Capteurs et Physique des Composants
M1 EEA
Exercice 11: Carrier Diffusion
1. Consider a sample of silicon at T = 300 K. Assume that the electron concentration varies
linearly with distance, as shown in the figure. The diffusion current density is found to
be Jn = 0.19 A/cm2 . If the electron diffusion coefficient is Dn = 25 cm2 /s, determine the
electron concentration at x = 0.
[n(0) = 0.25 × 1014 cm−3 ]
2. The electron concentration in a sample of n-type silicon varies linearly from 1017 cm−3
at x = 0 to 6 × 1016 cm−3 at x = 4 µm. There is no applied electric field. The electron
current density is experimentally measured to be −400 A/cm2 . What is the electron
diffusion coefficient?
[D = 25 cm2 /s]
3. The hole concentration is given by p = 1015 exp(−x/Lp ) cm−3 for x ≥ 0 and the electron
concentration is given by n = 5 × 1014 exp(+x/Ln ) cm−3 for x ≤ 0. The values of Lp and
Ln are 5 × 10−4 cm and 10−3 cm, respectively. The hole and electron diffusion coefficients
are 10 cm2 /s and 25 cm2 /s, respectively. The total current density is defined as the sum
of the hole diffusion current density at x = 0 and the electron diffusion current density
at x = 0. Calculate the total current density.
h
j = 5.2 A/cm2
i
4. The hole concentration in germanium at T = 300 K varies as
p(x) = 1015 exp
−x
22.5
cm−3
(1)
where x is measured in µm. If the hole diffusion coefficient is Dp = 48 cm2 /s, determine
the hole diffusion current density as a function of x.
h
jp = 3.41 exp (−x/22.5) A/cm2
i
5. The electron concentration in silicon at T = 300 K is given by
n(x) = 1016 exp
−x
18
cm−3
(2)
where x is measured in µm and is limited to 0 ≤ x ≤ 25 µm. The electron diffusion
coefficient is Dn = 25 cm2 /s and the electron mobility is µn = 960 cm2 /(Vs). The electron
current density through the semiconductor is constant and equal to Jn = −40 A/cm2 .
The electron current has both diffusion and drift current components. Determine the
electric field as a function of x which must exist in the semiconductor.
[E = 14.5 − 26 exp (x/18) V/cm]
6. The total current in a semiconductor is constant and is composed of electron drift current
and hole diffusion current. The electron concentration is constant and is equal to 1016
cm−3 . The hole concentration is given by
−x
p(x) = 10 exp
L
15
cm−3 (x ≥ 0)
(3)
where L = 12 µm. The hole diffusion coefficient is Dp = 12 cm2 /s and the electron
mobility is µn = 1000 cm2 /(Vs). The total current density is J = 4.8 A/cm2 . Calculate
(a) the hole diffusion current density versus x, (b) the electron current density versus x,
and (c) the electric field versus x.
h
i
(a)jpdif f = 1.6e−x/L A/cm2 , (b)jndrif t = 4.8 − 1.6e−x/L A/cm2 , (c)E = 3 − e−x/L V/cm