Find the current that flows in a silicon bar of 10-mum length having a 5-mum Tim

Question

Find the current that flows in a silicon bar of 10-mum length having a 5-mum Times 4-mum cross section and having free electron and hole densities of 105/cm3 and 1015/cm3 , respectively, when a 1 V is applied end-to-end. Use mu n = 1200 cm2?V.s and mu p= 500 cm2/V.s. In a 10-mum long bar of donor-doped silicon, what donor concentration is needed to realize a current density of 1 mA/mum2 in response to an applied voltage of 1 V. {Note: Although the carrier mobilities change with doping concentration, as a first approximation you may assume /mu n to be constant and use the value for intrinsic silicon, 1350 cm2/V.s).

Explanation / Answer

Current Density is given as

J = n*q*n*E

n-----------concentration

q----charge

n------mobility

E--------electric field = V/l

1 mA/m2 = 10^8 mA/cm2 = n * 1.6*10^-19 * 1350*[1/10*10^-4]

n = 4.63*10^17 /cm3

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