ELEC321-lab4-manu - ELEC321 LAB#4 LAB 4 THE PHOTOCONDUCTIVITY OF SILICON AND THE LIFE-TIME OF EXCESS MINORITY CARRIERS THE OBJECTIVES 1 To illustrate

ELEC321-lab4-manu - ELEC321 LAB#4 LAB 4 THE...

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ELEC321, LAB #4 LAB # 4 THE PHOTOCONDUCTIVITY OF SILICON AND THE LIFE-TIME OF EXCESS MINORITY CARRIERSTHE OBJECTIVES:1-To illustrate the photoconductive property of the silicon. 2-To measure the lifetime of the excess minority carriers in silicon.THE THEORY: - A photoconductor is essentially a bar-like piece of semiconductor material with ohmic contacts at the two ends of the bar as shown in figure 1. SEMICONDUCTOROhmic contactsFigure 1The semiconductors used in fabrication of photoconductors have typically low carrier concentrations under dark conditions. The resistivity of the material is high (ρ1/σ, and σcarrier-concentration, ρis the resistivity and σis the conductivity of the semiconductor). When the semiconductor is illuminated with photons of sufficient energy, due to the generated additional carriers, the conductivity of the semiconductor increases (resistivity will decrease). The Photoconductive property of semiconductors can be used to determine the excess minority carriers lifetime. The experimental set up is schematically illustrated in figure 2. Figure 2SCOPE+ VL(t) -RLRS(t)ALight PulseSemiconductor0.37ΔvLVI(t)τPage 1 of 8
ELEC321, LAB #4 The semiconductor sample is chosen to be a bar-shaped with a length of L and a cross-section of A. RSis the sample resistance, RLis a load resistance, VA is a dc voltage, τis excess minority carriers lifetime, and VLis the load or output voltage. RS, and therefore I and VLare time dependent parameters. VLchanges as the conductivity of the semiconductor varies. The variation of VLwith respect to changes in minority carrier concentrations inside the semiconductor can be derived as follows. In the following derivation it is assumed that: 1) The semiconductor is an n-type. 2) Uniform photogeneration throughout the semiconductor bulk. 3) Negligible surface recombination. 4) No end effects. The excess hole concentration Δp(t)inside the sample is described by the simplified minority-carrier diffusion equation LpGtpdttpd+Δ=Δτ)()((1) Where GLis the generation rate of electron-hole pairs due to light. During the light pulse, Δp(t)increases to a maximum value of Δpo= τp·GL. After the light pulse (t 0), GL = 0 and Eq.(1) with GLset to zero is readily solved to obtain the following: ⎡ −Δ=Δτtoeptp)(For t 0 (light-off) (2) The conductivity σ(t) of the semiconductor is defined as: [)()(1)(tptnqtpn+==μμρσ](3) ()()[])()()(tpptnnqtoponΔ++Δ+=μμσ(4) ()()(tpqNqtnpDnΔ++=μμμσFor noND»po, and Δn(t)= Δp(t))()(ttOσσσΔ+=(6) Thus for time t 0 the conductivity likewise decays exponentially with a characteristic time constant equal to τpThe next step is to relate VL(t) and Δσ(t). From figure 2 one can see that ()+==)()()(tRRRVRtItVSLLALL(7) On the other hand ()ALRoSO=σ(Sample with light-off condition or long after a light-pulse) (8)
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ELEC321, LAB #4

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