4.2 Point Defects
77
(a)
(b)
Fig. 4.7 (a) Depth of peak concentration of boron implanted in silicon for various acceleration voltages U . Data from
various sources, for U < 1 keV from [299]. Dashed line is linear dependence. (b) Simulated depth profiles of impurity
concentration for B, P, As, and Sb implanted into crystalline silicon with U = 100 keV and a dose of 10 15 cm −2 . Adapted
from [300]
RF-heated and liquid ‘float’ zone is moved through the crystal. In this case the impurity distribution is
given by
4
c(x) = c 0
1 − (1 − k) exp
−
k x
z
,
(4.20)
where x is the ratio of the crystal mass to the total mass, i.e. crystal, liquid and feed rod. z is the relative
mass of the (liquid) float zone, i.e. the ratio of liquid mass to the total mass. The impurity distribution
for CZ and FZ crystals is compared in Fig. 4.6b. Obviously the FZ process can create much more
homogeneous profiles.
5
Using epitaxy arbitrary doping profiles along the growth directions can be created by varying the
impurity supply during growth. Impurities can be introduced through the surface of the material by
diffusion from a solid or gas phase. In ion implantation [292] the impurity atoms are accelerated
towards the semiconductor and deposited with a certain depth profile due to multiple scattering and
energy loss events, depending on the acceleration voltage (increasing deposition depth with increasing
voltage, Fig. 4.7a) and ion mass (decreasing deposition depth with increasing mass, Fig. 4.7b). The
depth profile is often investigated using secondary ion mass spectrometry (SIMS) [293, 294]. The
profile also depends on the matrix material whose stopping power depends on its density and atomic
mass. While an implantation depth of about 50 nm is reached for boron in silicon (A ≈ 28) for 10 keV,
20 keV are necessary in germanium (A ≈ 72.6) [295]. The mean path length
6 d m depends also on the
crystallographic direction (channeling effects, Fig. 4.8) [296]. A simulation of the interaction of ions
and solids can be performed using the SRIM software [297, 298].
4 When the float zone moves through the crystal, the change of mass of impurities m m = c m z in the liquid is m
m =
c 0 − kc m . The first term stems from the melting of the polycrystalline part, the second from the solidification of the
crystal. Solving the resulting differential equation c
m = (c 0 − kc m )/z with c m (0) = c 0 and using c(x) = kc m (x) yields
(4.20).
5 We note that during directed solidification of Si:(B,P) a pn-junction forms due to the different distribution coefficients
of boron and phosphorus. This has been used in [89].
6 The mean path length is the distance integrated along the ion trajectory until its direction deviates by more than 4 ◦
from the incident direction.
77
(a)
(b)
Fig. 4.7 (a) Depth of peak concentration of boron implanted in silicon for various acceleration voltages U . Data from
various sources, for U < 1 keV from [299]. Dashed line is linear dependence. (b) Simulated depth profiles of impurity
concentration for B, P, As, and Sb implanted into crystalline silicon with U = 100 keV and a dose of 10 15 cm −2 . Adapted
from [300]
RF-heated and liquid ‘float’ zone is moved through the crystal. In this case the impurity distribution is
given by
4
c(x) = c 0
1 − (1 − k) exp
−
k x
z
,
(4.20)
where x is the ratio of the crystal mass to the total mass, i.e. crystal, liquid and feed rod. z is the relative
mass of the (liquid) float zone, i.e. the ratio of liquid mass to the total mass. The impurity distribution
for CZ and FZ crystals is compared in Fig. 4.6b. Obviously the FZ process can create much more
homogeneous profiles.
5
Using epitaxy arbitrary doping profiles along the growth directions can be created by varying the
impurity supply during growth. Impurities can be introduced through the surface of the material by
diffusion from a solid or gas phase. In ion implantation [292] the impurity atoms are accelerated
towards the semiconductor and deposited with a certain depth profile due to multiple scattering and
energy loss events, depending on the acceleration voltage (increasing deposition depth with increasing
voltage, Fig. 4.7a) and ion mass (decreasing deposition depth with increasing mass, Fig. 4.7b). The
depth profile is often investigated using secondary ion mass spectrometry (SIMS) [293, 294]. The
profile also depends on the matrix material whose stopping power depends on its density and atomic
mass. While an implantation depth of about 50 nm is reached for boron in silicon (A ≈ 28) for 10 keV,
20 keV are necessary in germanium (A ≈ 72.6) [295]. The mean path length
6 d m depends also on the
crystallographic direction (channeling effects, Fig. 4.8) [296]. A simulation of the interaction of ions
and solids can be performed using the SRIM software [297, 298].
4 When the float zone moves through the crystal, the change of mass of impurities m m = c m z in the liquid is m
m =
c 0 − kc m . The first term stems from the melting of the polycrystalline part, the second from the solidification of the
crystal. Solving the resulting differential equation c
m = (c 0 − kc m )/z with c m (0) = c 0 and using c(x) = kc m (x) yields
(4.20).
5 We note that during directed solidification of Si:(B,P) a pn-junction forms due to the different distribution coefficients
of boron and phosphorus. This has been used in [89].
6 The mean path length is the distance integrated along the ion trajectory until its direction deviates by more than 4 ◦
from the incident direction.