Elements of Modern Physics
288
v ≥ (ε c – ε v )/h
(8.79)
incident on the depletion region of a pn junction (see Fig. 8.9), or near it (within
about the diffusion length). This photon may be absorbed by an electron in the
valence band as a result of which it may move into the conduction band, thus
creating an electron and a hole. The electron and the hole are separated by the
electric field in the depletion region, the electron moving into the n-region and
the hole moving into the p-region. The direction of the resulting current I v , is
that of the current produced by a reverse bias. If therefore an external potential
V is applied to the junction (V > 0 corresponds to forward bias), the current is
I = I 0 [e
cV kT
– 1] – I v
(8.80)
where the first term is the current in the absence of radiation [see Eq. (8.743)].
If the circuit is open, I = 0, and an effective forward bias voltage V appears
at the terminals, given by
V =
0
ln 1
+
v
I
kT
e
I
(8.81)
This voltage is essentially due to the accumulation of the excess photoelectrons in the n-region and photoholes in the p-region (this reduces the potential
difference across the junction). The expression for the photovoltage in Eq. (8.81)
is valid for V ≤ ε c – ε v (for V = ε c – ε v , there is no longer a potential difference
across the junction to separate the electrons and the holes). If the terminals are
connected to an external load resistance R, a voltage V ′ somewhat less than V in
Eq. (8.81), appears across the junction, and the net current is
I L = I 0 (exp (eV′/kT) – 1) – I v
(8.82)
The voltage across R is
V L = V ′ – | I L | R c
(8.83)
where R c is the resistance of the solar cell. These relations together with
V L = I L R, alow us to determine V ′, V L and I L for given I v , R c and R. Thus a pn
junction can be used to convert radiation energy into electrical energy. This is
the principle behind the use of a pn junction in photometers, detectors and in
solar cells.
For using a pn junction as a photometer, the terminals are usually short
circuited i.e., V = 0. The resulting current [Eq. (8.80)] is – I v . Its magnitude is
proportional to the intensity of the incident radiation, and hence it is used in
photometers for estimating the intensity of radiation. For the use of a photodiode
as a γ-ray or particle detector, it is noted that the energy of a photon in x-ray
γ-rays is much greater than the energy gap. Such a photon creates a highly
energetic electron and a hole. These produce other pairs and the process continues
till their energies are comparable to the energy gap. The number of carriers
indicated by the current gives a measure of the initial photon energy. It may be
noted that in order to collect the carriers quickly (collection time required is
288
v ≥ (ε c – ε v )/h
(8.79)
incident on the depletion region of a pn junction (see Fig. 8.9), or near it (within
about the diffusion length). This photon may be absorbed by an electron in the
valence band as a result of which it may move into the conduction band, thus
creating an electron and a hole. The electron and the hole are separated by the
electric field in the depletion region, the electron moving into the n-region and
the hole moving into the p-region. The direction of the resulting current I v , is
that of the current produced by a reverse bias. If therefore an external potential
V is applied to the junction (V > 0 corresponds to forward bias), the current is
I = I 0 [e
cV kT
– 1] – I v
(8.80)
where the first term is the current in the absence of radiation [see Eq. (8.743)].
If the circuit is open, I = 0, and an effective forward bias voltage V appears
at the terminals, given by
V =
0
ln 1
+
v
I
kT
e
I
(8.81)
This voltage is essentially due to the accumulation of the excess photoelectrons in the n-region and photoholes in the p-region (this reduces the potential
difference across the junction). The expression for the photovoltage in Eq. (8.81)
is valid for V ≤ ε c – ε v (for V = ε c – ε v , there is no longer a potential difference
across the junction to separate the electrons and the holes). If the terminals are
connected to an external load resistance R, a voltage V ′ somewhat less than V in
Eq. (8.81), appears across the junction, and the net current is
I L = I 0 (exp (eV′/kT) – 1) – I v
(8.82)
The voltage across R is
V L = V ′ – | I L | R c
(8.83)
where R c is the resistance of the solar cell. These relations together with
V L = I L R, alow us to determine V ′, V L and I L for given I v , R c and R. Thus a pn
junction can be used to convert radiation energy into electrical energy. This is
the principle behind the use of a pn junction in photometers, detectors and in
solar cells.
For using a pn junction as a photometer, the terminals are usually short
circuited i.e., V = 0. The resulting current [Eq. (8.80)] is – I v . Its magnitude is
proportional to the intensity of the incident radiation, and hence it is used in
photometers for estimating the intensity of radiation. For the use of a photodiode
as a γ-ray or particle detector, it is noted that the energy of a photon in x-ray
γ-rays is much greater than the energy gap. Such a photon creates a highly
energetic electron and a hole. These produce other pairs and the process continues
till their energies are comparable to the energy gap. The number of carriers
indicated by the current gives a measure of the initial photon energy. It may be
noted that in order to collect the carriers quickly (collection time required is