Semiconductor based Diode: Schottky Diode: (6023 Exp 1)

1. Experiment Objective:
The objective of the experiment is to determine from I-V characteristics of
metal/semiconductor contacts the temperature dependence of some fundamental
parameters like the idealities factor, and the barrier heights. From C-V characteristics is to
determine the Built-in potential and the doping profile (doping concentration as a
function of the junction depth). Determination of the Schootky barrier height in n type
and p-type semiconductor is important for the determination of band gap of the
semiconductor as well as the band discontinuities in the case of heterostructures. The
temperature dependence will be analyzed to extract like the Schottky barrier height, , the
bulk doping concentration.

2. Theoretical Background

2.1. Band Diagrams

Metal-Semiconductor junctions are of fundamental importance in modern electronics

applications and in understanding many semiconductor devices. They are present in many
electronic devices (such as MOSFET, MODFET, etc...). They can behave either as a
Schottky barrier (Schottky diode) or as an ohmic contact dependent on the characteristics
of the interface, the work function of the metal, the doping type of semiconductor as well
as on the doping concentration of the semiconductor. The Metal-Semiconductor contacts
are often realized by depositing a metallic thin film under vacuum into intimate contact
with the cleaned surface of semiconductor.
The work function is the energy difference between the vacuum level E0 and the Ferm
level EF. This quantity is denoted by qm (m in volts) for the metal and equal to qs =
q(+Ec-EF) in the semiconductor, where q is the electron affinity measured from the
bottom of the conduction band Ec to the vacuum level E0 and Ec-EF is the energy
difference between Ec and Fermi level EF.

E0 E0 E0
E0

Without contact

With contact
Figure 1. Energy band diagram of the metal and n-type semiconductor
To reach thermal equilibrium, electrons/holes close to the metallurgical junction diffuse
across the junction into the metal. This process leaves the ionized donors (acceptors)
behind, creating a region around the junction, which is depleted of mobile carriers. We
call this region the depletion region, extending from x = 0 to x = W (see Figure 2). The
charge due to the ionized donors and acceptors causes an electric field, which in turn
causes a drift of carriers in the opposite direction. The diffusion of carriers continues until
the drift current balances the diffusion current, thereby reaching thermal equilibrium as
indicated by a constant Fermi energy in the whole structure.
From Figure 1, it is clear that the Schottky barrier height bn in metal/n-type
semiconductor Schottky contact is given by:
q bn  q m  q (1)
The barrier height is the difference between the metal work function and the electron
affinity of the semiconductor.

The Schottky contacts as shown in Figure 2 consist of a metal with high work function or
low work function deposited on moderately n-type doped semiconductor or p-type doped
semiconductor, respectively.

Metal Sc p-type
Metal Sc n-type

bn Vbi EC
EC
Eg
Eg
EF
EV
EV bp Vbi
W: depletion layer W: depletion layer

Figure 2. Energy band diagram of a Schottky junction (a) n-type semiconductor and (b) p-type
semiconductor.

For an ideal contact between a metal and a P-type semiconductor, the barrier height qFbp
is given by:
q bp  E g  (q m  q ) (2)
As shown in Figure 2, for a given metal the barrier height on n-type semiconductor
added to the barrier height on p-type semiconductor should be equal to the band gap of
the conserned semiconductor.
q bn  q bp  E g (3)
In thermal equilibrium no external voltage is applied between the n-type or p-type
material and the metal, there is an internal potential, Vbi, which is caused by the work
function difference between the metal work function and the semiconductor. This
potential equals the built-in potential defined by:
 Nc
qVbi  q bn  k B TLn (n-type semiconducteur) (5)
Nd
N
qVbi  q bp  k B TLn v (p-type semiconductor) (6)
Na

Nc, Nd, Nv and Na are the effective density of states in the conduction band, the
density of the donor impurity, the effective density of states in the valence band and the
density of the acceptor impurity, respectively. kB is the boltzman constant and with
kBT/q=26 mV at 300K.

2.2. C-V and I-V characteristics of Metal/Semiconductor Schottky diodes

Metal n-type
n-type Metal
qbn
q(Vbi-VF)
EC qbn
qVF
EF q(Vbi+Vr)
EFm EFm
qVr Ec
EF

EV
EV

(a) Forward bias (b) Reverse bias

Figure 3. Energy band diagram of a metal-semiconductor junction under (a)

forward and (b) reverse bias

2.2.1. Depletion layer

0For a metal/n-type semiconductor and under the abrupt approximation and that the total
charge  = qND for x < W and  = 0 and the electric field is equal to zero for x >W where
W is the depletion width and ND is the doping density.

From Poisson’s equation we obtain:

 2V E   qN D
     for 0<x<W (7)
x 2
x  s  0  sc  0  sc

qN D
E ( x)  ( x W ) for 0<x<W (8)
 0  sc
Where s, 0, sc are the semiconductor permittivity, the permittivity in vacuum and the
semiconductor dielectric constant, respectively.

qN DW
Em  where E m is the max imum electric field at the junction ( x  0) (9)
 0  sc

Integrating equation 7 gives the potential distribution V(x)

qN D x2
V ( x)  (Wx  ) (10)
 0  sc 2

qN DW 2
Vbi  V ( x  W )  (11)
2 0  sc

2 0  sc (Vbi  V )
W (12)
qN D

2.2.2. Capacitance

The depletion layer capacitance is defined as:

q 0 sc
C  SdQ/dV  Sd(qN D W)/d[(qN D /2 s W  S s W  S (Vbi  V ) 1 / 2 (13)
2

Where S is the the area of the contact, Q total charge per unit area.

