1. Department of Electronics Semiconductor Devices 25 Atsufumi Hirohata 11:00 Monday, 1/December/2014 (P/L 005)

2. Exercise 4 Calculate the depletion layer width of an abrupt p-n junction diode which is made from Silicon and has the following properties: p-region: doping density of N A = 2  10 21 m -3 n-region: doping density of N D = 1  10 21 m -3 permittivity:  =    0 = 12.0  8.854  10 -12 F/m and q = 1.6  10 -19 C.

3. Answer to Exercise 4 The depletion layer widths are defined as By substituting the given values into the above relationship, (Here, V bi = 590 mV from the previous exercise 3.)

4. 25 Metal Semiconductor Junction Work function Metal / n-type semiconductor Metal / p-type semiconductor Einstein relationship Schottky barrier

5. p-n Diode * http://www.wikipedia.org/ A junction made by attaching p- and n-doped semiconductors : Widely used to insulate transistors. Common circuit to convert ac to dc in a battery charger.

6. Metal Junctions Work function  : Na 11+ 1s 2s 2p 3s vacuum level EFEF  Current density of thermoelectrons :  Richardson-Dushman equation A : Richardson constant (~120 Acm 2 /K) Metal - metal junction : vacuum level  A  B E FA E FB  A -  B = E FA - E FB  A -  B : contact potential ------ +  A  B E FA E FB AB E FA E FB AB barrier E FA = E FB

7. Metal - Semiconductor Junction - n-Type Metal - n-type semiconductor junction : vacuum level  M  S : electron affinity E FM E FS M n-S E V : valence band E D : donor level E C : conduction band  S qV d =  M -  S : Schottky barrier height E FM E FS M n-S EVEV EDED ECEC  M -  S -------- + depletion layer * http://www.dpg-physik.de/

8. Metal - Semiconductor Junction - p-Type Metal - p-type semiconductor junction : vacuum level  M  S : electron affinity E FM M p-S EVEV ECEC  S qV d =  S -  M E FM E FS M p-S EVEV ECEC  S -  M ++++++++ depletion layer E A : acceptor level E FS EAEA

9. Schottky Barrier Definition of energy at the Schottly barrier : * S. M. Sze, Physics of Semiconductor Devices (Wiley, New York, 2006). 

10. Einstein Relationship At the equillibrium state, Numbers of electrons diffuses towards -x direction are ( n : electron number density, D e : diffusion coefficient) EFEF EDED ECEC EVEV x Drift velocity of electrons with mobility  e under E is Numbers of electrons travel towards +x direction under E are As E is generated by the gradient of E C, E is along -x and v d is +x. (-x direction) (+x direction) (equillibrium state) Assuming E V = 0, electron number density is defined as

11. Einstein Relationship (Cont'd) Now, an electric field E produces voltage V CF = V C - V F Accordingly,  Einstein relationship Therefore, a current density J n can be calculated as

12. Rectification in a Schottky Junction By applying a bias voltage V onto a metal - n-type semiconductor junction : * H. Ibach and H. Lüth, Solid-State Physics (Springer, Berlin, 2003). forward bias reverse bias  M -  S q ( V d - V )  M -  S q ( V d - V ) J V

13. Comparison between p-n and Schottky Junctions Current-voltage characteristics : * S. Kishino, Physics of Semiconductor Devices (Maruzen, Tokyo, 1995). Schottky diode Current I Voltage V p-n diode

14. Transport across a Schottky Barrier Four major transport across the Schottly barrier : * S. M. Sze, Physics of Semiconductor Devices (Wiley, New York, 2006). Forward bias Thermionic transport Tunnelling transport Recombination Hole injection

15. Exercise 5 State the following metals in contact with Si to form either Schottky or Ohmic contacts based on their energy diagram. Assume the following parameters: Si electron affinity:  = 4.05 eV and Si bandgap: E g = 1.11 eV. MetalWork function  M [eV] n-type Si p-type Si Pt6.30 Au4.80 Cu4.18 Ni4.01