Page 177 - Sami Franssila Introduction to Microfabrication

156 Introduction to Microfabrication

technologies the S/D sheet resistances are rapidly secondary ion mass spectrometry (SIMS). The dynamic
increasing because junction depths are scaled down. range of SIMS is six to eight orders of magnitude,
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3
that is, dopant concentrations of 10 14 to 10 /cm can
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22
be detected (silicon atom density is 5 × 10 /cm ).
14.2.1 Infinite dopant supply (constant surface The spreading resistance (SRP) measurement measures
concentration of dopant) resistance with probes at the surface, and then bevelling
or anodic oxidation is done in order to have access to the
The infinite dopant supply corresponds to the gas-
phase doping in which a new dopant is constantly dopants deeper inside the silicon. SRP data needs some
being injected into the diffusion tube. A heavily doped heavy calculations before dopant profiles are obtained.
thin film (polysilicon or CVD oxide) can act as an Both SIMS and SRP are sample destructive methods.
approximation to an infinite source when diffusion times
and temperatures are moderate. Concentration profile of 14.3 SIMULATION OF DIFFUSION
the dopant in silicon is given by the complementary error
function (erfc): All the high-temperature process steps contribute to
√ diffusion; therefore, diffusion is the omnipresent process
N(x, t) = N o erfc (x/ 4Dt) (14.6)
to be simulated in the front end of the process. There
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where N o is the dopant concentration (1/cm ) in the can easily be tens of steps that contribute to dopant
surface layer, x is the depth (cm), t is the time (s) and profiles. Segregation effects during oxidation and dopant
D is the diffusion coefficient at a given temperature outdiffusion from free surfaces add to computational and
2
(cm /s). Longer doping times will lead to deeper modelling loads.
diffusions but the surface concentration is unchanged. Simulation of phosphorus diffusion needs to consider
at least five species:
14.2.2 Limited dopant supply (constant dopant – phosphorus (P)
amount) – vacancies (v)
– interstitials (i)
The limited dopant supply case describes the case of
– phosphorus-vacancy pairs (P-v)
pre-deposition: the dopants are definitely in limited
– phosphorus-interstitial pairs (P-i).
supply because no new ones are introduced. This
is the case of ion implantation. Longer diffusion
Vacancies and interstitials are not permanent species
times will lead to deeper diffusions but the surface
like phosphorus atoms, and we must account for anni-
concentration decreases.
The concentration profile is Gaussian: hilation of point defects via the reaction v + i = nil.
Point defects can also form pairs like v–v. To make
√ 2
N(x, t) = (Q o / πDt) exp(−(x /4Dt)) (14.7) the situation even more difficult to analyse, many
of the species are charged: diffusion models have
o
−
where Q o is the total amount of dopant on the surface to account for equilibrium processes like P + v ⇔
o
2
−
(1/cm ). The junction depth is given by Pv − (charged phosphorus-vacancy pair) or P + i ⇔
−
Pi . Clustering and precipitation of dopants leads to
√ √
x j = 4Dt × ln(Q o /C subs πDt) (14.8) inactivation. These phenomena are especially impor-
tant when concentrations are near the solid solubility
This equation cannot be solved in an analytical form for limit.
diffusion time. An approximate solution for diffusion A standard simulator requires the following as inputs
time can be obtained by a graphical solution: calculate for diffusion simulation:
x j for a few diffusion times, plot the results and estimate
the junction depth from the graph. Simulators are used – wafer orientation <100>/<111>
for more accurate estimates.
– wafer-doping level/resistivity
– dopant type
14.2.3 Diffusion profile measurement – concentration of dopant (gas phase/solid phase/
implanted)
The diffusion profiles are measured either physically – temperature
or electrically. The standard physical measurement is – ambient (oxidizing/inert/reducing).