Equation (13) can be written in the form

1 2(V  V ) d (1 / C 2) 2
 2 bi , then  2 (14)
C 2
S q 0  sc N D dV S q 0  sc N D

If ND is constant throught the depletion region, the slope plot of /C2 versus V should give
the doping concentration ND and the intercept should give the built in potential Vbi.

Thermionic emission

Operation of a metal-semiconductor junction under forward and reverse bias is illustrated

with figure. 3. As a positive bias is applied to the metal Figure (3.a) the Fermi energy of
the metal is lowered with respect to the Fermi energy in the semiconductor. This results
in a smaller potential drop across the semiconductor and leads to a positive current
through the junction.
The thermionic emission theory assumes that electrons, with an energy larger than the top
of the barrier, will cross the barrier provided they move towards the barrier. One can have
two current fluxes, one from the metal to the semiconductor the other from
semiconductor to the metal. The fraction of electrons with enery higher than the barrier
height bn and acrossing this barrier is given by the boltzman factor (exp (-bn/kT). Then
the density of current Jm sc is proportional to this factor. For the current density from
semiconductor to the metal Jsc m is a function of the barrier seen by the lectron from
the semiconductor side exp (-q(Vbi-V/kT).

The total density of current is

 qV 
J T  J scm  J m sc  J sat exp( )  1
 kT  (15)

with J sat  A*T 2 exp( bn )
kT

As a negative voltage is applied figure (3.b), the Fermi energy of the metal is raised
with respect to the Fermi energy in the semiconductor. The potential across the
semiconductor now increases, yielding a larger depletion region and a larger electric field
at the interface. The barrier height, which restricts the electrons to flow from the metal to
the semiconductor, is unchanged so that barrier limits the flow of electrons. The metal-
semiconductor junction with positive barrier height has therefore a pronounced rectifying
behavior. A large current exists under forward bias, while small current exists under
reverse bias.

The current through the metal–semiconductor interface due to thermionic emission can
be expressed as (Sze, page 255-279)

 0bn   q (V  Rs I  
I  A ST exp ( 
* 2
) exp   1 (16)
k BT   nk BT  
where bn is the effective barrier height at zero bias, A* is the Richardson constant (112
AK-2cm-2 for n-Si and 55 AK-2cm-2 for n-Ge: Richardson constant for SiGe should be
calculated by assuming a linear dependence on Ge content), S is the area of the diode, T
is the temperature of the metal/semiconductor junction, kB is the Boltzmann constant, n is
the ideality factor of the diode which depends on the conduction mode across the diode
and Rs is the series resistance

The ideality factor should be obtained from the slope of the plot of Ln I as function (V)
for V>3kT and the extrapolated value of the current (Isat) at zero voltage should give the
barrier height from the equation
A* ST 2
bn  k B T ln( ) (17)
I sat
3. Lab Assignment
N-type, SiGe(100) sample with a resistivity of 0.05–0.1  cm (ND ≈ 8 × 1016 cm-3) were
used for the experiments. The Schottky contact of palladium on n-type Si0.90Ge0.10
with a circular of 0.77 mm in diameter and 200 nm thick were resistively evaporated on
the N-type sample. Low resistivity ohmic back contacts to the back side of Si wafers
were made by using In-Ga alloy (figure 4)

Cathode:
Metal

n-type semiconductor

Cross view
Ohmic contact

Figure 4. Energy band

3.1 IV characteristics with temperature as a parameter

3.1.1. Using the Keithley Parameter allowing measuring the I-V characteristics.
3.1.2. Place the probe on the n-type Pd/n-Si0.90Ge0.10 Schottky diodes.
3.1.3. Switch on the vacuum.
3.1.4. Mesure I-V at 300 K and plot the I-V (300K) graph in the linear scale
3.1.6. Plot the I-V (300K) graph in the semi-log scale
3.1.8. Extract the saturation current Is and the ideality factor n from the
exponential fit.
3.1.9. Change the temperature from 100 K to 280 K and extract again Is and n.
3.1.10. Plot the Is/T2 vs 1/T(K) on a semi log scale.
3.1.11. Extract the barrier height ΦB according the thermoionic theory. Is the
value match the equation:  B   M   ?
3.1.12. Explain the difference if any.
3.1.13. Plot the ideality factor (n) vs T(K) graph on a linear scale.
3.1.14. Using the 4192A Impedance Analyser Mesure C(V) at 300K and Plot the
C(V) at room temperature (300 K)
3.1.15. Extract the built-in potential Φi
 3.1.16. Derive the doping concentration ND. Compare the result to the doping
level corresponding to the Si0.90Ge0.10 semiconductor resistivity range: 0.05-0.1
ohm.cm.
References
S.M. SZE "Semiconductor Devices Physics and Technology", 2nd edition, John Wiley &
Sons (1981) p.245-296.