1. EE 5340 Semiconductor Device Theory Lecture 08 – Spring 2011 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc

2. ©rlc L08-15Feb20112 Second Assignment Submit a signed copy of the document posted at www.uta.edu/ee/COE%20Ethics%20Statement%20Fall%2007.pdf

3. ©rlc L08-15Feb20113 Test 1 – Tuesday 22Feb11 11 AM Room 129 ERB Covering Lectures 1 through 9 Open book - 1 legal text or ref., only. You may write notes in your book. Calculator allowed A cover sheet will be included with full instructions. For examples see http://www.uta.edu/ronc/5340/tests/.

4. ©rlc L08-15Feb20114 Diffused or Implanted IC Resistor (Fig 2.45 1 )

5. ©rlc L08-15Feb20115 An IC Resistor with L = 8W (M&K) 1

6. ©rlc L08-15Feb20116 Typical IC doping profile (M&K Fig. 2.44 1 )

7. ©rlc L08-15Feb20117 Mobilities**

8. ©rlc L08-15Feb20118 IC Resistor Conductance

9. ©rlc L08-15Feb20119 An IC Resistor with N s = 8, R = 8R s (M&K) 1

10. ©rlc L08-15Feb201110 The effect of lateral diffusion (M&K 1 )

11. ©rlc L08-15Feb201111 A serpentine pattern IC Resistor (M&K 1 ) R = N S R S + 0.65  N C R S note: R C = 0.65  R S

12. ©rlc L08-15Feb201112 The equilibrium carrier concentration ahd the Fermi energy are related as The potential  = (E f -E fi )/q If not in equilibrium, a quasi-Fermi level (imref) is used Fermi Energy

13. ©rlc L08-15Feb201113 Electron quasi-Fermi Energy (n = n o +  n)

14. ©rlc L08-15Feb201114 Hole quasi-Fermi Energy (p = p o +  p)

15. ©rlc L08-15Feb201115 E x -field when E f - E fi not constant Since  = (E f - E fi )/q = V t ln(n o /n i ) When E f - E fi = is position dependent, E x = -d  /dx = -[d(E f -E fi )/dx] = - V t d[ln(n o /n i )]/dx If non-equilibrium  n = (E fn -E fi )/q = V t ln(n/n i ), etc E xn = -[d  n /dx] = -V t d[ln(n/n i )]/dx

16. ©rlc L08-15Feb201116 Si and Al and model (approx. to scale) q  m,Al ~ 4.1 eV EoEo E Fm E Fp E Fn EoEo EcEc EvEv E Fi q  s,n q  si ~ 4.05 eV EoEo EcEc EvEv E Fi q  s,p metaln-type s/cp-type s/c q  si ~ 4.05 eV

17. ©rlc L08-15Feb201117 Making contact be- tween metal & s/c Equate the E F in the metal and s/c materials far from the junction E o (the free level), must be continuous across the jctn. N.B.: q  = 4.05 eV (Si), and q  = q   E c - E F EoEo EcEc EFEF E Fi EvEv q  (electron affinity) qFqF qq (work function)

18. ©rlc L08-15Feb201118 Equilibrium Boundary Conditions w/ contact No discontinuity in the free level, E o at the metal/semiconductor interface. E F,metal = E F,semiconductor to bring the electron populations in the metal and semiconductor to thermal equilibrium. E o - E C = q  semiconductor in all of the s/c. E o - E F,metal = q  metal throughout metal.

19. ©rlc L08-15Feb201119 Ideal metal to n-type barrier diode (  m >  s,V a =0) E Fn EoEo EcEc EvEv E Fi q  s,n qsqs n-type s/c qmqm E Fm metal q  Bn qiqi q’nq’n No disc in E o E x =0 in metal ==> E o flat  Bn =  m -  s = elec mtl to s/c barr  i =  Bn -  n =  m -  s elect s/c to mtl barr Depl reg

20. ©rlc L08-15Feb201120 Metal to n-type non-rect cont (  m <  s ) E Fn EoEo EcEc EvEv E Fi q  s,n qsqs n-type s/c qmqm E Fm metal q  B,n qnqn No disc in E o E x =0 in metal ==> E o flat  B,n =  m -  s = elec mtl to s/c barr  i =  Bn -  n < 0 Accumulation region Acc reg qiqi

21. ©rlc L08-15Feb201121 Ideal metal to p-type barrier diode (  m <  s ) No disc in E o E x =0 in metal ==> E o flat  Bn =  m -  s = elec mtl to s/c barr.  Bp =  m - (  s + E g )= hole m to s barr.  i =  m -  s,p = hole s/c to mtl barr. E Fp EoEo EcEc EvEv E Fi q  s,p qsqs p-type s/c qmqm E Fm metal q  Bn qiqi q  p <0 Depl reg q  Bp qiqi

22. ©rlc L08-15Feb201122 Metal to p-type non-rect cont (  m >  s ) No disc in E o E x =0 in metal ==> E o flat  B,n =  m -  s = elec mtl to s/c barr  Bp =  m - (  s + E g ) = hole m to s  i =  m -  s,n = s/c to mtl barr. E Fi EoEo EcEc EvEv E fP q  s,n qsqs n-type s/c qmqm E Fm metal q  Bn q(  i ) qpqp Accum reg q  Bp qiqi

23. ©rlc L08-15Feb201123 Metal/semiconductor system types n-type semiconductor Schottky diode - blocking for  m >  s contact - conducting for  m <  s p-type semiconductor contact - conducting for  m >  s Schottky diode - blocking for  m <  s

24. ©rlc L08-15Feb201124 References 1 and M&K Device Electronics for Integrated Circuits, 2 ed., by Muller and Kamins, Wiley, New York, 1986. See Semiconductor Device Fundamentals, by Pierret, Addison-Wesley, 1996, for another treatment of the  model. 2 Physics of Semiconductor Devices, by S. M. Sze, Wiley, New York, 1981. 3 and ** Semiconductor Physics & Devices, 2nd ed., by Neamen, Irwin, Chicago, 1997. Fundamentals of Semiconductor Theory and Device Physics, by Shyh Wang, Prentice Hall, 1989.