Laboratory work № 6 – 10 studying of a photoeffect in a p-n junction

Figure 27 – Principle of operation of the photocell.

1 Goal of the work

Studying the photoeffect in a p-n junction and measuring of dark and light current-voltage characteristics.

2_Main concepts

2.1 P-N junction (see work 6-9)

2.2 Photodiode properties

Figure 25 – Band diagram of non-illuminated (а) and illuminated (b) p-n junction.

Photovoltaic effect consists in appearing of a photo-emf in a valve (i.e. rectifying) contact while it’s illuminated. The lowest frequency f₀ (the highest wavelength λ₀) at which the photoeffect still possible called the photoeffect red border. It can be determined for given semiconductor from the condition:

hf₀ = E_g,

that means that energy of photons hf₀ must be not less than the forbidden energy gap width.

On the Fig. 26 (curve 1) represented current-voltage characteristic of non-illuminated p-n junction. It can be described by such equation:

(78)

Figure 26 – CVC of the non-illuminated (curve 1) and illuminated (curve 2) р-n-junction.

here I_S – saturation current of non-illuminated p-n junction, k – Boltzman constant, e – elementary charge, T – temperature in Kelvins, U – external applied voltage.

Now let’s p-n junction be illuminated by light with energy of photons not less then forbidden gap width of the semiconductor. The internal photoeffect will lead to generation of electron-hole pairs, concentration of which will decrease with increasing of distance from illuminated surface. Electrons and holes will move to the junction, where they will be separated. Majority carriers of the region will be held by internal built-in electric field. Accelerated minority carriers will freely path through p-n junction, and create photocurrent I_PHOTO, which flows in the reverse direction (from n- to p - region).

If the circuit is open, then on the borders of p-n junction appears volume charge that opposes to further migration of charge carriers. This volume charge produces photo-emf U₀ with polarity reverse to polarity of built-in potential. Potential barrier of depletion region decreases (Fig. 25b). That leads to appearance of leakage current I_L flowing in the reverse direction. The photo-emf will be increased until the photocurrent will be compensated by increasing current of majority carriers.

If we connect to p-n junction load resistance R_LOAD (Fig. 27), than, in obtained circuit will flow a current I which can be represented as:

I = IPHOTO­ - IL

(79)

Leakage current I_L can be calculated by formula (78) for non-illuminated p-n junction when an external forward bias voltage U_LOAD = IR_LOAD­ is applied:

.

Let’s consider the critical modes of operation of such photocell.

1. Short-circuit mode appears if R_LOAD­ = 0. Then U_LOAD = 0, I_L = 0 and short circuit current I_SC is equal to photocurrent I_PHOTO which is proportional to light intensity Ф:

   ISC = IPHOTO ; IPHOTO Ф

   (80)

2. Open-circuit mode will take place if R_LOAD­ = . The open-circuit voltage

V_OC = U_PHOTO, total current I = 0 and I_PHOTO = I_L­. Equation (78) gives

(81)

from where we get

(82)

where U_PHOTO – is a photo EMF generated in the photocell.

Thus, valve photocells allow to transform radiant energy directly into electric one. That is why they also called the photogalvanic elements and used as sources of EMF in the solar cell batteries.

Figure 28 – photocells’ CVC at different light intensities.

The current-voltage characteristic of illuminated p-n junction shown on the Fig. 26 (curve2). Segment OA (U = 0) refers to short-circuit current (R_LOAD = 0), segment OB (I = 0) – to open-circuit voltage (R_LOAD =∞). Changing external load from 0 to ∞ we’ll get segment AB, which is a current-voltage characteristic of p-n junction in a photogalvanic mode at constant light intensity Ф. Segment BC characterize work of the photocell at forward bias voltage, segment AD – at reverse bias (photodiode mode).

The CVCs will be displaced and change their shape under the change of light flux intensity. The photocell CVCs in a photogalvanic mode for different light intensities are shown on the Fig.28. Straight line, drawn from the coordinate origin under the angle α ( ), intersects the CVC at point, which X coordinate is equal to voltage drop on the load R_LOAD , and Y coordinate – current in the external circuit (for example U₁ = I₁·R_LOAD1). Dashed area (Fig.28) is proportional to power P, generated on the load R_LOAD1:

(83)

Optimal load resistance chosen in such way that this power will be maximal. Efficiency of the photogalvanic cell η determined as:

(84)

where Ф – light intensity in Watts, P – useful power, emitted on the load.