Hall Effect. Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India

Transcription

1 all Effect 1 Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India

2 all effect all effect was discovered in 1879 by Edward. all Exists in all conducting materials It is particularly pronounced and useful in semiconductors. all effect sensor is one of the simplest of all magnetic sensing devices Used extensively in sensing position and measuring magnetic fields

3 all effect When a magnetic field is applied perpendicular to a current carrying conductor or semiconductor, voltage is developed across the specimen in a direction perpendicular to both the current and the magnetic field. This phenomenon is called the all effect and voltage so developed is called the all voltage. Let us consider, a thin rectangular slab carrying current (i) in the x-direction. If we place it in a magnetic field B which is in the y-direction. Potential difference Vpq will develop between the faces p and q which are perpendicular to the z-direction.

4 Z + V P Y Q B X i P type semiconductor

5 Z - V P + Y Q B X i N type semiconductor

6 all Effect in p & n-type semiconductors all effect sign conventions for p-type sample all effect sign conventions for n-type sample

7 all Effect When a magnet field is applied perpendicular to the direction in which a charged particle (electron or hole) is moving, the particle will be deflected as shown The force on the particle will be F = q(x+vxb) In the x-direction, the force will be Fx = q(xx+vyxbz) To counter the flow of particles in the x-direction, a field xy=vxbz will be created so that the net force is zero. The applied field is called the all effect, and the resulting voltage, V=xyd

8 Drift velocity for an electron in the x-direction is: <v x >=-J x /qn where J is the current density, n is the number of carriers and q is the charge Defining the all coefficient, R =1/qn, then E y = v x B z = - J x B z /qn = R J x B z and n 1 qr J xb qe Measuring the resistance gives the resistivity: y z I x B wt q V z I AB / w qtv AB r (Wm)= Rwt/L = (Vcd/Ix)/(L/wt) where w is the width of the bar. Since conductivity, s = 1/r = qmnn, the mobility is: mn = s/qn = (1/r)/q(1/qR ) = R /r x B z

9 all Effect Moving electrons experience a force due to a perpendicular B field F q B An electric field develops in response to this force. The sign of this field perpendicular to the flow of current determines the carrier type. Carrier Density and mobility can also be calculated. m 1 qnr E y J x B qn z r resistivity

10 all effect - principles Consider a block of conducting medium through which a current of electrons is flowing caused by an external field. A magnetic filed B is established across the conductor, perpendicular to the current (. The electrons flow at a velocity v A force perpendicular to both the current and field is established. F = qvbsin vb [N]

11 Magnetic deflecting force F q( v B) d all electric deflecting force F qe When an equilibrium is reached, the magnetic deflecting force on the charge carriers are balanced by the electric forces due to electric Field E. q( v E d ( v Where B) d v B) d is qe drift velocity

12 The relation between current density and drift velocity is v d J ne Where n is the number of charge carriers per unit volume. E E E E R ( v d B) J ( B) ne 1 ( JB) ne R JB ( all,. coefficien t) 1 ne E JB

13 If V be the all voltage in equilibrium,the all electric field. V E d Where d is the width of R R If I J dt V R V R E JB 1 V JB d t is the thickness of Then its cross section is dt and current density R Vt IB JBd ( ) B I t the slab. the sample,

14 Since all the three quantities E, J and B are measurable, the all coefficient R and hence the carrier density can be found out. Generally for N-type material since the all field is developed in negative direction compared to the field developed for a P-type material, negative sign is used while denoting hall coefficient R.

15 all voltage The electrons are pulled towards the front side surface of the conductor (holes in semiconductors move towards the back) A voltage develops between the back (positive) and front (negative) surface. This voltage is the all voltage and is given by: V out = IB qnd V d is the thickness of the hall plate, n is the carrier density [charges/m 3 ] and q is the charge of the electron [C]

16 all voltage If the current changes direction or the magnetic field changes direction, the polarity of the all voltage flips. The all effect sensor is polarity dependent, - may be used to measure direction of a field - or direction of motion if the sensor is properly set up. The term 1/qn [m 3 /C] is material dependent and is called the all coefficient K.(or R ).

17 all coefficient The hall voltage is usually represented as: V out = K IB d V all coefficients vary from material to material Are particularly large in semiconductors. all voltage is linear with respect to the field for given current and dimensions. all coefficient is temperature dependent and this must be compensated if accurate sensing is needed.

18 all coefficient - cont. all coefficient is rather small - of the order of 50 mv/t Most sensed fields are smaller than 1 T The all voltage can be as small as a few mv Must in almost all cases be amplified. Example, the earth s magnetic field is only about 50 mt so that the output is a mere 25 mv

19 all Effect and Mobility The all effect is easier to measure in semiconductors than in metals, since the carrier concentration is smaller: When one carrier dominates, we have a all coefficient: R E JB 1 nq where V we all measurements can tell us whether a semiconductor is n- type or p-type from the polarity of the all voltage: I B p-type + - n-type w When one carrier dominates, we can write the conductivity: So the mobility can be written: s nem m R e s ( pemh) Measuring R and s will thus give: sign, concentration, and mobility of carrier,

20 General Form of all Coefficient For a semiconductor with significant concentrations of both types of carriers: R E JB 2 pmh e( nm e 2 nme pm ) h So if holes predominate (pmh > nme ), R > 0 and the material is said to be p- type, while if R < 0 (as for simple metals), the material is said to be n-type.

21 all effect sensors - practical considerations all voltages are easily measurable quantities all sensors are among the most commonly used sensors for magnetic fields: simple, linear, very inexpensive, available in arrays can be integrated within devices. Errors involved in measurement are mostly due to temperature variations and the averaging effect of the all plate size These can be compensated by appropriate circuitry or compensating sensors.

22 all effect sensors - applications Example: measuring power The magnetic field through the hall element is proportional to the current being measured The current is proportional to voltage being measured The all voltage is proportional to product of current and voltage - power

23 all element power sensor

24 all sensors used to control a CDROM motor