Semiconductor Device Physics

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1 1 emiconductor Device Physics Lecture

2 emiconductor Device Physics 2 M Contacts and chottky Diodes

3 3 M Contact The metal-semiconductor (M) contact plays a very important role in solid-state devices. When in the form of a rectifying contact, the M contact is referred to as the chottky. When in the from of a non-rectifying or ohmic contact, the M contact is the critical link between the semiconductor and the outside. The reverse-bias saturation current I of a chottky diode is 10 3 to 10 8 times larger than that of a pnjunction diode, depending on the type of material. chottky diodes are proffered rectifiers for low-voltage highcurrent applications. pn-junction diode I V A chottky diode

4 4 M Contact A vacuum energy level, E 0, is defined as the minimum energy an electron must possess to completely free itself from the material. The energy difference between E 0 and E F is known as the workfunction (Φ).

5 5 Workfunction E 0 : vacuum energy level F M : Metal workfunction E FM : Fermi level in metal c i = 4.03eV F : emiconductor workfunction E F : Fermi level in semiconductor c: electron affinity

6 Ideal M Contact: F M > F, n-type Band diagram instantly after contact formation E 0 is continuous Band diagram under equilibrium condition 6 F = F B M c urface potential-energy barrier

7 Ideal M Contact: F M < F, n-type 7 Band diagram instantly after contact formation E 0 is continuous Band diagram under equilibrium condition

8 8 Forward Bias n-type M Contact Current is determined by majoritycarrier flow across the M junction. Under forward bias, majoritycarrier diffusion from the semiconductor into the metal dominates. Under reverse bias, majoritycarrier diffusion from the metal into the semiconductor dominates. Reverse Bias Reverse bias Forward bias

9 9 Metal-emiconductor Contacts There are 2 kinds of metal-semiconductor (M) contact: I Rectifying ( chottky diode ) V A I Non-rectifying ( Ohmic contact ) V A

10 10 Metal-emiconductor Contacts E F E F E c E v E c E v E F E F E c E v E c E v

11 11 The semiconductor is depleted to a depth W: In the depleted region (0 x W ): = q( ND NA) n= 0, p= 0 The Depletion Approximation Beyond the depleted region (x > W ): = 0 n = n, p = p V = F ( E E ) q bi B c F FB V bi : built-in voltage

12 12 According to Gauss s Law: E( x Dx) E( x) A = DxA Poisson s Equation Area A Or: E( x Dx) E( x) Dx de dx 2 dv = = = 2 dx E(x) Dx E(x+Dx) E : electric field intensity (V/m) : relative permittivity (F/cm) : charge density (C/cm 3 ) = K 0 0 = F/cm For i, K = 11.8

13 E d dx 0 x E de Poisson s equation: = W x qn qn D ( x) = ( W x) D dx M Contact Electrostatics E D + = The solution is: Furthermore: qn W W qnd ( ) E( ) ( ) V x = x dx = W x dx x x qnd 2 = ( W x ) 2 13

14 14 qn V x = ( W x) 2 W D 2 = 2 V qn D bi The potential in the semiconductor side is chosen to be the zero reference. At x = 0, V = V bi The depletion width is given by Depletion Layer Width W + W decreases as N D increases

15 15 Previously, qn V x W x 2 D 2 ( ) = ( ) W = Depletion Layer Width W for V A 0 At x = 0, now V = (V bi V A ) 2 ( V V ) bi A qn D + W decreases as N D increases W increases as V A increases (V bi V A )

16 16 Thermionic emission current results from majority carrier injection over the potential barrier. Electrons can cross the junction into the metal if: * 2 KE = 1 x n x ( bi A) 2 m v q V V Or: v v = 2 q ( V V ) x min * bi A mn Thermionic Emission Current The current for electrons at a certain velocity is: I M, v =qavxn vx x v min ( ) The total current over the potential barrier is: I =qa v n( v ) dv M x x x

17 17 For a non-degenerate semiconductor, it can be shown that: *2 4 ktm * 2 n ( EFEc)/ kt ( mn / 2 kt ) vx n( vx ) = e e 3 h We can then obtain * 2 FB I A T e e = B M kt qv kt A I V Characteristics Where And B m = B m0 * * n 2 4 qm0k B = = 3 h A (cm K )

18 18 I V Characteristics In the reverse direction and equilibrium condition, the electrons always see the same barrier F B, so Therefore I ( V = 0) = I ( V = 0) M A M A I :reverse bias saturation current Finally, combining the total current at an arbitrary V A, I = I e ( qva kt 1) Where * 2 I = AB T e F B kt

19 19 In an M contact, charge is stored on either side of the M junction. The applied bias V A affects this charge and varies the depletion width. If an a.c. voltage v a is applied in series with the d.c. bias V A, the charge stored in the M contact will be modulated at the frequency of the a.c. voltage. Displacement current will flow. mall-ignal Capacitance i dv C a dt C = A W = s

20 20 W = ince in general 2 ( V V ) bi A qn D mall-ignal Capacitance Then C = A W = A = 2 ( Vbi VA ) qn D A qn D 2( V V ) bi A Or 1 2 = ( Vbi VA ) C qn A 2 2 D

21 21 Practical Ohmic Contact In practice, most M-contacts are rectifying. In order to achieve a contact that can conduct easily in both directions, the semiconductor is to be doped very heavily. Depletion width W becomes so narrow that the carriers can tunnel directly through the barrier.

22 22 Voltage Drop Across the M Contact Under equilibrium conditions (V A = 0), the voltage drop across the semiconductor depletion region is the builtin voltage V bi. If V A 0, the voltage drop across the semiconductor depletion region is V bi V A. qv bi q(v bi V A ) q(v bi V A )

23 23 A 2 ( ) = ( ) W = M Contact with p-type emiconductor If p-type semiconductor is used, the depletion layer width W of the M contact for V A 0 is given by qn V x W x 2 At x = 0, V = V bi + V A, 2 ( V V ) A bi qn A W increases as V A increases W decrease as N A increases E V???

24 24 1. Homework 9 (Nea.EC.10.27) An M-junction is formed between a metal with a work function of 4.3 ev and p-type i with an electron affinity of 4 ev. The doping concentration in semiconductor is cm 3. Assume T = 300 K. (a) ketch the thermal equilibrium energy band diagram; (b) Determine the height of the chottky barrier; (c) ketch the energy band diagram with an applied reverse-bias voltage of V A = 3V; (d) ketch the energy band diagram with an applied forward-bias voltage of V A = 0.25 V.

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