where we have a certain energy gap $(E_g)$ less then the energy of a photon $(E)$. When a photon hits the material, it is able to free one electron from the valence band $(E_V)$ and promote it into the conduction band $(E_C)$. So we have the creation of a free electron in the C.B. and a hole in the V.B.

• $\lambda$ : wavelength.
• $\nu$ : frequency.

So given a certain wavelength $(\lambda )$ we will obatin a response in the form of more free carriers, so more conduction, ==⇒ less resistance==:

• $h$ : Planck’s constant, usually denoted as $\hslash$, approximately equal to: $6.626\times 10^{-34}J\cdot s$ (Joule-seconds).
• $c$ : speed of light $\simeq 3\cdot 10^8\frac{m}{s}$.
• So we find a certain ${\lambda }_{\text{MAX}}$ that defines the maximum wavelenght, above which we will have no response, no change in resistance, we can find it as:${\lambda }_{\text{MAX}}=\frac{c\hslash }{E_g}$In reality there is also a ${\lambda }_{\text{MIN}}$, but we will not consider it.

IMPORTANTE The visible light has a wavelength:$0.4\mu \text{m}<\lambda <0.7\mu \text{m}$And a corresponding energy: $1.78\text{eV}<E<2.8\text{eV}$ A common photoresistor can be made out of $CdS$ or $CdSe$ semiconductors:

• If we use the cadmium sulfide $(CdS)$ semiconductor, which as an $E_g=2.4\text{eV}$ we will have a ${\lambda }_{\text{MAX}}=0.5\mu \text{m}$.
• Or we can use the cadmium selenide $(CdSe)$ semiconductor, which as an $E_g=1.8\text{eV}$ we will have a ${\lambda }_{\text{MAX}}=0.6\mu \text{m}$

While IR cameras (Infra-Red) use $PbS$ or $PbSe$:

• $PbS$ : lead sulfide, $E_g=0.4\text{eV}$ ⇒ ${\lambda }_{\text{MAX}}=3\mu \text{m}$.
• $PbSe$ : lead selenide, $E_g=1.5\text{eV}$ ⇒ ${\lambda }_{\text{MAX}}=0.83\mu \text{m}$.

The conductance of a semiconductor is calculated as:$G=(qn{\mu }_n+qp{\mu }_p)\cdot \frac{A}{l}$Where:

• $G=\frac{1}{R}$ represents the conductance.
• $q=-1.602\times 10^{-19}\text{C}$ charge of the electron.

IMPORTANTE For a photoresistance we will find that the resistance value is calculated using the relationship between the light and the resistance, proportional to the illuminance (measured in lux, a flux of light):$R=A_x{E}_{\nu }^{-\alpha }$Where:

• $E_{\nu }$ : illuminance is measured in lux (measure unit) $\left[\text{lux}=\frac{\text{cd}\cdot \text{sr}}{{\text{m}}^2}\right]$
  • cd : candela (measure unit).
  • sr : steradian (measure unit).
• $\alpha$ : exponent, which is in the range $[0.9,0.7]$.
• ==A photoresistance is non-linear sensors, in fact is used more as a light detector==.

So the resistance of a photoresistive material varies, a lot, the ration between the same material, once illuminated, once in darkness is:$\frac{R_{\text{ILLUMINATED}}}{R_{\text{DARK}}}=10^{-4}$

Finally, ==these are slow devices, and they show hysteresis==. Their rise time $\tau$ is:${\tau }_{63\%}\approx 10\text{ms}$Meaning that usually it takes about 10 milliseconds, to have a $63\%$ variation with respecto to the final value. They are used for threshold measurement, for photography and sometimes also for infrared cameras.

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Memory Card

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This device operates using the photoelectric effect. The photoelectric effect is based on the use of a semiconductor, where we have a certain energy gap:

• $h$ : Planck’s constant, usually denoted as $\hslash$, approximately equal to $6.626\times 10^{-34}J\cdot s$ (Joule-seconds)
• $c$ : speed of ligth $\simeq 3\cdot 10^8\frac{m}{s}$
• $\lambda$ : wavelength
• $\nu$ : frequency

If this energy is larger than the energy gap, the photon hitting the material is able to free one electron from the valence band ($E_V$) and promote it into the conduction band ($E_C$). So we have the creation of a free electron in the C.B. and a hole in the V.B.

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~Ex.: Photoresistance for Visible Light

• IR: Infra-Red
• $G=(an{\mu }_n+ap{\mu }_p)\cdot \frac{A}{l}$
  • $G$ represents the conductance.
  • $q$ charge of the electron.
  • $n$ represents the electron concentration.
  • ${\mu }_n$ represents the electron mobility.
  • $p$ represents the hole concentration.
  • ${\mu }_p$ represents the hole mobility.
  • $A$ represents the cross-sectional area.
  • $l$ represents the length.

• But the phenomena of recombination is really slow.
• $R$: resistance.
• The relationship between the light and the resistance, proportional to the illuminance (measured in lux, a flux of light)
• $R=\frac{1}{G}=A_x{E}_{\nu }^{-\alpha }$
  • $E_{\nu }$ is measured in lux (measure unit).
  • cd : candela (measure unit)
  • sr : steradian (measure unit)
  • $\alpha$ : exponent, which is in the range $[0.9,0.7]$.

So the resistance of a photoresistive material varies, and a lot, this is the ration between the same material, once illuminated, once in darkness:

• $R_{ILL}$: resistance of a photoelectric material when illuminated
• $R_{DARK}$: resistance of the same photoelectric material when in darkness (not illuminated)
• And then the last thing we have to see to see is that ==these are slow devices, and they show hysteresis==.
  Usually, you find the value of the $\tau$ constant, which gives you a $63\%$ variation with respect to the final condition, which is about 10 milliseconds.
• They are used for threshold measurement, for photography and sometimes also for infrared cameras.