Chp14. MS Contacts and

Chp14. MS Contacts and Schottky Diodes

184

14. MS Contacts and Schottky Diodes

M / S junction

① Connection between semiconductor and outer circuit

② Interconnection between devices within ICs M / S junction types

① Rectifying contacts , blocking contacts , Schottky barrier contacts.

② Ohmic contacts , non – rectifying contacts, electrodes I

V

V

I

Assume ① no layers between M / S

② no interdiffusion between M / S

③ no impurities at interface 14. 1. IDEAL MS CONTACTS

186

Energy band diagram under equil. conditions

Figure 14. 1 Surface-included energy band diagrams for a metal (left) and n-type semiconductor (right).

E

: vacuum level

 : work function 

=  + (E

– E

)

Metal Semiconductor



E

E

E

E



E

E



Figure reference: “Semiconductor Device Fundamentals”

Robert F. Pierret, Addison-Wesley Publiching Company

At equil. , E

constant throughout the system.

_B

= 

-

Figure 14.2 energy band diagrams for ideal MS contacts between a metal and an n-type semiconductor : _M> _S system (a) an instant after contact formation and (b) under equilibrium conditions ; _M< _S system (c) an instant after contact formation and (d) under equilibrium conditions.

_M> _S _M< _S

Metal n-type

semiconductor Metal n-type

semiconductor E_c

E_FS E_V

E₀ E₀

E_c E_FS E_V E_FM

E_FM

_M _M  _S

(a) (c)

_B

(b) (d)

E_V E_V

E_c

E_F E_c E_F

188

Effect of biasing the M / S junctions

Figure 14.3 Response of the _M > _S (n-type) MS contact to an applied d.c.

bias. (a) Definition of current and voltage polarities. (b) Energy band diagram and carrier activity when V_A > 0. (c) Energy band diagram and carrier activity when V_A < 0. (d) Deduced general form of the I - V characteristics.

Metal n-type

semiconductor

I

(a) (b)

E_c E_FS E_V

I

I

(c)

E_c E_FS

E_V (d)

I

V

Figure reference: “Semiconductor Device Fundamentals”

Robert F. Pierret, Addison-Wesley Publiching Company

Figure 9-12 Ideal energy-band diagram of a metal - n - semiconductor ohmic contact (a) with a positive voltage applied to the metal and (b) with a positive voltage applied to the semiconductor

.

Table 14.1 Electrical Nature of Ideal MS Contacts.



 



 

n-type

semiconductor n-type

semiconductor

Rectifying Ohmic

Ohmic Rectifying E_F

(a) (b)

E_c

E_V

E_V E_c E_F

190

14. 2. SCHOTTKY DIODE 14. 2. 1 Electrostatics

Built – in Voltage V

qV

= 

– (E

– E

) = 

-



, ε , V

 

qN

0  x  W 0 x  W

x

W

For metal side, ε

0 , V = constant

Figure 14.4 Electrostatic variables in an MS (n-type) diode under equilibrium conditions. (a) Equilibrium energy band diagram. (b) - (d) Charge density, electric field, and electrostatic potential as a function of position.



Ec_F

E_v

(E_c-E_F)_FB

(a)

x

 qN_D

(b)

x_n = W

0 x_n

-function of negative

charge

(c) 0 W E

x

(d) 0 W V

x

-V_bi

192

Using the Poisson’s eq.,

same as p

n diode!

Under equil. , V = -V

at x = 0 When V

≠ 0 , V

→ V

- V

Depletion width

   

    ^{0 x W}

2

W x

0

2 0

0





















x K W

x qN V

x K W

x qN

S D S

D



 

 

2

A bi

D

S

V V

qN

W   K  

14. 2. 2 1 - V Characteristics

Similar to pn diode.

MS diode electrostatics

shape of I – V characteristics

- Difference ? minority – carrier device majority – carrier device E_c

E_Fn E_T

E_v

(a) p⁺n junction diode

E_FP

I_DIFF Negligible

I_R-G

E_c E_FS E_T

E_v

(b) MS diode

0 W x

_B

Dominant q(V_bi – V_A)

Figure 14.5 Negligible and dominant current components in a forward-biased (a) p⁺-n junction diode and (b) MS diode.

194

• thermionic emission current

• A

Richardson’s Constant

Schottky barrier lowering (in reverse bias)

_B0

: barrier height at ε = 0 at the MS interface ε : electric field at the semiconductor surface

_B

= 

-

 

kT S

kT qV S

B A

e T AA I

e I I

2 /

*

/

1









2 / 1

4

 





 



 

  



S s

B

K

q q

Figure 14.6 Measured I-V characteristics derived from a MBR040 MS diode : (a) forward bias ; (b) reverse bias. The dashed lines in (a) are theoretical

estimates of the diffusion (I_DIFF) and recombination-generation (I_R-G) currents flowing in the diode. The experimental data were obtained employing an

HP4145B Semiconductor Parameter Analyzer.

V_A(volts) 10^-1

10^-3 10^-5 10^-7 10^-9 10^-11 I (A)

V_A(volts)

-50 -40 -30 -20 -10 0

0 0.2 0.4 0.6 0.8 1.0

(a) (b)

-1.0 -0.8 -0.6 -0.4 -0.2 0

q/kT

I_R-G

I_DIFF

I (

㎂

196

14. 2. 3 a. c. Response

Small a.c. bias (~mV) super imposed on a d.c. bias (V

)

→ change fluctuation inside the diode

→ small a. c. current

→ capacitance measurement

Figure 14.7 Charge fluctuations inside an MS (n-type) diode in response to an applied a.c. signal. |v_a| ≪ V_bi – V_A.

n-type +v_a- +V_A-



W

x

Figure reference: “Semiconductor Device Fundamentals”

Robert F. Pierret, Addison-Wesley Publiching Company

A : 극판면적

From the slope of vs. V

From the intercept at

→ N

→ V

(and 

)

198

 

0

0 0

0

2 



 



 







A bi

D S

S S

S

V qN V

K

A K

W A K

d A C K













S

D

K A V V

qN

C  

2 0 2

2 1



2

1 C

1 0

2



C

14. 3. PRACTICAL CONTACT CONSIDERATIONS 14. 3. 1 Rectifying Contacts

MS contacts deviate from the ideal case,

• native oxide (5Å ~ 25Å)

• “ surface states ”

→

≠ 

-

E

E

Relative density of surface states →

Figure 3.16 Approximate

distribution of Tamm-Schottkley states in the diamond lattice.

The distribution appears to peak

sharply at an energy roughly one- third of the bandgap above E

200

14. 3. 2. Ohmic Contacts

→ Ohmic contacts

Practically, all MS contacts are Schottky barriers in nature.

Ideally , 

(n – type)

_M  _S

(p – type)

Figure 14.10 Ohmic contact formation. (a) Heavy doping of the semiconductor beneath the MS contact to facilitate ohmic contact formation. (b) Emission currents across a barrier-type contact as a function of doping. The emission is shown varying from solely thermionic emission at low semiconductor dopings to predominantly field emission (tunneling through the barrier) at high semiconductor dopings.

SiO₂

Metal

N⁺ N - Si

(a)

Low doping

(b) Moderate doping

High doping

202

Figure 3.22 diagrams for ideal metal-semiconductor Schottky diodes.

Thermal- Equilibrium Band Diagram

Thermal- Equilibrium

Charge Distribution

Electric Field

Band Diagram (Forward bias)

Band Diagram (Reverse Bias)

n - type semiconductor p - type semiconductor

Figure reference: “Semiconductor Device Fundamentals”

Robert F. Pierret, Addison-Wesley Publiching Company

Schottky Barrier Lowering

Electron energy

Figure 3.9 Classical energy diagram for a free electron near a plane metal surface at the thermal equilibrium [E₁(x)]. and with an applied field – E_x[E₂(x)].

Metal

x Semiconductor

q

q_B q_B0

E₁(x) for zero field

E₂(x) for constant applied field - E_x

0 x_m

204